Archive for March, 2020

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.

Greediots and Pythagoras. 2: How church/colonial education spreads false myths

Wednesday, March 18th, 2020

As pointed out in the previous blog entry, there are, in fact, no axiomatic proofs in Greek math. But there is a widespread and sticky belief to that effect.

Why is this false belief about axiomatic proofs among Greeks so widespread and sticky? In fact, Western/church education spread the false myth.

Cambridge foolishness

Thus, on (1) that false myth of axiomatic proofs among Greeks, linked to (2) the false myth about the person Euclid and his intentions, (3) the order of theorems in the Elements was regarded as very important, and the key contribution made by “Euclid”.

This third myth was so important that the Cambridge Board of Studies foolishly laid down in its exam rules in the 1880’s that students must follow that order. This Cambridge foolishness is extraordinary because the Cambridge syndics commissioned a new text, which liberally uses empirical proofs, including, of course, the empirical proof of SAS (Side angle Side or proposition 4). Order is unimportant once an empirical proof is used: for instance the Indian proof of the “Pythagorean theorem” in the युक्तिभाषा proves the theorem in one simple step, without needing 46 earlier propositions.

The Cambridge foolishness in insisting on the order of the propositions, while using a text which gives empirical proofs tells us how the education system propagates Greediotic myths for centuries, and teaches students to ignore facts.

Church hegemony over the Western mind

Even Bertrand Russell, as a product of Cambridge, continued to believe in the “Euclid” myth of axiomatic proofs, though he realized the myth did not fit the actual book. He foolishly declared it to be Euclid’s error and not the error of the false myth of Euclid and his intentions!

That is the effect of the church control over the Western education system, and consequent hegemony over the Western mind, including the minds of those opposed to the church. This church “education” from Cambridge widely spreads myths and superstitions, which were then globalised by colonial education. It created “Greediots, Greediots everywhere and not a stop to think”.

A politically convenient reinterpretation

As Proclus explains (and the reason why he wrote his Commentary on the Elements), the Elements is a “pagan” religious text, i.e. a text on Egyptian mystery geometry which is meant to arouse the soul, exactly as Plato argued in Meno. The book Elements was never intended to be about axiomatic proofs. How did “Euclid” fit church needs to a T?

The church simply re-interpreted the book to suit its politics of reason. The church was well aware that most people are gullible, because of childhood indoctrination. And such was the fear of the church (not only the Inquisition, but even in England), that the church as well aware that no one would dare to challenge its interpretation. The facts is the no one did so for centuries.

During this time the church used the Elements to teach reasoning to its priests: a special kind of metaphysical reasoning, which suited the church, since its divorced from facts, and involving faith based or axiomatic proofs.
The church monopoly on education, through the “reputed” institutions it set up and controlled, such as Oxford and Cambridge, resulted in spreading this superstition widely among Westerners.

So widely, that when the myth of axiomatic proofs in “Euclid” ultimately collapsed (among the knowledgeable), people like Russell and Hilbert created formal mathematics to save it.

The Pythagorean calculation

Curiously, Greediots and Western historians, intent on glorifying themselves, never ever speak of the “Pythagorean CALCULATION”, though a formal proof of the “Pythagorean proposition” has no practical value, and all practical value derives from the ability to use it to CALCULATE the diagonal of a rectangle whose sides are known.

Western historians are silent about the process of calculation among Greeks. Why? (more…)

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

Wednesday, March 18th, 2020

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

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.

The key point of my talk was that much present-day school math is an inferior sort of math which Europeans appropriated from Indian ganita without fully understanding it, and then returned during colonial times by packaging it with a false history and declaring it superior. A philosophical comparison between ganita and math was done in earlier posts and publications.

This post focuses on the false history aspect, going back to the purported Greek origins of the “Pythagorean theorem”.

False Western claim

Egyptians built massive pyramids very accurately. One would assume that to achieve that marvellous feat of engineering they knew the so-called “Pythagorean theorem”.

But in his book Mathematics in the time of the pharaohs, Richard Gillings speaks of “pyramidiots”: people who claim various sorts of wonderful knowledge is built into the pyramids of Egypt. Gillings’ argues in an appendix (citing the Greek historian Heath) that “nothing in Egyptian mathematics suggests that Egyptians were acquainted with…[even] any special case of the Pythagorean theorem.” Heath adds, “there seems to be no evidence that they [Egyptians] knew [even] that the triangle (3, 4, 5) was right-angled”. The Egyptologist Clagett chips in, “there have been exaggerated claims that Egyptians had knowledge of the Pythagorean theorem which is, of course, a formal Euclidean theorem of the Elements.”

First, Gillings, Heath etc. are not honest enough to add that there is no evidence for Pythagoras. Nor is there any evidence for the claim that he proved any sort of theorem. So, one should rightfully say, “There have been persistent false claims about a Pythagoras having proved a theorem, though there is no evidence that there was any Pythagoras nor any evidence that he proved any theorem.”

Obviously, Western history of Greeks is of very inferior quality, since the tacit norm is that stories about Greeks need no evidence and must be accepted on mere faith in Western authority: it is only stories about others which require evidence!

That is why I use the term Greediots to describe people who fantasize about all sorts of scientific achievements by Greeks without any evidence, starting from the “Pythagorean theorem”: if they can believe in that they can believe anything on their blind faith.

Religious connection of geometry

A key point: not only is there nil evidence for the story of the “Pythagorean theorem”, it is CONTRARY to all available evidence.

The Pythagoreans were a religious cult: their interest was in the connection of geometry to the RELIGIOUS belief in the soul as described by Plato, in Meno, Phaedo, Republic, etc. Anyone can check in two seconds this connection of geometry to the soul by searching for the 2nd, 3rd, and 4th occurrence of “soul” in Meno, a primary source for Plato readily available online from the MIT repository. But for Greediots the story of a theorem is what is important: so they don’t and won’t check facts. (Is Plato evidence for Greek thought? If not, why has no one ever explained the grounds for rejecting Plato? And what are the other “reliable” sources, if any, for Greek history? )

Proclus, in his Commentary, explicitly asserts that this religious belief linking geometry to the soul was the sole concern of the Pythagoreans with geometry. But Greediots not only have no evidence for their beliefs, they ignore all the counter-evidence.

As Proclus further explains in his Commentary (on the book Elements today falsely attributed to an unknown “Euclid”) the book does geometry with exactly the same religious concerns. The subtle issue here is to understand Egyptian mystery geometry (and related Greek mathematics) as a sort of meditative discourse which drives the attention inwards and away from the external world.

All this is explained at great length in my book Euclid and Jesus: how and why the church changed mathematics and Christianity across two religious wars, Multiversity, 2012. See the webpage, or look inside. But Greediots will be Greediots they not only have no concern with facts they will not tolerate a counter-narrative or allow any space for it.

No axiomatic proofs in Elements

The interesting thing is how this “virgin-birth history” propagated by Greediots creates false “facts”. Clagett’s claim that “the Pythagorean theorem…is, of course, a formal Euclidean theorem of the Elements” is one such false “fact” which is widely believed.

The real fact is there is no axiomatic or formal proof of the “Pythagorean theorem” in the book Elements of “Euclid”. One has only to read the book; its very first proposition has an empirical proof not an axiomatic one. But just as most people do not read Plato, most people do not read the Elements. They just naively assume that even if the myth about its author as Euclid is false, the myth about the book must be correct. (Ha, Ha, they don’t know how thick are the layers of church lies!)

After centuries, some including Bertrand Russell finally understood the absence of axiomatic proofs in the Elements. What is shocking is for how many centuries Western scholars collectively failed to realize that even the first proposition of the Elements is contrary to the myth of axiomatic proofs in it.


The Eleven Pictures of Time: the Physics, Philosophy, and Politics of time beliefs

Wednesday, March 4th, 2020

(elaborated and simplified)

An interactive workshop at the Berlin festival for time issues 24, 25 March 2020, 1500-1800 Berlin time. Facebook live stream:
will be only of the conference talk on the 21st March 1430 to 1600 Berlin time (1900 to 2030 IST).

The workshop will cover the following 12 topics related to the book. Each topic will be covered in an average of approximately 20 minutes. After each hour there will be questions for around half an hour.

The book begins and ends with the Fisherman’s story: to marry a mermaid the Fisherman wants to lose his soul, but does not know how to do so.

  1. Life after deathMany ancient cultures believed in the soul and life after death, as in the stories of Nachiketa, Socrates, Chuang Tzu (butterfly’s dream), or sufi poems like those of Rumi
  2. Sceptics Equally, however, many ancient and modern sceptics rejected the belief in life after death. An ancient sceptic, Payasi, performed a variety of experiments with dying persons to test and reject the belief in life after death.
  3. Cosmic recurrence or “cyclic” timeHowever, Payasi’s experiments refute only a simplistic belief in life after death. The correct understanding of the ancient belief in life after death is in the context of cosmic recurrence (as in Bhagvad Gita), or as in the Nietzsche’s attempted reconstruction. Ancient symbols of cyclic time include the Egyptian Ouroboros, the Buddhist Kalachakra, the Maya/Aztec calendar stones, and the Nataraja (dancing Shiva). With cosmic recurrence, not only are people reborn, everything in the cosmos repeats. Roughly, this corresponds to cyclic time. This notion of life after death with “cyclic” time meets all the objections raised by sceptics, both ancient and modern. But is it science?
  4. Cosmic recurrence in physicsCosmic recurrence or “cyclic” time is scientifically possible. In Newtonian physics, on the Poincare recurrence theorem, the cosmos must recur if it is closed. That is, every microstate of a closed cosmos must repeat to an arbitrary degree of precision, infinitely often. The theorem can be extended to general relativity (case of geodesic flow), and a similar theorem holds in quantum mechanics. I point out the flaws in the text-book resolution of the recurrence paradox of thermodynamics.
  5. The curse on cyclic timeApart from physics we need to understand also the politics of time beliefs. The church, after it married the Roman state, cursed this belief in life after death in the context of cosmic recurrence. Early Christianity derived from Egyptian mystery religion (“paganism”). As elaborated by Origen, it accepted cosmic recurrence; it also accepted equity. But the later-day post-Nicene church misrepresented cosmic recurrence as the collapse of morality. The real political reason was to promote inequity: the state-church wanted to project exclusive benefits for converting to Christianity, to be able to sell Christianity. (more…)