__Draft__

**Background:**

The 38^{th}
ISSA issued a call
for participation in open debate on the philosophy of
mathematics.^{1}
The current idealistic philosophy is called formalism; and currently
the only comprehensive alternative to it is my realistic philosophy
of zeroism.

A very distinguished formal mathematician (FM) attended, and the following are the minutes of an informal conversation.

**Minutes**

1. CKR: Why are real numbers needed for calculus?

FM: That is how the calculus developed in the West. It was used successfully for applications to physics.

2. CKR: So the issue is practical applications? Most practical applications of physics are done today on computers using floating point numbers. So, we should teach floating point numbers.

FM: No, understanding is also important.

3. CKR:

[3.1. Newton failed to
understand the calculus. As I have argued, Newton's physics failed
because of the resulting intrinsic conceptual confusion.^{2}
Where Newtonian physics worked, it involved only the Indian method of
numerical solution of ordinary differential equations (as done on a
computer today, using floating point numbers). ]

3.2. There are alternative ways to understand calculus using Indian non-Archimedean arithmetic and zeroism. Why not use them instead of reals and formalism? A critical comparison is needed to demonstrate that one is superior to the other. Who did it?

3.3. Real-number
calculus fails in numerous situations in contemporary physics (e.g.
discontinuities and shock waves, S-matrix expansion).^{3}
This failure cannot be resolved by replacing calculus with Schwartz
distributions or even using non-standard analysis.^{4}
Non-Archimedean arithmetic works where both fail. But a new
philosophy (zeroism) is needed to handle the situation where there
are an infinity of infinitesimally different entities. This
philosophy is like the natural language practice of using one name pi
to denote the multiplicity of distinct entities 3.14, 3.1415, etc.

3. FM:

3.2. I intuitively prefer real numbers.

3.3. I don't know physics.

CKR: Zeroism uses empirical proof, as Indians did. For practical applications, empirical proof is certainly adequate. Why not use it instead of deductive proof?

FM: Empirical proof is fallible.

CKR: Yes, this is accepted. A rope may be mistaken for a snake, and vice versa. But what makes you think deductive proof is infallible? Mathematical proof uses 2-valued logic. Why choose it? On cultural grounds? Just because the church said that a particular logic is universal since it binds God? That is not true; there are many logics such as Buddhist and Jain logic. Mathematical theorems are relative to both postulates and logic. So how is logic decided? If logic is decided culturally, theorems are only cultural truths. If logic is decided empirically then the choice of logic is itself fallible, by your argument, so theorems based on that are even more fallible. So, in either case, deductive proof is more fallible than empirical proof.

FM: You are obsessed by the church.

(CKR: I have already
explained in this very meeting the theoretical importance of studying
the church in understanding the West and its superstitions which
plague mathematics and science to this day.^{5
})

CKR: Anyway, when you choose real numbers on grounds of intuition that is a cultivated intuition. In other words that is indoctrination. Why should this indoctrination be imposed on millions of students? What if Dinanath Batra were to say the same and impose his intuitive preferences on millions? Are you not making that equally legitimate?

FM: You are ignoring the aspect of aesthetics.

CKR: Where is the aesthetics in math? I left formal math since I found it ugly and repulsive. Millions of students hate math, and find it hard. They would not do so if there really was beauty in it. On the contrary, I have demonstrated an alternative way to teach calculus which makes it easy. Students like it.

FM: Your sample size is very small.

CKR: But the sample on
the other side is very large as clear from my lifelong personal
experience or the responses to my articles in *Dainik Bhaskar*
which went to 15 million people.

FM: Whatever way you teach mathematics students will hate it, because the basic problem is that teachers are bad.

[CKR: That is a counter-factual assertion being used to maintain status quo. A bad volleyball coach does not make students hate volleyball.]

At this point the conversation was discontinued, since FM was finding it very stressful.

(Minutes prepared by C. K. Raju (CKR).)

**Summary of round 1
and further questions for round 2.**

**Background:**
Colonialism was con-all-ism. It just made stupid claims of
superiority, like the stupid racist claims for which the West is
famous. Macaulay said the West is immeasurably superior in science,
based on racist history. Colonial education taught blind imitation,
and rewarded it with some bribes.

Q 1. You are basically
advocating the “ape the West” superstition, which we
should eliminate, along with supporting bogus myths like “Euclid”.
**If it is not aping, you need a critical examination of
alternatives. Have you done so? Did any one else do so in two
centuries?**

2. Most people
understand numbers empirically. They manage arithmetic and its
everyday applications to commerce lifelong without ever hearing of
Peano's axioms. I support that everyday practice. But you say that
most people lack understanding. As proof you only repeat the racist
myth “West is superior”. Why? **Why is an empirical
understanding of numbers as in natural language inferior?**
(Religious connection: Peano's axioms bring in infinity by the
backdoor. That metaphysics of infinity is tied to the key church
theology of eternity and is actually INFERIOR to other concepts of
infinity/eternity.)

3. Deductive proofs are
INFERIOR since they are MORE fallible than empirical proofs. That
holds whichever way you decide logic: culturally or empirically. That
knocks the bottom out of formal math. **So why continue with formal
math?** (Religious connection: That superstition relates to
Crusading church theology that logic binds God, but not facts, so
that God cannot create an illogical world, but can create the facts
of his choice. That is, the West put logic above God who was above
facts. Hence, the Western superstition that 2-valued logic is
universal, and proofs based on it are superior to empirical proofs.)

4. **Why do we teach
math?** We should teach math for its practical value. That is why
most students want to learn it; for its practical value. Calculation,
not proof, is central to practical value. Hence, we should teach
calculation. You evade the issue by shifting from practical value to
understanding. In actual fact, most students of physics and
engineering never learn about real numbers (since too complicated),
and hence never understand real-number calculus. They learn the
formula that *(d/dx)e*^{x}* = e*^{x}
but do not understand what *e*^{x} is. So, what
you actually teach them is to accept your authority, WITHOUT
understanding, based solely on your claim of “superiority”
which was never established. (Religious connection: The church had
little use for calculation except to calculate the date of Easter and
everyday commerce. It wanted to persuade others, especially Muslims,
hence valued a “universal” method of persuasion or proof.
We should value practical calculation, not metaphysical proof.)

5. You speak of the
value of math to physics. **A cocktail of practical value and
metaphysics is dangerous, because there is no link between the
metaphysics of formal math and its value to physics.** (E.g.
physical time may be discrete, not like the real line.) Numerical
calculations not deductive proof is good for most practical
applications of physics. So if math has value because of applications
to physics, the real stuff is the calculation which is what we should
teach. **Do you agree?** Further, when I probe deeper into the
physics, pointing out that the real-number calculus does NOT work in
many situations, you evade it by saying you don't know physics.
Well, in that case, don't talk of value to physics. Also tell that to
the government. In future all formal mathematicians should ethically
desist from masquerading as experts, and prescribing what sort of
math should be taught to physicists and engineers (and social
scientists). You offer neither practical value nor a critical basis
for what you call “understanding”, but only insist that
status quo should be maintained. (Religious connection:
Colonial/church education is all about instilling imitative practices
*without* understanding. That is what is actually taught.)

6. When I offer an
alternative understanding of calculus through traditional Indian
“non-Archimedean” arithmetic and zeroism, you evade it by
appealing to your personal intuition. That is not intuition but
indoctrination. Others too can appeal to their intuition and dismiss
yours. **Can we justify what we teach to millions on grounds of mere
personal intuition?** If so, whose intuition? (Religious
connection: Western philosophers from Plato to Kant valued
“intuition” on account of their superstition linking math
to the soul and to its innate knowledge.)

7. You say math is
concerned with aesthetics, when the fact is that millions of students
hate it. I left formal math because I found it repulsively ugly. **What
is the basis of the claim of aesthetics in formal math?**
(Religious connection: this claim of aesthetics too is linked to
Western superstitions about the soul. Plato clubbed math and music,
as arousing the soul (hence linked aesthetics to virtue). But, today,
most people still find music aesthetic, but find math as unaesthetic.
Something happened to math. The church grabbed it. So, the claim of
aesthetics survives only as a superstition contrary to facts.)

8. The claim that
students would dislike any other way of understanding and teaching
math is a facile counter-factual, and an attempt to preserve status
quo. **Are you afraid to allow alternatives to be tried?**

2For
further elaboration and references, see
__http://ckraju.net/papers/Calculus-story-abstract.html__.

3See abstract cited above.

4Applying
non-standard analysis to define products of Schwartz distributions
is inadequate, since the ambiguity was only partly resolved by
demanding that the final result should be standard. In the presence
of discontinuities, different forms of differential equations become
inequivalent. (E.g. Riemann's mistake was to suppose that even in
the presence of shocks the fluid dynamical equations of conservation
of (a) mass, momentum, and energy are equivalent to the equations of
conservation of (b) mass, momentum, and entropy.) So the correct
form of the equations (or the correct association of factors) must
be decided empirically. This situation (of an infinity of
infinitesimally different entities) inevitably arises even with
Colombeau's product of distributions: where there are an infinity of
different entities associated with δ^{2}.
However, with that inferior product, there is no way to fix things
because a huge infinity of alternatives is involved.

5
Specifically, the church and its education system is an important
determinant of what Marxists call "superstructure". Church
education started during the Crusades, and developed for the church
aim of imperial expansion through “soft power” or
organized falsehood (after force failed against Muslims during the
Crusades) Western universities were under church control from the
11^{th} c. Univ of Bologna, and until the end of the 19^{th}
c. That education was designed to produce an army of indoctrinated
missionaries who would spread superstitions. Contrary to Marxist
theory, this education system developed independently of capital.
But this superstructure was neglected by Marx and even Gramsci in
his understanding of education. Macaulay 1847 proposed to use church
education as the cheapest means of counter-revolution. This
proposal was based on the observation that church education
indoctrinates and enslaves minds. Colonial education was church
education when it first came to India in a big way in 1847.