[Fis] Fwd: Unpleasant answer ? From Bruno Marchal

[Pedro C. Marijuan]

Dear Pedro, dear Jerry, dear List,



On 07 Mar 2017, at 04:36, Jerry LR Chandler wrote:

de Chardin has also cast a long and durable shadow over my mind for 
decades for decades. His writings both provides some guidance on the 
form of time and opens rich questions that bring fruit.


   While I appreciate the flow of concepts emerging from Bruno’s 
“poetry”, its guidance appears to exclude chemistry and biology.


The approach that I have sketched here is top down.


I show that if we assume a (rather weak compared to most version in the 
literature) Digital Mechanist hypothesis, biology and chemistry/physics 
have to be derived from arithmetic. To be exact, physics has to be 
derived from the introspective "theology" of the universal machine 
(which has the cognitive ability to know that she is universal), and 
that is reducible to elementary arithmetic (although the complete logic 
of the proper theological part escape its computable part: after Gödel 
we know that elementary arithmetic is in-exhaustively complicated. The 
amazing thing is that the propositional part of that theology is 
decidable, and that is enough to get the propositional part of the 
physics and compare it with the logic of the observable (quantum logic).


I can explain more or give references. It is not obvious and ask for 
some amount of work, even more for those not familiar with the work of 
Church, Post, Kleene, Turing, Gödel and many others.


We have something like:


Number(with + and *) => Number's dreams statistics => Physics => human 
biology



Thus, Bruno’s  associations are not so clear to me.


This provides evidence you have a sane mind :)


  No problem. I am summarizing many years of work based on results which 
are not well known as I have eventually understood.

The basic idea is simple, but hard to swallow for the physicalists, and 
they are somehow mocked and insulted, as pagan theology, since 1500 years.



So, I will be a “spoil sport” and look toward a more “life-friendly” 
flow of both symbols and numbers with only a tad of poetry.

On Mar 3, 2017, at 11:51 AM, Bruno Marchal <marchal at ulb.ac.be 
<mailto:marchal at ulb.ac.be>> wrote:



My favorite de Chardin's proposition is, from memory:


    "We are not human beings having spiritual experiences, we are 
spiritual beings having human experiences.



That is close to the theology of the neopytagorean Moderatus of Gades, 
and close to the neoplatonist Plotinus, Porphyry, ... And they are 
formally close to the "theology" of the universal numbers. (and even 
intuitively so assuming the computationalist hypothesis in cognitive 
science, through sequence of thought experiences).


The tensions between the computational natures of discrete and the 
“continuous” numbers haunts  any attempt to make mathematical sense out 
of scientific hypotheses. I am uncertain as to the logical implication 
of the “computationalist’s hypothesis" in this context.



If you are aware of the notion of first person indeterminacy, it is not 
so difficult to understand how the appearance of the continuum can be 
explained to be unavoidable in the digital-mechanist frame. The physical 
reality will emerge from a statistics on infinities of computations 
(including many with Oracles). Amazingly, in the digitalist frame, it is 
the digital which remains hard to understand a priori, but the 
mathematics of self-reference gives important clue.


The key here is that mechanism makes us duplicable, and we can't be 
aware if some delay is made for the reconstitution of one of the copy. 
It is that invariance for the delays of reconstitution which makes 
indetermined on an infinity of computational relations, themselves 
embedded in non computational relations with many numbers. But we cannot 
invoke oracles, except the halting oracle and the random oracle. 
Mechanism predicts the necessity of an apparent continuum at least.




Is the reference grounded in Curry’s combinatorial logic or otherwise?


It does not. The reasoning is independent of any basic universal theory 
chosen. We get the same laws of physics, if we assume only combinators, 
or only number, or a quantum computer, etc. I use the numbers because 
people are familiar with them, and they are not "physicalist", so we 
can't be accused of "treachery" in the derivation of physics.


Of course, it is more difficult to prove that elementary arithmetic is 
Church-Turing Universal than the same for the combinators, but it is a 
well known standard result in logic.





It reminds me also of Shrî Aurobindo, when he said:


"What, you ask, was the beginning of it all?


And it is this ...

Existence that multiplied itself

For sheer delight of being

And plunged into numberless trillions of forms

So that it might

Find

Itself

Innumerably"


I have some minor problems with the present essay, but substituting some 
of the excessively teleological "purposive" terms about life (perhaps 
all of them?), and using instead a more austere description of 
organizational facts.... who knows! If life contains a unitary 
principle, I think it is more subtle, and cannot be expressed in 
unilateral physical terms



Provably so if we assume mechanism. Contrarily to a widely spread 
opinion: mechanism is not compatible with even quite weak form of 
materialism, or physicalism.


The connotations of the term “mechanism” varies widely from discipline 
to discipline.

The sense of “mechanism” in chemistry infers an electrical path among 
the discrete paths of  illations that “glue” the parts into a whole.  By 
sublation, this same sense is used in molecular biology and the 
biomedical sciences.



Bruno, could you expand on your usage in this context?



Mechanism, as I use it, is the hypothesis that a level of digital 
substitution exist where I would survive through a physical digital 
computer in place of the "brain", in some generalized sense. the 
consequence does not depend on the level chosen: it could be at the 
level of string theory, with a brain as great as the observable 
universe. In that sense the hypothesis is very weak. Even if you 
estimate that to survive, we need to emulate the quantum evolution 
(known to be Turing emulable) at the level of quark, the consequence 
would follow. Non-mechanist have to justify the need of actual 
infinities, or substantial spiritual entities. Diderot defined 
"rationalism" by such Cartesian Mechanism. Yet, such Mechanism is 
incompatible with the *assumption* of an ontologically primary physical 
universe.




How do the senses of “computationism" and “mechanism” refer to the 
material world, if at all?



The notion of computation is born in pure mathematics, and eventually 
shown to be a purely arithmetical notion (even sigma_1 arithmetical: it 
needs only a very tiny part of elementary arithmetic). Whatever you can 
do with a (physical or not) *digital* computer is "already" done in 
elementary arithmetic, which contains the description and execution of 
all programs.


The "universal dovetailer argument" ---that you can found here for example:


http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html 
<http://iridia.ulb.ac.be/%7Emarchal/publications/SANE2004MARCHALAbstract.html>


explains how the appearance of the material world has to emerge from all 
relative computations. The math explains then that they do emerge 
indeed, until now. Physics becomes a relative statistics made on all the 
infinitely many computations (which exists in arithmetic) going through 
or local (relative) computational state. I predicted both the quantum 
logical formalism and the "many-world" view of the physical reality from 
computationalism, well before I grasped that quantum mechanics confirms 
this. Indeed, before learning abaout quantum mechanics, I thought being 
close to a refutation of Mechanism.


Some clues make also very plausible that we will get the reversibility 
and linearity/unitarity of the fundamental equation of physics.




such as maximum entropy production, symmetry restoration, free energy 
maximization, etc. Well, symmetry and information have more clout and 
hidden complexity, so I express not a rejection but some uneasiness 
regarding too direct "orthogenetic" views on biological and social 
evolution.


My further suggestion --could it be a good idea that you change Monod's 
style "unpleasantness" (Oh, we the accidental discover that we are alone 
in the cosmos!) and point towards some of Teilhard's and Vernadsky's 
noosphere and the Omega Point? You would have several curious items to 
choose...


More opinions??



God created the natural numbers, and saw that it was good.


Would it be more accurate to that “"God" created the internal creativity 
of the atomic numbers."



I was just saying, albeit poetically indeed,  that  the "theory of 
everything", (still in the frame of the digital mechanist 
hypothesis), can't assume more than classical logic + the following axioms:


0 ≠ (x + 1)

((x + 1) = (y + 1))  -> x = y

x = 0 v Ey(x = y + 1)



Together with (just below):




Then she said: add yourself, and saw that is was good.



x + 0 = x

x + (y + 1) = (x + y) + 1


And:



Then she said: multiply yourself.



x * 0 = 0

x * (y + 1) = (x * y) + x


And nothing else.




And then ... she said: oops, ... and lose control.



Because, once you have addition and multiplication of natural numbers, 
you get Turing-universality, and the universal machine. If you can agree 
that 2+2=4" independently of you and me, then the behavior of all 
machines becomes realized, and this independently of any other assumptions.


I agree that it seems amazing, but that follows from the mathematical 
(and then arithmetical) discovery of the Universal Machine (by Turing, 
and others). I tend to prefer calling the universal machine *universal 
numbers*, to emphasize their finite nature and arithmetical nature. 
Turing made its machine having an infinite tape, but it is not part of 
the description of the machine, and that tape plays only the role of an 
environment. Computer and universal machine are essentailly finite 
entities, and they provably exist in the arithmetical reality (in any 
"model" (in the logician sense) of some elementary arithmetic theory). 
But they are confronted to infinities, and even different types of 
infinities according to the points of view possible (the arithmetical 
hypostases).






The addition of the atomic numbers has bounds because it is not linked 
to the concept of variables.  How does one see the internal controls 
without the geometry associated with variables?   (In the absence of a 
Cartesian co-ordinate system?)


This is unfortunately very long to explain.


  In a nutshell, taking the risk of being too much poetical, variables, 
geometries, time, any physicalities, is in the mind of the universal 
numbers, and emerge from the statistics of personal continuations, which 
are infinitely distributed in the arithmetical reality.


We are light years away from getting the "atomic number", or of the atom 
itself, or even elementary particles. We get the quantum logic, and may 
be the symmetries of the Hamiltonian; not the constant, if that exists. 
The point is that we have no choice: if digital mechanism is correct, 
atomic number, quantum chemistry, etc must be derived from just 
arithmetic, or be recongnized as historico-geographical (and not *laws*, 
then).



Like the complexity of the prime numbers distribution already 
illustrates, the logicians know that classical logic + addition of 
integers + multiplication of integers leads to the Church-Turing 
Universality of the reality under concern, "generating *all* universal 
numbers, and they know that the universal machines, or universal numbers 
put a lot of mess in Plato Heaven. The price of universality is loss of 
controllability, and the appearances of realms defying all complete 
theories.


The perplexity of the atomic numbers creates its internal co-ordination 
without an apparent source of “universality” or “universal numbers”.  
The ampliative logic of electrical bindings appears to create irregular 
self-regulation without a concept of mechanical control. Can a vision of 
"Plato’s heaven” take root and grow without universal numbers?  In Curry 
combinatorial logic sufficient?



The universal numbers are just there, although it would be more exact to 
talk about "universal computable relations", but they can be identified 
with numbers once we have fix the basic ontology (be it numbers, 
combinators, whatever).


They are there, like prime numbers are there, or like the 
(semi-computable) order relation are there, etc.


The amount of arithmetical realism needed is the same as the one you 
need to just agree with the axioms given above. No need of special 
metaphysical platonism here. The lin with consciousness is done with the 
believe in survival through digital transplant *at some level*. It needs 
to be a bet, as no machine can justify its substitution level.



The physical reality is the border of the arithmetical reality "seen 
from inside (by the universal numbers)". The breaking of symmetries are 
in the universal mind, like the symmetries themselves. The universal 
mind is the mind common to all universal numbers. ("universal" always 
taken in the Church-Turing-Kleene-Post-Markov sense).


The "god" of the machine (the relatively locally finite being) seems to 
be like a universal baby playing hide and seek with itself.


I doubt we are alone in the probable apparent Cosmos that we can 
observe, but we are not alone in Arithmetic, provably so if you assume 
Digital Mechanism (a thesis equivalent with the belief that 
consciousness is invariant for some recursive permutations).



If I suppose that the dynamics of the associations of atomic numbers are 
internally motivated (that is, metabolism, a.k.a., organic mathematics),


As long as you don't invoke explicitly actual infinities, or some very 
special non-computable relations, the reversal physics/biology 
consequences will follow. The carbon based organicity, if necessary, has 
to be derived from arithmetic, and if contingent, will not belong to 
physics but to geography (meaning that our universe can implement life 
without carbon).



What within Life pre-supposes invariance?


Here, we need to assume that we remain conscious and well alive for a 
digital brain transplant. See more in the sane04 paper refered below, or 
in my last JPBMB papers refered below.



What within Life pre-supposes a stationarity such that recursive 
permutations are meaningful arithmetically?


Things go in the different direction. It is "easy" to prove the 
existence of the recursive permutation in arithmetic, and life is 
derived from there.


The amazing thing is that life appears on different planes, including 
non physical one, which predicts varieties of possible after-life, 
without adding any assumption other than arithmetic at the base level, 
and computationalism at the meta-level (from which I start the reasoning).

But we don't need to die to test/refute the theory. We need only to 
compare the mandatory physics which is "in the head" of any universal 
number/machine ,with the empirical observations, and thanks to the 
quantum weirdness, it fits up to now.


Let me slightly more precise: The mathematical theory works for any 
machine (or even a large collection of non-machine which lives also in 
arithmetic) willing to bet on such relative transplants, accept 
Church-Turing thesis, and thus believe in the axioms given above (and 
taught in high school, although not in such form).




Does Organic Mathematics reach it’s zenith in the genesis of physical 
and mathematical poetry?


If it works at all. I predicted in the 1970 that this would be refuted 
well before 2000.



We are only at the beginning. I have underestimated the faith of the 
Aristotelians. Not so much philosophers and scientists seems aware that 
mechanism makes the invocation of a physical universe in the attempt to 
solve or even formulate the mind-body problem logically invalid. I 
thought for a large part of my life that every scientists knew this 
since Plato! My point is that the correct machine can't miss this when 
introspecting itself (and remaining correct).




Just some fleeting thoughts on the phenomenology of life during a long 
winter's night in the cold Northland.


I hope my answer did not make you even colder. Take a good cup of some 
hot tisane!


Best,


Bruno


(*)


http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html 
<http://iridia.ulb.ac.be/%7Emarchal/publications/SANE2004MARCHALAbstract.html>


Marchal B. The computationalist reformulation of the mind-body problem. 
Prog Biophys Mol Biol; 2013 Sep;113(1):127-40


Marchal B. The Universal Numbers. From Biology to Physics, Progress in 
Biophysics and Molecular Biology, 2015, Vol. 119, Issue 3, 368-381.



PS I have a provider problem, and I will be disconnected at least up to 
the 17 March (hopefully not much later).



Best wishes to you, and all,


Bruno




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