[Fwd: HARDY and Mathematical versus Physical Reality]

From: Joao Leao <jleao.domain.name.hidden>
Date: Tue, 28 Oct 2003 15:21:17 -0500

> Bruno,
> I took your mention of Hardy, perhaps naively, as an exihibit
> of commonsense on your part but I see that was hasty. If you
> pardon this observation your comments seem to wonder from
> this branch of the Universe's wavefunction where we all live
> and think to your own private branch where words have the
> meanings you assign them. You engage, in other words, in
> HumptyDumptese, a mode of expression perilously close,
> I am afraid, to EmptyDumptese!
> I did look up your URL which is definitely into that other
> branch, but I manage to extract from it a paper of your which
> seems to be directed at physicists (al least the first section),
> called "Computation, Consciousness and the Quantum".
> Unfortunately in that section you elaborate on a statement
> of yours which is at best ambiguous and at worst entirely
> false (a telling characteristic of Humpty Dumptese): you
> "put it this way: all sufficiently realist interpretations
> of quantum mechanics accept the existence of parallel
> situations"! I take it by "situations" you mean alternatives,
> no? Otherwise I don't know what you are talking about.
> If that is what you mean than your statement is misquantified:
> most self-professed realist interpretations admit the existence
> of parallel alternatives from which the outcomes of measurement
> are drawn in some fashion. But Bohmian mechanics, the single
> example you mention, does not. It is a fully deterministic
> interpretation so it determines the singular outcome of each
> experiment. So the little connundrum you revel in at the end
> of that section simply does not obtain because Bohmians do
> not interpret superpositions in the same was as Everettians.
> Now I have no particular sympathy for either but that does
> not allow me to abuse their standpoint to agrandize my own.
> Let us put it that way...
> Something tells me the rest of your "proof" is likely to be
> filled with the same self delusional presumptions as you
> so blatantly exihibit here...
> Be careful how you sit on that wall...
> Kindly,
> -Joao
> Bruno Marchal wrote:
>> To avoid mailbox explosion I give short and related answers
>> to many post in one post.
>> Joao Leao (jleao.domain.name.hidden ) wrote:
>> >By no means does this translate to the identification you
>> >suggest between what is empirical is what is... "incomplete",
>> >If anything physical reality sees mathematical reality "from
>> >the outside", and it is this "map" that is incomplete and likely
>> >to remain so, not because of the sparseness of empirical
>> >data, but due to the limited resources of physicists. As far
>> >as nature is concerned what is weird is not what cannot be
>> >mapped to math but what can (as in Wigner's famous
>> >"unreasonableness"paper)!!
>> I agree with your answer, and I guess I have not been enough
>> clear, because you repeat what I said, except for my use of
>> Church thesis. I was (implicitely) assuming the computationalist
>> hypothesis in the cognitive science. Knowing that from comp
>> physics is reduced into a measure on the self consistent
>> extension, empiricalness and all contingencies is justified by
>> incompleteness. Now that is not obvious. Look in my URL for
>> links to the proof. Note that by Godel second theorem a consistent
>> machine cannot prove the existence of even just one consistent
>> extension, but yet can prove a lot about the geometry of those
>> consistent extensions, once they exist.
>> ======================
>> "CMR" <jackogreen.domain.name.hidden> wrote (to Joao Leao)
>> >I would tend to agree with Chaitin that your apparent confidence in
>> the
>> >"precise accessibility" of Mathematics as opposed to that of
>> physics may be
>> >misplaced; I would also agree that Leibniz's insights are probably
>> more
>> >useful than Plato's on the ultimate "nature" of reality:
>> >
>> >
>> > >From "Should Mathematics Be More Like Physics? Must Mathematical
>> Axioms Be
>> >Self-Evident?"
>> Just to be clear on that point, I agree totally with Chaitin.
>> Now, some truth (like 317 is a prime) are clearer than any physical
>> proposition. But, as I said, there will be more and more
>> mathematical
>> propositions, in the future, which will have "experimental" status,
>> and
>> this follows from incompleteness phenomena.
>> ===================
>> "Norman Samish" <ncsamish.domain.name.hidden> wrote:
>> >What are the philosophical implications of unsolvable mathematical
>> problems?
>> >Does this mean that mathematical reality, hence physical reality,
>> is
>> >ultimately unknowable?
>> It is not because some question are unsolvable in one domain, that
>> all the question are unsolvable in that domain. Reality is most
>> plausibly *partially* knowable. With Godel we know that our
>> uncertainties
>> are proportional to our certainties. This is perhaps related to the
>> free-will question btw.
>> ======================================
>> "Hal Finney" <hal.domain.name.hidden> wrote
>> >If, from a set of axioms and rules of inference, we can produce a
>> >valid proof of a theorem, then the theorem is true, within that
>> >axiomatic system.
>> >
>> >
>> >I'd suggest that this notion of provability is analogous to the
>> >"reality" of physics. Provable theorems are what we know, within
>> >a mathematical system.
>> >
>> >
>> >Now, one problem with this approach is that it focuses on the
>> theorems,
>> >which are generally "about" some mathematical concepts or objects,
>> >but not on the objects themselves. For example, we have a theory
>> of
>> >the integers, and we can make proofs about them, such as that there
>> >are an infinite number of primes. These proofs are what we know
>> about
>> >the integers, the "mathematical reality" of this subject.
>> >
>> >
>> >But what about the integers themselves? They are distinct from the
>> >theorems about them. Maybe we would want to say that it is the
>> integers
>> >which are "mathematically real", rather than proofs about them.
>> Yes. Important point. Why do you ask? I am afraid you are confusing
>> levels. Let me be precise on this because a lot of people are wrong
>> or confused. So, roughly speaking.
>> Number theory is the study of numbers. That is, a number theorist
>> works on numbers, and its main methodology is informal proof,
>> conjectures,
>> and nowadays : computer experimentation, and tomorrow perhaps
>> physical
>> experiment.
>> Geometry is the study of spaces. That is a (mathematical) geometer
>> works on spaces (Euclidian, non euclidian, riemannian, hilbert
>> spaces,
>> projective spaces, etc.). and its main methodology is informal
>> proof,
>> conjectures, etc.
>> Proof theory (a branche of logic) is the study of formal proofs.
>> That is, a proof theorist works on proofs and proofs system (quantum
>> like, intuitionnist, monotonic, modal, classical, non standard,
>> etc.).
>> And its main methodology is, like any other mathematicians,
>> *informal
>> proof*, conjecture, etc.
>> No mathematician do formal proofs. All proof in mathematical
>> books and papers are informal (although rigorous). To formalise
>> a proof is made only by proof theorist, because formal proof are
>> their
>> object of study, but then they make informal proofs *about* those
>> formal proofs.
>> So, the number theorist learn about numbers, the geometer
>> learns about spaces, the proof theorist learns about proofs.
>> And then they exist bridges between those branch, and
>> applications, etc.
>> But a mathematician does not learn about proofs per se
>> (of course by practice he develops skills for proving things), but
>> he learns about its subject matter (numbers, spaces, etc.)
>> *through* proofs.
>> ======================================
>> "Stephen Paul King" <stephenk1.domain.name.hidden> wrote:
>> >This is at the heart of my argument against proposals such as those
>> of
>> >Bruno Marchal. The "duration" required to instantiate a relation,
>> even one
>> >between a priori "existing" numbers can not be assumed to be zero
>> and still
>> >be a meaningful one.
>> I don't want to look presumptuous, but then, I want to be clear
>> about
>> what I have done (or at least about what I think, and apparently
>> some other
>> people thinks I have done). In particular, I don't think I have
>> made a
>> *proposal*. I provide a proof. A proof that *if* we postulate the
>> hyp., *then* it
>> follows that physics is a branch of number theory. See my URL for
>> the
>> proof, and
>> don't hesitate to ask question if some steps are unclear.
>> Note that the proof assumes almost nothing in mathematics. Only the
>> attempt
>> of an actual derivation of the logical skeleton of the physical
>> propositions
>> assumes a lot of mathematical logics. But the proof itself of the
>> necessity
>> of the
>> reduction assumes nothing more that the comp hyp, and of course
>> some reasoning abilities, if this should be mentioned at all.
>> I am completely open to the idea that comp will be refuted, and that
>> what
>> I have done could lead to such a refutation. But currently comp
>> seems to be
>> confirmed by the facts. For example, the most obvious and oldest
>> fact
>> which follows from comp is the Many-World-like ontology, and through
>> physics, the idea is slowly made seemingly reasonable.
>> Bruno
>> http://iridia.ulb.ac.be/~marchal/
> --
> Joao Pedro Leao ::: jleao.domain.name.hidden
> Harvard-Smithsonian Center for Astrophysics
> 1815 Massachussetts Av. , Cambridge MA 02140
> Work Phone: (617)-496-7990 extension 124
> VoIP Phone: (617)=384-6679
> Cell-Phone: (617)-817-1800
> ----------------------------------------------
> "All generalizations are abusive (specially this one!)"
> -------------------------------------------------------

Joao Pedro Leao  :::  jleao.domain.name.hidden
Harvard-Smithsonian Center for Astrophysics
1815 Massachussetts Av. , Cambridge MA 02140
Work Phone: (617)-496-7990 extension 124
VoIP Phone: (617)=384-6679
Cell-Phone: (617)-817-1800
"All generalizations are abusive (specially this one!)"
Received on Tue Oct 28 2003 - 15:55:50 PST

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