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