Science and Mathematics

Mathematics deals with perfection, with absolute truths. Scientific theories on the other hand always have a sense of approximation. Whereas a mathematical statement like the theorem of Pythagoras holds true for all right angled triangles (and hence may be used to define a right angled triangle), scientific theories like the theory of gravitation are subject to constant revision and updating. In science, people come up with hypotheses to explain phenomena. If experiments then corroborate the predictions made by these hypotheses, then they gain credibility and are elevated to the status of a theory and become part of our everyday understanding of the world around us.

Here’s a question which serves to illustrate the difference. You have a chessboard in which two squares from opposite corners are removed. So instead of 64 squares, you now have 62. And you are given 31 dominoes that cover 2 squares each. Is it possible to cover the board with the dominoes? (source : Simon Singh, Fermat’s Last Theorem)

The scientific way to answer this question would be to try filling the board in different ways and see for yourself whether the question permits a solution. After a few dozen attempts you may come to the conclusion that it is not possible to fill the squares with dominoes but still an element of doubt prevails. This is now a theory based on experiment and is readily overturned if even a single counter-example can be produced.

Another way is to argue using logic. You notice that the squares on opposite corners of a chessboard are always of the same colour (say, black). Hence, if you remove those squares you’ll be left with 32 white squares and 30 black squares. Also any two adjacent squares in a chessboard (which we wish to cover using dominoes) must necessarily be of opposite colours. Hence after 30 dominoes, we’ll be left with two white squares and a single domino. But since the two white squares cannot be adjacent, we can conclude with absolute certainty that  it is impossible to fill the squares with the dominoes. It is this absolute nature that gives mathematics its beauty.

Prof. V. Balakrishnan once told us in class that although we (physicists) know that the photon has zero rest mass, the state-of-the-art experiments can only confirm that its mass is less than 10-54 kg. So if the photon has a mass, it must be less than 10-54 kg. This blatant acceptance of its limitations, I believe,  may be why we  would never be able to convince a creationist (or a climate-change denier) of the truth and explanatory power of some of the theories in science. They just don’t understand the way science works1, that there is such a thing called the relativity of wrong. As Asimov nicely puts it:

When people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.

The shape of the Earth is not oblate spheroidal either though it is a better approximation still. Now the shape of the Earth has a special name – geoid – which in Greek means “shaped like the Earth” (The mathematics now gets more complicated though.) So our  Earth is a geoid (no surprises there). To me, it is this sense of adventure and exploration, deepening our knowledge  while at the same time remaining humble of its limitations that gives science its beauty.


1. There is this funny little story about the philosopher Ludwig Wittgenstein (1889-1951). Once he asked one of his friends why people always say that it was natural for men to assume that the sun went around the earth rather than the earth was rotating. His friend said: “Well, obviously, because it just looks as if the sun is going around the earth.” To which the philosopher replied: “Well, what would it look like if it had looked as if the earth were rotating?”
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4 comments

  1. Yet another delightful post :)I have to mildly disagree with one of your points, though… Mathematical thinking, in my op., is synonymous with scientific thinking. In the chessboard puzzle, for instance, the second solution is as scientific as it is mathematical. (I don't know if I'm saying that because I've been a theory person all my life. But I don't think experimentalists are as empirical as in the first solution.)And here (in the second lecture), Feynman apologizes to laymen for the liaison between science and math: http://research.microsoft.com/apps/tools/tuva/index.html#data=3|||

  2. My point was that mathematical precision is what science aspires for but very often finds itself stymied by practical limitations. Pythagoras theorem is as absolute now as it was 2000 years ago and will be 2000 years into the future. It could be because mathematics in its pristine unadulterated form exists in the Platonic realm. And science is the closest we have come in applying our mathematical knowledge to real world problems. We are inexorably moving ever more closer to mathematical precision which was what I think Asimov was suggesting.

  3. Hey Nice Post !As far as explaining science to creationists, forget about it. To me science is all about coming up with a method of agreement and math is just a subset. To explain what I mean by that, lets say someone says X is true, science is the method by which we all agree whether S is true. And the method is emergent and rapidly evolving ( too bad for the creationists 🙂 ). In a way, when someone said long back that the earth was flat, people agreed cause correlation with the bible was their scientific method. The scientific method that we know of now might be rather primitive a few centuries from now. But what is important is that it is best method we know of as of now. And as long as we keep an open mind we should be fine.

  4. Yes, there is a steady shift in our scientific understanding which is precisely why it the exact antithesis of religion with its irrational fixation to Stone Age ideologies. As J.B.S. Haldane said "The world shall perish not for lack of wonders but for lack of wonder". On the other hand, we have all sorts of pseudo-scientific nonsense which is just imagination run amok in minds with an incomplete understanding of scientific principles. We should have an open-mind towards new ideas but at the same time we should not be so open-minded that our brains fall out.

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