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.

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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 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---