WHAT AIN'T IN ORISHA-IFA: MATHEMATICS
Alashe Michael omo'Oshoosi cautions Yoruba ("Orisha/Ifa") practitioners to be skeptical about the projections and introjections of some to import into the religion Westernized ideas like Hermet- icism ("Egyptian") religion, "gnosticism, "mathematicism," astrology, melanin-racism theory, rel- igious sectarianism, Tarot card divination, "chakras," (from Kundalini-Buddhist theosophy), num- erology, or Hindu religion. Comparisons and analogies to other schools of thought are sometimes useful to further our education, but naive syncretism is unwise and disrespectful to self and kind. (Advocates of "pan-African spiritualism" (PAS) may get away with this, but practitioners of African Traditional Religions(ATR) should avoid this lack of self-discipline and not confuse the two). In particular, he finds objectionable the idea that just because Orisha /Ifa uses numbers (as labels or seniority ranks for the odus, and ceremonial numbers for the orishas) that any mathematical oper- ations are actually going on "in" the religion. Especially ill-advised is the notion that the "dark"--"light" polarities in our Ifa octagrams represent numbers or "base 2 " binary digital notations. This is not exactly true; not, at least, as stated. Many people, especially those with Kemetic religious or other doctrinaire variants of al-Islam or Christian backgrounds, might find these theses challenging. But this religion is not for everyone, so when you "knock on the door, you get what is behind the door. "To our mathematically-minded friends he says: "Reconsider your hitherto, perhaps inadequately examined, cultural assumptions," for when you are mainly equiped with a mathematical hammer, everything will start looking like a mathematical nail"! WHAT AIN’T IN IFA ?—MATHEMATICS By Alashe Michael omo’Oshoosi © All Rights Reserved, 2019 Preface My task here is to address the view that the divination system of Ifa (especially its method for mar- king down the 256 octagrams--figures or diagrams--that distinguish one odu from another) should be regarded as "mathematical," in general, or something like spiritually significant numbers written in "binary mathematical" form, specifically; when, in fact, they are not interval numbers at all. (For now, let's call an "odu" a "chapter" in the many books of Ifa wisdom), There are some who have too lit- erally taken to this idea and so I will critique a sample of their writings in the appendices to this essay. Let me clear something up immediately. There is obviously mathematics in the culture and language ofthe Yorubas. They count, calculate and compute as do all people; though they do not typically deal in very large numbers (borrowing large number nomenclature from other cultures). In fact, their count- ing and numbering system is “Base 20”; meaning that counting starts over again at "20" and multiples of ten thereafter. For example, 1 to 10 are simple numbers and names. 11 to 15 are said as 10 + 1,2, 3, 4, and 5. 16 through 19 is said this way: 16 is 20-4, 17 is 20-3, 18 is 20-2, and 19 is 20-1, while 20 itself is "20“or "ogun”). It is said that Yoruba numerics is "base 20" (but after "20" its numeration repeats every 10 integers). There is an Orisha-Ifa owe (aphorism or saying) that holds "that which touches 30, touch- es 20." This mean 'pay attention to the order of things.' But in the divination system, when I say that there is “no math,” I specifically mean that there are no mathematical calculations nor computations. That is, no addition, substraction, multiplictation nor division. Even when the sixteen palm nuts (ikin) method of divination is used, there is no “0” that comes up on the divination mat or tray as a "sign" or "odu." However, in the case when 16 cowrie shells are used (the "owo dilogun" or "merindilogun" method) when none of the 16 shells fall on the mat face-up or "speaking" (i.e., when they all fall face-down and when, therefore, it is said that "none are speak- ing"; is akin to a"0." And such a sign is called “Opira”—and is a very unusual occurance, to say the least. And, accordingly, it has its own special interpretations. But, in any case, once the signs--whatever they are--reveal themselves no mathematical operations actually become involved, thereafter, in order to interpret the "reading." Thus, for now, let us stick with the formulation that there is no “math” in Orisha /Ifa per se, meaning no mathematical calculations no computations. That said we can get on to the main theses of this tome. So, let me first start with an example of a place where this idea is better expressed than usual. In this case, it is a narrator of a publicity video entitled "The House of Oduduwa," whose narration, generally, celebrates the life and mission of the current Ooni of Ile Ife HRH Ooni Adeyeye Ogunwusi Ojaja II in commenting on the grand cultural history of Ife civilization. But he does mention the Ifa divination system and the idea of it being "mathematical" or, at least, so in one notable respect. In his view the d'afa marks (i.e., the Ifa octagram diagrams) that reflect the messages that the Ifa oracle presents during a divination session are (or certainly look like) the "binary codings of (1's) and (0's) in some re- spects. For example, here we have one of 256 types of "da'fa" marks or signatures. ("Da = to cast" "Fa = Ifa"): THIS IS WHAT AN IFA OCTAGRAM LOOKS LIKE
I I I I that they say could be written "in binary" as 1100, 1100 I I I I ↓ I I I I ↓ ↓ ↓ Ifa Odu Marks "Binary" Notation Sequences
Thankfully, the narrator's explanation is of the highest quality precisely because he stresses that the two systems--Ifa and "binary"--are "akin" to each other or may be "likened" to each other. And then, quite appropriately, he goes no further. For example, this narrator is appropriately silent on the ques- tion of the historical relationship (if any at all) between Ifa practice of more than a thousand years, on the one hand, and north African Arabic (and eventually European) "base -2" notation, on the other. Also, he does not address any substantive contents of the Ifa oracle in this video because such an ex- plination was not the purpose of his project. By contrast, I respectfully submit that calling the Ifa div- ination practice “mathematical” is not necessarily the best way to describe the interplay of “light” and “dark” polarities--which is what they actually are--that get marked down in the divination ses- sion. Going on, in pertinent part, he said (at 5'04") of the video: "Ifa retells the destiny of men and nations”… “Contemporary thoughts liken the div- ination system of 16 Opeles and mathematical probability to the binary system which is the basis of computer technology (at 5’25”).Is it a coincidence that in logarithms there are 256 logs and in Ifa there are 16 opele each having 16 odu all totaling 256. Is that a co- incidence?...The binary system uses implicit arrangements of zero which is akin to the odu system…” (Emphases added). PAGE 2 I find these statements to be believable and appropriately self-limiting. “Liken” and "akin” are del- iberate words that express themselves perfectly. Ifa’s octagrams, on the one hand, and “binary (mat- hematical--sil vous plait) coding, are similar. This, however, does not mean that they are the same nor that they entered into Yoruba thinking or informed European/American mathematical and computer engineering practices through the same nor through reverse or reciprocal historical routes. By contrast,this paper will examine the limits of the wisdom in—too literally—regarding Ifa divination as “mathematical”or saying (or implying) that it is a system of“binary mathematical” notation and, from that, implying that it is a system mathematical computation. In“mathematizing” Ifa, they tend to overstate their case, tend to attribute Ifa divination methods to others than the Yoruba themselves without distinguishing the “marking” of symbols (i.e., the octagons as a recording method) from the substance of the odus’ folk wisdom that is sui generis to the Yorubas alone. I think that these other writers (see Apendices A, B, C, and D, herein) should take the same care in expressing their views as did the narrator in “The House of Oduduwa.”
Finally, because this video, which is only 15 minutes long, is so good in explaining the history of the Yoruba world-view, and the great character and plans of the Ooni of Ile Ife, I shall review it in the End- notes to this essay.(12) Again, the narrator's comments are a part of his successful YouTube video cal- led "The House of Oduduwa." This public relations video features the new Ooni of Ile Ife: his history and his august mission and destiny. It may be found at:
https://mail.yahoo.com/d/folders/1/messages/AODiOR4wrZCkXhq69QBdwAfUih0?.src=fp Let me provide for you another good example of how to state the relationship between a mathematical idea, on the one hand, with a wholly cultural qualitative idea, on the other. The true relationship between nature, culture, and mathematics can be exemplified in the work of thebrilliant African-American mathematician and theoretical physicist S. James Gates, Jr. of the Univer- ersity of Maryland. He is one of the originators of the concept of “supersymmetry” in physics. He was inspired by the idea that the visual geometric paintings or textile designs of the Akan of Ghana and the Gyamen of the Ivory Coast—that express cultural concepts like aphorisms (“truisms”) and proverbs—would also be good illustrations of physics’ mathematical and, indeed, computer computational mod- els and geometry.—especially because of their use of super-symetry The Adinkra design--see the top of this page, please--semantically means “He who does not know can become knowledgeable through learning”; an obviously qualitative precept not involving mathematic calculations. *(Supersymetry theory is one of the newer additions to the western"standard model" theoretical phy- sics paradigms--starting around 1980--that holds that many sub-atomic particles that the universe has have their opposites in a particle that has mass (if it is a fermion of some sort, and vice-versa. At least it is true, these physicists and mathematicians believe, that there mathematical equations that illustrate those physical, geometical and electrical properties and the terms of which on one side of their equations can be manipulated such that--even when manipulated (i.e., addressed in a different order)--the resulting solutions on the other side of the equations will come out the same. If they do not, then it is said that the symetry, i.e., the mathematical symetry, is considered "broken." Dr, Gates even beIieves that computer programs objectively exist in nature that show "super-symetry." The geometric diagram above was only used by him to help people visualize "symetry"; and not to suggest that the Adinkra are engaged in calculating geometric mathematics). By contrast, as an example of inappropriate “mathematicism,” I will critique the video of a certain Shangodare Fagbemi, in Appendix D, in highlighting the many instances where he interjects or proj- ects mathematics into Orisha/Ifa religion as a whole (i.e., not just into its divinatory processes). For example, he said that the Fibonacci sequence of numbers is determined by simply adding a number to the last number in the sequence in order to get the next number: 1 + 2=3, 2+3=5, then 3 + 5 =8, then 5 + 8 =13, then 8 +13 = 21, and then 13 + 21 = 34 and so on. Therefore, the sequence is 3, 5, 8, 13, 21, 34… In the video lecturer, Mr. Fagbemi, then declares that because the orisha (i.e., an Orisha/ Ifa deity) Oshun’s ceremonial number is “5” and because the orisha Obatala’s number is “8,” this then proves that 'Os- hun’s and Obatala’s place in the orisha pantheon is based on mathematics because their numbers are also in the Fibonacci sequence.' PAGE 3 This, of course, is preposterous. For example, the orishas Yemoja and Oshoosi share the ceremonial “number” 7. Did God forget to ordain them with a number that was in the Fibonacci sequence--as illus- trated above? How about Oya, whose number is “9”; did our "God of Mathematical Nature" forget her? In fact, there are variations on the theme of creation in the religion: Some say that are 400+1 orishas in Yoruba religion while others have it at 601 orishas. So one is given to wonder who else did not make the "Fibonacci Top 40")? II. Introduction to the Main Issues I humbly ask that those people who are already familiar with the concept of “odu(s)” in Orisha/Ifa rel- igion, and its divination practices, to be patient with me in respect of these introductory remarks. I promise that I will clearly demonstrate why I say that there are no embedded mathematical processes “in” Orisha /Ifa religion--particularly in its divinatory rituals--despite ever-popular misconceptions to the contrary. In- stead, I say that the religion is entirely qualitative in nature. But in order to demon- strate this--for the sake of those who are not familiar with the religion at all, let alone its divinatory practices, some introductory remarks are obligatory. The problem confronting this writer is that there are readers who know a lot about math but only a little about Orisha/Ifa religion. And there are those who know a lot about the religion but are modestly school ed in math (like me). And then, of course, there are those who know a lot about both, yet some who know nothing about either. For these reasons, a good deal of introductory commentary must issue in order to contextualize the arguments contained herein. Therefore, I ask for persons, especially those who are new to Yoruba’s “Orisha/Ifa” divination practices, as described below, to be indulgent while I set forth what are the main theses contained in this paper--for the sake of the skeptics and for those who are familiar with the topic of Orisha/Ifa divination alike. What sparked my interest in this subject are two things. First, in 1996, I wrote a book entitled “AfricanSpirituality vs. The African American.” My main aim in that book was to caution African-Americans who--like me—were pursuing a bi-cultural existence that contained our American (i.e., Western) world view, on the one hand, with what we could re-capture of our west and central African intellec- tual and religious heritage, on the other, about the fact that we were far more Western in our mental- ities than our romantic inclinations would allow us to easily believe. As the great W.E.B. DuBois once remarked: ‘there is no one so American as the American Negro.’ I recognized then that most of us are functionally ignorant about the nature and importance of under- standing the influence of Grecian philosophy and mathematics, of Hebraic Kabbalistic theological and literary culture of antiquity, of Arabic-Islamic science (especially its penchant toward mathematics), European Hermeticism (including Gnosticism, alchemy, astrology, Rosicrucianism, and Freemason- ry), as well as European and Anglo-American empiricism (that fostered a new methodology of scien- ce), among others, on our thinking—even as we valiantly sought to distinguish ourselves from “Euro- centrists" and Eurocentrism(7)” For this reason, after I read and saw videos of various African-American and Nigerian intellectuals asserting that “mathematics” was at the root of our qualitative nature religions of west and central Africa, foremost among them Yoruba Orisha/Ifa religion, I was moved to respond. Such a proposition arose, and could only arise, I believe, from those with mathematical acumen but who are inclined to project into or onto Orisha /Ifa religion a ‘mathematicism’ (to coin a term) that, otherwise, they could never have found there except for their projections and those of like-minded people. Accordingly, I have identified the culprit as being an unrecognized Grecian Platonism in their thinking; i.e., non-conscious biases in thinking styles and beliefs that were born of educations in Western dominated post-colonial schools (for our African kindreds) or our general American education system and med- ia in which, for us, we were all wholly immersed. PAGE 4 Additionally, we are usually unaware of the Arabic cultural biases on us about mathematics (which, for them, included the primacy of algebra as the internal language of all mathematics domains including arithmetic), not to mention their astrology, numerology and geomancy (the technique of cutting div- ination symbols into the sand as octagrams) on our ways of thinking. So, not only do I assert, by con- trast, that there are no mathematics (meaning no mathematical operations) in Orisha/Ifa theology but, moreover—consistent with the fact that ours is the most robust religion of nature and ancient communal societies--I must also suggest that there were, and remain, no mathematics embedded “in nature” either.(13) Mathematics is, I suggest, embedded in our minds and rooted in human labor in- teractions, mechanics, trade, coinage, astronomy, the applied physical sciences, innovation, and socialization over the eons. This is not to say that we cannot learn something from the mathematically-minded who are interested in Yoruba Orisha/Ifa religion nor that it would not be of, at least, passing interest to the rest of us for the purposes of intellectual entertainment. Entertainment, indeed, as many of them do seek to “wow!” us with talk of ‘fractals,’ Fibonacci sequences, ‘golden ratios (phi ratios) , the constants of physics, “base 2” binary coding and computations, the Boolean algebra of “sets,” and on and on, as illustrative of mathematics embedded “in” nature itself—transcendent above and independent of all human beings and human cognition. Those who are themselves embedded in Platonic assumptions about the Univ- erse believe that there are embedded in the universe [perfect] [essential] [forms] of [everything] in- cluding numbers, numerals (their written symbols), and mathematical ideas, formulae, and operat- ions—all independent of any human thought processes or reflection.(1) This view was introduced by Pythagoras and Plato into Western and all Mediterranean-rim cultures’ mentalities (eventually including North African Arab and Moorish groups as well). But what one is actually likely to learn from them—the fetish priests of mathematics--is a lot about mathematics but only a modest amount (at best!) about Orisha/Ifa religion! Accordingly, what one does learn from them will have no bearing whatsoever on the cultivation nor enlargement of one’s ashe (pronounced "ah-shay") or spiritual knowledge, power and effectiveness as a priest or priestess in this, nor any other, truly (sub-Saharan) African traditional religion. Small wonder then that you have never seen a babal- awo nor any other diviner pull out a hand-held calculator, a slide-rule, nor paper-and-pencils to do arithmetic in a divination session using the Orisha/Ifa oracle. Mathematics for use in material culture was invented in Africa and by Africans. Cite, for example, theworld's 2nd oldest mathematic calculator (akin to the "abacus" or slide rule) called the Ishango Bonefound in the Congo in 1950; it is 22,000 years old. But older than that, from Wikipedia, is "the oldest known possibly mathematical object (...) the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC. It consists of 29 distinct notches cut into a baboon's fibula." And various African cultures have always had simple to complex numbering systems with var- ious bases. Interestingly, the Yoruba culture's mathematics, the very culture from which Orisha-Ifa religion is born, uses "base 20" enumeration (not "base 2" binary notation as our "Ifa mathematizers" would have it). PAGE 5 III. The Main Assumptions and Theses For your perusal, let me set forth these ideas: 1. Orisha/Ifa Religion Is Far and Away Qualitative In Nature, Not Quantitative When considering Orisha/Ifa as a corpus of received wisdom—substantive folk wisdom—there are no numerical operations (meaning no calculations), nor any other versions of mathematical (binary) computations, axioms, theorems, proofs, nor algebraic expressions in it. Orisha/Ifa theology is, prac- tically-speaking, entirely qualitative in nature. The few “numbers” thought about in it or numerals written down in it are virtually incidental, having only nominal uses, i.e., “naming,” labeling, or des- ignation roles, but are not used for measurement, calculation nor computational ones. For example, certain odus (we will cover what they are later) may have numbers--as labels--associated with them and certain orisha (deities) may also have varying numbers associated with them while the offerings given to them will use their "numbers" as designations. Some rituals may be associated with deter- mining the span of the appropriate number of days or nights, or certain hours of the day or night to do them, as may be deemed conventional by local customs. But none of these numbers are actually used for calculation nor computat- ional mathematical operations.(2) Unfortunately many writers, whenever they see a ( I ) in a sentence written in close proximity to ( 0 ) or to ( II ) automatically think that the first symbol is a “one” and the second is a “zero” or binary polarity. So, from there they declare that these are “binary” numerals (bytes) derived from “base 2” enumera- tion. Not necessarily true! These symbols could also mean, qualitatively-speaking “something” as contrasted to “not something”; that is, the quality of “somethingness” vs. the quality of “nothingness.” Polarities do not necessarily mean numbers. By contrast, this is exemplified by the qualitative polar- ities of “pregnant vs. not pregnant” or “night vs. day.”No numbers are necessary to depict these polar- ities, and no numbers nor "bytes" are relevant to Orisha-Ifa divination either for the same qualitative reasons. Quantitative cognition is simply inapposite to qualitative depictions of things and phenom- ena. They simply do not relate to each other no more than one can multiply "6" apples x. "4" snow- flakes." What is the product? Nothing. What then can one achieve by digitizing or declaring that binary bytes in the dafa octogram markings or signs of Orisha-Ifa divination have meaning? Nothing. Now, friends, the very first objection to "binary" digitalization as a construct purportedly inherent in Orisha-Ifa divination lies in conflating "binary" (1 or 0 as bytes) with "polarities." A binary notation can only mean a single, discrete, "number"--"1" or "0" (e.g. "on" or "off"). By contrast, polarities are spec- tral in nature, not discrete singular "numbers" or integers. Day vs. night are polarities--but yet there are gradations in their qualities (meaningful gradations!). There are, as time passes, varying degrees of darkness at night. "Peace" vs. "turmoil" is another example of a polarity that is spectral in its nat- ure. There are diffrent kinds and degrees of "peacefulness" relative to "turmoil." Orisha-Ifa divination is very much tied to the qualitative essence of one aspect or the other of a polarity (and this, in fact, allows for the dialectical interpeneration of these opposities such that one may contain some of the qualities of the other and--at times--transform itself into its opposite's qualities. Discrete "binary" bytes are good only for counting and quantitative calculation; having nothing to do with the qualities and properties of life and its vissisitudes in the real and supernatural world. And having nothing to do with the qualitative. interpretation of odu. They will even go so far as to write out the binary number equivalents to the 16 odu figures that Yoruba priests use to denote the “16” odu (Olodu) signs or signatures.(3) For example: see the odu quality fig- ure when written here as the analogue to the binary quantity notation numbers that these writers proffer: I (light) This odu equivalent would, they believe, be written in I (light) “binary” as the following number sequence: I I (dark) ➔➔➔➔➔ becomes ➔➔➔➔➔ 1 1 0 1 * I (light) This is a quadragram named “Irete” (in Nigerian Ifa divination) or “Merindilogun" (in Afro-Cuban dilogun divination)._____________________________ *Frankly, the very idea of writing the sequence of dafa marks down and claiming that they represent binary notation is preposterous in the first place. "1101" has nothing to do with the qualitative odu "Irete." "1101" in binary is actually the integer "13" (and in no system of Ifa divination does the numeral "13" have anything to do with the Odu "Irete." Another way to illustrate the absurdity of "mathematiz- ing" Ifa's dafa marking system would be this. Let's take the odu Irete again. Since there are 5 separate marks here, why not call the sign Irete "5" in 'math-ese' notation? Do you not see the absurdity of adding elements of a quadragram of a light-dark sequence as if they were num-bers? Is it not equally absurd to "binary" dafa mark quadragrams as if these lines constituted the bin- ary "bytes" written as "1101" ? Comparing inapposite things is but an exercise in comparing incom- parables; pure sophistry. I will go into legitimate questions about doing this in Appendices A, B, C and D of this essay as I des- cribe what odus are. (Much mental and cultural mischief flows in the wake of this misunderstanding if it were left standing as a misrepresentation of Orisha/Ifa divination because it would wreak havoc on a key aspect of Yoruba divination that is common to all of its legitimate variations—namely the decis- ions that have to be made that depend on each “sign’s” or octagon’s seniority rank vis. a vis. the other 15 main signs, or their 256 derivative ones; their "omo'dus."). (4) PAGE 6 2. Albeit, as a non-mathematician, my opinion is that all mathematical operations must ultimately in- volve measurement, calculations or computations with numbers. Which is to say that, at some fun- demental level, they must ultimately involve number ideas and numerals (i.e., number symbols for them) and numerically quantized measurements expressly scaled as units of some kind that are--for their parts, finally-- acted on by the simple and “operators” of arithmetic (that is, by +, - , x or / opera- tions ). Thus, by the use of these operators. symbols are followed in strict adherence to a set of immut- able and very basic rules and algorithms. In my view, regardless of how esoteric and symbolically expressed are the mathematical operations or symbolic logic, I would go so far as to say that if they do not ultimately involve the contemplation and calculation of numbers—in the final analysis—we are not dealing with mathematics—or, at least, not with mathematical operations at all. The eminent philosopher of mathematics (and physics), Nick Bostro, (the University of Oxford) wrote in the breath-taking foray of a magazine booklet entitled "The Nature of Reality: How Mathematics, Physics and Consciousness Combine To Define Our World" in the New Scientist: Essential Guide No.1 (2020) also agrees: "...what is mathematics made of? At some level, all of mathematics is built on numbers and the relations between them" (at p. 20). In nature there can only be "observables" and "intrinsics" (like phenotypes and genotypes), including intrinsic regularit- ies in the op-erations of things, the various iterations of which can be measured and counted with numbers. The numbers and calculations themselves are not intrinsic. And, finally, if we are dealing with mathematics then all of its measurements (i.e., its measured units of weight, speed, time-intervals etc.) must be scaled. The scaling might be in the nature of an ordinal scale (where quantities get ranked numerically as being in 1st, 2nd, 3rd or 4th place, etc.) or a ratio scale (where some number is considered to be a percentage, square or inverse square of some other relevant number). Finally, things may be meassured using an interval scale where the “interval” is the amount of ‘stuff’ or time between any two adjacent natural numbers: say the amount of “stuff” or units between 6 and 7, is known to be the same amount of ‘stuff’ as between, say, 10 and 11. And, of course, there are other types of scales like, for example, logarithmic or exponential scales (where numbers are expressed as multipliers of themselves). By contrast, “nominal” or labeling numerals or integers—such as the few that appear in Orisha/Ifa practices—are only, at most, “designators” that simply identify and distinguish one thing from anot- her. These numerals, like the numerals on the tops of various autos in a car race, are not scaled. They are only numerals used as “names” for the purposes of identification, not measurements. Nomin al “numerals” are used in Orisha/Ifa divination, but not for the purposes of mathematic calculation nor computation. And, in fact, they are completely dispensable (though this is impractical). That is, the rules and methods of Orisha/Ifa divination can be written down as words alone, including words that denote “seniority” rules and algorithms, as will be discussed later in Part VI, below) and followed with- out any numerals appearing anywhere! What do I mean by the idea that some numbers are only used as identifiers or “designators”? Again, I mean that they are only nominal in nature, as categorizers. For example,‘this person has “type 1” diab- etes, while these other two patients have “type 2” and "type 3” diabetes (brain starvation), respectiv- ely.' You see, these numbers only designate types or categories of the diseases, but there are no arith- metic calculations involving addition, subtraction, multiplication nor division using those numbers in clinical medicine. They are only identifiers of one thing used to distinguish something from an- other similar thing, e.g., like the numbers on a soccer team’s players’ uniforms or on race car roofs. Those kinds of numbers do not interact with each other. They are merely nominal (name labeling) “designators.” * Similarly, there are “ordinal scales” the numbers of which only serve the purpose of informing us about the sequence or ranking of things that have been identified. This information only tells us what place or rank in a list of things does the thing we are interested in fall in a sequence of similar things. For example, saying that “Mr. Smith’s car came in “1st place” in the race,”while Ms Green’s car came in“2nd place” and Mr. Brown’s car came in “3rd place. This example of ordinal information does not tell us nor suggest how fast either of the was traveling, nor how much distance at the end of the race lay between Mr. Smith’s car and Ms Green’s car, as compared to how much distance there was between her “2nd place” car and the “3rd place” finisher. It has been scientifically shown that monkeys (monkeys!) have a perception of the relative sizes of objects and collections and rank orderings. That is, they un- derstand ordination but cannot carry out any mathematical calculations beyond the simple percep- tion of the objects' sizes, weights, or the lengths of the things of interest to them. *PAGE 7 In other words, no calculations nor computations ensue from this information. They are merely num- eric information denoting which place a car finished the race. Hence, no mathematical operations are invol- ved. Similarly, in Orisha/Ifa divination there is minor use of ordinal numbers—e.g., this odu here is “senior” to that odu (ranked older or higher) "over there," while both of them are “junior” to these remaining odus. This information is useful—indeed obligatory-- to know in some parts of the divnation session--but has nothing to do with arithmetic calculations nor computations with other numbers. These kinds of incidental numbers (1st , 2nd place etc.), numerals, digits or integers (or what ever one wishes to call them) cannot, therefore, be used to assert that Orisha/Ifa contains “in” it any essential mathematical processes. The point here is “designators,” or identifiers. And they may be us- ed as “rankers” or “raters” but otherwise not be further involved in any mathematical calculations nor computations. The Probabilities of the Various Patterns Showing Up Are Not Relevant to the "Reading" Hence, No Statistical Calculations Are Relevant Either to Ifa Divination [An aside: the throwing of obi abata, coconut shells or pieces, cowrie shells, the opele chain of shells or the ikin (palm nut kernals) are all versions of Ifa divination because they all "pull down" odu(s). But, in order to do this, these tools are random generators of a finite number of patterns--16 (or 17 of them, as in the case of cowrie shell divination). As such, a statistician --an outside observer--might show some interest in the probabilities of the various patterns showing up for any given "throw" or casting (dafa) of the tools. Parametric statistics, including adducing probabilities, obviously involves calcul- ations. But, these inquiries are those of people interested in the patterns ("odu(s)") of Ifa as seen from the "outside" of the Ifa divination process. But, seen from the inside of the Ifa divination process (i.e., that is, as seen and experienced by those actualy engaged in the divination process), the probabilities of any given pattern showing up are irrelevant and never considered in the qualitative interpretations that are the total essence of the Ifa divination experience]. The relevance of this will soon become clear, as some of the “things” that we will be talking about a little later as being “in” Orisha/Ifa theology are things called “odus” that have nominal numeral labels. These odus are like the chapters and verses of Yoruba folk wisdom, originally only stored, and recited orally from generation to generation. The odus (which double as “deities” as well!) have names and numbers assigned to them. But, again, they are merely “nominal” numbers. Their numbers serve only to distinguish them from various other odus among the 256 total possibilities. [I shall explain the cen- trality and nature of odus in Part VI of this paper].
That is, these number labels for the odus—because numbers, otherwise, state the magnitude or length of something—are used to identify which of the odus are relatively older or “senior” to others, as men- tioned above. But after such ranking is taken into consideration in the methodological choices a div- iner has to make during the session, they have no further calculation, computational, nor inter pretive value in divination results. So, again, since no arithmetic calculations nor computations are involved there is—in short—no “math” is involved (i.e., no adding, subtracting, multiplying nor dividing)—in Orisha/Ifa theology, generally, nor its divination methods or substantive narratives in particular. 3. Again, What Does An Odu Sign, Symbol (or Octagranal Da’fa Mark) Look Like When Written or Etched Into Powder On A Tray or Chalked In As An Inscription On A Straw Mat? They look like this, where ( I ) = “light” and ( II ) = “dark”: I = I I One “leg” of Ifa → I ←Two “legs” of Ifa → I ←One “leg” of Ifa I I I I I I (As a quick aside, there is a “weak force energy” sensitivity, metaphorically-speaking, at each of the four levels in the two "legs" octagram that "senses" whether its counterpart is of the same radiant “energy,” i.e., whether or not it is in a qualitative state of “lightness” or “darkness,” over there on the same level of the other side of the octagram" . This is how one “leg” of Ifa can sense if the other, in the octagram viewed as a whole, is a “meji” (its identical double) or is a fraternal twin of some other sort. This feature is of minor interpretive value and is discussed in Appendix D). Since these Orisha/Ifa’s divination’s odu “da’fa marks” or “signs” only signify different ones among the total 256 possibilities, i.e., signs that are marked such as “I" or "I I,” or “X"or "O,” or “I" or "O” etc., only designate “light” or “dark” patterns that are not actual numerals or digits. And since the da’fa figures never involve more than four such mark such levels (of an I, an O, or an X) for each “leg of Ifa” quadra- grams, there never is any actual “counting” of them. [Please see Part VII, below, for complete illustra- tions of the 16 odus’ “da’fa” figures quadragram/octagrams like those above]. *PAGE 8 4. No Counting? (!) Nope! This is because the “counting” of objects (any objects)—such as those things (e.g., shells, nuts, etc.) that indicate which da’fa “mark lines to write or etch down in Ifa divination, or in any other sit- uation in life, does not begin until the collection of things contains five or more objects. Provocative, huh? That is, “counting” does not begin until we humans perceive five or more things in a collection owing to the neuropsychological principle of “subtizing” which has proven that human “counting” does not occur until the sum of objects visible to or audible by us in a collection of things has passed the number “4.” Notice that a da’fa sign always has only four levels. In Yoruba religious culture the number "4" is the most sacred number. The world was created in "4" days. And everything else is built around "4" or its multiples. Thus, nothing ever needs to be “counted,” per se. Both the diviner and the client can immediately see or witness the odu (the pattern) that has just been pulled down to the mat or to the divining tray. And, for similar reasons, this is why in some elemental cultures, the only “math- ematics” that they have--for them--is in a rather complete numbering system for "enumeration" that is in the nature of the following: “one, two, three, four, and many.” *(It has been shown that infants of one or two month’s age can demonstrate a brain-embedded, a priori, awareness that a collection of two objects is different than a collection or three or four of them. But for years to come they can count no more. A similar innate capacity for understanding the simple struc- ture of spoken language—regardless of culture—i.e., the rules for grammar, syntax and prosody--were discovered by Noam Chomsky sixty years ago. It “comes in on a gene”—so to speak—since these rules of speaking and comprehending cannot be taught to an infant or toddler. They learn to speak, more or less, correct syntax by exposure to spoken language operating on this innate capacity. Only later, in school, can they be taught the rules of grammar. Similarly, it has been shown that even monkeys can perceive different collections of quantities (without counting individual things within the "set" or collection) according to their 'ordinal magnitude." For example, this set contains the same, less, more or the most items by visual inspection, or things that are smallest, smaller, larger or largest along the same fashion--by inspection. This is not based on language processing ('counting'). (See "Monkey Math Mirrors Our Own," by Bjorn Carey, LiveScience, in Proceedings of the National Academy of Sciences, 2005). Now back to the subject at hand: Orisha/Ifa theology and divination does not contain nor depend on any mathematical operations of calculation and computation. That said, the only, very minor, excep- tion to this generalization about the Ifa oracle is evident in the merindilogun (or, in Afro-Cuba, as the "dilogun") divinatory method--cowrie shell divination--that is a version of it. This approach uses cow- rie shells to derive or “pull down” the relevant odu signs in the divination session. In this method of Ifa divination (of which there are about eight different methods) a diviner does “count” up to 16 shells in order to add up the shells’ "mouths," among them, that are face-up (or “speaking”) on the mat as per each cast. So, yes, there is a smidgen of "counting" going on in that sole case, but it means nothing more than id- entifying how many cowrie shells are "speaking." The odu, as such, is but one among the 16 possible ones for any given throw of the shells. But, thereafter, no arithmetic computations or calculations bec- ome involved. (Also, this kind of Orisha/ Ifa divination is the only method where “0” can come up as a result of a casting, i.e., where all 16 shells fall facing downwards --i.e., "not speaking"is possible.(5) In such a case, this odu is named “Opira” and is an odu which has its own very unique “substance” and unique way of being responded to by the diviner. The word "speaking" is the analogue to "light-side up" and conversely, "not speaking" is the same as "dark-side up" and would be marked I and II (or 0 and I), respectively. * In fact, the very word—“merindilogun”—as the name of the “16 cowrie shell” version of Orisha/Ifa div- ination—means “twenty minus four” or “sixteen” (things)--inherently a numerical subtraction idea—because, again, in this kind of Ifa divination sixteen cowries are used.(6) After that, however, this is only a “numerical word” that simply labels or describes this one type of Orisha/Ifa’s divination met- hod, beyond which there are no mathematical operations in determining the interpretation of the odu “signs” that are revealed by each cast of the cowies that ‘fall onto the mat.” *PAGE 9
In the appendices to this paper I shall critique the contributions of some who assert that, in its essen- ce, Orisha/Ifa religion is “mathematical” at its deepest levels. I hope to make the argument that this idea should be rejected along with the lunacy of some professional mathematicians, theoretical phy- sicists, and cosmologists-in-the wild who maintain that the ‘Universe itself is—or can be reduced to--some profound single equation ‘in the sky.’ 5. Mathematics Is Embedded In Human Thought, Not In Transcendent “Objective” Nature. Last, in Part V of this essay, I will make the argument that Ifa, in regard to its substantive content, is a religion of nature and west African social experience and that there are no mathematics embedded in either it or nature! I am fully aware that this blasphemy may exercise the mathematics adepts among us who passionately believe the contrary But I suggest that despite all of their mathematical acumen, they have yet to escape the Platonic(Mediterranean-rim) cultural core at the root of their convictions. Some may discover—perhaps to their dismay—just how Eurocentric (Pythagorean, Platonic , Aristot- elian and Hermetic) are their actual mind-sets when they make projections onto Orisha/Ifa theology propositions like “mathematics is embedded in Orisha/ Ifa divination systems"; i.e., that they are, es- sentially, mathem- atical in substance and methodology.
I recommend that one read the foundational points in “Where Mathematics Comes From (George Lak- off & Rafael Nunez, Perseus Books, 2000) that exhaustively makes the cognitive, neuropsychological and philosophical case that mathematics is not some thing that exists objectively in nature—i.e., apart, detached from, and transcendent “above” humanity—as, Pythagoras, Plato and other seminal Greek philosophers of mathematics believed. Indeed, the stubborn persistence of their "mathematical idealism" is evident in the recent publication of the booklet "The Nature of Reality:" How Mathematics, Physics, and Consciousness Combine to Define Our World," (edited by Richard Webb, New Scientist magazine, 2020). *Interestingly, even Pathagoras' conception of mathematical idealism ('numbers," however abstract, are a priori, embedded in objective nature)' did not arise from mathematics. Rather, it arose from the qualitat- ive and semantical language that described the observable polarities in the real material world: light vs. dark, up vs. down, good vs. evil, hot vs. cold, etc. as properties that "objectively" were observed "embedded in the universe." Polarities seemed universal! So, from these qualitative pol- arities, when they were applied to the sequential numbers involved in counting and also became view- ed as objectively existent in the world. From there, in his mind, the polarized math sprung into existen- ce as (and in) the form of alternating "odd numbers" and "even numbers." Last, therefore, they were presumed to also exist objectively in the world just like the 10 or 12 wordly polarities he had prior id- entified. (See "Studies In Ancient Greek Society" pp. 260-261). *He also believed that musical tones reflected mathematical regularities as one moved from tone (pitch) to tone, or octive to octive, by way of mathematic constants, i.e., ratios. But the important point is that abstract numbers and enumeration arose from energy and matter (sound and bow strings) that pointed to the nature of music properties, but were not, themselves, the music itself. In all cases, num- bers and their interactions (mathematics) were thought to underlie and exist objectively independent of the the energies and matter observed in the world. The abstract of numbers gave way to the reific- ation of them as entities in themselves and were among the perfect (eternally hidden and abstract) forms responsible for the things that we hear, see and thing in real life. Our mathematizers of today--including the Afrocentric ones, still are captive to the mathematical idealism taught to them by their Mediterrannean-rim and western mentors. They simply declare that mathematical idealism (ideas precede realities) is really mathematics realism or reality. For them, math is to be "discovered" in nat- ure; not "invented" by human cognition. PAGE 10 IV. Who Am I To Opine On These Lofty Topics? This line of argumentation will be particularly difficult for many skeptics to accept coming from a mere intellectual wayfarer such as myself! After all, I am not a mathematician. (In fact, I am lucky to be able to balance my own checkbook). So, what could I know about such esoterica? Well, all I know is that it does not take mathematical genius to understand, contemplate, nor comment on mathematical ideas where no mathematical operations exist; such as in nature or in Ifa theology--the religious ex- pression of nature. To make matters more interesting yet, I am also not a babalawo in the Orisha/Ifa religion (babalawos and iyan'ifas are its divinatory specialists). However, in my humble defense, I proffer the following: I am an olorisha (a priest of Oshoosi and Oya within Yoruba religion) with thirty-six years of experience in the religion; as of 2020, thirty-one of them “made” or “crowned.” I have a fundamental level of Ifa initiation as well, though I am not—and never intended to be--a babalawo. Authorized as a “made” (i.e., deeply initiated) priest, for decades, I have regularly used some of the various Orisha/Ifa methods of divination--though not hardly with the putative skills of an italero or oba-oriate--who, like babalawos, are divinatory specialists in my branch, the Cuban Lucumi, branch of Yoruba’s Orisha/Ifa religion. It is the case, however, that I do have some modest educational and professional achievements: For ex-ample, I have a Ph.D. in clinical-social psychology (The Wright Institute, Berkeley, 1976), and a J.D. de- gree in law (Boalt Hall School of Law, U.C. Berkeley, 1981). I also have triple board certifications in foren- sic psychology (American Board of Professional Psychology, American Board of Forensic Psychology, and the American Academy of Forensic Psychology since 1989) which required me to have developed expertise in clinical psychology, psychopathology, neuropsychology and cognitive psychology along the way. These experiences afford me a certain confidence in my abilities to deconstruct the complex- ities involved in this diatribe. My interest is in ferreting out European-thinking, as it may non-consciously and semi-consciously operate in our minds, as we adopt a bi-cultural “traditional African religious world-view in addition to our natal perspectives, and is not new. As mentioned, in 1996, I authored African Spirituality vs. The African-American, favorably reviewed by Dr. John Henrick Clarke at the time, in which I addressed some of these topics. It mostly focuses on identifying Pythagorean, Platonic and Aristotelian think- ing (i.e., mathematical idealism, as well as other important Eurocentric and Mediterranean-rim cul- tural ideas and influences, on our contemporary African and African-American thinking styles and biases; those that concern me as a priest, psychologist and reformer. In my view, we African-Americans are notably inclined to eclectically incorporate all kinds of thoughtsand ideologies and religions into our bi-cultural practices of traditional African religion but, unfor- tunately, do so naively; not recognizing the Mediterranean-rim philosophical roots (that are not sub-Saharan in nature) involved in what we proclaim as “knowledge.” Accordingly, in my series of “What Ain’t In Ifa” essays I will interrogate whether many ideas, e.g. religious mathematicism (e.g., geman- tria), astrology (especially astrology!), chakra ideas, racist "melanin "theory," sectarianism, sexual-guilt , Kemetic mystery religion thought, Hermeticism and gnosticism (and other topics) are even rec- ognized, let alone helpful to our understanding of Orisha/Ifa religion. Just because there are a few in- stances where words in Yoruba might share etymological roots as cognates or counterparts in other cultures and languages, specifically, does not mean that there are deep or underlying connects am- ong them. (7) PAGE 11 *They are not—regardless of how interesting (and even instructive) may be their contents and anal- ogues to our religion when studied for their comparative concepts and deities. Analogous and meta- phorical illustrations drawn from other lines of thought, knowledge, religions and other fundam- ental cultural worldviews can be—heuristically-speaking—very interesting so long as one does not naively incorporate –let alone—syncretize them with our traditional sub-Saharan intellectual leg- acy (owning to our naïve Western-biased projections and introjections). Orisha/Ifa religion does not need any external legitimization and, conversely, it is not subject to external impeachment. Compar- isons and conceptual analogues are fine, but they must not be incorporations. Now having made intro- ductory and contextualization remarks, let me describe for new comers to these subjects basically how Orisha/Ifa religion is, how it works, and what some claim are its mathematical properties in the area of divination. * V. What is Orisha/Ifa Theology? Orisha/Ifa is a sub-Saharan, west African, religious system that has some content and ritual methods —though minimal--from central Africa, from far west coast Africa, from the Sudan and Sahil of east Africa, and the etymology of some words from far North-east Nilotic (Egyptian or Kemetic) antiquated roots as well. Ours is a nature-based and animistic religion and worldview. Ifa is rooted in human ex- perience and in nature itself for its substantive wisdom. As a religious system,it is replete with a priesthood, deities, spiritual “possessions” by some of its prac titioners, the complex and sophisticated divination system. The divination system in the religion helps its practitioners discern, in light of a question or problem, what spiritual or mystical forces and factors are at work behind the scene, and what can be done with an offer to the honored ancestors or the orish-as (the gods) in order to understand the problems or challenges, and to secure satisfactory resolutions. The traditional religious and psychological wisdom contained in these divinatory “oracles” was oral in nature. That is, it was given and received in the form of stories, proverbs, allegories, poetry and ritual remedies -- that were passed on from generation to generation based on pure memory and recitation. These Ifa oracles--or wisdom-- can be consulted on a daily basis if so desired. And please note that within Orisha/Ifa divination there are anywhere from 6 to 10 different methods for consulting its or- acle--depending on the country in which the practice is being done and which kind of priest or priest- ess, within the religion, is doing the divination. (8) And, as mentioned, these wisdom -containing ‘s stories and poems contain the entire corpus of cultur- al, psychological, proverbial, medicinal, and substantive religious and ritual wisdom passed down to us for centuries and millennia in West and Central Africa as a complete religious system. The Orisha /Ifa practitioners now number in the tens of millions in West-central Africa, Brasil, the Caribbean is- ands and Mexico, and in other places in Latin America and now, not least, in the United States. But the main locations of these practice are Nigeria, Cuba, Brazil, and in multiple cities in the United States. The Orisha/Ifa religious system and worldview goes under various names: in Nigeria it may be called Ifa, orisha religion or, specifically, Isheshe Alagbaye. In Cuba it may be referred to as Lucumi, Santeria and, in a sense, we can include Palo Monte & Moyombe (which is Cuban-Congolese) in so far as chamal- onga divination practices--which is identical to Yoruba and Cuban "obi" divination--is concerned. In Brasil it is known as Candomble, Macumba, and Umbanda. While in the United States and Puerto Rico, we refer to it as “O’cha” (a contraction of “orisha”). Though in lesser numbers, the Orisha/Ifa system of divination practice in Benin (Dahomey) and in Haiti is known as “Fa,” in Ghana as “Afa,” (9) PAGE 12 VI. The Concept of Odus As “Chapters of Wisdom on Life’s Conditions” That Constitute the “Oral” Books and Libraries of Ifa-- Centuries Old—That Orisha/Ifa Priests and Priestesses Are Consulting On Behalf of a Client During Divination Sessions. As mentioned, the accumulated knowledge contained in this complex “black” African religious world-view was stored in oral libraries. The multiple containers or “oral books” were organized into “chapters” which are called odus ("odu" for the singular case). Traditionally, the priest and priestesses in Orisha/Ifa‘s religion recited the stories (important parables are called itan or itan-pataki while the poetry is called and ese Ifa. They are illustrative of spiritual folk wisdom aplenty passed to each other from generation to generation based on rote memorization and echolalic repetitive recitations (which took the average person decades to grasp and retain even a usable portion there- of, because the entire corpus of knowledge contain tens of thousands of separate stories, parables and poems). For the last 80 years, or so, many of these stories and poems-- that is, the ese Ifa (again, the odu poetry) have been written down in collections and books. (10) But, in toto, there are tens of thousands of them, and no one knows them all. A priest who had been taught to do Orisha/Ifa divination methods can, for himself, herself, or ot- hers, divine or inquire into the background circumstances that are at work affecting the client (or people of concern to the client), explain those circumstances in terms of which spiritual entities and deities were at work producing them, and affecting or changing them, to explain how the client arrived at his or her present station. The odus at work in the background can be identified by the artful practice of Orisha /Ifa divination--discovering what are the present, behind-the-scenes, dynamics at work, and how the cir- cumstances are likely to play out in the foreseeable future. With this knowled- lge a client can make of- ferings (or avoid certain behaviors) in order to achieve favorable outcomes regarding the problems that he or she sought divination to elucidate. A very important aspect of the wisdom contained in the odu stories, parables, allegories and poems are creation accounts. For example, in one odu we may find ‘how love came into the world’ while in another we may learn the origin of certain rituals or proverbs. Indeed, thousands of references as to how this phenomenon, or that idea (like the relationships between certain allegorical animals or orishas came about). These are the types of things to which I refer when I later speak of the substan- tive contents of the odus. Arabic (Islamic) culture would find all of this the stuff of “witchcraft” which is why writers that claim that “Ifa came from North-African Arabs” (when what they mean is that the current use of octa- grams to represent Ifa’s odus came from them) is so dangerously wrong! (See Appendix D, below). We would also find in them anecdotal stories and illustrations of problems that the orishas (the gods) encountered when they inhabited the world long ago, And, most importantly, which incantations, cur- es, offerings, sacrifices and advice that they use to solve their problems. All of these things—lessons and cautionary tales—are in the 256 odus.* And, in any given divination session for a client, one or many of these odus may ‘fall to the (divination) mat and become central to the diviners’ assessments of the client’s issues and question. Following that will come instructions on what to do about them. Last, the odus that fall to the mat may inform the diviner what others close to the client are doing or needing and even what is the client’s personal attitude toward the diviner and the oracular session itself may be. _________________________________ * In Ifa divination, proper, called "Awos(h)e" or "Iwos(h)e," there are a total of 256 olodu and omodu (16 x 16 combinations of odu(s) plus the original odu meji or 'double odu.' This equals 256 in total. But in Merindilogun, or cowrie shell divination (called 'Owo Merindilogun,' 'Owo Eyo,' 'Owo Esha,' or 'Dilog- un Caracoles' (in Spanish) there are 17 basic olodu (the 17th is called "Opira"). This means, then, that there are 257 total odu(s) (16 + 15 x 16 =256 + 1 = 257. We do not count "Opira" more than once since it is never paired with any other Olodu. (But note, Mason, "Four New World Yoruba Rituals," at page 92, ln 2 says that there are a total of 289 omo'du. The mistake that he is making with this number, in my view, is that he is counting Opira a total of 17 times as if it were matched, at any given time, with another Olodu But this Opira should only be counted as adding one more odu to the total; not 17 more, because it is never matched with any of the other 16 Olodu. PAGE 13 Odu(s) Are Also Deities In The Own Rights So then, what in the heck are the odu(s)? This term can mean three related things: Odu(s) are “containers” of narratives about the types of conditions in life that may, at any given time, be coloring-- indeed controlling—the experience of a person or group as she, he, or they proceed through day-to-day, week-two-week, or year-two-year experiences here on earth. There are 16 truly basic odu(s) (called “Olodus") in Orisha/Ifa religion. However, a diviner will most often “pull” pairs of these odu "signs” (the omo’du(s )or “children of odu”) down onto the divination mat to explain to a client what his or her situation is (as well as to give an explanation of how the situation came about and where it is likely to be headed). Thus, there are 240 octagons (or pairs) of the 16 basic ones, thus making 256 total “odu” types once one has added the original 16 to the 240. It is only for convenience sake that these 256 odu(s) are number- ed. But what is indispensable is that each of them has its own name. And, as mentioned in Part III, no mathematical calculations nor computations are involved in (nor as between or among) these odus once, using one Orisha /Ifa divination method or another, the odu’s signs have been cast down on to the mat during the divination session. Next, as described immediately above, the stories and their wisdom and moral and practical advice are also (loosely) called “odu(s)” but, more exactly, are called patakins or apatakis in Cuba (the correct wordfor these stories is itan. --Finally, odus are also considered to be orishas (gods) in their own rights. As such, they can be prayed to, they can be given offerings, they can be invoked and addressed verbally. And in their stories ot- hers among the more well-known orishas (like Shango, or Yemoja or Elegua etc.) appear (i.e.,they “are born” in them) and speak giving advice and ritual instructions for suggested offerings and sacrifices to the clients of the divination sessions. Odus parade through one’s life on a weekly, monthly, yearly or life-time basis ever unpredictable—and in no discernable order (to humans). It is said that “odus are born every day” (read: ‘changing “circumstances” of which there are recognizable as distinctive types that, for the individual, are pregnant with unique blessings and challenges “are born every day.)” PAGE 14 Each other 256 odu(s), as mentioned, has its own octogonal graphic “sign,” symbol, or “signature.” The signs represent only “light” and “dark” (or "speaking" and "not speaking") patterns that are, by virtue of that fact, entirely qualitative in nature. Numerals are not important. The odu(s) are only en- umerated in certain lists for the purpose of convenience in ordering them (i.e.,rank ordering them by “age” or “seniority”). But the number assigned to each of them has no further importance in inter- preting them and varies—a little (and only a little) between two or three Yoruba sub-groups (which shows that there is nothing sacrosanct about each odu’s designation “number.” Note: Its number lab- el or designation number is not to be confused with its seniority rating (an ordinal number), though neither are parts of mathematical operations. In fact, in the Afro-Cuban version of Yoruba (Orisha/Ifa) religion, the odus also have “number labels” attached to them but to insure that people do not confuse these “numerals” assigned to them with mathematical numerals, they call them “letras” or “letters!” For example, in inquiring what were the results of someone’s Orisha/Ifa reading or divination results, they will ask “what were the letters that were 'pulled down' in that divination session?” By using certain ritual tools of a natural nature—for example, nuts or shells— the diviner can cast them down onto a mat in response to each question of interest to him, her, or the client and observe the patterns shown by the way the shells or nuts fall onto the divination mat (or, when the tools are large palm nuts, the way they fall from one hand of the diviner into the other hand). These patterns will produce observable results: Some of the tools would have either the “light” or “dark” sides showing once they had fallen to the mat. In the case of the cowrie shell tools--16 of which would be used in any given divination session--many would fall to the mat with the “speaking” (light) side up while others would land with the “non-speaking” (dark) side up; an example of another non-numerical or non-digital version of visual duality or polarity. As mentioned, the theological wisdom contained in the thousands upon thousands of oral stories and poems (some now written) would be classified into 16 main olodus or “main oral books.” The diviner would also cast—for any given question --the divination tools a second time in order to get a second set of patterns. Each odu would have its own four-part pattern of light and dark showings that randomly fell to the mat. In the use of some divination tools, the light-dark (four-level) pattern would be im- mediately visible. And each of the 16 basic patterns of light vs. dark “signs” of the odus would have its own unique name. Once the tools-- whether shells or nuts— are thrown to the mat for the second time, the patterns would still retain the same names even if they appeared twice. These types of Ifa octa- grams are called "meji(s)" or twins or doubles. The only exception to this no-counting-is-necessary rule occurs when the cowrie shells are used as divination tools. In that case, the number of shells with the “speaking side” facing up would determine which odus were signified as having fallen to the mat. (After that, no “numbers” were particularly sig- nificant-- except for denoting which pattern's number was higher in “seniority” than another odus pattern’s number). But aside from the simple cursory act of counting the number of “speaking” shells that fell to the mat for each cast, there were no mathematical calculations nor computations involved in divination. The odus, and their light versus dark signage, and the stories, poetry, and wisdom con- tained in them was—and will forever be— qualitative in nature. The important thing here, is that Orisha/Ifa divination does not involve numerical computations, cal- culations, nor symbols that involve any counting or mathematical operations (with, again, the sole excep- tion being the cowrie shell method which would require a person briefly to observe and count from “0” shells “speaking” up to 16 of the shells speaking). But after that no further addition--and certainly no subtraction, multiplication, division--calculations or computations would be involved in recognizing and interpreting the odu that had fallen to the mat for that particular question. PAGE 15 As stated at the outset of this essay, it is indeed difficult to simplify this complex system of divination in a few paragraphs. However, for the convenience of persons for whom this is entirely new, I will illus- trate how the odus are written down as light-dark, four-part, patterns once a given “throw” or “cast” has arrived on the divination mat for the perusal of the diviner and the client. VII. About the Odu “Octagrams””Figures,”“Signs,” or “Signatures” That Get Cast or “Pulled Down” In An Orisha/Ifa Divination Session FIRST: What Are The 16 “Odu” (“Olodu”) Marks That Are Available For A Diviner To Scratch Into “The Sand” (Or Into A Special Powder On A Tray) Or To Be Written Down On A Pad During the Divination Session? [ BELOW A “I” MARK SIGNIFIES THE QUALITY OF “LIGHTNESS” AND A “II” MARK SIGNIFIES THE QUALITY OF “DARKNESS” ] THESE MARKS ARE NOT NUMBERS, NUMERALS, DIGITS NOR INTEGERS MEASURING QUANTITIES. THEY ARE THE “SIGNS” OF THE QUALITIES OF “LIGHT” OR “DARK” THE NUMERALS THAT SIT ATOP THE FIGURES ARE MERELY THEIR “RANK ORDER” IN “STANDARD” IFA. (THESE NUMBERS ARE MERELY RANKING LABELS; THEY DO NOT ENTER INTO ANY MATHEMATICAL OPERATIONS; I.E., THEY ARE NOT ADDED TO, SUBTRACTED FROM, NOR MULTIPLIED OR DIVIDED BY ANYTHING. (PLEASE IGNORE THEM FOR NOW). ALSO, NOTE THAT IN DIFFERENT PARTS OF NIGERIA, OR CUBA OR BRASIL, THE YORUBA PRIESTS AND PRIESTESSES MAY HAVE SLIGHTLY DIFFERENTRANKING ORDERS AND SLIGHTLY DIFFERENT NAMES BECAUSE THEY OFTEN USE DIFFERENT DIV-INATION “TOOLS”,E.G., COWRIE SHELLS, COCONUT PIECES, KOLA NUTS, ETC. BUT WRITTEN BELOW IS THE STANDARD IFA SCHEME FOR DENOTING THE 16 MAJOR ODUS). ADVISORY!! DO NOT CALL THE NAMES OF ODU AND WRITE/SCRATCH THEM DOWN AT THE SAME TIME. ONE CAN INADVERTENTLY "PULL THEM" THIS WAY. UNDER THEM I WILL LIST THE MOST COMMON NIGERIAN (ILE IFE TOWN) IFA NAME FOR EACH (BUT THEY DO HAVE “ALIASES”). AFRICAN AND AFRO-CUBAN IFA NUMBERS FOR EACH ODU (NOT IN ORDER OF SENIORITY) * 1 2 9 10 13 14 5 3 6 4 15 16 8 7 11 12 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I O O O O O I I I O O O O O O I O G Y G S T R R W W D S F K B K T B E U A U E O O O I H U A A A U E K N R T S R N E N N R R U D A E U I R R A O A N I A P N N 0 N THE CORRESPONDING AFRO-CUBAN DILOGUN NUMBER FOR EACH ODU* 8 2 3 9 15 16 4 12 11 7 5 10 1 6 13 14 E O O O O M I M I E I O O O O O O I M M J Y G S F E R E R J W W D C F K B K E E I E U A U R E R O I O A I H U A A A T R K N N U T I S L R N E N N R A I O U D N E N U A I I A A N N G A K L D N M L L B A A I A A A E N L F R O U A G N N U N *____________________________* Technically, in the merindilogun (cowie shell or owo ero) divination version of Ifa, there is a 17th Olodu called "Opira" which occurs when no cowries "are speaking." This cannot occur in Ifa divination with Ikin (palm nuts) or the Opele chain method because there are no "nonspeaking" castings or throwings of the divination tools. Technically, since Opira is an Olodu also, the sum total of all odus is actually 257 in meridilogun or dilogun system of cowrie shell divination. And since Opira is never combined with any other Olodu, it only adds one more to the total count of 256 odus (i.e., it does not add 17 more odus). PAGE 16 Second You will recall that I choose to use an “I” mark to signify a “light” side of a divination tool falling face up. And the dark side of a divination tool is signified by a “II” mark. Most Orisha/Ifa divination books use these two marks. But remember, these marks are not numbers nor “Roman numerals.” They are sim- ply the marks for “light” or “dark.” There are other choices! Let’s take the Odu named “Ogunda” (the third column above). I have written it as: I I I I IBut if I decided that “O” represented “light” and “X” represented “dark” I would mark “Ogunda” likethis: O O O XIf I decided to use an “L” for “light” and a “D” for “dark, I would still mark “Ogunda” this way: L L L DSimilarly, if I choose to mark the light/dark polarity (as a qualitative, not numerical, thing) using + and –symbols, Ogunda would look like this: + + + --And, finally, the quadragram or octagram figures of "lightness" and "darkness" symbols may be written in the Afro-Cuban Ifa style this way, where "I" = Light and "0" = Darkness for Ogunda: I I I 0You see, it simply does not matter which symbols for "light" or "dark" you may choose to use. Any sym- bol could be used to signify “light” while any other symbol could be used to represent “darkness.” It is the sequence or pattern of “light” and “dark” marks that make the odu announce itself as “Ogunda.” These symbols are not numerals! In fact, one could use two numerals to represent “light” and “dark,” respectively (as Wm. Bascom did inhis seminal volume “Ifa Divination,” Indiana Univ. Press, 1991, at Page 48, where he uses the numeral“1” to represent “light” and the numeral “2” to represent “dark”). But these numerals also are simply used as symbols and are not arithmetic “numbers” used for any counting nor arithmetic operations like adding, subtracting, multiplying nor dividing anything. In other words, no math is involved in the methodology of Orisha/Ifa divination. The numbers—when they are used at all—are merely nominal designations for the purpose of indication “light” and “dark” sequences or patterns (and, as mention- ed, in some parts of the divination session, the “numbers” may represent ordinal scaling—simply listing which odu is senior” when compared to one that is “junior’). [Please see Part II, (2) above for a brief descrip- tion of an ordinal scale]. PAGE 17 The take home message here, again, is that Orisha/Ifa’s divination's numbers (when they are used at all) have nothing to do with mathematical calculations nor computations like we see in arithmetic or in com- puter digital programming. Nothing. Orisha/Ifa divination is entirely qualitative. They are not “base 2” digital computations at all. “Light(ness)” and “Dark(ness)” are quality states—not “numbers” that enable mathematical operations of any sort. That is why you will never see a babalawo, nor an italero (both are specialists in Yoruba divination), nor any kind of Yoruba priest or priestess resort to pulling out a hand calculator, a slide rule, or a pen and pencil to do arithmetic before, during, nor after a divination session. “Math” has got nothing to do with it. Finally, you may wonder why marks like “I” and “O” are not the same as “base 2” numerals so familiarto mathematicians and computer programmers? The reason is that for them a series of “I”s and “O”sleads directly to a real number crunching (inside the computer program) and then, maybe, to a real let- ter, or a real “yes” or “no” choice in the computer's operations. After that, a series of these numbers, in turn, usually (though indirectly) “add up” to indicate a numerical summation (and then go on to a let- ter, word or semantic symbol that we end up seeing on a computer screen). The same digital language may also be the information that causes the computer to make choices via some algorithm in the soft- ware’s or hardware’s pre-programmed functioning. By contrast, a light-dark duality (or di-unital) signs in Ifa divination like: I Lead directly to a word/s After that, an arbitrary numeral may (or may I I ➔ e.g., “Odi,” the name of not) be assigned, by local convention, to that I I an odu or “container of ➔ label “Odi.” In Nigeria that rank number is I verbal folk wisdom” with- “4” but in Afro-Cuba Odi’s number is “7.” out any numerals being Hence, the number-tag is arbitrary and is involved. used to show “seniority rank” in that local Ifa system. Again, the “number” never enters into calculations nor (digital binary) comput- ation as in computer program operations. Again, there is no math in Orisha/Ifa divinat- ion because there is no calculation nor com- putation in it. Such numbers, as they go, re- main only nominal or ordinal designators” devoid of arithmetic roles. Just a final note on the nature and appearance of the “signs” or markings of odus in the Orisha/Ifa div-ination process. The first thing a diviner will do when the casting of the shells or nuts begin during thesession is to find the two odus that are most influential, consequential, and informative for the clientat that time and in that geographic location. At that very early stage of the session, what the client’sview of his or her issues or questions are, is not dealt with. These odus express what the orishas or an-cestral spirits want the diviner and the client to know first. After that, the client will get the chance to ask (out loud or covertly) the questions of interest to him or her that they brought to the session in thefirst place. PAGE 18 A sample: I I I I I I I I I I I I I I I I I (A quadragram) (an octagram) A single line da’fa mark is called But The diviner will always cast a second “one leg of Ifa.” In Ifa, this odu’s time (or use a method that allows the name is “Owonrin.” two odus to be revealed together on one throw of the tools) in order to get the second “leg of Ifa.” When read right to left this odu (called an omo’du since it contains “two legs of Ifa”) is here called “Ofun-Ogunda.”A diviner using the Afro- Cuban method of cowrie shell divination called dilogun would simply write down the right-hand odu on the left side first (but it’s still the same, "Ofun-Ogunda ”). Most often, however,they will write down the odus’ number labels; its "letras" (its "letters") for identification, not comput- tional) reasons.In this example the letter would be “10-3” in the Afro-Cuban Yor- uba dilogun system. And, finally, when the diviner has cast the divination tools to determine which are the relevant odu’s affecting a client’s present circumstances, he or she will give the client a brief interpretative summary ofwhat has appeared on the mat. Then, after the diviner’s turn, the client’s turn for asking specific qu- es- tions of the oracle arises in order to get “yes” or “no” answers to the questions they came with. The ques tions like “Should I do this or that?” or “Is this offering sufficient to appease the orishas or ances- tors so that they will aid me?). The diviner will cast the shells or nuts many times in order to obtain the oracles answers and advice. The names of the odus (or their assigned numeral labels) may or may not be written down in this part of the session. The answers to the questions are what matters to the client. That is, the only thing that the client needs to know is whether the answer was “yes” or “no” to partic- ular question--perhaps in a series of follow-up questions as well. This process of asking specific ques- tions of the oracle is where knowing the seniority rank (usually, but not necessarily a “numeral”) of a given odu comes into play. Knowing the seniority of the odu when compared to possible junior ones is an important matter in the area of questioning because the client is active in participating in how the question will be answered “yes” or “no” by certain choices his or her “hands and “ori” or “head”) make. (But this is too detailed to go into here). What is important to know, however, is that these seniority ranks, labeled as numerals, never get involved in arithmetic operations, calculations, nor computations with each other. Hence, again and again, even though numerals may be involved in the divination procedures, they are not mathematically relevant to anything in the process. One could just as well learn the “seniority rules” among the odus by using their Yoruba names alone. For example, “Eji Ogbe” is senior to “Oshe” but not because “Eji Ogbe’s “number” (which in Ifa is“1”) is senior to, say, “Oshe’s number” (which is ranked at “15”), but for qualitative reasons. (In Cuban dilogun, “Eji Ogbe‘s” number is “8” and is, of course, senior to “Oche’” (whose number happens to be “5”), to "Obara" (labeled "6") , to "Odi" (label "7") but also to “Osa” (labeled “9"), and to “Owani” (whose number is “11”) as well. You see, the magnit- ude of the odus numeral label is not necessarily connected to that odu’s seniority rank, though some- times it is. But, even so, neither are related to the mathematical operations of calculation or comput- ation (and could be dis- pensed with entiely if one simply resolved to remember them in the sequence of their qualitative names alone). PAGE 19 * * * * * * * * * * * * Third: The Ifa Problem With “Mathematizers” And “Digitilizers” As I alluded to earlier, there are those who when the see qualitative polarity symbols like an ( I ) and a( II ) automatically think (in this digital age!) of binary “1’s“ and “0’s”—numerical digits or “numerals."They then rush to conclude that these simple Orisha/Ifa “da’fa” markings are merely “binary” numbers in essence and can, therefore, be re-expressed as binary numbers as commonly written. You will recall the example I gave on page 3, above: I (light) Which, they think, should be written I (light) “in binary” as the following number I I (dark) sequence: →→→→ 1 1 0 1 I (light) named “Irete” (in Nigerian Ifa) “Merindilogun” (in Afro-Cuban dilogun) Here is what the problem with digitalizing otherwise purely qualitative da’fa marks. The best negative example of this can be found in an otherwise exquisite book on African mathematics entitled: “Sup- reme Mathematic: African Ma’at Magic: by the “African Creation Energy: (by Clarence 13x). In that book he writes out the binary equivalents of the Orisha/Ifa “da’fa” figures such that each odu would have a digital binary numerals written beside it in the fashion as illustrated immediately above. Thus, at (p.95), his first table gives the binaries for all 16 olodus where he uses the Nigerian names (e.g., “Ire- te” in the figure above) and lists them in the standard Ifa order. However, on the next page (at p.96), he also provides a second chart that lists the odus’ relative seniority in the order or sequence that his dig- ital binary numbers would dictate. ( Thus his version of odu seniority rankings is unknown in the world.) (Please see Appendix C for a full critique). This is a notable error in my view which I will review in Appendix B as I discuss this book and his YouTube video entitled "Ifá Mathematics and Quantum Computing – YouTube."
Fourth The Actual Roles of Numerals and Their Sequences in Orisha/Ifa Religion: Its Orishas and Its Div- ination (Where Not One of Them Involves the Mathematical Operations of Calculation, Let Alone “Binary Digital Computation”). A. Ceremonial Numbers Associated With Orishas (Afro-Cuba Santeria/ Lucumi) I am not certain if the number-tags associated with the various orishas differ in Nigeria from what they are in the diaspora, but in the Afro-Cuban Santeria/ Lucumi, with which I am familiar, most are ceremonial numbers. For example, the ceremonial number(s) for Elegua are 1, 3, and 21, yet he speaks in all odus. Yemoja’s is “7” (and the main odu in which she speaks is “Odi” which has an ordinal or label- ing number of “7” as well). Ogun’s number is “3” (and so he has the 3rd odu in which he speaks up most- ly —Ogunda). Oshoosi’s number is “7” (even though the odus in which he stands up most are Oyeku (“2”) and Irosun (“4”), while Shango’s is “6”; because he is prominent in the odu Obara (“6th in the ordinal list of dilogun odus). Next, is Obatala whose number is “8” in respect of the odu that he claims before ot- hers, Eji Ogbe (Unle or Umbo) which is 8th in the order of odu’s nominal numbers. *
There may be minor play with symbolic numbers. For example, the symbolic number for the orisha Oya is "9." She is associated with death and, therefore, the wheel of reincarnation. Without her per- mission in opening the gates to the graveyard, a living person cannot pass into death (nor can a dead soul leave the graveyard). It happens that the number "9" is the only number that when multiplied by any other number reproduces itself in summation. For example, 9x9= 81 (8+1=9), or 9x6= 63 (6+3=9), and so on. The sym- bolism here is that Oya, via her "number 9" reproduces herself and her ashe ad infinitum. This is, of cour- se, only emblematic "math"; there is no serious mathematical computation going on as the notion is only about the qualitative phenomenon of reincarnation, not on any quan- titative "math." *PAGE 20 *Of course, we cannot forget Oya. Her number is “9” (in recognition of the fact that she is prominanent by first in the odu Osa—the 9th in ordinal list of odus of the Lucumi dilogun cowrie shells method of divina- tion. Indeed, she is often referred to by her alias “Iya’nsan” which means “mother of 9.” In her case, her number is not only ceremonial but is also one of a symbolic identity as well since she is, at once, is the Niger River which, in Rivers State, Nigeria, has nine tributaries running to the sea (i.e., running to “that very last moment” before dissolution into the sea--the final resting place). Her “9” also refers to the nine colors of the egbe (lodge society) of Egungun—one of the ancestral cults whose masqueraders wear very colorful full-body disguises made of 9 multi-colors. Hence, her "9" is a cer- emonial number. Similarly, we should not forget Oshun--“Iyalode,”(meaning “head woman in charge of affairs” is also affectionately know as “Miss Thang"--smile).Her ceremonial number is “5” and so it is the case that her main odu “Oche” is 5th in the ordinal sequence of the Afro-Cuban Lucumi dilogun's odus--symbolic of the five needles with which she seamed together the Universe's fabric. These ex- amples illustrate the role of symbolic or ceremonial numbers in Orisha / Ifa religion. And so, on it goes. The ceremonial aspects of these numbers is mostly enacted in the determination of the number of items that are typically given to an orisha to please them. (For example, we might givefive peacock feathers to Oshun, or six cigars tied with six red ribbons attached to a bunch of six greenbananas to Shango. In a sense, I suppose, we are feeding them their odus in order to please them (but I do not know this for sure). The key thing is that these numbers, like all of the other kinds of number herein described—e.g., the nominal and ordinal numbers for the main 16 odus (the “Olodus”)—are not used in calculations or com- putations. In no event will you find a priest or babalawo adding, subtracting, multiplying nor dividing any of these numbers with any others. That is, no one is going to multiply (nor add, subtract, or divide Os- hun's “5” times Shango’s “6” in order to move a ceremony along. These numbers are not a part of any mathematical operations. They are only used to designate things. For example:. B. LabellingNumerals in Their Ordinal Sequence for The Odus’ Octagram Figures in Nigerian (Ile Ife) and Cuban Ifa For Purposes of Numerically “Labelling” Them. 1.(Ogbe) 2.(Oyeku) 3.(Iwori) 4.(Odi) 5.(Irosun) 6.(Owonrin) 7.(Obara) 8.(Okanran) 9.(Ogunda) 10.(Osa) 11.(Ika) 12.(Oturapon) 13.(Otura) 14.(Irete) 15.(Oshe) 16.(Ofun). Their octagonal odu figures may beviewed on page 13, above. C. RankingNumerals in Their Ordinal Sequence for The Odus’ Octagram Figures in Nigerian (Ile Ife) and Cuban Ifa For Purposes of Knowing and Viewing Their Relative Seniority (the same as above). 1.(Ogbe) 2.(Oyeku) 3.(Iwori) 4.(Odi) 5.(Irosun) 6.(Owonrin) 7.(Obara) 8.(Okanran) 9.(Ogunda)10.(Osa) 11.(Ika) 12.(Oturapon) 13.(Otura) 14.(Irete) 15.(Oshe) 16.(Ofun). The octagonal odu figuresmay be viewed in this section, above. D. LabellingNumerals in Their Ordinal Sequence for The Odus’ Octagraml Figures in Nigerian (Benin-Edo) Ifa for the Purposes of Numerically “Labelling” Them. 1.(Ogbe) 2.(Oyeku) 3.(Iwori) 4.(Odi) 5.(Obara) 6.(Okanran) 7.(Irosun) 8.(Owanrin) 9.(Ogunda) 10.(Osa) 11.(Etura) 12.(Irete) 13.(Eka) 14 (Ologbon) 15.(Oshe) 16.(Ofun). The octagonal odu figures may beviewed in this section, above. PAGE 21 E. Labelling Numerals in Their Ordinal Sequence for The Odus’ Octagraml Figures in Afro-Cuban Lucumi Dilogun Divination For Purposes of Numerically “Labelling” Them. 1.(Okanran) 2.(Oyeku) 3.(Ogunda) 4.(Irosun) 5.(Oche) 6.(Obara) 7.(Odi/Edi) 8. (Eji Ogbe/ Unle)9.(Osa) 10.(Ofun Mafun), 11.(Owani) 12.(Ejila Sebora) 13.(Metanla) 14.(Merinla) 15. (Marunla orOfun Kanran) 16. (Merindilogun) 17. (Opira—no cowries speaking). There are several variations of the names (aliases) in Cuba, but the odu octagram or da’fa figures rem- ain the same, and the ordinal order is the same across the country. During the divination sessions the odus are always referred to by name though in the course of the session itself---simply for “short- hand” purposes—the odus' numbers are jotted down--yet the final recording note pad will contain both the odus’ names and their “numbers.” Also the last 4 odus are usually not interpreted (the client is sent to (Cuban) Ifa babalawos because these odus have a much greater chance of “our Holy Mothers” standing up in them (i.e., red, white, or black “Iyamis”) which requires Ifa babalawos to root out their angst and “ebbo” or address it (though Obatala may temporarily appease them on the client’s behalf). Though skilled readers in the Santeria/ Lucumi system (oba oriates, obasas, italeros) can read, interpret, and ebbo the last four odus: Metanla, Merinla, Marunla and Merindilogun (these are the last four in the Afro-Cuban dilogun system of Ifa), or- dinary olorishas (priest/esses)—who, ipso facto, have the right to read--if they know how to--the dilogun odus with cowrie shells (“caracoles” in Spanish), really avoid doing so—and consistently ignore them even for purposes of seniority rules of decision-making. F. SeniorityIn Afro-Cuban dilogun practices, ordinal rankings (rendered numeric only for memory convenience) that denote seniority look like this: All seven “major” odus are, by definition, senior to the five minor ones (and the last four are ignored altogether for seniority determination purposes). The “majors” never contend with each other for seniority (because when a "major" appears, no second casting is done) but, for the purposes of thoroughness, here they are in their seniority order: The Olodu(s) (Nigerian & Cuban Ifa) 4 (1). Ogbe (2). Oyeku (3). Irosun (4). Odi *The Oju l'odu(s) (Nigerian & Cuban Ifa) 16(5) Iwori (6) Owani (7) Obara (8) Okanran (9) Ogunda (10) Osa (11) Ika (12) Oturupon (13) Otura (14) Irete (15) Oshe (16) Ofun (17 Opira in Meridilogun divination). *The Omodu(s) (Nigerian & Cuban Ifa & Dilogun) 240 All 240 Combinations of the Oju l'odu(s) The “Majors” Odu(s) (Afro-Cuban Dilogun--Lucumi) 8.(Ogbe) 10.(Ofun Mafun) 4.(Irosun) 3.(Ogunda) 2. (Oyeku) 1.(Okana) and 12 (Ejila Sebora). The “Minors” Odu(s) (Afro-Cuban Dilogun--Lucumi) 11.(Owani) 9.(Osa) 7.(Odi) 6. (Obara) 5.(Oche). Caveat: Anytime the "minor" odu "Obara" ("6") is fol- lowed by "Ogbe" ("8"), the situation may--at the option of the diviner--call for the diviner to ask the client to reveal what is in his or her "strong" (or left ) hand, That is, what kind of "ibo" (efun, shell, small rock, etc.) is in that hand as if a "major: odu hand falled to the mat in the first palce. The same is true for the combination of “6” and “9,” Obara and Osa) respectively. "Baba prevails over Shango" and Oya and Shango can never be allowed to fight" are the rationalizations for the departure from the normal way of discerning (through the use of ibos ) whether or not the client's "ori" agrees with the outcome of this or that particular casting. As usual, one can simply remember which odus, by name, are senior to others because the numbers, as labels of convenience, are simply not needed. And they do not involve mathematical measurements nor calculations. nor computations. *PAGE 22 *In Santeria/ Lucumi's Afro-Cuban version of Ifa (dilogun) there are roughly 143 opportunities for the need to consider the "seniority" of an odu during a reading. This inquiry is initiated when a "minor" odu falls to the mat in response to a question that the client may have (either spoken aloud to the div- iner or silently prayed into the hands holding the diloguns (the shells). There are five "minors" can be matched with any one of seven "majors" that come up on the second casting. This leads to 35 possibil- ities. Then the minor may find that it is followed by another "minor" which, then, adds 25 more com- bin ations. So this makes a total of 50 random outcomes of "minor-major" or "minor-minor" double castings. Now, since either minor may come up first, we have to add the number of additional 25 cases where a reverse combination may occur. Now, finally, we must add the 8 cases where a minor is fol- lowed by the "major" odu called "Eji Ogbe."There are an additional five opportunities for that to hap- pen. Now, in one of the cases where Eji Ogbe follows "Obara," this casting may optionally be "read" as saying "choose (i.e., 'see what's in') the strong (left) hand." *What might we mean by "choose the strong (or weak) hand" or "choose the right (or left) hand: when reading another person? What happens is this: The client is given two different small objects to put--wholly randomly--in the hands; one for the right hand, and one for the left. After doing this the diviner will cast the oracle which will direct him or her to tell the client to show me what's in the right (or left) hand, depending on what sign fell to the mat on the asking of that particular casting. These choice points are di-unital, like "Go, No go", and "Add" gates or choice points in computing. However, these rules do not involve mathematical calculations. They are simple algorithmic choice points of logic. Thus the qualitative choices are: (a) determining whether the light or dark side (or the "I" or "0" signs) are showing and (b) whether the right or left hand is to be chosen to determine if the client's "ori" (or subconscious mind, in this case) "agrees" with what the odu indicated in the of the question of con- cern. These decisions are a part of the algorithmic di-unital choice points and involve no arith metic calculations. *By my count, in any given reading (on each and every casting) there are aboiut 143 possible outcomes that--using a seniority rule--a choice of which hand will be tapped by the diviner to determine the hand's (and ori's or"head's") choices. That is 50 + 50 +25+5+ 8 = 143 possibilities. This is why knowing how to determine "seniority" is important. However, just because I added up the number of ways that a determination of seniority could come up and be addressed for each question asked by a client does not mean that this kind of counting or "odds" determinations go on during a reading. It does not. Still, in actually, no counting, calculations nor computations are done during the determination of senior- ity matters. Indeed, the same seniority rules apply if a diviner were simply to remember the names of the odus and ignore their "nominal" number "label." G. The “Mother” of The Olodus (The Basic 16) Is Odu Herself But There Is Intra-Odu Birthing As Well That Also Has Nothing to Do With Numerals 1. Okanran is born from Ofun Mafun 9. Osa is born from Odi 2. Oyeku is born from Eji Ogbe 10.Ofun Mafun is born from Osa3. Ogunda is born from Odi 11. Owanrin is born from Oshe4. Irosun is born from Owonrin 12. Ejila Sebora is born from Ogunda 5. Oshe is born from Eji Ogbe 13. Ika (Metanla) is born from Oshe and Ofun Mafun6. Obara is born from Iwori 14. Oturopon (Merinla) is born from Eji Oko and Obara7. Odi is born from Okanran 15. Ofun Kanran (Merunla) is born from Eji Ogbe and Osa8. Eji Ogbe is born from Irete 16. Merindilogun is born from Irete. H. Probabilities in Orisha / Ifa Divination Whether the method of Yoruba divination being used by a diviner is that of using palm nuts (ikin), theopele chain, obi nuts, dilogun (cowrie shells, caracoles), coconut pieces, or coconut shells, the likeli- hood of getting a "I" or a "II" on a given throw or casting is roughly "50%" for either. All that matters is that the throw or casting was "randomly generated"; i.e., no one had their thumb on the scale, so to speak (which could happen if the diviner dropped the shells too close to the floor or mat).The distribut- ion of likelihoods or probabilities of varying odus appearing in erindilogun casting, however, requires only a slightly different arithmetic process since "counting" the number of shells falling (and, thus, the calcul- ation of probabilities) involves ordinal rather than nominal scaling. Because of this, a few sim- ple "correction rules" exist in it to make sure that the ending likelihoods remain just about "50%" to "50%" when the odus "pulled" are written down as octagrams. PAGE 23 True, probabilities are in the realm of mathematics but not of Ifa practice since the divination process itself never involves any probability calculations in order to be complete. The description of probabi- lities is only of academic interest as applied to (not "in") Ifa divination. What’s Objectionable About “Binary Digital” Depictions of the “Math” That Some Propose Is Inherent In Ifa Divination? Just above a drawing of the deity of Ifa divination, Orunmila (Orunmila, incidently, does not have the shape of a human being!), Mr. Clarence 13x provides a chart of the “Binary Order” of odus that is com-pelled by his insistence that they can be written down as “binary code digits” (at p.96, op cit.). →→→ 0000 (Oyeku) 0001 (Okanran) 0010 (Oturapon) 0011 (Owonrin) 0100 (Ika) 0101 (Ofun) →→→ 0110 (Iwori) 0111 (Osa) 1000 (Obara) 1001 (Odi) 1010 (Oshe) 1011 (Otura) 1100 (Irosun) →→→ 1101 (Irete) 1110 (Ogunda) 1111 (Ogbe) Problem #1 A Violation of Oro (Traditional Custom) The people of the greater Nigerian area have been divining odus directly, or via their predecessors (Nok, Nupe, Igbo) for millenia. To my knowledge, no one has ever heard of a nominal nor seniority order of the odus like this. Can you imagine Eji Ogbe being ranked last? Compare this to the wholly representative listings I provide in sections A, B, C, and D above. The importation of Grecian, Hermet- ic,and Arabic cultural obsessions with “transcendent mathematics" that is implicitly embedded in the religion of nature (Ifa), even as the author wisely disclaims that mathematics is embedded in nature itself (see pp. 6-7, op. cit.), leaves one wondering what is the point of this foray into sophistry? Problem #2 An Irremedial Violation of Seniority Algorithms One cannot perform African nor Afro-Cuban Ifa divination, nor African merindilogun or Cuban dilogun, without authentic seniority determination algorithms. None exists here. *Problem #3 Inventing Things Inventing things, or importing them from non-sub-Saharan cultural sources just because one can con-ceive of doing so (or simply because math is “one's thang”) has not yet made its way into the Yoruba divination system. Truth comes from two things in this religion: the substantive content and wisdom as recited (and, now, read) from the odus themselves. Or it comes from the verbal pronouncements of spiritual beings that—from time-to-time—possess individuals. It does not come from enterprising invention. This well-meaning, I am sure, individual goes even further beyond using computing meta- phors to augment Ifa, he actually introduces "quantum computing" into stew as well. (Please see my critique of his book and YouTube video in Appendix B, below). PAGE 24 VIII. A Sample Client and Ifa (Cuban Dilogun) Divination Session Vingette [THIS IS EXCEEDINGLY SIMPLIFIED] This part will be short. It appears here only as an illustration of how a Yoruba divination session might work in “pulling down” odus so that the client can learn from the diviner what the odus and the orishas and honored ancestors speaking with them might have to say about the problem or questions that the client has brought to the divination session. * * * * * * * * * * * * “Mary Smith has received a proposal for marriage from a person who is sincere. Mary has already beenmarried thirteen times, so she thinks it wise—for the first time—to consult a Yoruba Orisha/Ifa diviner using the Afro-Cuban dilogun method of cowrie shells (caracoles) to see “what the lay of the land is” with this fourteenth prospect. When she sat down at the foot of the mat, the diviner casted the divination tools (cowrie shells in thisexample) to begin the session. She had not told the diviner what her specific questions are thus far. The diviner said opening prayers, gave salutations and incantations to the Ifa (dilogun) oracle.Then when the shells announced to the client which odus were speaking (six shells speaking the first time , followed by eight shells speaking in the second cast). With that, he gave her information about her current state of affairs, why she has arrived at her present station in life and, what the future was likely to hold. These insights had not anything to do with Mary’s questions nor her perceptions of her “issues.” They would get addressed in the second half of the session. Let’s say her odus, for this session (written down in the Afro-Cuban dilogun style) by her divination priest/ess were as follows: Obara-Eji Ogbe (6-8) I I I I I I I I I I I Osogbo (comes with “Ibi”= ‘contraction’ or ‘negative luck’ is at hand)—In the nature of “Ano” (a covert present sickness exists with the client) PAGE 25 The Problem Scenario Presenting Itself Here Is Her’s (Not a Relative’s) Lariche / Ebbo: Advisements and Remedies from Shango, Oshun & Obatala Shall Prove Helpful Shango Speaking Here (“Kawo Kabiesi!” “Stand-up and Shout-out for Shango!”) Shango says that this is a resourceful, but headstrong person. She often does not respect elders nor the exper- tise of others. In shunning good advice, she appears to others as vain and, at times, abusive. She should take heed and wear white a lot to off-set her hot temper. The diviner says something about ‘only jack-asses having ears above their heads.’ Because she is inherently smart, she can re- form her character, but first she must know that she is prone to illnesses that come from internal inflammation, that correspond to her external volatility. Shango adds that eventually, after going to Ifa for a further reading, that she is a candidate for deep initiation into Orisha/Ifa religion. If she listens well (for Shango only speaks once!) she will offer him six green bananas with a red string tying six good quality cigars to be tied to the door frame top in her house for six days and then left at the foot of a palm tree far away from her house. She will also offer Oshun five peacock feathers on the throne of an Oshun priest- tess, and ask permission to take “white baths” in this priest’s or priestesses’ home in the mornings for five con- secutive days. She should pay for these services. After the cleansing, she should avoid all hot spices and brown liq- quids going forward and go to the doctor to have her body examined for “hot spot” signs of inflammation and high cortisol levels. Obtain a red/black neckless of peonia seeds because it will help her with resolve to reform herself with- out ambivalence. She also needs ebbo’leri (a rogation) to “feed her Head, i.e., her Ori for spiritual alignment. This, by analogy, is like the idea of "aligning" her chakras. If she heeds this advice and makes the offerimgs necessary, her negative situation (“osogbo”) will turn into a positive sit- uation (“ire”) very quickly in accord with the odus that this reading closes with. "Ebbo Ti Pari !" (The Reading Is Ready to Close) Her Session’s Closing Odus: “Odi-Obara” (with ire--"good prospects") * I I I I I I I I I I I I I PAGE 26Mary’s reading closed with this odus. When the diviner explained to her that it forecast much good- ness, emotional contentment and good fortune foreseen for her (since Yemoja, especially, blesses marriagesin this omo’du (where the institution of marriage was born), she was so happy that she did not feel the need to ask any further questions. In view of her previous unconscientious conduct which could have prevented her odus coming at this time with “gbogbo ibi” (bad luck everywhere), the diviner left her with the following blessings or proverbs (owe) from Obatala for her to remember: “It is the Head that carries the body!” and “We heard the call and made the sacrifice. It will not be long, It is not far away. Orisha will make it come true like a Dream” My dear readers, as you will notice, this—“Mary’s”—reading did not involve any arithmetic calculations nor computations at all. No addition, subtraction, multiplication, nor division, no algebra, ” no “sets,” no “Boolean algebra of sets,” no “universal sets,” no “empty sets,” no “symbolic logic,” no “binary cod- ing,” no numeric “measurements,” no “numerology,” no “rational, irrational, imaginary nor complex numbers, no “geometry,” no “calculus,” no “axioms,” no “proofs,” no “theorems,” no “statistical tests,” no “recipro- cals” (there are light-dark patterns of mirror reflection of da’fa marks, but no “numeric reciprocals”) and no “probability calculations” involved. In other words, mathematics is not inherently “embedded” in Orisha/Ifa religion and its divinatory practices. The only numerals that ever show up are simply nominal (at most) or ordinal in nature and, even then, however convenient they may be, they can be done away with entirely without consequence bec- ause they do not play any roles in calculations nor computations with natural numbers. That is, they can be dispensed with—though somewhat impractical to do (which is why I do not advocate chan- ging our methods)—by simply using the names of the odus and remembering which are “senior” (or “junior”) to others similarly situated in the Ifa corpus of stories. I am simply trying to make the point that math is not indispensable, nor even involved, in the acquisition of natural knowledge using the Orisha/Ifa methods. APPENDIX A "The Mathematics of IFÁ—Part 1 by Tundé ADÉGBỌLÁ - YouTube", "https://www.youtube.com/watch?v=8VFXbMxyyS0" and "The Mathematics of IFÁ 2 by Tundé ADÉGBỌLÁ - Boulean algebra is based on Ifá. - YouTube", www.youtube.com/watch?v=_L9_FYjq8WI" This gentleman takes as his starting point professor Sophie Oluwole’s theses that “Ifa is not a religion, but contains religion.” “Ifa is not philosophy, but contains philosophy.” And, “Ifa is not science, but con- tains science.” He then extrapolates from these points to urge that ‘Ifa is not mathematics, but it con- tains mathematics.’ The “mathematics” that he perceives in Ifa are implied by the 256 octagrams of the Ifa odus (i.e. the 16 “olodus” and the 240 “omodus” or the “sons of Odu”). The symbol component of each of the eight parts of the octagram is either a ( I ) or a (I I) mark. He then construes these two marks as being polarities (they are). But he then steps into the same path that most “mathematizers” and “digitalizers” in mod- ern society do. He automatically assumes that they are numbers or, two binary numerical “bits.” But they are not: they are qualitative symbols of “lightness” and “darkness” that, in themselves, do not necessarily have anything to do with quantitative numbers, numerals, nor computational “bits.” *PAGE 27 *From there he, and many others, elect to do an unnecessary thing. They designate a single “leg” of the “octagram” (containing four of the “binary code bits”) to be a digital binary number—“within” Ifa divin- ation. For example: the one “leg” of the olodu Okanran is normally cast and marked as: I I But he informs us that it can be written “in binary” as 1110 ("bits"/numbers) I I as they would be if written in “base-2.” I I I To his credit, he also writes Okanran as “Bbbf” (meaning “back side,” “back side,” “back side”, and then “front side”) indicative of the four cowrie or opele shells that lie on one side of the opele chain when it is first cast to the mat--with "front side" meaning "light" or "speaking," and vice versa. This will prod- uce “one leg” of Ifa. ( It is standard that the other side of the opele chain’s strung-together cowries will produce the second series of cowries or opele shells that will also randomly show a combination of “fronts” and “backs” as well—i.e. create the second “leg of Ifa. This is because interpret- ation of the or- acle will involve considering both “legs.” In referring to the results, in the Afro-Cubans version of Yor- uba religion (Santeria-Lucumi) they call the odus' final "numbers" "letras" or "letters" to insure that people to do not think of them as "numbers" since it is obvious that there are no numerals contemplat- ed here. That is, there is nothing “mathematical” about this way of depicting this “leg” of Ifa in writing or as scrat- ched in sand or in the powder on a divination tray. Similarly, just as is the case here, there is nothing “mathematical” about the way Ifa diviners traditionally used ( I )(light) or ( II )(dark) symbols to describe a single, or both, “legs of Ifa” in a divination session. Construing these marks, ( I )(light) or ( II )(dark), as “digital binary numbers or “bits” is a purely elective choice. There is nothing “in Ifa” that requires it or recognizes the idea that the odus are “binary code”phenomena. And if it is not required, and was not ever conceived of this way (until the modern com- puter revolution by modern programmers), then it can safely be said that there are no obligatory num- bers and, therefore, no mathematical calculations nor computations “in Ifa.” Which is another way of saying that “there is no math (inherently) in Orisha/Ifa religion!”( Further, as will be dealt with in the Appendix B,below, a critique of Mr. Clarence 13x’s book and YouTube video, neither he nor his mathem- atical fellow travelers seem to contemplate the destruction wrought on Ifa’s concept of odu’s seniority ranks (and, therefore, the proper interpretation of Ifa’s odus for a client), when the odus are re-ranked for seniority along the ordinal scale dictated by binary digital representations of them—as they prop- ose must be done since numerical “binaries” are at the core of Ifa (as they would have it). I have already addressed the essentials of this issue on page 18, above. Now how Boolean's "algebra of sets" discovered in Europe around 1850 was learned from Ifa priests is a mystery to me. Our learned brother, in taking light-dark polarity signs (I) vs. (II) as mathematical in nature (simply because the are polarities) is again engaging in arbitrary conjecture. The signs could just as well have been (!'s) and (?'s). So long as a convention designated one to represent "light" and the other "dark," the Ifa oracle would continue to work perfectly well. He then engages in a "grandiose" logical error wherein he claims that if 'Boole had not come up with Boolean algebra (in the 1850's) the world would have been denied (robbed of) the brilliance o f Ifa divination because of its use of polarity signs.' (I am paraphasing him, but I invite the reader to listen to his words about six minutes into his seven minute presentation). All I can say is "what?" (Later, in Appendix C, below, in the section on misattributed causality in the thinking of many of us, I describe our childish tendency to claim that either "we got this brilliant thing from some 'august' them" or "they stole such-and-such a brilliant thing from us" even when there is not the slightest historical evidence of such a connection! Why is it so hard to simply accept that our people were capable (as were other people) of coming up with some rather clever ideas on our own--where such is the case? Just because different groups of people come up with similar things, does not mean that they are historically connected with each other. "Mathematizing" Ifa in order to compare or attribute it to Wes- tern mathematical ideas does not, in my view, further legitimize Ifa. (Some scholars of the Revealed Religions of Judaism, Christianity, and al-Islam believe, in the spirit of gemantria, that their religions contain direct mathematical codes; see End Note 14). PAGE 28 Unfortunately, for these mathematically-minded intellectuals in our religion, the “old Yoruba adage rings true: “When you’re working only with a (mathematical) hammer, everything around you starts looking like a (mathematical) nail. (This is not really a Yoruba owe or saying, but I think you get the point)! * APPENDIX B A Critique of Eclecticism and Sophistry In Yoruba Orisha/Ifa Discussions “Mathematizers” and “Digitalizers” “Supreme Mathematic: African Ma’at Magic”: by the “African Creation Energy: (by Clarence 13x). and "Ifá Mathematics and Quantum Computing - YouTube", "https://www.youtube.com/watch?v=fVz6g1rqiuQ" As I wrote in the critique of baba Shangodare’s lecture (see Appendix D,¸below), in Mr. Clarence 13x’sbook “Supreme Mathematic: African Ma’at Magic”: “He writes out the binary equivalents of the Orisha/Ifa “da’fa” figures such that each odu would have a digital binary numerals written beside it in the fashion as illustrated immediately above. Thus, this first table gives the binaries for all 16 Olodus (p.95) where he uses the Nigerian names (e.g., “Irete” in the figure above) and lists them in the standard Ifa order (see page 12, above). However, on the next page, (p.96), he also provides a second chart that lists the odus’ seniority order in the order or sequence that their digital binary numbers would dictate (as his version of seniority rankings).” I summarized his chart on page (p.18) above, but I will copy it here as well: →→→ 0000 (Oyeku) 0001 (Okanran) 0010 (Oturapon) 0011 (Owonrin) 0100 (Ika) 0101 (Ofun) →→→ 0110 (Iwori) 0111 (Osa) 1000 (Obara) 1001 (Odi) 1010 (Oshe) 1011 (Otura) 1100 (Irosun) →→→ 1101 (Irete) 1110 (Ogunda) 1111 (Ogbe) Wow! Anyone with the requisite knowledge of Yoruba divination anywhere on the planet would know that one cannot do this. In his “binary” order, the senior-most odus, for example, start with “Oyeku” and “Okanran” in the 1st and 2nd place of seniority. And “Ogunda” and “Ogbe” are in the last two spots (15th and 16th, respectively. All of the other seniority ranks are equally disordered in his version of “binary” Ifa as well. No Ifa nor Orisha priest in the USA, Nigeria, Brasil, Cuba, nor anywhere else would have ever heard of an odu ordering and ranking system like his. Attempts to use such a system by in- troducing “bin- ary” into Ifa would result in methodological and interpretive chaos. This violates trad- ition as it irrepar- ably nullifies the orderly methods of divination, and it constitutes an invention. All of this noise about Ifa divination being “binary digital,” reflecting “base 2” computation, is just that—noise. There is no point to it because in the divination process of Ifa no numerals are calculated or com- puted. All “numerals,” such as they exist, are merely for “odu” designation (or labelling) and seniority-ranking and, as among them, there are never any mathematic operations of arithmetic like addition, sub- traction, multiplication, nor division. PAGE 29 Some fetishize mathematical application, description and modeling so much that they declare it to bean intrinsic and essential part of nature and the Universe—irrespective of humanity. Fortunately, Mr. Clarence 13x is also aware that this is not true. He knows that math is a human-system of thought, lan- guage and mental analysis (see his book at pp. 6 and 7). And he is also aware, apparently unlike an aut- hor, Mr. Shangodare Fagbemi, whose lecture I critique in Appendix D of this paper, whose view is that Yoruba (Ifa) numeric culture is ‘as with all Africans’ “base 2” mathematics. It is not. Such was the math- ematical canon of North African Arabs. The mathematics of the western rain-forest cultures, which include Yoruba, is “base-20” or “vigesimal” in nature (see p.43). [ An aside: This is why the more original Ifa divination system in Yorubaland was 16-cowrie shell divin- ation called “merindilogun.” The term—as mentioned elsewhere—means the “20-4 system” or “16 cow- rie shell method” of divination owned by the orisha Oshun. Although Oshun rarely gets credit for it, as she is often seen as a fickle consort of the wise and settled master of Ifa’s Orunmila, who by dint of noblese oblige alone, capitulated to the insistence of Oshun, and taught her how to do 16-cowrie shell merindilogun. Incidentally, some itan (stories) say that it was Obatala who taught Oshun shell divin- ation]. However in “Ifa Mathematics and Quantum Computing (African Creation Energy.com), he again in- forms us that “the Ifa divination system, which originated in West Africa, utilizes a system of binary mathematics to retrieve answers to life’s questions and solutions to life’s problems... Performing Ifa divination is done by a “priest”/Mathematician called Babalawo (why is “priest” in quotation marks and mathematician is not. Is this a subtle dig at babalawos)? The system of binary mathematics is used by the babalawo to select one of the odus of Ifa occurs in this fashion... The eight nut shells on the opele chain are used as an '8 bit “random "number" generator.'(italics are mine) (Please note: a “random generator” can randomly generate anything including letters, black and white ping-pong balls bunched in a container, “light” and “dark” sides of the pieces of coconut shells, or the “speaking” vs. “not-speaking” sides of cowry shells in a collection or on an opele chain. What gets “ran- domly generated” does not have to be “numbers.” (This, therefore, is mathematician's projection, Ibelieve, to further install the idea in our heads that mathematics is in Orisha/Ifa divination in a found- ational way). “In computer science, eight bits, or binary digits is called a Byte...The open (speaking) side of the cowrie shell on the opele chain corresponds to binary digit of 1, and the closed (not speak- ing) side of a cowry shell on the Opele chain corresponds to a binary digit of 0,” says he. He then goes on to expound on the same rhetorical strategy as do all of the other mathematizers anddigitalizers of Ifa do, to wit: claim that each “bit” when inscribed as a series of 1’s and 0’s is the digital language of the odus. For exactly the reason stated above, this characterization is entirely elective and not a generic part of Orisha/Ifa divination. He sees divination, therefore, as synonymous with modern computer operations and computations. And then it goes downhill from there as he gives the viewer a synopsis of quantum computing. Quantum computing? What? That really has nothing to do with Ifa; i.e.,it has absolutely nothing to do with Ifa divination nor, for that matter, with human (let alone a baba- lawo’s) comprehension or mentation either. And he does not even claim that it does. So why go off onto that foray? To impress people with 'trendy' tangential trivia dressed up as 'knowledge?' *PAGE 30 APPENDIX C * “Odu: The Repository of the Secret of Orisha Tradition,” Dr. S.M. Opeola, Yoruba Kabbalah Centre, Publ., Lagos, 1988 This obviously learned man has succinctly set forward a treatise that proposed that the real mystical core of the Ifa oracle is “its” mathematics. I assert, by contrast, that Ifa does not have any mathematics (and certainly no mathematical processes) of “its” own. Rather, mathematically-minded people can im- pose or project mathematical models on to it: Some as simple as frequency tables, probabilities, binary-coded representation (and programs) of odus (Ifa’s “chapters” and “verses”), mathematical functions, and so on. True, its “signs” or odus are written down as light-dark patterns of quadragrams and octagrams which may appear to be “geometric” in nature, (see Parts III and IV, above), but since they do not include cal- culations of lengths, angles, vectors, operations, nor equations or solutions of an algebraic nature, they cannot be said to be truly mathematical geometry. They are, rather, visual information designed to identify, classify and distinguish 256 possible visual patterns, one from another, that reflect or pred- ict the 256 basic "conditions of life" (odus) that they stand for and which appear to fall on to the mats of divination. Thus, it is an error to talk about Ifa divination as itself containing any numerical esoterica (let alone having a mathematical “mystical core”) separate from (let alone “above”) its narrative wis- dom contained in its poetry and its stories, that is, "above" or "deeper than" it’s qualitative religious and moral-ethical core. Ifa divination, contrary to Dr. Opeola’s view, is not a “digital program” being run in divination practice, though it can be written as such if one is so inclined—however irrelevant to life that such an exercise might (see “Odu: The Repository of the Secret of Orisha Tradition,” Yoruba Kabbalah Centre, Publ., 1988, at pp.10 and 11). For although Ifa divination contains rules-of-decision (“choices” to be made in the course of a divination session; a la algorithms), Ifa’s divination’s oracle casting is based on random generation of its 256 signs and involves no mathematical computations nor calculations. In fact, it’s methods are most brilliantly designed to defeat human intentionality, calculation and the personal bias of a diviner. So, math may be used to describe the “sets” (i.e., Ifa’s containers of symbolic resources or notation that are possible in a divination session) optionally depicted as octagrams (and written in the binary not- ation appearing “numbers” of “I” and “I I” or “I” and “0”). And, as alluded to above, one can always proj- ect math onto its contents and methods in the form of mathematical models and descriptions, e.g. as probability tables of possible casting outcomes when using Ifa’s 2, or 4 or 8 or 16 or 256 variables, as mathematical “functions” (e.g., the formula “f + (b-1) = 15”, that Dr. Opeola, says expresses the mathem- atical nature of Ifa—in this example-- of 16 shell cowrie divination method of Ifa divination. That is, where "f" refers to the number of cowrie shells facing up (“speaking”), and "b" refers to the number of shells fac- ing down (with 16 shells total in play). But all he is saying is that regardless of the number of shells speaking (f) the remaining ones added to them can never exceed 16. Why? Because a diviner only has 16 shells to work with in the first place and they are all used for each casting. A diviner does not need any mathematics education to figure that out. (And, indeed, it is only in the cowrie shell version of Ifa divination that even any counting occurs at all; see Part III, Section 4 of this essay, above). *This doctor's excursion into the mathematization of Orisha-Ifa divination is expected when he or anyone starts to import 'into Orisha-Ifa the cultural mentalities and ideas of Mediterranean-rim peoples like like Jews (Kaballah) and Arab-Islamic thinkers. In fact, "closet" Christianity also crept its way in Ifa theology among some of the 1st and 2nd generation of British-schooled Ifa priests (and European divinity studn- ents) during the 1930's, 1940's, and 1950's in their doctoral theses--which were later published as learn- ed texts on the subject. PAGE 31 (Here’s an illustration: of a mathematical function sacredly ensconced in Ifa as suggested by the au- thor. Let’s say that (f)7 shells fall “speaking” + (b) 9 shells fall “not speaking” – 1 = 15. “No kidding?” Does one need a mathematical equation esoteric calculation to know that? The reason that this mathemat- tical ‘functional’ description is irrelevant to this method (and all methods) of Ifa divination is because when an odu falls to the mat(“Odi” or “Edi” in Afro-Cuban dilogun method of Ifa divination in this case), the only things that ever get interpreted are based on the number of shells observed to fall face-up, i.e., are seen to be “speaking.” That is what announces “Odi,” with all of its consequences for the client. And all of the shells falling face-down, i.e., ‘not speaking’ (as well as projected mathematical operations) need not apply for the job of being relevant to the reading's interpretation! The author claims that the proto-Yorubas brought this Kabbalistic esoteric knowledge (of Ifa) with them “from Egypt” which he describes as the ancient Cushite city of Meroe (actually located in the Sudan or upper Nubia; which is not Egypt). Yet, he describes its mathematics, i.e., the merely descrip- tive and wholly elective use or projections thereof, as Ifa’s ’ true core.’ This is why I am trepedatious about incorporating Mediterrean-rim (KMT, Grecian, Jewish, Islamic and even Chrsitian cultural ideas into authentic Yoruba (Ife civilization) thought and religiosity. Too many distortions and misrepresen- tations occur in the wake of enterprising inttectuals trying to "legitimize" and favorably "compare," Ifa to anything else. Ifa has seen it all. Ifa looks in all directions at once. * APPENDIX D OIDSI Class: The Esoterical Meaning of Odu and How It Comes Into Existence - YouTube" https://www.youtube.com/watch?v=s7l9F4rAX8M featuring Shangodare Fagbemi, [This video is sponsored by the “Obafemi Institute for the Divine Study of Ifa,” under the tuta- lege of the African-American Ifa priest of Yoruba, Chief Oluwo Obafemi Fayemi Epega. BackdropI have much skepticism about many of the “connections” to Ifa seen in this video; hence a long review.Here I review a YouTube video featuring a Yoruba Ifa priest, Shangodare Fagbemi who, among other things, has acumen in the field of mathematics. His was a guest lecture in a series of YouTube instruct- tional videos on the religion sponsored by the “Obafemi Institute for the Divine Study of Ifa,” under the tuteage of the African-American Yoruba Ifa priest named Chief Oluwo Obafemi Fayemi Epega, from the American state of Texas. First, in respect of the series of videos on Ifa presented by Oluwo Obafemi, I cannot stress how valuable I found them to be. I have watched all of them (several more than once) to see what he could add to my knowledge of Orisha/Ifa religion.And I found that his contributions were notable. Additionally, he per- sonally has a very folksy and accessible presentation style. I recommend his YouTube videos without res- ervation to all who wish to study Orisha/Ifa religion. Before embarking on this critique, I also wish to stress the several positive things that I have concludedabout baba Shangodare’s guest lecture. First, all sincere contributions to our theology are to be wel- comed. Next, he is apparently a learned man, so his contributions are especially welcomed. He only had less than an hour to present these topics—although addressing so many threads was his choice (an unfortunate choice, in my view), so due accord has to obtain in tolerating some of the eclecticism, non-sequitors, and tangentialities in his presentation. By contrast, I had the advantage of many hours to review this video and, indeed, have had many years beforehand to cogitate on these topics—first writing about them in 1996 in my book of that year “African Spirituality vs. The African-American” (available only through my website at Oshoosi .com). So, it would not be fair nor brotherly to be too harsh in a critique of his video lecture in light of these circumstances. Additionally, he does offer on-line courses where he may have written or taught more thorough and better reasoned opinions. I do not know. PAGE 32 And, finally, I actually enjoyed his presentation as a bit of intellectual entertainment. At times I found myself, in the spirit of camaraderie, chiming in with a few “oohs, and ah-ha’s, and ashes, and “deeee- eeep!” sub-vocalizations of my own to go along with his audience members’ enthusiasm. As my aburo —my junior brothers--in this religion, I can say with confidence that their oluwo Afolabi Epega whom, (though not a part of his personal life), I knew him as a fellow-travelor, would be exceedingly proud of what his omo—i.e., his spiritual godchildren--have accomplished. Iba--ee, iba-ee, iba-ee! Egun wa ire… ooo; sun (i)re…ooo! (Praise to our Ancestors, They Come With Good Fortune. May They Sleep Well).
In this case, baba Obafemi invited Shangodare Fagbemi to speak on the topic of the “esoterics” in Ifa theology, some of its history, and his (putative) sourcing of Ifa religion from a wide range of concepts and practices on everything from Arabic geomancy divination (‘the scratching of divination signs into the sand’ with a combination of four or eight vertical line or circular markings), the adoption of binary coding in Europe (“based on African teachings”) that these marks remind him of, to Hebrew numer- ology and gemantria (i.e., writing where the letters that make up words and sentences also add up to numerals that have their own independent and, most often, arcane and cryptic meanings). But this is only the beginning. (See End Note 11) In this sophistric tour de force (sophistry means: "I am wise… (the) wiseist, one who does wisdom”), his rhetorical strategy also proceeded to weave into Ifa religion concepts he believes came from the Hindu religion, arithmetic (“reciprocals and inversions”) and mathematical numbers theory (phi ratios, Fibonacci sequences, etc.), commentary on the religious personages in Orisha/Ifa religion (like Olod- umare and Osumare), Among other things, he believes that some Orisha/Ifa concepts and deities, like Oshun, originate in the Hindu religion (in her case from a similar goddess like Tripora) who is to be likened to Oshun, in his view. All of this in 45 minutes as he engages in conjectural etymology, alchemy and Indian lunar astrology. But all of these are disparate ideas, inductively reasoned, led, more often than not, to unsupported in- ferences being drawn owing to his use of specious connections, speculative linguistic associations, and speculative causal and historically attenuated linkages. Worse yet, he repeatedly shows his appet- ite for confirmation biases—(i.e., paying attention only to “evidence” that supports his inferences while making no attempts to test his generalizations against other possibilities or contrary evidence. Aside from that--especially in view of the copious “oohs,” and “ahs” and “wows” and “ashes!” (Yoruba for “right on!”) from his enthralled audience--his was very valuable piece of intellectual entertain- ment. Critique: 'Ifa’ Came From North African Arabic Astrological Geomancy (Oracles) a Thousand Years Ago.’ The way that the 256 odus octograms are marked or signed into the sand (or on a tray of rust-colored powder-- irosu or white clay powder--efun) during an Orisha/Ifa divination session is based on 9th and 10th century Arabic geomancy practices of North Africa. (He does not say how these Arabic-speaking North Africans ever came to the deep rainforests of West and Central Africa, so how this convention got there remained unaddressed). However, other authors, including myself, have accep- ted this historical account. (See my essay entitled: “Conceptions of Ifa: Old World vs. New World” in the appendix of my 1996 book, op cit. at p.388 et seq.). In my view, he does a very good job in depicting how this Arabic astrological geomancy got into Europe as a methodology for recording their divination res- ults as well as fostering mathematics there. The only problem with his history, and it is a big one, is that he fails to distinguish between Ifa’s history as a divination methodology (particularly as method of recording or writing down its oracular results), on the one hand, from Ifa’s history as a corpus of substantive content of oral poems and stories and cultural wisdom, sui generis to Yorubas (or their immediate sub-Saharan cousins), on the other. And, then, after omitting this, he also goes further to omit distinguishing either of these two (“Ifa’s” method of notating odus as octagrams vs. addressing Ifa as regards its substance: its “chapters and verses”),on the one hand, from addressing Ifa as an incarnation of “odu deities”, in their own rights. This latter phenomenon or concept is one that is uniquely sourced to Yorubas alone (and certainly not to Islamic Arabs, that is for sure as they tend to see us as a practitioners of witchcraft). Because of his failures to address either of the two latter conceptions of what Ifa “is” (content and deified odus) he chose to focus only on the writing down or “marking” of the divination figures as octagrams—a minor methodologic -al convention matter, standing alone, at most. PAGE 33 Thus, his over-generalization—the “Ifa” came from these north-African Arabs, stands weakly on its legs, as stated or implied.Therefore, by stressing so much the similarities of the “marked” figures--as between ween between Arabic and Yoruba conventions—he, therefore, lamentably left unaddressed how he sees the substantive contents of Yoruba odus matching up with (or failing to match) with the contents of any of his other proffered ‘sources’ of Ifa’s substantive theological sources, e.g, its putative origins in Arabic or Indian cultural folkways. Here is what I think actually happened a thousand (or less) years ago. First, Yorubas and their cultural forebearers among the Igbo, the Nupe, the Nok and others always had their divination practices and their odus. Their methods and tools originally were cowrie shells and obi abata (nuts) or other im- plements--perhaps including palm nuts (ikin) as well. The exact history has never been explained to me, but they must have had some kind of notational method—even if transiently used during a divin- ation session--which may now have been lost to antiquity. But…in adopting these Arabic geomancy and astrological figures and marking conventions for their Yoruba odus, what our spiritual fore-fat- hers in Ifa did—by crude analogy—to go from a local “DOS platform” to an Arabic “Windows” or “Apple” platform of geomancy octagoms) in order to re-organize their Ifa “oral libraries” into a more efficient file storage and retrieval system. I reason that this cultural appropriation must have happened, but I do not know exactly when or how. (But I am sure that they did not first learn about the concept of divination itself from Arabs merely one thousand years ago, when they putatively adopted these current geomantic ways of marking odus!) And just as the Windows system (as compared to the old DOS system) was designed to provide for the new computers of the 1990’s newer methodologies, procedures, and decisional algorithms to store and retrieve information, nevertheless neither operating system had anything to do with the qualitative contents of the “documents, pictures, stories, poems, ebbos, or legends contained in their files, librar- ies or installed “software.”(In fact--speaking figuratively--I’d bet that our Ifa priests of yore even had "anti-malware" and "anti-virus" programs to help protect the integrity of their classical oral corpus—that body of wisdom that we now know as the contents of the Yoruba odus, specifically, and the Niger-Benue confluence of cultures, generally, from Arabic content. It is this body of ideas, religious prac- tices and social folkways that are at the heart of the Yoruba Orisha/Ifa cultural world (once tribal, but now national and international). And this world had nothing to do with Arabs or Arabic cultures nor, for that matter, much to do with the cultural world of Kemet 6,000 years ago either. Critique: Shangodare’s “Mathematizing” Orisha/Ifa Religion Is Not Instructive—It Is Eurocentric! Before getting into his penchant for “mathematizing” Ifa divination, it is necessary to carry on just a bit further with how he characterizes—in his view—the Arabic astrological divination “octagons,” “signs,” ”signatures” or whatever one wants to call them (we call them da’fa marks: da=to give or ren- der, fa= Ifa). He appears to have made a slight error in how he illustrated theArabic-Islamic North African astrologers' writing out of these figures. At ‘39:”45 minutes into the video he illustrates a sam- ple of one of their “binary code” markings this way: O OO O OO This was probably the video equivalent of a “typo.” Obviously, this is not a binary coded figure of any- thing. First, his “O,” if it were used in a digital binary code, would have to be accompanied by a “I” some- where; otherwise you would not have a polarity of “light” vs. “dark” nor any other kind What I suspect he probably meant to write (save for the “typo” on his board) as a sample of Arabic geomantic marking was: I (light) OO (dark) I (light) OO (dark) PAGE 34 However, in the world of geomancy--especially in Orisha/Ifa religion, which most likely did incorpor- ate odu octograms similar to this--these markings do not represent numerals. Instead, they represent light vs. dark poles or positive vs. negative charges or valences. No numeric calculations nor computat- ions issue from them. They are merely visual symbols for various categories or “chapters” of—in our parlance —“odus” that actually have names. (Please see Parts VI and VII of this essay). But, what is real- ly most important is that he gives us no clue as to what are the names for these Arabic figures not to mention their substantive contents--“astrological” or otherwise--as “containers” each of “knowled- ge.” (By Arabic cultural I am disposed to imagine “knowledge”that is astrological in nature This, would have been, in- deed, very interestingly since, as I understand it, al-Islam, like the other two main Rev- ealed Religions, is hostile to astrology. So addressing the presumed cultural content of these Arabic astrological diviners so that we might eventually compare them to our odus’ substantive contents—octagon for octagon (realistically, only a few examples would have been sufficient). If nothing else, what is of importance about odus are their names and the substantive content of the teachings. Of only secondarily importance is which “figure,” “sign,” “signature,””mark” or “numeral” has—by way of local convention—has been assigned to it. The odus are the stuff of qualitative substance expressed as poems, nature stories and allegories (pat- akins), proverbs (owe), legends (orikis), and parables creation myth explanations of where all things of importance to humanity and religion come from, anecdotes of the lives and times of the ancestors or the orishas, ritual instructions, prayers, incantations, and their recommended offerings and sacrifices (ebbos) to be made to the deities to obtain their interventions and help, and so on. It is these things that are the true substances of the odus in Orisha/Ifa religion--regardless of what their “signature” or da’fa figure markings are. I (light) I (light) I I (dark) I I (dark) “IROSUN” Since astrology (Arab or otherwise) plays no notable role in Ifa theology, and since Yoruba animism could not gain much purchase in an Arabic cultural setting either, I doubt that the “odus” of each (or whatever the Arabs called their divinatory or astrologic caterories), I doubt that there could be any meaningfuloverlap of religious substance and content. That said, if that was his aim was simple to show that we share similar recording conventions--then let us take this as historical information—interesting on its face—but of little importance. But no sooner than he leaves us with this ambiguity, he enters into other erudite and, in this case, “mathematically-tinged” propositions which are ex- emplified by his next discussion: a tangent on to the arithmetic topics of numerical “reciprocals” and “inversions.” For example, he informs us that the some of examples reciprocals might be: 1 -1 2 = 2 2 = -1/2 The idea here was for him to I I I I 2 -2 show us that a "reciprocal," I I I I 2 = 4 2 = -1/4 in the realm of odu signs, are I I I I 3 a sort of "twins." The numerals I I I I 2 = 8 2 = -1/8 on the left, though converse 4 -4 (as they go into negative num- 2 = 16 2 = -1/16 bers), are still numeric "reci- procals. The da'fa octogram on right are clearly "twins" (or mejis). "Reciprocals" "Reciprocals" "Oyeku Meji" The Source Domain: Math The Target Domain: Da’fa Mark PAGE 35 *What is the point of showing us that “the reciprocal” of “Oyeku” is its twin--“Oyeku?” Next, let’s look at Shangodare’s point about mathematical “reciprocals” and “inversions” because, as“math-talk,” it can get really interesting (but likely of very minor importance in Ifa interpretation) when it comes to da’fa marks. Numeric “inversions” in math, he labors to tell us, mean “the opposite.” He does not give any examples, of them but I shall, using the following rule: “In mathematics, a mul- tiplicative inverse or reciprocal for (the) number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number. When depicted in Ifa’s da’fa marks or “signatures,” this might be an example: ¼ x 4 or x 4 = 4 I I I I I I 1/7 = 7/1 vs. I I I I I I Odi Iwori “Inversions” In The Source Domain “Inversions” In The Target Domain Math Da’fa Marks Well, that’s cute. But so what? If you cannot show that “Odi” and “Iwori” as visual opposites or “inver- sions” of each other are the opposites of each other in regard to their substantive contents--and, by the same token, are also not the opposites of any of the other 14 olodus in regard to their substantive con-tents (this is the issue of ignoring discriminant validation)--and certainly, the content of “Odi” is not the mirror opposite of the content of “Iwori”--then this “analogue” is meaningless and teaches us nothing about Orisha/Ifa religion and its divination practices. So what’s the point? This is my concern: If his point is that Yoruba’s Ifa, at some point a millennium or so ago, started using Arabic geomantic “signatures” to conveniently mark or visually-label the 16 main odus (the “Olodus”) and replaced the methods that they had previously been using for one to several thousand years bef- orehand, then so be it. PAGE 36 Critique: The Practice of “Visualized” Interpretations of Orisha/Ifa’s Odu Octagrams or Signatures But what I think he is trying to slip into the minds of his audience by referencing the mathematical terms “reciprocals” and “inversions”—since it is obvious that he is not dealing with any of the sub- stantive con-ents of the figures--is the notion that the very physical appearance of the “odu” figures themselves serves, among other things, an mathematically interpretive role in ferreting out the wisdom that the client would benefit by knowing. For example, for justification, he said that the top half of this figure being the same as the bottom half illustrates the Hermetic “law of correspond- ence" (“As Above, So Below”). (See Endnote 7). An illustration: I I I I I I
OFUN The same two lines at the top the octagram are repeated in its bottom half. So why do we need a Greek“Hermetic law” (originating in ancient Kemet or not) to explain that which is visually patently obvious? Was Hermes Trismesgistus, the Greek Mediterranean-rim author who is credited with formulating the “Seven Universal Laws of the Universe” (of which “As Above, So Below” is but one) an Ifa babalawo on asojourn in Greece from Yorubaland? Further, speaking subtantively, what is there about the sub- stance of Ofun that illustrates this “Hermetic principle”at all? Why seek to import Hermeticism’s “laws” into Ifa at all? Indeed query: Which Orisha/Ifa odus instructs an Orisha/Ifa diviner to import any other philosophical system or religion into the Ifa corpus that is not already there? I suggest that doing so is the stuff of pure sophistry.(7) (Speaking editorially for a moment: It seems to me that many African-Americans possess an attitude toward Orisha/Ifa religion—that one can syncretize or import anything one wants into it—as a pecul- iar habit, in my experience, of those who have backgrounds in the romantization of Kemetic theology and Hermetic (Greek) theosophy. You never see Afro-Cubans, Brasilian Candomble practitioners, Puerto Ric- ans, Mexican-American Orisha/Ifa taking such eclectic and syncretizing liberties with our religion. Only us! Why? It betrays —likely unknown to them—their tacit Platonic idealism, Pythagorean “mathematicism,” and Aristotelian ideas about logic and causation that they are so fond of portray- ing as so much “deeeeeep knowledge….” And this reflects their cultural inferiority complex whereby they seek to legitimize Orisha/Ifa religion by introjecting stuff from all kinds of other sources. By contrast, I do not believe that Orisha/Ifa religion is enhanced one iota by importing these Mediter- anean-rim (and, usually, medieval European or Arabic) concepts —like latter-day Hermeticism, as- trology, “mathematicism,” nummerology, alchemy, Kundalini chakras, and so on, into it. Thank you very much (but no thank you)! Now, back on point: We also see the habit among some to interpret odu da’fa markings directly from their visual appearances in other ways. For example, they will suggest that there is a phenomenon or property within them of internal (vertically downward) “movement”—from one level of the figure downward to the next lower position—as indicative of how one’s fate (once under the power of an odu) progresses, or even how one odu changes successively into another, i.e., how one odu “gives birth,” res-olves or “modulates” (to use a term from music) from one to the next one in regard to visual patterning and, implicitly, into the ever evolving life of the client itself. This is an example of how some believe that the “energy” or “circumstance” of a person can be discovered by discerning the “energy move- ment” downward “inside” an odu (for lack of a better term) that, at any given time, is influencing him or her. Well, this is correct, but since we are dealing with “weak force energy” ashe (my use of the term "weak force" is merely an analogy from physics offered for illustration purposes only), the interpretative im- portant is very minor in any real case. I will set forth now what I think baba Shangodare was trying to get at in his video in regard to the visual interpretation of odu octagons. *PAGE 37 Fraternal Om’odu Octagrams Resolve Their Affinities In Other Odus: This Is a Legitimate Option for Helping To Interpret The Lives of Odus
Fraternal octograms are regarded as “fraternal twins” (because, though “twins,” except for the mejis, they are not identical twins, i.e., they are not exactly the same). They are twins who resolve their ashe to one of four settled odus (Ogbe, Oyeku, Ejila Sebora or Odi. There are basically four types of “fraternal” configurations for these special twelve omo’dus: (1) Those omodus’ that are complete op- posites of each other (I suppose this is what the lecturer meant by “inversions”), (2) those that are mejis, (3) those that are mirror reflections of each other (even if one is standing upside down), and (4) an “internal” reversal” when compared to its fraternal twin. Examples: I I beside I I beside I I I beside I I I beside I I I I I I I I I I I I I I I I ashe I I I ashe I I ashe I I I ashe I I I I ↔ I I I ↔ I I I I ↔ I I I ↔ I I Iwori Edi Oshe Oshe Oturupon Ika OTURA IKA Visual Opposites Mejis Mirror Reflections Internal Reversal *These odu octograms have “life” in them in the sense that they contain both sensitivity and moving “ashe” (“energy”)! They are, after all, considered living deities as well. I imagine the amount of the ener- gy to be in the nature of a relatively “weak force” analogous (just an analogy here!) to the “weak force” that binds electrons to an atom’s nucleus. (It, like gravity, is pretty weak, as things go—when contrasted lighting bolt power of electro-magnetism or the strong force that binds sub-atomic particles whose bonds, when broken, release nuclear reactions). This movement of ashe “energy” within and the omo'’du octagrams is nicely addressed in the book “The Holy Odus,” by Fategbe Fatunbi Fasola, 2014, at pages (pp. 9-11). There is a simple algorithm that determines how they combine to “resolve to” either Ogbe (for the Vis- ual Opposites), to Oyeku (for the Meji’s), to Odi (for the Mirror Reflections) or to Oshe (in the case of "In- ternal Reversals). “Resolve” means (again, by way of analogy!) that they go to a higher state of natural entropy. I believe that baba Shangodare was getting at this kind of idea when he was speaking about “reciproc- als” and “inversions” (using mathematical images and the aura of certainty that math gives one a sense of). My point is that all questions regarding odus’ interactions with each other—inter-sensitivi- ities, “birthing” each other, morphing into successive odus when left to the own devices, so to speak, are fundamentally matters of a qualitative nature not of a numerical, nor a digital, nor (for God’s sake!) not some “quantum computing” relationship as Clarence 13x would venture (whatever, in Heavens name, that could possibly mean in Ifa)? (Please see Appendix B, above, for a critique of that idea). Although baba Shangodare did not go into the idea of a vertical ashe (“energy” flow) downward in anodu such that its top “line” mark sort of pushes downward such that its bottom level gets displaced to the top and become a new odu (like Ogunda beoming Osa) ,or then person subject to the effects of theodus feels and experiences a similar “movement” downward and vertically through the light and dark levels of the odus as she or he passes through it). *PAGE 38 An example of interpreting “movement within an odu sign might be this (see Baba Obafemi’s YouTubevideo on the odu Irosun). I (light) Where this person sees clearly their way (sees the light) I (light) starting out, but then descends into the darkness of Irosun’s I I (dark) traps as he or she proceeds downward while under its in- I I (dark) fluence; eventually to emerge more mature and better in- formed (that is, once he or she has gone back to the top). Irosun I have my doubts that the visual patterns of the figures play a substantive interpretive role like this. Also, an example of how some interpret the putative downward movement of an odu’s da’fa markings as explaining how an odu changes (“births”) from one to the next (and forecasts how a client’s fortunes will change from one state to the next, accordingly). This mark moves down → ↘ I (light) I I (dark) This is how some suggest (pushing all of the ones I (light) I (light) that one odu becomes the below downward too. I I (dark) ↑ like this: I (light) the next. But I seriously While this mark is forced I I (dark) I I (light) doubt the wisdom of this to return to the top of the → ↑ as applied to individuals. stack. Thus, changing the IROSUN IWORI In life, only Ifa, through stack in this illustration through a reading's closing from “Irosun” to “Iwori,” cast, on a case-by-case bas- is--knows which odu is likely to come next for that person at the readings end. * * * * * * * * * * * * * In my book, op cit. I took pains to point out that when talking about “Ifa” in scholarly writing one mustspecify if you are talking about (1) Ifa ritual methodology, (2) Ifa’s stories, proverbs, ebbos, anecdotes,morality lessons, etc. as a matter of cultural contents and ideas, or (3) if you are talking about “Ifa’s” ”Orunmila,” analogous to Kemet’s Thoth or Tehuti, who--for us--is a shapeless and formless deity that is primordial and exceedingly wise in getting us out of problems. (But follow the guidance of Obatala and Yemoja, and you won’t have the problems in the first place!) Baba Shangodare failed to do this utterly in so far as the You Tube video is concerned. (See Oshoosi, Michael, "African Spirituality vs. The African American." IKO LLC, publ, 1997 (Appendix A: "Ifa Conceptions--Old World and New" Available through my website "Oshoosi.com."). The subtext here, I suspect, is that oluwo (Ifa priest) Shangodare’s mathematics acumen, as with so many people, has lead him to want to “mathematize” Ifa as part and parcel of sophomoric tendencies toward eclectic pronouncements, perhaps religious syncretism, and a felt need to further legitimize Ifa by conflating it with historically foreign religions, philosophical orientations (especially Platon- ism’s obsession with man-transcending “essences” and perfectly pure “forms” of everything in the universe). And one may add to this the more recent Arabic-Islamic mathematicians who, for their parts, and building on Grecian and Indian sources, gave us ‘perfectly abstract algebraic’ language (and techniques) to capture the universally-embedded mathematics “of it all”. I suggest that we should resist this impulse. Ifa is a perfectly competent qualitative and substantive system in its own right. It does not need any scientific nor mathematic validation (though we should always be open, indeed enthusiastic, about what mathematics and science has to offer humanity within their proper scopes). The fact that it uses geo- mantic da’fa marks to conveniently categorize and denote the 256 possibilities does not change that. This adoption, I suspect was merely to (then) upgrade Ifa’s “file storage system” to “Ifa 2.0” a thousand years ago. PAGE 39 Critique: More On Baba Shangodare’s Video Lecture Ideas: Da’fa Octagram As “Binary Code.” Following Mr. Clarence 13x’s lead (see the critique in Appendix B, above), he informs us that “Ifa” is a 1,000 year old north-African Arabic geomantic and astrological divination practice. The evidence is that they use four level figures with polarities marked as ( I ) and ( O ), or ( O ) and ( X ) or ( I ) and ( II ). He does not tell us the names of their odus nor what are their “astrological” contents. Unfortunately, he does not point out that these “signatures” or figures are merely the methodology for inscribing the “odus” or divination categories that their diviners “pulled down.”And though, it is in quite plausible that our Ifa priests of yore did adopt that “operating system’s” method of notation, it is wrong to called the notation system “Ifa.” Ifa is the Yoruba culture’s religious (mostly oral) literature that substan- tively con- tained those peoples’ tribal and nation heritage (something that had nothing to do with Arabs nor their cultural folkways). (11) Next, he informed us that the binary nature of these markings also was religiously interpretable (as well as being the reason Europeans learned--from the Islamic Arabs--“binary” computation and calculus). Even so, that possibility is irrelevant to students of Ifa. But next, he then turns to the “Laws of (Grecian) Hermeticism” (“The law of opposites” and “As above, so below,” among others) to assert that in the visual inspection of these four-part divination signs or signatures one could discern some thing about the (their) “odus” content natures: To the skilled eye, movement and meaning in the polarities could be discerned. For example, if the top two “lines” were the same as the bottom two, then this meant that the wholesign (the odu ) exemplified the Hermetic law of “As above, so below” or “universality”--evidence of the isomorphism between Heaven and Earth (which is really what this “law” is implying). (See Endnote 7). As fully explained on pp. 25 and in Appendix B, above, I have abiding doubt that one can project inter- pretive “binary”--the alphabet of modern computer programming. And, he adds that “binary” “came from Africa”—something that, as stated, is misleading. (That it came from Arabic North Africa is simply irrelevant trivia having not much of anything to do with Orisha/Ifa religion or divination. (11) This tendency to wish to add rigor to Ifa by “mathematizing” it or by alluding to various and sundry other cultures’ similar ideas to propose and demonstrate its august sourcing and company (among the other world-class cultures of antiquity) that Ifa enjoys is folly. Reifying mathematics into something that is the substrate of the Universe (or, nearer to home) the substrate of peoples’ qualitative folk cultures here on Earth reflects unadulterated Eurocentrism, to wit: Grecian philosophy and its exten- sions into Arabic-Is- lamic mathematics and science, as well as even into Christianity. (Many African Ifa priests have, unwittingly I suppose, allowed it—and even Grecian Christianity--to seep into Ifa, from earlier in the mid-20th century, when some of Nigeria’s doctoral students of divinity were writ- ing their seminal theses and books, for the first time, on the subject of Ifa while studying in the United Kingdom. However, upon sober reflection in this post-colonial world, Ifa does not need European nor Mediterranean-rim—including Kemetic--comparisons to add legitimizations. Their similarities should only be passing points of interest. (Again see, Oshoosi, Michael, "African Spirituality vs. The African American." IKO LLC, publ, 1997 (Appen- dix A: "Ifa Conceptions--Old World and New" available through my website "Oshoosi.com."). PAGE 40 The Importation of More Grecian and Medieval Hermeticism (Lunar Astrology and the "Seven Laws" ) Into Ifa Is Surplusage and Syncreticism Third, finally we arrive at a few of baba Shangodare’s other speculations—all uttered toward the same end. Now, as we near the conclusion, we must note that we also learned from him that:
“Africans learned about the (Hermetic) “laws of opposites” from observing “the 16 phases” of the moon.” And somehow the existence of 16 odus which were created by the Yoruba orisha Oshun, he says is related to this. Problem: The sun- light reflected by the moon is a continuum. Thus, technically, the moon does have any specific number of “phases.” Nevertheless, in African and Western astronomy the phases—such as they can be said to exist at all--number eight (8): the New Moon, the Waxing Cresent, the First Quarter, the Waxing Gibbons, the Full Moon, the Waning Gibbons, the Last Quarter, and the Waning Cresent. Shangodare sup- ports this proposition by pointing out that the in Hindu religion the moon has 16 phases (the kalas) corresponding to the 16 Nitya goddesses, generally, and the progenitor of the orisha Oshun (he says) named “Tripora” whose number just hap- pen to be 16 and who is reputed to have 16 desires—chief among them being ho- ney. The evidence that our Yoruba ancestors knew the first thing about “Tripora” is not provided. It is in the nature of sophistry to turn similarities into causation. The “Mathematization” of Nature, the Universe and Religion Next, our intrepid lecturer serves up for us a tangential foray into simple math in order to convince us that mathematics is a priori embedded in the universe. He starts with the well-known Fibonacci sequence of numbers that is constructed such that a given number in a series is the sum of the two numbers that preceded it: 1+2= 3, then 3+2=5 and then 5+3=8 and so on. So, an extended sample would look like this 1, 2,3,5,8, 13,21, 34 and so on ad infinitum. The importance of this, so far is nothing. But, as Johannes Kepler discovered a few hundred years ago, if one divides any given number in this sequence by the number immediately prec- eding it, one will come up with a constant number (1.61904…)—e.g.34/21= 1.619… This sequence can be extended indefinitely. What he also discovered is that if one were to graph these sequences geometrically, the resulting curve would look like a spiral (if graphed 2-dimensionally) or a cone (if graphed 3-dimensional) as a never ending “clone” of itself. That is, it would look like a “cyclone” (an endless cycle cloning itself. In three dimensions this would look like the pattern of a snail shell, a vortex (like a hurricane viewed from above, water drain- ing out of a bath tub, the proliferation of cells growing in a plant or in animal tissue, or the magnetic vortex of spiral galaxies). In nature, one can observe this ratio being played out he opines. He then goes on to suggest—in “mathematizing” nature—that without this phi ratio (a numerical constant in nature—where, moreover, the very lan- guage of God is this mathematical constant) that “there would be no Buddhism, no religion, and no Ifa. His indoctrination and commitment to the “mathematization” “digitalization” of Ifa is complete (as absolutely useless as is the enterprise). * * * * * * * * * * * Problem: Mathematicians have projected mathematical constants (which are prod- ducts of mathematical reasoning) onto nature in dozens of illustrations to describe the otherwise non-numerical repetitive patterns that are observable in numeric terms. (In nature, nobody is counting—not even “God” Olodumare. No odus depicting Yor- uba creation myths refer to “God” as dealing with numbers except for the simple en- umeration of items, but never for purposes of calculation or computation covertly embracing numeric codes or arithmetic operations. The discovery of mathematical constants is man’s doing, not “God’s.” One of the primordial orishas--Oshumare (or Osumare)—is the god of the rainbow, signifying that Heaven and Earth have an agree- ment that one shall reflect the other in the phenomenon of “cycles,” periodic renew- als (after the completion of repetitive cycles and patterns). But that is where it stops. *
PAGE 41 * In the religion, no mathematical measurements nor operations attach to the cycles. The numerical measurements of natural phenomena—producing mathematical “ constants” such as those well-known to physics, is man’s alone—albeit a very use- ful art indeed. And as for the primordial conical snail (snail shell) that God gave to Obatala to help create the world-- though an interesting idea—the notion that the snail was a mathematician has not yet made it into the canons of the odus corpus. The “language of mathematics” has no more of independent existence in “the Uni- verse”—a priori to or transcendent above the mentation of Humanity than do the languages of English, Yoruba, Aleut or ki-Swahili. The well-known African Sankofa bird that, in embarking on a flight from one tree, to the next, briefly returns to the tree it was in prior to arriving at its present stat- ion. Thus, in moving onward, its flight patterns take on the appearance of sequential loops. Is this bird flying out a Fibonacci numerical sequence? Did anyone tell the bird that? What, if on occasion, the bird is required to depart from its usual flight pattern (e.g. if a predator climbs the preceding tree)? If the bird’s flying pattern in nature is arithmetically determined (because math is “100%” deterministic) did God give the bird a “hall pass” to depart from what the numbers, otherwise, dictate? EUROCENTRIC RHETORIC AND THE WAGES OF HERMETIC SOPHISTRY IN HIS LECTURE The Exaggeration Habit I used the lecture of baba Shangodare Fagbemi as an example of what adherents to Orisha/Ifa religion want to be skeptical about. The Reification and Abstraction Habit We saw in the video the unenviable habit of him reifying, (i.e., making something concrete that is, in reality, a process or an abstracttion (like algebra) into an intrinsic “law of the universe or nature.” Mathematicians, in their projections, can go so far as to declare that “the universe is, when reduced to its essence, a mathematical equation.” This kind of thinking is the stuff of Pythagorean and Platonic philosophy (championed in subsequent centuries in Arabic culture). This is where the idea that math was al- ways “embedded in the universe came from. ”In reality, mathematics, as a socially-shared “language” was embedded in society by peoples’ experiences with the need to handle large collections of items for purposes of counting, accounting, trade, navigation and astronomy, money and coinage!(which is where the need for complex math arose for Pythagoras), as well as fo rconstruc- tion and mechanics, and the maintenance of class hierarchies. In regard to the source of mathematics that is embedded in the minds of individuals within a society, the embedding lies in the astounding complexity of the brain’s 100 billion synapses (each with a few to 20,000 synaptic connections to other neurons; the total permutations of which—in every human cran- ium—outnumber the total number of stars in our Milky Way galaxy by an order of 100! (That is, even if each neuron had only 100 synapses, the total number of synaptic connections in each human brain would exceed 10 trillion connections. Talk about a computer!). Specifically, the areas of the brain that sub-serve mathematical ideas are the supra-marginal and angular gyri in the parietal lobes of both of its hemispheres in the posterior brain in coordination with the anterior brain’s pre-frontal cortex and its memory portions of the brains limbic system. Mathem- atical ideas rise upon, and parallel exactly, the natural spoken languages of human beings and drawn on our every-ay empirical experiences with collections of items often arrayed before us, with dis- tances that we have to travel along paths (numbers as point along lines), containers of things (“sets’), and spatial experiences (“up,”“below,”“near,”“on,”“underlying,” etc.) that, by way of “mapping” or met- aphorical mapping on to numbers and symbols of numbers the arts of mathematical calculation, com- putation, geometric drawing, digital language coding and computer modeling. Mathematics is not embedded in nature per se, nor in anyone’s religion (except the religion of Grecian idealists and those who cannot examine their own Eurocentric indoctrination. PAGE 42 The Nullification of Logic Problem The modern-day sophists cannot think critically and rely solely on “convergent validation” (i.e., they can only pay attention to those highly sought-out facts that support their ideas. For example, imaging this conversation: “I was thinking about ‘aunt Sally’ just yesterday and, lo and behold, she called me this morning. I must be clairvoyant!" “Well, not so fast my friend: Before you arrive at that conclusion did you consider all of the times you also thought about ‘aunt Sally’ and she did not call you? How about the number of times when she called you when you had not been thinking about her beforehand? And how about all of the possible times she called you, and you were not at home to know about the call? What would this information (this discriminant information) due to your confidence in your clairvoyance?” Our sophist friend would be forced to be a little more modest about possessing “esoteric” knowledge or supernatural powers because he or she would have to acknowledge that discriminant validation (paying attention to alternate or contrary facts) is every bit as important as convergent validation. Sophistry lies in selling an audience—because of proffered ‘superior knowledge’ on a line of specious and illogical reasoning (and false causal relationships) through the use of a rhetorical strategy des- igned to “wow” an audience with a parade of “ah-ha” moments. But this is entertainment no less so than that of a magician who is skilled in making the audience keep their eyes on his right hand instead of on what the left hand is doing to create the magic illusion. Other versions of corrupted logic can be exemplified this way: “All dogs have four legs. That thing over there in the corner definitely has four legs. Therefore, that thing must be a dog!” “Well not so fast my friend. I have it on good authority that the “thing” in the corner over there to which you refer is a table!” The Causal-Connection Illusion We believe that we can see causal chains or linkages when we discover interesting similarities in the “mental” ideas, concepts and artifacts as we go from one classical culture to another (ore to our own culture). In baba Shangodare’s case, let’s use the connection between the Yoruba deity “Oshun,” on the one hand, and the Hindu goddess “Tripora,” on the other. Is there a connection? Says who? What was the mechanism of this cultural transplantation? And in what time period? Unfortunately, we very paranoid Africans and African Americans—whose self-images and need for ex-ternal validation is inexhaustible owing to our histories of European-American slavery and colonial- ism --are quick indeed to make specious causal connections to anything that might make us feels red- eemed or even superior by identification with someone’s else’s classical cultures; whether it be Kem- etic, Indian, or Moorish cultural achievements (or whatever). Implicit in this defensive grandios- ity on our parts is the tacit belief that cultural ideas are linear or even lineal. The idea that the same idea might arise independently in numerous cultures that share similar stages of development and am- bient conditions is one that they cannot afford to entertain. But there is another way of looking at this which is just as plausible. PAGE 43 Let’s considered common numeral symbolism first. Almost all cultures will, independent of each ot- her, fetishize the number “3” (trinities),“5” (reaching thresholds and renewals), “4” (subtizing), “7” (civilities), “10” (authority), “12” (hours and divinities) or “16”(the impulse to “subtize the act of subtiz- ing the number “4” itself will produce a fetish for the number 16 that groups of people can easily agree on and remember as noteworthy collection of ideas or rules. So, when we discover something of cul- tural importance that is associated with any of these numbers, it simply may be that this is merely an expression of an inherently common idea or image (like one of Jung’s archetypes writ “numerical”) that many cultures share in common. (Mr. Clarence 13x gives wholly different “archetype” numbers for the common practice of numerology in cultures that developed relatively independent of each other. No problem). My only point here is that similar archetypes of numbers, symbols, deities, and so on, exist world-wide from antiquity in cultures that were more often than not independent of each other in geography and in time. And my goodness, just how many cultures can it be said that do not have some deity maiden who is clev- er, sweet, harmonious, sexy in her essence and who likes babies and honey? But though we may encoun- ter records of some people in antiquity—of various cultures-- who have such a maiden does not mean that we (or our version of the maiden) is descended from them. Nor does it mean that if we find this archetype among several other rather contemporary cultures and nationalities that it means we “got her from them” ‘over there’ or that those in the other culture who “stole her from us.” This is an example of silly causal connections illogic that sophists eat for breakfast on a daily basis. I can assure you that authentic linguistic and conceptual connections across time and distances requires careful, not casual, analysis. The "they stole it from us" (sometimes a paranoid cultural delusion of persecution) and "we got it from them--these prior great thinkers" (sometimes a paranoid cultural delusion of grandiosity) are the kinds of claims that need to be examined closely for their validity. (The grandiose version of paranoid thinking also obtains: 'Ifa is the father of all of the world's religions'). CONCLUSION I hope that brother Shangodare Fagbemi, whose lecture I have taken to task (respectful task, I hope) by exemplifying its eclecticism and syncretization as something to be avoided, and those who are under- standably impressed with sophistry this kind ( I say again, even I admit that it is entertaining), will at least consider the validity of my forensics here and, in good faith and a kindly spirit, think deeply about the world-views I have drawn out here. Indeed, I am concerned that many folk—African and African-American alike (especially those with prior commitments to romanticizing Kemetic studies, its mystery religions (and the unrecognized Grecian and medieval European pseudo-Egyptian Her- met icism that flows in its wake!) are seeking to come to Yoruba’s Orisha/Ifa religion for a genuine experience of authenticity, validity, reliability and a useful immersion into a tradition (West and Cen- tral African and Atlantic diasporan) that is actually the stuff of their true West or Central African ancestry. Hopefully, they will benefit from the adage: “I never learned anything while I was talking.” These religions are not for everyone. And aiding each other in bi-culturalism is the right thing to do—starting with a willingness to examine and cull much in the way of our fundamental assumptions about how the world of psychology and culculture actually work (including how they have worked historically). Shangodare has made a strong point is relating Ifa’s Odu figures, the octagrams, to North African Arab-ic-Moorish astrolocical sources. (Some have even suggested the very word Ifa comes from the Arabic word f’al meaning “omen.” But, for all we know, it is just as likely than if the Arabic word f’al came from the Yoruba word Ifa). Next, he goes to great pains to “mathematize” Ifa divination. But Ifa can explain itself on its own terms; its own sub-Saharan cultural terms! It does not need legitimization and “sourcing” (as far as the sub- stan- tive content of the religion and culture go) from Grecian Europe, from Grecian influenced Chris- tians, Arabs, Jews, medieval Hermeticists nor mathematicians. Mathematics is good for descriptions and predictions (we’d be lost in this world without) but, with Orish/Ifa religion mathematics has very little to describe that words and quality ideas have not done a more than adequate job for eons all along. Going into hypermodern forays about “digital, binary computations” and odus to try to add further “scientific-sounding” jargon and ideas to it, seems hardly worth the effort in my view. And it does not have the added benefit of being the truth, in any event. *
PAGE 44 *This essay has been directed to enlightening (actually, I prefer “enblackening” you) our fellow-travel- ors –if I can-with the opinion that mathematics reflects the metaphors of actual daily living and hum- an activity, and models it, but by no means suffuses it. Mathematics, devoid of addition, subtraction, multiplication or division—as it is in Orisha/Ifa religion is a hungry critter indeed. And it is an orphan. It is not inherently embedded in the Universe, transcendent and a priori to the minds of Humanity, and it is not inherently embedded in the religion of all of nature: Orisha/Ifa. The better view is to use it and to respect it, but not to fetishize it. * * * * * * * * * * * * When, many years ago, my padrino, the gifted Anya bi Osun (iba…eee!), brought me into our ile (i.e., ourcongregation and rama (our Afro-Cuban Lucumi Yoruba lineage that goes directly back into west Af- rica), as our ile’s "oludamoran" (consigliere”or counselor), he told me that there were but two rules in our house: Rule # 1 “Don’t Make 'Stuff' Up” and Rule # 2 “Don’t Forget Rule #1” Footnotes/ End Notes 1. “Where Mathematics Comes From,”Lakoff, (How The Embodied Mind Brings Mathematics Into Being), George and Nunez, Rafael, Perseus Books,2002. This approach sounds in a neuropsychologicalbasis for mathematical ideas; a refutation of Platonic mathermatics (mathematical idealism), on the one hand, and social constructivists' views that math is pure a social construct that varies from one ethic group to another. Please see "When Math Worlds Collide: Intention and Invention in Ethnomath- ematics Author(s): Ron Eglash Source: Science, Technology, & Human Values, Vol. 22, No. 1 (Winter, 1997), pp. 79-97. Also see "Is Mathematics Invented or Discovered?" a YouTube interview with the world -class physicist Sir Roger Penrose, for the same point on the delusions of "Platonic mathematical real-ity" that has to do with physical (let alone biological, psychological nor spiritual) reality. https://www.youtube.com/watch?v=ujvS2K06dg4&t=323s “Where Mathematics Comes From: How The Embodied Mind Brings Mathematics Into Being,” (Reviewed) Madden, James J., The American Mathematical Monthly, August, 2002. See: file:///C:/Users/arrop/Desktop/YOU%20TUBE%20&%20WEBSITE%20PROJECTS/Where_Mathematics_Comes_From_How_the_Embodied_Mind.pdf And see: Mathematical Cognition HOW DID HUMAN BEINGS ACQUIRE THE ABILITY TO DO MATH?https://www.youtube.com/watch?v=NnVubBrATIU&t=789sSee YOU TUBEKeith Devlin, STANFORD UNIV 2012STANFORD UNIV 2012
50 CENTURIES IN 50 MINUTES: A BRIEF HISTORY OF MATHEMATICSA BRIEF HISTORY OF MATHEMATICS JOHN DERSHhttps://www.youtube.com/watch?v=YsEcpS-hyXw The theses here powerfully demonstrate, based on current findings in cognitive and neuropsychology, that math ematical operations are solely based on humanity’s empirical experiences in life with “paths” and “lines,”” directionality,” “locations,” “collections of objects,” and “containers” etc., give rise the use of metaphors mapped into the terrain of mathematics to give us arithmetic, algebra, trigon- ometry, geometry, Boolean algebra, sets, calculus, and symbolic logic. There are no a priori , perfectly abstract, and transcendent numbers nor mathematical operations “in the Universe” aside from hum- anity’s cogit- ation on the same; no more than any other form of semantic language exists in the Univ- erse independent of humanity.
PAGE 45 2. No books on Orisha/Ifa religion that I read in preparation for this article express the view that the divination practices of Orisha/Ifa religion utilize numerical calculations or binary computations: The titles list that follows only includes books and articles directly dealing with divination: --The World Atlas of Divination, Matthews, John, Bulfinch Press, 1992, pp.101-108 --The Dilogun, Ocha’ni Lele, Destiny Books, 2003, --The Secrets of Afro-Cuban Divination, Ocha’ni Lele, Destiny Books, 2000 --Ifism: The Complete Work of Orunmila, Ibie, C. Osamaro, Efehi Ltd, Lagos, 1986 --The Odu of Lucumi, Kulevich, James, Ile Orunmila Comm., San Bernadino, 2003 --Ifa Divination, Bascom, Wm.,Indiana Uni. Press, 1969 --Sixteen Cowries, Bascom, Wm., Indiana Univ. Press, Bloomington, 1980 --Fundamentals of the Yoruba Religion,” FAMA, Chief, Ile Orunmila Comm, 1993 --The Osha, Cortez, Julio Garcia, Athelia Press Inc., New York, 2000 --The Holy Odu, Fasola, F. F., and Soto, Stuart, B, Publ.?, 2014, (calls the Ifa da’fa marks “binary oracles” at p.3. only. No “mathematizing” of Ifa exists in the book save this one-time use of this term). --Ifa: An Exposition of Literary Corpus, Abimbola, W, Oxford Univ Press, 1976. --African Divination Systems…Peek, P.M., Indiana Univ. Press, 1991 --African Worlds: Studies in the Cosmological Ideas and Social Values of African Peoples,” International African Inst., Oxford Univ. Press, 1954. and -- The Basis of Yoruba Religion, and “What Is Ifa?, Rev. Epega, Daniel, Ijamido Printers, Nigeria, 1973 --“La Geomancie a l’accienne Cote des Esclaves,” Mercier, P., at pp 210-234 --Short Catechism for Ifa Children, and “Orunmilism, The Basis of Jesusism, Beyioko, Fagbenro, Dr. O.A., 1943. --African Spirituality vs The African American, Oshoosi, Alashe Michael, IKO Publ, 1996 (a collector’s item available only through “Oshoosi.com” 3. --Supreme Mathematic: African Ma’at Magic, African Creation Energy, Pub. and "Ifá Mathematics and Quantum Computing,” "https://www.youtube.com/watch?v=fVz6g1rqiuQ" by Clarence 13x), 2010. 4. End Note: The mechanism by which the seniority rankings of minor odus relative to each other, or of odus to each other (generally) is too much information for this article. Knowledge of these obligatory techniques must be taught to them by the godparents of a deeply initiated olorisha (priests/esses) or awo (the students of babalawos). 5. End Note: The odu that, when using the merindilogun (erindilogun, dilogun, caracoles by alternative names), is called “Opira” occurs when the Orisha Elegua is not present for the cast. Small, but obligatory responses by the diviner, are necessary when such a “letter” falls to the mat—espcially if the divination is occurring in the ceremonial context of a neophyte’s initiation during the “Ita” (do not confuse with Ifa) destiny reading of his or her life. *6. End Note: Merindilogun is the formal name for cowrie shell divination method of Ifa in Africa, but is most often called “dilogun” or “caracoles” in the Santeria/Lucumi version of Yoruba religion in Afro-Cuba. There are minor differences in the way it is carried out as between the two places. In both cases, certain rules are followed to ensure that the random generation of possible outcomes is not biased and so that neither the diviner nor the client can “stack the decks” during the reading. It may be the case that the odu Cuban dilogun (qualitatively speaking!) do not correspond to the odu as read by some babalawos. This is because some of them believe that the dilogun order of the olodu is different from the Cuban (and Nigerian) orders of the Olodu. For example, the first olodu in dilogun is "Okana sode" or "Okanran." However, the first Olodu in Ifa is Eji Og- be. So, this means in their view that if an italero (Cuban diviner using cowrie shells) reads a person whose opening odu is "Okana/ Okanran" he or she would look to the corpus of Lucumi / Santeria for an interpretation. But if additional information is desired and he/ she chooses to look into a book that contain Ifa verses, he would not look at their Olodu "Eji Ogbe" because it is Ifa (proper's) first Olodu. They would not look into the interpret- of Ifa's version of "Okana / Okanran." Though this does not make "a lick of sense" to me, I am in no position to declare this to be a wrong approach if such is truly the practice among some Cuban babalawos. (See "Electric Santeria," by Aisha M. Beliso-De Jesus, 2015, p. 192). But giving primacy to the ordinal place of an Olodu in an Ifa list of sixteen over the qualitat- ive properties of the corresponding ordinally-placed Olodu as pulled-down in dilogun divin- ation is a dubious thing to do in so far as I can see (in regard to authenticity and validity). But, I am always willing to learn how that came about if I understand what she has written.. *PAGE 46 * 7. End Note: End Note: Hermeticism is a loosely congealed perspective on wisdom that is (or was) regarded as Egyptian in source--going back to at least the 18th dynasty with the deity Thoth or Tehuti (similar to Ifa's Orunmila) as the custodian of knowledge-- all knowledge. In reality, it comes from books--mostly gone--that combined "Egyptian lore" as formulated by Macedonians and Greeks as they constituted the ruling class of Egypt from the 3rd cen. BCE. With the consolidation of books and all Mesopotamian (Babylonian), Assyrian, and Persian "knowledge" (including the astrologies from these Mediterranean-rim cultures) at the time, along with with Egyptian religiosity, it passed down the ages to influence Greek and Alxeandrian Christianity toward the end of foster- ing Christian and Jewish Gnosticism. It served as a basis for "Gnostic religious science" (a heretical alternative to organized religions of all types) and the practice of the Isis cult of "Egyptian religion during the Roman-dominated period. From there it flourished as a European world view that eventually gave rise to Rosicrutianism, various versions of European astrology, and philosophy (until the reassertion of Platonism and neo-Plat- onism in Europe during the age of Enlightenment). And from there we find it in the Gnostic flavor of Freemasony. This route is how we ended up with "Egyptian" religion lying at the heart of Freemsonry and latter-day Rosicrutionism and being claimed by white people as a safe and sanitized European heritage or "cradle of civilization." The core of Hermeticism was its distillation of its famed "Seven Laws of the Universe:" 1. The law of mentalism. 2. The law of correspondence ("as above, so below") 3. The law of vibration. 4. The law of polarity (opposites exist everywhere) 5. The law of rhythms (ebbs and flows) 6. The law of causation (all things have causes and effects) 7. The law of gender. Thus far, I have never heard of an orisha speaking of any of these "laws" in an odu. One can always project or interpret any story or account as exemplifying "opposites" or "gender" and so on, but I am yet unaware of the systematic formulation of any Univ- ersal "laws" (except, perhaps "the law of Eshu!"--i.e., "stuff" happens). It is not unlikely that our ancients never felt the need to learn philosophy from the Greeks pretending to be Egyptians. So why do we? Is it in our nature to learn wisdom through "codes," i.e., through 'lawful codifications?' Why do some of us think and teach Hermetic for- mulations as enhancing our understanding of Orisha/Ifa or aiding us to channel ashe? (When, indeed, it adds nothing, except more Eurocentrism to our already heavy bur- dens). * Please be referred my series of articles entitled “What Ain’t in Ifa” to be found at my website “Oshoosi.com” for other commentaries on how to weed out (but only so that they may be identified) Eurocentric ideas in our African-American and even educated (in Eurocentric schools) African kindred. 8. End Note: Traditionally, a Yoruba specialist in divination is called either a babalawo (a male “owner” of the mysteries of Ifa) or, if female, she is called an iyan’ifa (a mother of Ifa). The training went on for at least 20 years, starting in childhood. They not only hand to learn to recite odu stories and poetry a plenty for each of the 256 omo’dus (odu com- binations) through echolalic recitation, but they had to learn numerous ceremonial and ritual tasks. (Iyanifas are not recognized in Afro-Cuban Yoruba, but those roles may play- ed by an obasa (who is the female version of an oba oriate—a ritual master-of-cermon- ies) who is an accomplished italera/o (an accomplished diviner in their own rights). PAGE 47 9. End Note: Arguably, there are more "New World" practitioners of Yoruba's traditional Orisha/Ifa religion (or a variant of it, like Vodu) than in Nigeria. That country has 190 mil- lion people in it. About 60 million are Yoruba's proper (Africa's largest ethnic group), but only one third of them practice the traditional religion, whereas the other two-thirds are Christians and Muslims. By contrast, there are more than 20 million Candomble/ Macum- ba practitioners in Brasil alone; not to mention Cuba, Puerto Rico, the United States and Mexico added in. *10 End Note: When I speak of African traditional religion I use two--admittedly arbitrary dates (though reasonable). What do we imagine of know of how the religion was prac- ticed around 1500 C.E. (before any culturally signficiant European contact at all) and, again, around 1885 C.E. (before the advent of formal colonization). After that, and es- pecially from the 1930's onward, colonial education and churches affected the way that all colonial subjects who had been brought up on a steady diet of Western philosophy and Christian theology (no less than what we were exposed to in the "New World," it it is no wonder than many a babalawo (i.e., those who were formally exposed to Western educations, also have allowed Mediterranean worldview ideas (especially Christianity) to seep into Ifa as well (though not much of it). Please see my "African Spirituality vs. The African American" 1996 book's Appendix on "Ifa." (Available only through "Oshoosi. com.)" *
11. The earliest recorded Arabic-speaking individual, at the time of the advent of al-Islam (pro- nounced ‘az-Islam’) was named ‘Nawbakht the Persian (born in 679) and was the court astrol- oger to Caliph al-Mansur until 775.’ The names of the Jewish astrologer, Masha’allah , one of Nawbakht’s assistants, another Arabic-speaking astrologer, is also mentioned in history be- cause his son, in turn, inherited his role until 815, and then his grandsons followed suit until, six generations later, until 940. The Arabs studied in great detail the books on Grecian, Bab- ylonian, and Persian astrology.’During this period, of course, Arabic-speakers, riding the crest the crest of the wave of Islamic religion prosyletization, took Arabic culture into the north Af- rica (the southern coast of what I have referred as the “Mediterranean-rim.” I have paraphra- sed this brief history from “A History of Horoscopic Astrology…,” James Herschel Holden, Am- erican Federation of Astrology, 1996. There is no information on how their divination methods categorized the thousands of “omens” or “f’al” (from which some have said that the word "Ifa" comes from) of concerned to them nor how their reputed octagrams may have worked their way into the sub-Saharan world of Africa’s Ifa. * In a post on the Internet, an unattributed author with the Astrological Society of the Unit- ed States wrote, in essence, the following account of how the art of “sand cutting” came in- to being as a part of Arabic culture. He then suggests that this practice of cutting octagons in the sand (or some figures) was then related, by them, to Arabic astrology by a certain Ibn Khaldoun sometime before 1406, when he died. This author believed that the Arabs (at that time) did not have sufficient mathematical acumen to carry out astrological calculations.So, instead, they created a sand cutting technique whereby using a stick, a hazi (a diviner) would draw as many lines as quickly as he could (almost trance-like) into the sand, and the allowing the wind to blow new sand onto the existing lines. As the erasures occurred—down to a cer- tain number of the remaining lines—this would then constitute an interpretable figure. The pretable figure. The diviner could also wipe some of the lines out in groups of two. Eventually, either one line or two would necessarily be left. If one line was left then the omen was “good fortune” but if two were left, then the omen was considered negative. * PAGE 48 * The author wrote this in his essay relating Arabic geomancy techniques to Orisha/Ifa divination recording techniques. And this approach to obtaining a divinatory figure, and the answers to polarity questions (“good” or “bad” outcomes predicted) is very mindful of the methods by which Ifa divination (especially with Ikin—palm nuts) works. However, he did not say that the content of the figures the Arabic diviners adduced had anything to do with the content of the Olodus of Orisha /Ifa. Moreover, he points out that the Arabic astrologers rejected the idea that the geomantic figures had any substantive content at all (something, of course, that is diametrically opposed to the way that Orisha/Ifa diviners regard our Olodus—that not only have serious differentiated to the meanings, but are deities in their own rights)! Finally, the Astrological Society author explains that the Arabs had conflicting views about the relation- ship of geomancy to their versions of astrology (with substantive contents)—eventually rej- ecting any connection. But that need not concern us because Orisha/Ifa divination had and has nothing to do with astrology in the first place (Please see my essay in this series entitled “What Ain’t in Ifa?—Astrology”, and for this society’s account see: https://www.astrologicalsociety.us/astrogeomancy/2-rami-and-islamic-origins.html). *12. END NOTE "The House of Oduduwa."is a public relations video which features the new Ooni of Ile Ife: his history and his august mission destiny. It may be found at: https://mail.yahoo.com/d/folders/1/messages/AODiOR4wrZCkXhq69QBdwAfUih0?.src=fp If you are a Yoruba (Orisha/Ifa) practitioner, this YouTube video will make you feel especially proud. First, it details the Yoruba’s view of the history of Humanity as starting in the town of Ile Ife, in present-day Nigeria, and then spreading eastward across the rain-forest belt and the savannah in the direction of the Sudan and southwest Ethiopia. Later, says the narrator did cultural influences also its way back toward the western parts of Africa from those areas (this is the story of Oduduwa’s flight from the east toward Ile Ife when he was reincarnated as a living being. He, after found the seven sub-nationalities of the Yoruba, died and his spirit en- tered the Earth at Ile Ife as he was again deified (and also gave rise to the major social control institution of Ogboni). * Next, it showcases the numerous cultural achievements of the Yoruba (and related) peoples. And it culminates, after listing all of the previous Ooni of Ile Ife and their roles as kingmakers and overseers of the religious institutions found in Yorubaland. It also depicts the world-wide spread of Yoruba culture. Finally, it describes the august and current mission-destiny of the newly installed Ooni of Ile Ife HRH Oba Adeyeye Ogunwusi. This 45 year-old gentleman’s bearing shows all that one needs to know about Yoruba dignity and those of us who seek to emulate it. 13. There is an area of mathematics called “mathematical biology.” It is mainly about the application of mathematical equations or computer coding that mimics the observable rates of biological events (e.g., the number of times a certain cell type divides under certain conditions) or geomet-- ric patterns of the flow of energy in biological tissue or organelles (e.g., the patterns of innerva- tion among neurons). Once the models are constructed, then different values can be plugged into them that represent biological parameters. The computer program can then predict how changes in any of these variables will affect the others or the affect the entity (cell, tissue, or- ganelle, or organ) as a whole. There is a priori no math “in” the biological material itself; it’s just that the entities properties can be mathematically modeled and experimented with. *14. It has been written that in the Old Testament, the Christian Holy Bible, and the Holy Ko’ran have gematric (or mathematical) codes and ciphers embedded in their words and sentences. This is very close to saying that mathematics is “in” these religions. Interestingly, if these books contain not only the words of the Most High but, in the case of al-Islam (where the words in Arabic are Allah himself), this means that God was, among other things, a mathematician. No such concep- tion exists in traditional sub-Saharan African religions and world views. No poetry or parables in the Olodus suggest that Olodumare was a mathematics major in college as s/he blew emi (the breath of Life) into Humankind.