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On July 15 2013 18:51 Vandrad wrote:Show nested quote +On July 01 2013 10:13 SergioCQH wrote:On July 01 2013 10:12 aksfjh wrote:
As far as we can tell, yes. Although, one hopes there is more to it than that. Why? Why does one need anything more when what we have is already so wonderful? Because when you die you will just rot away like everything else?
I'd rather have a wonderful life and then rot away than the opposite and spending an eternity anywhere.
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On July 15 2013 18:37 Umpteen wrote:Show nested quote +On July 15 2013 17:56 Reason wrote:On July 15 2013 11:52 Shiori wrote: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... >< That is indeed cool! Can you suggest a way to "decrypt" Pi? How would you write Pythagoras' theorem using numbers 1-9? Theoretically you could use any key or language and you would still find all the information in the universe within Pi so you every one you create would eventually work. Okay maybe this will be quite difficult... Wildly off-topic, but fun  Pretty sure what you're saying is wrong though. Lazy proof: 1. For it to be guaranteed that Pi could map any key/language to the state of the universe, Pi would need to contain all possible integer sequences. Let K be a key which maps the integer n to something that does not exist in the universe. From 1) Pi contains n infinitely many times in all possible contexts, therefore K will not map Pi to the current state of the universe. Basically Pi contains too much. Culling it correctly would be entirely down to the key/language, therefore it would be the key/language that would actually represent the state of the universe, not Pi.
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.
Currently though it is neither known whether pi contains all possible integer sequences of finite length nor whether the state of the universe could be encoded by a finite sequence of integers.
What studying pi does show though, is that curvature is a pretty complex topic. Add to add something at least halfway relevant to the discussion, normal numbers (those that contain all integer sequences with equal propability) do also serve to show that all the "complexities" a stochastic process supposedly contains are also contained in fully determinstic processes and also that the results of deterministic processes are not necessarily predictible, only repeatable.
Edit: Added "on topic" paragraph.
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On July 15 2013 19:03 Reason wrote:Show nested quote +On July 15 2013 18:37 Umpteen wrote:On July 15 2013 17:56 Reason wrote:On July 15 2013 11:52 Shiori wrote: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... >< That is indeed cool! Can you suggest a way to "decrypt" Pi? How would you write Pythagoras' theorem using numbers 1-9? Theoretically you could use any key or language and you would still find all the information in the universe within Pi so you every one you create would eventually work. Okay maybe this will be quite difficult... Wildly off-topic, but fun Pretty sure what you're saying is wrong though. Lazy proof: 1. For it to be guaranteed that Pi could map any key/language to the state of the universe, Pi would need to contain all possible integer sequences. Let K be a key which maps the integer n to something that does not exist in the universe. From 1) Pi contains n infinitely many times in all possible contexts, therefore K will not map Pi to the current state of the universe. Basically Pi contains too much. Culling it correctly would be entirely down to the key/language, therefore it would be the key/language that would actually represent the state of the universe, not Pi. I don't get it .... =(
Sorry; lazy proof too lazy. I'll try again:
1. For it to be guaranteed that Pi could map any key/language to the state of the universe, Pi would need to contain all possible integer sequences.
Proof: Let n be an integer not found anywhere in Pi. Let there be a particle P in the universe, and K be a key such that K(n) describes the state of P. Since n is found nowhere in Pi, it is impossible to use K to derive the state of the universe from Pi.
Therefore, for ALL possible keys to map Pi to the universe, Pi must contain all possible integer sequences.
However, I'm less convinced myself about the second part of the proof. I'll think on it
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On July 15 2013 19:38 Umpteen wrote:Show nested quote +On July 15 2013 19:03 Reason wrote:On July 15 2013 18:37 Umpteen wrote:On July 15 2013 17:56 Reason wrote:On July 15 2013 11:52 Shiori wrote: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... >< That is indeed cool! Can you suggest a way to "decrypt" Pi? How would you write Pythagoras' theorem using numbers 1-9? Theoretically you could use any key or language and you would still find all the information in the universe within Pi so you every one you create would eventually work. Okay maybe this will be quite difficult... Wildly off-topic, but fun Pretty sure what you're saying is wrong though. Lazy proof: 1. For it to be guaranteed that Pi could map any key/language to the state of the universe, Pi would need to contain all possible integer sequences. Let K be a key which maps the integer n to something that does not exist in the universe. From 1) Pi contains n infinitely many times in all possible contexts, therefore K will not map Pi to the current state of the universe. Basically Pi contains too much. Culling it correctly would be entirely down to the key/language, therefore it would be the key/language that would actually represent the state of the universe, not Pi. I don't get it .... =( Sorry; lazy proof too lazy. I'll try again: 1. For it to be guaranteed that Pi could map any key/language to the state of the universe, Pi would need to contain all possible integer sequences.Proof: Let n be an integer not found anywhere in Pi. Let there be a particle P in the universe, and K be a key such that K(n) describes the state of P. Since n is found nowhere in Pi, it is impossible to use K to derive the state of the universe from Pi. Therefore, for ALL possible keys to map Pi to the universe, Pi must contain all possible integer sequences. However, I'm less convinced myself about the second part of the proof. I'll think on it
If Pi is infinite and never repeating how could it not contain all possible integer sequences?
Even if that can't be proved, since it hasn't been disproved there's no problem... yet. Right?
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On July 15 2013 19:41 Reason wrote:
If Pi is infinite and never repeating how could it not contain all possible integer sequences?
Exactly. Stop messing around with math that's above your heads in a thread that has the obvious answer "yes".
Especially when this obsession with a specific transcendental number is so absurd. Why not choose any other?
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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.
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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'
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On July 15 2013 19:48 Umpteen wrote:Show nested quote +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.
Sure, I'm not saying Pi is just the universe neatly described, you'd get loads of gibberish interspersed with random lines from Shakespeare and the occasional mathematical proof etc =P
I think it could be fun to try...
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On July 15 2013 19:51 Umpteen wrote:Show nested quote +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'
The decimals of pi seems by all means possible to us like a sequence that conforms to normality and randomness. It may or may not be provable, but it's damn likely to be a fact.
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On July 15 2013 19:51 Umpteen wrote:Show nested quote +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.
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On July 15 2013 19:48 Umpteen wrote:Show nested quote +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
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On July 15 2013 19:41 Reason wrote:Show nested quote +On July 15 2013 19:38 Umpteen wrote:On July 15 2013 19:03 Reason wrote:On July 15 2013 18:37 Umpteen wrote:On July 15 2013 17:56 Reason wrote:On July 15 2013 11:52 Shiori wrote: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... >< That is indeed cool! Can you suggest a way to "decrypt" Pi? How would you write Pythagoras' theorem using numbers 1-9? Theoretically you could use any key or language and you would still find all the information in the universe within Pi so you every one you create would eventually work. Okay maybe this will be quite difficult... Wildly off-topic, but fun Pretty sure what you're saying is wrong though. Lazy proof: 1. For it to be guaranteed that Pi could map any key/language to the state of the universe, Pi would need to contain all possible integer sequences. Let K be a key which maps the integer n to something that does not exist in the universe. From 1) Pi contains n infinitely many times in all possible contexts, therefore K will not map Pi to the current state of the universe. Basically Pi contains too much. Culling it correctly would be entirely down to the key/language, therefore it would be the key/language that would actually represent the state of the universe, not Pi. I don't get it .... =( Sorry; lazy proof too lazy. I'll try again: 1. For it to be guaranteed that Pi could map any key/language to the state of the universe, Pi would need to contain all possible integer sequences.Proof: Let n be an integer not found anywhere in Pi. Let there be a particle P in the universe, and K be a key such that K(n) describes the state of P. Since n is found nowhere in Pi, it is impossible to use K to derive the state of the universe from Pi. Therefore, for ALL possible keys to map Pi to the universe, Pi must contain all possible integer sequences. However, I'm less convinced myself about the second part of the proof. I'll think on it If Pi is infinite and never repeating how could it not contain all possible integer sequences? Even if that can't be proved, since it hasn't been disproved there's no problem... yet. Right?
no, you would have to prove that first. i think pi could be infinite and never repeating and yet not contain all possible integer sequences. imagine the number 1 stopped appearing.
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On July 15 2013 19:57 Reason wrote:Show nested quote +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.
No, you're completely right. The problem is that Pi is not a mathematically random sequence. There are functions we can use to generate it. So the question of whether or not it contains every integer sequence cannot be reduced to a statement of probability.
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On July 15 2013 19:57 Reason wrote:Show nested quote +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.
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On July 15 2013 20:02 MiraMax wrote:Show nested quote +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:Show nested quote +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 +
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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...
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On July 15 2013 20:04 Umpteen wrote:Show nested quote +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. No, you're completely right. The problem is that Pi is not a mathematically random sequence. There are functions we can use to generate it. So the question of whether or not it contains every integer sequence cannot be reduced to a statement of probability.
If it is infinite and non repeating, why not?
On July 15 2013 20:10 Umpteen wrote:
You're not actually 'using' Pi itself, other than in its capacity as a big ol' box of undifferentiated numbers.
Agreed, but since Pi is so awesome and stuff has a habit of being linked to other stuff I think it's definitely more appealing to use Pi, just in case 
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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... Show nested quote +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
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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.
well, it's near 0, it can't possibly be 0 right ?
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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's a very very interesting point, however ....
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.
https://en.wikipedia.org/wiki/Probability
Probability (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.
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