Looking for an interesting challenge

[Knotted]

Not exactly. If some day it was proven right or wrong that outcome would still be a human invented solution for a problem proposed by means of a human construct (mathematics). The solution of such a problem is not knowledge, but it can count as the suggestion thereof, constructed by and limited to human perception by default.

salaam.

I was thinking of the question of the probability that it is true not the question whether the conjecture is true. The question was really about the nature of probability.

Is that a question of human construct?

Its a question which seems elusive - what calculation do we make to work out the probability? But is its elusiveness due to it being out of reach or is it merely a meaningless question? (I think the latter.)

This genuinely interests me.

 

[Aldebaran]

Good for you, I don't and I'm always surprising myself

That is not quite the same as recognizing its limitations.

a) IQ is only a measure of a specific function, it is not a measure of limitation.
b) maybe now, we have no way of telling what the human brain is capable of in the future.

a) In fact it demonstrates limitations of all kinds more than it demonstrates abilities.
b) As long as we stay the species we are, no human shall be able to reason beyond innate human limitations.

BTW Alderbaran your argument comes across as extremely defeatist.

"I have found my limitations, it does not explain enough, so I will turn to god."

My argumentation has nothing to do with any of that. There is no need for belief in God to recognize human limitations. Anyone who thinks there are no limits to what human brains are capable off lives in a fantasy floating on wishful thinking.

salaam.

 

[Aldebaran]

I'm a statistician - I don't approve of certainty at all.

Statistics are pure horror for me.

I'm also of the opinion that you cannot learn without being wrong. I understand the desire to know, and to be right (in case you hadn't noticed ), but on an intellectual level, certainty is a complete dead-end.

Depends on which level we are talking about certainty.
For example my certitude that my brain (and perception of the world, which depends on it and influences it both) is limited does not prevent me from exploring where these boundaries are. I'm sure I haven't found the limits of mine yet, but I'm not sure I shall find them before my brain functions undergo the biological effects of aging, which up to now nobody can escape.

So what did you actually mean by that post if your conclusions have nothing to do with science? How can you talk about the order and beauty of the universe and our inevitable inability to ever understand all of it without discussing science?

I don't need science or scientists to observe and reflect on my observations. If science has contributed, it is support of my conclusions and I have no doubt science shall continue to do so.

I know you have no clue where it comes from - I'm talking about hypotheses and you're talking about Truth. They're not compatible discourses - which is exactly what I'm objecting to.

I'm not talking about Truth. There is no such thing possible in human understanding.

Hypotheses are testable - if they fail the test they're rejected; if they pass the test the new knowledge is used to make further testable hypotheses. It's an infinite process. You can't just read a few books, scratch your head and conclude that it's all a bit complicated so it must be God after all. Not if you're also claiming to bring science into it, anyway.

This makes no sense to me for reason that you obviously can't step outside a certain amount of prejudice, induced by your knowledge that I believe in God. It is limiting your view and the way you read my posts. Therefore you fail to understand that I don't need to be religious to write them.

I don't have any problem whatsoever with your faith - just the (apparent) attempt to put it in a scientific context and claim it as evidence- rather than faith-based.

I don't do any of that.

salaam.

 

[ymu]

I was thinking of the question of the probability that it is true not the question whether the conjecture is true. The question was really about the nature of probability.

Is that a question of human construct?

Its a question which seems elusive - what calculation do we make to work out the probability? But is its elusiveness due to it being out of reach or is it merely a meaningless question? (I think the latter.)

This genuinely interests me.

Even if you could build a reasonable model (which I doubt), you'd never be able to populate it with any meaningful parameters - and it'd be so complex God or science or both would have given up on us by the time there was any output.

You could try a Bayesian approach - essentially weighting hypotheses by their plausibility - but Bayesian approaches are absolutely useless for proving anything to people with stubborn priors - ie Theists and A-Theists. This is because they assign a prior probability of zero to their being wrong - so the posterior probability that they are right will always be 1 from their perspective.

Any individual (or cohesive group) is theoretically able to determine their own estimated probabilities - in much the same way a professional gambler does - but these are based on their personal degree of doubt and have no simple relationship to reality.

 

[Aldebaran]

I was thinking of the question of the probability that it is true not the question whether the conjecture is true. The question was really about the nature of probability.

Ah, OK. Much more interesting

Is that a question of human construct?

I would see probability as standing on itself, but interpretations and applications inevitably are of human construct.
Which partially answers your next question

Its a question which seems elusive - what calculation do we make to work out the probability? But is its elusiveness due to it being out of reach or is it merely a meaningless question? (I think the latter.)

As soon as you want to apply probability and thus make it visible, it looks as if you need to calculate its possible appearance too. I don't think that is a correct reasoning because it limits probability and hence it is no longer a probability but a given.
(and I hope I have here a correct understand of the English word "probability" and what it means to you. Language is a difficult tool.)

salaam.

 

[ymu]

I would see probability as standing on itself, but interpretations and applications inevitably are of human construct.

Correct. Gold star.

As soon as you want to apply probability and thus make it visible, it looks as if you need to calculate its possible appearance too. I don't think that is a correct reasoning because it limits probability and hence it is no longer a probability but a given.
(and I hope I have here a correct understand of the English word "probability" and what it means to you. Language is a difficult tool.)

I'm not sure what you mean here - it might be language, it might be stats.

You do have to assign a value to a probability in order to make predictions based on it - but the prediction does not then consist of a simple yes/no answer - it comes in the form of a probability of a particular event occurring, or a probability distribution calculated over all possible outcomes.

Statistics is not about certainty - it's about establishing the reasonable limits of our certainty. It's the science that underpins experiment.

Say you claim to have discovered a miracle cure for cancer and show me evidence that 3 people recovered when you gave it to them - I'll laugh at you and write nasty articles about you until you stop being reckless with peoples' lives. Show me evidence that 200 out of 400 recovered when only 120 out of 400 recovered on the conventional treatment, and I'll think about doing a confirmatory trial.

By the way, even if my second trial confirmed the initial result, we'd still be only around 97% confident that it was correct.

 

[max_freakout]

I think that what we perceive is not even a fraction of what really exists.

salaam.

there are ways to reduce perceptual fılters, and thereby expand perceptual awareness

 

[Cid]

I know the limitations of my brain. Doesn't function differently from others.



a) Experts in the field have also no idea of my IQ. Does that mean it is unlimited? mmm... Nice
b) No need to think about God to recognize human limitations. They are self-explained by humanity.

salaam.

How fast can the human mind calculate? Not very... and yet we have designed a computer that can perform a petaflop, that's more than 1.026 quadrillion calculations per second, and the rate our technology progresses is staggering. We have built the capacity to perform far outside of the limits of 'nature', who knows what advances will occur within the next 100 years?

 

[Knotted]

I would see probability as standing on itself, but interpretations and applications inevitably are of human construct.
Which partially answers your next question

Can't agree with that, but I'm not going to argue at this point.

As soon as you want to apply probability and thus make it visible, it looks as if you need to calculate its possible appearance too. I don't think that is a correct reasoning because it limits probability and hence it is no longer a probability but a given.
(and I hope I have here a correct understand of the English word "probability" and what it means to you. Language is a difficult tool.)

salaam.

I don't think there is a correct understanding of "probability"! I would assume that a probability is some sort of quantified likelihood.

I want to outline why it is very tempting to say that GC is "almost certainly true". Its easy to verify it and its extremely easy to check it up to huge numbers using modern computers. So on a crude inductive principle it looks true. But more than that, there are more and more ways to find two primes to add up to an even number the larger that even number, so it seems less and less likely that a counter example will be found. That's a rule of thumb of course and not a uniform tendency, but after a while it becomes almost inconceivable that a counter example will be found.

But at the same time it feels very odd talking about the likelihood of a mathematical conjecture. This isn't because the conjecture is either just true or false, but the type of calculation you should perform to work out the probability of it being true or false from our current knowledge is just as up in the air as the conjecture itself.

I could put it this way - I would certainly recommend trying to prove it over trying to disprove it, but at the same time its quite possible that it will never be proved or disproved. What sort of recommendation would that be?

Mathematician's existential angst.

 

[ymu]

Can't agree with that, but I'm not going to argue at this point.



I don't think there is a correct understanding of "probability"! I would assume that a probability is some sort of quantified likelihood.

I want to outline why it is very tempting to say that GC is "almost certainly true". Its easy to verify it and its extremely easy to check it up to huge numbers using modern computers. So on a crude inductive principle it looks true. But more than that, there are more and more ways to find two primes to add up to an even number the larger that even number, so it seems less and less likely that a counter example will be found. That's a rule of thumb of course and not a uniform tendency, but after a while it becomes almost inconceivable that a counter example will be found.

But at the same time it feels very odd talking about the likelihood of a mathematical conjecture. This isn't because the conjecture is either just true or false, but the type of calculation you should perform to work out the probability of it being true or false from our current knowledge is just as up in the air as the conjecture itself.

I could put it this way - I would certainly recommend trying to prove it over trying to disprove it, but at the same time its quite possible that it will never be proved or disproved. What sort of recommendation would that be?

Mathematician's existential angst.

Sorry - forgot you were interested in the GC thing and answered you re: the Big Bang.

I'm a crappy mathematician but a decent statistician, and I don't think stats is compatible with proving a mathematical conjecture because it has to be proved axiomatically true to become a theorem - that's the nature of maths. Stats is just a set of ideas which are easier to express in Maths than English. There's no such thing as certainty in statistics.

I doubt you could even get a reliable estimate of the probability that it isn't true. To extrapolate from the observed to the unobserved, we have to be reasonably confident that the observed measurements are representative of the unobserved measurements. In GC we know that isn't true, so we can't apply the most basic assumption required for the results of any statistical calculations to be valid.

 

[Knotted]

Sorry - forgot you were interested in the GC thing and answered you re: the Big Bang.

I'm a crappy mathematician but a decent statistician, and I don't think stats is compatible with proving a mathematical conjecture because it has to be proved axiomatically true to become a theorem - that's the nature of maths. Stats is just a set of ideas which are easier to express in Maths than English. There's no such thing as certainty in statistics.

You can calculate a probability with certainty. In real life this involves making assumptions, but once they are made then can proceed with mathematical certainty. Having said that I appreciate that non-parametric stats is more of an art than a science. (Probability ignoring conditional probability is just a branch of measure theory).

I doubt you could even get a reliable estimate of the probability that it isn't true. To extrapolate from the observed to the unobserved, we have to be reasonably confident that the observed measurements are representative of the unobserved measurements. In GC we know that isn't true, so we can't apply the most basic assumption required for the results of any statistical calculations to be valid.

That's right. Its also problematic that we are looking at an infinite range of numbers.

There is a deeper philosophical point. Is GC true or false at all when it has not been proven? Is the truth of a mathematical theorem anything other than the proof that it is true? On a intuitionist or constructivist account, then it would make no sense to test whether as a statistical hypothesis it is true.

But I would still say that I think it is more likely that the GC will proven than that it will be disproven.

I just love the way the mathematician relates to mathematics is beyond quantification. That's the real magic of the subject.

 

[ymu]

You can calculate a probability with certainty. In real life this involves making assumptions, but once they are made then can proceed with mathematical certainty.

Do please explain how. We've been working on how to get rid of chance for centuries now and we haven't got as far as you.

I know the precise probability of rolling a 6 with a fair die - but it's not a terribly interesting thing to experiment with. We already know the true underlying probability, so why would I waste my time? If you can't measure it directly, you have to estimate it - and that's where Lady Luck steps in to fuck us over.

Having said that I appreciate that non-parametric stats is more of an art than a science.

No, and even if it was yes it would be the other way around. Non-parametric methods require fewer assumptions than parametric methods, and are generally preferable, but they are sometimes more awkward to work with or less appropriate for some reason. Most real world applications involve a mixture of the two - non-parametric to get the estimate then invoke the Central Limit Theorem to get a confidence interval. That's where Aldebaran's comment about subjectivity comes in - the result you get depends on the question you asked, and stats is good at asking lots of subtly different questions.

Both approaches are affected by the play of chance. If they weren't, it wouldn't be statistics - it'd be maths.

That's right. Its also problematic that we are looking at an infinite range of numbers.

There is a deeper philosophical point. Is GC true or false at all when it has not been proven? Is the truth of mathematical theorem anything other than the proof that they are true? On a intuitionist or constructivist account, then it would make no sense to test whether as a statistical hypothesis it is true.

But I would still say that I think it is more likely that it will proven than that it will be disproven.

I just love the way the mathematician relates to mathematics is beyond quantification. That's the real magic of the subject.

Ask Schroedinger? He'll say "Nah man - my cat could have been alive or dead, but your conjecture was only ever true or false."

You can assign a probability based on your knowledge and experience - exactly the same way a professional gambler does - but that number only reflects your view of reality; it's not the kind of probability that can kill a cat.

 

[Knotted]

Do please explain how. We've been working on how to get rid of chance for centuries now and we haven't got as far as you.

I'm not a statistician (but my other half is) and I don't want to lecture you on your proffession. What I mean is that statistics is as inherently uncertain as applied mathematics. Both deal with the uncertainties of the real world. Just because statistics deals with probabilities does not make it less certain.

Ask Schroedinger? He'll say "Nah man - my cat could have been alive or dead, but your conjecture was only ever true or false."

I think Schroedinger didn't even think that the cat was in a superposition of alive and dead. He was trying to show the absurdities of such a view.

Its possible he would have said the reverse of what you say!

You can assign a probability based on your knowledge and experience - exactly the same way a professional gambler does - but that number only reflects your view of reality; it's not the kind of probability that can kill a cat.

That's what I think. But the conjecture isn't about a reality. Its about a proof that nobody has yet made.

 

[Aldebaran]

I'm not sure what you mean here - it might be language, it might be stats.

I'm not talking about statistics, I'm looking at it in a very general sense. In that context there is no need for a specific value being attributed to probability.

You do have to assign a value to a probability in order to make predictions based on it - but the prediction does not then consist of a simple yes/no answer - it comes in the form of a probability of a particular event occurring, or a probability distribution calculated over all possible outcomes.

Perfect example of a case where probability is no longer a probability but a constructed given that has no longer the freedom a probability should have to be a probability.

salaam.

 

[Aldebaran]

Can't agree with that, but I'm not going to argue at this point.

I would like to discuss it though. Why don't you agree?

I don't think there is a correct understanding of "probability"! I would assume that a probability is some sort of quantified likelihood.

I would see it as only a likelihood unlimited in its likeliness with the freedom to quantify itself or not. In my view view a pure probability can't be externally quantified because of the inherent limitation coming with it. Once you attribute a limiting factor you don't have a probability, but a factor of a calculation.

The most logical approach if the GC would be that it is true, but I find reasoning within the pre-set frames of logic far too limiting.

But at the same time it feels very odd talking about the likelihood of a mathematical conjecture. This isn't because the conjecture is either just true or false, but the type of calculation you should perform to work out the probability of it being true or false from our current knowledge is just as up in the air as the conjecture itself.

Exactly.
I always found mathematics that fascinating that it scares me too much to get into it. There are not many things I avoid but I do avoid that as if it brings the plague. It is a subject that would drive me straight to the madhouse (and that is not because Dyslex plays games on that filed too, although it was always my excuse to be a half-idiot when it comes to mathematics).

salaam.

 

[Knotted]

I would like to discuss it though. Why don't you agree?

Basically I don't believe that you can define probability the way you are doing (though I'm not entirely sure what you are doing). See below.

I would see it as only a likelihood unlimited in its likeliness with the freedom to quantify itself or not. In my view view a pure probability can't be externally quantified because of the inherent limitation coming with it. Once you attribute a limiting factor you don't have a probability, but a factor of a calculation.

I think the word "externally" here is crucial to understanding what you are saying. Perhaps given a certain amount of knowledge that a mathematician has of the problem then there is a certain probability from her (the mathematician's) point of view that the conjecture is true. The only problem is that it is impossible to calculate this probability.

But if she does calculate the probability using various assuming various facts and idealisations and using various methods, then this is not an interpretation. This is a real calculation and even if there is a large degree of arbitrariness to it, it is the only type of thing that we can concretely talk about when we are talking about probability. Though having said that there are more vague notions of likelihood and judgements that we can use.

My view is that there is not necessarily a probability at all. Its a bit like asking what the length of the coast of Britain is. To measure it depends on how accurate you are but a great deal more accuracy means you have a much larger figure. If we get more and more careful we don't get nearer and nearer the true figure.

The most logical approach if the GC would be that it is true, but I find reasoning within the pre-set frames of logic far too limiting.


Exactly.
I always found mathematics that fascinating that it scares me too much to get into it. There are not many things I avoid but I do avoid that as if it brings the plague. It is a subject that would drive me straight to the madhouse (and that is not because Dyslex plays games on that filed too, although it was always my excuse to be a half-idiot when it comes to mathematics).

salaam.

Perhaps you shouldn't fear it. You overcome the limits when you find them.

 

[Knotted]

I've got to apologise. I missed this post.

Even if you could build a reasonable model (which I doubt), you'd never be able to populate it with any meaningful parameters - and it'd be so complex God or science or both would have given up on us by the time there was any output.

Good point.

You could try a Bayesian approach - essentially weighting hypotheses by their plausibility - but Bayesian approaches are absolutely useless for proving anything to people with stubborn priors - ie Theists and A-Theists. This is because they assign a prior probability of zero to their being wrong - so the posterior probability that they are right will always be 1 from their perspective.

I would think that a Bayesian approach is the only one with any hope, but even then I don't think it would really say anything. I'm glad you mentioned it, though.

Any individual (or cohesive group) is theoretically able to determine their own estimated probabilities - in much the same way a professional gambler does - but these are based on their personal degree of doubt and have no simple relationship to reality.

I presume you are talking about a Bayesian approach still.

I tend to think that the philosophy behind Bayesianism is incoherent. What does it mean to quantify our doubt by only looking at our doubt?

Whether it is useful or not as a method is another question, though.

 

[Knotted]

I'm a crappy mathematician but a decent statistician, and I don't think stats is compatible with proving a mathematical conjecture because it has to be proved axiomatically true to become a theorem - that's the nature of maths. Stats is just a set of ideas which are easier to express in Maths than English. There's no such thing as certainty in statistics.

I'll reply to this again - I think you are mistaken about maths rather than statistics.

I think that mathematics has genuine uncertainties. Once the mathematician has finished the job and everything is proven then everything is certain.

But during the actual work everything is completely uncertain. You might be flying down a blind alley - you usually are. But you can still judge what strategy is best. Is that judgement quantifiable? I think not - but this in itself is a judgement that I can't quantify.

 

[ymu]

I'll reply to this again - I think you are mistaken about maths rather than statistics.

I think that mathematics has genuine uncertainties. Once the mathematician has finished the job and everything is proven then everything is certain.

But during the actual work everything is completely uncertain. You might be flying down a blind alley - you usually are. But you can still judge what strategy is best. Is that judgement quantifiable? I think not - but this in itself is a judgement that I can't quantify.

Sure, but we're talking about different types of (un)certainties.

A conjecture becomes a theorem when it's truth is certain; any uncertainty to that point is due to a lack of proof and is fundamentally unmeasurable. If, however, we're trying to estimate something about a population we can only ever measure this with error - our sample may or may not be representative of the population, and our measurements can only be made to a given degree of accuracy. Statistics is about quantifying and compartmentalising that error in order to determine how uncertain we are about the true value.

There's no problem with Bayesian approaches - you have to use them sometimes. The controversy is largely manufactured by academics trying to make a living - Frequentist vs Bayesian is a bit of a false dichotomy.

 

[Knotted]

Sure, but we're talking about different types of (un)certainties.

I'm not sure its quite as different as you think. There can be uncertainties even when a theorem is proven in mathematics - say if it relies on the axiom of choice. It can depend on the foundational assumptions you make. Just as in statistics it depends on the assumptions, the sample and methods, but you still come out with definite answers (even if the answers are error bounds).

Of course the emphasis is very different.

 

[fractionMan]

I find the possibility and implications of true artificial intelligence fascinating. Will we create our own 'gods'?

 

[Aldebaran]

Basically I don't believe that you can define probability the way you are doing (though I'm not entirely sure what you are doing).

Probability on itself exists without the need for it to be placed in context of human constructions or ideas. It occurs inevitable - as itself within and from within - because nothing is ever perfect,
That is why I said: I would see probability as standing on itself, but interpretations and applications inevitably are of human construct.

I can be wrong, but it seems to me that a probability only occurs as being its own likelihood and only receives a human defined value because captured and placed within a human perception.

I think the word "externally" here is crucial to understanding what you are saying.

Yes, of course.
Otherwise inevitably you think about probability in context of whatever application you have in mind, like in your case here: mathematics.
Your approach is to make a practical use of it, mine is only reflecting purely on its existence.

To take your example of measuring the coast:I don't think that is a correct reasoning you follow because if in the end you have all the necessary accuracy in your larger and larger figures until there isn't anything to better left, you get the true figure.
Nevertheless the probability still exists that even while you are writing that outcome down and declare the problem solved, something happens (if only a piece of rock falling down and swept away by a wave) and there you can start all over again. Such is even very likely to happen.

Perhaps you shouldn't fear it. You overcome the limits when you find them.

I don't think mathematics has limits. I get already half mad when I listen to Bach for too long.

salaam.

 

[Aldebaran]

I find the possibility and implications of true artificial intelligence fascinating. Will we create our own 'gods'?

No, because AI shall always depend on humans to be created, even if AI starts to create AI. Without humans, no AI.

salaam.

 

[fractionMan]

No, because AI shall always depend on humans to be created, even if AI starts to create AI. Without humans, no AI.

salaam.

Putting the idea that gods are also creators, I still think the possibility of advanced AI is interesting. Could we create something that becomes near omnipotent?

 

[max_freakout]

human beıngs ARE AI!

 

[Knotted]

Probability on itself exists without the need for it to be placed in context of human constructions or ideas. It occurs inevitable - as itself within and from within - because nothing is ever perfect,
That is why I said: I would see probability as standing on itself, but interpretations and applications inevitably are of human construct.

I can be wrong, but it seems to me that a probability only occurs as being its own likelihood and only receives a human defined value because captured and placed within a human perception.

I'm not sure if you can be wrong because I'm not sure if you can be right. I don't know what it is you are referring to.

But at the same time I think I understand what you are saying. Its more that I just don't have a taste for inneffable concepts.

I don't think mathematics has limits. I get already half mad when I listen to Bach for too long.

salaam.

I know what you mean.

 

[Aldebaran]

Putting the idea that gods are also creators, I still think the possibility of advanced AI is interesting. Could we create something that becomes near omnipotent?

I don't see AI ever capable to be uncreated and to create a universe.
Secondly, it is depending on human invention and intervention to be created itself.
Maybe AI can be brought to see humans as gods.
AI & Creationists, the New Future

salaam.

 

[DotCommunist]

Putting the idea that gods are also creators, I still think the possibility of advanced AI is interesting. Could we create something that becomes near omnipotent?

Perfect AI's always Sublime.

 

[Aldebaran]

But at the same time I think I understand what you are saying. Its more that I just don't have a taste for inneffable concepts.

I described clearly enough though (well.. I think I did).

If probability occurs it is because it independently exists as itself = being its own likelihood. Otherwise it would be merely human construct, which obviously it is not.

salaam.

 

[DotCommunist]

I don't see AI ever capable to be uncreated and to create a universe.
Secondly, it is depending on human invention and intervention to be created itself.
Maybe AI can be brought to see humans as gods.
AI & Creationists, the New Future

salaam.

What a repugnant idea. AI, true AI should be accorded the status equal to basic human rights. Anything else is slavery.