[Fis] _ Re: SYMMETRY & _ On BioLogic

[Louis H Kauffman]

I will make one short comment.
There is a difference between the physical nature of the wave function as a sum 
over possibilities and the actuality of a measurement.
One can believe in the actuality of all the possibilities.
This is David Deutch’s contention.
It is a matter of debate.
There is no question that the wave function as a whole has physical meaning, 
but what has physical actuality is what can be measured.
What has mathematical actuality is another matter. The highest orders of 
infinity have mathematical actuality. 


> On Mar 28, 2016, at 9:45 AM, Bruno Marchal  wrote:
> 
> Dear Lou and Colleagues,
> 
> 
> On 25 Mar 2016, at 19:51, Louis H Kauffman wrote:
> 
>> Dear Karl,
>> 
>> Thank you for this very considered letter.
>> I would like to ask you about your entry
>> 
>> "6.  Quantum information. By keeping an exact accounting about which 
>> predictions are being fulfilled to which degree we see a self-organisation 
>> evolve on competing interpretations of a+b=c. Using the property of an 
>> element to belong to a cycle with cardinality n, we can use the negated form 
>> of not-belonging to different other cycles to transmit information. 
>> Information is a statement about something that is not the case. We can show 
>> the impossibility of a spatial arrangement of arguments of a sentence to 
>> cause impossibilities of coexistence of commutative arguments of the same 
>> sentence. “
>> 
>> My question: How is your comment about quantum information related to the 
>> orthodox minimal model for quantum information that we usually use?
>> I will detail this model in the next paragraph. I do understand that your 
>> paragraph refers to the complementarity aspects of quantum information. The 
>> description below is a concise formulation of the entire quantum model.
>> What is lacking for physics is the addition of the structure of observables 
>> and the relationship of the temporal evolution of the unitary transformation 
>> with the Hamiltonian (i.e. with formulations of physical energy).
>> Lifted in this way from the particular physics, this description is minimal 
>> take on quantum theory that can be used in discussing its properties.
>> 
>> Quantum Theory in a Nutshell
>> 1. A state of a quantum system is a vector |psi> of unit length in a complex 
>> vector space H. H is a Hilbert space, but it can be finite dimensional. 
>> Convectors are denoted by  is a complex number and 
>>  is a positive real number.
>> 2. A quantum process is a unitary transformation U: H ——> H. Unitary means 
>> that the U* = U^{-1} where U* denotes the conjugate transpose of U.
>> 3. An observation projects the state to a subspace. The simplest and most 
>> useful form of this is to 
>> assume that H has an orthonormal basis { |e_1> ,|e_2>,…} that consists in 
>> all possible results of observations.
>> Then observing |psi> results in |e_n> for some n with probability |> psi>|^2.
>> Note that the Sum_{n} ||^2 = 1 since |psi> is a vector of unit 
>> length.
>> 
>> This description shows that quantum theory is a dynamic sort of probability 
>> theory. The state vector |psi> is a superposition of all the possibilities 
>> for observation, with complex number coefficients.
> 
> It seems to me that what is truly remarkable in quantum mechanics (without 
> collapse) is that the superposition are *not* superposition of possibilities, 
> but of actualities. If those where not actualities, we would not been able to 
> exploit the interference between parallel computations like we can do with a 
> quantum computer (but which is also already illustrated in the two slits 
> experiments).
> 
> Then this confirms the "computationalist theory of everything", which is 
> given by any formalism, like Robinson Arithmetic (the rest is given by the 
> internal machine's phenomenology, like the one deducible from 
> incompleteness). Indeed, in that theory, the stable (predictible) observable 
> have to be given by a statistics on all computation going through our actual 
> state. This (retro-)predicts that the physical obeys to some quantum logic, 
> and it can be derived from some intensional nuance on the Gödel 
> self-referential provability predicate (like beweisbar('p') & 
> consistent('t')).
> 
> In quantum mechanics without collapse of the wave during observation, the 
> axiom 3 is phenomenological, and with computationalism in the cognitive 
> science (the assumption that there is a level of description of the brain 
> such that my consciousness would proceed through any such emulation of my 
> brain or body at that level or below) the whole "physical" is 
> phenomenological. 
> Physics becomes a statistics on our consistent sharable first person (plural) 
> experiences. With "our" referring to us = the universal numbers knowing that 
> they are universal (Peano Arithmetic, Zermelo Fraenkel Set Theory, viewed as 
> machine, are such numbers).
> 
> An actuality is a possibility seen from inside, 

Re: [Fis] SYMMETRY & _ On BioLogic (was Re: The Measurement Problem from the Perspective of an Information-Theoretic Interpretation of Quantum Mechanics

[Bruno Marchal]

Dear Koichiro, dear John and Colleagues,

I bump this older post, as it is related to my recent post to Lou.

On 27 Nov 2015, at 02:06, Koichiro Matsuno wrote:


At 4:28 AM 11/27/2015, John C. wrote:

A paper by my former graduate advisor, Jeff Bub, who was a student  
of David Bohm’s.

http://www.mdpi.com/1099-4300/17/11/7374

The Measurement Problem from the Perspective of an Information- 
Theoretic Interpretation of Quantum Mechanics


   Yes, Bub’s insistence on the absolute randomness would remain  
invincible as far as third-person probabilities are taken for  
granted from the outset in comprehending what messages would QM  
convey to us. On the other hand, once one may happen to feel at ease  
with the first-person probabilities (see, for instance,  James  
Hartle’s “Living in a superposition” http://arXiv.org/abs/ 
1511.01550 ), the first-person probability of the occurrence of such  
an agent assuming the first-person status would come to approach  
unity even within the framework of the decoherent-histories  
interpretation of QM.


I think I agree (modulo some possible ambiguity perhaps).

If we take seriously that we might not be more than relative universal  
machine ourself, this extends in the "decoherent-histories" internal  
(made by the universal numbers) interpretation of Arithmetic.
I discovered the first person arithmetical probabilities before  
knowing anything about quantum mechanics. It is still possible that  
the arithmetical possibilities does not interfere like they should,  
but that is shown to be testable.


Personally, I don't think that a third person indeterminacy makes  
"interesting sense". Like Einstein, I tend to think that God does not  
play dice, and that there is no spooky action at a distance (but that  
too has not yet been derived completely from computationalism, to be  
sure).


This is my second post of the week.

Best,

Bruno






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Re: [Fis] SYMMETRY & _ On BioLogic

[Bruno Marchal]

Dear Lou and Colleagues,


On 25 Mar 2016, at 19:51, Louis H Kauffman wrote:


Dear Karl,

Thank you for this very considered letter.
I would like to ask you about your entry

"6.  Quantum information. By keeping an exact accounting about  
which predictions are being fulfilled to which degree we see a self- 
organisation evolve on competing interpretations of a+b=c. Using the  
property of an element to belong to a cycle with cardinality n, we  
can use the negated form of not-belonging to different other cycles  
to transmit information. Information is a statement about something  
that is not the case. We can show the impossibility of a spatial  
arrangement of arguments of a sentence to cause impossibilities of  
coexistence of commutative arguments of the same sentence. “


My question: How is your comment about quantum information related  
to the orthodox minimal model for quantum information that we  
usually use?
I will detail this model in the next paragraph. I do understand that  
your paragraph refers to the complementarity aspects of quantum  
information. The description below is a concise formulation of the  
entire quantum model.
What is lacking for physics is the addition of the structure of  
observables and the relationship of the temporal evolution of the  
unitary transformation with the Hamiltonian (i.e. with formulations  
of physical energy).
Lifted in this way from the particular physics, this description is  
minimal take on quantum theory that can be used in discussing its  
properties.


Quantum Theory in a Nutshell
1. A state of a quantum system is a vector |psi> of unit length in a  
complex vector space H. H is a Hilbert space, but it can be finite  
dimensional.
Convectors are denoted by  is a complex  
number and  is a positive real number.
2. A quantum process is a unitary transformation U: H ——> H. Unitary  
means that the U* = U^{-1} where U* denotes the conjugate transpose  
of U.
3. An observation projects the state to a subspace. The simplest and  
most useful form of this is to
assume that H has an orthonormal basis { |e_1> ,|e_2>,…} that  
consists in all possible results of observations.
Then observing |psi> results in |e_n> for some n with probability | 
|^2.
Note that the Sum_{n} ||^2 = 1 since |psi> is a vector of  
unit length.


This description shows that quantum theory is a dynamic sort of  
probability theory. The state vector |psi> is a superposition of all  
the possibilities for observation, with complex number coefficients.


It seems to me that what is truly remarkable in quantum mechanics  
(without collapse) is that the superposition are *not* superposition  
of possibilities, but of actualities. If those where not actualities,  
we would not been able to exploit the interference between parallel  
computations like we can do with a quantum computer (but which is also  
already illustrated in the two slits experiments).


Then this confirms the "computationalist theory of everything", which  
is given by any formalism, like Robinson Arithmetic (the rest is given  
by the internal machine's phenomenology, like the one deducible from  
incompleteness). Indeed, in that theory, the stable (predictible)  
observable have to be given by a statistics on all computation going  
through our actual state. This (retro-)predicts that the physical  
obeys to some quantum logic, and it can be derived from some  
intensional nuance on the Gödel self-referential provability predicate  
(like beweisbar('p') & consistent('t')).


In quantum mechanics without collapse of the wave during observation,  
the axiom 3 is phenomenological, and with computationalism in the  
cognitive science (the assumption that there is a level of description  
of the brain such that my consciousness would proceed through any such  
emulation of my brain or body at that level or below) the whole  
"physical" is phenomenological.
Physics becomes a statistics on our consistent sharable first person  
(plural) experiences. With "our" referring to us = the universal  
numbers knowing that they are universal (Peano Arithmetic, Zermelo  
Fraenkel Set Theory, viewed as machine, are such numbers).


An actuality is a possibility seen from inside, somehow, in this  
context or theory (QM without collapse, or Computationalism).


Personally, it seems that quantum mechanics, when we agree on the  
internal phenomenological of actuality in the possibilities, confirms  
the most startling, perhaps shocking, consequence of computationalism  
(digital mechanism). Note that it does not make the physical itself  
computable a priori.



Via the absolute squares of these coefficients |psi. can be regarded  
as a probability distribution for the outcomes that correspond to  
each basis direction. Since the coefficients are complex numbers and  
the quantum processes preserve the total probability, one has room  
for complexity of interaction, phase, superposition, cancellation  
and so on.


OK.

Best,

Re: [Fis] SYMMETRY & _ On BioLogic

[Karl Javorszky]

Dear Lou,



we agree that the word quantum refers to a minimal unit. Applied science
may use the word according to its own definitions. It has not yet been used
in the context of a minimal unit of information. The term information has
been defined by deictic methods, using the tautomat (a kind of a
multiplication-cum-truth table, in the form of large databases, which
detail on which places the arguments *(a,b) * of the logical sentence *a+b=c
*can be under the prevalence of which aspects of *a+b=c *over which other
aspects of *a+b=c*)
*. *


In this construct, we do need a term for a minimal unit. If you object to
using the term quantum for the concept of a minimal unit of change in
certitude of where is what and where will be what and where can not be
what, then I have to respectfully withdraw this suggestion.


This discussion running about Symmetry anyway, let me use the opportunity
of this dialog about quantum to advertise another of the advantages of the
tautomat:


The two Euclid spaces that are generated by rectangular axes relating to
readings *(a+b, a) * (b-2a,a) * (a-2b, b-2a) *in case of the *left *space
and *(a+b,b) * (b-2a,a-2b) * (a-2b,a) *in case of the *right *space are in
one sense the epitome of symmetry, in another sense they are not exactly
symmetric. Their central elements are on different coordinates. Importing
the addresses of the points in the Euclid spaces into a common Newton space
leaves one with *two *centres of agglomeration.  The usage of the words
neutron and proton seems to be not that far-fetched to describe concepts
relating to basic tendency of material to become agglomerated if there is
order among the manifold aspects of *a+b=c.*


So it is for the benefit of the FIS audience if we continue the exchange
about which terms are understood to mean what, in their dichotomy, once as
applied to concepts substantiated by observations of Nature, and once as
concepts that come from observations of natural numbers. They should by no
means contradict each other.


Karl

2016-03-28 6:04 GMT+02:00 Louis H Kauffman :

> Dear Karl,
> Thank you for your letter. I will think about the model that you present
> there.
> I submit that quantum theory does not go beyond the bounds of language. It
> is the metaphors that we use for objects that come into question.
> As you can see from my “Nutshell”, there are specific observations that
> can be described and labeled as |e1>,|e2>,… corresponding to events that
> scientists can agree upon in ordinary language.
> The quantum state is a formal sum with complex coefficients of these |ek>
> as POSSIBILITIES. What evolves in time without observation is the structure
> of this collection/superposition of possibilities.
> It does not confuse possibility with actuality then the model has clarity.
> Of course it is a mystery why this model works as well as it does!
> Best,
> Lou K.
>
> On Mar 26, 2016, at 1:23 PM, Karl Javorszky 
> wrote:
>
> Dear Lou,
>
>
> Thanks for the invitation to elaborate on the concept of quantum and how
> it connects to Wittgenstein’s taboo words and information.
>
> We may have problems understanding the concept of a quantum because the
> idea appears to be non-expressible by rational, logical speech. The grammar
> of logical sentences creates constraints on what can be said intelligibly
> (as Wittgenstein has pointed out). We can discuss the present King of
> France (even if there is no such thing there, in Russell’s example) because
> the grammar allows us to speak of places and things. The essence of
> rational speech is that it is consistent. We cannot speak exactly of things
> that may or may not be there, that may or not may have properties.
> Specifically, we cannot speak of *unique, individual *concepts, which we
> cannot contrast to such other concepts which we know.
>
> Let me show you what the natural numbers offer as a possible definition of
> such a concept that is transcending some logical categories.
>
> a)  Preparation
>
> We do an accounting exercise on some numbers. (For some numerical reasons,
> it is best to speak of a collection that has 16 distinguishing categories
> on two kinds of objects: that is, we have *(a,b) *appearing as tuplets *(1,1),
> (1,2), (2,2), (1,3), (2,3), (3,3), (1,4), (2,4), …, (16,16),* that is
> altogether 136 elements of a set.) These we sort on some aspects. Then we
> re-sort them into a different sorting order, based on some different
> aspects of *(a,b). * What we register is the properties of the cycle each
> element in included in during a reorder.
>
> b) Action
>
> We pick 1,2,3,… of the elements and discuss if, and if yes, in which and
> how many altogether, cycles these elements can be included while
> contemporaneous. Contemporaneous means “free of logical contradictions, is
> the case, consistent, assigning a place to an element” in spoken language,
> in the deictic language of numbers and tables it means that there is