Do random experiments actually exist?
$begingroup$
I am studying probability and in most of the books that i have read they mention that for an experiment to be random-- (1)there should be more than 1 possible outcome--(2)even when the experiment is repeated under similar conditions the outcomes must not be predictable.The second point really confuses me...if we take a coin toss for example and we repeat the experiment under totally similar conditions of gravity,air resistance,apply the same force,etc won't we be able to predict the exact outcome every time and as long as the conditions remain same my intuition tells me that i will get the same outcome every time....so do random experiments exist?and if they do what can be considered as a random experiment?
probability probability-theory
asked Dec 12 '18 at 19:18
Suzie WatersSuzie Waters
553
$endgroup$
add a comment |
$begingroup$
I am studying probability and in most of the books that i have read they mention that for an experiment to be random-- (1)there should be more than 1 possible outcome--(2)even when the experiment is repeated under similar conditions the outcomes must not be predictable.The second point really confuses me...if we take a coin toss for example and we repeat the experiment under totally similar conditions of gravity,air resistance,apply the same force,etc won't we be able to predict the exact outcome every time and as long as the conditions remain same my intuition tells me that i will get the same outcome every time....so do random experiments exist?and if they do what can be considered as a random experiment?
probability probability-theory
asked Dec 12 '18 at 19:18
Suzie WatersSuzie Waters
553
$endgroup$
$begingroup$
I don't know why you're confused by the second point. You correctly deduced that a coin toss is not random. Also, talking about "random" in the real world is not rigorous. Maybe you should post this question on some physics or engineering page
$endgroup$
– mathworker21
Dec 12 '18 at 19:23
1
$begingroup$
Whatever a "random experiment" is, it is supposed to include things like rolling a die and shooting a free throw. You are right that if the same exact experiment were performed we would get the same result every time (except perhaps in quantum mechanics). The axiomatic approach to probability sidesteps this issue. Mathematical modelers are then free to use the axioms of probability to predict what will happen if you roll a die a large number of times, etc. By the way, an alternative viewpoint is that probabilities represent degrees of belief.
$endgroup$
– littleO
Dec 12 '18 at 19:35
add a comment |
$begingroup$
I am studying probability and in most of the books that i have read they mention that for an experiment to be random-- (1)there should be more than 1 possible outcome--(2)even when the experiment is repeated under similar conditions the outcomes must not be predictable.The second point really confuses me...if we take a coin toss for example and we repeat the experiment under totally similar conditions of gravity,air resistance,apply the same force,etc won't we be able to predict the exact outcome every time and as long as the conditions remain same my intuition tells me that i will get the same outcome every time....so do random experiments exist?and if they do what can be considered as a random experiment?
probability probability-theory
asked Dec 12 '18 at 19:18
Suzie WatersSuzie Waters
553
$endgroup$
I am studying probability and in most of the books that i have read they mention that for an experiment to be random-- (1)there should be more than 1 possible outcome--(2)even when the experiment is repeated under similar conditions the outcomes must not be predictable.The second point really confuses me...if we take a coin toss for example and we repeat the experiment under totally similar conditions of gravity,air resistance,apply the same force,etc won't we be able to predict the exact outcome every time and as long as the conditions remain same my intuition tells me that i will get the same outcome every time....so do random experiments exist?and if they do what can be considered as a random experiment?
probability probability-theory
probability probability-theory
asked Dec 12 '18 at 19:18
Suzie WatersSuzie Waters
553
asked Dec 12 '18 at 19:18
Suzie WatersSuzie Waters
553
asked Dec 12 '18 at 19:18
Suzie WatersSuzie Waters
553
asked Dec 12 '18 at 19:18
Suzie WatersSuzie Waters
553
asked Dec 12 '18 at 19:18
Suzie WatersSuzie Waters
553
553
$begingroup$
I don't know why you're confused by the second point. You correctly deduced that a coin toss is not random. Also, talking about "random" in the real world is not rigorous. Maybe you should post this question on some physics or engineering page
$endgroup$
– mathworker21
Dec 12 '18 at 19:23
1
$begingroup$
Whatever a "random experiment" is, it is supposed to include things like rolling a die and shooting a free throw. You are right that if the same exact experiment were performed we would get the same result every time (except perhaps in quantum mechanics). The axiomatic approach to probability sidesteps this issue. Mathematical modelers are then free to use the axioms of probability to predict what will happen if you roll a die a large number of times, etc. By the way, an alternative viewpoint is that probabilities represent degrees of belief.
$endgroup$
– littleO
Dec 12 '18 at 19:35
add a comment |
$begingroup$
I don't know why you're confused by the second point. You correctly deduced that a coin toss is not random. Also, talking about "random" in the real world is not rigorous. Maybe you should post this question on some physics or engineering page
$endgroup$
– mathworker21
Dec 12 '18 at 19:23
1
$begingroup$
Whatever a "random experiment" is, it is supposed to include things like rolling a die and shooting a free throw. You are right that if the same exact experiment were performed we would get the same result every time (except perhaps in quantum mechanics). The axiomatic approach to probability sidesteps this issue. Mathematical modelers are then free to use the axioms of probability to predict what will happen if you roll a die a large number of times, etc. By the way, an alternative viewpoint is that probabilities represent degrees of belief.
$endgroup$
– littleO
Dec 12 '18 at 19:35
$begingroup$
I don't know why you're confused by the second point. You correctly deduced that a coin toss is not random. Also, talking about "random" in the real world is not rigorous. Maybe you should post this question on some physics or engineering page
$endgroup$
– mathworker21
Dec 12 '18 at 19:23
$begingroup$
I don't know why you're confused by the second point. You correctly deduced that a coin toss is not random. Also, talking about "random" in the real world is not rigorous. Maybe you should post this question on some physics or engineering page
$endgroup$
– mathworker21
Dec 12 '18 at 19:23
1
1
$begingroup$
Whatever a "random experiment" is, it is supposed to include things like rolling a die and shooting a free throw. You are right that if the same exact experiment were performed we would get the same result every time (except perhaps in quantum mechanics). The axiomatic approach to probability sidesteps this issue. Mathematical modelers are then free to use the axioms of probability to predict what will happen if you roll a die a large number of times, etc. By the way, an alternative viewpoint is that probabilities represent degrees of belief.
$endgroup$
– littleO
Dec 12 '18 at 19:35
$begingroup$
Whatever a "random experiment" is, it is supposed to include things like rolling a die and shooting a free throw. You are right that if the same exact experiment were performed we would get the same result every time (except perhaps in quantum mechanics). The axiomatic approach to probability sidesteps this issue. Mathematical modelers are then free to use the axioms of probability to predict what will happen if you roll a die a large number of times, etc. By the way, an alternative viewpoint is that probabilities represent degrees of belief.
$endgroup$
– littleO
Dec 12 '18 at 19:35
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
There is a long standing question of whether true randomness actually exists. Sometimes these discussions delve closer to theology than math or physics. Computers have long been criticized for the low quality of their random number generators.
Radioactive decay, and quantum properties are considered to be random. They are definitely unknowable.
Chaos theory says that many systems have a high degree of sensitivity to initial conditions. And so, as we move away from these initial conditions, the future state of the system becomes increasingly difficult to predict. This means that no matter how good our data is, we will never be able to generate good long-range weather forecasts. It also suggests that coin flipping, dice rolling and bingo hoppers tend to be good random number generators.
So, while we probably can build a coin flipping machine that flips head every time, it is safe to say that a human who has not practiced his coin flipping will only flip heads 50% of the time.
answered Dec 12 '18 at 19:48
Doug MDoug M
45.3k31954
$endgroup$
add a comment |
$begingroup$
In classical physics it is true that if you were able to reproduce the initial conditions exactly, the result would be the same. However, in quantum mechanics it is not. If you measure an observable in a state that is not an eigenstate of that observable, the results you get are not determined. Such a measurement does constitute a "random experiment" in the sense of probability theory.
This is not just theory: you can buy a device that conducts such experiments to produce random numbers
answered Dec 12 '18 at 19:25
Robert IsraelRobert Israel
325k23214468
$endgroup$
add a comment |
$begingroup$
This has nothing to to with mathematics but with physics.
A few years ago I had a discussion with some person who claimed that something is impossible because some process is "random"; this is why I was searching the internet for an answer to your question:
According to the website I found it was not possible to find out if there really are processes that are what you call "random". I think that this still is not possible.
However that website said that there are different "levels" of randomness:
One "level" is: Although the outcome of the experiment is predetermined, it is not possible to predict the outcome. Such experiments definitely exist.
answered Dec 12 '18 at 19:39
Martin RosenauMartin Rosenau
1,1661410
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add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
There is a long standing question of whether true randomness actually exists. Sometimes these discussions delve closer to theology than math or physics. Computers have long been criticized for the low quality of their random number generators.
Radioactive decay, and quantum properties are considered to be random. They are definitely unknowable.
Chaos theory says that many systems have a high degree of sensitivity to initial conditions. And so, as we move away from these initial conditions, the future state of the system becomes increasingly difficult to predict. This means that no matter how good our data is, we will never be able to generate good long-range weather forecasts. It also suggests that coin flipping, dice rolling and bingo hoppers tend to be good random number generators.
So, while we probably can build a coin flipping machine that flips head every time, it is safe to say that a human who has not practiced his coin flipping will only flip heads 50% of the time.
answered Dec 12 '18 at 19:48
Doug MDoug M
45.3k31954
$endgroup$
add a comment |
$begingroup$
There is a long standing question of whether true randomness actually exists. Sometimes these discussions delve closer to theology than math or physics. Computers have long been criticized for the low quality of their random number generators.
Radioactive decay, and quantum properties are considered to be random. They are definitely unknowable.
Chaos theory says that many systems have a high degree of sensitivity to initial conditions. And so, as we move away from these initial conditions, the future state of the system becomes increasingly difficult to predict. This means that no matter how good our data is, we will never be able to generate good long-range weather forecasts. It also suggests that coin flipping, dice rolling and bingo hoppers tend to be good random number generators.
So, while we probably can build a coin flipping machine that flips head every time, it is safe to say that a human who has not practiced his coin flipping will only flip heads 50% of the time.
answered Dec 12 '18 at 19:48
Doug MDoug M
45.3k31954
$endgroup$
add a comment |
$begingroup$
There is a long standing question of whether true randomness actually exists. Sometimes these discussions delve closer to theology than math or physics. Computers have long been criticized for the low quality of their random number generators.
Radioactive decay, and quantum properties are considered to be random. They are definitely unknowable.
Chaos theory says that many systems have a high degree of sensitivity to initial conditions. And so, as we move away from these initial conditions, the future state of the system becomes increasingly difficult to predict. This means that no matter how good our data is, we will never be able to generate good long-range weather forecasts. It also suggests that coin flipping, dice rolling and bingo hoppers tend to be good random number generators.
So, while we probably can build a coin flipping machine that flips head every time, it is safe to say that a human who has not practiced his coin flipping will only flip heads 50% of the time.
answered Dec 12 '18 at 19:48
Doug MDoug M
45.3k31954
$endgroup$
There is a long standing question of whether true randomness actually exists. Sometimes these discussions delve closer to theology than math or physics. Computers have long been criticized for the low quality of their random number generators.
Radioactive decay, and quantum properties are considered to be random. They are definitely unknowable.
Chaos theory says that many systems have a high degree of sensitivity to initial conditions. And so, as we move away from these initial conditions, the future state of the system becomes increasingly difficult to predict. This means that no matter how good our data is, we will never be able to generate good long-range weather forecasts. It also suggests that coin flipping, dice rolling and bingo hoppers tend to be good random number generators.
So, while we probably can build a coin flipping machine that flips head every time, it is safe to say that a human who has not practiced his coin flipping will only flip heads 50% of the time.
answered Dec 12 '18 at 19:48
Doug MDoug M
45.3k31954
answered Dec 12 '18 at 19:48
Doug MDoug M
45.3k31954
answered Dec 12 '18 at 19:48
Doug MDoug M
45.3k31954
answered Dec 12 '18 at 19:48
Doug MDoug M
45.3k31954
45.3k31954
add a comment |
add a comment |
$begingroup$
In classical physics it is true that if you were able to reproduce the initial conditions exactly, the result would be the same. However, in quantum mechanics it is not. If you measure an observable in a state that is not an eigenstate of that observable, the results you get are not determined. Such a measurement does constitute a "random experiment" in the sense of probability theory.
This is not just theory: you can buy a device that conducts such experiments to produce random numbers
answered Dec 12 '18 at 19:25
Robert IsraelRobert Israel
325k23214468
$endgroup$
add a comment |
$begingroup$
In classical physics it is true that if you were able to reproduce the initial conditions exactly, the result would be the same. However, in quantum mechanics it is not. If you measure an observable in a state that is not an eigenstate of that observable, the results you get are not determined. Such a measurement does constitute a "random experiment" in the sense of probability theory.
This is not just theory: you can buy a device that conducts such experiments to produce random numbers
answered Dec 12 '18 at 19:25
Robert IsraelRobert Israel
325k23214468
$endgroup$
add a comment |
$begingroup$
In classical physics it is true that if you were able to reproduce the initial conditions exactly, the result would be the same. However, in quantum mechanics it is not. If you measure an observable in a state that is not an eigenstate of that observable, the results you get are not determined. Such a measurement does constitute a "random experiment" in the sense of probability theory.
This is not just theory: you can buy a device that conducts such experiments to produce random numbers
answered Dec 12 '18 at 19:25
Robert IsraelRobert Israel
325k23214468
$endgroup$
In classical physics it is true that if you were able to reproduce the initial conditions exactly, the result would be the same. However, in quantum mechanics it is not. If you measure an observable in a state that is not an eigenstate of that observable, the results you get are not determined. Such a measurement does constitute a "random experiment" in the sense of probability theory.
This is not just theory: you can buy a device that conducts such experiments to produce random numbers
answered Dec 12 '18 at 19:25
Robert IsraelRobert Israel
325k23214468
edited Dec 12 '18 at 19:30
answered Dec 12 '18 at 19:25
Robert IsraelRobert Israel
325k23214468
answered Dec 12 '18 at 19:25
Robert IsraelRobert Israel
325k23214468
answered Dec 12 '18 at 19:25
Robert IsraelRobert Israel
325k23214468
325k23214468
add a comment |
add a comment |
$begingroup$
This has nothing to to with mathematics but with physics.
A few years ago I had a discussion with some person who claimed that something is impossible because some process is "random"; this is why I was searching the internet for an answer to your question:
According to the website I found it was not possible to find out if there really are processes that are what you call "random". I think that this still is not possible.
However that website said that there are different "levels" of randomness:
One "level" is: Although the outcome of the experiment is predetermined, it is not possible to predict the outcome. Such experiments definitely exist.
answered Dec 12 '18 at 19:39
Martin RosenauMartin Rosenau
1,1661410
$endgroup$
add a comment |
$begingroup$
This has nothing to to with mathematics but with physics.
A few years ago I had a discussion with some person who claimed that something is impossible because some process is "random"; this is why I was searching the internet for an answer to your question:
According to the website I found it was not possible to find out if there really are processes that are what you call "random". I think that this still is not possible.
However that website said that there are different "levels" of randomness:
One "level" is: Although the outcome of the experiment is predetermined, it is not possible to predict the outcome. Such experiments definitely exist.
answered Dec 12 '18 at 19:39
Martin RosenauMartin Rosenau
1,1661410
$endgroup$
add a comment |
$begingroup$
This has nothing to to with mathematics but with physics.
A few years ago I had a discussion with some person who claimed that something is impossible because some process is "random"; this is why I was searching the internet for an answer to your question:
According to the website I found it was not possible to find out if there really are processes that are what you call "random". I think that this still is not possible.
However that website said that there are different "levels" of randomness:
One "level" is: Although the outcome of the experiment is predetermined, it is not possible to predict the outcome. Such experiments definitely exist.
answered Dec 12 '18 at 19:39
Martin RosenauMartin Rosenau
1,1661410
$endgroup$
This has nothing to to with mathematics but with physics.
A few years ago I had a discussion with some person who claimed that something is impossible because some process is "random"; this is why I was searching the internet for an answer to your question:
According to the website I found it was not possible to find out if there really are processes that are what you call "random". I think that this still is not possible.
However that website said that there are different "levels" of randomness:
One "level" is: Although the outcome of the experiment is predetermined, it is not possible to predict the outcome. Such experiments definitely exist.
answered Dec 12 '18 at 19:39
Martin RosenauMartin Rosenau
1,1661410
answered Dec 12 '18 at 19:39
Martin RosenauMartin Rosenau
1,1661410
answered Dec 12 '18 at 19:39
Martin RosenauMartin Rosenau
1,1661410
answered Dec 12 '18 at 19:39
Martin RosenauMartin Rosenau
1,1661410
1,1661410
add a comment |
add a comment |
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$begingroup$
I don't know why you're confused by the second point. You correctly deduced that a coin toss is not random. Also, talking about "random" in the real world is not rigorous. Maybe you should post this question on some physics or engineering page
$endgroup$
– mathworker21
Dec 12 '18 at 19:23
1
$begingroup$
Whatever a "random experiment" is, it is supposed to include things like rolling a die and shooting a free throw. You are right that if the same exact experiment were performed we would get the same result every time (except perhaps in quantum mechanics). The axiomatic approach to probability sidesteps this issue. Mathematical modelers are then free to use the axioms of probability to predict what will happen if you roll a die a large number of times, etc. By the way, an alternative viewpoint is that probabilities represent degrees of belief.
$endgroup$
– littleO
Dec 12 '18 at 19:35