Monte
Carlo simulations are close to a toy than anything I have seen in
my adult life. One can generate thousands, perhaps millions, of
random sample paths, and look at the prevalent characteristics of
some of their features. The assistance of the computer is
instrumental in such studies. The glamorous reference to Monte
Carlo indicates the metaphor of simulating the random events in
the manner of a virtual casino.
It is a fact that 'true' mathematicians do not like Monte Carlo
methods. They believe that they rob us of the finesse and elegance
of mathematics. They call it 'brute force'. For we can replace a
large portion of mathematical knowledge with a Monte Carlo
simulator (and other computational tricks). For instance, someone
with no formal knowledge of geometry can compute the mysterious,
almost mystical π (Pi). How? By drawing a circle inside
of a square, and 'shooting' random bullets into the picture (as in
an arcade), specifying equal probabilities of hitting any point on
the map (something called a uniform distribution). The ratio of
bullets inside the circle divided by those inside and outside the
circle will deliver a multiple of the mystical Pi, with possibly
infinite precision. Clearly, this is not an efficient use of a
computer as Pi can be computed analytically, that is, in a
mathema-tical form, but the method can give some users more
intuition about the subject matter than lines of equations. Some
people's brains and intuitions are oriented in such a way that
they are more capable of getting a point in such a manner (I count
myself one of those). The computer might not be natural to our
human brain; neither is mathematics. |