• Notion of ātman central to Hinduism and its ethics.
• Is it (ātman) science or faith?
• Will use this talk at 25th Vedanta Congress as background reference.

• Different systems of ethics/laws prevail: e.g sex as original sin vs kāma as ethical.
• How to choose between them? Solely on faith (or compulsion of law)?
• Or is there something intellectually more compelling, like (real) science?
• Starting point: These systems of ethics depend upon notion of soul.

• the best way to understand how altering notion of soul changes ethics.
• "Dharmic vs Abrahamic" wrong, simplistic!
• Ātman ≈ soul, in EARLY (pre-Nicene) Christianity:
• Origen related ethics of karma-samskāra to equity and justice.¹ BUT

• Ātman ≠ soul, for post-Nicene church notion of soul (Augustine, 4th c. on)
• Why? Post-Nicene church married state, sought power, got politicised,
• created doctrine of sin, hellfire, frightened people.
• Altered notion of soul to support iniquitous politics of Christan supremacy.

• Fought religious wars, initially against "pagans" in Roman empire and Europe,
• then against Muslims and Jews (Crusades),
• then against indigenes (Africans, Inca, Maya…)
• and against all non-Christians (except pre-Christian Greeks).

• Belief in ātman depends on nature of time:
• a key concern of SCIENCE,
• but also of religious POLITICS (e.g. nature of eternity)
• Hence, much confusion surrounding time beliefs.

• Term "cyclic" time used to describe two CONFLICTING notions of time:
• (a) quasi-cyclic time and (b) supercyclic time
• term "linear" time also used to describe two CONFLICTING notions of time:
• (a) mundane time (you decide some future) and (b) superlinear time (laws of physics decide all future).

• Using ONE term for two CONTRADICTORY notions
• enables one to draw ANY pre-desired conclusion (\(B\)) since ($A ∧ ¬ A ⇒ B.$)
• E.g. Quasi-cyclic time can be confounded with supercyclic and rejected as deterministic (Augustine, Stephen Hawking).
• E.g. Determinism of superlinear time of physics can be confounded with creativity of mundane time. (Most Western philosophers.)

• Popper's (Poincaré's) criterion of (empirical) falsifiability or refutability: science must be refutable.
• Simplified formulation: we must (in principle) be able to perform an experiment to test a scientific theory.
• What is non-refutable is metaphysics, NOT science.
• Science may be good or bad. Good science: a scientific theory not already or trivially refuted.

• But when did the experimental method begin?
• First recorded use concerns the soul:
• EXPERIMENTS performed in India to test whether the soul exists.
• (Western texts will NOT acknowledge the truth of this.)

• Pāyāsi asked his friends both good and bad
• who were dying
• to come back and report to him what they encountered after death.

• "Weigh this man.
• "Strangle him with a bowstring [so that no blood is spilt]
• "then weigh him again"
• No change observed, hence soul has no weight

• "Put this man in a pot, seal its mouth well, and heat it till the man dies."
• "Then make a small hole in the pot to see if any tiny object [the soul] comes out."
• Conclusion: soul cannot be seen.
• Many other experiments and doubts.

• Note: pre-Buddhist India was "Hindu",
• since no Christianity, Islam, Buddhism or even Jainism then.
• Pāyāsi's expts, NOT chance effort.
• Systemic reasons found in Indian philosophy and traditions.

• 1. Empirically manifest (प्रत्यक्ष) accepted as first means of proof by ALL traditional Indian schools of philosophy.
• 2. Complete freedom to criticize: but other people's theories were attacked, not their persons.
• Let me elaborate a bit.

• Nyāya, Vaiśeṣika, sānkhya, yoga, mimāmsā, Buddhist, Jain, Lokāyata,
• accepted the empirically manifest (प्रत्यक्ष) as the FIRST means of proof.
• E.g. the Nyāya Sutra of Gotama says in sutra 2
• प्रत्यक्ष (manifest), अनुमान (inference), उपमान (analogy), शब्द (testimony) are the means of proof (प्रमाण).

• Pratyaksh is the first means of proof, the strongest,
• anumāna = inference/deduction weaker,
• shabd ("reliable source") is the weakest means of proof, weaker even than analogy.
• (Buddhists reject upamāna and shabda, Lokāyata reject also anumāna, inference/DEDUCTION as unreliable.)

• Pāyāsi's critique found in THE major Buddhist RELIGIOUS text.
• (Naive responses by child monk Kassapa.)
• To understand value of this Indian tradition, let us compare with West.

• Why? Western thought developed under long-term church hegemony (4th-19th c.).
• Hence, relied on śabd (shabda) pramāṇa ("faith", "gospel truth").
• Mildest criticism brutally suppressed (e.g. during Inquisition, and mass burning of heretics, censorship….)
• Why? Any critique seen as challenge to church power (=soft power), based on false claims/narratives of superiority, not weapons.

• Claim of racist supremacy: that "Whites are superior to Blacks"
• Based on "gospel truth": Bible defence of slavery (curse of Kam/Ham)
• REPLACED earlier assertion of Christian superiority used to demand genocide and slavery as a MORAL duty (Bull. Romanus Pontifex)²,
• AFTER Black slaves in Americas converted to Christianity.

• After Columbus "discovered" America, millions of native inhabitants lost their right to land.
• That is, racism originated from religious politics.
• Shabda pramana used since claim of racist supremacy cannot be defended by fact (pratyaksh) or argument (anumana).
• Hence, technique of "saving the claim" by attacking the PERSON not the argument or any facts.

• Due to church hegemony, excessive reliance on shabd pramana/authority affected Western academics
• since the church started Western universities during Crusades.³
• Affects also Western SCIENCE: heavy reliance on rePutabality (NOT reFutability).
• Social reputation persuasive, but irrelevant for REAL science.⁴

• So, these methods (relying on शब्द प्रमाण) are all pervasive today.
• You might judge what I say using this. That would not be right.
• So will dwell on it a bit.
• Let me give 3 examples of how this works TODAY.

• My article, "To decolonize math stand up to its false history and bad philosophy" first published in Conversation. (24 Oct 2016)
• Went viral. Taken down by its South Africa editor.
• Why? Because I said "Euclid" was probably a black woman.
• Reproduced AND censored worldwide, also in India (by Scroll and Wire, Wire put it back).

• No issue about "peer review", published in FULL in peer-reviewed J. Black Studies, Rhodes Must Fall book
• Why censor math? If you don't like it publish a rebuttal.
• Explain how you concluded "Euclid" from Africa was a White male (as shown in school texts, Wikipedia)!
• Obvious: No one could do so.

• Witzel from Harvard attacked me (personally) saying I am "Hindutva".
• On Western rules of debate (since Inquisition) no proof needed for accusation: I am deemed guilty and required to prove my innocence
• EVEN if I prove my innocence (e.g. thrown out of various jobs by nationalist govt.)
• the proof would be just ignored, as editor of H-Asia did until pushed.

• To establish his authority Witzel told 2 BRAZEN lies:
• (1) that I used Wilson's translation of the RgVeda (FALSE, I used my own, easily checked that my translation different);
• (2) that I talked of six-faced dice in early India (FALSE, no mention of six-faced dice in my article online).
• But shabd pramana from Harvard believed, and my response published with great difficulty, ignored.
• My imp. point (that probability on Buddhist logic similar to quantum probability) completely LOST since beyond Witzel.

• Hawking's serious book POSTULATES "Chronology condition":
• no "cyclic" time (no closed time-like curves),
• using Augustine's defective argument: that "cyclic" time against "free will".
• Concludes with claim of singularity as a moment of CREATION.⁵

• No metaphor as bluntly stated in Tipler's books. Quote, Quote contd.⁶ (Tipler published in Nature)
• During a visit to Univ. of Cape Town, to discuss Decolonised math and science, I offered to debate both
• the theology and mathematics of singularities in the math dept. which had Ellis,
• as I had debated with Penrose in 1997.

• All hell broke loose. No one addressed ANY of my arguments.
• But I was denounced by South African press as "Hindutva".
• The ultimate and final Western rebuttal for every criticism!
• For the accused must defend, and the defence is discarded.

• Smuggling Augustine's theology in the middle of Hawking's 391 page serious book is OK.
• Not Christutva: they are "rePuted scientists".
• Demanding that science should avoid Christian theology is "Hindutva"!
• PS. My response to Penrose given Nobel for singularity theory, ultimate argument from rePutability.

• of how shabd pramana is used today to slip in myths and superstitions everywhere.

• who came 2 THOUSAND years after Payasi!
• Actually, Bacon believed in primacy of shabd pramana: or gospel truth.
• Said "The word of God [Bible]…[is] the surest medicine against superstition" (Novum Organum, 4, p. 89).
• According to me shabd praman is the SOURCE of superstition, e.g. racism.

• Said Egyptians "out of vanity have made this monarchy some thousands of years older than the world" (Chronology of Ancient Kingdoms Amended)
• Belief in shabd pramana results in superstitions.
• And: if scientists are superstitious, those superstition creep also into science.

• Newton's "LAWS of motion", "LAW of gravitation".
• How does one know there are eternal "laws of nature"? (Belief in "Laws" of nature religious: part of church dogma, not found in Hinduism or Islam).
• Barrow (Newton's mentor) wrote time could be represented by a "a strait or circular Line"
• Newton chose linear time. Why? (Because of the church curse on "cyclic" time!)

• Barrow TRIED to define "equal intervals of time"
• Newton avoided a defn, thought time known to God. (His physics HENCE failed.)
• E.g. conceptual problem: what is meant by "uniform motion" in 1st law? Rate of change in 2nd law?
• Assigning meaning requires a defn of "equal" times, i.e. a specified clock.

• Yes, through formal math.
• Gaṇita accepts empirical proof, formal math bans it.
• "Laws of nature"= differential equations of physics.
• Differential equations require calculus.

• On formal math, calculus requires "real" numbers. (Shabda pramāṇa, reals not required for calculus in gaṇita.)
• Use of reals for ODE/PDE forces time in physics to be like a line (superlinear time).

• You work with computers which CANNOT use a single REAL number such as \(π\).
• (Storing infinite decimal expansion requires infinite storage.)
• Hence, computational math uses floats. (See extract on floats from my "Lecture notes on C".)
• Floats don't even obey the associative LAW for addition. (See Hawai'i paper, or write a small program.)

• But you believe practice is erroneous and university texts on math are right! 😄 That's superstition!
• More details for another day.

• Indian tradition accepted प्रत्यक्ष as first means of proof.
• Western tradition relied on शब्द प्रमाण.
• Hence, superstitions creep into Western science directly (e.g. chronology condition)
• or through axiomatic math entire dependent on Western shabd pramāṇa.
• But let us get back to the central topic.

• Even in popular-level Hinduism (Bhagavad Gita)
• rebirth takes place in successive cycles of the cosmos.
• (And each cycle takes a very long time.)

• Do NOT refute the Hindu notion of rebirth
• in successive cycles of the cosmos
• or successive days of Brahmā
• But how can such rebirth happen?

• All past and future states of the system determined by specifying the "initial" state: positions and momenta of all particles.
• If the gas has n particles, its state determined by specifying 3n positions and 3n momenta (i.e., by a single point in 6n dimensional phase space).
• There is a unique trajectory through each point of phase space; trajectories never intersect.

• with each point in the swarm representing a possible state of the system, then
• in 19th c. terminology: the evolution of the system is like the flow of an incompressible fluid.
• (Incompressible since trajectories never intersect.)
• Volume is preserved in the flow of an incompressible fluid (Liouville's theorem).

• there is only a finite amount of volume available.
• Therefore, the evolution of the system will be quasi-cyclic.
• This theorem the basis of the famous recurrence paradox of thermodynamics: the entropy cannot increase.
• Formal mathematical statements and proofs of the Poincare recurrence theorem and the Liouville theorem are in my 1994 book.

• Belief in repeated lives after death is science, NOT superstition.
• Don't misunderstand. Saying it is science means it is refutable, NOT that it is always true. (That would make it non-science.)
• Poincaré recurrence MAY fail because (a) Newtonian physics fails, or (b) the cosmos is not closed.
• Belief in repeated lives after death may or may not be true, but it is NOT a superstition.

• Repeated crucifixion of Christ = destruction of Christian morality,
• for Christ is unable to save himself, leave alone others.
• "Heaven forbid that we should believe this for Christ having died once for our sins, rising again, dies no more."

• Augustine's solution: replace reincarnation (repeated lives after death)
• by resurrection (life after death exactly once). (Christ resurrected on Easter.)
• Makes current Christian notion of soul pure metaphysics:
• notion of resurrection irrefutable.

• "Now I find among the bad things written by Origen the following: that there are innumerable worlds, succeeding one another in eternal ages…
• "that in restitution…Archangels and Angels, the devil, the demons
• "and the souls of men whether Christian, Jews or Heathen will all be of one condition and degree [i.e., they too will be saved], and…
• "we who are now men may afterwards be born women, and one who is now a virgin may chance then to be a prostitute".

• These two "saints" Augustine and Jerome deliberately lied and misrepresented Origen.
• Origen explicitly rejected eternal/exact recurrence.
• Said reincarnation meant equity (since all people initially created equal)
• + justice (since they were rewarded or punished in the next life on the MERIT of their deeds).

• it turned AGAINST equity to suit its politics.
• E.g. Jerome wanted only Christian to go to heaven not Jews and heathens.
• Church concurred: Christians must get special treatment.

• Origen, like Hinduism, believed in karma samskāra (deeds-disposition)
• what happens in next life depends on deeds in this one, not religious affiliation.
• Also denied eternal recurrence, or chance ("virgin may chance to be a prostitute"), as misrepresented by key church figures.

• How is karma-samskāra possible across cosmic cycles?
• More basic question: how is karma-samskāra possible in everyday life?

• Not using the theologically loaded term "free will".
• (Where is the free will in the Hilbert-Einstein equations?)
• Using instead mundane experience and "mundane time".
• E.g. preparing for exams makes you better disposed to doing well
• (not quantifying or getting into questions of what is probability).

• Flaw in Newtonian physics was failure to define equal intervals of time or a preferred clock.
• "Uniform motion", "rate of change" make no sense without a clock.
• Flaw became prominent with Maxwell's equations which had time dependent forces
• unlike time-independent forces of Newtonian gravitation,
• which allowed time to be eliminated.

• Defined equal intervals of times by declaring speed of light constant.
• Bouncing photon between parallel mirrors:
• times between bounces conceptually equal,
• defines equal intervals of time.

• BUT speed of light becomes a limiting speed, since mass increases with (relative) velocity (\(m = γ m₀\)).
• Hence, finite speed of interactions (instead of Newtonian instantaneous action at a distance).
• Hence, equations are functional differential equation (FDEs).

• Poincare's relativity (uses FDE) destroys the assumptions of recurrence theorem.
• "Newtonian paradigm": Ordinary differential equations (ODE) e.g. \[y'' = -k^2y.\]
• admits unique soln. from initial data:

\[ y(0) &= y_0 ,\] \[ y'(0) &= y_1.\]

• \[y'(t) = y (t - 1) .\]
• needs PAST data.
• If we try to integrate

\begin{align} y (1) &= y(0) + \int_0^1 y'(t) dt \\ &= y(0) + \int_0^1 y(t-1) dt. \label{int} \end{align}

• We need to know \(y(t-1)\) for all \(t \in [0, 1]\) i.e., \(y(t)\) for all \(t \in [-1,~ 0]\).

• ODEs can also be solved backward from final data.
• But phase collapse for FDEs, hence cannot be solved backward.
• E.g. 3 different solns of \(y ' (t) = b(t) y(t-1)\)
• where \(b\) vanishes outside [0, 1], and \(\int_{-\infty}^{\infty} b(t)~dt = \int_0^1 b(t)~dt = -1\).
• DIFFERENT pasts but same FUTURE.

• \(Tₜ\) no longer a group (time asymmetry of FDEs).
• Phase flow no longer preserves volume (phase collapse with retarded FDEs).
• Why past dependence? Because FDEs = COUPLED system PDEs (Maxwell's equations) + ODEs (Heaviside-Lorentz force "law").
• Such coupled systems little studied.

• Qualitative differences between FDEs and ODEs show that retarded FDEs cannot be approximated by ODEs
• as Einstein and many others tried to do.
• Counter e.g. \(y'(t) = y(t-\tau) - y(t)\) ), \(τ\) small,
• approximated by 2nd order ODE, \(y'(t) = \{ y(t) - \tau y'(t) + \frac{\tau^2}{2!}y''(t) \} - y(t)\)

• Has soln. \[y_{\rm approx} = c_1 + c_2 e^{st}\]
• (\(s = \frac{2(1 + \tau)}{\tau^2} > 0\), \(c_1\), \(c_2\) constants determined by the initial data.)
• unbounded if \(c_2 \neq 0\)
• But all solns of original FDE bounded.

• people who copy make mistakes (Einstein did not understand FDEs),
• like students who cheat in an exam.
• Hence, in suspicious circumstances, mistakes = proof of copying.
• Hence, Einstein copied relativity from Poincaré (who understood the need for FDEs).

• also never solved FDEs for a CENTURY
• even for the 2-body problem of classical electrodynamics
• which involves soln. of PDE (Maxwell's equations) COUPLED with ODE (Heaviside-Lorentz force law)
• coupled PDE+ODE = FDE.

• COULD NOT point to a flaw in my math in 30 years 😁, but
• give monkey argument "who are you to challenge Einstein"?
• Who am I? Nobody! Just someone who from age 17 sought to learn more instead of earn more. So, I learnt.
• But monkeys understand status, not relativity!

• So my argument from shabd pramāṇa is this.
• Michael Atiyah, only mathematician to get both Fields medal + Abel prize
• in his Einstein centenary lecture,and its report repeated my claim about FDEs,
• just added "don't forget I suggested this"!

• Whether or not Atiyah plagiarised (SSV case no. 2 of 2007)
• he FAILED to understand the key point about by FDE thesis.
• That is NOT about Einstein's mistake nor about RETARDED FDEs and QM.
• Let me explain: relativity arose from trying to reconcile Newtonian physics with electrodynamics.

• which has two types of solutions: retarded and advanced.
• Retarded solns are usual ripple in a pond spreading out from the centre,
• advanced solns. are the time reverse.
• Using advanced propagators results in advanced FDEs.

• Such as \(y'(t) = y (t+1)\) need FUTURE data. Determine past IF future known.
• E.g. three solutions of the advanced FDE \(y ' (t) = a(t) y(t+1)\) ,
• where \(a\) vanishes outside [0, 1], and satisfies

\[\int_{-\infty}^{\infty} a(t)~dt = \int_0^1 a(t)~dt = 1 .\]

• Hence: advanced phenomena cannot be predicted from the past. Characteristic feature.
• Do we observe some phenomena which CANNOT be explained from the past?
• (Just as retarded phenomena cannot be explained teleologically.)

• Solns show both features: branching + collapse.
• How do MFDEs arise?
• From the use of convex combination of retarded and advanced Green functions/Fields.
• \(G_m = α G_{adv} + (1-α) G_{ret} \quad 0 < α < 1\), (\(α\) small at current epoch).
• \[ F_m = αF_{adv} + (1-α) F_{ret} \quad 0 < α < 1.\]

• Theory 1: Based on Wheeler-Feynman absorber theory
• Abandoned since WF theory circular, my replacement not fully satisfactory.
• Theory 2: convex combination most general solution
  • instead of assuming causality (\(α = 0\)) establish it empirically starting from most general solution.

• Destruction of determinism, strict causality: - MFDEs correspond to a tilt in the arrow of time
• give rise to spontaneity (resolves Popper's pond and Grandfather paradoxes)

• Newtonian physics conceptually faulty: failed to define equal intervals of time.
• Corrected by relativity;
• finite speed of interaction forces change to FDEs.
• FDEs imply destruction of Poincaré recurrence theorem of Newtonian physics (supercyclic time).

• MFDEs destroy also determinism,
• imply spontaneity needed for mundane time (everyday karma-samskāra),
• needed for science to be able to design experimental tests.

• When retarded interactions dominate entropy increases towards future
• (more information about past than future).
• When advanced interactions dominate, entropy decreases towards future,
• i.e., time runs forward then backward returning approximately to initial state.
• NOT arrow of time, but boomerang of time.

• we can have quasi-cyclic time.
• With this model no fundamental difference between karma-samskāra within a cycle of cosmos
• and karma-samskāra across cycles of the cosmos.
• Moksha/nirvana = freedom from rebirth, the ultimate goal.

• एषा ब्राह्मी स्थिति: पार्थ नैनां प्राप्य विमुह्यति |
• स्थित्वास्यामन्तकालेऽपि ब्रह्मनिर्वाणमृच्छति || 72||
• Having attained this Brahma-state, O Partha, one is never again deluded.
• Established in it even at one's last moment, one attains nirvāṇa (liberation from the cycle of life and death and rebirth).

• Moksha/nirvāṇa seems a far off ideal.
• At an intermediate level there is my Harmony principle:
• "act so as to increase harmony in the cosmos".
• which subsumes but transcends evolutionary ethics of acquiring status, territory etc.

• whether the West with its control over math and science
• will permit something contrary to church dogma.
• In the past, church superstitions helped West to dominate (e.g. enslave Blacks for free labor).
• But today church superstitions in math and science impede technology development.