On Sun, 27 Jul 1997 Hal Finney <hal@rain.org> Wrote:
>>Me:
>>Forget about "reality", I want to know if the Mandelbrot Set
>>is different in some very fundamental way from the Virgo Cluster.
>Then it depends on what you mean by "fundamental", right?
Right. I'm interested in how my views on this subject will evolve, you're
free to believe what you want.
>The Virgo cluster is made of atoms, the Mandelbrot set is not. The
>Virgo cluster interacts with matter and energy, the Mandelbrot set
>does not.
All true, but will there come a day when these facts will have no more
fundamental physical significance TO ME than the fact that the USA has 50
States or the solar system has 9 planets or the stooges have three members?
>The Mandelbrot set has thickness zero, the Virgo cluster has a
>nonzero thickness.
That's sort of interesting. The Mandelbrot set doesn't have a thickness
exactly, but just like any 3 dimensional object, the surface of the set is
2 dimensional. In 1991 Mitsuhiro Shishikura proved that the boundary line of
the Mandelbrot Set is as convoluted and wiggly as it is possible for a line
drawn on a flat surface to be, that means it has a fractal or Hausdorff
dimension of 2.
"Nicholas Bostrom" <bostrom@mail.ndirect.co.uk> On Mon, 28 Jul 1997 Wrote:
>"Perry E. Metzger" <perry@piermont.com> Wrote:
Actually you were quoting me.
>What about the old distinction in logical positivism between
>propositions true (solely) in virtue of their meaning and
>propositions whose truth also depend on how the world is?
But that's the question, if something is logically consistent does that make
it part of the world? I'm not a big fan of Logical positivism either,
Russell's theory of types is really ugly. Also, the idea that a every
question must have a clear and precise answer or it's totally meaningless
seems impossibly restrictive to me. After Godel we know that even the best
logical systems will be inconsistent or incomplete or both, and English is
far from the best, and yet with all its imperfections people have still
managed to get quite a bit of mileage out of it.
>Are you a Quinean?
I've read Quine but don't usually call myself a Quinean.
John K Clark johnkc@well.com
-----BEGIN PGP SIGNATURE-----
Version: 2.6.i
iQCzAgUBM9w6Pn03wfSpid95AQEaswTvaYay4NX0luiJ+NxjppQf1KiCfN/6mKHf
NN3Z7OXmoGt+YAFJ3FcVTsgH4LcRpK8aApmeLkwSQ9qEwdjBUuynah6jxd/NVvWa
ELAfw8TW+FoY8HLzwdgxR+Svzw8F8lZXkQW8E4mCrVnuYT8mYlAoG2BZzOIxSQuF
qwe0uPdG3Xy1QXS7qeohLY8vGPyRXky0mFZd02UMsMSVOtyf14I=
=8ga3
-----END PGP SIGNATURE-----