Random Ruminations of the Third Kind

Mathematics has always been considered the Queen of All Sciences. And one doesn't have to be a genius to figure out why..

And, it can be more fun, when you try to figure out its manifestations in things and situations around you, which are so beautifully camouflaged, that sometimes, even the most observant eye can miss them.
In fact, it took an exceptionally gifted rare gem(the phrase's enuf!) & me, to figure out one such natural embodiment of a theorem, called The Central Limit Theorem, that is very fundamental to the study of Random Distributions, the other day at jogging.

BITSian campus abounds in Pigeons. They are here, in every size and psyche imaginable. They adorn all structures here, which sometimes even includes our shoulders and what lies between them. But the most dangerous, and interestingly, the most mathematically significant place that they may ever perch on, is a tree.

To begin with, let us define an element x, where {x | x ϵ {BITSian}∪{BITSian}' }

Now, consider the following mutually exclusive and exhaustive events(in the probabilistic sense) :

Event A: A pigeon comes, perches on a tree, sits there for sometime waiting for x, an element x passes by, pigeon shits, manages a bulls-eye, shit lands on element x.

Event B: A pigeon comes, perches on a tree, sits there for sometime waiting for x, an element x passes by, pigeon shits, misses aim, shit lands on land under the tree.

Event C: A pigeon comes, perches on a tree, sits there for sometime waiting for x, no element x passes by, pigeon gets call of nature, pigeon shits, shit lands on land under the tree.

The following are presumed:

1. Whenever any one of the events B or C occurs, a shiny white-spot is created at a point on the ground under the tree.
2. The boundary of the area containing these points is limited by the absolute girth and peripheral expanse of the tree's branches.
3. All points inside and on the boundary are within convenient reach of pigeons.
4. Highly energetic and oblique squirtings do occur, but are so few in number that their contribution is negligible.
5. The tree can hold a considerably large number of pigeons at any given time.
6. Each pigeon perching on the tree can shit anytime, voluntarily.
7. A spot once created stays there for a considerably long period of time, so long, that the spot may be assumed to be permanent.The individual spots thus additively contribute to the total.
8. Two spots may, or mayn't overlap.

In the light of the above assumptions and subsequent observations, the following was proposed during our jogging:

Let n be the number of occurences of the event s, where {s | s = B or s = C}

"Over a long period of time, as n tends to infinity, the shape of the distribution of pigeon-shit spots under the tree tends to be approximately Gaussian or Normal."

At first, this 'remarkable result' may seem to be too trivial in its implications. But it can have far reaching consequences. Detailed studies can lead to development of methods to determine the optimum extent & frequency of trimming of trees, so as to reduce the number of spots on ground all over the campus, thus inturn reduce the frequency of occurence of event A.

Besides, it can give homo sapiens a deep insight into the dynamics of pigeon-droppings and behavioural characteristics of the members of the Class Aves of Animal Kingdom.

This discovery kept revisiting us all that day, and on subsequent jogs.
We are still to evolve a complete mathematical model based on the above theory, quantifying the mean and variance of the randomly distributed spots.

But as of now, the next time you go jogging, do wait to take a look at this marvel of nature!!
Meanwhile, the tree outside looks lonely(and safe!); i'll just go and give it a hug..