On Thu, Apr 23, 2009 at 11:37:35AM -0700, Robert Howard wrote: > I suppose Dennett is implying that the linear congruential generator below > would take at least the number of bits in variables a, b, m, and x[0]. If > those are 1-byte integers, then the bit count is at least 32 bits. Theres > overhead for the actual code too. How do you measure that? Suppose the > answer is 100 bits for the code including state. Then if you use it to > generate a sequence of one gazillion values, that sequence would only > contain the equivalent of 100 bits of information because it can be > generated by a 100 bit algorithm. >
Yes. > > > I still suspect there might be circular logic here. Do we place no value on > the energy needed to generate it? > That's right. Information is a purely information theoretic construct. Energy doesn't come into it. > > > What if our entire universe can be described in a very simple equation that > is just generated recursively or fractally by many iterations? If that > equation was less than a megabyte, then would we argue that the entire works > of Shakespeare must have less information? > No, because the universe did not produce Shakespeare by a deterministic process. Every time a quantum measurement is taken of something that might have one of two values, a bit of information is generated. Information can be also be lost, a process known as quantum erasure. This explains why the universe we see today is less complex than it would naively seem if every particle generated a new bit of information each Planck time. This is perhaps most easily seen in the Many Worlds Interpretation, although it is not necessary for the MWI to be true for information to increase in our universe. In the MWI, the Universe splits each time a measurement is taken, so one ends up with some enormous number of parallel universes. In most of those universes, Shakespeare never existed, and so the works of Shakespeare never materialised. Only in our special neck of the woods are there Shakespearian tragedies, and many more things that even more complex (eg human brains). The really cool thing about this is that the total complexity of the Multiverse is really, really small, namely that of a fairly simple equation called Shroedinger's equation like you suggest. If you want to know more, please take a look at my book "Theory of Nothing". Cheers -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 hpco...@hpcoders.com.au Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
