Archive for the ‘History of Astronomy’ Category

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…)

Alternative math: media reports

Thursday, July 5th, 2018

Here are the media reports for the Rajju Ganit workshop from Dainik Bhaskar, Nai Duniya, Talk show by Global Herald, and Free Press Journal

Global Herald talk show प्रसिद्ध गणितज्ञ सीके राजू से खास चर्चा

Global Herald talk show

Dainik Bhaskar

Dainik Bhaskar Indore 26 June 2018

Nai Duniya26 June 2018

Nai Duniya Indore 26 June 2018

Global Herald e-paper 30 June 2018

Global Heral news

Free Press journal

Free Press journal, Indore, 27 June 2018

Decolonisation of education (Math, science, and History and philosophy of science) links

Wednesday, June 4th, 2014

New videos

Here is a link to a video interview (over 9 hours) with Claude Alvares on a variety of issues concerning decolonisation of education. This has been posted by Multiversity TV, and I should have posted it long ago on my blog.


History and Philosophy of Science

Part 5 of the above video series has interviews with students of the new “decolonised” course on History and Philosophy of Science (HPS). Some details of the new course, pictures of students etc. were earlier posted on this blog at

The genesis of the HPS curriculum, the international conference which preceded it, and minutes of discussion at Universiti Sains Malaysia are posted at

The actual curriculum of the courses which ran at AiU are posted at



Math education

As for math education, my experiments with my decolonised course on calculus have already been reported in scholarly articles such as


History and Philosophy of Science: a new course

Monday, May 6th, 2013

This new course is a world first. It was formulated after an intensive curriculum deelopment workshop already mentioned in an earlier blog.

The West has systematically produced false history as propaganda to glorify itself and belittle others. This has further resulted in a bad philosophy of science and math. Typical courses in HPS in Western universities blank out the non-West. Western academics (like Wikipedists) seem incapable of debating the point seriously: they merely strike superior poses, pile on the falsehoods, vilify, censor, etc. Clearly they aim for the dim-witted and gullible.

For example, Kuhn’s “Copernican revolution” was written AFTER it became known to Western scholars that Copernicus was merely a priest who copied Ibn Shatir’s work from its Greek translation (available in the Vatican) and was too frightened of the Inquisition to acknowledge his non-Christian sources . As for the myth of Claudius Ptolemy, the Almagest is manifestly an accretive work with the current pole star at the head of its star list, and some parameters given to an accuracy of 13 decimal places, while the length of the year is wrong in the second decimal place. Indeed, Greeks and Romans were a superstitious lot who regarded astronomy as a crime, and punished it with death, as in the case of Socrates or Anaxagoras. The Julian calendar reformed the Greek, but remained hopelsssly unscientific (as the Gregorian still is). The wrong length of the year in it for centuries proves the Greeks and Romans never had any access to any advanced astronomy! (Hence, the long-standing confusion about the dates of Easter; they have just celebrated Easter in Palestine in May.)

Likewise the tale of the Newtonian revolution is bunkum. As I have shown in my book on Cultural Foundations of Mathematics, the calculus developed in India over a thousand year period, and was imported to Europe by Jesuits based in Cochin. Europeans, with their primitive and religious understanding of mathematics, failed to understand the infinite series and blundered like Descartes or even Newton with his “fluxions”.

The truth comes out from simple things like the inability of Westerners to measure the size of the earth until 1672, which is something that was well known in the non-West, from more than a thousand years earlier, at least since Aryabhata (5th c.), Bhaskara I (7th c.), al Mamun (9th c.), al Biruni (10th c.) etc, and probably since the Egyptians.

Unlike the parochial HPS courses in Western universities, the new HPS course suits the international character of the students of AlBukhary International University. Here the students of the new HPS course take a trip near equinox to see how simple it is to measure the size of the earth, so they can have a good laugh at those false Western tales.

Students of AlBukhary International University setting out to measure the earth

At the observation point, after sunset

National year of mathematics and delayed monsoon

Sunday, May 6th, 2012

But why a year on the Christian calendar? That calendar embodies the European ignorance of elementary arithmetic and simple fractions (hence their persistent inability to determine Easter correctly until the Gregorian calendar reform of 1582 when they got the length of the year from Indian books). Click the image for the text version. This newspaper has a circulation of 40 million.

Even so, the Gregorian calendar retains the unscientifc chaos about months. This is a disaster for Indian agriculture. (More details of the monsoon mess in my book Cultural Foundations of Mathematics, or an early preliminary article at

More recent newspaper clips on the “delayed monsoon” effect are at



Islam and the Philosophy of Science

Saturday, May 5th, 2012

The Pusat Islam organized a talk on Islam and the philosophy of science. (Click the image for the paper. But the paper does not cover the queston of ethics of science, taken up during the talk.)

New curriculum for history and philosophy of science

Saturday, May 5th, 2012

A workshop was held at Al-Bukhari International University to formulate a new curriculum for the history and philosophy of science. Scholars from 3 countries participated. Here is the announcement for the workshop, and an earlier one on the Multiversity site.

The issue is part of the decolonisation agenda, but was precipitated when a person who trained as a missionary in Singapore Bible College, and never acquired any knowledge of science or philosophy, but got a PhD from Cambridge in the philosophy of science, started trying to use the classroom as a pulpit. See the minutes of the discussion, and the draft syllabus.

Here is a group photo

and a press report in Alef (Iran). (Click image to go to site, and use Google translate for hilarious results.)

Ending Academic Imperialism: a Beginning

Wednesday, July 6th, 2011

Here is my new book (ISBN: 978-983-3046-15-7).


Academic imperialism begins with Western education, which has not been seriously challenged in hard sciences. Colonialism changed the system of education to stabilise Western rule through indoctrination. The change was possible (e.g. by Macaulay in India) just because a large section of the colonised elite had already swallowed the 18th c. racist history, that only the West had innovated in science. That bad history was bolstered by a bad philosophy of science, both fundamentally warped by the religious fanaticism which overwhelmed Europe from the Crusades in the 11th c. until the 17th c. Therefore, to end academic imperialism it is necessary to take the following steps.


Khwaza Nasiruddin Tusi and Copernicus

Saturday, April 2nd, 2011

Believing the propaganda regarding trouble in Iran, I nearly postponed my visit there. However, the situation was entirely peaceful, even at Khorramshahr, the border with Iraq. There was an invasion of dust, so all flights were cancelled, and we had to travel back to Tehran by road, a distance of some 18 hours.  Here is what the dust haze looked like.

A sunken ship as seen in the dust haze
Remarkably, the Iranian Deputy Minister for Education, who was among those who attended the meet at Khorramshahr, also travelled back by bus, and stopped at wayside dhabas to eat and watch TV. I  did not see any guns, except those pointed at Iraq. I cannot imagine an Indian minister travelling thus, for they are always fearful, and seen only with gunmen even in meetings of philosophers in this “stable democracy” called India. Even the centre of Delhi is infested with guns, but no one says there is any trouble in India!

But then, this sort of propaganda is to be expected from those who passed off the priest Copernicus as a revolutionary scientist, though all he did was to translate the work of Ibn Shatir and the Maragheh  astronomers from Greek (into which it had already been translated) to Latin. Of course, he claimed “independent rediscovery”, as Europeans invariably did, for he could hardly have risked being tortured by the Inquisition like his friend Scultetus.

It was a real treat to visit Maragheh and see Tusi’s observatory at first hand.

 Nasiruddin Tusi\'s Observatory