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.
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.
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.
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.
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.
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”.)
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.
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).
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.
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?
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.)