Colin Geoffrey Hales wrote:
> 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.
None of them change if it isn't.
> 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.
If empirical reality isn't necessarily mathematical, how can it be
necessarily computational.
> As to what the non-ideal numbers are....
>
> Well there aren't any.
But you said there were. That's why I asked.
> 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.
Hmm. Well, we have a way of mathematising the world. It is called
physics, and it bases don't have much to do with it. Real numbers
symmetry, and smooth funciton do.
> The human (and all the space that expresses it) is one single number
Didn't you just say numbers odn't exist? Do you mean "representation
of a number", or something like that?
> 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.
How do you know?
> 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.
How do you know?
> 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 - 18:25:41 PDT