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More of a rant, but since I began to implement algorithms from various papers for my PhD, my aversion to mathematical notation grows steadily. More often than n

by davnn 6y ago

More of a rant, but since I began to implement algorithms from various papers for my PhD, my aversion to mathematical notation grows steadily. More often than not it's imprecise and hard to reproduce.

wdkrnls 6y ago
This reminds me of: https://dspace.mit.edu/handle/1721.1/6707 https://dspace.mit.edu/handle/1721.1/6707 https://www.significancemagazine.com/2-uncategorised/593-cargo-cult-statistics-and-scientific-crisis https://www.significancemagazine.com/2-uncategorised/593-car...
rahimiali 6y ago
your objection might be to the author of the notation, not the notation itself. or maybe to the review system that's supposed to catch this kind of imprecision. as with any language, it's possible to write nonsense or even self-conflicting statements in mathematical notation.
- davnn 6y ago
  Well, I believe the authors do their best to convey their ideas, but due to the fact that the notation is mostly informal it's easy to miss details. Also, different institutes might use their own special notation to describe the same ideas and even individual authors prefer some notation over another. All in all, imprecise probably was the wrong term. The statements are precise for the people working in this specific "bubble" of research, because they might know the implicit assumptions made and in the worst case, the only one who knows the implicit assumptions is the author.
  - grayclhn 6y ago
    TBF, if key assumptions are left implicit, it’s not math.
dorkwood 6y ago
I also sometimes have to translate mathematical notation to algorithms. As a non-mathematician, math notation seems similar to naming all your variables 'a', 'b', 'c' etc. and then writing a key elsewhere that explains that 'b' stands for 'car deceleration rate'. This would be insane to do in code, why is it normal in mathematics? Note: I had this example in my head while writing https://www.traffic-simulation.de/info/IDMsstar.png https://www.traffic-simulation.de/info/IDMsstar.png
- abdullahkhalids 6y ago
  Because one of the main purposes of mathematical symbols is to be manipulated by humans by hand, so short variable names are essential. For programming, the same constraint does not apply.
  - dorkwood 6y ago
    Right, so it's all stems from mathematicians working with pencil and paper. Are mathematicians ever frustrated that they don't understand what the variables mean? Or are you able to look at the above equation and infer the meaning of the variables based on experience? I understand that there are symbols such as "delta" which basically always mean the same thing. But would you have been able to tell what "b" meant without someone telling you?
    - abdullahkhalids 6y ago
      > Are mathematicians ever frustrated that they don't understand what the variables mean? Yes, if the presenter does not define them, or if the variables don't have a "usual" definition within the field. > But would you have been able to tell what "b" meant without someone telling you? Probably not. Mathematicians, being humans, are not perfect by any means. They will sometimes fail to define things properly. But they are not stupid - they do have a cultural norm of defining everything, that is obeyed most of the time. Conversely, readers of mathematics are not perfect either. They will sometimes skip over the definitional part of a paper/book and jump straight to the results, and wonder why they can't understand.
abdullahkhalids 6y ago
The anti-dote to your problem is to try to write a serious mathematical paper yourself. After spending 6 months writing it, and how many months/years of research, you will realize that writing a paper whose technical results are easy to reproduce and has precise notation, but which also conveys understanding to other human beings is an extremely difficult task, that even the smartest people on the planet can't always do. For most people, with their limited writing skills, understanding and precision have a tradeoff, and there is no perfect paper.
- davnn 6y ago
  Absolutely! I'm just not sure if we have chosen the right notation to describe our ideas. There are many interesting developments in formalizing mathematics and I hope that the field of mathematics is gravitating towards such solutions.
grayclhn 6y ago
Math without notation is 1000x less precise and harder to reproduce, unfortunately.

by davnn 6y ago

wdkrnls 6y ago

This reminds me of: https://dspace.mit.edu/handle/1721.1/6707 https://dspace.mit.edu/handle/1721.1/6707 https://www.significancemagazine.com/2-uncategorised/593-cargo-cult-statistics-and-scientific-crisis https://www.significancemagazine.com/2-uncategorised/593-car...

rahimiali 6y ago

your objection might be to the author of the notation, not the notation itself. or maybe to the review system that's supposed to catch this kind of imprecision. as with any language, it's possible to write nonsense or even self-conflicting statements in mathematical notation.

davnn 6y ago
Well, I believe the authors do their best to convey their ideas, but due to the fact that the notation is mostly informal it's easy to miss details. Also, different institutes might use their own special notation to describe the same ideas and even individual authors prefer some notation over another. All in all, imprecise probably was the wrong term. The statements are precise for the people working in this specific "bubble" of research, because they might know the implicit assumptions made and in the worst case, the only one who knows the implicit assumptions is the author.
- grayclhn 6y ago
  TBF, if key assumptions are left implicit, it’s not math.

dorkwood 6y ago

I also sometimes have to translate mathematical notation to algorithms. As a non-mathematician, math notation seems similar to naming all your variables 'a', 'b', 'c' etc. and then writing a key elsewhere that explains that 'b' stands for 'car deceleration rate'. This would be insane to do in code, why is it normal in mathematics? Note: I had this example in my head while writing https://www.traffic-simulation.de/info/IDMsstar.png https://www.traffic-simulation.de/info/IDMsstar.png

abdullahkhalids 6y ago
Because one of the main purposes of mathematical symbols is to be manipulated by humans by hand, so short variable names are essential. For programming, the same constraint does not apply.
- dorkwood 6y ago
  Right, so it's all stems from mathematicians working with pencil and paper. Are mathematicians ever frustrated that they don't understand what the variables mean? Or are you able to look at the above equation and infer the meaning of the variables based on experience? I understand that there are symbols such as "delta" which basically always mean the same thing. But would you have been able to tell what "b" meant without someone telling you?
  - abdullahkhalids 6y ago
    > Are mathematicians ever frustrated that they don't understand what the variables mean? Yes, if the presenter does not define them, or if the variables don't have a "usual" definition within the field. > But would you have been able to tell what "b" meant without someone telling you? Probably not. Mathematicians, being humans, are not perfect by any means. They will sometimes fail to define things properly. But they are not stupid - they do have a cultural norm of defining everything, that is obeyed most of the time. Conversely, readers of mathematics are not perfect either. They will sometimes skip over the definitional part of a paper/book and jump straight to the results, and wonder why they can't understand.

abdullahkhalids 6y ago

The anti-dote to your problem is to try to write a serious mathematical paper yourself. After spending 6 months writing it, and how many months/years of research, you will realize that writing a paper whose technical results are easy to reproduce and has precise notation, but which also conveys understanding to other human beings is an extremely difficult task, that even the smartest people on the planet can't always do. For most people, with their limited writing skills, understanding and precision have a tradeoff, and there is no perfect paper.

davnn 6y ago
Absolutely! I'm just not sure if we have chosen the right notation to describe our ideas. There are many interesting developments in formalizing mathematics and I hope that the field of mathematics is gravitating towards such solutions.

grayclhn 6y ago

Math without notation is 1000x less precise and harder to reproduce, unfortunately.