Gaṇita vs formal math:
re-examining mathematics,
its pedagogy,
and implications for science
Aim of project:
Swaraj in thought,
विचार में स्वराज or
दिमागी आज़ादी.
To communicate, I need to know how much you know.
- So, I will begin with a questionnaire.
Q. 1. How many of you know mathematics and science?
- Specifically, how many understand (ordinary, partial, functional) differential equations needed to do physics?
Q. 2. Your ignorance of math is whose fault?
- (a) your fault: you were bad at math
- (b) teacher's fault: you had a bad teacher
- (c) not an individual issue: a bad teaching method is used to teach math
- (d) some other reason.
Q. 3. How many believe math is universal? That 1+1=2 always?
Q. 4 If you are ignorant of math how do you know math is universal?
- Specifically, to prove 1+1=2 why did Russell need 378 pages?
Q. 4 (contd) What did Russell add to the "universal" knowledge of 1+1=2 in those 378 pages?
- Was it any practical knowledge?
- (Absolutely not, you manage your daily groceries without knowing one sentence of Russell's proof.)
- And we teach math for what impractical purposes?
Q. 4 (contd.)(Let's try another tack)
- In formal math 1+1=2 in integers is different from 1+1=2 in "real" numbers.
- Do you know the proof of 1+1=2 in real numbers (from first principles, without assuming axiomatic set theory)?
- Do you know even a SINGLE PERSON who does?
Q.5 If there is a dispute about math teaching whom would you trust?
- an IIT Professsor (with a degree from abroad)
- a top formal mathematician from Cambridge, such as Michael Atiyah or Stephen Hawking
- an Indian origin professor from Princeton, with a Fields medal viz. Manjul Bhargava
- you will critically check the claims and counter-claims on your own.
IIT professors may lack basic knowledge of math. (My experience, of course, but look at a public demonstration of ignorance at http://ckraju.net/blog/?p=165)
Or see, 
You believe, Fields medal is never given for political reasons,
- it was given to an Iranian woman purely for mathematical reasons (which you don't understand).
- What was the PRACTICAL benefit of Manjul Bhargava's mathematics for ANY Indian.
TRUST MINUS KNOWLEDGE = SUPERSTITION
- Of course you also believe the West is too honest and ethical ever to exploit your ignorance + "trust the West" syndrome.
Q. 6 In 2015, Harsh Vardhan said, "India gave "Pythagorean theorem" to the West. What do you believe?
- (a) This is a case of Hindu chauvinism.
- (b) sulba sutra-s only stated the result, Pythagoras gave a proof. (E.g. Prabir Purkayastha).
- (c) Euclid in the -3rd c. CE gave a proof of the "Pythagorean theorem"
- (d) Tales of "Pythagorean theorem" and "Euclid" are pure myths which have been used to hijack the teaching of math.
My project involves three questions:
(1)Which is better? Gaṇita or formal math?
- (Q. about the philosophy of math.)
(2) What math should be taught at school and undergraduate level?
- (Q. about pedagogy of math.)
(3) If math changes will science change?
- (Q. about applications of math to science.)
What has this to do with Tagore?
"Educational" aspect of Tagore is relatively neglected
Shantiniketan succeeded in inspiring artists, but has lost out to the juggernaut of mainstream education.
My project also contests colonial education, and aims to decolonise it,
- hopefully with greater success.
But, my starting point is different.
I do NOT see colonial education as utilitarian.
- (It provides some utility, of course.)
I see colonial education as propagandist and as a subtle technique of indoctrination.
This is a point which all earlier educators including Tagore missed.
Colonialism was not mere military conquest.
It involved a capture of the mind.
Decolonisation, therefore, is a project of liberating the mind.
The political freedom we got 70 years ago is not enough.
- We also need mental freedom or swaraj in thought.
How do we achieve it?
- To cure a disease we must correctly understand its cause.
- To achieve mental freedom we need to understand how the colonised mind was captured.
The colonised mind was captured through colonial education
- (which involved collaboration of church with colonial state).
Colonial education was church education;
- Missionary schools, of course were meant for church indoctrination.
- But the big universities like Oxford, Cambridge, and Paris were directly controlled by the church for centuries.
- That education was designed to produce missionaries.
Western education was a church monopoly.
- No secular education in Britain before the British Elementary Education (Forster) Act of 1870-71,
- long after arrival of colonial education in India.
Colonial education involves years of indoctrination modeled on missionary "education".
- The propagandist and doctrinaire aspects of colonial education have been little noticed.
- The colonised foolishly imagined that church education was designed for their benefit.
Very simple e.g.: case of the Christian/Gregorian calendar.
- Propagandist: e.g. AD/BC, historicity of Jesus etc.
- E.g. ties Jesus to your identity,
- secular festivals (Independence day, Republic day) defined only on the Christian calendar.
Anti-utilitarian:
- unscientific, e.g. months
- damages Indian agriculture based on the monsoon and the traditional calendar.
To reiterate, utilitarian aspects of colonial/Western education are acceptable.
- Propagandist and doctrinaire aspects must be eliminated.
- This requires a critical re-examination of colonial education which we have never done and refuse to do today (E.g. NCERT).
Since colonial education purportedly came for science, critical re-examination must begin from
- mathematics,
- science
- (and the history and philosophy of science).
The difficult part is to understand how propaganda and dogma infiltrate mathematics and science.
- Through history and philosophy of science
→ mathematics → science.
I have understood (E.g. Eleven Pictures of Time), but how to explain to others?
- given the widespread ignorance about mathematics and science,
- and even the history and philosophy of mathematics and science
- spread by colonial education due to church chauvinism.
Many people readily admit ignorance of math and science.
- But we have the superstition the "the West knows best". E.g. Manjul Bhargava.
- That superstition prevents change to anything non-Western.
And we also have a variety of prejudices, based on Western myths. E.g. the myth that math is universal,
- or the myth that science and the church are at war since Galileo.
- or the myth that Pythagoras proved some theorem after him
- or that Euclid did geometry in some special way.
This ignorance, superstition, and prejudice are not accidental.
- They arose because colonial education was church education. And ignorance, superstsition, and prejudice are the basis of church power.
If you are ignorant of math, how do you know that math is universal?
Colonial education changed the teaching of math from normal math to formal math.
What is the difference?
- Normal math (gaṇita) accepts both empirical proof and reasoning,
- formal math prohibits empirical proof.
What difference does it make to 1+1=2?
- Consequence, 1+1=2 proved in 378 pages by Russell.
- This enhanced difficulty adds nothing to practical value.
Key question: can mathematics be decolonised? If so, how?
- Short answer: yes. How? by reverting to normal math.
Much work has already been done over the past decade.
(1) Decolonised pedagogy of calculus without limits.
(2) Pedagogical experiments and text on rajju ganit (or string geometry)
(3) Retarded gravitation theory.
(4) Teaching of course on the alternative history and philosophy of science.
Summaries of past work in
- Censored article: To decolonise math stand up to its false history and bad philosophy. (Rhodes Must Fall)
- Mathematics and censorship
Three ways to decolonise science (summary for UCT debate)
- Decolonising mathematics (Censored keynote for Palestine technical university)
- Decolonising mathematics (Keynote at 11th HEC Durban.) (Deduction is MORE fallible than induction.)
(1) RGT, Oumuamua, two-satellite experiment etc.
(2) Dissemination. Why hasn't the changed pedagogy of math caught on widely?
- Lack of textbooks (rajju ganita),
- Western control of knowledge (math and censorship),
- Indoctrination of the colonised
Draft chapter scheme. (Each part will consist of two chapters)
- Part 1: Colonial capture of the mind: the church connection (a) The nexus between the church and the colonial state. The role of colonial/church education. (b) Decolonisation by critiquing and eliminating the propagandist elements in colonial math education.
- Part 2: The religious roots of Western ethnomathematics. (a) Plato and Neoplatonism. (b) Its condemnation then appropriation into the church theology of reason as it developed during the Crusades.
- Part 3: Decolonisation by eliminating the myths and superstitions of Western ethnomathematics. (a) The myths of Euclid, Pythagoras etc. (b) The superstitious belief in the infallibility of deduction and the metaphysics of infinity.
- Part 4: The pedagogical experiments in decolonised teaching (a) history and philosophy of science, (b) calculus without limits, and (c) rajju ganita.
- Part 5: The implications for science. (a) The European failure to understand calculus and the failure of Newtonian physics. (b) The two satellite experiment.
