Archive for the ‘History and Philosophy of Mathematics’ Category

Astrology in university education – twenty years after

Saturday, September 11th, 2021

(Note: The following article speaks the truth, instead of taking sides. However, the Indian media being totally polarised, I could not publish the article in either English or Hindi. Hence, am now posting it on my blog, since I feel it is important for me to take a stand on the matter.)

Astrology is a superstition, but why are the colonised unwilling to admit that Johannes Kepler was a superstitious astrologer, who got his livelihood from astrology, and wrote in praise of astrology.  And what of Isaac Newton who superstitiously believed in Biblical creationism and apocalypse. His superstitions rubbed off into science and math as in the “eternal laws of nature”, not to mention his superstitions about the Indian calculus, all of which church superstition we happily teach in schools today.  But there is no outrage among the colonised who blindly accept all church superstitions in mathematics and science. That is exactly why it was the church which brought Western ethnoscience and Western ethnomath to the colonised in general and to India in particular. The real issue is about Western dominance, not science vs superstition.

The Indira Gandhi National Open University recently introduced a postgraduate course in astrology. A similar issue had arisen twenty years ago when the University Grants Commission (UGC) announced a scheme to open 16 university departments, to teach astrology across the country, in 2001. This was hugely opposed, and the late Kapila Vatsyayana organized a public debate, between scientists and astrologers, in the India International Centre, on the desirability of astrology in university education. The late Pushpa Bhargava, Raja Ramanna and I represented scientists. But the astrologers ran away from the debate, though I did later discuss this issue publicly with some other astrologers in other forums. The UGC eventually scrapped the scheme. However, some clarifications given 20 years ago are still relevant. First, the term “jyotish”, which means time-keeping (through astronomy), is wrongly confounded with astrology (called “phalit jyotish”). The earlier UGC scheme was announced as pertaining to Vedic astrology. However, there is no mention of astrology in the Veda-s. Then, at the India International Centre, I had challenged the assembled scholars, in front of the international press, to show me a single sentence on astrology in the core text of Vedanga Jyotish.1 No one could do so, and some started asking for my copy of the Vedanga Jyotish, which they had obviously never seen before. The Vedanga Jyotishe is a manual of timekeeping, completely disjoint from astrology. Indians persistently separated astronomy from astrology, which separation is not limited to the Vedanga Jyotish, last updated around -1500 CE. Thus, Nilakantha’s commentary on the Aryabhatiya is dated to +1500 CE.2 During this 3000 year period, there were numerous books written on astronomy in India. These included the Surya Siddhanta, the Aryabhatiya, the Laghu and Maha Bhaskariya of Bhaskar 1, the Brahmasphutasiddhanta of Brahmagupta, the Shishyadhivrddhida of Lalla, Vateshwar Siddhanta, and Gola, Tantrasangraha, Yuktidipika, etc. In none of these books do we find a single sentence related to astrology. The beginning of astrology in India is credited to the 6th c. Varahamihira, and his Brihat samhita, but even Varahamihira’s astronomy book Pancasiddhantika does not have a single sentence on astrology. However the colonially educated are deluded that jyotish means astrology. The same colonial education also impacts nationalists. Hence, they repeatedly return to the claim that astrology was an important aspect of Indian tradition since Vedic times. Twenty years ago, Pushpa Bhargava had challenged the teaching of astrology in the Madras High Court. In response, the UGC had said that astrology was an important aspect of ancient Indian tradition, a claim happily accepted by the judge (Kalifulla J.) Nobody asked for evidence that astrology was a significant part of Indian tradition, and nobody offered it. To the contrary, the Buddha explained3 that common people praise him because he does not earn a livelihood by the unethical means of predicting uncertain future events, such as predicting the victory or defeat of kings in a war, or predicting good or bad rainfall. This was not any specifically Buddhist ethics, since it was the common people (then pre-Buddhist Hindus) who praised the Buddha thus. In contrast, the West traditionally believed in prophecy. Herodotus4 begins his History with the story of Croesus, from Lydia (Turkey), who first made Ionian Greeks his vassals. Before fighting the Persians, Croesus checked the outcome with the Oracle of Delphi. “A great empire will fall” was the prophecy. Unsure about which Empire would fall, Croesus again sent an emissary to ask how long his own rule would last. “Until a mule rules the Medes (Persia)”. Croesus thought that hardly likely and battled Cyrus the Great and lost. The prophecy was then explained that Cyrus  was the mule since he was of mixed descent. Of course, had the outcome been different, there would have been no need for an explanation. This illustrates how foretelling the future was traditionally based on subtle con-tricks. Prophets were given a very high religious status in the West. Hence, during the Crusades, the church tried to put down Muslims by the criticism that Paigambar Muhammad made no prophecy. Unfortunately, the strange response of Muslims to this critique has been to translate Paigambar (meaning messenger) as Prophet! Traditional Western superstitions did not magically disappear with the advent of science. Johannes Kepler, famous for his “laws” of planetary motion, wrote on the fundamentals of astrology.5 Before he grabbed the high church position of Astronomer Royal to the Holy Roman Empire, Kepler was a practising astrologer, and he wrote that providing astrology as a means of livelihood to astronomers was proof the of pre-established harmony created by God! Even Isaac Newton superstitiously believed in Biblical creation, some 6000 years ago. He explicitly used it to deny the antiquity of Egypt.6 He also believed the Bible correctly foretold the future apocalypse of the world at the “seventh trumpet”.7 Indeed, belief in prophecy, or the belief that the future can be foretold, persists in the scientific belief in the mechanistic evolution of the world according to some “eternal laws of nature”. This belief in “eternal laws of nature” is a Christian dogma first propounded by Thomas Aquinas.8 This dogma, is not, for example, acceptable in Buddhism,9 or Islam,10 or Hinduism.11 But, both Newton and Kepler believed in this dogma, and we teach it in our schools today.12 This dogma asserts that the future is determined and predictable by the knowledgeable, like prophets and Laplace’s demon. (On Karl Popper’s formulation, Laplace’s demon is a super-scientist, who knows all the laws of nature, a super-observer, and a super-computer, who can hence calculate the future.13) Of course, no one knows how the “laws of nature” or equations of physics (supposedly) causally determine human actions, any more than anyone knows how planets determine human actions. So, the difference between the demon and astrology is a matter of technique, not of principle. The colonially educated believe Indians were especially superstitious. But the experimental method was used in India, long before Bacon,14 and many traditional Indian astronomers spoke out against superstition. For example, it is said that Indians believed that Rahu  and Ketu are the cause of eclipses. This myth is undoubtedly found in the Purana-s. However, the eighth century Lalla titled the 20th chapter of his Sisyadhivrdhida15 as the “Correction of mythical knowledge”. Here he gives several arguments why demons such as Rahu, cannot be the cause of an eclipse. In the 26th sloka he says “In a solar eclipse, people in different parts (of the earth) see different portions of the Sun eclipsed. Some do not see (the eclipse) at all. Knowing this, who can maintain that an eclipse is caused by Rahu?” Further, Lalla (20:22) asks why eclipses occur only near the full moon or new-moon. In contrast, the Bible (Luke 23:44-45) states the superstition that God caused a solar eclipse at noon on the crucifixion of Jesus, which is impossible, because Easter, or the supposed date of resurrection of Jesus, is linked to the full moon when a solar eclipse is impossible. Before the 19th c., which Western astronomer rejected this Biblical assertion as a superstition? The conclusion is that scientific thinking is a much older part of Indian tradition than astrology which was probably imported in the 6th c., and true nationalists ought to encourage that older tradition. On the other hand, church superstitions still flourish in science (and math) and the tail-wagging colonised who believe science is a matter of Western approval, not critical thinking, need to understand that.

1K. V. Sarma, ed., Vedanga Jyotisa of Lagadh, trans. & notes T. S. Kupanna Sastri (New Delhi: INSA, 1985).

2K. Sambasiva Sastri, ed., Aryabhatiya of Aryabhatacarya with the Bhasya of Nılakanthasomasutvan (University of Kerala, Trivandrum, 1930).

3Maurice Walshe, trans., Digha Nikaya: Long Discourses of the Buddha (Boston: Wisdom Publications, 1995), 68–72 Brahmajala sutta, section on Mahashila.

4Herodotus, The History, trans. G. C. Macaulay, n.d., https://www.gutenberg.org/files/2707/2707-h/2707-h.htm.

5J. Bruce Brackenridge and Mary Ann Rossi, ‘Johannes Kepler’s on the More Certain Fundamentals of Astrology Prague 1601’, Proceedings of the American Philosophical Society 123, no. 2 (1979): 85–116.

6Isaac Newton, “Chronology of Ancient Kingdoms amended”, https://www.gutenberg.org/files/15784/15784-h/15784-h.htm#chapII.

7C. K. Raju, The Eleven Pictures of Time: The Physics, Philosophy and Politics of Time Beliefs (Sage, 2003) chp. 4, ‘Newton’s time’.

8Thomas Aquinas, Sumnma Theologica, First part of the second part, 91,1, n.d., http://www.newadvent.org/summa/2091.htm.

9C. K. Raju, ‘Buddhism and Science’, 2016, https://youtu.be/SkS1HM6g0O4, a conversation with the Dalai Lama.

10C. K. Raju, ‘Islam and Science’, keynote address, in Islam and Multiculturalism: Islam, Modern Science, and Technology, ed. Asia-Europe Institute University of Malaya and Japan Organization for Islamic Area Studies Waseda University, 2013, 1–14, http://ckraju.net/hps-aiu/Islam-and-Science-kl-paper.pdf.

11Minutes of a meeting in the University Sains Malaysia, 2011, to discuss whether the belief in “laws of nature” should be part of a course in the philosophy of science. http://ckraju.net/usm/Psc-minutes.html.

12See, e.g., the 2021-22 NCERT text on science for class IX, chp. 10, p. 133. http://ckraju.net/papers/presentations/images/NCERT-class-IX-science-chp-10..pdf

13For Laplace’s demon see C. K. Raju, Time: Towards a Consistent Theory (Springer, 1994).

15For a general account, see “Indians against superstition”, extract from “Proofs and Refutations in Mathematics and Physics: an Indian Perspective”, in History of Science and Philosophy of Science, ed., P. K. Sengupta, Pearson Longman, 2012. For the original source see Lalla, ‘शिष्यधीवृद्धिद’, ed. Bina Chatterjee (Delhi: Indian National Science Academy, 1981).

“Euclid” must fall: racism, the church, and the axiomatic method (collected resources)

Friday, July 2nd, 2021

(Keynote Tübingen/Pretoria 13 May 2021. Related articles now online.)

Video: https://www.youtube.com/watch?v=kAP1BcK8mLE

Presentation: http://ckraju.net/papers/presentations/Euclid-must-fall.html

Articles:

Part 1: Racist prejudice and the false history of “Greek” achievements in math and science

Abstract.To eliminate racist prejudices, it is necessary to identify the root cause(s) of racism. American slavery preceded racism, and was closely associated with genocide. Accordingly, we seek the unique cause of the unique event of genocide + slavery. This was initially justified by religious prejudice, rather than colour prejudice. This religious justification was weakened when many Blacks converted to Christianity, after the trans-Atlantic slave trade. The curse of Kam, using quick visual cues to characterize Blacks as inferior Christians, was inadequate. Hence, the church fell back on an ancient trick of using false history as secular justification for Christian superiority. This trick had resulted in a false history of science during the Crusades when scientific knowledge in translated Arabic texts was indiscriminately attributed to the early Greeks, without evidence. This false history enabled belief in religious superiority to mutate into a secular belief in White superiority. After colonialism, and the Aryan race conjecture, the belief in White superiority further mutated into a belief in Western civilizational superiority, openly propagated today by colonial education. Hence, to eliminate racist prejudice, it is necessary to engage simultaneously with the allied prejudices about Christian/White/Western superiority, based on the same false history of science.

Full article at: http://ckraju.net/papers/Tubingen-Pretoria-part-1.pdf

Part 2: The practical failure (and political success) of the axiomatic method (or the church understanding of reason) in math

Abstract. Previously we saw that racist prejudice is supported by false history. The false history of the Greek origins of mathematics is reinforced by a bad philosophy of mathematics. There is no evidence for the existence of Euclid. The “Euclid” book does not contain a single axiomatic proof, as was exposed over a century ago. Such was never the intention of the actual author. The book was brazenly reinterpreted, since axiomatic proof was a church political requirement, and used in church rational theology adopted during the Crusades, as a counter to Islamic rational theology. Deductive proofs are MORE fallible than inductive or empirical proofs. Even a validly proved mathematical theorem, such as the “Pythagorean” theorem (based on Hilbert’s axioms, say), is invalid knowledge in the real world. There is no concept of approximate truth in formal mathematics. Nevertheless, the myth of “superior” axiomatic proofs in the “Euclid” book continues to be reiterated by Western historians, and colonial education teaches axiomatic mathematics. Actually, superior practical value comes from the two “Pythagorean” calculations well known to Indian/Egyptian tradition, but unknown to Greeks. The advantage of related decolonized courses in mathematics has been pedagogically demonstrated. But understanding and political will is needed to change colonial/church education.

Full article at: http://ckraju.net/papers/Tubingen-Pretoria-part-2.pdf

Alternative to current school teaching of Christian chauvinist “Euclid’s” geometry

“Euclidean’ geometry vs Rajju ganita” Bengaluru, 5, 6 June 2021)

Details of workshop: http://ckraju.net/blog/?p=200

Prior reading list: http://ckraju.net/geometry/Reading-list-geometry-rev.pdf.

Presentations: Day 1, Day 2 (space bar moves to the next slide)

Videos: Day 1, Day 2 (2:45:55, and 2:55:59)

School text for class IX: http://ckraju.net/geometry/Rajju%20Ganita%20cover-front-back-r.pdf

See also, Euclid and Jesus: How and why the church changed mathematics and Christianity across two religious wars, Multiversity, Penang, 2012.

“Euclidean” Geometry vs Rajju Ganita

Tuesday, June 8th, 2021

All the lies and obscurities of “Euclidean” geometry, as taught in the NCERT class VI, IX, and X school texts, stand exposed in these presentations and videos of the workshop held on 5 and 6 June 2021.

Presentations: Day 1, Day 2 (space bar moves to the next slide)

Videos: Day 1, Day 2 (2:45:55, and 2:55:59)

Both “Euclid” and the related philosophy of “superior” axiomatic proof are just a church fraud concocted during the religious fanaticism of the Crusades, to provide support for Christian theology of “reason” set up by Aquinas and the schoolmen.

Sad that Indians have been fooled for 2 centuries, and refuse to think. This incapacity is a design objective of colonial/church education. Sad that the top formal mathematician in the country and abroad are running away from public debate in the manner of fraudulent astrologers: they have no concern for truth or for the future of children.

Rajju Ganita or traditional Indian/African string geometry is so much better.

Rajju ganita cover

Rajju Ganita workshop Bengaluru, 5-6 June 2021

Friday, May 21st, 2021

UDHBHAVAHA

brings you

SHOULD OUR SCHOOL CHILDREN LEARN

“EUCLIDEAN” GEOMETRY OR RAJJU GANITA?

By

Prof. C.K RAJU

A 2-day workshop to discuss:

(1) The falsehoods and obscurities in “Euclidean” geometry, as currently taught
(2) Why Indian śulba (string) geometry is a better way to teach geometry.

DATE: 5th and 6th June, 11AM to 1PM

Who can attend: Math Teachers, Home schoolers, anyone curious and interested in a new perspective on Ganita

Prerequisites : Participants are expected to have read the geometry sections in NCERT math texts (available online) from class VI to class IX. They should also attempt the home assignment at this link. For a further reading list see here.

Registration : Click Here

Poster

“Euclid” must fall

Friday, May 14th, 2021

To access the presentation for my zoom talk on ‘”Euclid” must fall’, described in the previous post, click the image below.
Euclid fallen

A video of the recording premieres on 23 May 2021 at 12 noon IST.

‘“Euclid” must fall’. Keynote: Tübingen/Pretoria 13 May 2021

Wednesday, May 5th, 2021

The keynote is on the origin of the excessively foolish, but persistent, belief in racist superiority, AND its cure. Here are the details of the International Colloquium and an extended abstract. The times in the program are German times.

How does this concern Indians? Because the colonial myth of civilizational superiority of the West mutated from the myth of racist superiority of Whites. Both myths are based on essentially the same false history of science and mathematics. We still teach that false history of science to our schoolchildren, under colonial influence. See the chapter 5 on “Introduction to Euclid’s geometry” in the class IX NCERT school math textbook.

Euclid and Jesus coverDespite an enormous amount of secondary literature, there is no primary evidence for the existence of “Euclid”, or that he, or any person or group near his purported date, was the author of the text attributed to him, or that the author was a white male, as shown in our school texts (or Wikipedia etc), or that the text was written for remotely the purposes attributed to “Euclid”. (My challenge prize of Rs 2 lakhs for such primary evidence has been standing unclaimed for the last ten years.) But our government has laid down that, for Western history, we must follow the Wikipedia “standard” that SECONDARY Western (or Western-approved) sources MUST be regarded as definitive proof, because the colonized have no right to demand primary evidence for the master’s tales.

Indian historians seem to have implicitly accepted this historical “principle” of differential evidence, for there was never any hullabaloo regarding false Western history in Indian school texts. Indeed, in two centuries no one else ever checked even the blatantly false and propagandist history of science used by Macaulay, though we changed our education system based on it. Cross-checks will not happen in the near future either, for there are no serious historians of science in any of our numerous university history departments. (It is necessary to emphasize publicly this persistent and collective failure of our historians, because in these time of a Corona tidal wave no one can be sure how long they will last, so if the bitter truth is not stated now it may never be stated.)

“Euclid” (= Uclides = aql-i-des = rational geometry) is a Christian chauvinist myth concocted by the Crusading church in the 12th c. The myth of Greek origins of all science was first used to appropriate all scientific knowledge in Arabic texts to early Greeks. The Crusades failed because Christian Europe was far behind Muslim Europe in scientific knowledge, badly needed even for a religious war. But the church also required an excuse to appropriate it, since the church had earlier declared all non-Christian books as heretical. Attributing the origin of that knowledge to Greeks made it a theologically correct Christian inheritance, since Eusebius had declared early Greeks as the sole “friends of Christians”.

The same trick was later used for a purpose more vital to the church—to support its sudden theological shift to Christian rational theology (set up during the Crusades to compete with Islamic rational theology or aql-i-kalam), by giving “reason” a false Greek origin, to appropriate reason as a Christian inheritance. Note that the fake history of “Aristotle” (of Toledo, not Stagira) alone1 was not enough to appropriate the kind of “reason” the church needed, since “Euclid”, or rather the brazen church “reinterpretation” of the book falsely attributed to him, provided the sole purported example of axiomaticreasoning prior to the Crusading church. Since then, the “Euclid” myth was used to dodge the reality that such peculiar metaphysical reasoning was actually an invention of the crusading church for its political gain.

The world-over everyone used normal reasoning based on facts, as e.g. in India in the Nyaya, Buddhist, or Jain syllogisms. But Christian rational theology used a special type of reasoning, called formal (or faith-based) reasoning, which began from (faith-based) axioms, rather than facts, because facts are so often nakedly contrary to church dogmas. An example is Aquinas’ axiomatic reasoning about angels (which don’t exist, in fact), to deduce that many angels can fit on a pin, in his Summa Theologica. However, most people confound normal reasoning (based on facts) with formal reasoning (why bypasses facts, and is based on faith in axioms), because of the church doublespeak of using only one word “reason” for both.

The Western claim that axiomatic reasoning is a “superior” form of reasoning is a mere church superstition, which glorifies church metaphysics. However, this claim of a “superior” form of reasoning is critical to the claim of civilizational superiority. Hence, even though it has been publicly exposed, over a century that the book, purportedly authored by “Euclid”, does not contain a single axiomatic proof, from its first proposition to its last, even supposedly responsible historians like Needham keep regurgitating this false myth of axiomatic proofs in “Euclid”, as proof of Western civilizational superiority.

And, of course, this myth of axiomatic proofs in “Euclid’s” book is repeated in our school texts, because of our differing standards of history, that for Western history we must blindly trust Western authority, and that no one should actually read an easily available book, imitating Cambridge dons who foolishly avoided reading the book carefully for over 750 years until the end of the 19th c.

Today, the myth of civilizational superiority is used to promote axiomatic mathematics as a “superior” type of mathematics, involving “infallible” deduction, though it is trivial to show that axiomatic deduction is highly error-prone, and, of course, even valid deduction need not result in valid knowledge, since any desired nonsense proposition whatsoever can be proved axiomatically as a theorem, by suitably selecting the axioms, as Aquinas did.

The axioms of mathematics (such as those of set theory) are a pure metaphysics of infinity (aligned to church dogmas of eternity), which are empirically irrefutable. They result in nonsense mathematical theorems such as the Banach-Tarski theorem that one ball of gold can be subdivided and reassembled, without stretching, in to two balls of gold identical to the first. These unrealistic theorems are then defended by further metaphysics such as “measurability” which few understand.

The axioms are to be accepted solely on the strength of Western authority: e.g. calculus must be taught using formal “real” numbers, not the “non-Archimedean” arithmetic and the normal mathematics with which the calculus originated in India, and as I teach it. All practical value (e.g. calculation of rocket trajectories) still comes from normal mathematics: e.g. calculation of rocket trajectories is today done on computers which cannot use formal real numbers, declared essential for calculus, but use floating point numbers instead, which are quite different. Similar remarks apply to AI.

Unlike the claim of racist superiority, which is firmly rejected by Blacks, the closely related claim of civilizational superiority, especially in mathematics and science, has been accepted and internalised by the colonized today, who rush to defend it, typically by abusing the critic. They resort to abuse because so few (none to my knowledge), even in our premier universities, understand or can state even the axiomatic proof of 1+1=2 in formal real numbers, for which I offered a reward of Rs 10 lakhs in JNU. Surprisingly, not a single faculty member in our premier university claimed this reward, or even the reduced reward of Rs 1 lakh offered for the full proof of 1+1= 2 in real numbers, if given in a week’s time.

The cure, as I stated in my censored article, which was censored worldwide, is to stand up to the false history AND bad philosophy of mathematics, at the base of the secular justification for the claim of religious/racist/civilizational (Christian/White/Western) superiority.

Anyone interested in attending the meeting may please get in touch with me or the organizers.

1The published version of this article on logic in the Springer Encyclopedia has gathered some gross gratuitous errors because of the reflexive and unilateral application of this false history by the editor/publisher: e.g. Organon dating factually to the Crusading time of 12th c. CE, has been dated by Springer to 12th c. BCE! 😀

Ganita vs formal math: an obituary of formal math

Wednesday, May 5th, 2021

Ganita vs formal math: an obituary of formal math

This is a video recording my concluding seminar (25 March 2021) as a Tagore Fellow at the Indian Institute of Advanced Study.

Twitter summary:
1. Ganita (गणित) differs from (formal) math,
2. it makes math easy, and
3. makes science better.
4. This is an obituary of formal math.

Slogan formulation
Formal math is dead,
long live normal math (गणित)

Detailed “abstract” (synoptic contents etc.) in three layers..

Presentation.

Best run on site (without downloading). Space bar moves presentation forward. Blue text indicates hyperlinks (for those who would like to examine the briefly displayed material in detail).

The first step to cure racism

Monday, June 8th, 2020

(In response to a post asking about the possible cure for racism, by Ron Eglash on the Isgem mailing list (International study group on ethnomathematics)

Well Ron,

Let us ask what we and Isgem, in particular, can do about it.

The false sense of racist superiority was created and is supported by false church and racist history, and the appropriations of Egyptian and other achievements to Greeks, as articulated by James, Diop, Bernal, various Afrocentrists (and me). But how to correct this and bring the correction to the “mainstream” schools and universities?

The problem is that the Western academic world is still living in the era of the medieval church, and imagines it can continue to control “valid” knowledge through pre-censorship (secretive “peer review”) and censorship in the name of “quality”, while constantly avoiding transparent public debate to try to preserve its falsehoods.

You might recall my censored article “Was Euclid a black woman?” which was censored by a racist editor of Conversation, in South Africa, and then worldwide, because racists in South Africa were enraged at the thought of their pet fantasies being challenged. The article was later reproduced as part of another article: “Black thoughts matter: Decolonised math, acdemic censorship, and the “Pythagorean” proposition” in Journal of Black Studies and also in Rhodes Must Fall (Oxford), Zed books.

It is a very silly idea to imagine that “valid knowledge” can be decided by some semi-literate White editor or reviewer sitting in judgment of a knowledgeable counter-opinion, without any detailed public response. As explained in my booklet Ending Academic Imperialism, the simple alternative in the digital age is to have post-publication public reviews, which are NOT anonymous.

That is, one simple way to eliminate the numerous falsehoods responsible for continued racism is to allow open debate, and replace the present archaic academic system.

While the Isgem mailing list is open, the Isgem journal Mathematics and Culture  follows similar regressive academic practices, and, for example, refused to publish my views on Euclid, though no one so far has come up with a single counter-point, or claimed my Euclid challenge prize for serious evidence about Euclid. That was just another attempt to preserve prejudices spread by racist and church falsehoods in the name of “quality control”. I never submitted anything to that journal again.

Incidentally, for a recent review of the issue see the blog post: Greediots and Pythagoras. 3: Was Euclid a black woman? The term “Greediots” is in response to the term “pyramidiots” invented by Gillings: it refers to people who believe without serious evidence that much science and math was invented in early Greece, though the early Greeks were bad even at basic arithmetic, as my censored article emphasized.

And look at the ridiculous “quality”that has resulted from this method of knowledge control called “quality control”.

Greek history for idiots: Greediots and Pythagoras. 1: No axiomatic proofs in Greek math.

See, also, part 2 of the blog on the foolishness of the Cambridge University math syllabus.

So, once again, I think the first step is to try to reform universities to abandon this attempt at knowledge control by force of authority. Let us demonstrate an alternative system in Isgem and in math education.

And if it is not done, that leaves only the inevitable alternative of violent overthrow. The US abandoned slavery only after the civil war, it abandoned segregation only after the agitation following the Rosa Parks episode, and abandoned its strong support to apartheid only after it became impossible to sustain that regime. Likewise, it took action against racist police officers for the first time after a sustained violent agitation.

But the situation is changing. The mess in Covid management in the US and Europe (compared to China), and the resulting economic recession has exposed the possibility that the temporary reign of the West is over, and the West is crumbling because of the social disharmony due to the excessively unjust system it set up.

So, the other alternative may be to do nothing and just wait for a few years!Emoji

Did Indian learn trigonometry from Greeks? Responses to the Aryan race conjecture in the African context, and the relevance to Indology

Wednesday, March 18th, 2020

Recently, I presented my talk on “Pre-colonial appropriations of Indian ganita: epistemic issues”. This was at a round table at IIAS Shimla which replaced the now-postponed conference on Indology. My talk was primarily about the inferior math we teach in school today based on the European misunderstanding of the Indian ganita which Europe imported.

Shimla Indology lecture

But as a sidelight, I took up a novel aspect of the Aryan race conjecture. Indologists have so far talked about the Aryan conjecture solely in the Indian context. However, I pointed out the need to link this discussion also to the Aryan race model as it applies to the African context. In particular, to the issue of the Aryan model vs Ancient model as in Martin Bernal’s Black Athena, vol. 1: The fabrication of ancient Greece 1785-1985. (The date of 1785 alludes to William Jones whose philological researches started these wild speculations on race.)

The fabrication of ancient Greece has a direct bearing on the history of Indian math. But first let us understand how racists did it.

Racist history

Bernal’s key point was that after 1785 racist historians systematically rewrote history to appropriate all achievements of Black Egyptians to White Greeks. This aligned with George James’ Stolen Legacy: Greek philosophy is stolen Egyptian philosophy. But instead of philosophy, Bernal applied it, for example, to architecture where the evidence of Greeks copying Egyptians is not easily contested: the so-called Greek architecture of columns is manifestly copied from Egypt and Iran (Persepolis).

Bernal made only scattered remarks on math and science, perhaps out of deference to his father J. D. Bernal, who wrote his famous (but now hopelessly dated) volumes on the history of science. However, after going through my PHISPC volume Cultural Foundations of Mathematics, Bernal (Jr) strongly encouraged me to look at the related issues of concern to the history of math where undue credit has been given to Greeks (as explained in an earlier blog “Greediots and Pythagoras”, which also provides the relevant background to this post).

One point in my above book relates closely to Afrocentrist concerns about undue credit to Greeks in the history of math.

Thus, my point (later summarised e.g. in Is Science Western in Origin?) was that the church falsified history even before racist historians. This process of falsifying history went virulent during the Crusades against Muslims. (Bernal agreed with me here.) The Toledo mass translations of Arabic texts into Latin, beginning 1125, involved learning from the books of the religious enemy. The church, which had earlier consistently burnt heretical books, needed to justify learning from the books of the religious enemy. It provided this justification through the coarse falsehood that all scientific knowledge in Arabic books came from the sole “friends of Christians”, the early Greeks. As such, it claimed that knowledge in Arabic books as a Christian inheritance: and that Arabs contributed nothing to it. Later racist historians modified the church thesis by insisting that the authors of Greek books, even in Africa, were white-skinned, hence claimed it as part of White achievements. The racist historian Florian Cajori is an example of how religious chauvinism was absorbed into racist chauvinism. No evidence exists, and none was needed!

Egyptian and Persian texts were translated into Greek, by Alexander and the Ptolemy dynasty, but any material coming from these texts was all attributed by racist historians to Greeks. Western historians against Afrocentrism, such as Lefkowitz, falsely state that there is no evidence for such translation. As I pointed out in my UNISA lectures, Zoroastrians have been complaining about the burning and Greek translation of their texts for over 2000 years. Western historians rightly assume that their parochial readers would be unfamiliar with those texts. Obviously, also, for the Greediotic brain it is equally easy to imagine (when required) that skin color relates to the language of the text: thus, any Indian author writing in English, such as this one, must be white-skinned! There are no early original Greek sources available, but even if they were a claim of any Greek originality (e.g. on Sphere and Cylinder, attributed to Archimedes), would need proof, since this is also found in the Ahmes papyrus from a thousand years earlier, as pointed out by Diop. Lefkowitz has only some utterly foolish comments to offer claiming that Archimedes compared the area of a cylinder to the volume of a sphere. That is the typical standard of racist historians.

Relevance to Indology

Anyway, the fact is (1) that the Abbasid khilafat in Baghdad made huge investments in knowledge (e.g. Bayt al Hikma), so that, following the knowledge gradient, numerous Arabic texts were translated FROM Arabic into Byzantine Greek (then Constantinople was a tributary of Baghdad). The fact also is that (2) much Indian knowledge travelled to Baghdad, as is well known and as repeated and explained during my talk (e.g. al Khwarizmi’s Hisab al Hind). As stated in the abstract, a striking example of both (1) and (2) is the case of the Panchatantra which was translated from Sanskrit to Farsi to Arabic and then to Byzantine Greek to other European languages as Aesop’s fables. Knowledge of Indian math could similarly have got into late Arabic and Byzantine Greek texts.

So, the question that arises, and was raised in Cultural Foundations of Mathematics, was this: could Indian knowledge have been mis-attributed to Greeks in the process of appropriating Arabic texts to Greeks? Specifically, on the strength of this appropriation, people like Pingree and his students have been clamouring that trigonometry was transmitted from Greeks (“Ptolemy”) to Indians. My question challenged this claim (and Pingree ducked the challenge in 2004 when, on a trip to the US, I directly challenged him to publicly debate the claim).

My counter-points to that claim are the following. (more…)

Greediots and Pythagoras. 3: Was Euclid a black woman?

Wednesday, March 18th, 2020

My point in part 1 and part 2 of this post was that there were no axiomatic proofs among Greeks, and that the cult of Pythagoreans as also the book Elements were both concerned with religious beliefs about the soul linked to geometry. The church reinterpreted the book Elements, to suit its politics. Church education then spread the ridiculous false belief that Euclid’s” book was somehow allied to its theology of reason, which used faith-based reasoning. Colonial education spread these beliefs far and wide.

But the church was hardly the only culprit. Following in the footsteps of the church, this technique of using false history for self-glorification and denigrating the other was later picked up by racist historians.

As a result, our current class IX school text poisons the minds of young children by showing them a racist image of a white-skinned Euclid as does Wikipedia a partner in the crime of racist propaganda.. There is no evidence for even the existence of Euclid (my prize of Rs 2 lakhs for serious evidence about Euclid is still open after a decade) so how did these Greediots know the color of Euclid’s skin? But Greediots will be Greediots!

I shook this equilibrium by arguing to the contrary that the author of the Elements was a black woman as depicted on the cover of my book Euclid and Jesus. Curiously, because of childhood indoctrination, people ask for “evidence” only when one speaks of black skin; these are the very same people who, as children, never asked for evidence and never objected to the depiction of Euclid as white-skinned without the slightest evidence.

Anyway, what is my evidence? How exactly do I know the gender or skin color of the author? Well, all Greek manuscripts of the Elements describe the book Elements as authored by Theon or based on his lectures. (Euclid is never mentioned as the author in any Greek manuscript or commentary, one more nail in the coffin of utterly Greediotic history.) Theon was the last librarian of the Library of Alexandria before it was burnt down by rampaging Christian mobs. Proclus a short while later writes a commentary on the Elements. So, the real author of the Elements must be between Theon and Proclus. (The subject of Egyptian mystery geometry, of course, existed from long before, we are speaking of the author of a particular book on the subject, the Elements.) That leaves Theon’s daughter as the most likely author of the Elements. This is, of course, some 800 years after the purported date of Euclid, and in vastly different social circumstances.

This belief in the gender of the author is further corroborated by the fact that Greek commentaries speak anonymously of “the author of the Elements”, though they mention all others from Aristophanes to Zeno by name. Why the anonymity? Obvious: none else is a woman, and we know that Christians regard women as inferior, and never accepted a woman as a pope. This anonymity further suggests that something terrible happened to the author. Indeed, as is well known Hypatia was raped and brutally killed on the altar of a church.

As the last event demonstrates, changing the author (hence the date) changes the social circumstances. That naturally does change our understanding of the book: a book written in another time and another place would have different motivations.

In accord with Proclus’ stated understanding of the Elements as a religious text intended to arouse the soul, Hypatia was trying to defend her pagan beliefs about the soul through geometry. But this was at a time when those pagan beliefs about the soul were under vicious attack by the church which had demolished every last pagan temple in the Roman empire. Hypatia hence aroused the ire of the church. This atrocious hate crime by a Christian mob led by a hate-mongering bishop was no local rivalry as church apologists maintain: it was part of a dirty religious war waged by Christians against pagans, the first religious war known to mankind.

And how do I know the color of her skin? Well, I go by the standard of “balance of probabilities” for history. The author of the Elements (i.e., Theon’s daughter the 5th c. Hypatia) was from Alexandria in Egypt which is part of the African continent. So, black is the default skin color until proved otherwise. Go ahead, produce contrary evidence for the skin color of the author from the text and I will change my views, provided the remark is not an obviously forged one. And if you can’t produce the evidence for the skin color of the author (and no one has for so many centuries) then accept that I am right. Accept that the depiction of Euclid as a white man is false racist propaganda carried on for centuries.

My reasoning about the author as a black woman writing to defend her religious beliefs is certainly far better than the mere myth that the author was a white male, or the contra-factual claim that the book is about axiomatic proofs, a belief so politically convenient to the Crusading church that it adopted the Elements as a text book to teach faith-based (axiomatic) reasoning to its priests.

At this stage there are those who will jump up to say, as a person did after my talk, that skin color (or gender) of the author does not matter. First the real author does matter, because changing the author changes our understanding of the book from a book about axiomatic proofs to a semi-religious text of little practical importance. But the skin color of the author also matters: else why did my article on “Was Euclid a black woman?” create such a storm in South Africa? Tens of thousands of people found it interesting, therefore it was reproduced worldwide. But then the South Africa editor of the Conversation censored it: she wanted to preserve the false myths of white achievements in math. She exercised her editorial authority to censor it. On the system of blind faith in editorial wisdom, the article was censored worldwide (e.g. by Scroll in India). Why censor it if the skin color really does not matter? (See, Mathematics and censorship.)

At this stage, when racists ;have no arguments to offer, they resort to the church technique of vilification: this requires no academic skill, any dog can bark. The racist press in South Africa and the related church reports in US called me a “conspiracy theorist”. Obviously, their greatest and best formal mathematicians can think of nothing better to do than to serially plagiarise my work. (See this blog on Plagiarism by the President of the Royal Society.) This racist slur of “conspiracy theory” was repeatedly used by another participant in the Shimla round table, as an acknowledgment of his lack of academic skills All the above arguments are a conspiracy theory aren’t they?

And (if skin color really does not matter) are Greediots willing to change the image of “Euclid” children see in our school texts from a white man to a black woman? Will they even try changing it in Wikipedia which is supposedly open to change? Will they openly admit there is no evidence for the white skin of the author of the Elements as they have been falsely peddling for centuries? Like the worm turning, could they even add a comment in Wikipedia about the existence of different opinions? No way! Actions speak louder than words. If skin color really does not matter, don’t just say it, show it with your actions! And if you don’t we know what your true beliefs are for we judge by actions!

The trick to spread these Greediotic and racist lies is to use childhood indoctrination, through education, and reinforce it by propagandist and racist instruments like Wikipedia. Greediots everywhere, evidence nowhere.