# Re: Causality = 1p Continuity?

```Hi Bruno,

Sometimes I feel that you are not reading what I write at all. :(```
```
-----Original Message-----
From: Bruno Marchal
Sent: Sunday, April 03, 2011 1:03 PM
Subject: Re: Causality = 1p Continuity?

On 03 Apr 2011, at 05:15, stephenk wrote:

snip>
> [SPK] That logical structures alone are insufficient to model our
> existence.

[BM]Correct. But arithmetical structure are enough (or please mention a
flaw in UDA).

[SPK] Please reread my last post. I think that your idea is correct but is a
piece of a larger picture.

> We need the physical world to be the interface between our
> separate minds,

[BM]Eventually with comp, the physical world is recovered by defining it
as an interface between our different minds, or as the gluing dreams
processes. We need a physical world. No doubt on this. The point is
that we don't need a primary physical world.

[SPK] I am not claiming that the physical world is primary!  But I am claiming
that the number world is not primary either! Both the Ideal and the Physical
emerge simultaneously from the Nothing as dual aspects.

> otherwise we will be trapped in the UD in endless
> Poincare recursions. This is the nightmare that Nietzsche saw.

[BM]I doubt this, but if that were true, that would not been a reason to
abandon comp. Only a reason to hope that comp is false. But comp is
not yet sufficiently developed to start having premature fear of it.

[SPK] Unless there is something that acts as a limit on the expressions of the
UD then how do we recover inertia?

>
>>> Oh well, that is your choice,
>>
>> I am problem driven. I don't make choice.
>>
>
> [SPK] You are choosing to not consider multiple interacting minds.

[BM]Why do you say so? comp starts from the interaction between a patient
and its doctor.
Comp is an hypothesis. If it leads to solipsism, that would be a
reason to abandon it, indeed. But everything points on the fact that
there is all the room needed for mind interaction, and even that this
is what stabilizes the first person plural in the long run.

[SPK] Again, the "interaction" that occurs between patient and doctor is
symmetrical and (maybe) commutative, but this does not allow the representation
of true concurrency. The Doctor could be purely a construct of the patient's
mind, nothing prevents this! Where we consider a situation of many separate
minds having to simulate each other's 1p then one can see the issue that I am
considering. We need a notion of "space" to allow for a variation of minds so
that one can have a situation where two identical minds can have different
locations relative to a third and thus be different minds. There is no topology
in pure logic, thus we need the Stone and Pontryagin dualities to link logic
and topology. Logic tells minds how to think, Topology tells minds how to
differ.
We need both, not just one or the other.

> So
> far I have only seen discussions in your papers in terms of
> "interviews" between different logics.

[BM]There is an 'interview' between a human (you and/or me) and a
universal machine. The logics are related by representation theorems,
as usual.

[SPK] Yes, I understand that, but that same interview can be reproduced in the
case where the Universal machine is generating a simulation of a human and a
doctor having a conversation, but only if we assume that the Doctor and the
human have 1p experiences of the event. The fact that the simulation has the
identical information content that a 3rd person would experience that was an
invisible man in the doctor's office does not require that the invisible man is
real or his supposed experiences actual. We are conflating the act of writing
down the expressions of theorems with the existence of the signified of those
theorems if we do not distinguish between signified and interpretant. I invite
you to read a good book on Semiotics. The Theory of Semiotics by Umberto Ecco
is good. http://en.wikipedia.org/wiki/Semiotics  and
http://en.wikipedia.org/wiki/Semiotic_elements_and_classes_of_signs_%28Peirce%29
to start.

> What you are calling
> interviews, I would call them interpretations or mappings.

[BM]"interview" just means that I am in front of the machine, and I have
to ask her about each different points of view. I just translate the
usual classical theory of knowledge in terms that the machine can
understand. So of course, we are lead to mappings and representations.

[SPK] See previous. No, you are not "in front of the machine." You are
following an algorithm to derive expressions of a logic via the manipulation of
its symbols following the rules of it grammar. There is nothing in a logic that
can encode differences in topological points of view (diffeomorphisms between
manifolds) unless one uses the duality that I have mentioned, thus I claim that
we need this duality.

> There is no
> notion of separable entities having anything like what you and I are
> doing right now here.

[BM]You are not at the right level. You could criticize string theory
because it does not bring you a pizza at home tonight.

[SPK] No, I criticize string theorists that do not understand what it is that
they are thinking about.

[BM]The interaction comes from the linear combinatory algebra. But if I
posit at the start, I will lose the qualia. I have to derive that
linear algebra from the gluing property of the machine dreams (UDA
shows we don't have choice in that matter).
If eventually the machine dreams does not glue well enough, we will
know that comp is false, with some degree.

[SPK] Bisimulation is the glue between separate 1p. It allows us to recover
diffeomorphisms in the continuum limit on the topologies but unless we have a
means to define the delta-epsilonics and the Hausdorff property we cannot do
this. http://mathprelims.wordpress.com/2009/02/22/the-hausdorff-property/

> You wrote brilliantly about your idea of
> interviews here
> But I will continue to argue that "the logic of arithmetical self-
> reference" is not an exchange of information between separate minds.

[BM]It is not supposed to be that. The logic of Bp & Dp should bring such
a thing, or, if you can prove it prevents such exchanges, then comp
+Theaetetus is refuted.

[SPK] I am not trying to refute comp or Theaetetus or comp + Theaetetus! I am
just trying to argue that comp + Theaetetus is insufficient to model multiple
separate 1p interactions, i. e. true concurrency.

> It is at most the exploration of 1p aspect of a logic by that logic.
> It is solipsism at its most exquisite form. (Please understand that
> this is not a bad thing, solipsism is thinking and dreaming about
> one's thoughts in a closed and convex form).

[BM]It is not solipsism-the philosophy.
Bp & p, and Bp & Dp & p, leads to "lived solipsism", which is the case
for the first person internal experiences. But the modality without "&
p" are not solipsist at all. You are conflating different modalities.

[SPK] Read what I wrote again, please. Unless we have multiple separate 1p that
can have something that is like experiences of interacting with each other in a
way that is irreducible to the computation of a single classical computation
then something is obviously missing. I am arguing that we need bother multiple
quantum systems (logics and topos in each) that can act to constrain each
others possible experiences so that a world like that we experience can obtain.

>
> But there is something else that troubles me even more.
>
snip>
>  The problem is that "the set of all true arithmetical sentences" is
> a very narrow, but deep, interpretation of the One. How can I define
> such things as Zeno's paradox and its solution, for example?

[BM]It is basically solved at the start, because real numbers are
epistemological, or meta, construction. Comp suggests that the
ontology is discrete, because we can explain the beliefs and uses of
the rest from that.

[SPK] I understand that one can generate an arbitrary approximation of a Real
number by running a computation based on N to N maps, but this is not the same
as claiming that only the Integers exist! Comp only works because there are
physical systems that can implement the computations, just as you are able to
have "interviews" with logics because you can write symbols and manipulate them
on your chalk board (or equivalent)!

> There is
> no way to define an infinitesimal or a derivative that I can find.

[BM]Because comp makes the real numbers a simplification, and it makes
calculus a handy tool for manipulating big numbers and and
epistemological mind constructs. Analysis and physics are
epistemology. This follows from UDA + some amount of Occam.

[SPK] I wish that you might spend a week trying to solve the equations of
motion of 3 bodies mutually gravitating then come back and repeat that claim!

> How
> do I recover the calculus?

[BM]In the stable numbers' dream.

[SPK] And unless there are many separate dreamers then one is back the to the
pathological solipsism problem. The fungibility of numbers causes this, unless
on has a topology to differentiate the different dreamers then the is only one
dreamer.

> Your model has no expressions that can be
> used to act as a clock...

[BM] I told you that the definition of integers *is* a clock. Arithmetic
starts from a clock.
And besides, I have no model. Only a theory (that I am digitalizable
at some level, yes doctor + CT).

[SPK] NO! A clock requires at least one aspect of change, a scale to
parameterize the change and a comparator between the change and the scale.
Numbers alone will not do, at most they can act as labels on the scale. See my
further comments on time below.

> Thus it is no surprise that the whole
> structure is frozen.

[BM]The point is that after Gödel, nothing is more dynamical than
Platonia, when seen by the creature defined internally in Platonia.
If you assume a real fundamental time, you have just to abandon comp
(and special relativity which makes time an illusion too).
Anyway, time and space are things which I prefer to search an
explanation for, than assuming them at the start.

[SPK] Oh my! No,  Gödel (and Post, Turing, etc.) could have never accomplished
anything without the prior distinctions between signified, signifier and
interpretant.

> There is no room in it for the idea of evolution,
> nothing 'becomes".

[BM] When the UD is executed, all the becoming becomes. And so all possible
evolutions develop. You could as well criticize SR and GR, and QM
(without collapse).
I mean, this is a place where comp already agree with most physicists,
except Prigogine.

[SPK] But Bruuno, my point is that (assuming your ideas) the UD is eternally
“running” so there is no “when the UD is executed” as distinguished from “when
the UD is not running”! But this does not address the concurrency problem it
merely claims that all simulations exist. existence is not actual. Existence is
property indefinite and context free. Actual 1p are contextual and locally
determinate.

> Everything just "is".

[BM]Only in God's eye.

[SPK] The idea of an anthropomophic God is oxymoronic. There is no “observer”
or interpretant outside of existence.

> Every fiber of my being
> screams out in revulsion at this!

[BM]There is no reason, but apart from solipsism, we cannot use such
affirmation as an argument. You could say that Energy is not equal to
mc^2 because we can do horrible bombs with that idea.

[SPK] You know that I would not think or make claims that way... Please do not
insult my intelligence, however feeble and addled by age it may be.

> I am not a Σ1 sentence!

[BM]I guess you mean: my mental state is not UD-accessible. Just say "no"
to the digitalist surgeon, Stephen. I don't know if that is true or
not. My point is that if it is true, then physics is a branch of
number theory, and I show how time space and physics can indeed to be
retrieve. There is already subjective duration, but not yet space.

[SPK] No, I will not say “no”! You are missing my signified completely here. My
claim is that number theory requires topology to be expressive and concurrent.
So alone it is insufficient.

[BM]We would disagree only if you want both
- a fundamental basic *primary* time, and
- saying yes to the doctor.
OK?

[SPK] NO, I DO NOT WANT A BASIC PRIMARY TIME!!!!! DO you actually try to
understand these words? Let me see if I can find the French translation. Le
temps absolu n'existe pas. I am arguing for a local notion of time, based upon
the work of Hitoshi Kitada. See: http://kims.ms.u-tokyo.ac.jp/doc/time_V.pdf
and http://kims.ms.u-tokyo.ac.jp/doc/time_XI.pdf (These have a lot less math
than his other papers.)

snip

>> It is more correct to say that the first person defines it, and is
>> itself defined by number relations.
>>
>
> [SPK] OK, but  the numbers can code noise just as they can code the
> content of my 1p in this moment as I type this post. In fact it is far
> more likely that it codes noise. We have to resort to all kinds of
> fancy constructions to get around this fact and I find that the fact
> that this must be done is a sign that something is wrong in our
> thinking here.

[BM]My point is not that it is true, but that it is a consequence of the
comp hyp. If you can show that 'something is wrong', then you refute
comp.

[SPK] No, I do not wish to refute comp. I am OK with comp. I am just saying
that comp is incomplete even if we add AR.

>  The fact that we can represent a history of events as a sequential
> narrative is OK, but this is not time. Time is a measure of the change
> in one aspect relative to some other that can be decided by some third
> aspect. In a frozen structure there is no change, thus there is, by
> definition, no time. Strings of numbers are not time just as records
> of the output of a Geiger Counter is not time.

[BM] IN GR there is no time either, and even more so in most Quantum GR. At
the same time you can see GR as the science of time. You are confusing
God's point of view, with the relative points of view of the
"terrestrial" beings.

[SPK] It is abundantly clear to all that care to investigate that there is no
“God’s point of view” except as an absract idea in a finite mind, nor is there
an absolute ordering of events (Newton’s absolute time.) I am argue FOR a
notion of local time as had by the points of view of the  "terrestrial" beings.
How you keep not understanding this amazes, confuses and frustrates me!   Le
temps absolu n'existe pas.  Le temps absolu n'existe pas.  Le temps absolu
n'existe pas.

snip
>
> [SPK] OK, but please try to understand what I am trying to
> communicate. Your definition of 'times" seems to be just a sort of
> sequence, a string of numbers. How many possible strings are there?
> What is the chances of an arbitrarily chosen string to code, say
> Beethoven's 5th and not some randomness? See my previous claim!

[BM]Probabilities are relative to states, themselves relative to histories/
computation. Your question is meaningless. I'm afraid.

[SPK] Can you distinguish between orderings and differentiations? If you cannot
then I am trying to talk to a brick. Silly me!

>
>>> To the UD everything is simultaneously given. Additionally, the way
>>> that the dovetailing seems to work makes it so that the UD is dense
>>> on the space of computations in the same way that the Reals are
>>> dense in the continuum.
>>
>> Not exactly, at least for most UDs. If the Mandelbrot set is a UD,
>> then it is a UD dense in the space of its own version of all
>> computations, but it is an exceptional situation.
>>
>
> [SPK] Yes, but there are infinitely many such sets!

[BM]There is an infinity of UDs. But they reflect each other in a way
which makes them equivalent ontologically. They have the same internal
epistemologies. That is why we have to recover quantum computation
from number theory.

[SPK] And how are they seperable in the Hausdorff sense?
http://mathprelims.wordpress.com/2009/02/22/the-hausdorff-property/
http://en.wikipedia.org/wiki/Seperable_space

> We need a local
> version of the axiom of choice that does not lead to Banach-Tarski
> paradox. I think the solution is in the idea of the record keeping
> that you have mentioned... The idea is that the list of properties of
> a set is contained to be finite and constructable (but not necessarily
> Turing computational!) so that one is not needing to assume an
> infinite list of properties. Non-well founded sets allows us to do
> this but that is a discussion for some other day. Peter Wegner wrote
>  I am exploring this with Andrew Soltau. Hopefully we will have a
> result soon.

[BM] Nice. Note that Wegner says many things "against CT", which I believe
is true in the comp-physics, but irrelevant for the problem of
deriving physics from numbers.

[SPK] If we are only trying to derive the physics of the 1p of a single entity
we can do that easily from numbers, you have demonstrated that already, but if
you are trying to derive the physics of many separate 1p then you must include
topology.

snip
> [SPK] Could you elaborate on this bisimulation?

[BM]The B of the logic Z can be define in G by Bp & Dt, and the D of Z, by
Bf v Dp (the D of Z is really the usual logican's notion of relative
consistency).
Vandenbussche found that you can dually reverse that translation: the
B of G can be defined in Z by Bp v Df, and the D of G can be defined
in Z by Dp & Bt.
Be careful to interpret the B and D in the right logic. I should
perhaps write this in the following less ambiguous (but less readable)
way:

B_z A   ==   B_g A  &  D_g t
D_z A   ==   D_g A  v  B_g f

B_g A   ==   B_z A  v  D_z f
D_g A   ==   D_z A  &  B_z t

The two lines above are the usual definition of the Z box (the second
follows by duality on Bp & Dt)
The two last lines are Vandenbussche inversion. It leads toward an
axiomatization of Z, Z1, Z* and Z1*.

So despite their very different semantics, and "hypostasic role", G
and Z are variants of each other. The same for G1 and Z1, G1* and Z1*.

Unfortunately there is no such transformation available for the logics
X.    (X, X1, X*, X1*)
We conjecture that G and X are not bisimulable, nor probably S4Grz and
X.

[SPK]  I will have to study this further. My intuition is that bisimulation
must occur between multiple versions of logics for my idea to work. So this
presents a potential falsification. Good!

Onward!

Stephen

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