Mixing
Philosophy of mathematics
$begingroup$
There is a question which made my mind busy for a while: assume that we are working with the function: $ y = sqrt x$. when we draw it continuously, it means that for example the $x = pi $ or $x = sqrt 2$ exists.
but in real world it is impossible to specify a specefic length to these numbers (because in our best performance, we can divide the length to the subatomic levels).
what is the difference between length in the mathematics world and in reality?
it would be my pleasure to have your answers.
algebra-precalculus philosophy
edited Jan 9 at 17:43
user
4,0001627
asked Jan 9 at 13:03
AmirAmir
6
$endgroup$
|
show 3 more comments
$begingroup$
There is a question which made my mind busy for a while: assume that we are working with the function: $ y = sqrt x$. when we draw it continuously, it means that for example the $x = pi $ or $x = sqrt 2$ exists.
but in real world it is impossible to specify a specefic length to these numbers (because in our best performance, we can divide the length to the subatomic levels).
what is the difference between length in the mathematics world and in reality?
it would be my pleasure to have your answers.
algebra-precalculus philosophy
edited Jan 9 at 17:43
user
4,0001627
asked Jan 9 at 13:03
AmirAmir
6
$endgroup$
$begingroup$
In reality, you cannot even draw , lets say , a square with sides EXACTLY $1cm$ long.
$endgroup$
– Peter
Jan 9 at 13:12
$begingroup$
Well, I think you said it yourself already. In some sense, the real world is quantized and length (for example) can only get certain values ... Is there something else you're wondering about?
$endgroup$
– Matti P.
Jan 9 at 13:13
1
$begingroup$
The entirety of mathematics is idealized.
$endgroup$
– KM101
Jan 9 at 13:14
1
$begingroup$
Nobody knows whether "reality" contains real lengths like $sqrt{2}$ or not. Probably nobody will ever know. Almost certainly not in our lifetime. Sorry!
$endgroup$
– dbx
Jan 9 at 13:57
1
$begingroup$
All objects in mathematics are ideal objects that obey very simple rules with absolute certainty. It is not surprising that the real world does not exactly match these ideals. What is surprising is that the real world is close enough to these ideals to allow us to build pyramids, land on the Moon and talk to people on the other side of the world at the touch of a button.
$endgroup$
– gandalf61
Jan 9 at 15:34
|
show 3 more comments
$begingroup$
There is a question which made my mind busy for a while: assume that we are working with the function: $ y = sqrt x$. when we draw it continuously, it means that for example the $x = pi $ or $x = sqrt 2$ exists.
but in real world it is impossible to specify a specefic length to these numbers (because in our best performance, we can divide the length to the subatomic levels).
what is the difference between length in the mathematics world and in reality?
it would be my pleasure to have your answers.
algebra-precalculus philosophy
edited Jan 9 at 17:43
user
4,0001627
asked Jan 9 at 13:03
AmirAmir
6
$endgroup$
There is a question which made my mind busy for a while: assume that we are working with the function: $ y = sqrt x$. when we draw it continuously, it means that for example the $x = pi $ or $x = sqrt 2$ exists.
but in real world it is impossible to specify a specefic length to these numbers (because in our best performance, we can divide the length to the subatomic levels).
what is the difference between length in the mathematics world and in reality?
it would be my pleasure to have your answers.
algebra-precalculus philosophy
algebra-precalculus philosophy
edited Jan 9 at 17:43
user
4,0001627
asked Jan 9 at 13:03
AmirAmir
6
edited Jan 9 at 17:43
user
4,0001627
asked Jan 9 at 13:03
AmirAmir
6
edited Jan 9 at 17:43
user
4,0001627
edited Jan 9 at 17:43
user
4,0001627
edited Jan 9 at 17:43
user
4,0001627
4,0001627
asked Jan 9 at 13:03
AmirAmir
6
asked Jan 9 at 13:03
AmirAmir
6
asked Jan 9 at 13:03
AmirAmir
6
6
$begingroup$
In reality, you cannot even draw , lets say , a square with sides EXACTLY $1cm$ long.
$endgroup$
– Peter
Jan 9 at 13:12
$begingroup$
Well, I think you said it yourself already. In some sense, the real world is quantized and length (for example) can only get certain values ... Is there something else you're wondering about?
$endgroup$
– Matti P.
Jan 9 at 13:13
1
$begingroup$
The entirety of mathematics is idealized.
$endgroup$
– KM101
Jan 9 at 13:14
1
$begingroup$
Nobody knows whether "reality" contains real lengths like $sqrt{2}$ or not. Probably nobody will ever know. Almost certainly not in our lifetime. Sorry!
$endgroup$
– dbx
Jan 9 at 13:57
1
$begingroup$
All objects in mathematics are ideal objects that obey very simple rules with absolute certainty. It is not surprising that the real world does not exactly match these ideals. What is surprising is that the real world is close enough to these ideals to allow us to build pyramids, land on the Moon and talk to people on the other side of the world at the touch of a button.
$endgroup$
– gandalf61
Jan 9 at 15:34
|
show 3 more comments
$begingroup$
In reality, you cannot even draw , lets say , a square with sides EXACTLY $1cm$ long.
$endgroup$
– Peter
Jan 9 at 13:12
$begingroup$
Well, I think you said it yourself already. In some sense, the real world is quantized and length (for example) can only get certain values ... Is there something else you're wondering about?
$endgroup$
– Matti P.
Jan 9 at 13:13
1
$begingroup$
The entirety of mathematics is idealized.
$endgroup$
– KM101
Jan 9 at 13:14
1
$begingroup$
Nobody knows whether "reality" contains real lengths like $sqrt{2}$ or not. Probably nobody will ever know. Almost certainly not in our lifetime. Sorry!
$endgroup$
– dbx
Jan 9 at 13:57
1
$begingroup$
All objects in mathematics are ideal objects that obey very simple rules with absolute certainty. It is not surprising that the real world does not exactly match these ideals. What is surprising is that the real world is close enough to these ideals to allow us to build pyramids, land on the Moon and talk to people on the other side of the world at the touch of a button.
$endgroup$
– gandalf61
Jan 9 at 15:34
$begingroup$
In reality, you cannot even draw , lets say , a square with sides EXACTLY $1cm$ long.
$endgroup$
– Peter
Jan 9 at 13:12
$begingroup$
In reality, you cannot even draw , lets say , a square with sides EXACTLY $1cm$ long.
$endgroup$
– Peter
Jan 9 at 13:12
$begingroup$
Well, I think you said it yourself already. In some sense, the real world is quantized and length (for example) can only get certain values ... Is there something else you're wondering about?
$endgroup$
– Matti P.
Jan 9 at 13:13
$begingroup$
Well, I think you said it yourself already. In some sense, the real world is quantized and length (for example) can only get certain values ... Is there something else you're wondering about?
$endgroup$
– Matti P.
Jan 9 at 13:13
1
1
$begingroup$
The entirety of mathematics is idealized.
$endgroup$
– KM101
Jan 9 at 13:14
$begingroup$
The entirety of mathematics is idealized.
$endgroup$
– KM101
Jan 9 at 13:14
1
1
$begingroup$
Nobody knows whether "reality" contains real lengths like $sqrt{2}$ or not. Probably nobody will ever know. Almost certainly not in our lifetime. Sorry!
$endgroup$
– dbx
Jan 9 at 13:57
$begingroup$
Nobody knows whether "reality" contains real lengths like $sqrt{2}$ or not. Probably nobody will ever know. Almost certainly not in our lifetime. Sorry!
$endgroup$
– dbx
Jan 9 at 13:57
1
1
$begingroup$
All objects in mathematics are ideal objects that obey very simple rules with absolute certainty. It is not surprising that the real world does not exactly match these ideals. What is surprising is that the real world is close enough to these ideals to allow us to build pyramids, land on the Moon and talk to people on the other side of the world at the touch of a button.
$endgroup$
– gandalf61
Jan 9 at 15:34
$begingroup$
All objects in mathematics are ideal objects that obey very simple rules with absolute certainty. It is not surprising that the real world does not exactly match these ideals. What is surprising is that the real world is close enough to these ideals to allow us to build pyramids, land on the Moon and talk to people on the other side of the world at the touch of a button.
$endgroup$
– gandalf61
Jan 9 at 15:34
|
show 3 more comments
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$begingroup$
In reality, you cannot even draw , lets say , a square with sides EXACTLY $1cm$ long.
$endgroup$
– Peter
Jan 9 at 13:12
$begingroup$
Well, I think you said it yourself already. In some sense, the real world is quantized and length (for example) can only get certain values ... Is there something else you're wondering about?
$endgroup$
– Matti P.
Jan 9 at 13:13
1
$begingroup$
The entirety of mathematics is idealized.
$endgroup$
– KM101
Jan 9 at 13:14
1
$begingroup$
Nobody knows whether "reality" contains real lengths like $sqrt{2}$ or not. Probably nobody will ever know. Almost certainly not in our lifetime. Sorry!
$endgroup$
– dbx
Jan 9 at 13:57
1
$begingroup$
All objects in mathematics are ideal objects that obey very simple rules with absolute certainty. It is not surprising that the real world does not exactly match these ideals. What is surprising is that the real world is close enough to these ideals to allow us to build pyramids, land on the Moon and talk to people on the other side of the world at the touch of a button.
$endgroup$
– gandalf61
Jan 9 at 15:34