Probabilities in pi number and similar irrational numbers
There is a presentation on the internet about the number $pi$ stating that combinations of digits in this number are so vast that they can contain our date of birth, SSN number, bank account number, and it goes on to say that if we convert every letter into decimals, we would find in this number every word and even everything that we have ever done or said (link to presentation https://www.youtube.com/watch?v=4RldHTtd3O8). This does not sound possible according to my very limited mathematical skills.
How likely is it that such a set of digits would create the exact pattern of such a long list of digits? Would'nt the probability of that happening decrease with the length of the desired combination of numbers? This video implies that such thing would not just happen once, but an infinite number of times.
probability
edited Dec 27 '18 at 14:40
Qmechanic
4,86311854
migrated from physics.stackexchange.com Dec 27 '18 at 14:37
This question came from our site for active researchers, academics and students of physics.
add a comment |
There is a presentation on the internet about the number $pi$ stating that combinations of digits in this number are so vast that they can contain our date of birth, SSN number, bank account number, and it goes on to say that if we convert every letter into decimals, we would find in this number every word and even everything that we have ever done or said (link to presentation https://www.youtube.com/watch?v=4RldHTtd3O8). This does not sound possible according to my very limited mathematical skills.
How likely is it that such a set of digits would create the exact pattern of such a long list of digits? Would'nt the probability of that happening decrease with the length of the desired combination of numbers? This video implies that such thing would not just happen once, but an infinite number of times.
probability
edited Dec 27 '18 at 14:40
Qmechanic
4,86311854
migrated from physics.stackexchange.com Dec 27 '18 at 14:37
This question came from our site for active researchers, academics and students of physics.
1
See en.wikipedia.org/wiki/Normal_number for a more detailed explanation. We don't know yet if $pi$ is such a number. Be careful with the term "almost all" --it has a very specific meaning in measure theory.
– Apoorv Khurasia
Dec 27 '18 at 14:46
1
These wild statements could be true of many irrationals. There's nothing magic about $pi$. Why not $sqrt{2}$ as well?
– MPW
Dec 27 '18 at 14:55
As stated in the answer below, the number $pi$ is not known to have this property (normality), but it's considered likely that it does
– Sauhard Sharma
Dec 27 '18 at 15:11
add a comment |
There is a presentation on the internet about the number $pi$ stating that combinations of digits in this number are so vast that they can contain our date of birth, SSN number, bank account number, and it goes on to say that if we convert every letter into decimals, we would find in this number every word and even everything that we have ever done or said (link to presentation https://www.youtube.com/watch?v=4RldHTtd3O8). This does not sound possible according to my very limited mathematical skills.
How likely is it that such a set of digits would create the exact pattern of such a long list of digits? Would'nt the probability of that happening decrease with the length of the desired combination of numbers? This video implies that such thing would not just happen once, but an infinite number of times.
probability
edited Dec 27 '18 at 14:40
Qmechanic
4,86311854
There is a presentation on the internet about the number $pi$ stating that combinations of digits in this number are so vast that they can contain our date of birth, SSN number, bank account number, and it goes on to say that if we convert every letter into decimals, we would find in this number every word and even everything that we have ever done or said (link to presentation https://www.youtube.com/watch?v=4RldHTtd3O8). This does not sound possible according to my very limited mathematical skills.
How likely is it that such a set of digits would create the exact pattern of such a long list of digits? Would'nt the probability of that happening decrease with the length of the desired combination of numbers? This video implies that such thing would not just happen once, but an infinite number of times.
probability
probability
edited Dec 27 '18 at 14:40
Qmechanic
4,86311854
edited Dec 27 '18 at 14:40
Qmechanic
4,86311854
edited Dec 27 '18 at 14:40
Qmechanic
4,86311854
edited Dec 27 '18 at 14:40
Qmechanic
4,86311854
edited Dec 27 '18 at 14:40
Qmechanic
4,86311854
4,86311854
asked Dec 27 '18 at 14:33
M. Semiz
migrated from physics.stackexchange.com Dec 27 '18 at 14:37
This question came from our site for active researchers, academics and students of physics.
migrated from physics.stackexchange.com Dec 27 '18 at 14:37
This question came from our site for active researchers, academics and students of physics.
1
See en.wikipedia.org/wiki/Normal_number for a more detailed explanation. We don't know yet if $pi$ is such a number. Be careful with the term "almost all" --it has a very specific meaning in measure theory.
– Apoorv Khurasia
Dec 27 '18 at 14:46
1
These wild statements could be true of many irrationals. There's nothing magic about $pi$. Why not $sqrt{2}$ as well?
– MPW
Dec 27 '18 at 14:55
As stated in the answer below, the number $pi$ is not known to have this property (normality), but it's considered likely that it does
– Sauhard Sharma
Dec 27 '18 at 15:11
add a comment |
1
See en.wikipedia.org/wiki/Normal_number for a more detailed explanation. We don't know yet if $pi$ is such a number. Be careful with the term "almost all" --it has a very specific meaning in measure theory.
– Apoorv Khurasia
Dec 27 '18 at 14:46
1
These wild statements could be true of many irrationals. There's nothing magic about $pi$. Why not $sqrt{2}$ as well?
– MPW
Dec 27 '18 at 14:55
As stated in the answer below, the number $pi$ is not known to have this property (normality), but it's considered likely that it does
– Sauhard Sharma
Dec 27 '18 at 15:11
1
1
See en.wikipedia.org/wiki/Normal_number for a more detailed explanation. We don't know yet if $pi$ is such a number. Be careful with the term "almost all" --it has a very specific meaning in measure theory.
– Apoorv Khurasia
Dec 27 '18 at 14:46
See en.wikipedia.org/wiki/Normal_number for a more detailed explanation. We don't know yet if $pi$ is such a number. Be careful with the term "almost all" --it has a very specific meaning in measure theory.
– Apoorv Khurasia
Dec 27 '18 at 14:46
1
1
These wild statements could be true of many irrationals. There's nothing magic about $pi$. Why not $sqrt{2}$ as well?
– MPW
Dec 27 '18 at 14:55
These wild statements could be true of many irrationals. There's nothing magic about $pi$. Why not $sqrt{2}$ as well?
– MPW
Dec 27 '18 at 14:55
As stated in the answer below, the number $pi$ is not known to have this property (normality), but it's considered likely that it does
– Sauhard Sharma
Dec 27 '18 at 15:11
As stated in the answer below, the number $pi$ is not known to have this property (normality), but it's considered likely that it does
– Sauhard Sharma
Dec 27 '18 at 15:11
add a comment |
1 Answer
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First, $pi$ is not infinite: it's less than four.
There is a presentation on the internet about the number π stating that combinations of digits in this number are so vast that they can contain our date of birth, SSN number, bank account number, and it goes on to say that if we convert every letter into decimals, we would find in this number every word and even everything that we have ever done or said
That presentation is made by someone who doesn't know what they're talking about. This property is called normality, and we don't know if $pi$ is normal or not.
How likely is it that such a set of digits would create the exact pattern of such a long list of digits?
If you're uniformly randomly selecting a real number, 100%.
Would'nt the probability of that happening decrease with the length of the desired combination of numbers?
This isn't a problem, though.
This video implies that such thing would not just happen once, but an infinite number of times.
The video is wrong (assuming it's talking within the context of a single number).
answered Dec 27 '18 at 14:41
user3482749
2,633414
1
+1, but I don't understand your comment on the last point. Wouldn't any finite digit string occur infinitely many times in a normal number?
– saulspatz
Dec 27 '18 at 15:42
I may have been interpreting what the video was saying wrong: it was quite a long way from being clear.
– user3482749
Dec 27 '18 at 15:50
2
If $pi$ were normal then any finite sequence would occur infinitely many times and at a specific frequency. See mathworld.wolfram.com/NormalNumber.html. However, note that it has not been proved that $pi$ is normal.
– badjohn
Dec 27 '18 at 16:27
add a comment |
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First, $pi$ is not infinite: it's less than four.
There is a presentation on the internet about the number π stating that combinations of digits in this number are so vast that they can contain our date of birth, SSN number, bank account number, and it goes on to say that if we convert every letter into decimals, we would find in this number every word and even everything that we have ever done or said
That presentation is made by someone who doesn't know what they're talking about. This property is called normality, and we don't know if $pi$ is normal or not.
How likely is it that such a set of digits would create the exact pattern of such a long list of digits?
If you're uniformly randomly selecting a real number, 100%.
Would'nt the probability of that happening decrease with the length of the desired combination of numbers?
This isn't a problem, though.
This video implies that such thing would not just happen once, but an infinite number of times.
The video is wrong (assuming it's talking within the context of a single number).
answered Dec 27 '18 at 14:41
user3482749
2,633414
1
+1, but I don't understand your comment on the last point. Wouldn't any finite digit string occur infinitely many times in a normal number?
– saulspatz
Dec 27 '18 at 15:42
I may have been interpreting what the video was saying wrong: it was quite a long way from being clear.
– user3482749
Dec 27 '18 at 15:50
2
If $pi$ were normal then any finite sequence would occur infinitely many times and at a specific frequency. See mathworld.wolfram.com/NormalNumber.html. However, note that it has not been proved that $pi$ is normal.
– badjohn
Dec 27 '18 at 16:27
add a comment |
First, $pi$ is not infinite: it's less than four.
There is a presentation on the internet about the number π stating that combinations of digits in this number are so vast that they can contain our date of birth, SSN number, bank account number, and it goes on to say that if we convert every letter into decimals, we would find in this number every word and even everything that we have ever done or said
That presentation is made by someone who doesn't know what they're talking about. This property is called normality, and we don't know if $pi$ is normal or not.
How likely is it that such a set of digits would create the exact pattern of such a long list of digits?
If you're uniformly randomly selecting a real number, 100%.
Would'nt the probability of that happening decrease with the length of the desired combination of numbers?
This isn't a problem, though.
This video implies that such thing would not just happen once, but an infinite number of times.
The video is wrong (assuming it's talking within the context of a single number).
answered Dec 27 '18 at 14:41
user3482749
2,633414
1
+1, but I don't understand your comment on the last point. Wouldn't any finite digit string occur infinitely many times in a normal number?
– saulspatz
Dec 27 '18 at 15:42
I may have been interpreting what the video was saying wrong: it was quite a long way from being clear.
– user3482749
Dec 27 '18 at 15:50
2
If $pi$ were normal then any finite sequence would occur infinitely many times and at a specific frequency. See mathworld.wolfram.com/NormalNumber.html. However, note that it has not been proved that $pi$ is normal.
– badjohn
Dec 27 '18 at 16:27
add a comment |
First, $pi$ is not infinite: it's less than four.
There is a presentation on the internet about the number π stating that combinations of digits in this number are so vast that they can contain our date of birth, SSN number, bank account number, and it goes on to say that if we convert every letter into decimals, we would find in this number every word and even everything that we have ever done or said
That presentation is made by someone who doesn't know what they're talking about. This property is called normality, and we don't know if $pi$ is normal or not.
How likely is it that such a set of digits would create the exact pattern of such a long list of digits?
If you're uniformly randomly selecting a real number, 100%.
Would'nt the probability of that happening decrease with the length of the desired combination of numbers?
This isn't a problem, though.
This video implies that such thing would not just happen once, but an infinite number of times.
The video is wrong (assuming it's talking within the context of a single number).
answered Dec 27 '18 at 14:41
user3482749
2,633414
First, $pi$ is not infinite: it's less than four.
There is a presentation on the internet about the number π stating that combinations of digits in this number are so vast that they can contain our date of birth, SSN number, bank account number, and it goes on to say that if we convert every letter into decimals, we would find in this number every word and even everything that we have ever done or said
That presentation is made by someone who doesn't know what they're talking about. This property is called normality, and we don't know if $pi$ is normal or not.
How likely is it that such a set of digits would create the exact pattern of such a long list of digits?
If you're uniformly randomly selecting a real number, 100%.
Would'nt the probability of that happening decrease with the length of the desired combination of numbers?
This isn't a problem, though.
This video implies that such thing would not just happen once, but an infinite number of times.
The video is wrong (assuming it's talking within the context of a single number).
answered Dec 27 '18 at 14:41
user3482749
2,633414
answered Dec 27 '18 at 14:41
user3482749
2,633414
answered Dec 27 '18 at 14:41
user3482749
2,633414
answered Dec 27 '18 at 14:41
user3482749
2,633414
2,633414
1
+1, but I don't understand your comment on the last point. Wouldn't any finite digit string occur infinitely many times in a normal number?
– saulspatz
Dec 27 '18 at 15:42
I may have been interpreting what the video was saying wrong: it was quite a long way from being clear.
– user3482749
Dec 27 '18 at 15:50
2
If $pi$ were normal then any finite sequence would occur infinitely many times and at a specific frequency. See mathworld.wolfram.com/NormalNumber.html. However, note that it has not been proved that $pi$ is normal.
– badjohn
Dec 27 '18 at 16:27
add a comment |
1
+1, but I don't understand your comment on the last point. Wouldn't any finite digit string occur infinitely many times in a normal number?
– saulspatz
Dec 27 '18 at 15:42
I may have been interpreting what the video was saying wrong: it was quite a long way from being clear.
– user3482749
Dec 27 '18 at 15:50
2
If $pi$ were normal then any finite sequence would occur infinitely many times and at a specific frequency. See mathworld.wolfram.com/NormalNumber.html. However, note that it has not been proved that $pi$ is normal.
– badjohn
Dec 27 '18 at 16:27
1
1
+1, but I don't understand your comment on the last point. Wouldn't any finite digit string occur infinitely many times in a normal number?
– saulspatz
Dec 27 '18 at 15:42
+1, but I don't understand your comment on the last point. Wouldn't any finite digit string occur infinitely many times in a normal number?
– saulspatz
Dec 27 '18 at 15:42
I may have been interpreting what the video was saying wrong: it was quite a long way from being clear.
– user3482749
Dec 27 '18 at 15:50
I may have been interpreting what the video was saying wrong: it was quite a long way from being clear.
– user3482749
Dec 27 '18 at 15:50
2
2
If $pi$ were normal then any finite sequence would occur infinitely many times and at a specific frequency. See mathworld.wolfram.com/NormalNumber.html. However, note that it has not been proved that $pi$ is normal.
– badjohn
Dec 27 '18 at 16:27
If $pi$ were normal then any finite sequence would occur infinitely many times and at a specific frequency. See mathworld.wolfram.com/NormalNumber.html. However, note that it has not been proved that $pi$ is normal.
– badjohn
Dec 27 '18 at 16:27
add a comment |
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See en.wikipedia.org/wiki/Normal_number for a more detailed explanation. We don't know yet if $pi$ is such a number. Be careful with the term "almost all" --it has a very specific meaning in measure theory.
– Apoorv Khurasia
Dec 27 '18 at 14:46
1
These wild statements could be true of many irrationals. There's nothing magic about $pi$. Why not $sqrt{2}$ as well?
– MPW
Dec 27 '18 at 14:55
As stated in the answer below, the number $pi$ is not known to have this property (normality), but it's considered likely that it does
– Sauhard Sharma
Dec 27 '18 at 15:11