About vital role of Math in Science but not in philosophy, morals and religious/spiritual experiences; philosophy != science

An edited version of an exchange I (referred to as R) had with a correspondent who is a scientist (referred to as S) in the beginning of August 2015, on the title-topic is given below.

R: Here's an article …, [Name-snipped] Doesn’t Understand Science (or the Nature of the Universe), dated July 2012, http://nirmukta.com/2012/07/26/name-snipped-doesnt-understand-science-or-the-nature-of-the-universe/.

S: There is no polite word for the pseudo-science and anti-science he spouts. … but my guess is that any attempts to reconcile pre-scientific writing with modern science that can really only be expressed by math is unlikely to be helpful.

R: I think it may be fairer to say that some branches of science today like physics can really only be expressed by math. Math does not seem to play that important a role in life sciences including medicine.
S: You are wrong about that. There is a lot of math of various sorts in modern biology and medical research.
R: I see. Interesting and valuable input. However, I will keep an open mind on this matter until I get an opportunity to check out some articles on it, and also get the view of some biologists & medical researchers. Note that I was not saying that there would be no math but I expected the math involved to be rather limited in these fields. Your input gives an opposing view. Thanks for your input.
R: Philosophy, morals and study of religious/spiritual experiences are not science and do not really need Math.
S: Correct, as long as people studying those fields don't bend logic or make statements about physical reality.
R: Well said. They should stay out of fields like physics & chemistry & even biology which deal with physical reality, unless they can demonstrate under suitable scientific observation, their ability to impact physical reality. And they should NOT bend logic. That cheapens and brings disrepute to their fields in the eyes of discerning readers, even if such tactics gets them some support from their followers. 
In particular, new age Hindu gurus saying things like Higgs Boson and Higgs Field theory were, in concept, known to ancient Hindus, may get them some praise & support from followers who don’t know much about science, but such statements cheapen Hindu philosophy. Further, it amplifies the discord between Hindu spiritual philosophy & modern science, instead of Hindu spiritual philosophy dropping out the parts that have been invalidated by modern science, and focusing on its core spiritual philosophy aspects. 


S: I think it is useful to remember that some ancient Greeks had conjectured that everything was made up of very small particles ("atoms"), but that it took centuries of science and far, far more math than those Greeks could handle to prove that and provide a viable, predictable model of matter. In other words, there can be centuries of hard work between a simple idea (matter is made out of atoms, there might be a flying machine, the earth goes round the sun) and a proof, explanation, and proper predictive model. Non-scientists often don't get that.

R: I entirely agree about huge amount of hard work (centuries in the case of atom) between idea/concept and a proper theory expressed in precise language, validation of results predicted by the theory through experiments done objectively by multiple people (with repeatability) ....  And, I am slowly beginning to understand that many, but not all, religious & spiritual speakers/writers who do not have a science background, don't get that, and so make some pretty confused and inaccurate statements about spirituality/religion and science.

BTW Hindu philosophy also had the concept of atom called Anu. From https://en.wikipedia.org/wiki/Atom, "The idea that matter is made up of discrete units is a very old one, appearing in many ancient cultures such as Greece and India."

S: philosophy!=science
    idea!=theory (in the scientific sense)

R: Great equations! I agree :-)

-------------- end main exchange ---------------------

P.S. A clarification by R: My view is that claims of miracles should not be entertained by hard science fields like physics & chemistry unless they pass the test of hard science rigourous validation. But those same claims of miracles can certainly be, and are, entertained and considered reasonably credible, at times, by non hard science fields involving study of religious/spiritual experiences which gives significant value to large number of reliable eyewitness accounts of paranormal events (miracles). Hard science will not find large number of reliable witness accounts to be acceptable as evidence indicating/pointing to the truth, but even jurisprudence (court of law) does accept it in its methods of arriving at the highly probable truth (though not the completely certain truth).

S responded: I would disagree with your paragraph above, considering eyewitnesses unreliable and the legal system a poor substitute for truth.

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