The "Pythagorean" "theorem" and the rant of racist and civilizational superiority

C. K. Raju

- a group of influential Indian intellectuals decided
- we need to tell our own stories.
- Can't remain as characters trapped in another's story.

- how calculus was invented in India (5th-14th c.) with a different epistemology
- stolen by Cochin-based Jesuits in the 16th c.
- and falsely attributed to Newton and Leibniz (17th c.)
- neither of whom fully understood the calculus and its infinite series.

- a new way to teach also needed.
- Hence, started teaching courses on decolonised calculus (without limits),
- in India (2009), math students Malaysia (2010), social scientists Iran (2012), India(2012), and engineering students India (2018).
- New way of teaching strongly opposed by formal mathematicians and story of Euclid (article, poster, video)

- Identified an unexamined FALSE history AND a BAD philosophy of science
- as the root cause of continued post-colonial Western academic hegemony
- Anchored a week-long international workshop to design a new curriculum in history and philosophy of science (HPS)
- taught the new decolonised HPS course (see also students' reactions) to several batches.

- Visited Pretoria (UNISA) and spoke on my experiences with decolonising mathematics.
- This talk frightened some White racists in South Africa, one of whom (a professor of math education) wrote
- "Blacks and women are bad at math", and to "decolonise" math,
- one must teach them to think like the dead white men (like "Euclid") who supposedly invented math.

- could not have invented math
- and "Euclid" was anyway a black woman
- as depicted on the cover of my 2012 book Euclid and Jesus.
- Response was published in
*Conversation*, went viral, was reproduced worldwide and then CENSORED worldwide.

- Because, as described in
*Euclid and Jesus*, - the academic issue of lack of evidence for Euclid was settled way back in 2002
- when David Fowler the leading Western authority on history of Greek math admitted
- "'What is known about Euclid?' Nothing."
- Plenty of COUNTER-EVIDENCE that Euclid was a black woman.

- Three types of vested interests.
**White racists**: That Whites are "superior" since they created a "superior" kind of mathematics**Formal mathematicians**: That formal math (= Western ethno-mathematics) is the "superior" way to teach math (as currently taught in our universities)**Church dogma**: Euclid myth essential to post-Crusade church theology of reason.

- Above three vested interests are interconnected
- because racism is about the sense of "superiority" (Christian/White/Western), not primarily about the color of the skin.
- "Euclid" must fall, to destroy that sense of superiority.

- South Africa apartheid rule 1948–1994.
- Segregation 1865–1968).
- Slavery (of Blacks in Americas) 1501–1888.
- Today racism still persists (e.g. "Rhodes must fall", Peter Floyd etc.)

- But, today, I want to discuss something else.
- The belief that the color of the skin
- makes one human being SUPERIOR to another
- is an exceptionally FOOLISH belief.

- Not only common people but top Western intellects (e.g. Kant and Locke, and numerous others) accepted this foolish belief.
- Whole systems of ethics, law, and governance in the West were based on this foolish belief for centuries.
- Why were racists collectively and individually so foolish?
- Western scholars have never asked this question. Why not?

- And that sense of superiority, NOT color of the skin, is at the core of racism.

- In the West, the church is the key source of superstitions.
- E.g. the Bible Defence of Slavery involved the superstition
- that black color of the skin is due not to heat of the sun but
- due to the curse of the Christian god (curse of Kam).

- Question needs to be broadened.
- Not appropriate to study slavery alone
- Must study Genocide + Slavery
- ("Age of Enlightenment" should correctly be called "Age of Genocide+Slavery"!)

- And inappropriate to treat the genocide of "Red" Indians as separate from
- the genocide of the Maya, the Inca, the Aztecs
- (or the genocide of the Australian aborigine).
- Principle of "Occam's razor" or "simplicity of causes".

- Genocide (of indigenes) provided the free-of-cost land
- Slavery provided the free-of-cost labor
- (in Australia convicts were used instead).
- Genocide + slavery the basis of Western wealth.

- In the 15th-16th c., church morality still the dominant morality for Europeans.
- However, the church thought it moral TO DEMAND genocide or enslavement of all non-Christians.
- Bull Romanus Pontifex orders that all non-Christians should be killed or enslaved.
- And papal bull Inter Caetera declared non-Christians lost the right to land on being "discovered" by Christians (as upheld by US Supreme court).

- As described by Las Casas (who accompanied Columbus in his second voyage 1493)
- the subsequent genocide ("boil there you offspring of the devil" etc.)
- was a religious hate crime (his initial estimate 10 million killed).
- The criminals thought they were being "moral": only imitating what their Christian god would do in hell.

- In the 15th and 16th c. genocide and slavery were justified using Christian RELIGION.
- No mention of race anywhere.

- Q. What came first? Whiteness or slavery?
- A. Sense of superiority based on church dogma
- that Christians are "superior" and OUGHT to kill or enslave non-Christians.
- since initial "moral" ground for enslaving Africans was that they were non-Christian.

- after the trans-Atlantic slave trade
- when many Black Africans converted to Christianity.
- It was then that the "curse of Kam" was highlighted to
- declare Blacks as "inferior" Christians.

- Because church Inquisitors had earlier used the technique of quick visual cues
- such as adherence to Moorish dress
- to spot heretics or suspect Christian converts among Moors
- and use that to subject them to physical tortures.

- hence Immanuel Kant uses a different "secular" justification for his recommendation to whip Blacks
- he echoed Hume that "Blacks are not creative".
- Q. But would Kant/Hume have used this argument
- if they believed George James?

- (not literally that Aristotle plagiarized from the Great Library of Alexandria)
- but that Greek philosophy is derived from Egyptian
- due to TRANSLATIONS from Egyptian (and Persian) to Greek in Ptolemaic times
- and/or later-day APPROPRIATIONS by motivated racist historians (e.g. Bernal,
*Black Athena*) etc.

- E.g. no primary sources for Archimedes
- and a 16th c. scientific text reflects 16th c. scientific knowledge (scientific texts are updated)
- Too big an issue to cover in this talk (see my 5 Pretoria lectures on "Not out of Greece").

- From the 5th c., when the church first incorporated the myth of Christian superiority into its dogma
- it also created a secular justification for the myth using false history (Orosius,
*History Against the Pagans*). - This trick of systematically false history went ballistic during and after the Crusades
- when a false history of SCIENCE was concocted.

- because Muslim Europe was scientifically FAR ahead of Christian Europe.
- Hence, the church appropriated all scientific knowledge in Arabic texts
- made it theologically correct by the easy trick of attributing its origin to early Greeks.
- Why early Greeks? Because Eusebius declared them as the sole "friends of Christians". So, this made it a Christian inheritance.

- Zero evidence for "Euclid" (no primary Greek text with his name in it)
- "Euclid" (= Uclides= aql-i-des = rational geometry) a possible subtitle
- Plenty of counter-evidence.
- But "Euclid" was appropriated for reasons related to church dogma
- (will return to that later).

- saw a corresponding adjustment in the false history.
- Greeks were now portrayed as Whites (as they still are)
- rather than "friends of Christians".

- Need to expand the question beyond genocide+slavery
- to include also colonialism.
- Du Bois, in his Dark Princess, realized that the colonized were equally oppressed
- and dreamt of freeing the oppressed by uniting them against the oppressor.

- and the collapse of the fake-dream of a unipolar world after the end of the Cold War,
- given the rise of China,
- Du Bois's dream is no longer a romance but now seems a realistic possibility.
- False history a key element of both racist and colonial claims of superiority (e.g. Macaulay)

- Wild conjectures about the Aryan race grew after
- William Jones' 1786 linguistic observations.
- Led to the belief that colonized were of the same race (mythical "Aryans") as the colonizer.
- Therefore, claim of racist superiority mutated into a claim of civilizational superiority.

- Orosian model and Crusading model not the only two models of systematically false history due to the church
- e.g. Byzantine Greek translation of Syriac work of Ibn Shatir available in Vatican library
- attributed to Copernicus who merely translated it into Latin (with errors).
- But big story of "Copernican revolution".

- E.g. discovery of calculus attributed to Newton and Leibniz as first "Christian discoverers"
- Though e.g. infinite "Leibniz" series well known in India from centuries earlier
- was transmitted by Cochin-based Jesuits
- and my epistemic test shows that neither Newton nor Leibniz understood calculus.

- False history results in bad philosophy
- as in Kant's "ethical" conclusion that Blacks (since "not creative"), should be whipped into silence.
- To bring out how obnoxious is this conclusion, let us ask
- Should Kant's followers be whipped into silence?

- This false myth not confined to WHO is the author of a particular book (Elements)
- Amazingly, this false myth is also about the CONTENTS of that book.
- On the myth, the book first gave axiomatic proofs in geometry.
- But the book Elements does NOT have a single axiomatic proof.

- An axiom = postulate = assumption
- NOT 'a self evident truth'. (No such thing.)

- A sequence of propositions in which
- each proposition is either an axiom
- or is derived from preceding propositions by some 'rule of reasoning'
- such as Modus Ponens (\(A,~ A \implies B, ~\therefore B\)).

- An axiomatic proof EXCLUDES use of facts or observations, or anything empirical
- That is, it EXCLUDES
- "A is a fact, hence A" or
- "I observe A, hence A".

- Hence, axiomatic or FORMAL reasoning (reasoning MINUS facts)
- differs from NORMAL (or scientific) reasoning used worldwide (reasoning PLUS facts).

- E.g. 5th c. Aryabhata said (Gola 6) that the earth is round (like a Kadamba flower).
- 8th c. commentator Lalla explained (शिष्यधीवृद्धिद 20.36) this is INFERRED from the FACT (not axiom)
- that far off trees cannot be seen
- (and the observation that the horizon is circular).

- From
*Yuktibhasa*(see e.g. my 2001 article in Philosophy East and West - involves drawing a diagram on a palm leaf
- cutting, (rigidly) moving, and superposing (all empirical processes)
- to OBSERVE that the two areas are equal.

- E.g. in the
*Yuktibhasa*the "Pythagorean" proposition is the FIRST proposition - not the LAST (or second-last) proposition as in the
*Elements*. - On the "Euclid" myth, Euclid's primary contribution was to the arrangement
- or the ORDER of propositions in the Elements (so that the proof of each proposition depended only on the preceding).

- This myth repeated in e.g. foolish Cambridge exam regulations (toward end of 19th c.)
- for the Previous and Local examinations.
- Why do I call this foolish?
- Because, no one read the book. There are NO axiomatic proofs in the
*Elements*! - (And the prescribed Cambridge text had all empirical proofs!)

- Not of the first proposition (we OBSERVE the two arcs intersect, but no axiom for it)
- Not of the last (or second-last, Pythagorean proposition)
- whose proof depends on Prop. 4 (SAS)
- proved empirically by SUPERPOSING one triangle on top of another and OBSERVING the two are equal.

- If you don't believe me, and haven't read or won't read the book,
- like ALL Europeans failed to carefully read this prescribed text
- or even its first proposition for some 750 years,
- here is the "colonial proof" (what Western authorities have to say).

- Richard Dedekind (1878) tried to "correct" proof of Prop. 1, using axiomatic "Dedekind cuts" (formal real numbers).
- Bertrand Russell wrote: the proof of Prop. 4 is a "tissue of nonsense".
- David Hilbert 1898-99 wrote a whole book on Foundations of Geometry (English trans. 1950)
- to provide the axiomatic proofs missing in "Euclid" (and missing axioms).

- e.g. Hilbert's geometry is synthetic — no length measurement allowed.
- Those interested in further mathematical details, please join my geometry workshop next month.
- Today, my talk concerns racism and the related underlying political claim
- of a civilizationally "superior" form of mathematics — axiomatic mathematics.

- NEITHER of which exists,
- but which false claims of "superiority" are still being peddled
- by "reputed" Western historians such as Needham, Gillings, and Clagett.

- and utter disregard of easily verifiable facts
- publicly admitted over a century ago
- ("no axiomatic proofs in the actual Elements")
- entitles them to the title of Greediots!

- Recall that Cheikh Anta Diop pointed out that
- the that the Ahmes ("Rhind") papyrus (e.g. problem 41), etc.
- has the right formula for the volume of a cylindrical granary
- \[V = h \left(d - \frac{d}{9} \right)^2 = \frac{256}{81}r^2 h \approx 3.16 \cdot r^2 h \approx \pi r^2 h. \]

- but on accretive secondary sources from 16th c. with no clear connection to Archimedes.
- But Lefkowitz asserts in
*Not out of Africa*(p. 153) - "Archimedes determined that the volume of the cylinder was \(\frac{3}{2}\) the area of the sphere"
- (Comparing volumes and areas! 🤣, 🤣 and based on 16th c. texts.) But let us get back to the story.

- But they still accepted the SUPERSTITION that axiomatic proofs are "superior"
- (they all tried to provide such axiomatic proofs).

- "superior" for what purpose? to whom?

- During the Crusades the church suddenly switched to Christian theology of reason
- of Aquinas and the schoolmen.
- Why?
- Crusades aimed to convert Muslims by force
- the way "pagans" in Europe were earlier converted to Christianity by force.

- Further, Muslims could not be converted using the Bible which they rejected as corrupted.
- But Muslims then accepted reason
- as in Islamic rational theology (aql-i-kalam)
- advocated by Averroes (Ibn Rushd)

- We have seen how: by giving reason a Greek ancestry (since no mention of reason in Bible)
- But why? Isn't reason against church superstition?
- NO. Facts go against church dogma, not reason alone.
- Hence, the church accepted reason MINUS facts (formal reason).
- Starting point of reasoning would be an axiom or assumption NOT a fact.

- many angels can fit on a pin.
- Starting from the AXIOM that angels occupy no space
- since no FACTS about angels.
- Anything convenient can be authoritatively assumed to "prove" whatever one wants.

- Formal reasoning was read into Euclid (and that hid this tricky church invention).
- This was a brazen misreading, since NO formal proofs in Elements.
- But the book is full of figures which are "not rigorous" (Dedekind) and "logically worthless" (Russell)

- because it served the Crusading church's political purposes,
- but formally proved theorems not PRACTICALLY superior.
- Unfortunately, many people have the "it works" superstition that formal math "works".

- E.g. Egyptians built pyramids before formal math.
- You purchase your every-day groceries without knowing the formal proof of 1+1=2
- ab initio proof in real numbers (my Cape Town challenge, not met by anyone yet).
- For practical purposes (such as calculation of rocket trajectories today) what is used is still normal math of inexact calculation.

- E.g. "real" numbers deemed essential for formal math of calculus (as taught in universities)
- But trajectory calculations for rockets done using computers, which uses floating point numbers, NOT real numbers.
- [Calculus made simpler and better using Indian "non-Archimedean" arithmetic
- but math axioms for university teaching laid down solely by Western authorities (even in China).]
- Trick is to plant a superstition and make you obedient to and dependent on Western authority.

- E.g. even associative law for addition fails for floats.
- E.g use of "Pythagorean" theorem for European longitude problem, was A LIABILITY
- led to huge navigational disasters until the 18th c.
- (Problem recognized by governments: e.g. British parliament's longitude prize of 1713.)

- that "Pythagorean" theorem fails for navigation because of sphericity of earth
- as explicitly stated by Bhaskar 1 (7th c.) Mahabhaskariya II-5 (trans.)
- But calling the "Pythagorean" theorem an "approximation" is an inadequate defence
- "Approximation" worthless without error bounds (not available with the "exact" theorem)
- and which error bound require accurate knowledge of radius of the earth (unknown to Europeans until late 17th c.)

- Difference? "Pythagorean" CALCULATION (needed even for European navigation) requires knowledge of square ROOTS
- unknown to early Greeks, but known to early Egypt, Iraqis, and Indians.
- Note that calculation of \(\sqrt 2\) involves infinite series hence forever INEXACT.
- Practical value of math is all based on normal math of inexact CALCULATION, not theorem-proving.

- Reason given for rejecting empirical proofs is that they are fallible. True.
- But the related claim that "deduction is infallible" is a mere superstition.
- As any math teacher knows students err often and submit many wrong proofs.
- Authorities too have erred and published many wrong proofs (e.g. of Fermat's last theorem) etc.

- because human mind errs more easily than human senses.
- E.g. game of chess is an exercise in pure deduction
- if neither side makes an error, it must end in a draw.
- But, EVERY human being, makes an error in deduction almost EVERY time, hence loses to a computer.

- (because assumed axioms are not true in the real world).
- We have seen the example of the Pythagorean theorem.
- Another example is the Banach Tarski theorem of set theory based on the axiom of choice.
- In fact, any nonsense proposition
*whatsoever*can be proved as a formal theorem by selecting the axioms appropriately.

- Church said "logic binds god" who can create the facts of his choice, but not an illogical world.
- Therefore, it is believed that facts are "contingent" truth (true in some (Wittgensteinian) worlds),
- while the relation of axioms to theorems is a "necessary" truth (true in all worlds).
- This parochially assumes 2-valued logic used in formal math. But apart from axioms, logic too can vary.

- Logic NOT culturally unique (e.g. Buddhist catuskoti, Jain syadvada)
- If logic decided culturally, mathematical theorems are relative cultural truths.
- Logic NOT empirically unique (quantum logic, as the logic of structured time).
- If logic decided empirically, hence inductively, deduction already weaker than induction.

- Genocide and slavery were first mandated by the church (papal bulls Romanus Pontifex and Inter-Caetera),
- accepted also by Protestants and the US Supreme court till today.
- The underlying dogma of extreme Christian superiority (from 4th c. CE)
- was justified using false history (5th c.), and a false history of science (12th c., onward)

- Hold the church responsible for genocide + slavery.
- Join the indigenes to condemn the church and
- demand that the church recant publicly,
- and ban it from giving moral advice for at least another 500 years.

- Recognize that false history (of Greeks, and science) is a centuries-old church con-trick
- it is the basis of false claims of superiority used to support racism.
- To overthrow it INSIST on real primary sources for history.
- Learn to distrust Western authority and Wikipedia.

- Use non-textual evidence to cross-check bloated claims based on corrupted texts.
- Start your own courses in History and Philosophy of Science in every country.

- Euclid is an important symbol of the false history of math concocted during the Crusades.
- Total falsehood. Euclid did NOT invent axiomatic proof. NO axiomatic proofs in the book attributed to him.
- Axiomatic reasoning (reasoning from assumptions instead of facts) an invention of Crusading church
- very convenient for politics of Christian rational theology
- NOT "superior" in any sense. Formal math has no practical value, no special epistemic value.

- Destroying symbols important but not enough.

- Abandon Western formal math (an instrument to promote White/Western authority)
- Start teaching practical/normal math which makes math easy, as I have demonstrated
- e.g. calculus without limits
- traditional string geometry
- decolonised statistics.

- Colonial education began as church education and massively spreads superstitions
- so all education needs to be decolonised.
- But math and history and philosophy of science first priority because
- false history and bad philosophy of science are used to promote racism
- and colonial math wrongly believed to be "universal" and not in need of change.