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] ----- 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
