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Summary: It is commonly believed by the Learned that
mathematical evidence in support of any subject matter is the final proof of
the subject matter. However, it is not so. Interpretation of mathematical
evidence is determined, not only by mathematical tools and techniques but also
by applicable natural laws, nature of interacting entities and context of
interaction.
Scientists,
particularly Physicists and others regard Mathematics as the final proof of
anything. It is commonly held that once a proposition is able to find some
mathematical argument in its support, it is deemed proved and settled for good.
Physicists have even invented the term “Mathematico-logical derivation and
elevated it to the level of gospel truth. The current cosmic view held by
Physicists is a glaring example of where mathematico-logical derivation can
lead to, if applied in interpretation of natural events, without due
consideration of natural limitations of Mathematics. The current cosmic view in
Physics has its origin in two fundamental hypothesis of Einstein’s Theory of
Relativity, mathematically logically extrapolated to a theory of entire cosmos,
directed towards reconciliation with quantum physics. As a result of
unrestrained mathematico-logical derivation, the Physicist’s cosmic view has
landed in to a cosmos which is beyond sensory perception and is therefore just
not there. Strings of the string theory and M-Theory are beyond sensory
perception – direct or indirect. These efforts have led to theoretical models
which are quite similar to Ptolemy’s Model of Planetary System and Phlogiston
Theory of Combustion.
This leads us to
the question of natural limitations of Mathematics in understanding natural
events, things and the cosmos as a whole.
1)
Mathematics is not
all real: For example Complex numbers and Boolean algebra are not grounded in
natural events. These can be best regarded as mathematical fantasies, may be
useful as tools and techniques in certain situations.
I once met Professor O. P. Mishra (Now retd.)
of Department of Physics. He claimed that by application of Schwartz
Distribution Principle through dedicated software to the available data, it
would be possible to predict incidence of earth quakes. He cited the reason for
his belief that earth quakes can’t be predicted on the basis of available data
only because of inaccuracy of available data which can be rectified by applying
Schwartz Distribution Principle and thereafter accurate prediction of incidence
of earth quakes can be made.
However, I found it farfetched and
beyond comprehension. Mathematics is not like a magician’s hat that can
apparently produce things out of nothing. Until and unless, one clearly knows
what data is to be collected and how the relevant data is to be interpreted,
how mere application of a mathematical tool or technique can ever lead to
prediction of a natural event is clearly beyond comprehension.
Finally, these virtual components of
Mathematics are relevant only as tools and techniques so far as they lead to
results compatible with real world. If it is otherwise, then their use is
clearly unwarranted.
2)
Nature is hierarchically organized and rules vary from one
hierarchical level to another. Rules applicable to cosmic dust may not be the
same as rules applicable to celestial bodies such as planets, stars etc.
Therefore, unlimited mathematical extrapolation can’t be correct and proper.
For example, by supplying heat to a block of ice, it is possible to convert it
in to a liquid and then vaporize it to water vapor. But rules applicable to
solid, liquid and gaseous state of matter vary and hence mathematical
computation applicable to water in solid state can’t be valid when applied to
water in liquid state and so on so forth. Natural events often involve change
of state and change of phase with commensurate changes in applicable rules.
Hence unlimited mathematico-logical extrapolations are wholly unwarranted until
and unless it is shown that rules being so applied are valid across change of
hierarchical level, change of phase, change of state etc.
3)
Nature is not mathematico-logically perfect: Nature abounds
in non-linearties. All acts of natural origin and creation are nonlinear in
character. All phase changes and change of state are nonlinear in character. Some
of these nonlinear acts are recognized as singularities by Physicists. A
singularity in Physics means a strange point since Physicists fail to apply
Laws of Physics across a singularity.
No unconstrained
mathematico-logical extrapolation can be valid across a nonlinear act. All
these nonlinear acts are empirically determinate but at the present level of
human understanding are rationally indeterminate. For example decay of Uranium
in to lead is an empirically certain event but its occurrence can’t be predicted
on the basis properties of Uranium and known laws of Physics.
Therefore, we have to be guided by Nature
in application of mathematical tools and techniques towards interpretation of
natural events. Application of mathematical tools and techniques is valid only
so far as it corresponds to observations/ experimental results/ experience.
Notwithstanding the above said,
mathematical tools and techniques are quite useful in discovering hidden
conditions underlying things and events. Mathematical reconciliation of
observed data indicates adequate and fair understanding of the given subject
matter.
Hence in the book “Encounter of Science
With Philosophy – A Synthetic View” Mathematics has been defined as science and
art of computation of natural events.
Author: Dr Mahesh C. Jain is a practicing
medical doctor has written the book “Encounter of Science with Philosophy – A
synthetic view”. The book begins with first chapter devoted to scientifically
valid concept of God and then explains cosmic phenomena right from origin of
nature and universe up to origin of life and evolution of man. The book
includes several chapters devoted to auxiliary concepts and social sciences as
corollaries to the concept of God. This article points out limitations of
mathematics as determinant of natural events.
http://www.sciencengod.com/clipboard.htm
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