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- Xref: sparky sci.physics:14464 sci.math:11257
- Newsgroups: sci.physics,sci.math
- Path: sparky!uunet!mcsun!Germany.EU.net!prim!dave
- From: prim!dave@germany.eu.net (Dave Griffiths)
- Subject: Re: Computability of the universe
- Message-ID: <1992Sep11.181552.416@prim>
- Organization: Primitive Software Ltd.
- References: <1992Sep9.212748.1@sol.yorku.ca> <1992Sep10.021939.10087@murdoch.acc.Virginia.EDU> <18mgemINN34o@roundup.crhc.uiuc.edu>
- Date: Fri, 11 Sep 1992 18:15:52 GMT
- Lines: 66
-
- In article <18mgemINN34o@roundup.crhc.uiuc.edu> hougen@uirvld.csl.uiuc.edu (Darrell Roy Hougen) writes:
- >lfoard@Turing.ORG (Lawrence C. Foard) writes:
- >
- >I'm afraid you are laboring under several mistaken or naive
- >assumptions. This is not meant as a flame, but one should be wary of
- >thoughts that everything is simple and solved and knowable.
- >
- >) I've been arguing with several people over the "reality" of irrational
- >) numbers. By reality I mean a process in the real world that "operates"
- >) on irrational numbers. This is not to say that irrational numbers are
- >) meaningless since they represent the limiting case of many "real" things as
- >) the number of trials go to infinity.
- >
- >First of all, processes in the real world don't operate on numbers at
- >all. Numbers are just a mental abstraction of quantities that exist
- >in the world. Before dismissing irrational numbers, try to think of a
- >process that operates on rational numbers.
- >
- >If I give you a piece of metal and ask you how long it is, what will
- >you answer? If you measure it, you will undoubtedly arrive at a
- >rational number, but that is only because rational numbers have finite
- >representations in the usual representational scheme. Therefore,
- >measurements are always rounded to the nearest number of a given
- >precision. In reality, however, the length may not even be well
- >defined in a mathematical sense. As one magnifies the piece of metal,
- >substructure will emerge showing not one length but many lengths and
- >as the structure is magnified still further, fluctuating electron
- >clouds will appear and the boundary will become fuzzy. Thus, length
- >is an abstraction and measurements of length are only meaningful at
- >some scales. The length of an object is neither a rational nor an
- >irrational number, but it is convenient to represent it by the
- >rational number that best approximates it.
- >
-
- I think you've missed the point. You assume that there is "reality" out
- there that is infinitely subdivisible. You are thinking of a number or
- a measurement as being an approximation to the "real" size. What the
- original poster implied (I think :-) is that there is _no_ absolute reality
- out there.
-
- Question: how can you ever "know" that length in the real world is
- a continuum if you're always limited in the accuracy of your measurements?
- This is an act of faith on your part! It is a model of reality that so
- far has worked pretty well. But it has problems. Infinities crop up all
- over the place. And that doesn't make sense.
-
- Now imagine if you could build a massive computer, bigger than the universe
- and you ran a simulation of the "real" universe on it, and imagine if the
- match between the simulation and "reality" was sufficiently good. Result:
- intelligent life evolves in the simulation and from it's point of view the
- world feels pretty "real", it's just that it starts to notice wierd things
- like energy only being allowed in certain discrete quanta ;-).
-
- Now _if_ this was possible, what use is your model of a "real" world? Apply
- Occams Razor: there is no need for the infinite information content of a
- real world.
-
- Is the music on your compact disc somehow less than real? Would it continue
- to be so if the sampling rate was far in excess of what your ear could
- detect?
-
- The discrete model _is_ reality.
-
- :-)
-
- Dave Griffiths
-