## Thursday, April 5, 2007

### Why 42?

The answer to the ultimate question, i.e " life, universe and everything else" is forty two! But then, surely, it is not entirely arbitrary that the random number was chosen so randomly. It's apparent meaninglessness was because of the human inability to understand the subtleness involved in the number.
Long after this was understand by the Hungarian super brain, Paul E Erdos, he did try to evolve a proof for his mortal accompaniments to comprehend. His idea was to aloof himself from explaining such a complicated procedure to minds much less talented than his. As this was the reason, he did try to make his point clear centuries after his existence.
He introduced the idea( a notion till then considered impossible) of a network in those who did spend their time, penetrating into the land of the unknown , I mean, Research! Yes, I'm talking about the Erdos Number of any researcher in the field of computer science and math..

Well, a similar idea follows in social networks. Consider that anyone in the world knows you at least six people far away. If you are a person far away from Etnos, it means you know Etnos personally. For the time being, lets consider that you know Etnos means, Etnos knows you. If you are two people far away from Xia, it means, you know a person who knows Xia and you don't know Xia. And so on until the sixth person. The six degrees of separation, hypothesis states that every one in the world is at most six people away from each other. Equivalent to saying that all mathematicians have Erdos number with in six. Well, this is as logically equivalent to saying , you can pass a letter to Mr.Bush ,say, if you sent it across at most six people. People use this heuristics in most of their analysis of family trees etc. A job, really famous, is the Royal Office of British Genealogy, where they consider that all royalty of most European nations related by at most 3 families, i.e three linkages which change blood.
Coming back to six degrees of separation, if each person on an average knows psi people. Consider that, people he knows at the second level will be psi2 and at the sixth level will be psi6 and that means we should cover the total number of people in the earth, which is six billion by summing a Geometric Progression from psi6 to psi6. On making appropriate calculations and giving the right equations, we end up with psi = 42!!!

So.. now you know whats the motive behind the answer!

P.S with regards to Sidderich Shanovsky, a CSEmician from the Ilansky offe Instiutovick Technikov (Иланский институт технологии), and yes, they trust none until they virus scan.

Mohan K.V said...

Nice post :-)

"On making appropriate calculations and giving the right equations".. now where have I heard that before ? :-)

Seriously now, I had an argument with a prof regarding this, and we realized that the problem formulation could be made more accurate. The problem with the GP, as you know, is that it assumes that _everyone_ that my friend knows is unknown to me. One nicer formulation we came up with was to represent every person as a node in a graph, connect each and every node to every other node, and start removing the edges one by one, randomly. We continue doing this, and at every point we calculate what is the average number of nodes one node is connected with.. but then we gen gave up and moved on :-)

Vettius Carnaticae said...

Yes, in fact, graph theoretically, speaking it reduces to the assertion that the Diameter of the graph in question ( http://en.wikipedia.org/wiki/Distance_(graph_theory) ) is 6.
Now, we are required to prove that the average degree is 42. This is a rather specific question, i.e it depends on the nature of the graph, and no generalization can actually give the exact average degree. However, it gives us a range, and that is between 20 - 84.

Some exceptions to the hypothesis, include closed loops, say a group of people in Africa, who do not know any one. etc. etc.

N said...

Magaa, one hell of an illuminating post. Thank you!
So I must weed out inessential contacts from my life, unlearn memories of many friends, and taper my circle's strength down to 42.
H'm..where shall I start? By the way, who are you? ;)

Hetero sapien said...

why stop with 2 posts? The role of tech and math blogging, unfortunately vacated by KVM desperately needs to be filled!