On 7/14/2012 5:52 AM, Bruno Marchal wrote:

On 14 Jul 2012, at 11:16, Evgenii Rudnyi wrote:On 14.07.2012 11:00 Bruno Marchal said the following:On 14 Jul 2012, at 10:42, Evgenii Rudnyi wrote:...If to speak about your theorem, it is unclear to me, how the first person view accesses numbers and mathematical objects.Like a digital machine, which can access numbers encoded in their memory, through logical gates, and so one. More details are given currently on the FOAR list, but the idea is simple, with comp our bodies are statistical first person constructs related to infinities of number relations, so we access to them a bit like a fish can access water. The price of this is that we have to abandon physicalism eventually.I am not sure if I understand. I would like to have an explanationfor a phenomenon, for example1) I see a cat; 2) I see a piece of paper with 2 + 2 = 4. Yet, when you start explaining, the phenomenon seems to disappear.1) I see a cat. This is explained by the fact that your currentcomputational state belongs to an infinity of computations making yousingling out some stable patterns that you recognize, by access toyour previous experience as being cat. The qualia itself is explainedby the fact that when you refer to the cat, you are really referringto yourself (with the implicit hope that it corresponds to somerelatively independent pattern), and the math shows that such aself-reference involves some true but non rationally communicablefeature. The math explained why, if this justification is correct,machines/numbers will not be entirely satisfied by it, for the firstperson is not a machine from its own first person view.2) The same with "2+2=4 written on some paper". It is also a stablepattern in the computations going through your state. Here you mightjust refer to what you have learned in school, and you mightconsidered that the truth referred by that sentence on a paper is morestable than a cat, but the conscious perception of cat or ink on paperadmits the same explanation: some universal number reflect a patternbelonging to almost all computations going through your state. Youhave to take the first person indeterminacy into account, and keep inmind that your immediate future is determined by an infinity ofcomputations/universal number, going through your actual state. Forexample, all the Heisenberg matrices computing the state of the galaxyat some description level for some amount of steps. They all provablyexist independently of us in a tiny part of elementary arithmetic, andadmit at least as many variants as there are possible electronlocation in their energy level orbitals.I cannot be sure if this helps you as it relies to some familiaritywith the first person indeterminacy and the fact that our comp statesare distributed in an infinity of distinct, from a third person pov,computations (existing in arithmetic).Bruno

Dear Bruno,

`Please consider the following: from gowers`

`(mathoverflow.net/users/1459),/Non-principal ultrafilters on ?/,`

`http://mathoverflow.net/questions/15889 (version: 2010-02-20)`

4

`There is a nice class of problems that are equivalent to the existence`

`of a non-principal ultrafilter. One such, if I remember correctly, is`

`the existence of a colouring of the infinite subsets of the natural`

`numbers in such a way that no infinite set has all its infinite subsets`

`of the same colour. The obvious proof is to colour the sets in such a`

`way that if you add or take away a single element then you change its`

`colour. To make this proof work, you define two sets to be equivalent if`

`their symmetric difference is finite, and do the colouring in each`

`equivalence class separately. But to get it started you have to pick a`

`set in each equivalence class, and for that the obvious thing to do is`

`use AC.`

`But you can in fact do it with a non-principal ultrafilter as follows.`

`Given an infinite subset A, define its counting function f(n) to be the`

`cardinality of the intersection of A with {1,2,...,n}. Then take a`

`non-principal ultrafilter ? and define F(A) to be the limit along ?`

`of(-1)f(n). If you add an element m to A, then f(n) is unchanged up to m`

`and then adds 1 thereafter, so its parity is changed everywhere except`

`on a finite set, which implies that F(A) changes. So F gives you your`

`colouring.`

`I've never actually thought about the other direction (getting from such`

`a colouring to a non-principal ultrafilter) so I don't know how hard it`

`is. I'm not even 100% sure that it's true, but I'm pretty sure I`

`remember hearing that it was.`

`link`

`<http://mathoverflow.net/questions/15872/non-principal-ultrafilters-on/15889#15889>|flag|cite`

answeredFeb 20 2010 at 12:30 <http://mathoverflow.net/users/1459/gowers> gowers <http://mathoverflow.net/users/1459/gowers> 16.1k?8?73?124

`The idea here of a "colouring" is a partitioning that would relate`

`to your measure, I think.`

-- Onward! Stephen "Nature, to be commanded, must be obeyed." ~ Francis Bacon -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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