Incorrect description of multiplication in math exploration

[viscid coral]

“Multiplication gets its name from performing addition multiple times.”

This is incorrect. It doesn’t even qualify as an extreme oversimplification. The word multiplication is based on a Latin word that means to increase. In the context of the real numbers, multiplication is a scaling operation. It is only in the context of whole numbers that multiplication behaves the same as repeated addition but that isn’t what it IS. How does one add sqrt(2) to itself pi times?

Multiplication is defined for other mathematical objects as well. In the case of the complex number plane, multiplication results in scaling and or rotation about the origin. Vectors have two types of products, the dot product and cross product, which have specific meaning and properties. Matrix multiplication has its own behavior and properties.

Multiplication is therefore defined as a binary operation having a certain set of properties within the context of the mathematical objects being operated upon.

[past cliff]

One could define multiplication as the next up the sequence of hyperoperations from addition, so this isn't exactly a stretch.

Multiplication between complex numbers, for instance, can be extended from multiplication between naturals, then integers, then rationals, then continuously to reals and algorithmically to complex numbers.

I have no comment on the semantics.

[acoustic current]

@viscid coral @past cliff Hi y'all, thanks for reaching out! I'm Anthony, the primary author of the math event. I had not seen this thread earlier but someone else on the team just flagged it for me.

One could define multiplication as the next up the sequence of hyperoperations from addition

This is precisely what I had in mind when I wrote that definition, and my intent was to try to connect the idea of addition with multiplication in a way that makes sense logically to non-mathematical people.

The roots of "multiply" are "multi" and "plex", meaning "many fold", which is more specific than just "increase". Also, I would argue that it does get its name from multiple additions, whether or not we later defined non-whole-number objects.

However, I've been unable so far to find a clear source to when and why the name was originally attributed. If we want to avoid being really pedantic about it (remember, this is an educational game for general audiences, not a rigorous peer-reviewed mathematical paper, and as such minor poetic license can be justified), we could reword it very slightly as "Multiplication can be thought of as performing addition multiple times." This shouldn't be a problem to tweak, though at this point it would not be practical to try to go in and retranslate that into all of the languages we are distributed in.

Also, I appreciate your feedback on it! We've definitely caught a few unquestionable mistakes that I've made thanks to comments from players.

Multiplication is therefore defined as a binary operation having a certain set of properties within the context of the mathematical objects being operated upon.

This might be technically correct, but it's unfortunately not helpful for this sort of context.