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On July 15 2013 23:28 Reason wrote:Show nested quote +On July 15 2013 23:24 beg wrote:
well, i said "it has been said several times already. you need to prove this". what had been said several times already? that you have to make this proof for pi. yea, my language is a little loose there. thought it was clear in context.
i then gave an example of a non repeating infinite series not containing every set of integers. i dont see how this makes me fail to understand anything. When you bolded the wrong section of text your altered the context. If you hadn't bolded anything I would have assumed you were just talking about Pi, now that I'm looking at this in hindsight. The problem is you bolded the wrong section of my post, completely changing the context of what you said. The real problem comes when it takes pages to sort out what should have been a minor misunderstanding, you were not helpful in the slightest and had to have the same concepts explained to you over and over and over until finally you say "oh yeah, I understand what you're saying, obviously you don't understand what I'm saying" as if that is somehow acceptable. Show nested quote +On July 15 2013 22:26 Umpteen wrote:On July 15 2013 21:35 Reason wrote:
However, what reason do you have to believe that all the numbers aren't in there compared to any other random infinite non repeating sequence of integers?
Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated?
If so, why is the fact that Pi can be calculated so troubling in this regard? (Having huge fun here, btw; hope it's mutual  ) If a sequence is known to be truly random (each digit independent), we can be 'almost sure' it'll eventually yield any given sequence. We don't know that of Pi. It generates a sequence that 'measures well' in terms of randomness, but there are infinitely many sequences that would 'measure well' which exclude one or more possible subsequences. How do you estimate probability here? Hmm okay, yes been having lots of fun talking to you I actually thought you'd stopped responding to me and was a little sad. I guess your post was lost in the chaos there... How would you measure well for randomness?
Representation of digits in the sequence converging to equality. Association of each digit with preceding n digits also converging to equality for any given n (eg wherever you see 1234 in the sequence it's not followed by any specific digit more or less often than any other). I'm sure there are loads.
How likely is it that something could measure well for randomness but actually not be random? For every set that measures well for randomness but isn't actually random, how many more sets are there that measure well for randomness and are actually random?
I think it's more likely to be the other way around:
Take a random, non-repeating sequence S such that S contains every possible integer subsequence.
Let s be a specific subsequence of S.
In each instance of s in S, modify one digit at random to create S'
S' now does not contain s.
If s is a short sequence, that would probably affect the stats hugely. But if s is a trillion digits long then the effect of modifying each occurrence of it would require an impractical amount of analysis to detect.
Now, since S is defined as containing every possible integer subsequence, it follows that there are an infinite number of S' which can be generated from S, each lacking a specific subsequence and all of them measuring well for any given degree of analysis.
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On July 15 2013 23:50 Umpteen wrote:+ Show Spoiler +On July 15 2013 23:28 Reason wrote:Show nested quote +On July 15 2013 23:24 beg wrote:
well, i said "it has been said several times already. you need to prove this". what had been said several times already? that you have to make this proof for pi. yea, my language is a little loose there. thought it was clear in context.
i then gave an example of a non repeating infinite series not containing every set of integers. i dont see how this makes me fail to understand anything. When you bolded the wrong section of text your altered the context. If you hadn't bolded anything I would have assumed you were just talking about Pi, now that I'm looking at this in hindsight. The problem is you bolded the wrong section of my post, completely changing the context of what you said. The real problem comes when it takes pages to sort out what should have been a minor misunderstanding, you were not helpful in the slightest and had to have the same concepts explained to you over and over and over until finally you say "oh yeah, I understand what you're saying, obviously you don't understand what I'm saying" as if that is somehow acceptable. Show nested quote +On July 15 2013 22:26 Umpteen wrote:On July 15 2013 21:35 Reason wrote:
However, what reason do you have to believe that all the numbers aren't in there compared to any other random infinite non repeating sequence of integers?
Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated?
If so, why is the fact that Pi can be calculated so troubling in this regard? (Having huge fun here, btw; hope it's mutual ) If a sequence is known to be truly random (each digit independent), we can be 'almost sure' it'll eventually yield any given sequence. We don't know that of Pi. It generates a sequence that 'measures well' in terms of randomness, but there are infinitely many sequences that would 'measure well' which exclude one or more possible subsequences. How do you estimate probability here? Hmm okay, yes been having lots of fun talking to you I actually thought you'd stopped responding to me and was a little sad. I guess your post was lost in the chaos there... How would you measure well for randomness? Representation of digits in the sequence converging to equality. Association of each digit with preceding n digits also converging to equality for any given n (eg wherever you see 1234 in the sequence it's not followed by any specific digit more or less often than any other). I'm sure there are loads. How likely is it that something could measure well for randomness but actually not be random? For every set that measures well for randomness but isn't actually random, how many more sets are there that measure well for randomness and are actually random? I think it's more likely to be the other way around: Take a random, non-repeating sequence S such that S contains every possible integer subsequence. Let s be a specific subsequence of S. In each instance of s in S, modify one digit at random to create S' S' now does not contain s. If s is a short sequence, that would probably affect the stats hugely. But if s is a trillion digits long then the effect of modifying each occurrence of it would require an impractical amount of analysis to detect. Now, since S is defined as containing every possible integer subsequence, it follows that there are an infinite number of S' which can be generated from S, each lacking a specific subsequence and all of them measuring well for any given degree of analysis.
Can we conclude from this the probability of Pi actually being random, despite everything we've observed, is 0 (almost surely not)? 
It seems strange that general consensus is that it's random if such a notion can be so easily dismissed.
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It's not possible to deduce the randomness of a (non repeating) infinite sequence by analyzing a finite subsequence, as far as I know...
That said, "almost every" real number is apparently normal in base 10, so it would be very interesting if pi weren't, although it's never been proven (proving normality is pretty tough).
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On July 15 2013 23:58 Reason wrote:Show nested quote +On July 15 2013 23:50 Umpteen wrote:+ Show Spoiler +On July 15 2013 23:28 Reason wrote:Show nested quote +On July 15 2013 23:24 beg wrote:
well, i said "it has been said several times already. you need to prove this". what had been said several times already? that you have to make this proof for pi. yea, my language is a little loose there. thought it was clear in context.
i then gave an example of a non repeating infinite series not containing every set of integers. i dont see how this makes me fail to understand anything. When you bolded the wrong section of text your altered the context. If you hadn't bolded anything I would have assumed you were just talking about Pi, now that I'm looking at this in hindsight. The problem is you bolded the wrong section of my post, completely changing the context of what you said. The real problem comes when it takes pages to sort out what should have been a minor misunderstanding, you were not helpful in the slightest and had to have the same concepts explained to you over and over and over until finally you say "oh yeah, I understand what you're saying, obviously you don't understand what I'm saying" as if that is somehow acceptable. Show nested quote +On July 15 2013 22:26 Umpteen wrote:On July 15 2013 21:35 Reason wrote:
However, what reason do you have to believe that all the numbers aren't in there compared to any other random infinite non repeating sequence of integers?
Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated?
If so, why is the fact that Pi can be calculated so troubling in this regard? (Having huge fun here, btw; hope it's mutual ) If a sequence is known to be truly random (each digit independent), we can be 'almost sure' it'll eventually yield any given sequence. We don't know that of Pi. It generates a sequence that 'measures well' in terms of randomness, but there are infinitely many sequences that would 'measure well' which exclude one or more possible subsequences. How do you estimate probability here? Hmm okay, yes been having lots of fun talking to you I actually thought you'd stopped responding to me and was a little sad. I guess your post was lost in the chaos there... How would you measure well for randomness? Representation of digits in the sequence converging to equality. Association of each digit with preceding n digits also converging to equality for any given n (eg wherever you see 1234 in the sequence it's not followed by any specific digit more or less often than any other). I'm sure there are loads. How likely is it that something could measure well for randomness but actually not be random? For every set that measures well for randomness but isn't actually random, how many more sets are there that measure well for randomness and are actually random? I think it's more likely to be the other way around: Take a random, non-repeating sequence S such that S contains every possible integer subsequence. Let s be a specific subsequence of S. In each instance of s in S, modify one digit at random to create S' S' now does not contain s. If s is a short sequence, that would probably affect the stats hugely. But if s is a trillion digits long then the effect of modifying each occurrence of it would require an impractical amount of analysis to detect. Now, since S is defined as containing every possible integer subsequence, it follows that there are an infinite number of S' which can be generated from S, each lacking a specific subsequence and all of them measuring well for any given degree of analysis. Can we conclude from this the probability of Pi actually being random, despite everything we've observed, is 0 (almost surely not)? It seems strange that general consensus is that it's random if such a notion can be so easily dismissed.
That's because I'm almost sure I'm wrong :D
Yeah, turns out I am, although I'm fucked if I understand why.
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Yeah that's wayyyyy over my head.
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Well, every positive number is the product of two normal numbers (afaik) so even if pi isn't normal, we should be able to find an equally pathological normal number.
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Pi cant be a normal number,The secuence "Pi minus the last digit of pi" can be found once in the sequence and no other sequences with equall lenght as pi minus the last digit of pi can occur.
Or is this a realy silly way of looking at it lol?
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On July 16 2013 01:40 Rassy wrote:
Pi cant be a normal number,The secuence "Pi minus the last digit of pi" can be found once in the sequence and no other sequences with equall lenght as pi minus the last digit of pi can occur.
Or is this a realy silly way of looking at it lol?
Well, given that the sequence of digits of pi is infinite there is no 'last' digit of pi...
I'll leave it up to you to judge whether your proposal was silly though! Cheers!
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On July 16 2013 01:40 Rassy wrote:
Pi cant be a normal number,The secuence "Pi minus the last digit of pi" can be found once in the sequence and no other sequences with equall lenght as pi minus the last digit of pi can occur.
Or is this a realy silly way of looking at it lol?
You should submit this to a mathematics paper if you're so sure of yourself.
Determining the normality of any given number is usually pretty difficult, from what I understand. There's no real intuitive way to show that the distribution of all k length digit sequences in pi are equally likely.
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Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen :
+ Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
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United Kingdom13775 Posts
On July 16 2013 02:39 corumjhaelen wrote:Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen : + Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
That is not how mathematics works.
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On July 16 2013 02:44 LegalLord wrote:Show nested quote +On July 16 2013 02:39 corumjhaelen wrote:Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen : + Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
That is not how mathematics works.
Really ? I'm like, really really surprised.
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On July 16 2013 02:39 corumjhaelen wrote:Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen : + Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
I like.
In all seriousness though what does this whole conversation about integer subsequences in pi have to do with anything? And why are people making assertions that they seem to be 100% sure of while simultaneously saying they don't even study the field?
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United Kingdom13775 Posts
On July 16 2013 03:00 corumjhaelen wrote:Show nested quote +On July 16 2013 02:44 LegalLord wrote:On July 16 2013 02:39 corumjhaelen wrote:Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen : + Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
That is not how mathematics works. Really ? I'm like, really really surprised.
Not finding a proof yet does not imply that such a proof does not exist. Sometimes it does in physics, but never in mathematics.
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On July 16 2013 03:10 LegalLord wrote:Show nested quote +On July 16 2013 03:00 corumjhaelen wrote:On July 16 2013 02:44 LegalLord wrote:On July 16 2013 02:39 corumjhaelen wrote:Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen : + Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
That is not how mathematics works. Really ? I'm like, really really surprised. Not finding a proof yet does not imply that such a proof does not exist. Sometimes it does in physics, but never in mathematics.
Tell me more. Are you romanian ?
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So now were talking about pi, what did you guys think of The Life of Pi?
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On July 16 2013 03:05 wherebugsgo wrote:Show nested quote +On July 16 2013 02:39 corumjhaelen wrote:Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen : + Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
I like. In all seriousness though what does this whole conversation about integer subsequences in pi have to do with anything? And why are people making assertions that they seem to be 100% sure of while simultaneously saying they don't even study the field?
Well, if you'd been following this thread you'd know it was because of this post
On July 15 2013 11:52 Shiori wrote:Show nested quote +On July 15 2013 10:53 oneofthem wrote:
the biology is simple. if it's not simple, ie the brain is chemical and electricity plus gravity and particle X, then the thread would probably be changed to "is the mind all chemical and electricity plus gravity and particle X." Speaking of simplicity, I had a thought: As pi is an irrational number which is non-repeating and doesn't have any (as proved by mathematics up to this point) non-random distribution of digits, one could map every piece of information in the universe to distinct sequences contained in pi (one could actually encode all information in the universe in pi by this kind of method, totally hypothetically, but that doesn't matter). By this metric, pi is more complex (i.e. less simple) than anything in the universe, and is more complex than the entire physical universe in the sense of all the facts about energy/matter that exist pertaining to the universe (discovered or undiscovered) because there will always be an infinite number of unused sequences (given that energy is always conserved and the universe is finite implies that we can get a pretty meaningful representation of the information in the universe using finitely many elements). But think of it this way: find any circle, anywhere, be it in your mind or on a piece of paper. Pi is the circumference of that circle divided by the diameter of that circle. Every damn time. So from that point of view, it's simple and complex ^.^. I know it's not a bulletproof analogy since this idea would require a super-complex system to assign things to different sequences and identify them etc. etc., but it's cool to think about... ><
I don't think anybody is guilty of making assertions that they can't back up or they didn't qualify with "this is probably wrong" so I'm not sure what you meant by your last comment.
The actual on topic discussion has come to an end for the most part though.
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On July 16 2013 03:11 corumjhaelen wrote:Show nested quote +On July 16 2013 03:10 LegalLord wrote:On July 16 2013 03:00 corumjhaelen wrote:On July 16 2013 02:44 LegalLord wrote:On July 16 2013 02:39 corumjhaelen wrote:Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen : + Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
That is not how mathematics works. Really ? I'm like, really really surprised. Not finding a proof yet does not imply that such a proof does not exist. Sometimes it does in physics, but never in mathematics. Tell me more. Are you romanian ?
Are you implying that every single proof possible to verify in polynomial time have been found yet ? Even if a program can verify a proof in a polynomial time, you still have to write and find this program.
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On July 16 2013 03:24 DertoQq wrote:Show nested quote +On July 16 2013 03:11 corumjhaelen wrote:On July 16 2013 03:10 LegalLord wrote:On July 16 2013 03:00 corumjhaelen wrote:On July 16 2013 02:44 LegalLord wrote:On July 16 2013 02:39 corumjhaelen wrote:Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen : + Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
That is not how mathematics works. Really ? I'm like, really really surprised. Not finding a proof yet does not imply that such a proof does not exist. Sometimes it does in physics, but never in mathematics. Tell me more. Are you romanian ? Are you implying that every single proof possible to verify in polynomial time have been found yet ? Even if a program can verify a proof in a polynomial time, you still have to write and find this program.
It was a joke and you are taking it seriously
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EPT
