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On July 15 2013 20:07 Reason wrote:Show nested quote +On July 15 2013 20:02 MiraMax wrote:On July 15 2013 19:48 Umpteen wrote:On July 15 2013 19:37 MiraMax wrote:I am afraid that your proof is not only lazy, but rather barely coherent  If pi were to contain all integer sequences of finite length and each/any state of the universe at time t could be represented by a finite sequence of integers, then yes, pi would by necessity contain the coded state of the universe at (any) time t, i.e. your proof fails. No, there's a problem but that isn't it  You're correct that if Pi contains all finite integers, and n is a finite integer encoding the state of the universe, then Pi contains n. No argument there. However, the claim was that *any* key/language could be used to generate the universe from Pi. While it's trivially true that any key capable of generating the state of the universe from an integer n can generate it from a subsequence of Pi (since we're assuming Pi contains all possible n), it's not the case that we can feed THE WHOLE OF Pi into any old key and get the universe. Pi is infinite, the universe is not, therefore feeding Pi into a key would also generate a whole bunch of stuff that isn't in the universe - unless the key itself incorporates the sequence it needs to recognise, which means we're not really using Pi at all. The key only needs to know the starting index (seed) of the subsequence and could start to generate the universe from there. It is a well-known result that normal numbers can be used to encode any piece of information that can be represented by finite sequences and that it works for any decoding scheme that uses finite sequences, so please let's not discuss this any further. Sorry for derailing You're not derailing, your contribution is very much appreciated! Please continue to comment and explain without asking people not to discuss the matter, this is much more interesting than the previous discussion...
Well, here it goes then: Statistical tests on the distribution of pi's digits do indeed suggest that pi is normal, plus there is a well known theorem of number theory that suggests that almost all real number are normal. So there is some pretty strong evidence, but no conclusive proof yet. For your visual joy you can see a graphical representation of the first 100 billion digits of pi (to base 4) that are statistically equivalent to a random walk:
Pi's Digits
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On July 15 2013 20:17 Reason wrote:Show nested quote +On July 15 2013 20:17 DertoQq wrote:On July 15 2013 20:15 CoughingHydra wrote:On July 15 2013 20:07 Reason wrote:On July 15 2013 20:02 MiraMax wrote:On July 15 2013 19:48 Umpteen wrote:On July 15 2013 19:37 MiraMax wrote:I am afraid that your proof is not only lazy, but rather barely coherent If pi were to contain all integer sequences of finite length and each/any state of the universe at time t could be represented by a finite sequence of integers, then yes, pi would by necessity contain the coded state of the universe at (any) time t, i.e. your proof fails. No, there's a problem but that isn't it You're correct that if Pi contains all finite integers, and n is a finite integer encoding the state of the universe, then Pi contains n. No argument there. However, the claim was that *any* key/language could be used to generate the universe from Pi. While it's trivially true that any key capable of generating the state of the universe from an integer n can generate it from a subsequence of Pi (since we're assuming Pi contains all possible n), it's not the case that we can feed THE WHOLE OF Pi into any old key and get the universe. Pi is infinite, the universe is not, therefore feeding Pi into a key would also generate a whole bunch of stuff that isn't in the universe - unless the key itself incorporates the sequence it needs to recognise, which means we're not really using Pi at all. The key only needs to know the starting index (seed) of the subsequence and could start to generate the universe from there. It is a well-known result that normal numbers can be used to encode any piece of information that can be represented by finite sequences and that it works for any decoding scheme that uses finite sequences, so please let's not discuss this any further. Sorry for derailing You're not derailing, your contribution is very much appreciated! Please continue to comment and explain without asking people not to discuss the matter, this is much more interesting than the previous discussion... On July 15 2013 20:06 CoughingHydra wrote:On July 15 2013 19:57 Reason wrote:On July 15 2013 19:51 Umpteen wrote:On July 15 2013 19:41 Reason wrote:
If Pi is infinite and never repeating how could it not contain all possible integer sequences? Imagine it was infinite and never repeating but didn't contain the digit '7'. That's the problem with infinity: it doesn't necessarily mean 'everything possible' Okay, so there's 10 digits. 1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits? I'd maintain the answer to 3. is zero. 7 must appear in a random, non repeating infinite series of digits because as the number of digits in the sequence approaches infinity the probability of 7 not appearing approaches zero. I'm sure similar argumentation for 0.9999999... = 1 could be used to demonstrate this? I'm not a mathematician in the slightest so sorry if that's a family sized bucket of stupid. If the probability is zero, that doesn't mean it can't happen, same in when the probability is 1, it doesn't mean it will happen. Whaaaaaaaaaaaat? + Show Spoiler + E.g. choosing a random real number between 0 and 1, probability to choose any number is 0, but that doesn't mean it won't happen Oo because you will choose one. well, it's near 0, it can't possibly be 0 right ? It's a very very interesting point, however .... Show nested quote +On July 15 2013 20:15 CoughingHydra wrote:On July 15 2013 20:07 Reason wrote:On July 15 2013 20:02 MiraMax wrote:On July 15 2013 19:48 Umpteen wrote:On July 15 2013 19:37 MiraMax wrote:I am afraid that your proof is not only lazy, but rather barely coherent If pi were to contain all integer sequences of finite length and each/any state of the universe at time t could be represented by a finite sequence of integers, then yes, pi would by necessity contain the coded state of the universe at (any) time t, i.e. your proof fails. No, there's a problem but that isn't it You're correct that if Pi contains all finite integers, and n is a finite integer encoding the state of the universe, then Pi contains n. No argument there. However, the claim was that *any* key/language could be used to generate the universe from Pi. While it's trivially true that any key capable of generating the state of the universe from an integer n can generate it from a subsequence of Pi (since we're assuming Pi contains all possible n), it's not the case that we can feed THE WHOLE OF Pi into any old key and get the universe. Pi is infinite, the universe is not, therefore feeding Pi into a key would also generate a whole bunch of stuff that isn't in the universe - unless the key itself incorporates the sequence it needs to recognise, which means we're not really using Pi at all. The key only needs to know the starting index (seed) of the subsequence and could start to generate the universe from there. It is a well-known result that normal numbers can be used to encode any piece of information that can be represented by finite sequences and that it works for any decoding scheme that uses finite sequences, so please let's not discuss this any further. Sorry for derailing You're not derailing, your contribution is very much appreciated! Please continue to comment and explain without asking people not to discuss the matter, this is much more interesting than the previous discussion... On July 15 2013 20:06 CoughingHydra wrote:On July 15 2013 19:57 Reason wrote:On July 15 2013 19:51 Umpteen wrote:On July 15 2013 19:41 Reason wrote:
If Pi is infinite and never repeating how could it not contain all possible integer sequences? Imagine it was infinite and never repeating but didn't contain the digit '7'. That's the problem with infinity: it doesn't necessarily mean 'everything possible' Okay, so there's 10 digits. 1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits? I'd maintain the answer to 3. is zero. 7 must appear in a random, non repeating infinite series of digits because as the number of digits in the sequence approaches infinity the probability of 7 not appearing approaches zero. I'm sure similar argumentation for 0.9999999... = 1 could be used to demonstrate this? I'm not a mathematician in the slightest so sorry if that's a family sized bucket of stupid. If the probability is zero, that doesn't mean it can't happen, same in when the probability is 1, it doesn't mean it will happen. Whaaaaaaaaaaaat? + Show Spoiler + E.g. choosing a random real number between 0 and 1, probability to choose any number is 0, but that doesn't mean it won't happen Oo because you will choose one. https://en.wikipedia.org/wiki/ProbabilityProbability (or likelihood[1]) is a measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen).[2] The higher the degree of probability, the more likely the event is to happen, or, in a longer series of samples, the greater the number of times such event is expected to happen.
Yeah, an event that has probability zero is called an impossible event, but doesn't mean it is impossible for it to happen.
On July 15 2013 20:17 DertoQq wrote:Show nested quote +On July 15 2013 20:15 CoughingHydra wrote:On July 15 2013 20:07 Reason wrote:On July 15 2013 20:02 MiraMax wrote:On July 15 2013 19:48 Umpteen wrote:On July 15 2013 19:37 MiraMax wrote:I am afraid that your proof is not only lazy, but rather barely coherent If pi were to contain all integer sequences of finite length and each/any state of the universe at time t could be represented by a finite sequence of integers, then yes, pi would by necessity contain the coded state of the universe at (any) time t, i.e. your proof fails. No, there's a problem but that isn't it You're correct that if Pi contains all finite integers, and n is a finite integer encoding the state of the universe, then Pi contains n. No argument there. However, the claim was that *any* key/language could be used to generate the universe from Pi. While it's trivially true that any key capable of generating the state of the universe from an integer n can generate it from a subsequence of Pi (since we're assuming Pi contains all possible n), it's not the case that we can feed THE WHOLE OF Pi into any old key and get the universe. Pi is infinite, the universe is not, therefore feeding Pi into a key would also generate a whole bunch of stuff that isn't in the universe - unless the key itself incorporates the sequence it needs to recognise, which means we're not really using Pi at all. The key only needs to know the starting index (seed) of the subsequence and could start to generate the universe from there. It is a well-known result that normal numbers can be used to encode any piece of information that can be represented by finite sequences and that it works for any decoding scheme that uses finite sequences, so please let's not discuss this any further. Sorry for derailing You're not derailing, your contribution is very much appreciated! Please continue to comment and explain without asking people not to discuss the matter, this is much more interesting than the previous discussion... On July 15 2013 20:06 CoughingHydra wrote:On July 15 2013 19:57 Reason wrote:On July 15 2013 19:51 Umpteen wrote:On July 15 2013 19:41 Reason wrote:
If Pi is infinite and never repeating how could it not contain all possible integer sequences? Imagine it was infinite and never repeating but didn't contain the digit '7'. That's the problem with infinity: it doesn't necessarily mean 'everything possible' Okay, so there's 10 digits. 1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits? I'd maintain the answer to 3. is zero. 7 must appear in a random, non repeating infinite series of digits because as the number of digits in the sequence approaches infinity the probability of 7 not appearing approaches zero. I'm sure similar argumentation for 0.9999999... = 1 could be used to demonstrate this? I'm not a mathematician in the slightest so sorry if that's a family sized bucket of stupid. If the probability is zero, that doesn't mean it can't happen, same in when the probability is 1, it doesn't mean it will happen. Whaaaaaaaaaaaat? + Show Spoiler + E.g. choosing a random real number between 0 and 1, probability to choose any number is 0, but that doesn't mean it won't happen Oo because you will choose one. well, it's near 0, it can't possibly be 0 right ?
It is straight zero.
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On July 15 2013 20:15 CoughingHydra wrote:Show nested quote +On July 15 2013 20:07 Reason wrote:On July 15 2013 20:02 MiraMax wrote:On July 15 2013 19:48 Umpteen wrote:On July 15 2013 19:37 MiraMax wrote:I am afraid that your proof is not only lazy, but rather barely coherent If pi were to contain all integer sequences of finite length and each/any state of the universe at time t could be represented by a finite sequence of integers, then yes, pi would by necessity contain the coded state of the universe at (any) time t, i.e. your proof fails. No, there's a problem but that isn't it You're correct that if Pi contains all finite integers, and n is a finite integer encoding the state of the universe, then Pi contains n. No argument there. However, the claim was that *any* key/language could be used to generate the universe from Pi. While it's trivially true that any key capable of generating the state of the universe from an integer n can generate it from a subsequence of Pi (since we're assuming Pi contains all possible n), it's not the case that we can feed THE WHOLE OF Pi into any old key and get the universe. Pi is infinite, the universe is not, therefore feeding Pi into a key would also generate a whole bunch of stuff that isn't in the universe - unless the key itself incorporates the sequence it needs to recognise, which means we're not really using Pi at all. The key only needs to know the starting index (seed) of the subsequence and could start to generate the universe from there. It is a well-known result that normal numbers can be used to encode any piece of information that can be represented by finite sequences and that it works for any decoding scheme that uses finite sequences, so please let's not discuss this any further. Sorry for derailing You're not derailing, your contribution is very much appreciated! Please continue to comment and explain without asking people not to discuss the matter, this is much more interesting than the previous discussion... On July 15 2013 20:06 CoughingHydra wrote:On July 15 2013 19:57 Reason wrote:On July 15 2013 19:51 Umpteen wrote:On July 15 2013 19:41 Reason wrote:
If Pi is infinite and never repeating how could it not contain all possible integer sequences? Imagine it was infinite and never repeating but didn't contain the digit '7'. That's the problem with infinity: it doesn't necessarily mean 'everything possible' Okay, so there's 10 digits. 1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits? I'd maintain the answer to 3. is zero. 7 must appear in a random, non repeating infinite series of digits because as the number of digits in the sequence approaches infinity the probability of 7 not appearing approaches zero. I'm sure similar argumentation for 0.9999999... = 1 could be used to demonstrate this? I'm not a mathematician in the slightest so sorry if that's a family sized bucket of stupid. If the probability is zero, that doesn't mean it can't happen, same in when the probability is 1, it doesn't mean it will happen. Whaaaaaaaaaaaat? + Show Spoiler + E.g. choosing a random real number between 0 and 1, probability to choose any number is 0, but that doesn't mean it won't happen Oo because you will choose one. EDIT: You can prove stuff with probability but it's a bit different: http://en.wikipedia.org/wiki/Probabilistic_method
Its a very big difference to say something is infinitely close to zero and pure zero. There's a difference of perspective here. The chance that any one specific number in the sequence is picked is, well, infinitely small. The chance that any number in the sequence is picked, is obviously 100%, since a number is picked. The odds of a seven not showing up in an infinitely long random number-sequence is the same as the odds of any specific number in the range 0 to 1 being picked if you pick an infinite amount of times.
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On July 15 2013 20:15 CoughingHydra wrote:Show nested quote +On July 15 2013 20:07 Reason wrote:On July 15 2013 20:02 MiraMax wrote:On July 15 2013 19:48 Umpteen wrote:On July 15 2013 19:37 MiraMax wrote:I am afraid that your proof is not only lazy, but rather barely coherent If pi were to contain all integer sequences of finite length and each/any state of the universe at time t could be represented by a finite sequence of integers, then yes, pi would by necessity contain the coded state of the universe at (any) time t, i.e. your proof fails. No, there's a problem but that isn't it You're correct that if Pi contains all finite integers, and n is a finite integer encoding the state of the universe, then Pi contains n. No argument there. However, the claim was that *any* key/language could be used to generate the universe from Pi. While it's trivially true that any key capable of generating the state of the universe from an integer n can generate it from a subsequence of Pi (since we're assuming Pi contains all possible n), it's not the case that we can feed THE WHOLE OF Pi into any old key and get the universe. Pi is infinite, the universe is not, therefore feeding Pi into a key would also generate a whole bunch of stuff that isn't in the universe - unless the key itself incorporates the sequence it needs to recognise, which means we're not really using Pi at all. The key only needs to know the starting index (seed) of the subsequence and could start to generate the universe from there. It is a well-known result that normal numbers can be used to encode any piece of information that can be represented by finite sequences and that it works for any decoding scheme that uses finite sequences, so please let's not discuss this any further. Sorry for derailing You're not derailing, your contribution is very much appreciated! Please continue to comment and explain without asking people not to discuss the matter, this is much more interesting than the previous discussion... On July 15 2013 20:06 CoughingHydra wrote:On July 15 2013 19:57 Reason wrote:On July 15 2013 19:51 Umpteen wrote:On July 15 2013 19:41 Reason wrote:
If Pi is infinite and never repeating how could it not contain all possible integer sequences? Imagine it was infinite and never repeating but didn't contain the digit '7'. That's the problem with infinity: it doesn't necessarily mean 'everything possible' Okay, so there's 10 digits. 1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits? I'd maintain the answer to 3. is zero. 7 must appear in a random, non repeating infinite series of digits because as the number of digits in the sequence approaches infinity the probability of 7 not appearing approaches zero. I'm sure similar argumentation for 0.9999999... = 1 could be used to demonstrate this? I'm not a mathematician in the slightest so sorry if that's a family sized bucket of stupid. If the probability is zero, that doesn't mean it can't happen, same in when the probability is 1, it doesn't mean it will happen. Whaaaaaaaaaaaat? + Show Spoiler + E.g. choosing a random real number between 0 and 1, probability to choose any number is 0, but that doesn't mean it won't happen Oo because you will choose one.
Actually that's a super interesting one
What resolves the apparent paradox is that it's impossible in practice to give all real numbers (or even all decimals) between 0 and 1 an equal shot at getting picked. Any finite state machine you use is bound to miss some.
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On July 15 2013 20:21 CoughingHydra wrote:Show nested quote +On July 15 2013 20:17 Reason wrote:On July 15 2013 20:17 DertoQq wrote:On July 15 2013 20:15 CoughingHydra wrote:On July 15 2013 20:07 Reason wrote:On July 15 2013 20:02 MiraMax wrote:On July 15 2013 19:48 Umpteen wrote:On July 15 2013 19:37 MiraMax wrote:I am afraid that your proof is not only lazy, but rather barely coherent If pi were to contain all integer sequences of finite length and each/any state of the universe at time t could be represented by a finite sequence of integers, then yes, pi would by necessity contain the coded state of the universe at (any) time t, i.e. your proof fails. No, there's a problem but that isn't it You're correct that if Pi contains all finite integers, and n is a finite integer encoding the state of the universe, then Pi contains n. No argument there. However, the claim was that *any* key/language could be used to generate the universe from Pi. While it's trivially true that any key capable of generating the state of the universe from an integer n can generate it from a subsequence of Pi (since we're assuming Pi contains all possible n), it's not the case that we can feed THE WHOLE OF Pi into any old key and get the universe. Pi is infinite, the universe is not, therefore feeding Pi into a key would also generate a whole bunch of stuff that isn't in the universe - unless the key itself incorporates the sequence it needs to recognise, which means we're not really using Pi at all. The key only needs to know the starting index (seed) of the subsequence and could start to generate the universe from there. It is a well-known result that normal numbers can be used to encode any piece of information that can be represented by finite sequences and that it works for any decoding scheme that uses finite sequences, so please let's not discuss this any further. Sorry for derailing You're not derailing, your contribution is very much appreciated! Please continue to comment and explain without asking people not to discuss the matter, this is much more interesting than the previous discussion... On July 15 2013 20:06 CoughingHydra wrote:On July 15 2013 19:57 Reason wrote:On July 15 2013 19:51 Umpteen wrote:On July 15 2013 19:41 Reason wrote:
If Pi is infinite and never repeating how could it not contain all possible integer sequences? Imagine it was infinite and never repeating but didn't contain the digit '7'. That's the problem with infinity: it doesn't necessarily mean 'everything possible' Okay, so there's 10 digits. 1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits? I'd maintain the answer to 3. is zero. 7 must appear in a random, non repeating infinite series of digits because as the number of digits in the sequence approaches infinity the probability of 7 not appearing approaches zero. I'm sure similar argumentation for 0.9999999... = 1 could be used to demonstrate this? I'm not a mathematician in the slightest so sorry if that's a family sized bucket of stupid. If the probability is zero, that doesn't mean it can't happen, same in when the probability is 1, it doesn't mean it will happen. Whaaaaaaaaaaaat? + Show Spoiler + E.g. choosing a random real number between 0 and 1, probability to choose any number is 0, but that doesn't mean it won't happen Oo because you will choose one. well, it's near 0, it can't possibly be 0 right ? It's a very very interesting point, however .... On July 15 2013 20:15 CoughingHydra wrote:On July 15 2013 20:07 Reason wrote:On July 15 2013 20:02 MiraMax wrote:On July 15 2013 19:48 Umpteen wrote:On July 15 2013 19:37 MiraMax wrote:I am afraid that your proof is not only lazy, but rather barely coherent If pi were to contain all integer sequences of finite length and each/any state of the universe at time t could be represented by a finite sequence of integers, then yes, pi would by necessity contain the coded state of the universe at (any) time t, i.e. your proof fails. No, there's a problem but that isn't it You're correct that if Pi contains all finite integers, and n is a finite integer encoding the state of the universe, then Pi contains n. No argument there. However, the claim was that *any* key/language could be used to generate the universe from Pi. While it's trivially true that any key capable of generating the state of the universe from an integer n can generate it from a subsequence of Pi (since we're assuming Pi contains all possible n), it's not the case that we can feed THE WHOLE OF Pi into any old key and get the universe. Pi is infinite, the universe is not, therefore feeding Pi into a key would also generate a whole bunch of stuff that isn't in the universe - unless the key itself incorporates the sequence it needs to recognise, which means we're not really using Pi at all. The key only needs to know the starting index (seed) of the subsequence and could start to generate the universe from there. It is a well-known result that normal numbers can be used to encode any piece of information that can be represented by finite sequences and that it works for any decoding scheme that uses finite sequences, so please let's not discuss this any further. Sorry for derailing You're not derailing, your contribution is very much appreciated! Please continue to comment and explain without asking people not to discuss the matter, this is much more interesting than the previous discussion... On July 15 2013 20:06 CoughingHydra wrote:On July 15 2013 19:57 Reason wrote:On July 15 2013 19:51 Umpteen wrote:On July 15 2013 19:41 Reason wrote:
If Pi is infinite and never repeating how could it not contain all possible integer sequences? Imagine it was infinite and never repeating but didn't contain the digit '7'. That's the problem with infinity: it doesn't necessarily mean 'everything possible' Okay, so there's 10 digits. 1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits? I'd maintain the answer to 3. is zero. 7 must appear in a random, non repeating infinite series of digits because as the number of digits in the sequence approaches infinity the probability of 7 not appearing approaches zero. I'm sure similar argumentation for 0.9999999... = 1 could be used to demonstrate this? I'm not a mathematician in the slightest so sorry if that's a family sized bucket of stupid. If the probability is zero, that doesn't mean it can't happen, same in when the probability is 1, it doesn't mean it will happen. Whaaaaaaaaaaaat? + Show Spoiler + E.g. choosing a random real number between 0 and 1, probability to choose any number is 0, but that doesn't mean it won't happen Oo because you will choose one. https://en.wikipedia.org/wiki/ProbabilityProbability (or likelihood[1]) is a measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen).[2] The higher the degree of probability, the more likely the event is to happen, or, in a longer series of samples, the greater the number of times such event is expected to happen. Yeah, an event that has probability zero is called an impossible event, but doesn't mean it is impossible for it to happen. Show nested quote +On July 15 2013 20:17 DertoQq wrote:On July 15 2013 20:15 CoughingHydra wrote:On July 15 2013 20:07 Reason wrote:On July 15 2013 20:02 MiraMax wrote:On July 15 2013 19:48 Umpteen wrote:On July 15 2013 19:37 MiraMax wrote:I am afraid that your proof is not only lazy, but rather barely coherent If pi were to contain all integer sequences of finite length and each/any state of the universe at time t could be represented by a finite sequence of integers, then yes, pi would by necessity contain the coded state of the universe at (any) time t, i.e. your proof fails. No, there's a problem but that isn't it You're correct that if Pi contains all finite integers, and n is a finite integer encoding the state of the universe, then Pi contains n. No argument there. However, the claim was that *any* key/language could be used to generate the universe from Pi. While it's trivially true that any key capable of generating the state of the universe from an integer n can generate it from a subsequence of Pi (since we're assuming Pi contains all possible n), it's not the case that we can feed THE WHOLE OF Pi into any old key and get the universe. Pi is infinite, the universe is not, therefore feeding Pi into a key would also generate a whole bunch of stuff that isn't in the universe - unless the key itself incorporates the sequence it needs to recognise, which means we're not really using Pi at all. The key only needs to know the starting index (seed) of the subsequence and could start to generate the universe from there. It is a well-known result that normal numbers can be used to encode any piece of information that can be represented by finite sequences and that it works for any decoding scheme that uses finite sequences, so please let's not discuss this any further. Sorry for derailing You're not derailing, your contribution is very much appreciated! Please continue to comment and explain without asking people not to discuss the matter, this is much more interesting than the previous discussion... On July 15 2013 20:06 CoughingHydra wrote:On July 15 2013 19:57 Reason wrote:On July 15 2013 19:51 Umpteen wrote:On July 15 2013 19:41 Reason wrote:
If Pi is infinite and never repeating how could it not contain all possible integer sequences? Imagine it was infinite and never repeating but didn't contain the digit '7'. That's the problem with infinity: it doesn't necessarily mean 'everything possible' Okay, so there's 10 digits. 1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits? I'd maintain the answer to 3. is zero. 7 must appear in a random, non repeating infinite series of digits because as the number of digits in the sequence approaches infinity the probability of 7 not appearing approaches zero. I'm sure similar argumentation for 0.9999999... = 1 could be used to demonstrate this? I'm not a mathematician in the slightest so sorry if that's a family sized bucket of stupid. If the probability is zero, that doesn't mean it can't happen, same in when the probability is 1, it doesn't mean it will happen. Whaaaaaaaaaaaat? + Show Spoiler + E.g. choosing a random real number between 0 and 1, probability to choose any number is 0, but that doesn't mean it won't happen Oo because you will choose one. well, it's near 0, it can't possibly be 0 right ? It is straight zero.
Sorry, you're totally right.
https://en.wikipedia.org/wiki/Impossible_event
Learned something new today!
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On July 15 2013 20:10 Umpteen wrote:Show nested quote +On July 15 2013 20:02 MiraMax wrote:
The key only needs to know the starting index (seed) of the subsequence and could start to generate the universe from there. But knowing the starting index of the sequence is equivalent to knowing the sequence, since you would have to look through Pi and pick out the 'correct' sequence first. Pi contains all integer sequences. You just need to know where to look to find the one that generates the universe. The set of integers also contains all integer sequences. You just need to know where to look to find the one that generates the universe. You're not actually 'using' Pi itself, other than in its capacity as a big ol' box of undifferentiated numbers. EG I give you a list of all four-digit numbers and then tell you my pin code is the 5046'th entry...
Knowing the starting index is in no (relevant) way equivalent to knowing the sequence at least not in information theory. It just allows you to compute the relevant subsequence given that you know how to compute successive digits of pi. And you are then in fact using the actual structure of pi to represent the desired information. How do you think encryption works? That's the way I understood Shiori and also your "proof" to address. If all you wanted to show was that you can always develop a decoding scheme that fails to compute anything on the basis of pi, then there would have been much easier ways to go about. Cheers!
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On July 15 2013 20:30 MiraMax wrote:Show nested quote +On July 15 2013 20:10 Umpteen wrote:On July 15 2013 20:02 MiraMax wrote:
The key only needs to know the starting index (seed) of the subsequence and could start to generate the universe from there. But knowing the starting index of the sequence is equivalent to knowing the sequence, since you would have to look through Pi and pick out the 'correct' sequence first. Pi contains all integer sequences. You just need to know where to look to find the one that generates the universe. The set of integers also contains all integer sequences. You just need to know where to look to find the one that generates the universe. You're not actually 'using' Pi itself, other than in its capacity as a big ol' box of undifferentiated numbers. EG I give you a list of all four-digit numbers and then tell you my pin code is the 5046'th entry... Knowing the starting index is in no (relevant) way equivalent to knowing the sequence at least not in information theory. It just allows you to compute the relevant subsequence given that you know how to compute successive digits of pi. And you are then in fact using the actual structure of pi to represent the desired information. How do you think encryption works? That's the way I understood Shiori and also your "proof" to address. If all you wanted to show was that you can always develop a decoding scheme that fails to compute anything on the basis of pi, then there would have been much easier ways to go about. Cheers!
More importantly Pi doesn't necessarily contain all the secrets of the universe, though it almost surely does 
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... ><
You're almost surely correct! lol.
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On July 15 2013 20:13 Reason wrote:
If it is infinite and non repeating, why not?
Ok, suppose I give you a black box which spits out non-repeating random integers.
I tell you "Before I shut the lid, I flipped a coin to see whether I would add a circuit that prevented it yielding a specific sequence. I'm not telling you what the sequence is."
The odds are 50/50 that the box is incapable of generating every possible integer. How could you figure it out from the output?
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On July 15 2013 20:41 Umpteen wrote:Show nested quote +On July 15 2013 20:13 Reason wrote:
If it is infinite and non repeating, why not?
Ok, suppose I give you a black box which spits out non-repeating random integers. I tell you "Before I shut the lid, I flipped a coin to see whether I would add a circuit that prevented it yielding a specific sequence. I'm not telling you what the sequence is." The odds are 50/50 that the box is incapable of generating every possible integer. How could you figure it out from the output?
First you said specific sequence, then you said every possible integer, it doesn't matter though you wouldn't be able to figure it out either way.
There's no reason to believe Pi has such constraints though so I don't see how this answers ;
the question of whether or not it contains every integer sequence cannot be reduced to a statement of probability.
I think the probability is 1, almost surely. That's been established, no?
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On July 15 2013 20:30 MiraMax wrote:
Knowing the starting index is in no (relevant) way equivalent to knowing the sequence at least not in information theory. It just allows you to compute the relevant subsequence given that you know how to compute successive digits of pi. And you are then in fact using the actual structure of pi to represent the desired information.
But the information isn't in Pi. It's in the starting index, which is easy to prove when you consider 'information' as 'reduction in uncertainty'.
Suppose I give you my bank card. If I then give you a sheet of paper with all possible 4-digit numbers on it, have I given you any additional information that would help you access my bank account? No. I have not reduced your uncertainty, therefore I have not communicated any information.
Suppose instead I give you a sheet of paper with 'Pi' written on it, the intimation being that somewhere in Pi is my Pin number. Have I given you any additional information? No, because Pi contains all possible 4 digit sequences. I have not reduced your uncertainty, thus no information has been communicated.
If I tell you where on the page, or where in Pi, my pin number is to be found, THEN your uncertainty is reduced to zero. Therefore ALL the information is in the indexing.
If Pi did not contain all integer sequences, then handing you 'Pi' and telling you the code for the universe is in there somewhere would be communicating information, since it would reduce your uncertainty by excluding all sequences not in Pi. In that circumstance, the 'structure' of Pi WOULD contain information.
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On July 15 2013 20:47 Reason wrote:Show nested quote +On July 15 2013 20:41 Umpteen wrote:On July 15 2013 20:13 Reason wrote:
If it is infinite and non repeating, why not?
Ok, suppose I give you a black box which spits out non-repeating random integers. I tell you "Before I shut the lid, I flipped a coin to see whether I would add a circuit that prevented it yielding a specific sequence. I'm not telling you what the sequence is." The odds are 50/50 that the box is incapable of generating every possible integer. How could you figure it out from the output? First you said specific sequence, then you said every possible integer, it doesn't matter though you wouldn't be able to figure it out either way.
Sorry; edited a couple of times and messed it up :D I think you caught the drift though.
There's no reason to believe Pi has such constraints though so I don't see how this answers ;
the question of whether or not it contains every integer sequence cannot be reduced to a statement of probability.
I think the probability is 1, almost surely. That's been established, no?
When you say 'there's no reason to believe', what are you basing that estimate upon? Statistical analysis of the output, right?
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On July 15 2013 20:58 Umpteen wrote:Show nested quote +On July 15 2013 20:47 Reason wrote:On July 15 2013 20:41 Umpteen wrote:On July 15 2013 20:13 Reason wrote:
If it is infinite and non repeating, why not?
Ok, suppose I give you a black box which spits out non-repeating random integers. I tell you "Before I shut the lid, I flipped a coin to see whether I would add a circuit that prevented it yielding a specific sequence. I'm not telling you what the sequence is." The odds are 50/50 that the box is incapable of generating every possible integer. How could you figure it out from the output? First you said specific sequence, then you said every possible integer, it doesn't matter though you wouldn't be able to figure it out either way. Sorry; edited a couple of times and messed it up :D I think you caught the drift though. Show nested quote +There's no reason to believe Pi has such constraints though so I don't see how this answers ;
the question of whether or not it contains every integer sequence cannot be reduced to a statement of probability.
I think the probability is 1, almost surely. That's been established, no? When you say 'there's no reason to believe', what are you basing that estimate upon? Statistical analysis of the output, right?
If you're on board with stating probability is 1 (almost surely) for a random non repeating infinite sequence of integers containing every possible sequence of integers then I still don't understand why you feel Pi is different.
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just look at it, marvel at its beauty. 
someone will always try and go beyond something that is already known. it's what fuels the motion of 0 and 1.
if it helps, see determinism and nondeterminism only as believes subjective to the human mind one preceding the other ad infinitum. they have no effect on the universe be it known or unknown.
then, the question becomes not whether or not 0 is truer then 1 but rather what can come of this sucession of ones and zeroes.
you will then start to decipher/decode the software.
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On July 15 2013 21:00 Reason wrote:Show nested quote +On July 15 2013 20:58 Umpteen wrote:On July 15 2013 20:47 Reason wrote:On July 15 2013 20:41 Umpteen wrote:On July 15 2013 20:13 Reason wrote:
If it is infinite and non repeating, why not?
Ok, suppose I give you a black box which spits out non-repeating random integers. I tell you "Before I shut the lid, I flipped a coin to see whether I would add a circuit that prevented it yielding a specific sequence. I'm not telling you what the sequence is." The odds are 50/50 that the box is incapable of generating every possible integer. How could you figure it out from the output? First you said specific sequence, then you said every possible integer, it doesn't matter though you wouldn't be able to figure it out either way. Sorry; edited a couple of times and messed it up :D I think you caught the drift though. There's no reason to believe Pi has such constraints though so I don't see how this answers ;
the question of whether or not it contains every integer sequence cannot be reduced to a statement of probability.
I think the probability is 1, almost surely. That's been established, no? When you say 'there's no reason to believe', what are you basing that estimate upon? Statistical analysis of the output, right? Yes of course but in your example there's a 50/50 chance which is a damned good reason to believe, with Pi there is absolutely no reason to believe. I don't see how you can equate the two...
Ok, suppose I just gave you the box and didn't tell you about the coin-flip. Would that help?
Scratch that; try looking at it this way:
I'm happy with a statistics-based 'yes' answer to the question "Does Pi contain specific integer N?"
That's because even if Pi doesn't contain all integers, I'm very unlikely to pick one that's missing.
But "Does Pi contain all integer sequences?" is a tougher call, and I'm not convinced a statistical answer is appropriate.
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The pi thing is realy interesting.
Have a question: if the digits of pi are indeed random, then calculating pi would be a deterministic event with a random outcome?
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On July 15 2013 21:12 Umpteen wrote:Show nested quote +On July 15 2013 21:00 Reason wrote:On July 15 2013 20:58 Umpteen wrote:On July 15 2013 20:47 Reason wrote:On July 15 2013 20:41 Umpteen wrote:On July 15 2013 20:13 Reason wrote:
If it is infinite and non repeating, why not?
Ok, suppose I give you a black box which spits out non-repeating random integers. I tell you "Before I shut the lid, I flipped a coin to see whether I would add a circuit that prevented it yielding a specific sequence. I'm not telling you what the sequence is." The odds are 50/50 that the box is incapable of generating every possible integer. How could you figure it out from the output? First you said specific sequence, then you said every possible integer, it doesn't matter though you wouldn't be able to figure it out either way. Sorry; edited a couple of times and messed it up :D I think you caught the drift though. There's no reason to believe Pi has such constraints though so I don't see how this answers ;
the question of whether or not it contains every integer sequence cannot be reduced to a statement of probability.
I think the probability is 1, almost surely. That's been established, no? When you say 'there's no reason to believe', what are you basing that estimate upon? Statistical analysis of the output, right? Yes of course but in your example there's a 50/50 chance which is a damned good reason to believe, with Pi there is absolutely no reason to believe. I don't see how you can equate the two... Ok, suppose I just gave you the box and didn't tell you about the coin-flip. Would that help? Scratch that; try looking at it this way: I'm happy with a statistics-based 'yes' answer to the question "Does Pi contain specific integer N?" That's because even if Pi doesn't contain all integers, I'm very unlikely to pick one that's missing. But "Does Pi contain all integer sequences?" is a tougher call, and I'm not convinced a statistical answer is appropriate.
Okay, fair enough, I changed my post after you quoted it btw I don't know if that makes any difference....
So I guess I'm really just asking you, why do you feel comfortable with a statistics based "yes" to the single integer question but not the integer sequence question?
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On July 15 2013 21:00 Reason wrote:Show nested quote +On July 15 2013 20:58 Umpteen wrote:On July 15 2013 20:47 Reason wrote:On July 15 2013 20:41 Umpteen wrote:On July 15 2013 20:13 Reason wrote:
If it is infinite and non repeating, why not?
Ok, suppose I give you a black box which spits out non-repeating random integers. I tell you "Before I shut the lid, I flipped a coin to see whether I would add a circuit that prevented it yielding a specific sequence. I'm not telling you what the sequence is." The odds are 50/50 that the box is incapable of generating every possible integer. How could you figure it out from the output? First you said specific sequence, then you said every possible integer, it doesn't matter though you wouldn't be able to figure it out either way. Sorry; edited a couple of times and messed it up :D I think you caught the drift though. There's no reason to believe Pi has such constraints though so I don't see how this answers ;
the question of whether or not it contains every integer sequence cannot be reduced to a statement of probability.
I think the probability is 1, almost surely. That's been established, no? When you say 'there's no reason to believe', what are you basing that estimate upon? Statistical analysis of the output, right? If you're on board with stating probability is 1 (almost surely) for a random non repeating infinite sequence of integers containing every possible sequence of integers then I still don't understand why you feel Pi is different.
Because we KNOW Pi is not random.
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On July 15 2013 21:15 Umpteen wrote:Show nested quote +On July 15 2013 21:00 Reason wrote:On July 15 2013 20:58 Umpteen wrote:On July 15 2013 20:47 Reason wrote:On July 15 2013 20:41 Umpteen wrote:On July 15 2013 20:13 Reason wrote:
If it is infinite and non repeating, why not?
Ok, suppose I give you a black box which spits out non-repeating random integers. I tell you "Before I shut the lid, I flipped a coin to see whether I would add a circuit that prevented it yielding a specific sequence. I'm not telling you what the sequence is." The odds are 50/50 that the box is incapable of generating every possible integer. How could you figure it out from the output? First you said specific sequence, then you said every possible integer, it doesn't matter though you wouldn't be able to figure it out either way. Sorry; edited a couple of times and messed it up :D I think you caught the drift though. There's no reason to believe Pi has such constraints though so I don't see how this answers ;
the question of whether or not it contains every integer sequence cannot be reduced to a statement of probability.
I think the probability is 1, almost surely. That's been established, no? When you say 'there's no reason to believe', what are you basing that estimate upon? Statistical analysis of the output, right? If you're on board with stating probability is 1 (almost surely) for a random non repeating infinite sequence of integers containing every possible sequence of integers then I still don't understand why you feel Pi is different. Because we KNOW Pi is not random.
This actually ties in nicely with the following....
On July 15 2013 21:15 Rassy wrote:
The pi thing is realy interesting.
Have a question: if the digits of pi are indeed random, then calculating pi would be a deterministic event with a random outcome?
The outcome isn't random, it's the same every time you calculate Pi. It's just that the number itself does not repeat itself so therefore is described as random. Sorry
So, Umpteen, perhaps we are misunderstanding each other. I don't think you can say "we know Pi isn't random"
http://news.bbc.co.uk/1/hi/sci/tech/2146295.stm
"At the very least we have shown that the digits of pi appear to be random: because they are described by chaos theory."
I know that's old as fuck but I don't feel the need to dig deeper to communicate this point.
So... yes Pi is random, although not in the sense that it's different each time you calculate it, thus I am comfortable treating it as any other randomly generated sequence of non repeating integers and assigning the same probabilities to each of them containing everything.
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On July 15 2013 20:53 Umpteen wrote:Show nested quote +On July 15 2013 20:30 MiraMax wrote:
Knowing the starting index is in no (relevant) way equivalent to knowing the sequence at least not in information theory. It just allows you to compute the relevant subsequence given that you know how to compute successive digits of pi. And you are then in fact using the actual structure of pi to represent the desired information. But the information isn't in Pi. It's in the starting index, which is easy to prove when you consider 'information' as 'reduction in uncertainty'. Suppose I give you my bank card. If I then give you a sheet of paper with all possible 4-digit numbers on it, have I given you any additional information that would help you access my bank account? No. I have not reduced your uncertainty, therefore I have not communicated any information. Suppose instead I give you a sheet of paper with 'Pi' written on it, the intimation being that somewhere in Pi is my Pin number. Have I given you any additional information? No, because Pi contains all possible 4 digit sequences. I have not reduced your uncertainty, thus no information has been communicated. If I tell you where on the page, or where in Pi, my pin number is to be found, THEN your uncertainty is reduced to zero. Therefore ALL the information is in the indexing. If Pi did not contain all integer sequences, then handing you 'Pi' and telling you the code for the universe is in there somewhere would be communicating information, since it would reduce your uncertainty by excluding all sequences not in Pi. In that circumstance, the 'structure' of Pi WOULD contain information.
Oh my ... if the structure of pi does not contain information I wonder how it's used to compute the circumference of circles for instance ...
If I wanted to give you my 4 digit pin and gave you 4 different digits instead claiming that my pin is encoded in these 4 different digits by some deterministic key, I would not have reduced your uncertainty with regard to my actual pin even though my claim would be correct. The whole point of encryption is to make the encrypted data useless without the key. Please go back and read Shiori's post again (to which you objected) to see whether you read him right. His whole claim was that pi (as a data storage) is "complex" enough to store all the information of the universe using some deterministic coding scheme.
Finally, the fact that the index without pi (or a process to compute pi) would be equally useless should show you that some relavant information is in fact stored in pi. I realize that this is taking it way too far though, so maybe we should move it to pm. Cheers!
Edit: Added last paragraph.
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After going from page 1 to page 81 in this thread: boy, that escalated, as always. *Shakes head*
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EPT![[image loading]](http://i.imgur.com/FyeFIbj.gif)
