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Math notation is simple because it's heavily overloaded. For example, it does me no good to know about exponentials when a superscript is used in a different co

Math notation is simple because it's heavily overloaded. For example, it does me no good to know about exponentials when a superscript is used in a different context. Reading any nontrivial math requires knowing what the notation means in the particular context of the work. IME mathematicians typically assume the reader is familiar already and usually don't explain. Anyone targeting their work at non-experts should explain even what seems like trivial notation to them since they can't know what other meanings the reader may think the notation holds.

dmartinez 8y ago
I agree. The superscript example is a good one. In most contexts it refers to the exponent, but in the context of a cost function that minimizes a linear regression (for example), it indicates the index of the set. Computer languages benefit from the fact that poorly designed syntax can be deprecated (not in all cases, e.g. C++) by introducing new features to the language. Notation in math never advances in the same way for some reason.
newen 8y ago
But the fact is that math notation is the most widely known notation for writing down equations (let's make things specific to the OP case and say summation equations and partial derivative equations). Specifically for the superscript case, the vast vast vast majority of the cases, it will be obvious whether the superscript notation means exponentiation or indexing. When there are ambiguities, what the person explaining the equation should do is clarify the ambiguity. It doesn't do the world any good to make the entire engineering world learn (relatively) obscure programming languages in order to be slightly more clear (and let's not forget, much more verbose) when writing down simple equations, when all one has to do is clarify a couple of ambiguities when writing down equations. Let me make it very clear and say this: equations are meant to explain things. They are not standalone pieces of code that you can copy and paste into a REPL. They are tools to explain how something works. You should always have accompanying text that explains what all the variables in the equation mean and clarify unclear notations.
- telchar 8y ago
  I fully agree with your last sentence. Sadly I don't often see that actually happen in practice. And when the notation isn't explained I personally tend to waste a lot of brain cycles trying to decide what the notation means because I'm reading material that I don't already know (of course - if I already knew the material I probably wouldn't be reading it).
  - newen 8y ago
    Right but the thing is, people should be complaining about equations lacking explanations. Not about math notation in general.

dmartinez 8y ago

I agree. The superscript example is a good one. In most contexts it refers to the exponent, but in the context of a cost function that minimizes a linear regression (for example), it indicates the index of the set. Computer languages benefit from the fact that poorly designed syntax can be deprecated (not in all cases, e.g. C++) by introducing new features to the language. Notation in math never advances in the same way for some reason.

newen 8y ago

But the fact is that math notation is the most widely known notation for writing down equations (let's make things specific to the OP case and say summation equations and partial derivative equations). Specifically for the superscript case, the vast vast vast majority of the cases, it will be obvious whether the superscript notation means exponentiation or indexing. When there are ambiguities, what the person explaining the equation should do is clarify the ambiguity. It doesn't do the world any good to make the entire engineering world learn (relatively) obscure programming languages in order to be slightly more clear (and let's not forget, much more verbose) when writing down simple equations, when all one has to do is clarify a couple of ambiguities when writing down equations. Let me make it very clear and say this: equations are meant to explain things. They are not standalone pieces of code that you can copy and paste into a REPL. They are tools to explain how something works. You should always have accompanying text that explains what all the variables in the equation mean and clarify unclear notations.

telchar 8y ago
I fully agree with your last sentence. Sadly I don't often see that actually happen in practice. And when the notation isn't explained I personally tend to waste a lot of brain cycles trying to decide what the notation means because I'm reading material that I don't already know (of course - if I already knew the material I probably wouldn't be reading it).
- newen 8y ago
  Right but the thing is, people should be complaining about equations lacking explanations. Not about math notation in general.