## Table of Contents

## Introduction

- Find a starting joke often tough!
- No problem in this case.😃
- Many determined attempts to reduce Indian traditions to a joke.

### Some recent blunders

#### Space travel, Bharadwaj rishi

#### Vedic math

- My article in Hindu
- Article in Jansatta.
- Not vedic, not ancient, seeks to replace genuine Indian algorithms
- Response to comments by Atul Kothari and others.

#### Pythagorean theorem

- Dr Harsh Vardhan's speech in 2015 Science Congress
- Reports in The Hindu, Navbharat Times, Times of India etc.
- What's wrong? Issue NOT who did it first,
- School text (Class IX) says Greeks did it better.

### Why so many blunders?

- Repeat blunders means no learning from past mistakes
- AND there is a systematic cause
- Cause: Ignorant politicians trying to manage knowledge and the knowledgeable.

### Difference

- For the ज्ञानी loyalty is to proof.
- नेता demands (and gives) proof of loyalty.
- Hence, supports sycophants (and punishes the competent)
- i.e, puts ignorant loyal monkeys in charge who repeatedly cut off the nose (of Indian tradition)

### Interim summary 1

- Many attempts to glorify Indian tradition end up making a joke of out of it and damaging its credibility,
- since loyalty is valued not knowledge.

### To remind you: in Indian tradition

- ज्ञानी tells king what to do, not other way around.
- So, what is needed is (a) respect for knowledge, (b) loyalty to proof.
- So let us see the means of proof in Indian thought.

## प्रत्यक्ष (empirical) in science and Indic thought

### Proof in science

- science begins with observation
- and experiment
- Similar method used in Indian thought.

### Proof in Indic thought

- Notion of proof in Gotama's Nyaya sutra 2.
- Uses 4 means of proof: प्रत्यक्ष, अनुमान, उपमान, शब्द
- as explained earlier in this video,
- Examples of use in Indian गणित

### Disagreements, but all accepted प्रत्यक्ष

- Nastiks (Buddhists, Lokayata) rejected उपमान, and शब्द प्रमाण as unreliable.
- BUT ALL ACCEPTED प्रत्यक्ष = empirically manifest.
- Hence, Indic thought prima facie scientific.

### Use of experimental method in India

- World's FIRST recorded use of the experimental method is from India.
- Payasi (पायासी सुत्त, दीघ निकाय) performed numerous experiments with dying persons
- to try and refute belief in life after death.

### Ultra-chauvinist Western history

- attributes experimental methods to Francis Bacon from 2000 years later
Corrupt Bacon was superstitious, and said:

"the word of God [Bible] …[is] the surest medicine against superstition"

- Some more details on Payasi vs Bacon in this article on scientific temper in ancient India.

## अनुमान (reasoning)

- 2nd means of proof in Nyaya sutra 2 is अनुमान (accepted by all except Lokayata),
- Refutes foolish Western caricature that use of empirical excludes use of reasoning
- Did not so exclude in Indian thought any more than in science.

### Inferring earth is round (गोल)

- Āryabhaṭa (आर्यभट) in Gola 6 asserts the earth is round.
- NOT observed by travelling to space
- but DEDUCED from observation that far off trees cannot be seen as Lalla (20.36) explains.
- Earth rotation also inferred by Āryabhaṭa (Gola 9-10)

### Contrary to ultra-chauvinistic Western myths

- early Greeks and Romans could NOT make that deduction
- Hence, Latin Bible (Vulgate [and King James or NIV])asserts earth is flat
- (5th c. Vulgate contemporaneous with 5th c. Āryabhaṭa).

## उपमान (Analogy)

- 3rd means of proof in Nyaya sutra 2.
- Used as in Āryabhaṭa’s statement (Gola 7) that
- the earth is like a kadamba flower

### Āryabhaṭa's use of analogy

- is purely expository,
- and NOT used to draw any conclusions.
- Imp. since analogy rejected as invalid by Buddhists.

### BUT in contemporary science

- general relativistic cosmology makes ESSENTIAL use of analogy.
- In obtaining the basic Friedmann models
- by solving the Hilbert-Einstein equations \(G_{\mu\nu} = \kappa T_{\mu\nu}\)
- the stress energy tensor \(T_{\mu\nu}\) is
- assumed BY ANALOGY to be that of a "perfect fluid".

### "Perfect fluid" (by analogy)

- \(T_{\mu\nu} = (\rho + P)u_\mu u_\nu + P g_{\mu\nu}\)
- where \(u\) = velocity, \(\rho\) = density, and \(P\) = pressure
- In Newtonian physics, density and pressure are defined as statistical averages due to random molecular motion.
- In GRT, no molecules, no relativistically invariant probability measure to describe randomness.

### Hence, in contemporary science (cosmology)

- pure (inapplicable) analogy used in an essential way.
- Reason: Hilbert first gave correct equations for GRT
- Einstein quickly copied

### Hilbert vs Einstein

- Hilbert, a mathematician, concerned with geometry,
- NOT physical characterization of matter.
- (Used Poincaré's idea that force in Newtonian physics can be eliminated
- by appropriately modified geometry.)

## शब्द प्रमाण (Śabda pramāṇa, testimony)

- Used e.g. in Mānava śulba sūtra 10.10 ("Pythagorean theorem")
- तद विदो विदु: ("so say the knowledgeable")
- just because the author is an artisan (not himself a knowledgeable गणितज्ञ)
- HENCE invokes "proof by authority".

### Proof by authority has no place in real science

- but permeates contemporary science.

## RePutability vs refutability

- Contemporary science validated through publications, not experiment.
- Publications must be SECRETIVELY peer-reviewed.
- Value measured through citation index (a measure of popularity: like saying popular films are the best ones.)
- That is, truth in science decided today by rePutability, not refutability.

- And through impact parameter
- a racist measure which assumes that Western peer-reviewers are superior

- As in club membership in which
- "Indians and dogs not allowed".

### This method of validation

- through Western socially approved publications
- makes "scientific truth" subordinate to Western authority.
- Further discussion in Ending Academic Imperialism

### Interim summary 2

- Indian method of proof prima facie scientific.
- Contemporary science relies on methods of proof rejected as weak in Indic thought.

## Formal math: how it enables "fool and rule"

### Math and authority

- An even more insidious method of smuggling proof by (Western)( authority into contemporary science is through mathematics.
- Contemporary science uses FORMAL math
- "qm begins with a separable Hilbert space"
- "propagators of qft (in configuration space)are Schwartz distributions"

### Differential equations,calculus, reals

- Even at the most elementary level, most science uses differential equations
- e.g. Euler-Lagrange equations, Maxwell's equations, …
- This need calculus,
- and our texts teach that calculus needs (unreal) real numbers
- defined only in formal math.

### Formal math prohibits the empirical

- Unlike gaṇita (normal math) which uses "reasoning PLUS empirical (प्रत्यक्ष)"
- formal math uses "reasoning MINUS empirical".
- Prohibition of empirical in formal math bodes ill for science.

### Post-colonial mathematical illiteracy

- Most people unaware that formal math PROHIBITS the empirical
- though this is explicitly stated in the class IX school math text (p. 301)
- "Beware of being deceived by what you see"
- meaning "rely ONLY on axioms approved by Western authority"

- Divorce of formal math from empirical can be checked by reading any text in mathematical logic.
- And is discussed in my Hawaii keynote from 2000 to Durban keynote 2017 to now.
- Cause of divorce from empirical: church origins of axiomatic proof.
- But few people know enough formal math; class IX text, or to axiomatically prove 1+1=2 in real numbers.

### "It works" superstition

- Instead GULLIBLE and SUPERSTITIOUS people defend formal math (and contemporary science)
- by claiming "it works"
- "they have sent a rocket to the moon".
- ("It works" superstition also used by astrologers to defend astrology.)

### The problem with "it works"

- what EXACTLY works?
- The superstitious don't know. They never calculated a rocket trajectory.
- That calculation uses NORMAL math NOT formal math. What works is normal math.
- Easiest proof: trajectories calculated today on computers which use FLOATING POINT NUMBERS not formal real numbers.

### Most present-day school math from India

- arithmetic (e.g. "Arabic" numerals, algorithms, zero
- algebra (अव्यक्त गणित), probability, and statistics
- trigonometry and especially calculus.
- Went as NORMAL math returned as FORMAL math.

### Interim summary 3

- Formal math PROHIBITS the empirical but is used in contemporary science.
- "It works" because in practice normal math is used.
- Much math went from India to Europe as normal math, but returned as formal math.

## Calculus

### Especially West STOLE calculus from India

- In 16th c., Cochin-based Jesuits translated and sent Indian texts to Rome
- for the precise trigonometric values needed
- to solve the European navigational problem.
- From Rome they diffused—Galileo, Cavalier1, Fermat, Pascal, Newton, Leibniz.

### Because calculus STOLEN from India

- hence Europeans (Descartes,Newton, Leibniz) FAILED to understand it
- On my epistemic test, those who steal knowledge fail to FULLY understand it
- like students who cheat and copy in an exam.

### Practical value without full understanding

- Europeans COULD derive practical value from calculus
- (as the numerical solution of differential equations)
- to obtain precise trigonometric values needed for navigation.
- But they did not understand how to sum infinite series

### Indian way to sum infinite series

- Nīlakanṭh, आर्यभटीयभाष्य. comm. Gaṇita, 17
- using non-Archimedean arithmetic
- which has infinitesimals
- which can be discarded on zeroism
- only a Western superstition that math is exact.

### Western failure to understand calculus led to real numbers

- Europeans acknowledged their lack of understanding of calculus
- Hence invented real numbers (1880's) and axiomatic set theory needed for that (1930's).
- Real numbers more harmful than Payasi's objections which can be resolved.

### We teach calculus today in that inferior way

- which DESTROYS the core of Indic thought.
- Core of Indic thought is about आत्मन and मोक्ष,
- which needs quasi-cyclic time, like ethics (धर्म)
- but real numbers FORCE superlinear time) in physics (through METAphysics of formal math).

### Westerners understand that conflict between real numbers and CORE Indic thought

- between quasi-cyclic time needed for Indic thought
- and superlinear time of physics forced by real numbers
- video of my Berlin talk on decolonising time.

### But Indians don't get it.

- See my talk at 25th Vedanta Congress
- presentation online, but video not made public by Dr Balaram
- nor a recording given to me as promised.
- Because no understanding of its importance.

### Interim summary 4

- Calculus was stolen from India,
- hence poorly understood by Europeans,
- hence real numbers invented.
- Their use damages core of Indic thought.

## What should we do today?

- West fooled us once by stealing calculus
- Fooled us again with false history that "Newton and Leibniz discovered it"
- which false history we TEACH in our school texts!

### Fooled us yet again by claiming formal math and real numbers "rigorous", "superior"

- though it prohibits प्रत्यक्ष, hence is
- anti-science, AND
- goes against core beliefs in Indic thought.

### I tried to correct things

- by pointing that calculus is stolen from India
- and using original Indian philosophy of गणित
- makes it easy (taught in 5 days)
- and enables students to solve harder problems.
- Not even willing to discuss this teaching, since it involves confrontation with the West.

### Thesis that calculus stolen from India was itself stolen

- My Hawai'i talk of 2000 etc, plagiarised.
- Kak was the first to celebrate it by saying
- "Three Britishers claim calculus originated in India"
- Comic!🤣 were three Christians (two with Indian passports, one my post-doc, one Russian, none knew Sanskrit or math or Indian history.)

### This plagiarism was exposed

- Almeida, and John gave apologies
- In my book, I exposed elementary mistakes in their plagiarised paper.
- But the gullible can be fooled again and again.

### Hence plagiarism repeated by George Joseph and Almeida in 2007

- All Indian newspapers gave it front page coverage
- Only Hindustan Times carried a retraction.

### But gullible Indians can be fooled again, again, and AGAIN

- पाञ्चजन्य interviewed me
- Believed that fake news from 2007
- and ended by praising the serial plagiarist (and ignoramus) George Gheverghese Joseph!
- Seems West will keep fooling Indians for ever.

### Clearly there are SYSTEMIC problems

- Promotion of ignorant loyalists which damages credibility of Indian-origin sources
- Blind belief in reliability of Western/Christian sources (as taught by colonialism)
- Clamour to claim "we did it first"

- but failure to understand that often "we also did it different, and BETTER".
- and refusal to teach that difference,
- because of blind desire to imitate the West taught by colonial/church education.
- No hope of correction in near future.
- Post-independence betrayal of the freedom struggle.

### Interim summary 5

- Calculus was stolen, hence poorly understood, - hence real numbers invented. Not needed for science.
- They damage core of Indic thought, though this is little understood.
- Many practical advantages of (Indian) calculus without limits.

## Conclusions

- Indic thought was scientific and accepted प्रत्यक्ष (empirical),
- but rejected analogy and authority as weak.
- Contemporary science accepts analogy. Based heavily on Western social approval and authority.

- Contemporary science uses FORMAL math, which prohibits the empirical, forcing reliance on Western authority.
- Normal math works, formal math just grabs credit!
- Church superstitions (about infinity and eternity) creep in through formal math
- and are fatal to the core of Indic thought.