On Fri, Jan 16, 2004 at 10:27:49AM +0800, David Barrett-Lennard wrote:
> 
> I agree with everything you say, but did you really think I was making a
> point because Eugen happened to use hex?!

I've fallen behind on answering my email, so sorry if this is brief and a bit
out of context. This post is not talking about the universe metalayer at all.

I was using a specific natural number (a 512 bit integer) as an example for
creation and destruction of a specific integer (an instance of a class of
integers). No more, no less.

Existence of a specific integer has nothing to do with existence of a
production system for a class of integers. The recipe for a series is not the
dish itself. That recipe is also just information, requiring encoding in a
material carrier. It would have taken considerably more work to eradicate the
entire production system, as it is a bit more widespread, and has a lot more
vested interest than conservation of a specific, random integer, destilled
from turbulent gas flow.

The representation (hex, need to be told that above hex string represents an
integer (ignoring underlying representations as two's complements,
potentials, charge buckets and magnetic domains for the moment) indicates 
that even that "simple" information transfer was encrusted with lots of 
implicit context people take for granted. Roll back to
Sumer, and hand out little clay tablets with that hex string. What does it
mean? Nothing. Not even the alphabet to parse this exists.

Animals evolve representations for quantities, because resource management is
a critical survival skill. After a few iterations you get consensual
encodings for interactive transfer, then noninteractive consensual encodings.
I used patterns of luminous pixels (translated into Braille dots, for all what I know) 
instead of scratches on a bone fragent, because that encoding is more
familiar, and easier to transmit.

Wavefront reemitted from pebbles hitting retina, being processed on the fly,
tranformed into a spatiotemporal electrochemical activity pattern is an
instance of a measurement of a property. It takes a specific class of
detectors to do. You cannot conduct that measurement in their absence.

> You say the given integer exists because "it is it is physically
> realizable *in principle*".  That sounds like the platonic view to me -

To me, this sounds like a confusion between a specific integer, and a recipe
for such. It is quite difficult to feed a wedding throng with pages from a cookbook.  

> because the number is *not* actually physically realized and yet the
> number is purported to have an independent existence.  Are you saying
> otherwise?
> 
> I think any form of symbolic manipulation of numbers is implicitly using
> the platonic view.  To say they spring into existence as they are
> written down (which in any case only means they are realizable in

Numbers don't write down themselves. Systems generate them, translate them
into specific encodings, to be parsed by other instances of systems of the
same class. Use a system of a different class, and you'll only parse garbage.
ATGATAGTGGCCGTCCAACGGTAGACTCTAC might be a number, it might also be a
shorthand for a linear biopolymer (5'-3'? there's some implicit context for
you). 

> principle) just seems silly to me.

A cookbook is a promise of a meal, not the meal itself.
 
> The Platonic view just says that every mathematical system free from
> contradiction exists.  Ie if it can exist then it does exist.  There is

Exists where? Two production systems of the same kind generate the same
output. Surely, the output is contained within them? In there, somewhere?

Mathematicians are production systems. Input is coffee, output is theorem.

> no need to talk about different types of reality.

-- Eugen* Leitl <a href="http://leitl.org";>leitl</a>
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