Am I correct in stating that the study of topology is purely theoretical?Real life applications of...
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Am I correct in stating that the study of topology is purely theoretical?
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$begingroup$
Am I correct in stating that the study of topology is purely theoretical?
To clarify, the real world is discrete or quantized (ie; digital) whether we are discussing atoms, quarks, or strings, etc; but topology seems to depend upon everything being continuous or analog.
For example, if I draw a one inch line and a two inch line on a chalkboard, there is a topological mapping of every point on the one inch line to the two inch line, but in actual fact there are twice as many particles of chalk (or atoms, etc.) on the two inch line as there are on the one inch line. What real world value then does the study of topology serve?
Recommendations for books or publications that answer this fundamental question are welcome.
general-topology reference-request soft-question
edited 13 hours ago
J. W. Tanner
2,4931117
asked 13 hours ago
Ron DotsonRon Dotson
592
New contributor
Ron Dotson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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show 11 more comments
$begingroup$
Am I correct in stating that the study of topology is purely theoretical?
To clarify, the real world is discrete or quantized (ie; digital) whether we are discussing atoms, quarks, or strings, etc; but topology seems to depend upon everything being continuous or analog.
For example, if I draw a one inch line and a two inch line on a chalkboard, there is a topological mapping of every point on the one inch line to the two inch line, but in actual fact there are twice as many particles of chalk (or atoms, etc.) on the two inch line as there are on the one inch line. What real world value then does the study of topology serve?
Recommendations for books or publications that answer this fundamental question are welcome.
general-topology reference-request soft-question
edited 13 hours ago
J. W. Tanner
2,4931117
asked 13 hours ago
Ron DotsonRon Dotson
592
New contributor
Ron Dotson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
16
$begingroup$
Regardless of the true nature of reality, mathematical models are useful for describing reality. Whenever you use mathematics to talk about something in the real world, the most important thing to remember is that you're using a model, and that model will have limitations. The game is to balance these limitations against the ability of the model to make calculations and predictions. Continuous models have proven incredibly useful for making calculations (see: calculus).
$endgroup$
– Alex Kruckman
13 hours ago
4
$begingroup$
@AlexKruckman: Your remark would be worth expanding into an answer.
$endgroup$
– J W
13 hours ago
6
$begingroup$
Possibly related: Topology and the 2016 Nobel Prize in Physics
$endgroup$
– Burnsba
11 hours ago
7
$begingroup$
As a child, I learned to count. But then I realized that even if I have three apples and you have three apples, the apples will not be the same. So what's the point of numbers?
$endgroup$
– Carsten S
11 hours ago
3
$begingroup$
You could ask the same question about real numbers.
$endgroup$
– Barmar
6 hours ago
|
show 11 more comments
$begingroup$
Am I correct in stating that the study of topology is purely theoretical?
To clarify, the real world is discrete or quantized (ie; digital) whether we are discussing atoms, quarks, or strings, etc; but topology seems to depend upon everything being continuous or analog.
For example, if I draw a one inch line and a two inch line on a chalkboard, there is a topological mapping of every point on the one inch line to the two inch line, but in actual fact there are twice as many particles of chalk (or atoms, etc.) on the two inch line as there are on the one inch line. What real world value then does the study of topology serve?
Recommendations for books or publications that answer this fundamental question are welcome.
general-topology reference-request soft-question
edited 13 hours ago
J. W. Tanner
2,4931117
asked 13 hours ago
Ron DotsonRon Dotson
592
New contributor
Ron Dotson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Am I correct in stating that the study of topology is purely theoretical?
To clarify, the real world is discrete or quantized (ie; digital) whether we are discussing atoms, quarks, or strings, etc; but topology seems to depend upon everything being continuous or analog.
For example, if I draw a one inch line and a two inch line on a chalkboard, there is a topological mapping of every point on the one inch line to the two inch line, but in actual fact there are twice as many particles of chalk (or atoms, etc.) on the two inch line as there are on the one inch line. What real world value then does the study of topology serve?
Recommendations for books or publications that answer this fundamental question are welcome.
general-topology reference-request soft-question
general-topology reference-request soft-question
edited 13 hours ago
J. W. Tanner
2,4931117
asked 13 hours ago
Ron DotsonRon Dotson
592
New contributor
Ron Dotson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 13 hours ago
J. W. Tanner
2,4931117
asked 13 hours ago
Ron DotsonRon Dotson
592
New contributor
Ron Dotson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 13 hours ago
J. W. Tanner
2,4931117
edited 13 hours ago
J. W. Tanner
2,4931117
edited 13 hours ago
J. W. Tanner
2,4931117
2,4931117
asked 13 hours ago
Ron DotsonRon Dotson
592
New contributor
Ron Dotson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 13 hours ago
Ron DotsonRon Dotson
592
asked 13 hours ago
Ron DotsonRon Dotson
592
592
New contributor
Ron Dotson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Ron Dotson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Ron Dotson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
16
$begingroup$
Regardless of the true nature of reality, mathematical models are useful for describing reality. Whenever you use mathematics to talk about something in the real world, the most important thing to remember is that you're using a model, and that model will have limitations. The game is to balance these limitations against the ability of the model to make calculations and predictions. Continuous models have proven incredibly useful for making calculations (see: calculus).
$endgroup$
– Alex Kruckman
13 hours ago
4
$begingroup$
@AlexKruckman: Your remark would be worth expanding into an answer.
$endgroup$
– J W
13 hours ago
6
$begingroup$
Possibly related: Topology and the 2016 Nobel Prize in Physics
$endgroup$
– Burnsba
11 hours ago
7
$begingroup$
As a child, I learned to count. But then I realized that even if I have three apples and you have three apples, the apples will not be the same. So what's the point of numbers?
$endgroup$
– Carsten S
11 hours ago
3
$begingroup$
You could ask the same question about real numbers.
$endgroup$
– Barmar
6 hours ago
|
show 11 more comments
16
$begingroup$
Regardless of the true nature of reality, mathematical models are useful for describing reality. Whenever you use mathematics to talk about something in the real world, the most important thing to remember is that you're using a model, and that model will have limitations. The game is to balance these limitations against the ability of the model to make calculations and predictions. Continuous models have proven incredibly useful for making calculations (see: calculus).
$endgroup$
– Alex Kruckman
13 hours ago
4
$begingroup$
@AlexKruckman: Your remark would be worth expanding into an answer.
$endgroup$
– J W
13 hours ago
6
$begingroup$
Possibly related: Topology and the 2016 Nobel Prize in Physics
$endgroup$
– Burnsba
11 hours ago
7
$begingroup$
As a child, I learned to count. But then I realized that even if I have three apples and you have three apples, the apples will not be the same. So what's the point of numbers?
$endgroup$
– Carsten S
11 hours ago
3
$begingroup$
You could ask the same question about real numbers.
$endgroup$
– Barmar
6 hours ago
16
16
$begingroup$
Regardless of the true nature of reality, mathematical models are useful for describing reality. Whenever you use mathematics to talk about something in the real world, the most important thing to remember is that you're using a model, and that model will have limitations. The game is to balance these limitations against the ability of the model to make calculations and predictions. Continuous models have proven incredibly useful for making calculations (see: calculus).
$endgroup$
– Alex Kruckman
13 hours ago
$begingroup$
Regardless of the true nature of reality, mathematical models are useful for describing reality. Whenever you use mathematics to talk about something in the real world, the most important thing to remember is that you're using a model, and that model will have limitations. The game is to balance these limitations against the ability of the model to make calculations and predictions. Continuous models have proven incredibly useful for making calculations (see: calculus).
$endgroup$
– Alex Kruckman
13 hours ago
4
4
$begingroup$
@AlexKruckman: Your remark would be worth expanding into an answer.
$endgroup$
– J W
13 hours ago
$begingroup$
@AlexKruckman: Your remark would be worth expanding into an answer.
$endgroup$
– J W
13 hours ago
6
6
$begingroup$
Possibly related: Topology and the 2016 Nobel Prize in Physics
$endgroup$
– Burnsba
11 hours ago
$begingroup$
Possibly related: Topology and the 2016 Nobel Prize in Physics
$endgroup$
– Burnsba
11 hours ago
7
7
$begingroup$
As a child, I learned to count. But then I realized that even if I have three apples and you have three apples, the apples will not be the same. So what's the point of numbers?
$endgroup$
– Carsten S
11 hours ago
$begingroup$
As a child, I learned to count. But then I realized that even if I have three apples and you have three apples, the apples will not be the same. So what's the point of numbers?
$endgroup$
– Carsten S
11 hours ago
3
3
$begingroup$
You could ask the same question about real numbers.
$endgroup$
– Barmar
6 hours ago
$begingroup$
You could ask the same question about real numbers.
$endgroup$
– Barmar
6 hours ago
|
show 11 more comments
3 Answers
3
active
oldest
votes
$begingroup$
I would invite you to read Robert Ghrist's Elementary Applied Topology or check out Adams & Franzosa's Introduction to Topology: Pure and Applied to get a taste of some of the numerous applications of topology in the real world, regardless of whether the mathematical models involved match reality perfectly at all scales.
answered 13 hours ago
J WJ W
2,0131628
$endgroup$
add a comment |
$begingroup$
You have asked a philosophical question, not a mathematical one.
If by "purely theoretical" you mean something like "useless in the real world" then the answer is no. Topology has contributed significantly to our understanding of differential equations, which model many useful real world phenomena. In quantum mechanics, resolving the puzzling "wave particle duality" depends on seeing how the appropriate mathematical model can be treated with the mathematics of continuous systems. Without that kind of analysis we couldn't understand transistors and build computers.
String theory (which has not yet been useful in the real world) relies on lots of topological ideas - in particular, on the study of Calabi-Yau manifolds.
When you say
the real world is discrete or quantized
you are on shaky philosophical ground. We live in the real world, but we don't know what it "is". All we have in physics are mathematical models we use to make predictions about how it behaves. At the present time the best mathematical models for its small scale behavior are quantum mechanical, but they don't say the real world is "really made up of discrete pieces".
answered 8 hours ago
Ethan BolkerEthan Bolker
43.7k551116
$endgroup$
4
$begingroup$
And those supposedly "discrete" quantum mechanical models are actually expressed in terms of the mathematics of continuums. Perhaps it is possible to develop a truly discrete theory of quantum mechanics, but I've never heard of one.
$endgroup$
– Paul Sinclair
8 hours ago
$begingroup$
the tricky part to me seems to be that our computers are mostly discrete, while our theories are mostly continuous...
$endgroup$
– don bright
2 hours ago
$begingroup$
@PaulSinclair that's because QM is not discrete at all. It only says that certain phenomenon are discrete. Saying everything is discrete in QM is like saying everything is relative in relativity.
$endgroup$
– PyRulez
1 hour ago
$begingroup$
@PyRulez - Those "certain phenomena" include everything we can observe. That being the case, we cannot say with complete confidence whether the continuous underpinings we have given the theory of QM are requisite, or just an artifact of our lack of imagination. So the best we can say with confidence is that our continuous models work. We cannot say that they are the only things that work.
$endgroup$
– Paul Sinclair
42 mins ago
$begingroup$
@PaulSinclair frequency of events?
$endgroup$
– PyRulez
25 mins ago
|
show 1 more comment
$begingroup$
Topology is possible to apply, but to apply it you need to know it, which not particularly many engineers do. :)
Same with any other higher math. You can do really cool applied abstract algebra things too, given you get guy responsible on project to thumb you up. This rarely seems to happen if they are not confident they understand it.
answered 8 hours ago
mathreadlermathreadler
15k72263
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I would invite you to read Robert Ghrist's Elementary Applied Topology or check out Adams & Franzosa's Introduction to Topology: Pure and Applied to get a taste of some of the numerous applications of topology in the real world, regardless of whether the mathematical models involved match reality perfectly at all scales.
answered 13 hours ago
J WJ W
2,0131628
$endgroup$
add a comment |
$begingroup$
I would invite you to read Robert Ghrist's Elementary Applied Topology or check out Adams & Franzosa's Introduction to Topology: Pure and Applied to get a taste of some of the numerous applications of topology in the real world, regardless of whether the mathematical models involved match reality perfectly at all scales.
answered 13 hours ago
J WJ W
2,0131628
$endgroup$
add a comment |
$begingroup$
I would invite you to read Robert Ghrist's Elementary Applied Topology or check out Adams & Franzosa's Introduction to Topology: Pure and Applied to get a taste of some of the numerous applications of topology in the real world, regardless of whether the mathematical models involved match reality perfectly at all scales.
answered 13 hours ago
J WJ W
2,0131628
$endgroup$
I would invite you to read Robert Ghrist's Elementary Applied Topology or check out Adams & Franzosa's Introduction to Topology: Pure and Applied to get a taste of some of the numerous applications of topology in the real world, regardless of whether the mathematical models involved match reality perfectly at all scales.
answered 13 hours ago
J WJ W
2,0131628
answered 13 hours ago
J WJ W
2,0131628
answered 13 hours ago
J WJ W
2,0131628
answered 13 hours ago
J WJ W
2,0131628
2,0131628
add a comment |
add a comment |
$begingroup$
You have asked a philosophical question, not a mathematical one.
If by "purely theoretical" you mean something like "useless in the real world" then the answer is no. Topology has contributed significantly to our understanding of differential equations, which model many useful real world phenomena. In quantum mechanics, resolving the puzzling "wave particle duality" depends on seeing how the appropriate mathematical model can be treated with the mathematics of continuous systems. Without that kind of analysis we couldn't understand transistors and build computers.
String theory (which has not yet been useful in the real world) relies on lots of topological ideas - in particular, on the study of Calabi-Yau manifolds.
When you say
the real world is discrete or quantized
you are on shaky philosophical ground. We live in the real world, but we don't know what it "is". All we have in physics are mathematical models we use to make predictions about how it behaves. At the present time the best mathematical models for its small scale behavior are quantum mechanical, but they don't say the real world is "really made up of discrete pieces".
answered 8 hours ago
Ethan BolkerEthan Bolker
43.7k551116
$endgroup$
4
$begingroup$
And those supposedly "discrete" quantum mechanical models are actually expressed in terms of the mathematics of continuums. Perhaps it is possible to develop a truly discrete theory of quantum mechanics, but I've never heard of one.
$endgroup$
– Paul Sinclair
8 hours ago
$begingroup$
the tricky part to me seems to be that our computers are mostly discrete, while our theories are mostly continuous...
$endgroup$
– don bright
2 hours ago
$begingroup$
@PaulSinclair that's because QM is not discrete at all. It only says that certain phenomenon are discrete. Saying everything is discrete in QM is like saying everything is relative in relativity.
$endgroup$
– PyRulez
1 hour ago
$begingroup$
@PyRulez - Those "certain phenomena" include everything we can observe. That being the case, we cannot say with complete confidence whether the continuous underpinings we have given the theory of QM are requisite, or just an artifact of our lack of imagination. So the best we can say with confidence is that our continuous models work. We cannot say that they are the only things that work.
$endgroup$
– Paul Sinclair
42 mins ago
$begingroup$
@PaulSinclair frequency of events?
$endgroup$
– PyRulez
25 mins ago
|
show 1 more comment
$begingroup$
You have asked a philosophical question, not a mathematical one.
If by "purely theoretical" you mean something like "useless in the real world" then the answer is no. Topology has contributed significantly to our understanding of differential equations, which model many useful real world phenomena. In quantum mechanics, resolving the puzzling "wave particle duality" depends on seeing how the appropriate mathematical model can be treated with the mathematics of continuous systems. Without that kind of analysis we couldn't understand transistors and build computers.
String theory (which has not yet been useful in the real world) relies on lots of topological ideas - in particular, on the study of Calabi-Yau manifolds.
When you say
the real world is discrete or quantized
you are on shaky philosophical ground. We live in the real world, but we don't know what it "is". All we have in physics are mathematical models we use to make predictions about how it behaves. At the present time the best mathematical models for its small scale behavior are quantum mechanical, but they don't say the real world is "really made up of discrete pieces".
answered 8 hours ago
Ethan BolkerEthan Bolker
43.7k551116
$endgroup$
4
$begingroup$
And those supposedly "discrete" quantum mechanical models are actually expressed in terms of the mathematics of continuums. Perhaps it is possible to develop a truly discrete theory of quantum mechanics, but I've never heard of one.
$endgroup$
– Paul Sinclair
8 hours ago
$begingroup$
the tricky part to me seems to be that our computers are mostly discrete, while our theories are mostly continuous...
$endgroup$
– don bright
2 hours ago
$begingroup$
@PaulSinclair that's because QM is not discrete at all. It only says that certain phenomenon are discrete. Saying everything is discrete in QM is like saying everything is relative in relativity.
$endgroup$
– PyRulez
1 hour ago
$begingroup$
@PyRulez - Those "certain phenomena" include everything we can observe. That being the case, we cannot say with complete confidence whether the continuous underpinings we have given the theory of QM are requisite, or just an artifact of our lack of imagination. So the best we can say with confidence is that our continuous models work. We cannot say that they are the only things that work.
$endgroup$
– Paul Sinclair
42 mins ago
$begingroup$
@PaulSinclair frequency of events?
$endgroup$
– PyRulez
25 mins ago
|
show 1 more comment
$begingroup$
You have asked a philosophical question, not a mathematical one.
If by "purely theoretical" you mean something like "useless in the real world" then the answer is no. Topology has contributed significantly to our understanding of differential equations, which model many useful real world phenomena. In quantum mechanics, resolving the puzzling "wave particle duality" depends on seeing how the appropriate mathematical model can be treated with the mathematics of continuous systems. Without that kind of analysis we couldn't understand transistors and build computers.
String theory (which has not yet been useful in the real world) relies on lots of topological ideas - in particular, on the study of Calabi-Yau manifolds.
When you say
the real world is discrete or quantized
you are on shaky philosophical ground. We live in the real world, but we don't know what it "is". All we have in physics are mathematical models we use to make predictions about how it behaves. At the present time the best mathematical models for its small scale behavior are quantum mechanical, but they don't say the real world is "really made up of discrete pieces".
answered 8 hours ago
Ethan BolkerEthan Bolker
43.7k551116
$endgroup$
You have asked a philosophical question, not a mathematical one.
If by "purely theoretical" you mean something like "useless in the real world" then the answer is no. Topology has contributed significantly to our understanding of differential equations, which model many useful real world phenomena. In quantum mechanics, resolving the puzzling "wave particle duality" depends on seeing how the appropriate mathematical model can be treated with the mathematics of continuous systems. Without that kind of analysis we couldn't understand transistors and build computers.
String theory (which has not yet been useful in the real world) relies on lots of topological ideas - in particular, on the study of Calabi-Yau manifolds.
When you say
the real world is discrete or quantized
you are on shaky philosophical ground. We live in the real world, but we don't know what it "is". All we have in physics are mathematical models we use to make predictions about how it behaves. At the present time the best mathematical models for its small scale behavior are quantum mechanical, but they don't say the real world is "really made up of discrete pieces".
answered 8 hours ago
Ethan BolkerEthan Bolker
43.7k551116
answered 8 hours ago
Ethan BolkerEthan Bolker
43.7k551116
answered 8 hours ago
Ethan BolkerEthan Bolker
43.7k551116
answered 8 hours ago
Ethan BolkerEthan Bolker
43.7k551116
43.7k551116
4
$begingroup$
And those supposedly "discrete" quantum mechanical models are actually expressed in terms of the mathematics of continuums. Perhaps it is possible to develop a truly discrete theory of quantum mechanics, but I've never heard of one.
$endgroup$
– Paul Sinclair
8 hours ago
$begingroup$
the tricky part to me seems to be that our computers are mostly discrete, while our theories are mostly continuous...
$endgroup$
– don bright
2 hours ago
$begingroup$
@PaulSinclair that's because QM is not discrete at all. It only says that certain phenomenon are discrete. Saying everything is discrete in QM is like saying everything is relative in relativity.
$endgroup$
– PyRulez
1 hour ago
$begingroup$
@PyRulez - Those "certain phenomena" include everything we can observe. That being the case, we cannot say with complete confidence whether the continuous underpinings we have given the theory of QM are requisite, or just an artifact of our lack of imagination. So the best we can say with confidence is that our continuous models work. We cannot say that they are the only things that work.
$endgroup$
– Paul Sinclair
42 mins ago
$begingroup$
@PaulSinclair frequency of events?
$endgroup$
– PyRulez
25 mins ago
|
show 1 more comment
4
$begingroup$
And those supposedly "discrete" quantum mechanical models are actually expressed in terms of the mathematics of continuums. Perhaps it is possible to develop a truly discrete theory of quantum mechanics, but I've never heard of one.
$endgroup$
– Paul Sinclair
8 hours ago
$begingroup$
the tricky part to me seems to be that our computers are mostly discrete, while our theories are mostly continuous...
$endgroup$
– don bright
2 hours ago
$begingroup$
@PaulSinclair that's because QM is not discrete at all. It only says that certain phenomenon are discrete. Saying everything is discrete in QM is like saying everything is relative in relativity.
$endgroup$
– PyRulez
1 hour ago
$begingroup$
@PyRulez - Those "certain phenomena" include everything we can observe. That being the case, we cannot say with complete confidence whether the continuous underpinings we have given the theory of QM are requisite, or just an artifact of our lack of imagination. So the best we can say with confidence is that our continuous models work. We cannot say that they are the only things that work.
$endgroup$
– Paul Sinclair
42 mins ago
$begingroup$
@PaulSinclair frequency of events?
$endgroup$
– PyRulez
25 mins ago
4
4
$begingroup$
And those supposedly "discrete" quantum mechanical models are actually expressed in terms of the mathematics of continuums. Perhaps it is possible to develop a truly discrete theory of quantum mechanics, but I've never heard of one.
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– Paul Sinclair
8 hours ago
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And those supposedly "discrete" quantum mechanical models are actually expressed in terms of the mathematics of continuums. Perhaps it is possible to develop a truly discrete theory of quantum mechanics, but I've never heard of one.
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– Paul Sinclair
8 hours ago
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the tricky part to me seems to be that our computers are mostly discrete, while our theories are mostly continuous...
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– don bright
2 hours ago
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the tricky part to me seems to be that our computers are mostly discrete, while our theories are mostly continuous...
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– don bright
2 hours ago
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@PaulSinclair that's because QM is not discrete at all. It only says that certain phenomenon are discrete. Saying everything is discrete in QM is like saying everything is relative in relativity.
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– PyRulez
1 hour ago
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@PaulSinclair that's because QM is not discrete at all. It only says that certain phenomenon are discrete. Saying everything is discrete in QM is like saying everything is relative in relativity.
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– PyRulez
1 hour ago
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@PyRulez - Those "certain phenomena" include everything we can observe. That being the case, we cannot say with complete confidence whether the continuous underpinings we have given the theory of QM are requisite, or just an artifact of our lack of imagination. So the best we can say with confidence is that our continuous models work. We cannot say that they are the only things that work.
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– Paul Sinclair
42 mins ago
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@PyRulez - Those "certain phenomena" include everything we can observe. That being the case, we cannot say with complete confidence whether the continuous underpinings we have given the theory of QM are requisite, or just an artifact of our lack of imagination. So the best we can say with confidence is that our continuous models work. We cannot say that they are the only things that work.
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– Paul Sinclair
42 mins ago
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@PaulSinclair frequency of events?
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– PyRulez
25 mins ago
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@PaulSinclair frequency of events?
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– PyRulez
25 mins ago
|
show 1 more comment
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Topology is possible to apply, but to apply it you need to know it, which not particularly many engineers do. :)
Same with any other higher math. You can do really cool applied abstract algebra things too, given you get guy responsible on project to thumb you up. This rarely seems to happen if they are not confident they understand it.
answered 8 hours ago
mathreadlermathreadler
15k72263
$endgroup$
add a comment |
$begingroup$
Topology is possible to apply, but to apply it you need to know it, which not particularly many engineers do. :)
Same with any other higher math. You can do really cool applied abstract algebra things too, given you get guy responsible on project to thumb you up. This rarely seems to happen if they are not confident they understand it.
answered 8 hours ago
mathreadlermathreadler
15k72263
$endgroup$
add a comment |
$begingroup$
Topology is possible to apply, but to apply it you need to know it, which not particularly many engineers do. :)
Same with any other higher math. You can do really cool applied abstract algebra things too, given you get guy responsible on project to thumb you up. This rarely seems to happen if they are not confident they understand it.
answered 8 hours ago
mathreadlermathreadler
15k72263
$endgroup$
Topology is possible to apply, but to apply it you need to know it, which not particularly many engineers do. :)
Same with any other higher math. You can do really cool applied abstract algebra things too, given you get guy responsible on project to thumb you up. This rarely seems to happen if they are not confident they understand it.
answered 8 hours ago
mathreadlermathreadler
15k72263
answered 8 hours ago
mathreadlermathreadler
15k72263
answered 8 hours ago
mathreadlermathreadler
15k72263
answered 8 hours ago
mathreadlermathreadler
15k72263
15k72263
add a comment |
add a comment |
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16
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Regardless of the true nature of reality, mathematical models are useful for describing reality. Whenever you use mathematics to talk about something in the real world, the most important thing to remember is that you're using a model, and that model will have limitations. The game is to balance these limitations against the ability of the model to make calculations and predictions. Continuous models have proven incredibly useful for making calculations (see: calculus).
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– Alex Kruckman
13 hours ago
4
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@AlexKruckman: Your remark would be worth expanding into an answer.
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– J W
13 hours ago
6
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Possibly related: Topology and the 2016 Nobel Prize in Physics
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– Burnsba
11 hours ago
7
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As a child, I learned to count. But then I realized that even if I have three apples and you have three apples, the apples will not be the same. So what's the point of numbers?
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– Carsten S
11 hours ago
3
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You could ask the same question about real numbers.
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– Barmar
6 hours ago