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Unread October 29th, 2005, 05:19 PM
James Brody James Brody is offline
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Default A Note to Howard Bloom: The Power of Scale-Free

Someone, Duncan Watts?, commented that you're near a phase transition when power laws start popping out. This observation may be a hint about mysterious things but it is also a truism! If phase transitions are, by definition, a boundary between chaotic arrangements (in which every outcome is equally probable) and ordered ones (in which a very few outcomes are very probable) then the boundary will be one of congealing or melting events. Big things recruit smaller ones and a selective advantage accrues to the big things that recruit the most members and the most quickly. Organizations that fail to recruit also fall and organizations that don't eliminate junk will fail when resources erode. (JBS Haldane observed that the magnificent claws of a beetle or a crab lead to its faster extinction in hard times.) Evolution occurs...

Thus, a second truism unfolds, Kauffman's 1993 observation that evolution follows a phase transition. This could also be called Goldilocks' Rule: "Not too much, not too little, but just right." Power laws and phase transitions, thus, not only make life possible but also our understanding of its organization and the universe around it. Even science becomes possible because the arrangements in our minds are congruent with those in astro- or quantum physics.

We also find that whether grammars and vocabularies or parents and the toys they pick for their child, there are hubs and their collections of nodes. In the extreme, it can be argued that rich people collect poor people and even aspiring science writers have an idea but fill litter boxes with references in order to extend their market and to defend their core ideas.

Intelligence is associated with fluid thinking and rearrangements of ideas: an outcome only possible in emergent networks that have lots of participants and in arrangements that are nearly jam-proof, an outcome that is nearly inevitable given networks of a sufficient size.

Scale-free is perhaps an outcome of the numbers: there is no matter what the size of the units you study, their societies will be very similar. Thus, we can diagram termite societies by individuals or by functions: the networks are much the same. Pythogoras would be pleased...

References:
Bloom, H. (2000) Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century. NY: Wiley.
Conway Morris, Simon (2003) Life's Solution: Inevitable Humans in a Lonely Universe. NY: Cambridge University Press.
Kurakin, P, Malinetskii, GG, & Bloom, H. Conversational (dialogue) model of quantum transitions. Kurakin, P, Malinetskii, GG, & Bloom, H (2005) Conversational (dialogue) model of quantum transitions. http://arxiv.org/ftp/quant-ph/papers/0504/0504088.pdf
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