The great thing is we're not constraining our notation. As reikonomusha said, the standard notation is easier to read. Other notation is better for programming or certain things, and that's what we use there.

Re: your last paragraph. I only went to the end because I knew that there must have been a good example in the questions. If you want I can give you examples from the middle of a talk.

> the standard notation is easier to read

Only because you're used to it. In fact, standard notation is much harder to read because it's ambiguous, often to the point of actively introducing errors. See:

http://mitpress.mit.edu/sites/default/files/titles/content/s...

> If you want I can give you examples

No, I don't dispute that blackboards are useful. What I dispute is that their utility is so high that we ought to design mathematical notation around their limitations.

Ok, I can agree that we shouldn't design notation around their limitations. And I do like what they do in SICM. But, I'm just trying to root for the point up-thread:

>It seems tempting to have a single unambiguous notation for mathematics. But In constructing such a language, one will quickly realize that doing mathematics becomes an intensely arduous task.

When talking about math, our notation doesn't have to be precise, and that's ok.

> No, I don't dispute that blackboards are useful. Just obsolete :P

To constrain your infrastructure according to the needs of a computer is also silly. Imagine if, in order to hum a tune, one needed to write sheet music using a programming language. Or if every spoken conversation were halted the instant a word is used incorrectly.

Mathematics (and a lecture on mathematics) is closer in nature to a conversation than a road.

[edit sp]

Those are stupidly irrelevant examples. Nobody's suggesting that you would need to have a Coq parser between your keyboard and your display. You can type an incomplete or invalid expression just as easily as you can write one, but only with a computer can you have your statements automatically and reliably checked and errors flagged in realtime.

Essentially, that is the argument. If the point is to allow students to manipulate the lecture as data, then it must be error-free. That is literally putting a parser between the lecturer and the students.

And your condescending comment does not address my point, which is that a lecture would not benefit from (and is actively harmed by) the "features" being suggested. Real time error flagging would be extremely distracting, and writing mathematics as source code would be tediously slow and again distract from the point of understanding the mathematics.

Enabling multiple users to interact with the equations in realtime as they are being written is hardly the only possible benefit of using computers to communicate math, and even so it only requires that the equations be tokenized to be manipulable, not that the whole expression be completely error-free and the parser be running in an enforcing mode.

And your claim that writing mathematics as source code is too slow is very much lacking in proof. All we can say with confidence is that syntax like LaTeX markup on a standard keyboard layout is too inefficient for realtime use. This does not mean that realtime use is impossible if you allow for a more complicated IME and for a different final notation on-screen than the current standard math notation.

I'd like to hear your ideas for other benefits.