TO ERR IS HUMAN, TO APPROXIMATE IS DIVINE
Whatever you studied till date was not accurate. Your reaction?? A typical ‘Who cares!’ shrug. If I tell you that whatever you see does not exist in space at the point you think it is, you’ll be zapped. Then if I tell you that the earth revolving round the sun and the sun revolving round the earth are fairly accurate statements, you’ll feel I am using some alien multilingual verbal communication technique to crack a joke. But all this is true, though it denies the basics which we have used, to build upon them, a huge monument of knowledge.
Welcome to the world of approximations. Approximations, which do not hurt but make our lives easier. Approximations, developed by humans to fit huge packets of complex realities into smaller and convenient suitcases of observations and calculations. We won’t be wrong in saying that whenever physicists got stuck in calculations, mathematicians took over and whenever mathematicians got stuck, approximations too over.
Optics, mechanics, magnetism, electrostatics and dynamics, chemistry, mathematics or even real life, nothing remains untouched by approximations. When human capabilities fail, approximations revive them. Some approximations were born before their more accurate counterparts and some later. The former category includes Newton’s laws governing motion. Its accurate version was given by Einstein in mass energy equation and relativity. Other example is the formula to evaluate the speed of sound that needed the Laplace correction later.
Let me first justify the examples used in the opening of this article. The first example is related to the fact that till now we’ve studied only approximated versions of most of the theories and laws and never bothered to find the accurate statements, and why should we?? We needed to score marks which were possible by merely mugging these theories up. But the adverse affect of this was that these approximations have become our common sense and anything that denies them seems to be absurd. The third example is one such ‘acquired common sense’.
The earth revolves round the sun and the sun revolves round the earth depends upon which body we chose to keep stationary with respect to the other. Keeping the earth stationary, we find that the sun revolves round the earth. Other planets, though, undergo a complex path and may or may not return to their original position after some time in this case. This is nothing but the independent choice of frame of reference. We usually chose sun as centre only because the resultant paths of other planet come out to be simpler geometric shapes, be they ellipses or ellipsoids, in this frame of reference, thus making their study and observation easier.
The second example arises from the fact that we approximate the refraction of light caused by different layers of our surrounding media due to their varying density, be the reason be varying temperature or composition. But if we consider them, the objects we see will turn out to be the images of the object displace by a small distance from the actual position of object in space. This is because the reflected light from the object which is responsible for our vision gets refracted by the different layers in the medium and no longer has the same orientation in space as one would expect from a straight light ray.
Such approximations are so ingrained in our lives that we take them as default conditions. I wonder if a bill will be passed to accommodate the ‘Right to approximate’ in the constitution, though I would prefer the ‘Right to chose a frame of reference’. But before political bodies even remotely think of such a concept, you can approximate the value of this article as zero and forget it before you start questioning the ‘commonest’ of your common senses.
Welcome to the world of approximations. Approximations, which do not hurt but make our lives easier. Approximations, developed by humans to fit huge packets of complex realities into smaller and convenient suitcases of observations and calculations. We won’t be wrong in saying that whenever physicists got stuck in calculations, mathematicians took over and whenever mathematicians got stuck, approximations too over.
Optics, mechanics, magnetism, electrostatics and dynamics, chemistry, mathematics or even real life, nothing remains untouched by approximations. When human capabilities fail, approximations revive them. Some approximations were born before their more accurate counterparts and some later. The former category includes Newton’s laws governing motion. Its accurate version was given by Einstein in mass energy equation and relativity. Other example is the formula to evaluate the speed of sound that needed the Laplace correction later.
Let me first justify the examples used in the opening of this article. The first example is related to the fact that till now we’ve studied only approximated versions of most of the theories and laws and never bothered to find the accurate statements, and why should we?? We needed to score marks which were possible by merely mugging these theories up. But the adverse affect of this was that these approximations have become our common sense and anything that denies them seems to be absurd. The third example is one such ‘acquired common sense’.
The earth revolves round the sun and the sun revolves round the earth depends upon which body we chose to keep stationary with respect to the other. Keeping the earth stationary, we find that the sun revolves round the earth. Other planets, though, undergo a complex path and may or may not return to their original position after some time in this case. This is nothing but the independent choice of frame of reference. We usually chose sun as centre only because the resultant paths of other planet come out to be simpler geometric shapes, be they ellipses or ellipsoids, in this frame of reference, thus making their study and observation easier.
The second example arises from the fact that we approximate the refraction of light caused by different layers of our surrounding media due to their varying density, be the reason be varying temperature or composition. But if we consider them, the objects we see will turn out to be the images of the object displace by a small distance from the actual position of object in space. This is because the reflected light from the object which is responsible for our vision gets refracted by the different layers in the medium and no longer has the same orientation in space as one would expect from a straight light ray.
Such approximations are so ingrained in our lives that we take them as default conditions. I wonder if a bill will be passed to accommodate the ‘Right to approximate’ in the constitution, though I would prefer the ‘Right to chose a frame of reference’. But before political bodies even remotely think of such a concept, you can approximate the value of this article as zero and forget it before you start questioning the ‘commonest’ of your common senses.

