Wednesday, December 31, 2014
A Fuzzy Boundary with Randomness
Consider straight-forward, atomic level simulations of both a frog and a glass of water of roughly the same mass. The same amount of memory will needed store the position and velocity data (for a Newtonian version) or wave function correlations for both systems - in this sense both contain the same amount of information. But of course almost all of the information that describes the glass of water will be random in nature, while decent fraction of the frog's binary encoding is structured / nonrandom, i.e. nontrivial.
Going back to the cat/dog example it is also the case that real world objects, formed from arrangements of moles of atoms, necessarily have somewhat fuzzy descriptions (e.g. Fuzzy Set). One could decree that the first "true cat" was born 10,003 years ago (the offspring of two admittedly catlike creatures), but attempts at such exact definitions are almost always ambiguous (obviously enough, but one encounters the occasional debate over, say, what the true definition of life is). This type of fuzzy boundary also applies to our frog example, between what would count as structured and nontrivial in the description, and the random remainder (such as the orientations of the water molecules within the cells, etc...). More broadly this provides a pleasing way of viewing the world at large: full of hierarchical patterns (and thus amenable to science), but permeated by a fuzzy boundary with randomness.
Going back to the cat/dog example it is also the case that real world objects, formed from arrangements of moles of atoms, necessarily have somewhat fuzzy descriptions (e.g. Fuzzy Set). One could decree that the first "true cat" was born 10,003 years ago (the offspring of two admittedly catlike creatures), but attempts at such exact definitions are almost always ambiguous (obviously enough, but one encounters the occasional debate over, say, what the true definition of life is). This type of fuzzy boundary also applies to our frog example, between what would count as structured and nontrivial in the description, and the random remainder (such as the orientations of the water molecules within the cells, etc...). More broadly this provides a pleasing way of viewing the world at large: full of hierarchical patterns (and thus amenable to science), but permeated by a fuzzy boundary with randomness.
Monday, December 23, 2013
Constraints
I am not my brain, I am the information patterns that are encoded in my brain. The atoms in my brain are cycled out into the surrounding environment, the water molecules quickly, the others more slowly. And whatever the flux, the quarks and electrons within my skull are fundamentally indistinguishable from those in the trees and the air and all the rock below - only the arrangement differs. A sufficiently powerful computer, programmed correctly, could faithfully replicate the information processing carried out by my neurons, and I would accordingly find myself existing, experiencing the same qualia, typing out the same words. I am the information pattern, not the physical substrate.
And yet, I am the general type of information pattern that would be naturally generated by, embedded within, a physical substrate like a brain. An information pattern that is realized within a physical substrate in necessarily constrained by that substrate - only so much memory is available, and only some finite number of calculations can be performed, with a given number of atoms and useful energy. Being embedded with a physical environment also shapes the sensory input that a mind receives, and presents the challenge of continued survival. This is in contrast to abstract Turing machines effortlessly processing arbitrary input strings, out floating in Platonia. The constraints imposed from existence within a physical universe are key in generating nontrivial information structures, and nontrivial observers in particular.
And yet, I am the general type of information pattern that would be naturally generated by, embedded within, a physical substrate like a brain. An information pattern that is realized within a physical substrate in necessarily constrained by that substrate - only so much memory is available, and only some finite number of calculations can be performed, with a given number of atoms and useful energy. Being embedded with a physical environment also shapes the sensory input that a mind receives, and presents the challenge of continued survival. This is in contrast to abstract Turing machines effortlessly processing arbitrary input strings, out floating in Platonia. The constraints imposed from existence within a physical universe are key in generating nontrivial information structures, and nontrivial observers in particular.
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
33
Monday, September 17, 2012
A Full Simulation of the Brain is Possible, in Principle
Thursday, June 03, 2010
Larger than our Hubble volume...
Last Lights On - Mandelbrot fractal zoom to 6.066 e228 (2^760) from teamfresh on Vimeo.
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...
