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-
3) Nature is not mathematico-
No unconstrained mathematico-
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/
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.