A machine can never ever surpass human intelligence

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Re: A machine can never ever surpass human intelligence

#561  Postby SpeedOfSound » May 24, 2015 11:21 am

GrahamH wrote:
SpeedOfSound wrote:But! As usual we can clear it all up by coming up with a CONCRETE example of heuristic code to contrast with the code I provided. Naming programs is not a concrete example. The square block method is a one-iter that would require relaxing good enough considerably.


You can't have a 'concrete example of a heuristic code'. That's why it's call heuristic, the code you can write does not define the solutions it might produce.

You could look at the code for a deep learning ANN and it won't tell you much at all about how it discriminates cats from elephants.
How does Watson know the answer to the Jeopardy question about the third US president? You can't find that by just looking at the code. You have to look at the 'experience' of the Watson system, to see what it has 'learned' and how it 'reasons'.



You can look at that scala program all day long and you will not see the answer to the question: what is the square root of 8.
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Re: A machine can never ever surpass human intelligence

#562  Postby newolder » May 24, 2015 11:23 am

GrahamH wrote:What examples do we have of HPs that humans can solve and algorithms cannot?...

Chaitin's constant is known by humans to be unknowable (because p never halts) but an algorithm to calculate the sum of 2-p terms until p halts will never halt. An algorithm has no way to discover that the solution is unknowable. :scratch:
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Re: A machine can never ever surpass human intelligence

#563  Postby SpeedOfSound » May 24, 2015 11:26 am

newolder wrote:
GrahamH wrote:What examples do we have of HPs that humans can solve and algorithms cannot?...

Chaitin's constant is known by humans to be unknowable (because p never halts) but an algorithm to calculate the sum of 2-p terms until p halts will never halt. An algorithm has no way to discover that the solution is unknowable. :scratch:

How does any algorithm to calculate an irrational ever complete?
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Re: A machine can never ever surpass human intelligence

#564  Postby newolder » May 24, 2015 11:37 am

SpeedOfSound wrote:
newolder wrote:
GrahamH wrote:What examples do we have of HPs that humans can solve and algorithms cannot?...

Chaitin's constant is known by humans to be unknowable (because p never halts) but an algorithm to calculate the sum of 2-p terms until p halts will never halt. An algorithm has no way to discover that the solution is unknowable. :scratch:

How does any algorithm to calculate an irrational ever complete?

It's never happened (irrationals are infinite sequences) - such algorithms are forced to halt at an approximation after a specified period of calculation.
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Re: A machine can never ever surpass human intelligence

#565  Postby SpeedOfSound » May 24, 2015 11:53 am

newolder wrote:
SpeedOfSound wrote:
newolder wrote:
GrahamH wrote:What examples do we have of HPs that humans can solve and algorithms cannot?...

Chaitin's constant is known by humans to be unknowable (because p never halts) but an algorithm to calculate the sum of 2-p terms until p halts will never halt. An algorithm has no way to discover that the solution is unknowable. :scratch:

How does any algorithm to calculate an irrational ever complete?

It's never happened (irrationals are infinite sequences) - such algorithms are forced to halt at an approximation after a specified period of calculation.

So a heuristic is applied. As is it in the initial guess for sqrt above. Bad guess like 100 yields about 12 iterations. A good guess like x/2 lands at four or five.
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Re: A machine can never ever surpass human intelligence

#566  Postby newolder » May 24, 2015 12:00 pm

SpeedOfSound wrote:...
So a heuristic is applied. As is it in the initial guess for sqrt above. Bad guess like 100 yields about 12 iterations. A good guess like x/2 lands at four or five.

Yes, that works for some numbers but not Chaitin's things...
http://mathworld.wolfram.com/ChaitinsConstant.html wrote:A Chaitin's constant, also called a Chaitin omega number, introduced by Chaitin (1975), is the halting probability of a universal prefix-free (self-delimiting) Turing machine. Every Chaitin constant is simultaneously computably enumerable (the limit of a computable, increasing, converging sequence of rationals), and algorithmically random (its binary expansion is an algorithmic random sequence), hence uncomputable (Chaitin 1975).
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Re: A machine can never ever surpass human intelligence

#567  Postby SpeedOfSound » May 24, 2015 12:12 pm

newolder wrote:
SpeedOfSound wrote:...
So a heuristic is applied. As is it in the initial guess for sqrt above. Bad guess like 100 yields about 12 iterations. A good guess like x/2 lands at four or five.

Yes, that works for some numbers but not Chaitin's things...
http://mathworld.wolfram.com/ChaitinsConstant.html wrote:A Chaitin's constant, also called a Chaitin omega number, introduced by Chaitin (1975), is the halting probability of a universal prefix-free (self-delimiting) Turing machine. Every Chaitin constant is simultaneously computably enumerable (the limit of a computable, increasing, converging sequence of rationals), and algorithmically random (its binary expansion is an algorithmic random sequence), hence uncomputable (Chaitin 1975).

Not sure why that matters here.
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Re: A machine can never ever surpass human intelligence

#568  Postby SpeedOfSound » May 24, 2015 12:38 pm

newolder wrote:...
Well, I'm no expert in any of these matters but I was under the impression that the difference between algorithms and "what humans do" is neatly summed up in Turing's Halting problem. Algorithms that sum terms like 2-p, increment p and continue until p halts (the oddly named Chaitin's constant) are undecidable by the algorithm (incrementing p does not cause it to halt and so it continues for ever) but not by the human (who knows that p never halts). I've no idea how to implement a heuristic to solve this problem but perhaps it is already achieved. :dunno:

If we get rid of the heuristic goodenough in the sqrt program we have a pure algorithm and it never halts. So it is a mystery to me why this isn't recognized as a heuristic program here. A very simple on that can be used to figure out what it is we were originally talking about.
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Re: A machine can never ever surpass human intelligence

#569  Postby GrahamH » May 24, 2015 2:26 pm

newolder wrote:
GrahamH wrote:What examples do we have of HPs that humans can solve and algorithms cannot?...

Chaitin's constant is known by humans to be unknowable (because p never halts) but an algorithm to calculate the sum of 2-p terms until p halts will never halt. An algorithm has no way to discover that the solution is unknowable. :scratch:


Serious question: How do you know it never halts?

An algorithm could discover the recursion.
It seems feasible that an algorithm could enumerate the logical possibilities and find the logical contradiction.
Why can't an algorithm identify an asymptotic function without a threshold and thus determine the function never terminates?

In particular, why can't a heuristic algorithm learn such patterns?

This particular classs of function seems tractable.
Why do you think that?
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Re: A machine can never ever surpass human intelligence

#570  Postby GrahamH » May 24, 2015 2:58 pm

SpeedOfSound wrote:
newolder wrote:...
Well, I'm no expert in any of these matters but I was under the impression that the difference between algorithms and "what humans do" is neatly summed up in Turing's Halting problem. Algorithms that sum terms like 2-p, increment p and continue until p halts (the oddly named Chaitin's constant) are undecidable by the algorithm (incrementing p does not cause it to halt and so it continues for ever) but not by the human (who knows that p never halts). I've no idea how to implement a heuristic to solve this problem but perhaps it is already achieved. :dunno:

If we get rid of the heuristic goodenough in the sqrt program we have a pure algorithm and it never halts. So it is a mystery to me why this isn't recognized as a heuristic program here. A very simple on that can be used to figure out what it is we were originally talking about.


Never halting but for a 'goodenough' threshold is not what defines a heuristic algorithm. It's about discovering a way to a solution that is not coded in the algorithm.
I don't think that using a heuristic in an algorithm makes for what is generally meant by a heuristic algorithm. How is your sqrt() relevant to the AI question?
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Re: A machine can never ever surpass human intelligence

#571  Postby igorfrankensteen » May 24, 2015 3:09 pm

I was too exhausted by the combination of stresses in my private life, the attempt by some members here to "win by way of insult," and by the excursions into areas of detailed science which I have zero knowledge of.

However, to take up where I left off...

When I referred to machines having to CONSCIOUSLY do whatever they do, I was speaking in the context of what I said in those posts, which was that everything our current definition of "machines" do, is programmed into them directly, either mechanically or through software Even when random number generators are inserted into them, in order to make them develop more varied and randomized results, they are still doing WHATEVER they do, exactly as they are originally designed to do. They do not do anything that they are NOT specifically designed to do, in the way that humans can, when they act out of UNCONSCIOUS sources.

Some people might want to imagine that "subroutines in software are akin to subconscious calculation in human minds," but I would suggest that this is only wishful thinking on their part. Because we still have no real idea how human minds work, we only have partial understanding of how SOME of the electrochemical processes involved proceed.

One of the primary things I like to do here, and in other forums I participate in, is not necessarily to directly attack a given hypothesis. What I most like to do, is to try to point out or suggest how (as is very often the case) some very important "big picture" elements to the subject are being overlooked or assumed.

That is why especially in the case of a discussion comparing machine "intelligence" to human "intelligence," I hope to draw everyone's attention to the assumptions and overlooked items inherent to THIS situation. That includes especially, not only that "human intelligence" is hard to define, it also completely misses that "surpass" as a point of decision about machine performance, directly infers that both an officially recognized authority exists to make such a judgment (a VERY dicey assumption), and even more critical, that the act of "surpassing" is possible to recognize, when and if it happens.

I look in particular, at one of the gravest threats currently facing humankind: it is a machine of sorts, and there are a lot of people already declaring that this machine has ALREADY surpassed human intelligence, and should be declared to be our "decisional" overlord.

I am referring to the various people who insist that some variation of Capitalism is "smarter" than all humans, and that whenever the machine of "capitalism" decides that something should cease to exist, or that something or someone else should knuckle under and cease struggling, that all of the rest of us should accept the "machines" decision.

No, I am assuredly NOT trying to lead this thread on a tangent for political purposes. Since the people who promote this idea set, do proclaim that their financial models, which they can and do describe via computer programs, are superior to any decisions which humans as a group, or as individuals can make, they are an exact example of what this thread is focused on. They are also an excellent illustration of the "macro" concerns that I think must be addressed, in order to rationally discuss machine intelligence, as compared to human intelligence.
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Re: A machine can never ever surpass human intelligence

#572  Postby GrahamH » May 24, 2015 3:16 pm

igorfrankensteen wrote: When I referred to machines having to CONSCIOUSLY do whatever they do, I was speaking in the context of what I said in those posts, which was that everything our current definition of "machines" do, is programmed into them directly, either mechanically or through software Even when random number generators are inserted into them, in order to make them develop more varied and randomized results, they are still doing WHATEVER they do, exactly as they are originally designed to do. They do not do anything that they are NOT specifically designed to do, in the way that humans can, when they act out of UNCONSCIOUS sources.

Some people might want to imagine that "subroutines in software are akin to subconscious calculation in human minds," but I would suggest that this is only wishful thinking on their part. Because we still have no real idea how human minds work, we only have partial understanding of how SOME of the electrochemical processes involved proceed.


WHat about machines doing things the programmers didn't know how to do? If you can't design an algorithm to do X you might be able to write an algorithm to work out how to do X. This is the territory of heuristic algorithms such as GA or deep learning. Design a system that can learn and discover solutions you couldn't work out.

The bit the designer doesn't put into such systems is whatever they discover by 'experience'.
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Re: A machine can never ever surpass human intelligence

#573  Postby newolder » May 24, 2015 3:18 pm

GrahamH wrote:
newolder wrote:
GrahamH wrote:What examples do we have of HPs that humans can solve and algorithms cannot?...

Chaitin's constant is known by humans to be unknowable (because p never halts) but an algorithm to calculate the sum of 2-p terms until p halts will never halt. An algorithm has no way to discover that the solution is unknowable. :scratch:


Serious question: How do you know it never halts?

Because p going to p+1 has a) no limit and b) no effect on a boolean ("halts" does not become true because of addition).

An algorithm could discover the recursion.

What recursion?

It seems feasible that an algorithm could enumerate the logical possibilities and find the logical contradiction.

What logical contradiction?

Why can't an algorithm identify an asymptotic function without a threshold and thus determine the function never terminates?

I don't know. Perhaps you have written such an algorithm?

In particular, why can't a heuristic algorithm learn such patterns?

This particular classs of function seems tractable.

I look forward to reading your solution. :thumbup:
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Re: A machine can never ever surpass human intelligence

#574  Postby igorfrankensteen » May 24, 2015 3:35 pm

GrahamH wrote:
igorfrankensteen wrote: When I referred to machines having to CONSCIOUSLY do whatever they do, I was speaking in the context of what I said in those posts, which was that everything our current definition of "machines" do, is programmed into them directly, either mechanically or through software Even when random number generators are inserted into them, in order to make them develop more varied and randomized results, they are still doing WHATEVER they do, exactly as they are originally designed to do. They do not do anything that they are NOT specifically designed to do, in the way that humans can, when they act out of UNCONSCIOUS sources.

Some people might want to imagine that "subroutines in software are akin to subconscious calculation in human minds," but I would suggest that this is only wishful thinking on their part. Because we still have no real idea how human minds work, we only have partial understanding of how SOME of the electrochemical processes involved proceed.


What about machines doing things the programmers didn't know how to do? If you can't design an algorithm to do X you might be able to write an algorithm to work out how to do X. This is the territory of heuristic algorithms such as GA or deep learning. Design a system that can learn and discover solutions you couldn't work out.

The bit the designer doesn't put into such systems is whatever they discover by 'experience'.


This isn't what I'm talking about. We design even purely mechanical machines to do things that we can't do ourselves.

What you are referring to, isn't actually "something we don't know HOW to do." You are describing something which we very much DO know HOW TO DO, but don't have the hard computational skills and resources to carry out.

If we didn't know HOW TO DO IT, we a) wouldn't be able to write software to make it happen, and b) wouldn't be able to recognize the result as correct or not, after it was presented to us.

In order to REALLY be an example such as you wish to talk about, you would have to have something like a machine which you designed and programmed to, say, wash your clothes, suddenly decide on it's own, to take your spare change from your pockets, and invest it in a stock that then made you rich.
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Re: A machine can never ever surpass human intelligence

#575  Postby GrahamH » May 24, 2015 4:16 pm

newolder wrote:
GrahamH wrote:
newolder wrote:
GrahamH wrote:What examples do we have of HPs that humans can solve and algorithms cannot?...

Chaitin's constant is known by humans to be unknowable (because p never halts) but an algorithm to calculate the sum of 2-p terms until p halts will never halt. An algorithm has no way to discover that the solution is unknowable. :scratch:


Serious question: How do you know it never halts?

Because p going to p+1 has a) no limit and b) no effect on a boolean ("halts" does not become true because of addition).

An algorithm could discover the recursion.

What recursion?


Sorry, I combined HP and Chaitin there.

However, Halt(

,

)=0 when

(

) fails to terminate, and Halt(

,

)=1 when

(

)
terminates. Thus a contradiction is produced in either event of

(

). So we
know that Halt(P,I) cannot exist. So, there is no Turing machine program that
can tell us whether another program will ever terminate or not.

See Ch.3 here http://www.math.washington.edu/~morrow/ ... rendan.pdf



It seems feasible that an algorithm could enumerate the logical possibilities and find the logical contradiction.

What logical contradiction?

Why can't an algorithm identify an asymptotic function without a threshold and thus determine the function never terminates?

I don't know. Perhaps you have written such an algorithm? [/quote]

I have not, and I think it would be difficult task, but is there anything in C-T Thesis or Chaitin constant, or anything else, that shows it to be impossible?

newolder wrote:

In particular, why can't a heuristic algorithm learn such patterns?

This particular classs of function seems tractable.

I look forward to reading your solution. :thumbup:



Maybe a successor to Watson might make some progress. :dunno:
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Re: A machine can never ever surpass human intelligence

#576  Postby GrahamH » May 24, 2015 4:21 pm

igorfrankensteen wrote: What you are referring to, isn't actually "something we don't know HOW to do." You are describing something which we very much DO know HOW TO DO, but don't have the hard computational skills and resources to carry out.


I disagree. Take bipedal walking. It's hard to get right. It's easier to write a genetic algorithm that does randomised trial and error learning to evolve a control algorithm. It writes an algorithm the author didn't know how to write.

Humans are like this. We aren't born knowing how to walk or grasp or see properly. We get there by trial and error heuristics. We are equipped with the means to learn how. GI requires the means to learn how, not the how.
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Re: A machine can never ever surpass human intelligence

#577  Postby GrahamH » May 24, 2015 4:26 pm

igorfrankensteen wrote: In order to REALLY be an example such as you wish to talk about, you would have to have something like a machine which you designed and programmed to, say, wash your clothes, suddenly decide on it's own, to take your spare change from your pockets, and invest it in a stock that then made you rich.


Sure, this would be GI. Step one is probably to have significant populations of AI agents evolving smarter versions because I don't think humans are smart enough to just design a GI. We haven't really started yet.
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Re: A machine can never ever surpass human intelligence

#578  Postby newolder » May 25, 2015 9:17 am

GrahamH wrote:...somewhere in that post...
So we
know that Halt(P,I) cannot exist. So, there is no Turing machine program that
can tell us whether another program will ever terminate or not.

Yes. :thumbup:

Since we humans know (by heuristic inspection) that Chaitin's algorithm does not halt, we surpass machine intelligence. (Note: I'm not saying "never ever" as in the topic title but Turing and Chaitin show that an algorithmic solution is not possible. So, for machines to surpass human intelligence will take more than algorithms. Heuristics may well be the way - a non-algorithmic heuristic on a machine may be a route forward - but no one has posted or given a link to such a thing, yet...)

Happy holiday. :coffee:
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Re: A machine can never ever surpass human intelligence

#579  Postby GrahamH » May 25, 2015 10:14 am

newolder wrote:
GrahamH wrote:...somewhere in that post...
So we
know that Halt(P,I) cannot exist. So, there is no Turing machine program that
can tell us whether another program will ever terminate or not.

Yes. :thumbup:

Since we humans know (by heuristic inspection) that Chaitin's algorithm does not halt, we surpass machine intelligence. (Note: I'm not saying "never ever" as in the topic title but Turing and Chaitin show that an algorithmic solution is not possible. So, for machines to surpass human intelligence will take more than algorithms. Heuristics may well be the way - a non-algorithmic heuristic on a machine may be a route forward - but no one has posted or given a link to such a thing, yet...)

Happy holiday. :coffee:


This topic is all about 'never ever' and arguments supposedly settled today that rule it out. Saying humans exceed machine intelligence today isn't saying much. Poiting to C-T or Chaitin as things that computers cannot do saying something very different.

Now we are back to 'non-algorthmic heuristics'. How could such things be any use to machine GI? Heuristic algorithms might be very useful.

We can see that some algorithms will, or will not halt. It is well established that we can't simply write an algorithm to determine if ANY random algorithm will halt or not but humans can't do that either.

This middle ground is not settled,as far as I can see. Humans learn patterns, use trial and error and apply logic to work out that SOME algorithms will, or will not, halt. Algorithms can learn patterns, use trial and error and apply logic. No current algorithms can do that to match humans, and there is hardly any population of algorithms in a process of evolution to do such things better.

For a fairer comparison consider how the best deep learning systems with a month old human. The human is not at all good at maths problems. We have no machine equivalents of 20 year old maths students, AFAIK.
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Re: A machine can never ever surpass human intelligence

#580  Postby SpeedOfSound » May 25, 2015 10:17 am

GrahamH wrote:
SpeedOfSound wrote:
newolder wrote:...
Well, I'm no expert in any of these matters but I was under the impression that the difference between algorithms and "what humans do" is neatly summed up in Turing's Halting problem. Algorithms that sum terms like 2-p, increment p and continue until p halts (the oddly named Chaitin's constant) are undecidable by the algorithm (incrementing p does not cause it to halt and so it continues for ever) but not by the human (who knows that p never halts). I've no idea how to implement a heuristic to solve this problem but perhaps it is already achieved. :dunno:

If we get rid of the heuristic goodenough in the sqrt program we have a pure algorithm and it never halts. So it is a mystery to me why this isn't recognized as a heuristic program here. A very simple on that can be used to figure out what it is we were originally talking about.


Never halting but for a 'goodenough' threshold is not what defines a heuristic algorithm. It's about discovering a way to a solution that is not coded in the algorithm.
I don't think that using a heuristic in an algorithm makes for what is generally meant by a heuristic algorithm. How is your sqrt() relevant to the AI question?

I'm trying to figure what it is that we mean by a 'heuristic algorithm' exactly. You have given me a new clue just here. My sqrt() is AT LEAST a concrete item on which we can make measures. Flippant referenced to a nebulous and ill defined other class of programs without providing actual concrete code is where this kind of philosophical discussion turns into a hen's happy pecking party.

I have seen 'heuristic program' contrasted with 'algorithmic program' as opposites. So 'heuristic algorithm' becomes questionable. Though we all know that all programs are at the bottom based on algorithms. Wouldn't be programs if they didn't.

The relationship to AI is this. There is a similar flippant handwaving toward 'human intelligence' where THAT is never defined. Only named. So we are waving our hands at two ill definitions and all we have for sure is my sqrt().
Now the clue.
It's about discovering a way to a solution that is not coded in the algorithm.


How does that work? If you were hired to write such a thing how would you proceed to a design? Start coding something completely different and pray for a happy accident were a solution pops up? Kind of like evolution?
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