Hi John,

On 07 Jan 2014, at 23:20, John Mikes wrote:

Bruno, you made my day.

Reminds me of a Hungarian humorous author (P. Howard) who wrote about a blind philosopher (The Sleepy Elephant) and his assistant living in the deep Sahara - showing the Elephant's Life Oeuvre in a BIG book, the assistant was supposed to write as the old Blind Elephant dictated. It was all empty and the assistant asked somebody to inscribe: "I cannot write, but it makes him so happy when I pretend..." -

Lol



When reading your remarks I wonder what REALLY mean 'machine', 'comp', 'universal', and some more of your words I got used to over the past 2 decades, yet are not "clear"(??) enough in my mind to automatically click-in when used. Do you have a glossary I could download, to refresh those (brief!) meanings?

I have no glossary. Maybe I should do that. I use each term in the most standard sense used by the expert in the field. Computable is made ultra-standard, if I can say, thanks to the Church thesis.

Let me try an explanation, below,  for the notions mentioned above.

(I am aware that you appreciate Robert Rosen critics of Church Thesis, but as you know I have some reservation that it is really a critics of Church thesis, as a critic of possible misuse of Church's thesis).



I - and I believe some others, too - are immerged into our own vocabulary-meanings and to read your text requires a mental translation into your world of conceptualization. Maybe I am too old to do it 'en passant'. I cannot start reading your life's ouvre to get to those words.

Probably nobody can do that 'in passant'.  Nothing is obvious.




And sorry to denigrate your 'multiplication' into subtraction.

That happens.

:)





One word about 'refutable': it was - as far as I know - Popper's criterion for the 'scientific'. I like to go further and dethrone it in cases when we just don't know enough - neither to produce a suitable refutation, nor even to catch a (real?) meaning of something new.

I completely agree.

Note also that Popper's principle has been refuted in the Machine Learning theory (by John Case & Al.). Allowing an inductive inference machine to bet on some non refutable principle enlarges the class of computable functions that they can infer in the limit of the presentations of their <input, output>.

Don't mind too much. Popper criterion remains interesting, just not 100% correct.

Computationalism can justify that, in the matter of machine's psychology, every general assertions have to be taken with some amount of grains of salt.

Let me try to explain the three notions: 'machine', 'comp', 'universal'.

Computability theory is a branch of mathematical logic, and the notion of computable functions arise from studies in the foundations of mathematics. Gödel, in his 1931 negative solution to a problem asked by Hilbert, already defined a large class of computable functions, needed in his translation of the syntax of arithmetic in term of addition and multiplication.

This has led to the discovery that I sum up as the discovery of the universal machine, or of the universal interpreter, missed by Gödel, but not by Emile Post, Turing, Kleene, etc. Gödel will take some time to accept Church thesis. Eventually he will understand better than other, as he will be aware of what he called a *miracle*.

Church defined computable basically by a mathematical programming language.

All definitions of computable leads to that same class, and they all contains universal programs/machines/numbers.

Those are digital machines (programs) interpreted by layers of universal machine (interpreter or compiler of programming language) until the (analog) quantum field implementing it into your laptop or GSM.

Comp is the opinion of the one who agrees that his surgeon replaces his brain with a computer simulating it at some substitution level. More exactly comp is the assumption that this opinion is correct, for some (unknown) level.

It is an hypothesis. The game consists in taking it seriously and seeing where it leads. I have not yet seen any blatant contradictions. Just weirdness, quantum-like weirdness.

Comp is for computer science. Theoretical computer science is born well before computers appears and develop. By machine I mean "digital machine", and the universal machines are the one which can imitate, by coded instruction, all digital machines.

Those machines are enumerable. There is an enumeration of all of them: m_0, m_1, m_2, m_3, m_4, ...

So, you can fix one universal language, like a base, and identify each machine with a number. Each programming language, or computers boolean net, correspond to some m_i, and are universal m_i, as they can imitate all others machines (accepting Church thesis).

But I don't want you embarrassed by too much technicalities. Comp might be false, but at least it makes it possible to formulate the problems thanks to computer science and mathematical logic.

The discovery of the (Löbian) Universal Machines is the discovery *of* the mathematicians in arithmetic, *by* the mathematicians. And guess who put so much mess in Platonia? The mathematicians.

The arithmetical reality is full of life and dreams. Even without assuming comp. "Strong AI" is enough here.

Fee free to ask any question(s).

Best,

Bruno



On Tue, Jan 7, 2014 at 5:03 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

On 06 Jan 2014, at 23:56, John Mikes wrote:

Dear Telmo
(I suppose a 'freer mind than several nat.-scientist listers) allow me some musings (not that I want to hide them from the rest of the List). Thinking of Bruno's integer-restricted arithmetics with addition and subtraction only:

addition and multiplication (actually, just a detail).



it is the World Of ONE, multiplied as much as you wish (two ways: + and -). Numerals? So we elevated to some understanding of the "ONE" (unit?) and our uncontrollable mind made out of it the Entire World. Or we don't understand even that 'one'; Bruno applied his extremely educated (and disciplined) mind to elevate this 'one' into sophisticated logical systems (what I never studied, sorry to say).

I derived it from the computationalist *assumption*.



There are also opinionated remarks about 'physical' (etc.?) laws with fancy conclusions. In my opinion a physical law is the summation of observations WITHIN limits of our so far achieved knowledge and the 'majority' seems to be the "norm" ('law'). Then comes the condiment: lots of math and similar deductions and voila: our conventional sciences. Extend the limits (of our observations? or knowledge?) and the "laws" change. That happened in our (cultural? human?) history continually. I do not appreciate the level at which we are today: it will change as it changed from the past. Societal (communal?) 'law' is different: it is a compromise between interests of diverse classes of members of a society including the powerfuls' as giving the overtone.

Reality is beyond our (human) mental capabilities to detect,

It is beyond all machine's ability, not just the humans (I assume comp, of course). All machine believing in a reality can discover that indeed most of it will transcend his capacity, even when assuming comp. The ontology becomes very simple (only 0 and its successor, or only the combinators K and S, with their applications, ...), but the epistemology, which include the physics, get infinitely complex and rich.



I humbly disregard the "Slanted Realities" like mathematical, or religious, etc. partial views. Same with truth. I like to talk about my 'agnosticism' and MY beliefs based in it: the 'infinite copmp[lexity' beyond our (limited) model of knowables (because I cannot comprehend "infinite" - or - "complexity" as a simple-minded human).

We agree on this. The nice point is that absolutely all machines, when correct, agrees with this, and discover it by themselves.




So after having passed an old fashioned rigorous Ph.D. at a 5century old Universitas in chemistry, physics and math, published ~100 papers (both in research and technical implementation of own results mostly in the polymer-field) lectured on 3 continents and having gotten 38 patents to my inventorship, I do not believe in 'atoms' (molecules?)

Nor do any correct machine when introspecting enough.



and consider the physical world a 'human' makeup

It is a "machine" or "number" make up. Assuming comp. In that case the reasoning is constructive, which means that the physical laws can be deduced from the machine's (mathematical) points of view, and this makes computationalism refutable. (That is the main point).



for ever changing and poorly understood phenomena as their synthesis into a 'scientifically balanced' conventional view which, however, produced lots of (almost perfect?) practical results into our lives.

Have a prosperous 2014 and then more to come

Happy New Year 2014!

Bruno



John Mikes D.Sc.






On Mon, Jan 6, 2014 at 2:05 PM, Telmo Menezes <te...@telmomenezes.com> wrote: On Mon, Jan 6, 2014 at 6:31 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
> Dear Stephen,
>
>
> On 03 Jan 2014, at 20:21, Stephen Paul King wrote:
>
> Dear Bruno,
>
>   I do not understand something.
>
>
>
> OK. (good!)
>
>
>
> Your idea
>
>
> It is not an idea, but a result in an hypothetical context (or theoretical
> context).
>
>
>
> seems to me to be a very sophisticated and yat sneaky way of reintroducing > Newton/Laplacean absolute time and/or Leibnitz' Pre-established Harmony.
>
>
> It is only a remind of elementary arithmetic. The music 0, s0, ss0, sss0,
> ssss0, sssss0, ssssss0, sssssss0, ...
> You can see it as an elementary block digital time. If you want. And then
> all other times are relative indexicals, including the physical and
> subjective times.

Bruno,

I think I (perhaps naively) understand what you mean. My understanding
is that, if comp is true, then the relationship between comp and the
physical laws we observe is not a simple one. Even QM would be at a
high level of abstraction in relation to raw reality. In this case,
the recursive definition of integers would be the simplest possible
expression of a fundamental building block that is responsible for
time -- although the time we experience is a much more complex
phenomena.

It makes sense to me that time is strongly related to recursivity
(maybe because of a CS background). I imagine moments being "copied
forward" and changed in some fashion.

Would you agree with these intuitions?

>
>
>
>
>
> I recall reading how much Einstein himself loved the idea and was loath to > give it up, thus motivating his quest for a classical grand unified field
> theory. Physics has moved on...
>
>
> After Aristotle Physics has also moved on ... I think Einstein was right on > QM, and wrong on GR, in the sense that GR has to be justified by the > quantum, before, perhaps justifying the quantum by the "digital seen from
> inside".
>
>
>
>
>
> You recently wrote:
>
> "The only "time" needed for the notion of computation is the successor > relation on the non negative integers. It is not a physical time, as it is
> only the standard ordering of the natural numbers: 0, 1, 2, 3, etc.
>
> So, the 3p "outer structure" is very simple, conceptually, as it is given by > the standard structure, known to be very complex, mathematically, of the > additive/multiplicative (and hybrids of course) structure of the numbers (or
> any object-of-talk of a universal numbers).
>
> That is indeed a quite "static" structure (and usually we don't attribute > consciousness to that type of thing, but salvia makes some (1p alas) point
> against this)."
>
>
> Let me try to clarify how I am confused by this claim.
>
>
> OK.
>
>
>
> How many different versions of the integers "exist"?
>
> AFAIK, there can be only One and it is this *One* that acts as the "time"
> (maybe) in your argument for all other "strings" of integers.
>
>
> ?
>
> I have no clue what you are talking about. I am talking about the usual, > standard, finite and non negative integers, also known as natural numbers. > I am not doing philosophy, so any problem you might have with this might > comes from unecessary over-interpretation you make, over what you have been
> supposed to have learned in high school.
>
>
>
>
>
> Are the "strings" distorted and/or incomplete "shadows" of the One?
>
> Are we permitted to use the allegory of the cave here? :-)
>
>
>
> Yes, but you need to do the work to understand the "real thing". We start
> from arithmetic, that is:
>
> 0 ≠ s(x)
> s(x) = s(y) -> x = y
> x+0 = x
> x+s(y) = s(x+y)
> x*0=0
> x*s(y)=(x*y)+x
>
> or even just
>
> Kxy = x
> Sxyz = xz(yz)
>
> ((K x) y) = x
> (((S x) y) z) = ((x z) (y z))
>
> And we stay in that theory.
>
> In that theory we define the observer by a believer in the axioms:
>
>
> 0 ≠ s(x)
> s(x) = s(y) -> x = y
> x+0 = x
> x+s(y) = s(x+y)
> x*0=0
> x*s(y)=(x*y)+x
>
> together with the infinity of beliefs in the following induction axioms
> (with F any formula in logic + {0, s, +, *}):
>
> (F(0) & Ax(F(x) -> F(s(x))) -> AxF(x)
>
> Just that is already very long to do, but that is done in the literature and
> is basically the "known" arithmetization of meta-arithmetic.
>
> Then incompleteness entails the nuances between proof and truth, and > consistency, and the double completeness theorem of Solovay provides the 8 > hypostases, and we see that the classical introspecting machines can > understand by herself that what she observe might be only the shadow of the
> truth.
> Indeed.
>
>
>
>
>
> How many "shadows" are there and how are they "distinguished" from each
> other such that the notion of a computation is not lost?
>
>
> By the study of the degrees of unsolvability. Notably.
>
>
>
>
> In my work I have found that theoreticians in computer science completely > take for granted that a computation is a process that can only occur in the
> absence of randomness.
>
>
> That is well studied. It is computability relativized to oracles.
> Computability on random oracle has been studied.
>
>
>
>
>
> Imagine if the atoms making up the CPU of your computer where to suddenly > start changing their positions and states due to outside interactions in a
> random/uncontrolled way?
>
>
> That happens when I smoke a psychotropic plant, if not when I breath the
> polluted air.
>
>
>
>    No computation would occur!
>
>
> Let us not exaggerate. No need to smoke the grass of Fukushima.
>
>
>
>
> In fact, this is the situation that we find when, for instance, the cooler
> fan fails and the CPU overheats.
>
>
>
> Yes. The hypostases might be used to study the 1p associated to such extreme > events. Would this give a NDE? Difficult questions, which needs some
> technical progresses.
>
>
>
>
> My point here is that the string of states that is a von Neumann computation
>
>
> von Neumann, Babbage, Turing, Church, Conway, Post, McCarthy, etc. OK.
>
>
>
> is something that has to be separable and/or isolated to be able to be said
> to "occur" or -to use the Platonic metaphor- "exist".
>
>
> We start from the "E" interpreted in the usual way, like in "16 has a
> successor".
> And gives 8 different notion of existences, in the eight hypostases (which > are each a mathematics with an intensional arithmetical interpretation).
>
> You get physics when you restrict the arithmetical interpretation on the
> sigma_1 sentences, on the material hypostases.
>
>
>
>
> So, what exactly is separating the "strings of integers" from each other and
> the One, such that we can coherently discuss them as actually being
> computations and not just "representations of computations"?
>
>
> The trueness of their relative association, together with their
> redundancies. At the bottom, what do the separation are the additions and > multiplication, they separate the computations which halt from those who
> does not halt, the first person views do the rest.
>
> Hope this helps.
>
> Best,
>
> Bruno
>
>
>
>
> --
>
> Kindest Regards,
>
> Stephen Paul King
>
>
>
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