|letters and symbols instead of words
||[Jun. 20th, 2018|09:08 pm]
With time, I came to appreciate mathematical convention of writing letters and symbols instead of words. First, it is easier to comprehend a formula if it is compact, fits into a view. When learning mathematics, at least abstract mathematics, understanding is much harder than remembering meanings of letters. I spend more time pondering than remembering. IMHO, letters are actually more efficient than words, and names composed from several words will make mathematics unreadable. BTW, mathematicians use words, but abbreviated (for example, “lim”, “ker”, “dim”). Compactness is the key.
Second, as was pointed out, it is really hard to invent names for abstract entities. Our words come from everyday life which does not contain abstractions. At the end, “x_0”, “x_1”, “y_0”, “y_1” seem like really good names, especially if you write the same index for corresponding values. The real issue is that entities are abstract, not names. Example. When stating associativity, what variable names are better than (x_0 x_1 x_2), (x y z), or (x x' x'')? What “meaningful” names would you propose?
This does not mean that I do not see defects in mathematical notation. The drive for compactness led us to notation where some things are omitted and a symbol mean different things. “×” is omitted even in schools. Parentheses are used for grouping terms in expressions, tuples, GCD, permutations… Sometimes it really hinders understanding.