Re: Robotic Scientist
Well, I did not visualize a 'park' of machines. I was stuck with ONE.
I am still stuck with the 'selection' in
"...the interesting concept is the study of
classes of functions which* can be recognized* by a machine."
Can it recognize functions outside its inner capabilities? Or in such cases
serve the other (unlimited anount of) machines to help out? That would be
beyond me.
John
On Wed, Dec 30, 2009 at 1:20 PM, Bruno Marchal wrote:
> John,
>
> On 29 Dec 2009, at 20:57, John Mikes wrote:
>
>
> > excuse me if I suggest some circularity in you reply.
>
> You are welcome.
>
>
>
>
>
>
> > A "learning machine" is by def. learning SOMETHING
>
> Yes. Usually a total computable function, or a mechanically generable
> set, or things represented by those things.
>
>
>
>
> > and that SOMETHING comes from its inside, if we do not specify an
> > 'outside' it may explore (which would not be learning, rather
> > exploring - a quite different ballgame - maybe followed by 'and
> > learning IT').
>
> Hmm... I would say yes, and indeed much of learning procedure are
> based on exploration of some spaces of possible solutions.
>
> And the geometry or the math of those spaces can help to accelerate
> the search, etc.
>
> A learning machine is a machine which do the operation inverse of
> programming. An learning machine is a machine which receive as input
> the input-outputs of another machine, and which regularly output, from
> time to time, a sequence of machine M1, M2, M3, ... If that sequence
> converge on a machine having the same input/output than the one of the
> presented machine, we say that the second machine has learn the first.
> Trivially, all total computable function are learnable, (by the
> constant "its program"), and the interesting concept is the study of
> classes of functions which can be recognized by a machine.
> All mechanically generable classes of total computable functions are
> quasi-trivially recognized by dovetailers on those classes. There are
> no universal learner, unless you weaken the identification of function
> criteria (actually allowing an indeterminate finite number of error,
> and the right to change the explanation an infinity of times!). See
> the paper by Case and Smith.
>
>
>
> > The applied (ball)game of 'machine' (substituted for 'learning
> > machine', excluded per se from the 'exploring' function)
>
>
> ?
>
>
>
>
> > reminds me of the puzzle of my midle-school grandkid: which word is
> > the ONE spelled always incorrectly in every good dictionary? (My
> > wife found it out, immediately, not me). For the lucky guessers I
> > allow a Coke on NewYear's Eve at his own expense, of course.
> > It depends on 'machine'. Independent? that. too, has to be
> > explained. Maybe B&B did.
> >
> > Your question: "Can a machine find a new thing(?)".
>
> Can a spider find a new thing? Without judgment, nor metaphysical
> identity problem for the spider, I would say obviously "yes". Look at
>
> http://www.youtube.com/watch?v=bQABY9H1h1Y
>
> Some naturalist will explain the spider did not invent anythings. I
> think they are confusing levels. If it is obvious that no individual
> spider invented the lasso, it is a fact that a lineage did it.
> Eventually from deep inside, there is novelty at each instant.
>
>
>
> > I refer to Russell's "patentable" which I wanted to address: a
> > 'new' ('patentably new'?) thing is not necessarily a (sorry for the
> > Ger.) "noch nie dagewesen" - it can be not yet described (but
> > knowable - a new combination of elements usually applied for
> > different patterns etc.). A good example is in this thread about
> > "electricity" as NOT describable to a medieval scientist: it might
> > have been "brand new" and unknown, but it still fits into the
> > 'knowables', so I think about more 'real' novelty.
>
> Real novelty? You talk like if the dreamer could never awaken. For a
> platonist, there is a sense of saying there is no novelty at all,
> indeed there is no time, nor space. Just the natural numbers and their
> absolutely incommensurable problem of marrying addition and
> multiplication. From inside novelty is unbounded, and unavoidable, as
> a consequence of that problem. To live consists in solving the problem
> raised by living, and computers are needed to solve the problems
> raised by computers. Even in Plato Heaven, universal machine put some
> disorder and platonic shit happens.
> I guess that's why universal souls can "fall". Among the novelties,
> there are good surprises and bad surprises.
>
>
> > E.g. cousins of the Milky Way in outer space before the telescope.
> > That did not fit into the Flat Earth views. - A 'better mousetrap'
> > IS 'patentable and new'.
> > I agree with your ending: " How to define "new", [for example]. It
> > is a relative concept."
>
> To have "perception", even just self-perception, you need already two
> universal machines.
>
> No problem, there exists an infinity of them in elementary arithmetic.
> Interacting in all po
Re: Robotic Scientist
John,
On 29 Dec 2009, at 20:57, John Mikes wrote:
> excuse me if I suggest some circularity in you reply.
You are welcome.
> A "learning machine" is by def. learning SOMETHING
Yes. Usually a total computable function, or a mechanically generable
set, or things represented by those things.
> and that SOMETHING comes from its inside, if we do not specify an
> 'outside' it may explore (which would not be learning, rather
> exploring - a quite different ballgame - maybe followed by 'and
> learning IT').
Hmm... I would say yes, and indeed much of learning procedure are
based on exploration of some spaces of possible solutions.
And the geometry or the math of those spaces can help to accelerate
the search, etc.
A learning machine is a machine which do the operation inverse of
programming. An learning machine is a machine which receive as input
the input-outputs of another machine, and which regularly output, from
time to time, a sequence of machine M1, M2, M3, ... If that sequence
converge on a machine having the same input/output than the one of the
presented machine, we say that the second machine has learn the first.
Trivially, all total computable function are learnable, (by the
constant "its program"), and the interesting concept is the study of
classes of functions which can be recognized by a machine.
All mechanically generable classes of total computable functions are
quasi-trivially recognized by dovetailers on those classes. There are
no universal learner, unless you weaken the identification of function
criteria (actually allowing an indeterminate finite number of error,
and the right to change the explanation an infinity of times!). See
the paper by Case and Smith.
> The applied (ball)game of 'machine' (substituted for 'learning
> machine', excluded per se from the 'exploring' function)
?
> reminds me of the puzzle of my midle-school grandkid: which word is
> the ONE spelled always incorrectly in every good dictionary? (My
> wife found it out, immediately, not me). For the lucky guessers I
> allow a Coke on NewYear's Eve at his own expense, of course.
> It depends on 'machine'. Independent? that. too, has to be
> explained. Maybe B&B did.
>
> Your question: "Can a machine find a new thing(?)".
Can a spider find a new thing? Without judgment, nor metaphysical
identity problem for the spider, I would say obviously "yes". Look at
http://www.youtube.com/watch?v=bQABY9H1h1Y
Some naturalist will explain the spider did not invent anythings. I
think they are confusing levels. If it is obvious that no individual
spider invented the lasso, it is a fact that a lineage did it.
Eventually from deep inside, there is novelty at each instant.
> I refer to Russell's "patentable" which I wanted to address: a
> 'new' ('patentably new'?) thing is not necessarily a (sorry for the
> Ger.) "noch nie dagewesen" - it can be not yet described (but
> knowable - a new combination of elements usually applied for
> different patterns etc.). A good example is in this thread about
> "electricity" as NOT describable to a medieval scientist: it might
> have been "brand new" and unknown, but it still fits into the
> 'knowables', so I think about more 'real' novelty.
Real novelty? You talk like if the dreamer could never awaken. For a
platonist, there is a sense of saying there is no novelty at all,
indeed there is no time, nor space. Just the natural numbers and their
absolutely incommensurable problem of marrying addition and
multiplication. From inside novelty is unbounded, and unavoidable, as
a consequence of that problem. To live consists in solving the problem
raised by living, and computers are needed to solve the problems
raised by computers. Even in Plato Heaven, universal machine put some
disorder and platonic shit happens.
I guess that's why universal souls can "fall". Among the novelties,
there are good surprises and bad surprises.
> E.g. cousins of the Milky Way in outer space before the telescope.
> That did not fit into the Flat Earth views. - A 'better mousetrap'
> IS 'patentable and new'.
> I agree with your ending: " How to define "new", [for example]. It
> is a relative concept."
To have "perception", even just self-perception, you need already two
universal machines.
No problem, there exists an infinity of them in elementary arithmetic.
Interacting in all possible ways.
Problem: our experience fluxes are distributed among them all.
Observable and sensible realities escapes the computable, a priori.
Happy new year,
Bruno
http://iridia.ulb.ac.be/~marchal/
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Re: 'Mind Space' metaphor - relation between Symbolic, Bayesian and Analogical inference
Dear Marc, you emerged from the conventional figment of a 'physical world' view and elevated into the concept of "mind" (what I don't know where, what and how to define...) - anyway, to think in mental terms instead of the conventional physical figments. Then you use the complacent terms of the abandoned physical sciences to include into your better ideas. The 'definitely' human restrictions into the 'non-restricted' totality. Space, objects, human logics, (in first line: a Bayesian probability as we, humans, imagine how the 'next' will arrive in an unlimited openness) even 'geometry of mind', the forces, - all the human restrictions into the unlimited in which we humans are only a tiny part? I think your ideas are acceptable as a step forward from the conventional (reductionistic) human thinking, but I would see a more distinct 'possibility' of free ways, which - alas - are not yet available, not even the words are there to apply when going into them. (The worst thing is a reference to 'cognitive science' which established this unknowable domain as fully explained (as of today) in our so far learned (misunderstood?)physical/physiologica/behavioral figments and their conventional explanations.) Please, excuse my critical (negative?) attitude without proposing a better mousetrap. I developed my 'scientific agnosticism' pertinent to the totality (wholeness) of which we (in our epistemic enrichment) so far got hold of a tiny fraction and feel 'so smart'. I jumped onto your idea: it is a try in the right direction and I am for every step forward. Please think about it, your startup is commendable. Happy 2010 John M On Wed, Dec 30, 2009 at 5:51 AM, marc.geddes wrote: > I came up with this metaphor which hopefully indicates the > relationship between the three main types of inference (Symbolic, > Bayesian and Analogical). > > --- > > Picture a mind as a space, and 'the laws of mind' are analogous to the > principles of cognitive science. > > Now in this 'mind space' picture the 'mind objects' - I suggest these > are logical predicates - symbolic representions of real objects. How > do these 'mind objects' interact? I suggest picturing 'mind forces' > as analogous to the 'strengths of relationships' between the mind > objects (predicates or variables) so 'mind forces' are probability > distributions. But what about the background geometry of mind space? > I suggest picturing 'curvatures' in the geometry of mind space as > analogous to concepts (categories or analogies). > > Then Symbolic logic is the laws governing the mind objects (rules for > manipulating predicates). Bayes (Probability Theory) is the laws > govering the mind forces (rules about probability distributions), and > Analogical inference (categorizaton) is the laws governing the > geometry of mind space itself (concept learning and manipulation). > > --- > > If my metaphor is valid, the radical implication is that analogical > inference is the true foundation of logic, and Bayes is merely a > special case of it. Why? Consider that *apparent* Newtonian forces > operating across physical space are actually just special cases of > curvatures in the geometry of space-time itself. What I'm suggesting > is *exactly* analogous to that physical picture. I'm suggesting that > *apparent* probabilistic operations in mind space are actually just > special cases of 'curvatures' in the 'geometry' of mind space > (categorization and analogy formation). > > --- > > The question of course is whether my metaphor is valid. I'm very > confident, but I could be wrong. Comments or thoughts welcome. > > -- > > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-l...@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com > . > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: UDA query
Hi Bruno >> If the UD was a concrete one like you ran then it would start to >> generate all programs and execute them all by one step etc. But are >> you saying that because the UD exists platonically all these programs >> and each of their steps exist also and hence, by the existence of a >> successor law they have an implicit time order? >Yes. The UD exist, and is even representable by a number. UD*, the >complete running of the UD does not exist in that sense, because it is >an infinite object, and such object does not exist in simple >arithmetical theories. But all finite parts of the UD* exist, and this >will be enough for "first person" being able to glue the computations. >For example, you could, for theoretical purpose, represent all the >running of the UD by a specific total computable function. For example >by the function F which on n gives the (number representing the) nth >first steps of the UD*. Then you can use the theorem which asserts >that all total computable functions are representable in Robinson >Arithmetic (a tiny fragment of Pean Arithmetic). That theorems is >proved in detail, for Robinson-ile arithmetic, in Boolos and Jeffrey, >or in Epstein and Carnielli. In Mendelson book it is done directly in >Peano Arithmetic. >It is because our "3-we", our bodies, or our bodies descriptions, are >constructed within these steps. But our first person are not, and no >finite pieces of the UD can give the "real experience". This is a >consequence of the first six steps: our next personal experience is >determined by the whole actual infinity of all the infinitely many >computations arrive at our current state. (+ step 8, where we abandon >explicitly the physical supervenience thesis for the computational one). This “glueing” idea reminds me of David Deutsch’s attempt to explain how time is an illusion in “The Fabric of Reality”. I never have got this one! I can follow your argument but it seems to put a very special status on the ist person experience. You say that our “3-person”/ bodily descriptions are contained as subprograms in the (infinite) programs which collectively provide Observer Moments for them. But I think you saying that our 1-person experience (frog view) is emergent from the collective (infinite) computations which are consistent with this emergent experience which is elaborated in your steps 1-7. It seems to make this ist person experience somewhat mystical as to why it is “experienced” at all. Some people wonder why we cannot see the other worlds in QM but I am often amazed that we experience one at all! Anyway all of what you say seems consistent with the many worlds picture (which it should be). >> Time is not difficult. It is right in the successor axioms of >> arithmetic. I’ll come back to this >> Here again you confirm the invocation of the successor axioms. >Yes. It is fundamental. I cannot extract those from logic alone. No >more than I can define addition or multiplication without using the >successor terms s(-) : >for all x x + 0 = x >for all x and yx + s(y) = s(x + y) >You have to understand that all the talk on the phi_i and w_i, >including the existence of universal number >(EuAxAy phi_u() = phi_x(y)) can be translated in pure first order >arithmetic, using only s, + and *. >I could add some nuances. "To be prime" is an intrinsic property of a >number. To be a universal number is not intrinsic. To define a >universal number I have to "arithmetize" the theory. The theory uses >variables x, y, z, ..., so I will have to represent "to be a variable" >in the theory. The theory "understands" only numbers. I can decide to >represent the variables by even numbers (for example). "Even(x)" can >be represented by "Ey(x = s(s(0)) * y)". So "variable(x)" will be >represented by the same expression. Then I will represent "to be a >formula", "to be an axiom", to be a proof", "to be a computation", >using Gödel's arithmetization technic (which is just a form of >programming in arithmetic). This will lead to a representation of >being a universal number. Where can I find out about this arithmetization technique and what do you mean by a “universal number”? >Now, would I decide to represent the variable in some other way (by >the odd numbers, for example), the preceding universal number will >still be in a universal number (intrinsically), but I will not been >able to see it, or to mention it explicitly. But here, you have to >just realize (cf the first six step of uda) that the first person >experience depends on all universal numbers, in all possible sense/ >arithmetical-implementations. >In particular "you here and now" are indeed implemented in arithmetic >in both the universal numbers based on (variable(x) = even(x), and >variable(x) = odd(x)). *ALL* universal numbers will compete below your >substitution level. >The fact that elementary (Robinson) arithmetic is already (Turing) >universal is an impressive not obvious fact. But it is no more >astonishing t
Re: Definition of universe
Bruno,* * I still wait for the reasoning of the 'primitive' in your: *"...if this physical universe can be captured by a program (a number) or even by a mathematical structure. It is not a primitive structure. It has a reason linked to a statistics on computations.-..."* What primitive(?) structure serves the *computation*? (Statistics is a nono for me: the choice of identification (exactly what definition of elements to pick) and of the domain-boundaries (what to include into our 'picking' territory) make the 'statistical results' arbitrary). I may have missed your explanation on that, when the question came up. And: where do you take the 'mechanism' FROM, if you consider the numbers * primitive*? Does your parenthesis (above) mean that "a number" is a program? I assume you mean the "very long" number (with their mathematical structure?) to *express anything* - being considerable like a program, but do you indeed mean it that way? Also the mathematical alteration of the numbers bothers me: if addition, etc. are included, why not express just the final number? - It is too long anyway, so it is a thought-experiment at best. Is such an unexpectably long number more understandable than a semanic meaning? Granted, it is not easy to 'manipulate' semantic meanings, but with a better computing (e.g. *fully analogue*) it is imaginable, (*an analogue mechanism*) - maybe more so than a number-substitute (oops: the other way around: the analog meaning expression substituting for the (primitive?) number-based expression). I asked earlier, but the response did not make me wiser: is there a place where I could read a (not more than a short paragraph-long) identification for UD(A) and AUDA? The texts that appeared are too long for my limited capabilites. Happy New Year (I will try to be smarter in 2010). John Mikes On Wed, Dec 30, 2009 at 10:59 AM, Bruno Marchal wrote: > Hi Mindey, > > On 29 Dec 2009, at 15:07, Mindey wrote: > > > > I was just wondering, we are talking so much about universes, but how > > do we define "universe"? Sorry if that question was answered > > somewhere, but after a quick search I didn't find it. > > What do you mean by "universe"? Do you mean, like many, the physical > universe (or multiverse), or do you mean the ultimate basic reality > (the third person everything)? > > I think that if we assume mechanism, then it is absolutely undecidable > if there is anything more than positive integers + addition and > multiplication. Ontologically, if you want. > > All the rest belongs to the epistemology of numbers, or, put it > differently, of the inside views of arithmetic. The physical universe > becomes the sharable (first person plural) ignorance of the universal > numbers. It is an open question if this physical universe can be > captured by a program (a number) or even by a mathematical structure. > It is not a primitive structure. It has a reason linked to a > statistics on computations. Matter is sort of derivative of the > (machine's) mind. Cf the UDA reasoning, if you have followed. > > There is a Skolem like paradox. Arithmetic, from outside, is infinite, > but it is a relatively small and simple mathematical structure. Yet, > as seen from inside, it escapes the whole of mathematics, because it > looks *very* big for inside. So big that such a bigness is not even > nameable by any of the creatures which live there. > > There is a need of some amount of mathematical logic and computer > science to give sense on all this. Especially for expression like "as > seen from inside", etc. > > Bruno Marchal > http://iridia.ulb.ac.be/~marchal/ > > > > -- > > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-l...@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com > . > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: 'Mind Space' metaphor - relation between Symbolic, Bayesian and Analogical inference
You may be right. But it is still an open problem to just define probability (except the probability one) in the mechanist settting. Rich metaphor, but a promise for a lot of work, to make this precise enough in the mechanist frame. It would mean that not only we have a measure (and a linear base of observable/operators) but also a richer differential structure. Who knows? You may try to be more precise, even without taking the mechanist constraint into consideration. With non-mechanism, you may consider Penrose's (very speculative) idea that mind reduces the wave by being related to gravitation (space-time curve). Not sure it makes really sense, but then, with non-comp, we may try ... everything. It seems obvious to me that Bayes is a particular case of inference. There are *many* others. Bruno On 30 Dec 2009, at 11:51, marc.geddes wrote: > I came up with this metaphor which hopefully indicates the > relationship between the three main types of inference (Symbolic, > Bayesian and Analogical). > > --- > > Picture a mind as a space, and 'the laws of mind' are analogous to the > principles of cognitive science. > > Now in this 'mind space' picture the 'mind objects' - I suggest these > are logical predicates - symbolic representions of real objects. How > do these 'mind objects' interact? I suggest picturing 'mind forces' > as analogous to the 'strengths of relationships' between the mind > objects (predicates or variables) so 'mind forces' are probability > distributions. But what about the background geometry of mind space? > I suggest picturing 'curvatures' in the geometry of mind space as > analogous to concepts (categories or analogies). > > Then Symbolic logic is the laws governing the mind objects (rules for > manipulating predicates). Bayes (Probability Theory) is the laws > govering the mind forces (rules about probability distributions), and > Analogical inference (categorizaton) is the laws governing the > geometry of mind space itself (concept learning and manipulation). > > --- > > If my metaphor is valid, the radical implication is that analogical > inference is the true foundation of logic, and Bayes is merely a > special case of it. Why? Consider that *apparent* Newtonian forces > operating across physical space are actually just special cases of > curvatures in the geometry of space-time itself. What I'm suggesting > is *exactly* analogous to that physical picture. I'm suggesting that > *apparent* probabilistic operations in mind space are actually just > special cases of 'curvatures' in the 'geometry' of mind space > (categorization and analogy formation). > > --- > > The question of course is whether my metaphor is valid. I'm very > confident, but I could be wrong. Comments or thoughts welcome. > > -- > > You received this message because you are subscribed to the Google > Groups "Everything List" group. > To post to this group, send email to everything-l...@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com > . > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en > . > > http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Why I am I?
Bruno Marchal wrote:
>
>>
>>
>>
>>
>>
>> Bruno Marchal wrote:
>>>
Bruno Marchal wrote:
>
> The theory
> explains what exists, and how the rest emerges from it.
But then doesn't the "rest" exist, too? I just see a problem with
claiming
to explain what exists, when it is really not clear what existance
could
mean apart from the relatively meaningful, but vague, every day use.
>>>
>>> In that context existence is the same as in the expression "it exists
>>> a number having this or that property". Among the property there will
>>> be property like "relatively to that number this number observe this
>>> phenomenon". the rest belongs to the dream of numbers, and they do
>>> those dream because they describe computations. We assume
>>> mechanism, I
>>> recall.
>> Okay, though I still think it's advisable to not use simply
>> "existence" as a
>> word a here, because it sounds too exclusive. "What exists" sounds
>> like
>> "Everything that exists".
>> And I find "dreams of numbers" sounds as if the dreams where less
>> fundamental than the numbers.
>
> They are. Numbers are primitive. The variable x and y represents
> excusively those numbers. Finite pieces of computation are speical
> numbers, like prime numbers. To be a (finite piece of a) computation
> is a property of number, a relation which has to be defined in term of
> addition and multiplication of numbers. To be a computation are
> emergent property (emerging from addition and multiplication).
Sorry, I just don't get it. Your theory necessarily presumes dreams before
numbers, because for you numbers appear just in your dreams. Additionally,
the notion of numbers relies on the notion of truth, which is a notion that
fundamentally can't be defined, only known. Without *experiencing* truth
there is no sense to numbers. So there are numbers without there being
"dreaming"/experiencing first.
It seems to me that you call that "primitive", which relies already on the
truths ("there are dreams/experiences") of which it gives emergence to. Do
you see my problem with that?
Bruno Marchal wrote:
>
>> But since you don't only assume mechanism, but
>> also conciousness (like all theories)
>
> Digitam mechanism (comp) assumes consciousness explicitly (cf the
> sense of the "yes doctor"). Most theories does not assume
> "consciousness". The word does not appear in the description of the
> theories.
I don't think it's necessary to write that you assume conciousness. All
theories assume truth and still no one makes this implicit. Because it is
obivous; you simply can't deny there is truth or that you're concious. Well,
actually you can deny it, but then it is clear for me that your use of the
words "conciousness" or "truth" doesn't point to what I mean.
Bruno Marchal wrote:
>
>> and consensual reality (the dreams in
>> which the representations of numbers appear), I don't see how it
>> makes sense
>> to put numbers "before" conciousness and (perceived) reality.
>
> Well, it is a bit like "addition" comes before "being prime". You need
> addition in Robinson arithmetic to define what a prime number is. Then
> you need addition, and prime, before defining when a number represent
> a finite piece of computation. And you need that to eventually attach
> consciousness to computations. The "before" is logical, not temporal.
I need someone making sense of "addition in Robinson arithmetic" before I
(logically) can refer to addition in Robinson arithmetic (or if you want it
this way "I need the sense itself in 'addition in Robinson arithmetic'
before I can refer to addition in Robinson arithmetic").
It makes sense for me to say that we need numbers in order to link
conciousness to numbers, but that is already obvious. But you need
conciousness (the mysterious "senser" or "sensing") in order to make sense
of anything, including numbers.
Numbers just come before any *notion* of conciousness that is reflected in
the numbers, but they can't come before conciousness itself. Or at least I
don't get what this could mean.
Bruno Marchal wrote:
>
>>> But this is just insulting the machines, and nothing else.
>> My point is not to insult machines. A machine is identified by what
>> it does,
>> because feelings can not be uniquely linked with a machine.
>
> Why? We can, for all practical purpose, attach a mind to a machine.
> What we cannot do is to attach a machine to a mind, but "only" an
> infinity of machine to a mind.
How can we attach a mind to a machine? If you have the description of a
machine, you know what it feels? You are a machine lover indeed ;).
Bruno Marchal wrote:
>
>> Conciousness is already attached to an
>> infinity of machines and from our perspective we are at least
>> conciousness;
>> that which is always sure here and now. So every observer, just by
>> virtue of
>> observing *anything*, already feels the truth about an infinity of
>> machines.
>> But *a
Re: Definition of universe
Hi Mindey, On 29 Dec 2009, at 15:07, Mindey wrote: > I was just wondering, we are talking so much about universes, but how > do we define "universe"? Sorry if that question was answered > somewhere, but after a quick search I didn't find it. What do you mean by "universe"? Do you mean, like many, the physical universe (or multiverse), or do you mean the ultimate basic reality (the third person everything)? I think that if we assume mechanism, then it is absolutely undecidable if there is anything more than positive integers + addition and multiplication. Ontologically, if you want. All the rest belongs to the epistemology of numbers, or, put it differently, of the inside views of arithmetic. The physical universe becomes the sharable (first person plural) ignorance of the universal numbers. It is an open question if this physical universe can be captured by a program (a number) or even by a mathematical structure. It is not a primitive structure. It has a reason linked to a statistics on computations. Matter is sort of derivative of the (machine's) mind. Cf the UDA reasoning, if you have followed. There is a Skolem like paradox. Arithmetic, from outside, is infinite, but it is a relatively small and simple mathematical structure. Yet, as seen from inside, it escapes the whole of mathematics, because it looks *very* big for inside. So big that such a bigness is not even nameable by any of the creatures which live there. There is a need of some amount of mathematical logic and computer science to give sense on all this. Especially for expression like "as seen from inside", etc. Bruno Marchal http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: New Paper by Thomas Hertog and Stephen Hawking
On 30 Dec 2009, at 05:59, Colin Hales wrote: > > > Jason Resch wrote: >> Described in this article: >> http://www.bioedonline.org/news/news.cfm?art=2617 >> >> "This summation of all paths, proposed in the 1960s by physicist >> Richard Feynman and others, is the only way to explain some of the >> bizarre properties of quantum particles, such as their apparent >> ability to be in two places at once. The key point is that not all >> paths contribute equally to the photon's behaviour: the straight-line >> trajectory dominates over the indirect ones. >> >> Hertog argues that the same must be true of the path through time >> that >> took the Universe into its current state. We must regard it as a sum >> over all possible histories." >> >> > > So we "must", must we? Assuming mechanism, I don't see how we can avoid this. > > A mathematical construction by humans, happens to cohere to some > extent > with reality. > A mere description. > > A million other descriptions, also constructed by humans, could be as > predictive of how the universe appears. > > What extra belief system must exist in order that someone conclude > that > we 'must' chose a "sum of all histories" as "the" story? Why is the > universe compelled to be such a thing? Well, then it is also the simple explanation of the behavior of particles in nature. Something which, in my opinion, confirms the statistics on computations which is forced by digital mechanism. > > Rhetorical question...don't answer. Just think. Oops! > > happy new year, everythingers. Happy new year Colin, Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: UDA query
On 30 Dec 2009, at 03:29, ronaldheld wrote: > Bruno: > Is there a UD that is implemented in Fortran? I don't know. If you know Fortran, it should be a relatively easy task to implement one. Note that you have still the choice between a fortran program dovetailing on all computations by combinators, or on all computations by LISP programs, or on all proofs of Sigma_1 complete arithmetical sentences, or on all running of game of life patterns, etc. Of you can write a Fortran program executing all Fortran programs. All this will be equivalent. All UD executes all UDs, and this an infinity of times. Good exercise. A bit tedious though. Bruno > > > On Dec 29, 4:55 am, Bruno Marchal wrote: >> On 28 Dec 2009, at 21:24, Nick Prince wrote: >> >> >> Well, it is better to assume just the axiom of, say, Robinson arithmetic. You assume 0, the successors, s(0), s(s(0)), etc. You assume some laws, like s(x) = s(y) -> x = y, 0 ≠ s(x), the laws of addition, and multiplication. Then the existence of the universal machine and the UD follows as consequences. >> >>> Ok so the UD exists (platonically?) >> >> Yes. The UD exists, and its existence can be proved in or by very >> weak >> (not yet Löbian) arithmetical theories, like Robinson Arithmetic. >> The UD exists like the number 733 exists. The proof of its existence >> is even constructive, so it exists even for an intuitionist (non >> platonist). No need of the excluded middle principle. >> >> >> Better not to conceive them as living in some place. "where" and "when" are not arithmetical predicate. The UD exists like PI or the square root of 2. (Assuming CT of course, to pretend the "U" in the UD is really universal, with respect to computability). >> >>> Fine so the UD has an objective existence in spite of whatever else >>> exists. >> >> It exists in the sense that we can prove it to exist once we accept >> the statement that 0 is different from all successor (0 ≠ s(x) for >> all x), etc. >> If you accept high school elementary arithmetic, then the UD exists >> in >> the same sense that prime numbers exists. >> "exist" is used in sense of first order logic. This leads to the >> usual >> philosophical problems in math, no new one, and the UDA reasoning >> does >> not depend on the alternative way to solve those philsophical >> problem, >> unless you propose a ultra-finitist solution (which I exclude in comp >> by arithmetical realism). >> >> >> >> >> >> >> There is a "time order". The most basic one, after the successor law, >> is the computational steps of a Universal Dovetailer. Then you have a (different) time order for each individual computations generated by the UD, like >> phi_24 (7)^1, phi_24 (7)^2, phi_24 (7)^3, phi_24 (7)^4, ... where"phi_i (j)^s" denotes the sth steps of the computation (by the UD) of the ith programs on input j. >> >>> If the UD was a concrete one like you ran then it would start to >>> generate all programs and execute them all by one step etc. But are >>> you saying that because the UD exists platonically all these >>> programs >>> and each of their steps exist also and hence, by the existence of a >>> successor law they have an implicit time order? >> >> Yes. The UD exist, and is even representable by a number. UD*, the >> complete running of the UD does not exist in that sense, because it >> is >> an infinite object, and such object does not exist in simple >> arithmetical theories. But all finite parts of the UD* exist, and >> this >> will be enough for "first person" being able to glue the >> computations. >> For example, you could, for theoretical purpose, represent all the >> running of the UD by a specific total computable function. For >> example >> by the function F which on n gives the (number representing the) nth >> first steps of the UD*. Then you can use the theorem which asserts >> that all total computable functions are representable in Robinson >> Arithmetic (a tiny fragment of Pean Arithmetic). That theorems is >> proved in detail, for Robinson-ile arithmetic, in Boolos and Jeffrey, >> or in Epstein and Carnielli. In Mendelson book it is done directly in >> Peano Arithmetic. >> >> >> Then there will be the time generated by first person learning and which relies eventually on a statistical view on infinities of computations. >> >>> Is this because we are essentially constructs within these steps? >> >> It is because our "3-we", our bodies, or our bodies descriptions, are >> constructed within these steps. But our first person are not, and no >> finite pieces of the UD can give the "real experience". This is a >> consequence of the first six steps: our next personal experience is >> determined by the whole actual infinity of all the infinitely many >> computations arrive at our current state. (+ step 8, where we abandon >> explicitly the physical supe
Re: New Paper by Thomas Hertog and Stephen Hawking
Happy NewYear, Colin, you just came up shy from the notion that all this is a part of the anthropocentric maze. Physicists' hegemnony over (scientific?) thinking is embedded into the math-maze of numbers and this, too, may be a human invention (according to D. Bohm). So all the 'stories' and conclusions (including Russell's 'Occamistic simplification') are products of the human mind - not a 'MUST believe' for the existence we are part of. All is included in your 'perceived reality' we have access to. We are handicapped into our human limitations, tacitly we should accept that. Of course we cannot step out of our borders, but as a consequence of thinking 'human' we should be cautious when drawing ALL_generalized conclusions. We don't know 'what else' is going on. Even limitedly (distorted?) what we are concerned with. Everything is more than the everything we can imagine. John Mikes On Tue, Dec 29, 2009 at 11:59 PM, Colin Hales wrote: > > > Jason Resch wrote: > > Described in this article: > > http://www.bioedonline.org/news/news.cfm?art=2617 > > > > "This summation of all paths, proposed in the 1960s by physicist > > Richard Feynman and others, is the only way to explain some of the > > bizarre properties of quantum particles, such as their apparent > > ability to be in two places at once. The key point is that not all > > paths contribute equally to the photon's behaviour: the straight-line > > trajectory dominates over the indirect ones. > > > > Hertog argues that the same must be true of the path through time that > > took the Universe into its current state. We must regard it as a sum > > over all possible histories." > > > > > > So we "must", must we? > > A mathematical construction by humans, happens to cohere to some extent > with reality. > A mere description. > > A million other descriptions, also constructed by humans, could be as > predictive of how the universe appears. > > What extra belief system must exist in order that someone conclude that > we 'must' chose a "sum of all histories" as "the" story? Why is the > universe compelled to be such a thing? > > Rhetorical question...don't answer. Just think. > > happy new year, everythingers. > > cheers > colin > > > > -- > > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-l...@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com > . > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
'Mind Space' metaphor - relation between Symbolic, Bayesian and Analogical inference
I came up with this metaphor which hopefully indicates the relationship between the three main types of inference (Symbolic, Bayesian and Analogical). --- Picture a mind as a space, and 'the laws of mind' are analogous to the principles of cognitive science. Now in this 'mind space' picture the 'mind objects' - I suggest these are logical predicates - symbolic representions of real objects. How do these 'mind objects' interact? I suggest picturing 'mind forces' as analogous to the 'strengths of relationships' between the mind objects (predicates or variables) so 'mind forces' are probability distributions. But what about the background geometry of mind space? I suggest picturing 'curvatures' in the geometry of mind space as analogous to concepts (categories or analogies). Then Symbolic logic is the laws governing the mind objects (rules for manipulating predicates). Bayes (Probability Theory) is the laws govering the mind forces (rules about probability distributions), and Analogical inference (categorizaton) is the laws governing the geometry of mind space itself (concept learning and manipulation). --- If my metaphor is valid, the radical implication is that analogical inference is the true foundation of logic, and Bayes is merely a special case of it. Why? Consider that *apparent* Newtonian forces operating across physical space are actually just special cases of curvatures in the geometry of space-time itself. What I'm suggesting is *exactly* analogous to that physical picture. I'm suggesting that *apparent* probabilistic operations in mind space are actually just special cases of 'curvatures' in the 'geometry' of mind space (categorization and analogy formation). --- The question of course is whether my metaphor is valid. I'm very confident, but I could be wrong. Comments or thoughts welcome. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
