Natural Limitations of Mathematics by mjain3391

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									Natural Limitations of Mathematics
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.

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