(This mail has been sent previously , but without success. I resend it, with 
minor changes). Problems due to different accounts. It was my first comment to 
Mark Burgin new thread “Is information physical?”.

Dear Mark, Dear Colleagues,

Apology for not answering the mails in the chronological orders, as my new 
computer classifies them in some mysterious way!
This is my first post of the week. I might answer comment, if any, at the end 
of the week.

> On 25 Apr 2018, at 03:47, Burgin, Mark <mbur...@math.ucla.edu 
> <mailto:mbur...@math.ucla.edu>> wrote:
> Dear Colleagues,
> I would like to suggest the new topic for discussion
>                                       Is information physical?

That is an important topic indeed, very close to what I am working on. 

My result here is that 

IF indexical digital mechanism is correct in the cognitive science, 

THEN  “physical” has to be defined entirely in arithmetical term, i.e. 
“physical” becomes a mathematical notion.

The proof is constructive. It shows exactly how to derive physics from 
Arithmetic (the reality, not the theory. I use “reality” instead of “model" 
(logician’s term, because physicists use “model" for “theory").

Indexical digital mechanism is the hypothesis that there is a level of 
description of the brain/body such that I would survive, or “not feel any 
change” if my brain/body is replaced by a digital machine emulating the 
brain/body at that level of description.

Not only information is not physical, but matter, time, space, and all physical 
objects become part of the universal machine phenomenology. Physics is reduced 
to arithmetic, or, equivalently, to any Turing-complete machinery. Amazingly 
Arithmetic (even the tiny semi-computable part of arithmetic) is Turing 
complete (Turing Universal).

The basic idea is that:

1) no universal machine can distinguish if she is executed by an arithmetical 
reality or by a physical reality. And,

2) all universal machines are executed in arithmetic, and they are necessarily 
undetermined on the set of of all its continuations emulated in arithmetic. 

That reduces physics to a statistics on all computations relative to my actual 
state, and see from some first person points of view (something I can describe 
more precisely in some future post perhaps).

Put in that way, the proof is not constructive, as, if we are machine, we 
cannot know which machine we are. But Gödel’s incompleteness can be used to 
recover this constructively for a simpler machine than us, like Peano 
arithmetic. This way of proceeding enforces the distinction between first and 
third person views (and six others!).

I have derived already many feature of quantum mechanics from this (including 
the possibility of quantum computer) a long time ago.  I was about sure this 
would refute Mechanism, until I learned about quantum mechanics, which verifies 
all the most startling predictions of Indexical Mechanism, unless we add the 
controversial wave collapse reduction principle.

The curious “many-worlds” becomes the obvious (in arithmetic) many computations 
(up to some equivalence quotient). The weird indeterminacy becomes the simpler 
amoeba like duplication. The non-cloning of matter becomes obvious: as any 
piece of matter is the result of the first person indeterminacy (the first 
person view of the amoeba undergoing a duplication, …) on infinitely many 
computations. This entails also that neither matter appearance nor 
consciousness are Turing emulable per se, as the whole arithmetical 
reality—which is a highly non computable notion as we know since Gödel—plays a 
key role. Note this makes Digital Physics leaning to inconsistency, as it 
implies indexical computationalism which implies the negation of Digital 
Physics (unless my “body” is the entire physical universe, which I rather 

> My opinion is presented below:
>    Why some people erroneously think that information is physical
>    The main reason to think that information is physical is the strong belief 
> of many people, especially, scientists that there is only physical reality, 
> which is studied by science. At the same time, people encounter something 
> that they call information.
>    When people receive a letter, they comprehend that it is information 
> because with the letter they receive information. The letter is physical, 
> i.e., a physical object. As a result, people start thinking that information 
> is physical. When people receive an e-mail, they comprehend that it is 
> information because with the e-mail they receive information. The e-mail 
> comes to the computer in the form of electromagnetic waves, which are 
> physical. As a result, people start thinking even more that information is 
> physical.
>    However, letters, electromagnetic waves and actually all physical objects 
> are only carriers or containers of information.
>    To understand this better, let us consider a textbook. Is possible to say 
> that this book is knowledge? Any reasonable person will tell that the 
> textbook contains knowledge but is not knowledge itself. In the same way, the 
> textbook contains information but is not information itself. The same is true 
> for letters, e-mails, electromagnetic waves and other physical objects 
> because all of them only contain information but are not information. For 
> instance, as we know, different letters can contain the same information. 
> Even if we make an identical copy of a letter or any other text, then the 
> letter and its copy will be different physical objects (physical things) but 
> they will contain the same information.
>    Information belongs to a different (non-physical) world of knowledge, data 
> and similar essences. In spite of this, information can act on physical 
> objects (physical bodies) and this action also misleads people who think that 
> information is physical.

OK. The reason is that we can hardly imagine how immaterial or non physical 
objects can alter the physical realm. It is the usual problem faced by dualist 
ontologies. With Indexical computationalism we recover many dualities, but they 
belong to the phenomenologies.

>    One more misleading property of information is that people can measure it. 
> This brings an erroneous assumption that it is possible to measure only 
> physical essences. Naturally, this brings people to the erroneous conclusion 
> that information is physical. However, measuring information is essentially 
> different than measuring physical quantities, i.e., weight. There are no 
> “scales” that measure information. Only human intellect can do this.

OK. I think all intellect can do that, not just he human one.

Now, the reason why people believe in the physical is always a form of the 
“knocking table” argument. They knocks on the table and say “you will not tell 
me that this table is unreal”.

I have got so many people giving me that argument, that I have made dreams in 
which I made that argument, or even where I was convinced by that argument … 
until I wake up.

When we do metaphysics with the scientific method, this “dream argument” 
illustrates that seeing, measuring, … cannot prove anything ontological. A 
subjective experience proves only the phenomenological existence of 
consciousness, and nothing more. It shows that although there are plenty of 
strong evidences for a material reality, there are no evidences (yet) for a 
primitive or primary matter (and that is why, I think, Aristotle assumes it 
quasi explicitly, against Plato, and plausibly against Pythagorus).

Mechanism forces a coming back to Plato, where the worlds of ideas is the world 
of programs, or information, or even just numbers, since very elementary 
arithmetic (PA without induction, + the predecessor axiom) is already Turing 
complete (it contains what I have named a Universal Dovetailer: a program which 
generates *and* executes all programs).

So I agree with you: information is not physical. I claim that if we assume 
Mechanism (Indexical computationalism) matter itself is also not *primarily* 
physical: it is all in the “head of the universal machine/number” (so to speak).

And this provides a test for primary matter: it is enough to find if there is a 
discrepancy between the physics that we infer from the observation, and the 
physics that we extract from “the head” of the machine. This took me more than 
30 years of work, but the results obtained up to now is that there is no 
discrepancies. I have compared the quantum logic imposed by incompleteness 
(formally) on the semi-computable (partial recursive, sigma_1) propositions, 
with most quantum logics given by physicists, and it fits rather well.

Best regards,

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