3 ms·
Its worse than just notational differences (which probably could be solved good-enough with crowdsourcing). The bigger problem is that there is often not a sim
by gizmo686 10y ago
Its worse than just notational differences (which probably could be solved good-enough with crowdsourcing).
The bigger problem is that there is often not a simple English description for math terms, whose meaning might involve understanding concepts that take books to explain.
For example, consider the simple sentence "Let x be an arbitrary vector". What is a vector? There is no clear answer to this question. Formally speaking a vector is simply an element of the set V where V is the underlying set for some vector space. You could try to say that V is an ordered pair of n real numbers, which is true up to isomorphism for finite dimensional vector spaces over the real numbers. But, x could also be the function f(x)=x^2, or the matrix [3, 4; 7, 1+i]. In some contexts, the translator might be able to tell from context what vector space is being worked in. But if the source is a general statement about vector spaces (even if made in support of a more concrete point), there is no way to explain it without explaining the concept of a vector space. To explain vector spaces one would need to, at a minimum, explain fields.
There is also a question of which description to use. For example, suppose we needed to define complex numbers. In some contexts, it is most natural to think of them as points on the xy-plane, which is simple enough (although does not give intuition above what multiplication means, which is arguably an essential component of the "true" meaning of complex numbers). In other contexts, it is more natural to think of them as matrices of the form [a -b; b a]. Attempting to show all the (equivelent) meanings would likely overwhelm the intended user of the service.