Practical Ganita vs Religious Mathematics

• Padres ruled Europe for 1700 years
• using (idiotic) superstitions about religious dogmas + false history.
• To make those superstitions credible, they used tricks such as childhood indoctrination
• such as teaching belief in Jesus through unscientific Christian calendar used for birthday to children.

• We could not change it
• or even widely teach an alternative scientific and secular calendar
• in 79 years since independence.
• Ok, so AD-BC church superstate taught with ABCD clear enough, BUT

• Here is Bertrand Russell's 378 page proof of 1+1=2 in simple case of cardinals in his Principia Mathematca.
• How do YOU know it is VALID?
• You have FAITH in Russell's authority!

• That is what colonial/padreist education did to you.
• Instead of making you "superior" as Ram Mohun Roy imagined it would
• It made you SERVILE: forced you to rely on Western authority for even the simplest things like 1+1=2.

• This reliance on authority is not limited to mathematics.
• The present generation "fact checking" by turning to Google
• which takes you to chatbots trained on
• Wikipedia data designed to manipulate facts to suit Western opinion.
• We teach axiomatic mathematics because we wrongly believe it is "superior". Superior in what sense?

• Obviously, Russell's 378 page proof of 1+1=2 adds NIL practical value in a grocer's shop.
• This is equally true of "rocket science" or AI:
• axiomatic math adds NIL practical value.
• (I teach ballistics as part of my course on Calculus as Ganita).
• Rocket trajectories are today calculated using the 5th c. Āryabhaṭa's gaṇita method of finite differences.

• This calculation done using computers by NASA/ISRO
• Computers use floating point numbers which do not obey even the associative law for addition
• as mandated for ALL common axiomatic number systems ℕ, ℤ, ℚ, ℝ, ℂ.
• But colonial education taught us "do NOT apply your mind;wait for the Master's permission".

• BTW, when Macaulay boasted of "immeasurable superiority" of the West he obviously didn't have rocket science in mind.
• For the only rockets the British then knew were the Indian rockets used to defeat them, and earlier Jehangir.
• Indeed, the purported "superiority" of Western math does NOT relate to practical value
• for the West has a very long tradition of denigrating practical mathematics as inferior.

• Western mathematics was intertwined with religious belief about the soul since Plato (e.g., Republic VII.527)
• and his explicit rejection of practical mathematics.
• Boethius' 5th c. Arithmetic (taught for over a millennium in the church quadrivium)
• cited Plato's denigration of practical mathematics and taught "superior" "spiritual" arithmetic!

• This denigration of practical mathematics as inferior continued until the 20th c. Hardy (Mathematician's Apology).
• The colonized did not understand the meaning of "superior" in the padreist boast of superiority echoed by Macaulay
• that it relates to their "superior" "spiritual" value
• and foolishly thought and think it refers to superior practical value.

• arithmetic ("Arabic numerals")
• algebra,
• trigonometry and calculus and
• probability and statistics,
• first via Arabs from 10th c. then directly from India since the 16th c.

• the practical India ganita they imported (or stole)
• because of HUBRIS (or dullness) due to the chronic European delusions of supremacy,
• due to religious superstitions, including "superior" skin color.

• European BLUNDERS in trying to understand elementary Indian place-value arithmetic
• and the promotion for 900 year of primitive Graeco-Roman pebble arithmetic as superior
• as in De Morgan's 1837. Algebra, p. xi. representative assertion that -1 = 10 - 11
• was meaningless in "immeasurably superior" Western mathematics
• since there are no negative pebbles!

• De Morgan came AFTER Macaulay,
• and this stupidity persisted till end of 19th c. and spilled over into some school texts even of the 20th c. (Hall and Knight, Algebra)

• This was the "immeasurably superior" mathematics Macaulay meant
• for which Roy, before Macaulay, hankered
• and for which we changed our education system
• so we could do "better" rocket science as the colonized today believe!

• Colonial education, to force obedience to Western authority, made math difficult and the colonized mathematically illiterate.
• But even for the illiterate these assertions of supremacy of Western pebble arithmetic are ridiculous - and have been abandoned since the 20th c.,
• However, the other ridiculous supremacist assertions persist,
• in the case of the calculus and probability which too Europe got from India.

• Namely that a "superior" way to do calculus is with limits,
• and that probabilities need Kolmogorov's axioms.
• Superior because axiomatic.
• Limits need real numbers. So you cannot decide without knowing why 1+1=2 in real numbers.

• As stated above, I teach that practical value of calculus comes from calculations using Aryabhata's method of finite differences
• or its improvements to solve differential equations.

– Epistemic value (summing infinite series etc.) comes from the अव्यक्त गणित of Brahmagupta and Bhaskara II + Zeroism/śūnyavāda.

• Infinite series (of Aryabhata school in Kerala) used only to prove THEFT of calculus by Newton, Leibniz, Gregory.

• अव्यक्त गणित is polynomial arithmetic
• NECESSARILY non-Archimedean
• hence limits not possible (calculus as ganita = calculus without limits).
• In contrast, reals are "Archimedean".

• Recall that real numbers were invented by Dedekind just because Newton's fluxions were incomprehensible
• Also, neither Newton nor Leibniz knew how to sum the Indian infinite series each claimed.
• On my epistemic test, failure to understand is proof of theft,
• especially in the context of a wild claim of "independent rediscovery" just when dependent discovery was possible since 16th c.

• So what should we do today?
• Teach calculus as ganita without limits? or calculus with limits?
• Which is BETTER?

• The West/colonized claim limits (and Kolmogorov axioms) are better
• because they use the axiomatic method
• which is epistemically superior.
• But the claim of epistemic superiority is argued exactly like the claim of racist superiority using only myths and superstitions.

• On the Western myth, the axiomatic method began with a Euclid.
• However, there are no axiomatic proofs in the book Elements 1 attributed to Euclid.
• This absence of axiomatic proofs has been admitted even in the West for over a century
• since Hilbert's 1899 rewrite of the "Euclid" book to provide the axiomatic proofs missing in it.

• The book never intended axiomatic proofs (as the new myth goes)
• as is clear from the fact that Hilbert's rewrite changed its geometry from metric to synthetic.
• And the fact that the book is chock full of diagrams(irrelevant to axiomatic proof)
• but show its nexus to Platonic and Neoplatonic geometry where diagrams are very important.

• There is no evidence for the very existence of a Euclid
• and no response to my repeated challenge prizes of Ra 2 lakhs for any primary evidence of Euclid, Pythagoras, etc.
• NCERT response 1 (Hukam Singh 2007) "Why do you need evidence?"
• NCERT response 2 "If European masters believed it you must believe it too, how unreasonable to ask for evidence"
• This Illustrates how church myths and accumulation of hypotheses can be used to dissolve all facts.

• The common sense response is to ask: why is such a heap of lies necessary at the beginning of mathematics?
• Lies are told to hide something.
• The Euclid lie hides the fact that the axiomatic method originated with the Crusading Church theology of reason.

• Actually, the axiomatic method originated politically very convenient method in the Christian theology of reason.
• as first used by Aquinas to prove his Angel theorem (Summa Theologica, First Part, Q. 52, article 3)

• Apart from hiding the church origins of axiomatic proof, a bunch of lies were told by the preceding NCERT class 9 text.
• Lie 1. There is no notion of proof in other traditions such as Ganita.
  • The Nyaya sutra 2, defines a notion of proof which is used for all disciplines including mathematics.
  • No such definition of proof is found in Western/early Greek tradition.

• अनुमान means deductive inference
• According to me, the Aristotelian syllogism is not found in Greece and is derived from the Nyaya Syllogism via Al Ghazali and Ibn Roshd.
• However, it was incessantly criticised by the Lokayat, so that it has come to mean conjecture or अंदाजा.
• This critique is acknowledged in the NCERT Hindi text by the use of the word निगमन which is not found in the literature
• and means induction!

• Deduction is infallible or less fallible than scientific proof as used in ganita which accepts the empirical (प्रत्यक्ष)
• To the contrary, the Lokyata argued that deduction was highly fallible.
• Their argument was correct. From wrong premises, any wrong conclusion can be proved.

• The church counter to this argument was to make the axioms metaphysical
• whose truth can only be decided by authority.
• E.g. How does one decide the validity of Aquinas axiom that angels occupy no space? Only by authority.

• Likewise, the axioms of mathematics are metaphysics.
• That is why even the new class 6 text under NEP teaches that geometric points are invisible as taught in the church quadrivium.
• How then do you decide the validity of the axiom that between any two invisible points there is a unique invisible line?
• Obviously, only by authority.

• The axioms of mathematics are all laid down by the West.
• So teaching axiomatic mathematics has the advantage that it makes all mathematical knowledge dependent on Western authority.