Terry Tao on some desirable properties of mathematical notation

Re:Terry Tao on some desirable properties of mathematical no... by tsimionescu on Wednesday July 22, 2020 @03:19AM (#23914705)

There are some cases where this is true (the most infamous being Roman numerals, where the notation makes even simple arithmetic difficult - XI * VI = LXVI???), but in general notation is just something you learn once and mostly remember, as long as you understand the concepts.

However, I fully agree that reading a text that uses notation you are not familiar with without introducing it is almost futile. Even the simple fact of not knowing the names of the operators, which makes it impossible to read the formulas cursively in you mind (for example, when you encounter 'a + b' you can read it in your mind as 'a plus b', but for something like 'a <<=> b', even if given `a <<=> b = 2*a+b`, reading the text becomes a mental chore).

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Re:Terry Tao on some desirable properties of mathematical no... by OscarCunningham on Wednesday July 22, 2020 @03:57AM (#23914893)

Incidentally, the example of roman numeral multiplication you chose is actually fairly easy. Just break it up as (XI×V) + (XI×I). Then since X×V=L and I×V=V (Romans would have these memorised just like we memorise multiplication tables for all the decimal digits) so the first multiplication is LV and the second is XI, which add to give LXVI by simply interleaving the letters.

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Re:Terry Tao on some desirable properties of mathematical no... by madcaptenor on Wednesday July 22, 2020 @10:49AM (#23917615)

That example works well because you don't have to do V * V. You can do XVI * VI = (X + V + I) * (V + I) = (XV) + (XI) + (VV) + (VI) + (IV) + (II) = L + X + XXV + V + V + I = LXXXVVVI = LXXXXVI, which "simplifies" to XCVI, but it's already a good bit messier.

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