I think that this question is can
be answered with yes and no depending on how you interpret the question. I would
say yes, our number system has everything to do with what mathematics because
there is no way to represent what we know about math without using our number
system. For example, if we did not adopt our number system, how would we be
able to understand just about anything? Would we still understand or discover things
like calculus, algebra and physics? How would we quantify anything? How would
we make change at a grocery store? How would we add, subtract or multiply?

On the other hand, I would say no,
our number system does not have anything to do with mathematics. Our number
system doesn’t determine any truth about mathematics. What we know is true
about mathematics now will always be true. Our number system is just a way to
represent what we know. If we didn’t have our number system, we would more than
likely have another representation of what we have discovered about
mathematics. To answer the above questions, the concept of calculus, algebra
and physics would still remain. Whether it was discovered or represented with
our number system would be a different story. We would have found another way
to quantify things. Who knows, maybe we would still be using roman numerals. The
use of the words “one, two, three… etc.” are essentially just words we agreed
to use to represent those numbers. Our number system could go something like “popcorn,
carpet, pillow dinner” if that is what we use to represent what we now call “one,
two, three, four”. The number system itself does not determine anything about
math. It is simply a way for people to represent what they know that is
universally accepted so that information can be shared with others.

When I asked the question, I definitely meant more along the lines of the 2nd point. Without the concept of number, math is much different. As you pointed out, the quantifying idea alone.

ReplyDeleteclear, coherent, content: +

complete, consolidated: you probably would want to dig in a little deeper here in both paragraphs. Examples, explain your claims, etc. Then tie it together. The big summary question here is do we get anything out of even considering this idea?