Eliminating the anti-Islamic biases in Mathematics and Science

C. K. Raju

*Indian Institute of Advanced Study*

*Rashtrapati Nivas, Shimla*

- Simplest example is Newtonian physics (the science that most people understand)
- Why Newton's laws of motion?
- or his universal law of gravitation

- Because of the belief that there are eternal and universal laws of nature.
- But, how exactly do we know that nature obeys any laws?
- How do we know that these laws are eternal?
- Or universal?

- Newton's laws of motion failed and were replaced by special relativity over a century ago (1904). (Note: 1904, NOT 1905.)
- Newton's linked law of gravitation also failed and was replaced by general relativity also about a century ago (1919).
- (Failure due to conceptual confusion in Newtonian physics, as I have repeatedly explained.)
- Important fact right now is just the failure of Newton's laws.

- We also know, for about a century (ca. 1913-1930), that
- particles at the micro physical level are described by quantum mechanics
- they do NOT quite obey rigid laws, but behave probabilistically at best.

- We know that Newtonian gravitation (including general relativity) prima facie fails at the level of the galaxy (since ca. 1940)
- Of course the theory can be "saved" by accumulating hypotheses such as dark matter halos.

- Advance of Mercury perihelion (19th c.), shows that
- Newtonian gravitation fails to apply accurately even within the solar system.
- Flyby anomaly (2008) and
- the recent case of Oumuamua (2017)may be further indications of its failure.

- is an alternative formulation of the theory of gravitation (2012).
- But won't go into that today.
- What matters for this talk is not whether my theory of gravitation is right or wrong
- Immediate point is that Newtonian physics is definitely wrong.

- (1) there are no known laws of nature,
- (2) such laws as were thought to have existed failed a century ago, hence are not eternal, and
- (3) they are not universal (do not extend beyond the solar system to the galaxy) on current empirical evidence.

- Immediate question not about validity or invalidity of Newtonian physics (we know it is invalid),
- but about the religious bias in it.
**Belief in eternal and universal laws of nature is completely aligned with church dogma.**- Not surprising.

- Because church dogma was an important "means of knowledge" in the West in Newton's time.
- E.g. Newton superstitiously believed the story of Biblical creation some 6000 years ago.
- This affected his beliefs about history: In his
*Chronology of the Ancient Kingdoms Amended*, chp. II), he wrote that Egyptians were vain because their list of king was older than the world!

- Aquinas, Summa Theologica, First part of the Second Part, 91,1 said
- God was an ideal ruler who rules the world with laws.
- Since there is nothing non-eternal in the nature of God, the laws of God must be eternal.
- They are universal for God rules over all parts of the universe.

- on (post-Crusade) church dogma, God created the world once
- and thereafter does not interfere in it but rules it with fixed laws.
- See my 2007 article Benedict’s Maledicts, for the POLITICS why the church accepted this dogma
- while Islam (al Ghazali) rejected it.

- "the Bible is the Word of God,
- and Nature is the Work of God".
- Galileo believed eternal "laws of nature" were written in the (eternal) language of mathematics,
- he wrongly thought math is the language of eternal truth (as Westerners religiously believed since Plato).

- in his handwritten notes, he cancelled
*hypothesi*and wrote*lex*(law), - because of his vanity that God had revealed his laws to him.
- Newton thought of himself as a prophet
- since born on Christmas day on a wrong calendar!😜

- Failed to define equal intervals of time
- (thought God ensures the flow of time with an "even tenor")
- This foolish belief that "time" itself flows was also the basis of his failed doctrine of fluxions
- in his attempt to understand the Indian calculus. (Or see the whole 500 page book Cultural Foundations of Mathematics)

- Has written a whole book.
- The key question that he raises is this:
- despite a good start (in the Golden age of Islam)
- why did the Muslim world fall behind the West in science?

- Probably colonialism is a good answer.
- But Hoodbhoy locates the answer in Islamic theology
- He blames al Ghazali.

- On Islamic belief, creation is NOT a one time thing; it is a continuous process.
- Allah recreates the cosmos every instant.
- The similarities between one world and the world at the next instant are due to habit, not causal necessity.

- That is, al Ghazali asserted Allah creates smoke with fire
- not because of any necessary causal connection between smoke and fire,
- but out of habit (which could change)

- Al Ghazali's argument was copied centuries later by the racist David Hume (as usual without acknowledgment).
- And it is better known to Westerners as Hume's argument.
- Even if we observe smoke with fire a 1000 times,
- that does NOT establish a NECESSARY causal connection between the two.

- Buddhist belief in conditioned coorigination (paticca samuppad):
- that all thing cooriginate every instant, but conditioned by the past.
- [This could have got into Islam after the Arab conquest of Persia (e.g. influential Barmakid in Haroun al Rashid’s time, as in Alif Laila wa laila)
- like Pancatantra into Ikhwan us Safa.]

- Anyway, according to Hoodbhoy
- this denial of causal necessity by al Ghazali - is the reason why the Muslim world fell behind the West in science.

- Recall that early Western universities for centuries learnt about "Aristotle"
- from the texts of Ibn Rushd (Averroes)
- who ineffectively opposed al Ghazali.
- See, Islam and Science, my Keynote at Univ. of Malaya., also Benedict's Maledicts.

- I recently again refuted Hoodbhoy.
- Also see, the hilarious minutes of a discussion in the Philosophy department of USM,
- when a Christian priest tried to introduce the belief in "causality", and "laws of nature" in a course on philosophy of science
- Also see, also, for example, this huge propaganda.

- in a mathematically correct way
- without any dogmatic belief in rigid and mechanistic laws
- using a combination of past conditioning ("causal determinism") and creativity

- Also see, the series on Functional differential equations in
*Physics Education* - or the popular account in Eleven Pictures of Time.

- Newton's laws have failed they are neither eternal nor universal,
- the real world does not seem to be based on laws
- the belief in laws of nature is promoted by church dogma,
- it is anti-Islam.

- So, there is a pro-church and anti-Islamic bias in Western science
- since the time of Newton.
- But this is just the proverbial tip of the iceberg.

- Religious biases in science not limited to a single individual
- they commonly originate from religious biases due to
- systematic church influence on Western ethno-mathematics

- where is the religious bias in 1+1 = 2 they ask.
- So, let me explain how 1+1=2 involves church superstitions
- according to (colonial) math as taught today.

- Most people will repeat what they were taught as children
- they will say 1 orange and 1 orange make 2 oranges
- The first step is to understand that this is an empirical process,
- and empirical processes are disallowed in the formal mathematics (= Western ethno-mathematics) brought by colonial education
- Why is the empirical disallowed? We will see shortly.

- Because of the divorce from the empirical
- "1" does NOT have an ostensive definition (meaning by pointing) like "dog".
- Hence, 1 does not have any natural or fixed meaning in formal mathematics (= Western ethno-mathematics)
- 1 as a natural number is different from 1 as an integer is different from 1 as a real number.

- Colonial education teaches ignorance.
- (Why? Because it was church education. To "fool and rule" this education is designed to spread ignorance.)
- To demonstrate ignorance of 1+1 = 2 in a lecture in JNU, I offered a reward of ₹1 million to the faculty for a proper proof of 1+1 = 2 in real numbers.
- Or, see this video of a much older talk on calculus at MIT where a hall full of people refused to admit knowledge of real numbers.

- The proof of 1+ 1 = 2 in cardinals took Bertrand Russell 378 pages in his Principia
- To do the same with real numbers is much harder
- since it involves axiomatic set theory needed to construct real numbers
- To do it from first principles one has to know all of it.
- But most people (including most mathematicians) do not even know the correct definition of a set.

- Such widespread ignorance of even 1+1 = 2
- combined with the firm belief that there is no other way to do it
- is already a sure sign of superstition.
- But let us see in more detail how these are specifically church superstitions.

- a modification of the earlier claims of religious then racial superiority:
- "we are superior, you are inferior, imitate us."
- This propaganda is spread through colonial education which was 100% church education when it came.

- In mathematics, the false myth of Euclid
- and his purported superior axiomatic proofs
- was a key item used to propagate this agenda of civilizational superiority .

- in Indian class 9 math school text,
- which has chapter 5 on "Introduction to Euclid's Geometry".
- In this, children are told that what Greeks did was superior, and we should imitate them,
- since what all others (Indians, Egyptians, Maya) did in mathematics was inferior.

- the church did.
**"Euclid" is a mask for the church.** - The false myth of Euclid is used to foist a bad church philosophy as "superior".
- Most people get entangled in the false history
- And are unable to recognize the linked bad philosophy as something which suited church politics.

- to support its campaign against Muslims by building Christian rational theology to counter Islamic rational theology.
- To do so, it simply reinterpreted the text, in a way which suited its purpose of conversion, but which does not fit the text.

- Because the church was concerned only with persuasion or proof (not calculation)
- it said axiomatic proof is the key purpose of mathematics.
- It said Euclid gave such axiomatic proofs.

- and asking us to imitate it,
- we declare church dogma as superior and imitate it.
- All colonised people do that, including Muslims.
- The church rightly calculated that colonized are too gullible and too ignorant to see through the simple trick.

- But the church concocts a whole web of interconnected lies.

- 1. The historical aspect
- 2. The veracity aspect
- 3. The philosophical aspect
- Today I will avoid 1 and focus on 2 and 3.

- Did Euclid exist?
- When was the text Elements first written?
- Was the author a white man or a black woman? etc. etc.
- See my book Euclid and Jesus for those aspects in detail.

- are there any actual axiomatic proofs in the book
*Elements*attributed to Euclid? - Did ANYONE give any axiomatic proof of the so-called Pythagorean proposition before the 20th century?

- did proofs exist in other traditions? What sort of proofs were they?
- What exactly is "superior" about axiomatic proofs?
- Who first invented the doctrine that axiomatic proofs are somehow superior? The Greeks, or the crusading church?
- Are deductive proofs actually INFERIOR to empirical proofs as the materialist philosophers (Lokayata) in India long maintained?

- To answer the about question you need to know what an axiomatic proof is.

- An axiomatic proof (or formal mathematical proof) is a sequence of statements in which
- each statement is either an axiom or
- is derived from some preceding statements by means of some rule of reasoning (such as modus ponens, A, A implies B, therefore B)

- In an axiomatic proof you are NOT allowed to introduce any statement of the following type "I see this, therefore it is true".
- (Therefore, you cannot use oranges to prove 1+1=2 in Western ethno-mathematics).

- For example, to measure the length of a line segment you normally take a ruler
- and superimpose it on top of the line segment.
- But this process of superposition being empirical is DISALLOWED as any part of formal mathematical proof.

- This too is a false myth.
- For example, here is a proof of the so-called Pythagorean theorem from India.
- So, proofs DID EXIST in other cultures
- but these involved the empirical and were not axiomatic proofs.

- But gullible Westerners, under church influence, believed this to be true for over seven centuries.
- The very first proposition of the Elements involves an empirical proof.

- "to construct an equilateral triangle on a given line segment (say AB)."
- The proof involves drawing two arcs with centres at A and B respectively, and radius AB,
- The two arcs intersect at a point C which is then joined to A and B to give the equilateral triangle ABC.
- BUT, this is an empirical proof because we say "I see the two arcs intersecting therefore it is true that they intersect at C".

- in the late 19th century
- led to "Dedekind cuts"
- which are today called real numbers.
- (But Dedekind required set theory, so real numbers had to wait until at least until axiomatic set theory.)

- involves superimposing one triangle on top of another
- to see that the two triangles are equal.
- This proposition is required to prove the "Pythagorean theorem" in the Elements.
- That is, there isn't a single axiomatic proof of any proposition in "Euclid's Elements.

- For 750 years (from 1125 to around 1900)
- that there were axiomatic proofs in the Elements.
- For axiomatic proofs the order of propositions is important.

- that it was compulsory to follow the order of the propositions in Euclid's
*Elements*. - This was exceptionally foolish because at the same time Cambridge University commissioned a text
- full of empirical proofs.

- They (including NCERT) don't know this class IX mathematics.
- They won't check the sources.
- They will go by the story and
- put their blind trust in Western authority.
- (so let me give a proof from Western authority)

- The absence of axiomatic proofs in Euclid was accepted also by Western authorities such as Bertrand Russell.
- I have posted the paper publicly.

- In fact, David Hilbert wrote a whole book on Foundations of Geometry
- to provide the axiomatic proofs missing in "Euclid".
- But since length measurement requires an empirical process of superimposing the ruler on the line segment,it is prohibited in Hilbert's geometry.

- Therefore, Hilbert's geometry is called synthetic geometry
- as distinct from metric geometry in which length is defined.
- Though length is not defined area is (to enable proof of the Pythagorean theorem)!

- even after the absence of axiomatic proofs in "Euclid" was admitted.
- The supposedly enlightened historian Needham foolishly kept talking of superiority of Greek geometry,
- and asked why Chinese did not switch to axiomatic proofs.

- Likewise, the Egyptologist Clagget kept foolishly asserting till the end of the 20th century that
- Egyptians did not have a proof of the Pythagorean theorem which, he said, is a "formal mathematical theorem in Euclid".

- "axiomatic proofs are superior to empirical proofs".
- E.g., Dedekind saw there is no axiomatic proof of the first proposition in "Euclid".
- But what he do?
- He supplied an axiomatic proof on the belief that axiomatic proofs are superior!

- but he too blindly accepted the dogma that axiomatic proofs are superior.
- In fact the whole of the formal mathematics developed by Hilbert and Russell
- is based on the superstition that axiomatic proofs are superior.

- is that empirical proofs are fallible while detective proofs are infallible.
- (The very word infallible should warn you that a superstitious belief is ahead
- like the suppose infallibility of the pope.)

- This is accepted by all.
- The classical Indian example is rajju-sarpa nyaya that one may mistake a snake for a rope or vice versa.
- This is also accepted in science, as in the acceptance of experimental errors.
- The easy remedy is to repeat the experiment, and arrive at the truth inductively.

- Hence all traditional schools of Indian philosophy, without exception,
- accept the empirically manifest as the first means of proof,
- as the science.

- The Western superstition that deduction is infallible is LAUGHABLE for many reasons.
- First, as any mathematics teacher knows, students very often submit wrong proofs in examinations.
- Hence they often flunk.
- So,
*whose*deductions are infallible?

- Second, most people cannot check the validity of a complex deductive proof such as the proof of 1+1=2 in cardinals by Bertrand Russell.
- So they just trust authority.
- In that case the purported infallibility of deduction is the same as the silly superstition in the infallibility of the pope.
- The only differences that in the case of a mathematical proof people regardless of religion trust the authority of the mathematician.

- e.g. gospel truth vs science

- Third, given that there may possibly be errors in a deductive proof,
- the only way check validity is to repeatedly check the proof.
- This is an inductive process, hence not infallible.

**

- In fact, since the validity of deduction depends upon induction
- deduction is MORE fallible than induction

- As the game of chess demonstrates the human mind INVARIABLY errs when given a complex task of deduction.
- Thus the most authoritative Grand Master loses to the computer EVERY time.
- (And in chess losses are always due to an error, an error-free game must and in a draw.)

- (But church dogma contrary to human senses)

- In the West reason was cultivated by the church,
- which foolishly assumed that there is only one kind of logic which binds God.
- In India we know of a variety of different logics such as Buddhist logic, Jain logic etc.
- The logic of the real world may be quantum logic, which is not two valued.

- except by cultural prejudice
- or empirically
- If logic itself is decided empirically, hence inductively, that makes deduction deduction weaker than induction

- An axiomatic proof is one which begins not from facts
- but from some assumptions or postulates
- (postulates = axioms ≠ self-evident truth).

- No. Formal mathematics is divorced from facts. - E.g. consider the axiom "through any two points there is a unique straight-line".
- This axiom is not a fact. It is false for [[][any two visible dots which can be connected by more than one line.
- Formal mathematics is metaphysics (disjoint from empirical reality) not mere abstraction.
- Dots are an abstraction, size-less points are metaphysics.

- During the Crusades, the church wanted to appropriate reason, to contest Islamic rational theology.
- But reason + facts =science.
- The striking innovation of the Crusading church was that it could adopt reason MINUS facts,
- because it was primarily facts which went against church dogma,
- not reason alone.

- in Summa Theologica, First Part, Q. 52, article 3.
- in his reasoning about angels: that many angels could stand on a pin.
- No facts about angels
- but one can make any assumption one likes, fantasize anything.
- But such fantasy reasoning does not suit science.

- Ignorant colonised are superstitious; they fear any change will bring about a catastrophe.
- They ask how does formal mathematics work for science?
- The simple answer formal mathematics does NOT work for science.

- The formal mathematics of the calculus requires real numbers.
- But NASA calculates rocket trajectories using computers.
- Computers CANNOT represent real numbers. They cannot correctly do the arithmetic of real numbers.

- which do not obey even the associative law for addition of real numbers.
- At best they are only approximately like real numbers
- just as dots are approximately like points
- and you do all applied geometry with dots never invisible points.

- E.g. the "Pythagorean theorem" (first formally proved in the 20th c.)
- is NOT exactly true anywhere on the curved surface of the earth
- or anywhere in the universe (for space-time is also curved)

- (Indians definitely understood this by the 7th c. but British navigators kept drowning centuries later for they kept believing mathematical theorems are certain truths,)

- relative to the assumptions
- and the curved earth does not satisfy the assumptions used to prove the "Pythagorean theorem".

- As pointed out above postulates of mathematics are metaphysics.
- As such their validity cannot be decided empirically and can only be decided by authority.
- This authority is Western authority. For example all over the world people do calculus using real numbers.

- which few understand and
- which results in the
**Banach-Tarski paradox** - that one ball of gold can be divided and the parts reassembled to get any number of identical balls of the same size as the original.

- it will inevitably be twisted to suit Western prejudices.
- As Naqib al Atas pointed out this belief in the continuum is contrary to the belief of Al Ashari in discreteness.
- All practical applications of the calculus can be achieved with discrete number system such as the floating-point numbers used on a computer.

- It is much easier to teach calculus the way it originated in India
- using non-Archimedean arithmetic (instead of real numbers)
- It also enables students to solve harder scientific problems
- as I have demonstrated through pedagogical experiments in 5 universities in 3 countries.

- I am not the authority
- and colonial education has made common people too ignorant to decide on their own.
- so the colonised seem doomed by their superstition trust in the West.

- for having mathematically proved the existence of singularities
- See my article "A singular Nobel"

- a Big Bang is not necessarily a moment of creation
- A cosmological singularity is.
- To prove the existence of the cosmological singularity he assumes the chronology condition - very similar to Augustine's fiat about the nature of time

- This was taken to mean not that church dogma has influenced Western science
- But that science has proved the truth of one time creation
- and Judeo Christian theology

- which claims

this book [asserts] that theology is a branch of physics, that physicists can infer by calculation the existence of God and the likelihood of the resurrection of the dead to eternal life in exactly the same way as physicists calculate the properties of the electron.

- This book

purports to show that the central claims of Judeo-Christian theology are in fact true, that these claims are straightforward deductions of the laws of physics as we now understand them.

I have been forced into these conclusions [about Judeo-Christian theology as physics] by the inexorable logic of my own special branch of physics…the area of global general relativity…created…by the great British physicists Roger Penrose and Stephen Hawking

- Muslims need to stand up to the West and do their own re-thinking on math and science, independent of the West
- If not they are doomed like the "Red Indians" or the Incas or the Maya or the Australian aborigines
- At least they would be culturally dead.

- Resistance does not require any violent acts,
- just a CRITICAL rejection of Western/church education and resulting Western authority

- In particular, since calculus is needed for science,
- I invite any academic for an open discussion/debate
- on why to teach calculus in the manner they do of Western calculus texts
- using the Western misunderstanding of the calculus.