LZ:
> Colin Hales wrote:
>> I reached this position independently and you may think I'm nuts... I
can't help what I see... is there something wrong with this way of thinking?
> I don't see what you think a non-ideal number is.
This deficit of mine includes having trouble with ALL numbers. :-)
For the life of me I cannot imagine what an 'object' is that has
quintessential property of 'five' about it. Sitting in platonia somewhere
is this object. Somewhere else in platonia sit the objects 'red' and 'sad'
and 'big'. Here on the list we talk of integers and given them a label I
and then speak of operations on I. We tend to think of I as 'being' an an
integer..
...But it's not. Lets talk about the object with this property of five in
platonia as <5>. Here in reality what we are doing is creating a label I
and interpreting the label as a pointer to storage where the value in the
storage (call it [I]) is not an integer, but a symbolic representation of
property of five_ness as mapped from platonia to reality. What we are
doing is (very very metaphorically) shining a light (of an infinity of
possible numbers) on the object <5> in platonia and letting the reflected
light inhabit [I]. We behave as if <5> was in there, but it's not.
All the rules of integers act as-if <5> was there. At that moment the
storage pointed to by I contains a symbolic rearrangment of matter such as
binary 1001 implemented as the temporary state (an arrangement of charge
in space) of logic gates. We logically interpret this artrangement of
charge in space as having the effect of five_ness, which is property of we
assign at the moment we use it (such as one more than 4).
To me the actual numbers (things) don't exist at all. All I can really see
here in reality is logical relations that behave as-if the platonic
entities existed. This all may seem obvious to the rest of you. That's my
problem! But to me here watching the industrial scale manipulations of
symbols going on, I wonder why it is we think we are saying anything at
all about reality - the computation that literally _is_ reality - which,
again, I see as a pile of logical relations that sometimes lets the
platonic light shine on them in useful ways - say in ways that enable a
mathematical generalisation called an empirical law.
As to what the non-ideal numbers are....
Well there aren't any. Not really. At least I can't conceive them. However
the logical operations I see around us have the structure of numbers
correponding to a rather odd plethora of bases. Quantity is implicit in
any natural aggregation resulting from logical operations. One number
might be:
human.cell.molecule.atom.nucleus.proton.quark.fuzzy1.fuzzy2...fuzzyN
(fred.dandruffskincell.omega3.carbon.nucleus.3rd_proton.UP_quark1_string.loop_2.etc1.etc2.....)
If you work in base "atom" arithmetic you have and arithmetic where atoms
associate with a remainder, say a unit in another base called .photon
This is called chemistry.
The human (and all the space that expresses it) is one single number
consisting of 'digits' that are all the cells(and interstitial molecules)
collected together according to affinities of fuzzyN, which acts in the
above 'number' like the integer I does to the set of integers expressed in
binary I mentioned above.
There's no nice neat rows. No neat remainderless arithmetic.
But it's all created with logical operators on an assumed elemental
'fuzzyN' (see above) primitive. '.fuzzyN' can be treated as an underlying
structural primitive 'pseudo-object' as a fundamental 'thing'. But .fuzzyN
can be just another logical relation between deeper primitives. There is
no depth limit to it.
As to computation - I have already described what we do here in maths and
computation - all the same, really - all manipulating 'as-if' labeled
entities. At the instant we lose sight of the logical/relational nature of
what we are doing then we can delude ourselves that the symbols denote
real 'objects' such as those in platonia and - especially - if you happen
to 'be' a collection of these logical operations the rest of the logical
operations going on around you look very lumpy and thingy indeed! It looks
even more compellingly so when you it appears to obey empirical laws like
quantum mechanics and the Nernst equation when perception - made of the
same logical operations - presents you with a representation of it all
using that special logical aggregate called a brain.
In terms of the thread subject line, then, a chair is literally
mathematics going on. There's an infinity of other mathematics that can
symbolically fiddle with entities in an arithmetical base
linguistic_token_for_chair or perhaps linguistic_token_la_chaise, but in
coming into existence in the minds of humans we instantly lose the native
maths of which the chair is an expression - a computation - an unfolding
neverending proof - a theorem pushed along by the drive of the master
mathematician - the 2nd law of thermodynamics (= natural propensities for
.fuzzyN entities to associate recursively - see above).
I think I might make sense here but as usual I remain skeptical of myself.
cheers
Colin Hales
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Received on Mon Oct 09 2006 - 17:57:22 PDT