Archive for May, 2019

Decolonising mathematics: discarding church myths and superstitions

Tuesday, May 28th, 2019

Colonial education was church education, which changed our traditional math teaching by bringing in myths and superstitions, directly related to the post-Crusade church theology of reason. Most people fail to understand this, since colonial education ensured they know nothing about (a) mathematics or its philosophy, or (b) the church theology of reason, and (c) stuffed them full with prejudices (e.g. that math is universal).

But this understanding of colonial math makes  it easy to decolonise math. We need only to critically examine and junk church myths (such as Euclid) and related superstitions about axiomatic (or faith-based) math, and focus on the practical value of (normal) math. A key such superstition, brought in by colonial education, is that formal math is “superior” because deductive proofs are infallible.

The foolishness of this belief (irrespective of its church origins) has been argued out in detail in the article on Decolonising mathematics, published in AlterNation 25(2) pp. 12-43b. Download the whole paper by clicking on the link above or below.

Not only are deductive proofs highly fallible, they are more fallible than empirical/inductive proofs. The purported infallibility of deductive proofs is just another church superstition like the purported infallibility of the popes who erred in understanding even elementary arithmetic algorithms for addition and multiplication. Laughably, much Western  thought is founded on this superstition (because the church first hegemonised the Western mind).

The above article covers part of the keynote address I gave on “Decolonising math and science education” at the 11th Higher Education Conference, Univ. of Kwazulu Natal, Durban, in 2017. The video, presentation, and other details were given in an earlier post.

Formal math: based on church myths and superstitions

Monday, May 27th, 2019

Many smart alecs ask: what difference would it make if “Euclid” did not exist? They believe the lie about Euclid was told for no reason, and that it persists for no reason in our school texts today which mention “Euclid” 63 times, apart from giving children an image of “Euclid” (all of which makes them believe “Euclid” was real).

It is simple commonsense, however, that a lie is always told for a reason. But the reason in this case is beyond the understanding of our smart alecs. They miss the connection of the “Euclid” myth to church theology.

Our current school texts teach children the false history that “Greeks” did mathematics in some superior way which they must imitate. The myth goes that “Euclid” gave “irrefragrable proofs”, by using the axiomatic method. For this purpose, he supposedly arranged the theorems in a particular order.

Cambridge foolishness about “Euclid”

Cambridge University, a church institution, subscribed to this myth. As pointed out in this exhibit, it initially adhered to the practice of blind imitation of “Euclid’s” Elements. Then the Cambridge Special Board for Mathematics in its Report on Geometrical Teaching dated 10 May 1887 declared the proofs in “Euclid” need not be blindly imitated but the order of theorems in the Elements must be followed. On 8 March 1888 this was adopted by the Cambridge Senate as part of the amended regulations for the Previous examination.

This move by Cambridge University to “reform” mathematics teaching was excessively foolish. Thus,   while the book Elements has axioms and proofs, the simple fact is that it has no axiomatic proofs, as today understood in formal mathematics. Specifically, the first and fourth (SAS) proposition of the Elements have empirical proofs, and a chain is only as strong as its weakest link. (See, the detailed grievance against the NCERT.) If empirical proofs are admitted in one place, the order of the theorems becomes irrelevant, because the “Pythagorean theorem”, for example, can be proved in one empirical step, as was done in India. But the dons of Cambridge University failed to understand this, and made exam regulations based on their botched understanding.

Axioms but no axiomatic proofs in the Elements

The belief in axiomatic proofs in the Elements comes only from the “Euclid” myth not from a reading of the actual book, which our smart alecs never read. Even the dons of Cambridge University had not read it carefully from 1125 (when the book first came to Europe) until 1887. This Cambridge foolishness in mathematics, driven by the Euclid myth, easily exceeds  the foolishness of Sir John Lightfoot, Vice Chancellor of Cambridge University, who, in the 17th c., refined Bishop Ussher’s absurd date of creation, to fix the time of creation at exactly 9 am according to the gospel.

Eventually, Bertrand Russell, among others, pointed out the foolishness of the belief in axiomatic proofs in the Elements, calling the proofs in the Elements a “tissue of nonsense”. But, because of his Cambridge indoctrination, he kept believing in the Euclid myth that, the mythical “Euclid” intended axiomatic proofs. Hence, Russell along with David Hilbert invented formal math on that equally foolish belief in the intentions of a non-existent person, and in the church superstition about the superiority of deductive proofs (more details on that superstition in the next blog post).

Actual Greeks tied math to religion

Actual “Greeks” (Pythagoreans, Plato, Proclus) were NOT interested in axiomatic proofs, and interested only in the religious aspects of geometry, in arousing the soul and making it recollect its past lives (mathesis). This required turning the mind inwards. I have described this in great detail in various places, including my book Euclid and Jesus.

Axiomatic proofs a church tradition

But the church adopted the method of proof based on axioms (i.e., assumptions about the unreal), as in Aquinas’ proof about the number of angels that fit on the head of pin, based on certain axiomatic beliefs about the amount of space occupied by unreal angels. The church found the axiomatic method convenient, as part of its theology of reason (advocated by Aquinas and the schoolmen as the best way to convert Muslims). Obviously, basing reasoning on facts, as in universal normal math (including Indian gaṇita), would go contrary to all church dogmas (about angels etc.). As a loyal handmaiden of the church, Cambridge University, promoted the superstition that the axiomatic (or faith-based) method is “superior” to the empirical method, and that authoritatively laid down axioms (like Aquinas’ axioms about angels) are “superior” to facts.

We started imitating this way of doing mathematics as part of colonial education (which imitated Cambridge).

“Euclid” myth teaches us to imitate the church

So, when millions of students are taught the “Euclid” myth, and told that this way of doing math (formal math) is “superior”, they are being taught a church myth about “Greeks”, to teach them to imitate a foolish church practice. Neither they, nor our smart alecs,  understand this tricky way of indoctrinating children to teach them to imitate a church practice though a myth about the only “friends of the church” — the early Greeks. So, the Euclid myth is just a simple innocent lie, is it?

S. M. Mohd. Idris

Friday, May 24th, 2019

It was with a sense of shock that I heard of the passing away of Uncle Idris, which was untimely even at 93. When I last met him in March he was unwell, and in hospital, but looked well enough to carry on for another five years, or at least so I hoped.

He had some of the magic of Mahatma Gandhi: a leader who could inspire people to act in ways they never imagined they would. He inspired all Malaysia. Regretfully, I forgot to ask him the secret of that. Very widely read, up-to-date and sharp. Totally dedicated to others and unwaveringly honest. Therefore, even when we disagreed, there was never any rancour, just laughed it away. Here he is at the International Islamic University Malaysia (to receive an honor) wearing a robe which he did not want to wear, but did so anyway!

S. M. Mohd. Idris

Most obituaries have remembered him for his remarkable work on CAP and SAM and the Third World Network. But he also took a major initiative in education in the form of Multiversity and the many conferences he initiated to decolonise education, and the series of books he got published through Multiversity and Citizen’s International. As Tan Sri Dzulkifli Razak noted, that was way before #RhodesMustFall.

Uncle Idris will certainly live on through the numerous initiatives he took.

Second grievance against NCERT

Thursday, May 16th, 2019

Since the NCERT tried to evade all issues in the first grievance, a second grievance has been filed, asking NCERT to produce primary evidence for “Euclid” or delete all 63 mentions and image of Euclid from its 9th standard text. Further falsehoods will be taken up subsequently.

The new grievance is given below.


This grievance is raised as a response to the response received to grievance DOSEL/E/2019/01152 (signed Smt. Tulika Verma, Under Secretary).
The response received from Smt. Tulika Verma, unfortunately, does not address all the five points (falsehoods) DOSEL/E/2019/01152 contained, and at best, can be seen as a partial (and unsatisfactory) response to FALSEHOOD 2.

Vide this grievance, we request clarity on FALSEHOOD 1 in DOSEL/E/2019/01152:

1) Does NCERT consider Euclid a historical person who lived in the past (Yes / No / Not sure)
(There are 63 references to Euclid, and one image, in just the 9th standard NCERT math text)

2) If the answer to question 1 above is a yes, what is the serious evidence NCERT can furnish to support the claim that Euclid is historical

Serious evidence means evidence from PRIMARY sources. Tertiary sources like Wikipedia are unacceptable, as are secondary sources. The related point also being made is that Euclid is part of church propaganda. Therefore, merely producing some Western secondary text in support of the propaganda is NOT acceptable. (Or if NCERT regards it as acceptable, it must also agree to put a bold warning at the beginning of the school text that it has no serious evidence for the story stated about Euclid, and that its policy is that all Indian children are obliged to accept whatever nonsense is stated in Western secondary texts, and have no right to challenge those texts by demanding primary evidence).

Thank you for your attention.