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.
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]
_________________________________________________________________
Advertisement: Fresh jobs daily. Stop waiting for the newspaper. Search Now!
www.seek.com.au
http://a.ninemsn.com.au/b.aspx?URL=http%3A%2F%2Fninemsn%2Eseek%2Ecom%2Eau&_t=757263760&_r=Hotmail_EndText_Dec06&_m=EXT
-----
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
