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P vs NP in realtion to Cognitive Genius

Mhykiel
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5/27/2014 11:23:48 AM
Posted: 2 years ago
Can a brain that can evaluate a genius solution, also produce genius solutions?

I will cut and paste some posts from AlbinoBunny and Graincruncher to get readers up to spend.

At 5/27/2014 10:40:15 AM, AlbinoBunny wrote:
At 5/27/2014 10:34:45 AM, Mhykiel wrote:
At 5/27/2014 10:31:55 AM, AlbinoBunny wrote:
At 5/27/2014 10:17:06 AM, Mhykiel wrote:
At 5/27/2014 10:10:28 AM, AlbinoBunny wrote:
At 5/27/2014 9:29:38 AM, Mhykiel wrote:
At 5/27/2014 8:51:44 AM, AlbinoBunny wrote:

I'm arguing for a materialistic naturalistic secular worldview?


Personally I find it intellectually hypocritical on so many different aspects. If it is all brain chemistry, than P=NP. Awe but "smart" people want to think they are so special so P =/= NP.

I've heard of the P = NP problem from computer science, care to explain how it relates?

Interesting blog about it from Scott Aaronson http://www.scottaaronson.com...

And for more in-depth on it's philosophical impact of complexity theory a lengthy paper he wrote. http://arxiv.org...

P= solutions found NP= solutions verified. If they are equal than someone who can verify a solution should be able to find a solution equally as well. If thoughts and emotions are just chemical responses in the brain this would means:

A brain with the chemical response to verify a solution is the same brain that can find a solution. So if a brain can verify a crossword puzzle as being correct it has the ability to solve for the same difficulty of crossword. Extend this to say Mozart symphony. A brain that can register the interplay of the musical piece should have the same functioning capability to produce one.

Simply put people would rather believe p=/=NP so that creative leaps and genius can still be praised.

P=NP praise would be for the fastest computer, or the fastest thinker
p=/=NP would be to praise for the greatest processor pipeline, or the creative thinker.

It makes sense to me. Also;

That if you can verify something, you could also come up with it. It may depend on the type of problem though I guess. Not that I've provided any evidence.


What makes sense? are you agreeing or disagreeing with my previous statements?


"The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. ... The informal term quickly used above means the existence of an algorithm for the task that runs in polynomial time." - https://en.wikipedia.org...

I know what the problem is I don't need wiki.

Just thought I'd put that there because the "quickly" part is important.

Then We disagree and I provided 2 links that discus the likelihood P!=NP.


Why do you disagree?

"Personally I find it intellectually hypocritical on so many different aspects. If it is all brain chemistry, than P=NP. Awe but "smart" people want to think they are so special so P =/= NP."

If it is all brain chemistry then P = NP? Then anything that can be quickly verified can be quickly solved? Speed is the crux of the matter, actually. If you feel that your links show that to be false then explain how they do that.

At 5/27/2014 11:01:30 AM, Mhykiel wrote:
At 5/27/2014 10:56:33 AM, Graincruncher wrote:
At 5/27/2014 10:45:29 AM, Mhykiel wrote:
At 5/27/2014 10:35:42 AM, Graincruncher wrote:
And as AB has just pointed out, it is not merely about whether you can solve them and recognise them, but whether you can do so within a reasonable timeframe. In computer science, I believe the issue is that if P=NP then there are much more efficient ways we could be solving certain complex problems. If you can recognise the correct answer then you are, in principle, capable of coming up with that answer. If you could do it in a useful amount of time or not is a different question and ties in with what I just said about the processing capacity and abstract modelling; creative insight is not qualitatively different, but quantitatively so.

Yes but the time factor is not really represented when we take this problem into a philosophical meaning to brain chemistry and creative or emotional processing.

If the time factor is excluded then the PvNP problem disappears completely; the 'P' is a reference to polynomial time. It's a computational problem, not a philosophical one.

computationally time is a factor. But philosophically I think the factor is complexity of mental schema. And mental subroutines. So that is the measure of efficiency for a human brain. So I understand why you think intuitively that a brain with the mental schema to check a solution has the mental schema to produce it... I just argue that mathematically, socially, historically this doesn't appear to be the case.
Mhykiel
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5/27/2014 11:28:09 AM
Posted: 2 years ago
Can a brain that can evaluate a genius solution, also produce genius solutions?

I'm a proponent that P != NP (P =/= NP)

So I say No. A brain that can evaluate a solution like a symphony, Special Relativity, or a Soduko puzzle does not mean that same brain can produce such creative leaps.

Now a brain and it's schema may produce genius works and also be able to evaluate a solution. But the reverse is not true. A brain that can evaluate does not mean a brain that can produce.
Graincruncher
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5/27/2014 11:37:08 AM
Posted: 2 years ago
Reposts as requested:

Yes I understand you. I actually even wrote earlier

P=NP praise would be for the fastest computer, or the fastest thinker
p=/=NP would be to praise for the greatest processor pipeline, or the creative thinker.

My point is that both are matters of processing speed and complexity.

I am in the latter you are in the former.

Thanks for the compliment (I think!) but I'd actually definitely fall into the latter category.

I think you should check out at least the blog link I gave of Scott Aaronson. His paper on complexity theory I also linked is a great read. all 58 pages of it.

I think you're still misunderstanding how important the time component of the problem is. It isn't the case that you can either solve P or NP problems, The problem is of how long it takes to solve them and how much in the way of processing resources you have to do it.

In short, some problems are best solved using sequential processing and others are best solved using parallel processing. If I know how to solve something, it makes sense to dedicate my available resources do doing that. If I want to find out how to solve something, it may be better for me to try multiple models for solutions (abstract approximations) concurrently and then select from the best of those and repeat until I have something that works. One is linear and the other iterative. Or to put it another way - and please excuse me for drawing the parallel, but it's too perfect to resist - certain problems are better solved using a kind of evolutionary 'survival of the fittest' methodology.

One is "solving problem X" while the other is "solving the problem of solving problem X". The former is quicker to do than the latter (generally speaking, of course), but if you can do one then you can, given enough time, do both. Even with relatively little in the way of resources.

computationally time is a factor. But philosophically I think the factor is complexity of mental schema. And mental subroutines. So that is the measure of efficiency for a human brain. So I understand why you think intuitively that a brain with the mental schema to check a solution has the mental schema to produce it... I just argue that mathematically, socially, historically this doesn't appear to be the case.

If person X can check a solution then, given enough time, they have the capacity to produce it. The more intelligent person X is, the less time will be taken for both. As I said, I don't think it is a philosophical question at all.

Which is the contention I have of some one reducing say love to neurological chemical signals. I don't think that has enough explanatory power to express the emergence or "finding solution" of love."

I'm not sure what you mean by that last part, but all thought is neurological. We can identify neurotransmitters and hormones that are linked to emotional states. We can link processes within the brain to not just feelings but concepts. What is not being explained by this?
AlbinoBunny
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5/27/2014 12:03:29 PM
Posted: 2 years ago
Well do people often learn from these genius solutions? If they do then it's conceivable that they may not be able to ever solve those problems. If it's just a clever leap that the genius used, then it's conceivable that given enough time, a person who could verify the problem could also solve it.

I think P = NP, is also often (or always) attributed to the same hardware. I would argue that people run different hardware and software.

I remember that this all started when debating the concept of "love". Would you mind refreshing that idea here?
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AlbinoBunny
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5/27/2014 12:04:57 PM
Posted: 2 years ago
Oh and BTW, I'm on the fence with the P = NP problem, because I haven't really looked into it enough.
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dylancatlow
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5/27/2014 12:09:29 PM
Posted: 2 years ago
I don't really know anything about this, but it might be the case that certain problems are irreducibly complex to solve using blunt algorithms (for instance, problems that self-reference in some way), and that the only escape from an infinite regress is to be given something to check which "short-circuits" the infinite regress.
Mhykiel
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5/28/2014 2:21:19 AM
Posted: 2 years ago
At 5/27/2014 11:37:08 AM, Graincruncher wrote:
Reposts as requested:

Yes I understand you. I actually even wrote earlier

P=NP praise would be for the fastest computer, or the fastest thinker
p=/=NP would be to praise for the greatest processor pipeline, or the creative thinker.

My point is that both are matters of processing speed and complexity.

I am in the latter you are in the former.

Thanks for the compliment (I think!) but I'd actually definitely fall into the latter category.

I think you should check out at least the blog link I gave of Scott Aaronson. His paper on complexity theory I also linked is a great read. all 58 pages of it.

I think you're still misunderstanding how important the time component of the problem is. It isn't the case that you can either solve P or NP problems, The problem is of how long it takes to solve them and how much in the way of processing resources you have to do it.

In short, some problems are best solved using sequential processing and others are best solved using parallel processing. If I know how to solve something, it makes sense to dedicate my available resources do doing that. If I want to find out how to solve something, it may be better for me to try multiple models for solutions (abstract approximations) concurrently and then select from the best of those and repeat until I have something that works. One is linear and the other iterative. Or to put it another way - and please excuse me for drawing the parallel, but it's too perfect to resist - certain problems are better solved using a kind of evolutionary 'survival of the fittest' methodology.

One is "solving problem X" while the other is "solving the problem of solving problem X". The former is quicker to do than the latter (generally speaking, of course), but if you can do one then you can, given enough time, do both. Even with relatively little in the way of resources.


computationally time is a factor. But philosophically I think the factor is complexity of mental schema. And mental subroutines. So that is the measure of efficiency for a human brain. So I understand why you think intuitively that a brain with the mental schema to check a solution has the mental schema to produce it... I just argue that mathematically, socially, historically this doesn't appear to be the case.

If person X can check a solution then, given enough time, they have the capacity to produce it. The more intelligent person X is, the less time will be taken for both. As I said, I don't think it is a philosophical question at all.

Which is the contention I have of some one reducing say love to neurological chemical signals. I don't think that has enough explanatory power to express the emergence or "finding solution" of love."

I'm not sure what you mean by that last part, but all thought is neurological. We can identify neurotransmitters and hormones that are linked to emotional states. We can link processes within the brain to not just feelings but concepts. What is not being explained by this?

Given enough time anything is possible. Now this does not have to be a full on head dive into P=NP. But what the problem persist with is not if enough time can elapse. It is if a related amount of time is evident in P. So say P is a problem of combining 8 notes across 2 octaves to produce an aesthetic appeal (music). Is there something intrinsic about this problem that says okay it will take X time to find a solution, ans Y time to verify it.

Time is important in computer computation for a whole slew of reasons that are not relevant to this thread. I think when we bring the problem into philosophy, time is still relevant in that it should be efficient (not given any amount of time) but that it is about pathways and mental schema to solve problems.

Okay so now as you stated: We can measure these pathways. But I say these pathways are for the understanding or appreciation of certain thoughts and emotions. But they do not explain the emergence of the thought or emotion.

Okay say we have mapped that when I listen to Bach, my brain goes through a pathway of euphoria and happiness.

Well some one else exhibits the same pathways and chemistry when they listen to Mozart and NOT Bach.

If the same MRI scan shows the same chemicals but the stimuli are different than where did my love of Bach come from while someone else feels the same about Mozart. Reducing actions to the chemicals does not explain their emergence inside a personality.
Mhykiel
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5/28/2014 2:27:51 AM
Posted: 2 years ago
At 5/27/2014 12:03:29 PM, AlbinoBunny wrote:
Well do people often learn from these genius solutions? If they do then it's conceivable that they may not be able to ever solve those problems. If it's just a clever leap that the genius used, then it's conceivable that given enough time, a person who could verify the problem could also solve it.


Right, But where does this clever leap come from if the mechanic in the brain to make it did not exist before. Or better to the point is.. If a genius has an idea that solves a problem where does the means of verifying that solution come from if the solution is novel or new.

So as a person thinks an internal dialog may look like this: one idea (nope that's crazy), another idea (possibly..but nope), third idea (yes that's it)

And once he shares this idea with others they get (yep that's it) . they have the understanding to verify the solution, did they have the capability to generate it as well.

Given enough time yes. But for P to equal NP, the times would have to be related or proportional. I say p=/= np.

I think P = NP, is also often (or always) attributed to the same hardware. I would argue that people run different hardware and software.

I remember that this all started when debating the concept of "love". Would you mind refreshing that idea here?

I refresh the relevance in my last post to Grain.
Mhykiel
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5/28/2014 2:29:37 AM
Posted: 2 years ago
At 5/27/2014 12:09:29 PM, dylancatlow wrote:
I don't really know anything about this, but it might be the case that certain problems are irreducibly complex to solve using blunt algorithms (for instance, problems that self-reference in some way), and that the only escape from an infinite regress is to be given something to check which "short-circuits" the infinite regress.

Here's a wiki to it http://en.wikipedia.org...

If there is a relationship found between P and NP then there would be a quick check to see what processes on NP are most likely to be correct P.
AlbinoBunny
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5/28/2014 3:50:15 AM
Posted: 2 years ago
At 5/28/2014 2:27:51 AM, Mhykiel wrote:
At 5/27/2014 12:03:29 PM, AlbinoBunny wrote:
Well do people often learn from these genius solutions? If they do then it's conceivable that they may not be able to ever solve those problems. If it's just a clever leap that the genius used, then it's conceivable that given enough time, a person who could verify the problem could also solve it.


Right, But where does this clever leap come from if the mechanic in the brain to make it did not exist before. Or better to the point is.. If a genius has an idea that solves a problem where does the means of verifying that solution come from if the solution is novel or new.

So as a person thinks an internal dialog may look like this: one idea (nope that's crazy), another idea (possibly..but nope), third idea (yes that's it)

And once he shares this idea with others they get (yep that's it) . they have the understanding to verify the solution, did they have the capability to generate it as well.

Given enough time yes. But for P to equal NP, the times would have to be related or proportional. I say p=/= np.

That seems like a reasonable proposition to me.


I think P = NP, is also often (or always) attributed to the same hardware. I would argue that people run different hardware and software.

I remember that this all started when debating the concept of "love". Would you mind refreshing that idea here?

I refresh the relevance in my last post to Grain.

OK I'll read over it and maybe reply.
bladerunner060 | bsh1 , 2014! Presidency campaign!

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http://www.debate.org... - Running for president.
http://www.debate.org... - Running as his vice president.

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Graincruncher
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5/31/2014 4:13:22 AM
Posted: 2 years ago
At 5/28/2014 2:21:19 AM, Mhykiel wrote:
At 5/27/2014 11:37:08 AM, Graincruncher wrote:
Reposts as requested:

Yes I understand you. I actually even wrote earlier

P=NP praise would be for the fastest computer, or the fastest thinker
p=/=NP would be to praise for the greatest processor pipeline, or the creative thinker.

My point is that both are matters of processing speed and complexity.

I am in the latter you are in the former.

Thanks for the compliment (I think!) but I'd actually definitely fall into the latter category.

I think you should check out at least the blog link I gave of Scott Aaronson. His paper on complexity theory I also linked is a great read. all 58 pages of it.

I think you're still misunderstanding how important the time component of the problem is. It isn't the case that you can either solve P or NP problems, The problem is of how long it takes to solve them and how much in the way of processing resources you have to do it.

In short, some problems are best solved using sequential processing and others are best solved using parallel processing. If I know how to solve something, it makes sense to dedicate my available resources do doing that. If I want to find out how to solve something, it may be better for me to try multiple models for solutions (abstract approximations) concurrently and then select from the best of those and repeat until I have something that works. One is linear and the other iterative. Or to put it another way - and please excuse me for drawing the parallel, but it's too perfect to resist - certain problems are better solved using a kind of evolutionary 'survival of the fittest' methodology.

One is "solving problem X" while the other is "solving the problem of solving problem X". The former is quicker to do than the latter (generally speaking, of course), but if you can do one then you can, given enough time, do both. Even with relatively little in the way of resources.


computationally time is a factor. But philosophically I think the factor is complexity of mental schema. And mental subroutines. So that is the measure of efficiency for a human brain. So I understand why you think intuitively that a brain with the mental schema to check a solution has the mental schema to produce it... I just argue that mathematically, socially, historically this doesn't appear to be the case.

If person X can check a solution then, given enough time, they have the capacity to produce it. The more intelligent person X is, the less time will be taken for both. As I said, I don't think it is a philosophical question at all.

Which is the contention I have of some one reducing say love to neurological chemical signals. I don't think that has enough explanatory power to express the emergence or "finding solution" of love."

I'm not sure what you mean by that last part, but all thought is neurological. We can identify neurotransmitters and hormones that are linked to emotional states. We can link processes within the brain to not just feelings but concepts. What is not being explained by this?

Given enough time anything is possible. Now this does not have to be a full on head dive into P=NP. But what the problem persist with is not if enough time can elapse. It is if a related amount of time is evident in P. So say P is a problem of combining 8 notes across 2 octaves to produce an aesthetic appeal (music). Is there something intrinsic about this problem that says okay it will take X time to find a solution, ans Y time to verify it.

And the PvsNP problem is definitionally a problem of time. It is not that NP problems are definitionally non-computable, it is whether there are ways of computing them faster.

Time is important in computer computation for a whole slew of reasons that are not relevant to this thread.

Then we are not discussing PvsNP in relation to anything and the original objection is discarded as admittedly invalid.

I think when we bring the problem into philosophy, time is still relevant in that it should be efficient (not given any amount of time) but that it is about pathways and mental schema to solve problems.

I'm still unsure of how it can be considered a philosophical problem.

Okay so now as you stated: We can measure these pathways. But I say these pathways are for the understanding or appreciation of certain thoughts and emotions. But they do not explain the emergence of the thought or emotion.

I quite honestly don't really understand what you're saying here. That the way with think is different from the thoughts we have? I don't see how.

Okay say we have mapped that when I listen to Bach, my brain goes through a pathway of euphoria and happiness.

Well some one else exhibits the same pathways and chemistry when they listen to Mozart and NOT Bach.

Well yes. You do not share an identical brain, so we would expect differences like this.

If the same MRI scan shows the same chemicals but the stimuli are different than where did my love of Bach come from while someone else feels the same about Mozart. Reducing actions to the chemicals does not explain their emergence inside a personality.