48 replies to this topic

[Alric]

On a side note, if someone where able to solve the classic example given for P = NP, of making a list of 100 students from a list of 400, with certain pairs of students being banned, do you think that is enough to win the millennium prize reward?

http://en.wikipedia...._Prize_Problems

Or would you need to a lot better than that? The reason I ask, is because I think I know how a computer program might solve that specific problem in a very quick manner. Though I am rather rusty with computer programming, so it is a bit of work to look up all the basic commands and if they wouldn't accept that then it might not be worth the time.

[Alric]

Looking up more about it, I don't think they would just accept a computer program that does that. Though I still think that one could solve that specific problem without that much work. At least if I am understanding it correctly.

[MarcZ]

On a side note, if someone where able to solve the classic example given for P = NP, of making a list of 100 students from a list of 400, with certain pairs of students being banned, do you think that is enough to win the millennium prize reward?

http://en.wikipedia...._Prize_Problems

Or would you need to a lot better than that? The reason I ask, is because I think I know how a computer program might solve that specific problem in a very quick manner. Though I am rather rusty with computer programming, so it is a bit of work to look up all the basic commands and if they wouldn't accept that then it might not be worth the time.

I don't believe so, because the question is not asking to solve a problem, it's asking to prove that a computer can solve all problems in polynomial time.

[MarcZ]

Looking up more about it, I don't think they would just accept a computer program that does that. Though I still think that one could solve that specific problem without that much work. At least if I am understanding it correctly.

Yes, but you've got to remember there are small questions of NP too, but there are much larger ones which are almost impossible for a computer to do in any reasonable time.

[MarcZ]

Looking up more about it, I don't think they would just accept a computer program that does that. Though I still think that one could solve that specific problem without that much work. At least if I am understanding it correctly.

Yes, but you've got to remember there are small questions of NP too, but there are much larger ones which are almost impossible for a computer to do in any reasonable time.

Like a complex travelling salesman question for example.

Note: Sorry for the posts I thought I had clicked the edit button...

Edited by MarcZ, 04 May 2012 - 07:33 PM.

[CyberMisterBeauty]

Alric thinks that computers are already conscious, so I can see why he would believe that a machine could come up with original ideas within our lifetime. Our lifetime being 80 years, disregarding the shot at immortality (I believe I should refer to immortality pessimistically until it is proven, but I have the highest hope for it).

I'm not a mathematician, but I do think that quantum computers will be able to create codes that will be unbreakable and they will be able to crunch anything thrown at it. Making a new math or finding solutions that we would not understand if we saw the answer to would not happen by the 2070s which is around where all of our lifespans are on this forum.

A

And who told you you will live only till 2070?(I'll be 78 years old by the time.)And who told you that everyone in the forum will live only the 2070's decade?How do you know that?Do you have any crystal ball that know exactly what will happen in the future ahahahahahah?

[shane_allen]

This is a great thread, and I'm glad that the original poster, MarcZ, is so involved; tending to his thread.
I'm also glad we have a math major here, Shimmy.

I'm almost through my calc series and have 3 classes to go before I get my minor in Mathematics finished so I'm not nearly as qualified. So in my amature opinion in both mathematics and programming and my less then laymen opinion in psychology; I say that computers will be able to "do math" better then biological humans. By this I mean see a situation, frame it as a math problem and go to town on it. Proves, though, I take that next spring, so I don't have a firm grip on what that all entails, but I will point out that once "computers" more intelligent then humans or humans upload and upgrade, the term AI looses a part of it's meaning and "AI" will solve proves that humans either haven't or cannot because of the number of steps involved.

[MarcZ]

This is a great thread, and I'm glad that the original poster, MarcZ, is so involved; tending to his thread.
I'm also glad we have a math major here, Shimmy.

I'm almost through my calc series and have 3 classes to go before I get my minor in Mathematics finished so I'm not nearly as qualified. So in my amature opinion in both mathematics and programming and my less then laymen opinion in psychology; I say that computers will be able to "do math" better then biological humans. By this I mean see a situation, frame it as a math problem and go to town on it. Proves, though, I take that next spring, so I don't have a firm grip on what that all entails, but I will point out that once "computers" more intelligent then humans or humans upload and upgrade, the term AI looses a part of it's meaning and "AI" will solve proves that humans either haven't or cannot because of the number of steps involved.

I suppose, but we have to see where machine learning ends up, and whether AI can actually exceed human intelligence as AI is still based on logic principles humans have discovered remains to be seen.

I suppose it's possible in the very far future, but I don't see super powerful AI for a century or two.

Edited by MarcZ, 04 May 2012 - 08:09 PM.

[Alric]

It seems very unlikely it will take that long. You have to remember that we are experiencing exponential growth in computing and many other technologies so we can make huge gains in a relatively short time period. It is predicted in like 30-40 years. If things go badly maybe 50-60 years. A lot of people believe if it hasn't happened by then it means our advances in technology has been seriously derailed. Maybe we hit a limit and the computers can no longer get any faster. If that happens though, then it seems unlikely that it will ever happen.

Which makes sense, if we hit a hard limit where we can't physically increase computers speed, then no amount of time is going to help solve that issue. It seems unlikely we will hit a bump that stops all progress and get stuck there for 50 years and then suddenly solve it and continue forward.

So while it might not be possible, if it is we should be able to build it relatively quickly(within the next 50 years), if not then it probably isn't going to happen.

Edited by Alric, 04 May 2012 - 08:54 PM.

[MarcZ]

It seems very unlikely it will take that long. You have to remember that we are experiencing exponential growth in computing and many other technologies so we can make huge gains in a relatively short time period. It is predicted in like 30-40 years. If things go badly maybe 50-60 years. A lot of people believe if it hasn't happened by then it means our advances in technology has been seriously derailed. Maybe we hit a limit and the computers can no longer get any faster. If that happens though, then it seems unlikely that it will ever happen.

Which makes sense, if we hit a hard limit where we can't physically increase computers speed, then no amount of time is going to help solve that issue. It seems unlikely we will hit a bump that stops all progress and get stuck there for 50 years and then suddenly solve it and continue forward.

So while it might not be possible, if it is we should be able to build it relatively quickly(within the next 50 years), if not then it probably isn't going to happen.

It's possible but you have to unfaithfully believe in the accelerated returns argument, there are many people who argue that accelerated returns is not necessarily true. I'm sure you've read about singularity on the Wikipedia page where The Economist uses the argument because a razor-blade had one razor at the start of when humans began shaving and it has recently adopted two, then three in shorter time then the last, and four in shorter time, and five in even shorter time that this pattern will continue faster and faster towards infinity, which is silly. This may be true for computers as well, though currently we have no indication that it is. What is questionable however is not the power of the computers but their ability to simply come up and prove new mathematical reasoning that humans have not yet done. Which is why mathematicians will still have to make proofs of concepts and ideas and mathematics for a very long time in my opinion.

[MarcZ]

Also just a little off topic I found this article from 2004 about another of the Seven Millenium Problems known as The Riemann Hypothesis, which was also one of Hilbert's Problems which was the 23 problems which defined mathematical research of the 20th century and has been unsolved for nearly 150+ years, there are suggestions that it may be "close" to being solved though in the 8 years since this article was made it still has not been proved, but "close" is a subjective term in mathematics, Fermat's Last Theorem for example which was finally proved to be true in the 1990's was open for almost 400 years before being solved. Also fun to note that the Riemann Hypothesis which basically asks to explain the seemingly random distribution of prime numbers, may also cause major damage to encryption systems and financial security on the internet too. Though not to the same degree as P vs NP would. It should be noted that the The Riemann Hypothesis is the most famous unsolved problem in mathematics currently, and there is a lot of research going into it.

http://www.guardian....ucation.science

Edited by MarcZ, 04 May 2012 - 11:11 PM.

[Alric]

The razor thing is silly, and the reason is because it is entirely missing the point. The reason there is accelerating returns is because you use new technology to develop new technology. So you use a computer to design a new computer. That new computer is more powerful and so can design computers faster than the previous one. The computer you design using it, is even faster and better, and then you use that computer to build a newer better one.

In effect you are using better tools to build better tools. Since the newer tools are better that are always more efficient in some way. For accelerating return to stop, that means we are no longer building more efficient tools and stuck at whatever level we have at that moment.

That doesn't work with razor blades, because we don't use razor blades as a tool to improve our technology. Computers are used to make developing technology quicker, and so improvements in computers logically increases speed in development. So accelerating returns seems very logical to me.

Edited by Alric, 05 May 2012 - 12:30 AM.

[SG-1]

Alric thinks that computers are already conscious, so I can see why he would believe that a machine could come up with original ideas within our lifetime. Our lifetime being 80 years, disregarding the shot at immortality (I believe I should refer to immortality pessimistically until it is proven, but I have the highest hope for it).

I'm not a mathematician, but I do think that quantum computers will be able to create codes that will be unbreakable and they will be able to crunch anything thrown at it. Making a new math or finding solutions that we would not understand if we saw the answer to would not happen by the 2070s which is around where all of our lifespans are on this forum.

A

And who told you you will live only till 2070?(I'll be 78 years old by the time.)And who told you that everyone in the forum will live only the 2070's decade?How do you know that?Do you have any crystal ball that know exactly what will happen in the future ahahahahahah?

Please stay on topic. Also, as of NOW there is no cure for aging. Therefore, at THIS moment I will most likely live to be in my 80s. I also know that I am the among the youngest here. That most people here are in their mid 20s, therefore the average age people will live to here is around 2070. And I did all that math in my head with no crystal balls a...ha..ha

[MarcZ]

The razor thing is silly, and the reason is because it is entirely missing the point. The reason there is accelerating returns is because you use new technology to develop new technology. So you use a computer to design a new computer. That new computer is more powerful and so can design computers faster than the previous one. The computer you design using it, is even faster and better, and then you use that computer to build a newer better one.

In effect you are using better tools to build better tools. Since the newer tools are better that are always more efficient in some way. For accelerating return to stop, that means we are no longer building more efficient tools and stuck at whatever level we have at that moment.

That doesn't work with razor blades, because we don't use razor blades as a tool to improve our technology. Computers are used to make developing technology quicker, and so improvements in computers logically increases speed in development. So accelerating returns seems very logical to me.

I understand that concept of using tools to build better tools, however in the case of mathematics, tools which are different forms of mathematics like calculus and algebra, or when you get more up there like Ricci flow haven't been known to be developed by computers all of these have been developed by humans. Thus the question becomes can computers create mathematical tools or is the intuition and ability to create new mathematical types and tools something that only humans can do. As while machine learning and AI may allow a computer to learn and become what some may call intelligent it doesn't mean it allows the computer to become creative.

Edited by MarcZ, 05 May 2012 - 02:30 AM.

[CyberMisterBeauty]

Alric thinks that computers are already conscious, so I can see why he would believe that a machine could come up with original ideas within our lifetime. Our lifetime being 80 years, disregarding the shot at immortality (I believe I should refer to immortality pessimistically until it is proven, but I have the highest hope for it).

I'm not a mathematician, but I do think that quantum computers will be able to create codes that will be unbreakable and they will be able to crunch anything thrown at it. Making a new math or finding solutions that we would not understand if we saw the answer to would not happen by the 2070s which is around where all of our lifespans are on this forum.

A

And who told you you will live only till 2070?(I'll be 78 years old by the time.)And who told you that everyone in the forum will live only the 2070's decade?How do you know that?Do you have any crystal ball that know exactly what will happen in the future ahahahahahah?

Please stay on topic. Also, as of NOW there is no cure for aging. Therefore, at THIS moment I will most likely live to be in my 80s. I also know that I am the among the youngest here. That most people here are in their mid 20s, therefore the average age people will live to here is around 2070. And I did all that math in my head with no crystal balls a...ha..ha

You are right,you are the youngest I guess...You are 16 years old,I'm 20,Logically Irrational is 17,Craven is 26,Truthiness is 29,Caiman is 27,Dead Redshirt is 34 and Wjfox is 33 years old ehehehe...

[H3llion]

I am terrible at Math (besides multiplication, addition and substraction and possibly percentages) so I hope in future il have some sort of Mathematical implant in my brain so that I won't need a damn math degree :3

[MarcZ]

I am terrible at Math (besides multiplication, addition and substraction and possibly percentages) so I hope in future il have some sort of Mathematical implant in my brain so that I won't need a damn math degree :3

Lol, well that might help with the computation side of things.

[Saradus]

Alric thinks that computers are already conscious, so I can see why he would believe that a machine could come up with original ideas within our lifetime. Our lifetime being 80 years, disregarding the shot at immortality (I believe I should refer to immortality pessimistically until it is proven, but I have the highest hope for it).

I'm not a mathematician, but I do think that quantum computers will be able to create codes that will be unbreakable and they will be able to crunch anything thrown at it. Making a new math or finding solutions that we would not understand if we saw the answer to would not happen by the 2070s which is around where all of our lifespans are on this forum.

A

And who told you you will live only till 2070?(I'll be 78 years old by the time.)And who told you that everyone in the forum will live only the 2070's decade?How do you know that?Do you have any crystal ball that know exactly what will happen in the future ahahahahahah?

Please stay on topic. Also, as of NOW there is no cure for aging. Therefore, at THIS moment I will most likely live to be in my 80s. I also know that I am the among the youngest here. That most people here are in their mid 20s, therefore the average age people will live to here is around 2070. And I did all that math in my head with no crystal balls a...ha..ha

You are right,you are the youngest I guess...You are 16 years old,I'm 20,Logically Irrational is 17,Craven is 26,Truthiness is 29,Caiman is 27,Dead Redshirt is 34 and Wjfox is 33 years old ehehehe...

There's a lot of people in their 20s, that's cool I'm 22 just for reference!

[MarcZ]

Interesting new story related to one of the millennium problems the Riemann Hypothesis: http://phys.org/news...ties-prime.html

[MarcZ]

Hello folks just felt like posting this story to show you how primitive we still are in many fields such as mathematics: http://www.theaustra...6-1226368490521