Cultural foundations of science

C. K. Raju
Indian Institute of Advanced Study, Rashtrapati Nivas, Shimla 171 005

Extended summary

Time beliefs are at the core of both religion and science. So, which religious time beliefs are scientifically possible? In present-day science, time is like a line (“real” line, since, it is believed, “real” numbers are required for the calculus used in the differential equations of physics). Prima facie, this is contrary to the quasi-cyclic time (लगभग चक्रीय काल) required for Hinduism, Buddhism, or Neoplatnism/Sufism. (There are other important issues related to time, such as instantaneity, or the relation of time to logic, but here we focus on just one issue for simplicity.)

Even so, three things must be clearly understood

Not an issue of linear vs cyclic time. First, the issue is NOT about “linear” vs “cyclic” time, as is commonly caricatured. The categories “linear” time and “cyclic” time are incoherent and meaningless, since several mutually conflicting notions of linear and cyclic time are packed into each category, as explained in detail in my The Eleven Pictures of Time (Sage, 2003). For example, eternal recurrence (Poincare recurrence) is inevitable on Newtonian physics, in a closed cosmos. Eternal recurrence is a kind of cyclic” time, in which, too, people are repeatedly reborn. But it is the wrong kind of “cyclic” time, better called supercyclic time (पूर्ण चक्रीय काल) , for it makes deliverance (मोक्ष, निर्वाण) impossible. Nietzsche based his whole philosophy on eternal recurrence, confounding supercyclic with quasi-cyclic time (hence arrived at a completely different value system). This confusion was the key to the major changes in post-Nicene Christianity, culminating in the 6^th c. church curse on “cyclic” time. The related propaganda has ensured that both pro- and anti-church scholars in the West remain perpetually confused, and conflate quasi-cyclic time with eternal recurrence (e.g. T. S. Eliot, Mircea Eliade, Nietzsche etc.) unmindful of the huge difference it makes.

Not an issue of science at war with all religions. Second, this is NOT a simplistic case of science and all religions being at war, as is easily caricatured. Thus, it has long been argued that science favours Christianity. Especially, it has been claimed, general relativity, the big bang cosmology, and particularly Stephen Hawking’s singularity theory has proved the truth of Christian creation and “linear” (apocalyptic) time (कयामती काल). So, what we are being actually told is that science supports Christianity (which cursed “cyclic” time) but is at war with all non-Christian religions. This is what enables science to be used as a missionary weapon. But the gullible colonised mind never asked why science came to the colonised through missionary education: or why many of the best science colleges in India are still missionary institutions. The colonised just ignore the manifest, and keep repeating the 500 year old story of Galileo (without ever having checked the facts), because stories are all they know.

Must engage with science. This conflict between present-day science and non-Christian religions has long been ignored by non-Christians. But, especially in Indian traditions, knowledge was never compartmentalised into science vs religion. So, if one kind of knowledge conflicts with another, the conflict needs to be resolved. One cannot simply wish science away, for it is the dominant form of epistemic authority today. Regrettably, engaging with science is beyond text-based scholars who somehow declare themselves as the sole rightful owners of Indian tradition, wishing away all science, often on the wrong grounds that science (even astronomy) was no part of Indian tradition.

To resolve the conflict we must either accept all non-Christian religions as superstitions, or else engage with science at a very deep level. We first need to understand how an unexpected source—formal mathematics—has enabled Christian dogma to infiltrate science. To this end, we need to answer the following questions.

1. Is (current) science universal and objective? This is the belief. If we deny it, we need to (1) point out what exactly is wrong with present-day science, and (2) construct an alternative scientific theory, and (3) show that it is a better theory.
   
   

2. Science, however, is based on mathematics. Particularly the calculus. Newtonian physics is based on ordinary differential equations, general relativity and quantum mechanics are based on partial differential equations. Biology has been reduced to physics.
   
   

3. But is mathematics universal? No. As explained in Cultural Foundations of Mathematics (Pearson, 2007), formal mathematics has been influenced by cultural factors, particularly church metaphysics. While Indian ganita was practical, Western mathematics was always linked to religious beliefs, since Plato. The church appropriated and modified this religious math, and to suit its own agenda. The church first accepted reason as part of Christianity for a political reason. During the Crusades, it was militarily too weak to force Muslims to convert, the way Europe was earlier forced to convert to Christianity. Further, it could also not persuade Muslims using the Bible which Muslims rejected as corrupted. This left “universal” reason as the only choice open to the church.
   
   

4. How the church reconciled reason and faith by excluding facts as done in formal math. But the church had long emphasized faith: therefore, now the church had to reconcile reason and faith by inventing. It did so by inventing a new form of “faith-based reasoning”. This reasoning prohibited the use of facts, and glorified the rejection of facts, to save church dogmas from refutation. The church laid down that reasoning must begin not with facts, but with axioms (in which one must have faith). Further, facts should not enter the argument at any stage: Western scholars today still superstitiously believe that the total exclusion of facts (“pure deductive reasoning”, formal mathematical proof) is infallible like the pope. To mislead people, and hide its political intent, the church falsely attributed this faith-based method of reasoning to an early Greek called “Euclid”. The non-existence of “Euclid” enabled any convenient intentions to be assigned to him through myth. We teach that false myth today, in our class 9 school text that the Greeks alone used reason in math. This is blatantly false: (a) Greeks never used “reason” in the peculiar manner of the church (without facts), and (b) the whole world used reason, but used it with facts (normal reasoning), as in science. It is never explained anywhere today that “reason” in (formal) math means reason which excludes facts. What we teach today is not fact-based mathematics (normal math), but such faith-based mathematics (formal math), imitating what was taught by the church to its priests in Cambridge etc.
   
   

5. What is axiomatic math? Axioms (or postulates) are any assumptions, NOT uncontested truths, as even our class 9 math text correctly explains. These may be possibly wild rather than valid assumptions. (Russell: “we take any hypothesis which seems amusing”.) Axioms must be accepted on faith, for they involve non-physics (“metaphysics”, fantasy) which cannot be empirically tested. For example, Aquinas’ axiom states that angels don’t occupy any space. (Believing this axiom requires faith in angels, for there is no way to empirically test the existence of angels or the space they occupy.) From this axiom he deduced Aquinas’ famous theorem: several angels may fit on a pin. Axiomatic mathematics is exactly such faith-based mathematics, albeit presented in a way that most people don’t understand. For example, we teach school children the axiom that there is a unique invisible straight line through two invisible point. This is pure fantasy which cannot be empirically tested, but must be accepted on authority. Thus, the axioms needed for “real” numbers (e.g. of set theory, say axiom of choice) are assumptions about infinity/eternity which cannot be empirically tested, are unknown to most people, and are accepted solely on blind faith in Western authority.
   
   But this faith is irrelevant for practical applications of math to science. Math “works” just BECAUSE the metaphysics is useless and set aside in practice. For example, students can only handle visible straight lines through visible points. The calculus is today taught using the metaphysics of “real” numbers. However, practical applications of calculus, such as calculating rocket trajectories, is still done approximately, and numerically, on computers which use floating point numbers, and cannot use real numbers. (Of course, that add-on Western metaphysics in math does have political value: it DOES affects the relation of religion and science through the common interface of time beliefs. For example, the European modification of the Indian calculus forces time to be like a line, so that all non-Western religions based on another notion of time are declared superstition, since contrary to “universal” science, hence “inferior”.)
   
   

6. The metaphysical creep from formal math. Most people naively believe science is at war against all religions. Contrary to the story, the fact is that church dogmas and superstitions about one-time creation creep into (Western) science. For example, we still teach “laws of nature”, as in “Newton’s laws of motion”, as the first lesson in serious science. However, the fact is that this belief in “laws of nature”—that God rules the world with eternal laws of nature—was first formulated as part of Christian dogma by the theologian Aquinas, the same who also explained how to reason and prove theorems about angels using faith-based axioms. Western metaphysics (aka superstition) systematically creeps into science through the authoritative metaphysics of formal math. A great example is Stephen Hawking’s creationist conclusions, that the cosmic big bang is associated with a singularity or a beginning of time, or one-time creation of the cosmos, as described in the Bible. (A singularity involves a breakdown of the university calculus.) This conclusion of singularity theory is made quite explicit by Tipler (a general relativist who has five papers in Nature) that physics has hence proved the truth of Christianity.
   
   But Hawking’s conclusion is invalid if we use a different math, or even if we use a different axiom set or definitions within formal math. (For example, singularities are easily handled if we replace the derivative of university calculus by the Schwartz derivative with a related definition of the product of Schwartz distributions.) So, this is an example of how the prestige of science (and mathematical authority) is still being used to buttress Christian beliefs, and attack non-Christian beliefs. This may not fool all people for all time, but it has most people fooled for most of the time (and fooling 50% for all time is enough in a democracy). People are ignorant of science, hence easily persuaded that Hawking was a great scientist, though no one else in India has understood Hawking’s singularity theory well enough to explain what experiments can be performed to test it, or to decide whether it is even science. Therefore, people (especially journalists and editors who know no science) believe that whatever Hawking says must be treated as gospel truth, and cannot be publicly contested. But any kind of blind faith, including such blind faith in “science”, can be used for con-tricks.
   
   

7. However, the fact is that math is not universal. Indian ganita (normal math) differs from the formal (Western) mathematics we teach today. We can stop this metaphysical creep by switching back to normal math. What is the difference? For example, empirical proofs are accepted in ganita (or normal math) but are prohibited in formal math. The aim of ganita is useful calculation, not metaphysical proofs, as in formal math. This does not mean that proofs based on reason do not exist in Indian ganita, but proof is not the focus in Indian ganita, and it begins with facts, not axioms. For example, Indians knew the earth was round, and did “non-Euclidean” geometry on a sphere from centuries before Europeans even heard of “Euclid” (in 1125 CE). However, Indians did not talk about axioms about parallel lines, or what happens at (unattainable, hence metaphysical) infinity. Instead, they (e.g. Bhaskar 1) pragmatically pointed out the refutable local consequence: that the “Pythagorean theorem” is inexact on the curved surface of the earth. Hence, Bhaskar said, using that theorem to determine longitude is wrong. Recall that it was this error which led to the navigational disasters that plagued Europe for centuries (until the 18^th c.) Today, to test the curvature of “non-Euclidean” space-time we must do it the same way, through local triangles, and not arguing about what happens to parallel lines at infinity (which is untestable).
   
   

8. So, will the use of Indian ganita change science? Yes, without affecting its practical value. To reiterate, for most practical applications of mathematics to science and engineering, the metaphysics of formal math is set aside, in practice. For example, rocket trajectories are determined by using (normal) mathematics for approximate calculations (not formal proofs). These calculations are done on a computer which uses floating point numbers, not real numbers, to numerically calculate the solution of differential equations. These practical applications of mathematics to science and technology (anything done on a computer) will not change fundamentally, though ganita makes them easier. What will change is the Western metaphysical creep from formal math into science. Time beliefs are a most important aspect of this metaphysical creep from Christian theology to science, via formal mathematics, suggesting that science has proved the truth of Christian theology, and also that all other time beliefs are superstitions. The use of ganita would put an end to such metaphysical creep from mathematics into science.
   
   

9. So exactly how will science change? Short answer: we need to reformulate physics using functional differential equations of mixed type (with a tilt in the arrow of time). The process of metaphysical creep from Christian theology into science is found even with Newton. Newton needed calculus to formulate his physics, but he failed to understand the imported Indian calculus, and how it summed infinite series. He believed the eternal “laws of nature” were written by God in the perfect language of mathematics. Hence to make calculus perfect he made time metaphysical, and deemed it unnecessary to define equal intervals of time physically (unlike his mentor, Barrow). But a physical definition of equal intervals of time was needed for his “laws” of physics to even make sense (e.g. “uniform motion” is meaningless if we don’t know what equal intervals of time are). As I have explained in my book Time: Towards a Consistent Theory (Kluwer Academic, Dordrecht, 1994), Newtonian physics failed just because of Newton’s metaphysical assumptions about time arising from his religious beliefs about God and the laws of nature written in the “perfect” language of mathematics.. Correcting it, by rejecting that metaphysics, led to the special theory of relativity (due to Poincare, not Einstein), a century ago.
   
   If we carry this line of thought (eliminating Christian metaphysics from math hence physics) to its logical conclusion then, as a first step, physics must be modified to use functional differential equations (FDEs = coupled ordinary and partial differential equations), as explained in my above book, and as consistent with special relativity. But what kind of FDEs?
   
   

10. Causality vs the boomerang of time. Physicists often assert causality as a physical principle. But causality is only a theological principle: the power of the Christian priest flows from the false claim that his god will punish those who disobey the priest. To do so, the Christian god must be able to identify a person as the cause of a sin. if we discard the hand-imposed metaphysics of time (such as the belief in “causality”), then there must be a “tilt” in the so-called “arrow of time”. (That is, we use FDEs of mixed-type, as suggested in my book above.) Rejecting “causality” thus, and permitting a tiny “tilt”, is the simplest way to explain our mundane time beliefs based on lived experience (and needed to test science through experiment, and even in the criterion of refutability). If, further, the tilt in the arrow of time increases with time (though it is not known whether it does), then that would give us a “boomerang of time” or quasi-cyclic time, where the cosmos repeatedly (approximately) returns to its initial state (but deliverance is possible). That is exactly the time belief underlying Hinduism, Buddhism, Sufism (and also early Christianity); it is compatible with science.
    
    (Jaipur dialogues, 20 Oct 2019, Session 1, 10-11 am.)