--- Mitchell Porter <[EMAIL PROTECTED]> wrote: > > This is a good idea but some of the numbers seem wrong. In the first > scenario, the simulator is the computer connected to my brain (or the > software running on that computer, if you prefer); why should a synapse > count provide a good estimate of its complexity? And the complexity of > scenario five is a bit hard to quantify, but if you really thought it was > the same as that of the set of natural numbers, you might consider the > appropriate complexity to be that of the Peano axioms of arithmetic.
For the first scenario, I assume the environment would be complex enough to use all of the brain's processing power to learn. Otherwise our simulation could replace the brain with a less powerful computer. My estimate of 10^13 bits is very crude, anyway. Nobody has actually counted synapses. There are about 10^11 neurons with (some unknown number) of synapses each, thousands, I guess. Some neurons have 50,000 synapses, but I can't find any source that gives the average number in the cortex. Also the memory per synapse might be very small. It is about 1 bit per synapse in a Hopfield net, but maybe it is 0.1 or 0.0001 bits in the brain due to redundancy. We really don't know. The complexity of 5 is also hard to quantify. It depends on your choice of universal Turing machine. I could claim it is 0. > > >From: Matt Mahoney <[EMAIL PROTECTED]> > > > >As you probably know, Hutter proved that the optimal behavior of a goal > >seeking agent in an unknown environment (modeled as a pair of interacting > >Turing machines, with the enviroment sending an additional reward signal to > > >the agent that the agent seeks to maximize) is for the agent to guess at > >each step that the environment is modeled by the shortest program > >consistent with the observed interaction so far. The proof requires the > >assumption that the environment be computable. Essentially, the proof says > > >that Occam's Razor is the best general strategy for problem solving. The > >fact that this works in practice strongly suggests that the universe is > >indeed a simulation. > > > >With this in mind, I offer 5 possible scenarios ranked from least to most > >likely based on the Kolmogorov complexity of the simulator. I think this > >will allay any fears that our familiar universe might suddenly be switched > >off or behave in some radically different way. > > > >1. Neurological level. Your brain is connected to a computer at all the > >input and output points, e.g. the spinal cord, optic and auditory nerves, > >etc. The simulation presents the illusion of a human body and a universe > >containing billions of other people like yourself (but not exactly alike). > > >The algorithmic complexity of this simulation would be of the same order as > > >the complexity of your brain, about 10^13 bits (by counting synapses). > > > >2. Cognitive level. Rather than simulate the entire brain, the simulation > >includes all of the low level sensorimotor processing as part of the > >environment. For example, when you walk you don't think about the > >contraction of individual leg muscles. When you read this, you think about > > >the words and not the arrangement of pixels in your visual field. That > >type of processing is part of the environment. You are presented with a > >universe at the symbolic level of words and high-level descriptions. This > >is about 10^9 bits, based on the amount of verbal information you process > >in a lifetime, and estimates of long term memory capacity by Standing and > >Landauer. > > > >3. Biological level. Unlike 1 and 2, you are not the sole intelligent > >being in the universe, but there is no life beyond Earth. The environment > >is a model of the Earth with just enough detail to simulate reality. > >Humans are modeled at the biological level. The complexity of a human > >model is that of our DNA. I estimate 10^7 bits. I know the genome is 6 x > >10^9 bits uncompressed, but only about 2% of our DNA is biologically > >active. Also, many genes are copied many times, and there are equivalent > >codons for the same amino acids, genes can be moved and reordered, etc. > > > >4. Physical level. A program simulates the fundamental laws of physics, > >with the laws tuned to allows life to evolve, perhaps on millions of > >planets. For example, the ratio of the masses of the proton and neutron is > > >selected to allow the distribution of elements like carbon and oxygen > >needed for life to evolve. (If the neutron were slightly heavier, there > >would be no hydrogen fusion in stars. If it were slightly lighter, the > >proton would be unstable and all matter would decay into neutron bodies.) > >Likewise the force of gravity is set just right to allow matter to condense > > >into stars and planets and not all collapse into black holes. Wolfram > >estimates that the physical universe can be modeled with just a > >few lines of code (see http://en.wikipedia.org/wiki/A_New_Kind_of_Science > >), on the order of hundreds of bits. This is comparable to the information > > >needed to set the free parameters of some string theories. > > > >5. Mathematical level. The universe we observe is one of an enumeration of > > >all Turing machines. Some universes will support life and some won't. We > >must, of course, be in one that will. The simulation is simply expressed > >as N, the set of natural numbers. > > > >Each level increases the computational requirements, while decreasing the > >complexity of the program and making the universe more predictable. > > > > > >-- Matt Mahoney, [EMAIL PROTECTED] > -- Matt Mahoney, [EMAIL PROTECTED] ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=11983
