Science, reason, and superstition - 4:
Eliminating metaphysics, decolonising mathematics

C. K. Raju

Metaphysical reasoning, as designed by the church, is used in formal mathematics today, which is, in turn, used in present-day science. This metaphysics is an easy source of slipping superstitions in science. A key point: not only formal reasoning, but its starting point, the axioms or postulates, in both church reasoning and formal mathematics, are divorced from the empirical.

Thus, the Lokayata critique of reasoning or inference was that conclusions inferred from wrong assumptions are not valid knowledge. This critique is actually accepted in formal mathematics. However, instead of plainly stating that the theorems of mathematics are NOT valid knowledge, it is euphemistically stated that they are “relative truths”, relative to the axioms.  The idea of different types of truth, especially about metaphysical propositions, easily confuses most people. Therefore, the Lokayata critique needs to be forcefully restated: even valid deductive reasoning need NOT lead to valid conclusions: if the axioms are wrong, the conclusions (mathematical theorems) would be wrong.

So, how exactly do we know the axioms of formal mathematics are right? One way, followed by the vast majority, is to blindly trust the axioms laid down by some Western authority. But the sceptic should ask: how do we test the axioms of formal mathematics? We cannot, for they are metaphysics.

For example, consider an axiom from our current NCERT geometry school text: that a unique invisible straight line passes through two invisible points. With visible points this axiom/postulate is always false: a visible point has some size, so there is always a way to connect different parts of two visible points with more than one (visible) straight line. But one can maintain anything one likes about invisible points and lines, like one can do about non-existent angels, because neither exists in the real world, and the truth of metaphysical propositions can only be decided by authority.

In fact there is no way to test mathematical axioms which are irrefutable in the sense of Popper, hence pure metaphysics.  Bertrand Russell stressed this in his essay on “Mathematics and the metaphysicians”[1] but people don’t pay attention and don’t  understand the political implications of such metaphysics. This sort of metaphysical reasoning is extremely well suited to church agenda of spreading superstitions to enable its rule by superstitions, but our elite collectively believe “rationality is against superstition”!

In fact, as I have remarked earlier, most people do not know the axiomatic proof of even 1+1=2 or why Russell and Whitehead needed 378 pages for it. They uncritically trust (Western) authority, and falsely believe someone must have diligently checked those 378 pages! So, in practice, the advocacy of formal reason just becomes a way to subordinate people to Western authority (which lays down those axioms). This uncritical reliance on authority allows an easy route to slip in church superstitions about the metaphysics of eternity into science, through mathematical axioms about infinity[2] built into set theory on which all “modern” math is based.

For example, in science, today, the “laws of nature” are modelled as differential equations, such as the Schrodinger equation of quantum mechanics, or the Hilbert-Einstein equations of general relativity, or Maxwell’s equations, or even plain old Newton’s “laws”. Differential equations require the calculus, and on the Western (mis)understanding of calculus, so-called “real” numbers are needed for calculus. as I regrettably taught in the university for almost a decade. This ensures that time in physics fits into the idea of time in Christian theology.[3] School children are indoctrinated into regarding time as “linear” and like the “real line”, though the empirical evidence is contrary to it.

But the terminology of “real numbers” (like the word “reason”) is absolutely misleading, and there is nothing real about “real” numbers. Though they are deemed to be essential to calculus, they are never actually used for any real-life application, and cannot be. All practical calculations are done with rational numbers (to finite precision), and never with “real” numbers (infinite precision). In fact, almost all scientific calculations, such as calculations of a rocket trajectory to send a man to the moon, are today done on computers which can never use “real” numbers, and use instead what are called “floating point numbers”.[4] Most people don’t understand real numbers, or floating point numbers, and just uncritically accept mathematical authority.

But how trustworthy is that authority? Are mathematicians more honest than church priests? Uncritical acceptance of authority always invites abuse of authority, and mathematicians are no exception. I have already given examples of how the top-rated mathematician in the world repeatedly and brazenly plagiarised my prior published work, because he was supremely confident no one would dare challenge his authority. He was right. The American Mathematical Society then and even now is still covering up[5] that brazenly dishonest act, trying to pass it off as an innocent error. They know that those who uncritically trust authority can be easily misled.

The “expert” mathematician also proceeds on trust, not knowledge.  My “Cape Town challenge”, posed to a senior mathematician at the University of Cape Town, during a 2017 debate on decolonisation of math and science,[6] was the following. In formal mathematics, 1+1=2 in integers is different from 1+1=2 in real numbers. The challenge was to prove 1+1=2 in formal real numbers, from first principles, in the manner of Russell and Whitehead, without assuming any result of axiomatic set theory. Note that this challenge is NOT intended for the average colonially educated person who does not know formal real numbers or axiomatic set theory. It is intended for the professional mathematicians they trust: the mathematicians with a PhD from an elite university such as Cambridge, who teach or research in our own elite institutions, who are expected to know why 1+1=2.  Test it out.

Since so few are knowledgeable about even basic issues, and since ignorant people first proceed by guesswork, many people have this doubt: “it works”, they say, about formal mathematics. The question is what works? If a quack gives one a powder, and recites a charm, for arthritis, and it works, should we accept the entire package uncritically? THAT is superstition. Or should we investigate the active ingredient? It may be that the powder is of steroid pills, and the charm is irrelevant. Likewise, what works in practice is the normal mathematics of calculation: the formal math of metaphysical proofs is an irrelevant superstructure which can and should be discarded.

So, what is the remedy?  Obviously, the remedy is to reject formal mathematics in toto, and teach normal mathematics for its practical value. But for this we need to change our math teaching. But who will do it?  Clearly students and school teachers are not allowed to change our math teaching. Clearly, also, politicians and bureaucrats cannot do it, for they don’t know the subject. They will at best put some “experts” on the job, without knowing whether they are truly experts, and just by blindly trusting their Western degrees or community endorsement.  But as we just saw, the “experts” are unreliable; they may be both ignorant and dishonest.

Therefore, the only solution possible is transparent public debate. Two decades ago, when astrology was sought to be introduced in university departments by the UGC, the India International Centre tried to organize a public debate on astrology, because many did not trust the UGC experts operating behind closed doors. I participated in that debate, but the astrologers ran away, and didn’t participate in the debate.  Likewise, for the last several years (since about 2014) I have been trying to organize a debate around formal mathematics,[7] but the formal mathematicians have been running away from public debate like the astrologers. 

But while many recognize astrology as a superstition, almost no one understands the superstitions in formal mathematics. The formal mathematicians rule the university and school system: why should they debate to their detriment? And colonial indoctrination leaves most people paralysed, unable to critique the master, and unable to mount a critical public scrutiny of an “accepted” institution of the master. Those who celebrate the debate on Darwinism fail to insist on a public debate on formal mathematics. The so-called fighters against superstition never dared to challenge a single one of the master’s superstitions, they happily let their children be victims.  And the West merrily continues to rule through superstitions.

Will the colonised ever arise? If so when and which section of the colonised will do so? After the disintegration of the West, there may no longer be a window of opportunity to do anything. When will the colonised elite understand that in a public scrutiny they have nothing to lose but their superstitions!

References
1. Bertrand Russell, “Mathematics and the Metaphysicians,” in Mysticism and Logic and Other Essays (London: Longmans, Green, and Co., 1918), 74–96.
2. C. K. Raju, “Eternity and Infinity: The Western Misunderstanding of Indian Mathematics and Its Consequences for Science Today,” American Philosophical Association Newsletter on Asian and Asian American Philosophers and Philosophies 14, no. 2 (2015): 27–33.
3. C. K. Raju, The Eleven Pictures of Time: the physics, philosophy and politics of time beliefs, Sage, 2003.
4. C. K. Raju, “Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the YuktiBhāsā”, Philosophy East and West, 51:3 (2001) pp. 325–362, http://ckraju.net/papers/Hawaii.pdf.
5. C. K. Raju, “Plagiarism by Ex-President of the Royal Society. 2: The Cover-up by the American Mathematical Society,” n.d., http://ckraju.net/blog/?p=184.
6.Decolonising Science Panel Discussion: Part 1 (University of Cape Town, 2017), https://www.youtube.com/watch?v=ckbzKfRIi6Q&feature=youtu.be http://ckraju.net/papers/uct-panel-decolonising-science-ckr-summary.pdf; C. K. Raju, “Abstract: UCT Panel, Decolonising Science,” 2017, http://ckraju.net/papers/uct-panel-decolonising-science-ckr-summary.pdf.
7. See these 2015 minutes of a conversation with a top formal mathematician. http://ckraju.net/issa/conversation-draft-minutes.html.

(Concluded)

Prof. C. K. Raju, TGA Laureate, Honorary Professor, Indian Institute of Education Tagore Fellow, Indian Institute of Advanced Study

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Jun 10, 2020