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�€ more fundamental than e
Gauss's proof of God's existence was e^(i*�€) + 1 = 0. Since the five most important numbers are bound by
such beautiful identity, argued Gauss, therefore God must exists. π is arguably the most important constant
of geometry and e of complex algebra. Therefore to Gauss, a true mathematician, such an equation provided
infallible proof of the Almighty's existence (Douglas Adams has since then offered alternate explanations
though). So far so good, but problems start to pour in if we start thinking from a physics point of view.
The number e has no significance if we look from a physics point of view. How on earth can I dare to speak
such absurdities? After all, does e not occur in every single rate law and in every single perturbation
(oscillation) equation? Well, it does, but only as long as you choose to be the ostrich with its head buried
neck deep in sand. Each of those phenomena which involve e as their essential constant are described by
linear equations and linearity is at best a myth. The only reason why we have such abundance of linear
equations and consequently of e in physics is that the researchers of the past century preferred to be
ostriches.
All natural phenomena are hopelessly nonlinear. Reasons for this omnipresent nonlinearity are many. The
world that we live in is three dimensional. This makes it possible for objects to trace such paths the
description of which will necessarily bring in nonlinearities (anything which does not move on a straight line
in some coordinate system moves on a curve whose locus is described by a nonlinear equation).
Kinematically speaking a one-dimensional world would then be linear. The second reason for nonlinear
nature of nature is the fact that most fundamental interactions follow the inverse square law. This means
that the fundamental forces of nature vary nonlinearly with space. Since all inter-particle interaction can
ultimately be shown to be a manifestation of one of these forces (gravitational/electromagnetic/nuclear)
therefore these interactions have to be nonlinear in nature.
As contrast to e, π is free from all such aberrations because its roots are in pure geometry, something much
more profound and robust than equations of physics. A physicist may propose a new law of gravity and we
might have to bow to his superior insight or such a thing might never happen. The point is that we can't
prove conclusively that what Newton said was (or is) the absolute truth. Compared to this, a proof of the
fact that the perimeter of all circles is bound to their radii by π can be found in any elementary textbook of
plain geometry. This proof was, is, and will remain. An aberration to it is not possible under any
circumstance. In a space of any dimension there will always be a generalization of a sphere and hence the
importance of π in describing isotropic phenomena will remain unquestioned. Ironically, a one dimensional
space has no circle and hence no π and it is only space in which e has any physical relevance !!!
-------------------- Editing on 2nd Feb, 2006 -----------------------
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