Wednesday, August 11, 2004

Both nodes together or separately will be happy ever after

I am interested in complex systems…..When graph theory deals with complex systems as the internet, the cell, or even cocktail parties the regular graphs contain many ambiguities about their structure. Real graphs (as real relationships) from social networks to phone lines are not regular and nice. These graphs are hopelessly complicated. Humbled by their complexity some mathematicians assumed that these networks are random.
Humbled by this complexity and confusion a love story started randomly with 2 isolated nodes, me and a special someone. We decided that the simplest way to create “our love story” was to play dice: If you roll a six, place a link between us. For many other roll of the dice, do not connect us but cut a link or choose a different node and add a link. Therefore, the love story of me and the special someone was represented as fundamentally random.
We randomly added links between us …..we enjoyed playing dice… we believed that there are enough links between us……we believed that were connected with this simple and elegant way. But one morning a miracle happened: There were no connections between us, no links…. nothing.I was crying because I realised that random networks played no role in assembling the pieces of my heart….and then I hated the random graph theory. I hated maths. I could not believe that the more links we add, the harder it is to find a node that remains isolated, because I was this isolated node, full of fear and anxiousness….
Unfortunately, I was not lucky as the average neuron that is connected to dozens of others, some to thousands……I was taught that in my body the molecules take part in far more than a single reaction- some in hundreds. I was taught that there are very dense networks from which nothing can escape and within which every node is navigable…. I was taught that I cannot escape.
One day I took the risk: Let’s navigate along the links between other nodes…
You are not brave but you can escape…….….
I enjoyed the navigation.. ….I was not brave, but I was curious. I passed from a “special male” node. He was playing violin…..I decided to stay there for a day…And this is the time for my fairytale: girl meets a man, girl writes now her theses, girl loves to live with the man, man loves to live with the girl, girl loves the man, man loves the girl.........it does not matter if the fairytale continues ...because we all agree that when a pair of nodes connected in a relationship, something special happens: The network after placing a critical number of links, drastically changes. We have a giant cluster and both nodes together or separately will be happy ever after.

1 Comments:

Blogger thecocktailarch said...

until I have a proper comment, here's my blogspot address:

www.houseofgoodintentions.blogspot.com

and might I add, everything looks like a picasso if you flatten it out.

August 11, 2004 at 5:52 PM  

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