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Ubiquity

I’m currently reading the book ‘Ubiquity’ by Mark Buchanan and I find that it is written very well. Here are some thoughts that occurred to me while reading, feel free to comment :)

Power Law.
While on one hand, the fact that this law describes many different processes makes it certainly interesting to investigate, on the other hand one can come to question the use of this. The law is very generic, basically stating in mathematical equation:

log y = a * (log x) + b

The factor a, of course, corresponding to the factors the different people mentioned in the book have observed in different fields, such as for instance earthquakes.

First of all, I find it odd that so far that I have read, no mention is made of the factor b, while this could of course be very crucial. For instance when x is the calamity of an earthquake and y is the probability of such earthquake occuring, the factor b can play a crucial role. After all… decrease it just by a couple of units, and you already reduce the probability of a big earthquake happening by a order of magnitude.

Another question one can formulate is what the final use of this law is. This law, which the author refers to as the ‘Power Law’ predicates that it is impossible to predict events with a certain order of magnitude. Therefore one can not use it like one would use the laws of Kepler. In addition it does not model the behaviour of the system in question, and in such can not offer an explanation either, like the laws of Newton did in contrast to those by Kepler.

Maybe I’m missing the point, and for all the readers out there that have some affinity with this subject, I would love to get some feedback in case I missed something.

Scientific History
Having progressed after the previous text (which is a copy from my old blog) I have stumbled upon some interesting passages. The author refers to another writer named Kuhn who wrote about the history of scientifical developments.

The basic idea is that as long as it is possible, scientists stick to the current paradigms trying to accumulate more and more cases in nature to obey that law. However after a certain amount of evidence can no longer be accomodated by the current laws there forms a stress within the scientific community. Eventually enough stress leads to a paradigm shift. The author mentions that this happens constantly on the small scale. However sometimes the shifts can ripple throughout sciences and these are the typical historical breakthroughs that are famous, such as Einstein, Heisenberg, etc.. However, if one observes the powerlaw, then these cases are no more spectacular than the smaller paradigm shifts.

This agrees with a feeling I’ve had for a while that the famous scientists were in a sense ‘lucky’ to be there at the right time. I am not trying to discredit their work, the effort they made is of course not an easy one. However, the reason they became this famous is just because there was enough spread out stress to cause a ripple throughout the scientific community. In other words, it had been brewing long enough to spill over.

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