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 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. 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