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 explanation for a phenomenon, for example

1) 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 current computational state belongs to an infinity of computations making you singling out some stable patterns that you recognize, by access to your previous experience as being cat. The qualia itself is explained by the fact that when you refer to the cat, you are really referring to yourself (with the implicit hope that it corresponds to some relatively independent pattern), and the math shows that such a self-reference involves some true but non rationally communicable feature. The math explained why, if this justification is correct, machines/numbers will not be entirely satisfied by it, for the first person is not a machine from its own first person view.

    Hi Bruno,

No, the reverse is the case. The "belongs to an infinity of computations making you singling out some stable patterns" requires the prior existence of the "you" to select it. The observer (you here) effectively is the measure via a self-selection rule. I cannot discount my own existence given the immediate fact that I am experiencing myself as existing. Descartes' Cognito ergo Sum is a pointed statement of this unassailable fact. We cannot put the observer on a level that is emerging from the computations if the observer is the one that is selecting the class of computations that are generating said observer. A possible escape from this is to allow for non-well founded sets and such things as non-principle ultrafilters <http://mathoverflow.net/questions/15872/non-principal-ultrafilters-on>, but I don't know your stand on their existence. Our observation of the cat is a symmetric (within bounds) relationship, otherwise we fall into solipsism. My claim is that the same thing follows for mathematical entities. We cannot claim that mathematical (or any other "abstract" entity!) is such that we (the observers and understanders thereof) are emerging from them. This would require that the "independence" is not and cannot be an unbridgeable gap at all, but a analytic continuum connecting the particular instance of a physical system with the knowledge and meaning of the abstraction. Maths do not refer explicitly to the physical media that they are represented upon by patterns, but this does not allow us to imagine them as completely independent and thus severable from the physical instances.

Even Plato's idea of the Forms as "casting shadows on the wall of the cave" tacitly assumes continuity between the Forms and what we the ideas in our individual minds. If I am not mistaken the idea of conic sections where used to argue the idea. Shadow or projections cannot be severed from the object casting them!

2) The same with "2+2=4 written on some paper". It is also a stable pattern in the computations going through your state. Here you might just refer to what you have learned in school, and you might considered that the truth referred by that sentence on a paper is more stable than a cat, but the conscious perception of cat or ink on paper admits the same explanation: some universal number reflect a pattern belonging to almost all computations going through your state. You have to take the first person indeterminacy into account, and keep in mind that your immediate future is determined by an infinity of computations/universal number, going through your actual state. For example, all the Heisenberg matrices computing the state of the galaxy at some description level for some amount of steps. They all provably exist independently of us in a tiny part of elementary arithmetic, and admit at least as many variants as there are possible electron location in their energy level orbitals.

This paragraph 2) gets dangerously close to my criticism of your scheme and so it might help us come to some mutual understanding. For me, the "truth of the sentence 2+2=4" (i will denote this as X) is not the same thing as the "piece of paper with the symbols '2+2=4' on it" (I will denote this as Y). What is the "pattern belonging to almost all computations going through [one observers] state" generating in your thinking? Both X and Y? For me, X and Y are duals that are related by the fact that there exists at least one physical instance (experienced by multiple observers in a incontrovertible way) that implements a representation of "2+2=4". Similarly by the duality relation as I am using it, the particular abstract statement, "2+2=4" is true because there exists multiple observers that agree on its truth.

Truths are conditional in my accounting. They are only absolute if they are incontrovertible over *all possible* observers. Truths do not exist independent of observers, they are not severable from the possibility of observation of instances of their physical implementation.

I cannot be sure if this helps you as it relies to some familiarity with the first person indeterminacy and the fact that our comp states are distributed in an infinity of distinct, from a third person pov, computations (existing in arithmetic).


As I see it, 1p indeterminacy is strictly an a posteriori condition. One's theory must postulate the prior possibility of multiplicity of locations or instances that are distinguishable and that is not possible if there is not an observer (up to functional equivalence!). Does this help you understand my claim?



"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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