Can a hypercomputer solve random sequences? [closed]
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I would love to know the answer to this question. Lets have a hypercomputer which is capable of doing an uncountably many computational steps in finite time with infinite memory. Now could such a cumputer predict exactly all events that happened and will happen in our universe? That is model our universe with arbitrary precision? And if yes, would this machine need to know the initial state, or would it be able to also compute it?
I thought a lot about this and came up with two different scenarios. First one is that if our universe (its laws of physics) are entirely deterministic, then the answer is surely yes, but the second scenario is the one which I would like to ask you about. That is lets say that the Copenhagen interpretation of quantum mechanics is correct and our universe behaves randomly. Would previously mentioned hypercomputer still be able to precisely model our universe? Or I could turn this question into maybe a more formal one, that is could such hypercomputer predict digits in a random sequence?
Thank you very much for your answer,
have a nice day.
set-theory turing-machines random-functions
asked Nov 21 at 21:09
Pan Mrož
252
closed as off-topic by Lord Shark the Unknown, Henrik, Jean-Claude Arbaut, Eric Wofsey, Matthew Towers Nov 21 at 22:51
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is not about mathematics, within the scope defined in the help center." – Lord Shark the Unknown, Henrik, Jean-Claude Arbaut, Eric Wofsey, Matthew Towers
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
1
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I would love to know the answer to this question. Lets have a hypercomputer which is capable of doing an uncountably many computational steps in finite time with infinite memory. Now could such a cumputer predict exactly all events that happened and will happen in our universe? That is model our universe with arbitrary precision? And if yes, would this machine need to know the initial state, or would it be able to also compute it?
I thought a lot about this and came up with two different scenarios. First one is that if our universe (its laws of physics) are entirely deterministic, then the answer is surely yes, but the second scenario is the one which I would like to ask you about. That is lets say that the Copenhagen interpretation of quantum mechanics is correct and our universe behaves randomly. Would previously mentioned hypercomputer still be able to precisely model our universe? Or I could turn this question into maybe a more formal one, that is could such hypercomputer predict digits in a random sequence?
Thank you very much for your answer,
have a nice day.
set-theory turing-machines random-functions
asked Nov 21 at 21:09
Pan Mrož
252
closed as off-topic by Lord Shark the Unknown, Henrik, Jean-Claude Arbaut, Eric Wofsey, Matthew Towers Nov 21 at 22:51
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is not about mathematics, within the scope defined in the help center." – Lord Shark the Unknown, Henrik, Jean-Claude Arbaut, Eric Wofsey, Matthew Towers
If this question can be reworded to fit the rules in the help center, please edit the question.
How do you define randomness?
– rtybase
Nov 21 at 21:54
A sequence (let's say binary) is unpredictable if $P(x_{n+1} mid x_n x_{n-1} x_1 x_0)=frac{1}{2}$, i.e. the knowledge of the previously generated bits reveals nothing about the next bit. A sequence is random (in terms of Kolmogorov complexity) if and only if it is shorter than any computer program that can produce it, i.e. the sequence is incompressible. It has nothing to do with super/hyper nature of the computers.
– rtybase
Nov 21 at 22:20
Your question is not about mathematics, it's about the mathematical model of the universe. This is as relevant to mathematics as asking if it could compute "the meaning of life". (Yes, that's not the same question, the relevance to the mathematics, however, is similar.)
– Asaf Karagila♦
Nov 21 at 23:19
add a comment |
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1
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up vote
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I would love to know the answer to this question. Lets have a hypercomputer which is capable of doing an uncountably many computational steps in finite time with infinite memory. Now could such a cumputer predict exactly all events that happened and will happen in our universe? That is model our universe with arbitrary precision? And if yes, would this machine need to know the initial state, or would it be able to also compute it?
I thought a lot about this and came up with two different scenarios. First one is that if our universe (its laws of physics) are entirely deterministic, then the answer is surely yes, but the second scenario is the one which I would like to ask you about. That is lets say that the Copenhagen interpretation of quantum mechanics is correct and our universe behaves randomly. Would previously mentioned hypercomputer still be able to precisely model our universe? Or I could turn this question into maybe a more formal one, that is could such hypercomputer predict digits in a random sequence?
Thank you very much for your answer,
have a nice day.
set-theory turing-machines random-functions
asked Nov 21 at 21:09
Pan Mrož
252
I would love to know the answer to this question. Lets have a hypercomputer which is capable of doing an uncountably many computational steps in finite time with infinite memory. Now could such a cumputer predict exactly all events that happened and will happen in our universe? That is model our universe with arbitrary precision? And if yes, would this machine need to know the initial state, or would it be able to also compute it?
I thought a lot about this and came up with two different scenarios. First one is that if our universe (its laws of physics) are entirely deterministic, then the answer is surely yes, but the second scenario is the one which I would like to ask you about. That is lets say that the Copenhagen interpretation of quantum mechanics is correct and our universe behaves randomly. Would previously mentioned hypercomputer still be able to precisely model our universe? Or I could turn this question into maybe a more formal one, that is could such hypercomputer predict digits in a random sequence?
Thank you very much for your answer,
have a nice day.
set-theory turing-machines random-functions
set-theory turing-machines random-functions
asked Nov 21 at 21:09
Pan Mrož
252
asked Nov 21 at 21:09
Pan Mrož
252
asked Nov 21 at 21:09
Pan Mrož
252
asked Nov 21 at 21:09
Pan Mrož
252
asked Nov 21 at 21:09
Pan Mrož
252
252
closed as off-topic by Lord Shark the Unknown, Henrik, Jean-Claude Arbaut, Eric Wofsey, Matthew Towers Nov 21 at 22:51
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is not about mathematics, within the scope defined in the help center." – Lord Shark the Unknown, Henrik, Jean-Claude Arbaut, Eric Wofsey, Matthew Towers
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Lord Shark the Unknown, Henrik, Jean-Claude Arbaut, Eric Wofsey, Matthew Towers Nov 21 at 22:51
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is not about mathematics, within the scope defined in the help center." – Lord Shark the Unknown, Henrik, Jean-Claude Arbaut, Eric Wofsey, Matthew Towers
If this question can be reworded to fit the rules in the help center, please edit the question.
How do you define randomness?
– rtybase
Nov 21 at 21:54
A sequence (let's say binary) is unpredictable if $P(x_{n+1} mid x_n x_{n-1} x_1 x_0)=frac{1}{2}$, i.e. the knowledge of the previously generated bits reveals nothing about the next bit. A sequence is random (in terms of Kolmogorov complexity) if and only if it is shorter than any computer program that can produce it, i.e. the sequence is incompressible. It has nothing to do with super/hyper nature of the computers.
– rtybase
Nov 21 at 22:20
Your question is not about mathematics, it's about the mathematical model of the universe. This is as relevant to mathematics as asking if it could compute "the meaning of life". (Yes, that's not the same question, the relevance to the mathematics, however, is similar.)
– Asaf Karagila♦
Nov 21 at 23:19
add a comment |
How do you define randomness?
– rtybase
Nov 21 at 21:54
A sequence (let's say binary) is unpredictable if $P(x_{n+1} mid x_n x_{n-1} x_1 x_0)=frac{1}{2}$, i.e. the knowledge of the previously generated bits reveals nothing about the next bit. A sequence is random (in terms of Kolmogorov complexity) if and only if it is shorter than any computer program that can produce it, i.e. the sequence is incompressible. It has nothing to do with super/hyper nature of the computers.
– rtybase
Nov 21 at 22:20
Your question is not about mathematics, it's about the mathematical model of the universe. This is as relevant to mathematics as asking if it could compute "the meaning of life". (Yes, that's not the same question, the relevance to the mathematics, however, is similar.)
– Asaf Karagila♦
Nov 21 at 23:19
How do you define randomness?
– rtybase
Nov 21 at 21:54
How do you define randomness?
– rtybase
Nov 21 at 21:54
A sequence (let's say binary) is unpredictable if $P(x_{n+1} mid x_n x_{n-1} x_1 x_0)=frac{1}{2}$, i.e. the knowledge of the previously generated bits reveals nothing about the next bit. A sequence is random (in terms of Kolmogorov complexity) if and only if it is shorter than any computer program that can produce it, i.e. the sequence is incompressible. It has nothing to do with super/hyper nature of the computers.
– rtybase
Nov 21 at 22:20
A sequence (let's say binary) is unpredictable if $P(x_{n+1} mid x_n x_{n-1} x_1 x_0)=frac{1}{2}$, i.e. the knowledge of the previously generated bits reveals nothing about the next bit. A sequence is random (in terms of Kolmogorov complexity) if and only if it is shorter than any computer program that can produce it, i.e. the sequence is incompressible. It has nothing to do with super/hyper nature of the computers.
– rtybase
Nov 21 at 22:20
Your question is not about mathematics, it's about the mathematical model of the universe. This is as relevant to mathematics as asking if it could compute "the meaning of life". (Yes, that's not the same question, the relevance to the mathematics, however, is similar.)
– Asaf Karagila♦
Nov 21 at 23:19
Your question is not about mathematics, it's about the mathematical model of the universe. This is as relevant to mathematics as asking if it could compute "the meaning of life". (Yes, that's not the same question, the relevance to the mathematics, however, is similar.)
– Asaf Karagila♦
Nov 21 at 23:19
add a comment |
2 Answers
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In a universe like ours where quantum randomness exists, the answer is clearly No. The randomness is built-in. Thus even a hypercomputer could not calculate when a particular unstable atom decays, only what its half-life is.
But even in an alternate universe where all laws of physics are known and all laws are deterministic and somehow the initial state of the entire universe (which could be infinite) is known to infinite precision, the answer would still be No, unless perhaps if time and space was discrete.
Calculating stuff to an arbitrary precision is not enough if the "stuff" can have any real number value. An arbitrary precision is not generally an infinite precision. And you need infinite precision if you want to claim being able to exactly predict every action from some starting point in time and on into infinity.
If, however, the alternate universe had a smallest unit of time and space, it seems to me that a hypercomputer would be able to accurately predict any future event.
However, in such a universe, I'm not sure it would be possible to actually generate a truely random sequence.
answered Nov 21 at 22:46
Jens
3,6392928
It doesn´t matter if the universe is discrete or continuous. If you have deterministic universe then a such hypercomputer could predict everything even in continous reality as it is by description capable of doing uncountably many comp. steps which means at least the same number of steps as is the cardinality of a set of all real numbers.
– Pan Mrož
Nov 22 at 12:19
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0
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You confuse me. I would assume it couldn't predict digits in a random sequence because they're random, right? Or maybe it's a paradox like "If God can do anything, then can God make a rock that He can't break?" That is the thing with hypothetical machines. You can give them properties that contradict what you said earlier without realizing. Not that God is hypothetical.
Other paradoxes include recursive statements like "This statement is true. Is the previous statement true or false?" where we cannot evaluate them because in order to evaluate them we must recursively evaluate them and we assume it is true but really it may be some indeterminate form of true and false but I digress.
tl;dr no.
answered Nov 21 at 21:33
cmarangu
1118
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2 Answers
2
active
oldest
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2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
In a universe like ours where quantum randomness exists, the answer is clearly No. The randomness is built-in. Thus even a hypercomputer could not calculate when a particular unstable atom decays, only what its half-life is.
But even in an alternate universe where all laws of physics are known and all laws are deterministic and somehow the initial state of the entire universe (which could be infinite) is known to infinite precision, the answer would still be No, unless perhaps if time and space was discrete.
Calculating stuff to an arbitrary precision is not enough if the "stuff" can have any real number value. An arbitrary precision is not generally an infinite precision. And you need infinite precision if you want to claim being able to exactly predict every action from some starting point in time and on into infinity.
If, however, the alternate universe had a smallest unit of time and space, it seems to me that a hypercomputer would be able to accurately predict any future event.
However, in such a universe, I'm not sure it would be possible to actually generate a truely random sequence.
answered Nov 21 at 22:46
Jens
3,6392928
It doesn´t matter if the universe is discrete or continuous. If you have deterministic universe then a such hypercomputer could predict everything even in continous reality as it is by description capable of doing uncountably many comp. steps which means at least the same number of steps as is the cardinality of a set of all real numbers.
– Pan Mrož
Nov 22 at 12:19
add a comment |
up vote
1
down vote
In a universe like ours where quantum randomness exists, the answer is clearly No. The randomness is built-in. Thus even a hypercomputer could not calculate when a particular unstable atom decays, only what its half-life is.
But even in an alternate universe where all laws of physics are known and all laws are deterministic and somehow the initial state of the entire universe (which could be infinite) is known to infinite precision, the answer would still be No, unless perhaps if time and space was discrete.
Calculating stuff to an arbitrary precision is not enough if the "stuff" can have any real number value. An arbitrary precision is not generally an infinite precision. And you need infinite precision if you want to claim being able to exactly predict every action from some starting point in time and on into infinity.
If, however, the alternate universe had a smallest unit of time and space, it seems to me that a hypercomputer would be able to accurately predict any future event.
However, in such a universe, I'm not sure it would be possible to actually generate a truely random sequence.
answered Nov 21 at 22:46
Jens
3,6392928
It doesn´t matter if the universe is discrete or continuous. If you have deterministic universe then a such hypercomputer could predict everything even in continous reality as it is by description capable of doing uncountably many comp. steps which means at least the same number of steps as is the cardinality of a set of all real numbers.
– Pan Mrož
Nov 22 at 12:19
add a comment |
up vote
1
down vote
up vote
1
down vote
In a universe like ours where quantum randomness exists, the answer is clearly No. The randomness is built-in. Thus even a hypercomputer could not calculate when a particular unstable atom decays, only what its half-life is.
But even in an alternate universe where all laws of physics are known and all laws are deterministic and somehow the initial state of the entire universe (which could be infinite) is known to infinite precision, the answer would still be No, unless perhaps if time and space was discrete.
Calculating stuff to an arbitrary precision is not enough if the "stuff" can have any real number value. An arbitrary precision is not generally an infinite precision. And you need infinite precision if you want to claim being able to exactly predict every action from some starting point in time and on into infinity.
If, however, the alternate universe had a smallest unit of time and space, it seems to me that a hypercomputer would be able to accurately predict any future event.
However, in such a universe, I'm not sure it would be possible to actually generate a truely random sequence.
answered Nov 21 at 22:46
Jens
3,6392928
In a universe like ours where quantum randomness exists, the answer is clearly No. The randomness is built-in. Thus even a hypercomputer could not calculate when a particular unstable atom decays, only what its half-life is.
But even in an alternate universe where all laws of physics are known and all laws are deterministic and somehow the initial state of the entire universe (which could be infinite) is known to infinite precision, the answer would still be No, unless perhaps if time and space was discrete.
Calculating stuff to an arbitrary precision is not enough if the "stuff" can have any real number value. An arbitrary precision is not generally an infinite precision. And you need infinite precision if you want to claim being able to exactly predict every action from some starting point in time and on into infinity.
If, however, the alternate universe had a smallest unit of time and space, it seems to me that a hypercomputer would be able to accurately predict any future event.
However, in such a universe, I'm not sure it would be possible to actually generate a truely random sequence.
answered Nov 21 at 22:46
Jens
3,6392928
answered Nov 21 at 22:46
Jens
3,6392928
answered Nov 21 at 22:46
Jens
3,6392928
answered Nov 21 at 22:46
Jens
3,6392928
3,6392928
It doesn´t matter if the universe is discrete or continuous. If you have deterministic universe then a such hypercomputer could predict everything even in continous reality as it is by description capable of doing uncountably many comp. steps which means at least the same number of steps as is the cardinality of a set of all real numbers.
– Pan Mrož
Nov 22 at 12:19
add a comment |
It doesn´t matter if the universe is discrete or continuous. If you have deterministic universe then a such hypercomputer could predict everything even in continous reality as it is by description capable of doing uncountably many comp. steps which means at least the same number of steps as is the cardinality of a set of all real numbers.
– Pan Mrož
Nov 22 at 12:19
It doesn´t matter if the universe is discrete or continuous. If you have deterministic universe then a such hypercomputer could predict everything even in continous reality as it is by description capable of doing uncountably many comp. steps which means at least the same number of steps as is the cardinality of a set of all real numbers.
– Pan Mrož
Nov 22 at 12:19
It doesn´t matter if the universe is discrete or continuous. If you have deterministic universe then a such hypercomputer could predict everything even in continous reality as it is by description capable of doing uncountably many comp. steps which means at least the same number of steps as is the cardinality of a set of all real numbers.
– Pan Mrož
Nov 22 at 12:19
add a comment |
up vote
0
down vote
You confuse me. I would assume it couldn't predict digits in a random sequence because they're random, right? Or maybe it's a paradox like "If God can do anything, then can God make a rock that He can't break?" That is the thing with hypothetical machines. You can give them properties that contradict what you said earlier without realizing. Not that God is hypothetical.
Other paradoxes include recursive statements like "This statement is true. Is the previous statement true or false?" where we cannot evaluate them because in order to evaluate them we must recursively evaluate them and we assume it is true but really it may be some indeterminate form of true and false but I digress.
tl;dr no.
answered Nov 21 at 21:33
cmarangu
1118
add a comment |
up vote
0
down vote
You confuse me. I would assume it couldn't predict digits in a random sequence because they're random, right? Or maybe it's a paradox like "If God can do anything, then can God make a rock that He can't break?" That is the thing with hypothetical machines. You can give them properties that contradict what you said earlier without realizing. Not that God is hypothetical.
Other paradoxes include recursive statements like "This statement is true. Is the previous statement true or false?" where we cannot evaluate them because in order to evaluate them we must recursively evaluate them and we assume it is true but really it may be some indeterminate form of true and false but I digress.
tl;dr no.
answered Nov 21 at 21:33
cmarangu
1118
add a comment |
up vote
0
down vote
up vote
0
down vote
You confuse me. I would assume it couldn't predict digits in a random sequence because they're random, right? Or maybe it's a paradox like "If God can do anything, then can God make a rock that He can't break?" That is the thing with hypothetical machines. You can give them properties that contradict what you said earlier without realizing. Not that God is hypothetical.
Other paradoxes include recursive statements like "This statement is true. Is the previous statement true or false?" where we cannot evaluate them because in order to evaluate them we must recursively evaluate them and we assume it is true but really it may be some indeterminate form of true and false but I digress.
tl;dr no.
answered Nov 21 at 21:33
cmarangu
1118
You confuse me. I would assume it couldn't predict digits in a random sequence because they're random, right? Or maybe it's a paradox like "If God can do anything, then can God make a rock that He can't break?" That is the thing with hypothetical machines. You can give them properties that contradict what you said earlier without realizing. Not that God is hypothetical.
Other paradoxes include recursive statements like "This statement is true. Is the previous statement true or false?" where we cannot evaluate them because in order to evaluate them we must recursively evaluate them and we assume it is true but really it may be some indeterminate form of true and false but I digress.
tl;dr no.
answered Nov 21 at 21:33
cmarangu
1118
answered Nov 21 at 21:33
cmarangu
1118
answered Nov 21 at 21:33
cmarangu
1118
answered Nov 21 at 21:33
cmarangu
1118
1118
add a comment |
add a comment |
How do you define randomness?
– rtybase
Nov 21 at 21:54
A sequence (let's say binary) is unpredictable if $P(x_{n+1} mid x_n x_{n-1} x_1 x_0)=frac{1}{2}$, i.e. the knowledge of the previously generated bits reveals nothing about the next bit. A sequence is random (in terms of Kolmogorov complexity) if and only if it is shorter than any computer program that can produce it, i.e. the sequence is incompressible. It has nothing to do with super/hyper nature of the computers.
– rtybase
Nov 21 at 22:20
Your question is not about mathematics, it's about the mathematical model of the universe. This is as relevant to mathematics as asking if it could compute "the meaning of life". (Yes, that's not the same question, the relevance to the mathematics, however, is similar.)
– Asaf Karagila♦
Nov 21 at 23:19