Reasonable Effectiveness Of Mathematics In Natural Sciences

Wigner questioned the unreasonable effectiveness of Mathematics in Science. It appears to be a human brainchild that is not ‘Unreasonably Effective’ but it has been fabricated to be ‘Reasonably Effective’.

‘In Science as in everyday life, when faced by a new situation, we start out with some guess. Our first guess may fall wide of mark, but we try it & according to degree of success, we modify it more or less. Eventually, after several trials & several modifications, pushed by observations & led by analogy, we may arrive at a more satisfactory guess’

Hungerian Mathematician George Pólya (‘How To Solve It)

At the dawn of the evolution of civilization, human beings got the opportunity to explore nature as it was the only resource available that could serve & save them. Zeal to survive drove this exploration further and deeper. Once humans emerged as ‘The most intelligent creature’ on earth, they started discovering nature by means of curiosity. In the modern era, we call this ‘science’. Science used to exist in historical civilizations in a broader sense but in the present time, it is much more distinct in its approaches.

The medium of scientific investigation is Mathematics. It is a branch of science that depicts the patterns of nature. Numbers, geometrical shapes, operators, functions concoct it & enable it to augment those patterns elegantly. It seems that humans can simulate nature using pen & paper, with aspirations of discovering the ultimate truth underlying.

Photo: L Sudmann

Mathematics Is An ‘Enigma’

But wait!!!! How Mathematics is so effective in explaining the universe? How much the precision of its predictability is superlatives-worthy? Apparently, we understand how it works but have little or no clue about why it fits so well. Physicist & Math whiz Eugene Wigner first published an article, back in 1959, questioning its ‘Unreasonable Effectiveness’ in natural sciences. His approach tried to define what Math is & ‘HOW’ it is effective, not exactly ‘WHY’ it’s effective.

That has been criticized as well as justified several times by preeminent scholars in the last three decades of the twentieth century. They were practitioners in various fields. Affluent names like Richard W. Hamming (Computer Science), Ivor Grattan-Guinness (Mathematics), Vela Velupillai (Economics), Arthur M. Lesk (Molecular Biology), etc. must be mentioned in this regard. They kept pondering about its effectiveness in their peer-reviewed publications but couldn’t provide the reason for its superior efficacy in natural science. That motivated me to pen down some thoughts about its ‘Reasonable Effectiveness’ that may present a well-rationalized argument to this half-centenarian question.

Photo: Unicon

Unexplained Mathematical Features

To interpret what it is, firstly we need to comprehend the mystery knots that we’re yet to untangle. Well, it’s true that this is going to be a philosophy rich approach that people in science little care about but it’s worth noting that philosophy is the only way for justification when science can’t proceed further.

1. The Quantum Riddle: When classical theory fell short to account observations in the femtoworld, myriad of hypotheses evolved chronologically trying to offer a valid explanation. Finally, it could be construed by Niels Bohr’s theory with astounding accuracy. He took the radical assumption of quantization, like Max Planck (Blackbody radiation) & Albert Einstein (Photoelectric effect), to produce a new set of math that was appropriate to explain spectral series of the Hydrogen atoms, albeit no reasonable argument was furnished to justify the introduction of quantization was provided.

2. Illusive Thermodynamics: Entropy, Gibbs energy, Helmholtz energy-these are mathematical quantities that give extraordinary insights into processes occurring in the universe. These can be calculated using data of experimentally determinable quantities, like enthalpy or internal energy. Although all of these mathematical parameters can only be used to anticipate the properties of a process or system, they have absolutely no physical existence.

Wigner, Hamming, Grattan-Guinness provided a handful of exemplary arguments in their articles. Numerous other examples can be cited in this context. Eventually, we can culminate that Mathematics not only functions well in natural sciences but also in social sciences, evident from articles of Velupillai, with some obvious exceptions. As nothing in our universe is ideal or operates perfectly, those exceptions also occur in Mathematics. As per Guinness & Velupillai’s articles, Math also fails in remote areas of natural & social sciences.

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