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 <marc...@ulb.ac.be
<mailto:marc...@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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