Few months back there were some discussion about science and superstitions in bulletin board. Needless to say, much of the arguments ‘for’ superstitions were in fact attacking the idea of science. Few questioned the superstitions in the science too, which I thought was valid(strangely, though it was not the intention of the questioner to point out the beauty of science) - do you believe in Einstein’s special relativity theory? Do you believe in Schrodinger’s experiments? Do you..?. Science has nothing to do with believing something. Science is that which is enquired upon, it is the liberty to do experiment and question the properties and nature of the natural world. People who believe in some scientific theory, because it is an accepted theory, are nowhere different from a person believing in ghost. Having that innate itching to question things is the real scientific temper because scientific theories could be wrong. Long ago Anaximander proposed an idea of geocentric model of universe. His philosophy, simple and backed by many accurate observational points, was that the earth is at the center of universe which revolve around it. Similarly Rutherford’s model of atom was a well known hypothesis. Though their theories have now been proven wrong, it doesn’t take away the scientific methodology adopted by either. We know, Later the church adopted and somewhat ‘base lined’ the geocentric theory. They attacked the scientists who put forward the heliocentric theory, and were marked and killed as heretics. The interesting part of this argument is pointing to how the same theory were defined as scientific and superstitious based on how the lines are drawn around it.
I believe classical science played a major role in drawing the lines between the hypothesis and proven facts, it didn’t give space for approximation or caveats and was persistent in defining the natural world with classical mathematics. But there were always something that baffled the scientists and mathematicians which finally brought forward the idea of Convergence. For instance, we know 1/3 + 2/3 is 1, but 1/3 is .333.. and 2/3 is .6666.. and when you add that up it just comes to .99999…. which a classical mathematician equated to 1 with a glass of water. Philosophical thinkers which dominated the scientific fraternity didn’t have anything other than the convergence theory to agree upon that .9999… converges to 1.
There was a famous paradox, which is often used to explain the convergence theory in a classical physics experiment. It was the same old story of the Hare and Tortoise, quite popular hence very likely that you have heard of it. In this story, Hare was confident that he will not sleep on the way and Tortoise, as usual, appeared cool and unperturbed. He approaches the Hare with a humble request, “Mr. Hare, Since you are very quick why don’t you give me a little advantage of starting 10 meters ahead of you, 10 meter is all what I am asking from you”. Hare laughed out loud thinking of Tortoise’s inanity and agreed to the condition. Now the Tortoise will start from a point 10 m ahead of Hare’s starting point. Monkey blows the whistle and the race starts. Now let us apply classical theories into their race..
The hare running at V velocity takes T1 time to cover the first 10 meters, ie after T1 seconds Hare reached the point where Tortoise started. But, Tortoise was not simply standing there, he was walking with a velocity of U and has, by now, covered a distance of U*T1 meters and is still ahead of the Hare. Now Hare takes another T2 seconds to cover the distance U*T1 meters and reaches the point where the Tortoise was, at the end of T1 seconds. But the bugger Tortoise is again U*T2 meters(however small) ahead of Tortoise. Going by this, Tortoise will always be U*Tx meters ahead of hare..which means as per the above explanation the hare would never overtake tortoise!! (Or will this race ever end?). But in reality we know the race would end, and hare would overtake the tortoise. The only explanation to this could be given by the convergence theory, i.e. as the distance between the hare and tortoise becomes infinitesimally small after infinitesimally small fragments of Tx, it is safe to assume that the distance between the hare and tortoise is 0! I.e. as limit Tx->0, the U*Tx->0 and hence after sometime Hare and tortoise would end up in same line. That was the only way this race could be explained with mathematics. To many, it was a failure of classical mathematics in clearly explaining the natural physics, which was otherwise considered as the ‘unambiguous language’ of physical nature. The idea that, a measurable quantity like 1 sec or 1 cm could be divided into infinite quantity of infinitesimally small units even gave the prominence of infinity in mathematics and natural science a stronger base.
Classical science relied on the observation and observational experimentation which involved macro subjects that are quite readily available, visible to human eyes and comprehensible to the human brain. Chemistry was probably something that split the philosophers as the experiments often convoluted into magic, but the idea of science and philosophy were, very much, hand in hand until the end of macro science and evolution of micro science. Now the uncertainty and approximation has changed the way things are seen. It has gone beyond the limits of human imagination, looking at the way the scientific reasoning during the age of enlightenment lead to evolution of the classical science, as we get into the age of nano science. Things are changing, The modern physics may not be able to appreciate philosophers. With the evolution of nanotechnology, philosophy of physical science had been getting heavily dependent on ultra-precision equipments and confined to the walls of expensive laboratories. Astronomy is probably the only classical realm that still remains undiscovered to a large extend. This well known arm of philosopher’s physics still manages to elude the boundaries of human imaginations.
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