Monday, March 11, 2013
Cloud of randomness
What is the difference between a cat and a dog? These (classes of) entities are truly different - it's not as if the differences are entirely subjective or purely a matter of opinion. And yet, there can be no complete, precise, and unambiguous definition that cleaves the two, as is demonstrated by the fact that they share a common ancestor. The principle holds in general: all emergent structures (those formed out of arrangements of vast numbers of mathematical building blocks) are surrounded by clouds of randomness. For instance, the particular orientations of the water molecules in your brain were completely unimportant during your reading of this paragraph. But this fundamental randomness is also not irrelevant: it is a central component of the engine for generating nontrivial information, i.e. iterative trial and error.
Tuesday, September 25, 2012
New Mandelbox zoom
Friday, September 21, 2012
Monday, September 17, 2012
A Full Simulation of the Brain is Possible, in Principle
Thursday, June 03, 2010
Larger than our Hubble volume...
However, the CMB is a fairly uniform temperature, and space is quite flat... If one adds a scalar field to GR in such a way that the potential energy is much larger than the kinetic energy, then spacetime responds by growing exponentially. This inflation provides a nice explanation for the uniform temperature of the CMB and the flatness (among other things). The scalar field can then decay at a point and bring inflation to an end, as it did in our region of the multiverse after expanding the scale of the metric by about a factor of e^60. However, generally speaking there will be regions where the scalar field has not yet decayed and inflation is continuing. After each e-fold expansion, the spacetime volume will have grown by a factor of e^3 ~ 20, thus if the probability that the scalar field does not decay is greater than 1/20, then inflation will continue forever - this is eternal inflation. If the e-folding time is the Planck time, which is ~ 5*10^-44 seconds, and there have elapsed ~ 1.37*10^10 * 365 * 24 * 3600 seconds so far in our Hubble volume, then there has been expansion in scale over the multiverse of about e^(8*10^(61)) since the big bang... In fairness however, the video didn't exhaust the Mandelbrot set...