Some Musings on Mathematics
solipsys.co.uk
Some Musings on Mathematics
1–10 of 49 posts
Re: Some Musings on Mathematics
#2To me, personally and practically, mathematics became impactful, and even beautiful when I came to the realization that it was a universal modeling notation for comprehending our world. Math did not come easy to me, but as I persevered through my aerospace engineering degree I came to appreciate its importance to, and role in modeling. There is so much churn in systems modeling approaches such as SysML and UML et al, that I appreciate math as a modeling notation all the more. It remains pretty stable and elegant as it is. Thanks for the links; I'll check them out.
Re: Some Musings on Mathematics
#3[deleted]
Re: Some Musings on Mathematics
#4Two quotes that sums up this article for me:
"The whole point of pure maths is that there are problems to solve, and you're working to solve them."
"So why don't we do what we did before? When we couldn't solve equations like x+8=5 we invented the negative numbers. When we couldn't solve equations like 3x=5 we invented fractions. When we couldn't solve equations like x2-x-1=0 we invented the algebraic numbers."
To me, I look at math as a collaborative language of precision in dealing with units. Math isn't static. It's collaborative, it's inventive. It's desire is to accurately communicate measurements. I'm still in my undergrad for Applied Mathematics but that's my two cents.
Re: Some Musings on Mathematics
#5Meaning is not something that is particularly an end goal. That is why there is specific differenciation between the syntax (structure) and its semantics. Once you isolate them, one could think of the structure itself and manipulate its related symbols, without worrying about their meanings. Sometimes surprisingly, some of these results map back to the meaning of the structure, but that is purely a byproduct.
Re: Some Musings on Mathematics
#6To me, personally and practically, mathematics became impactful, and even beautiful when I came to the realization that it was a universal modeling notation for comprehending our world. Math did not come easy to me, but as I persevered through my aerospace engineering degree I came to appreciate its importance to, and role in modeling. There is so much churn in systems modeling approaches such as SysML and UML et al,…
The thing you realized is also what the guy is arguing is not the case. There's no one right view, but that's the point of his argument.
Re: Some Musings on Mathematics
#7> The truth is far simpler. Mathematicians are solving puzzles, and some of those puzzles don't come from the real world at all, and can't be motivated in that way.
Why is it that mathematicians are unable to see the recursion: Pure maths is maths applied to maths, so it is applied maths, nevermind how often this operation had to be repeated until the result would be substantiv?
Re: Some Musings on Mathematics
#8Meaning is not something that is particularly an end goal. That is why there is specific differenciation between the syntax (structure) and its semantics. Once you isolate them, one could think of the structure itself and manipulate its related symbols, without worrying about their meanings. Sometimes surprisingly, some of these results map back to the meaning of the structure, but that is purely a byproduct.
The manipulation of symbols it itself meaningful, because the symbols are real things that exist in nature. You may be working at a different layer of indirection, but it makes no difference to the usefulness of your work, because nature itself does no indirection (as far as we can tell); your results are always applicable to something real.
Even if many mathematicians are so poor at explaining it that they'll just pretend it isn't true; that mathematics doesn't need a purpose. It does -- it just always has one.
Re: Some Musings on Mathematics
#9> The truth is far simpler. Mathematicians are solving puzzles, and some of those puzzles don't come from the real world at all, and can't be motivated in that way. Why is it that mathematicians are unable to see the recursion: Pure maths is maths applied to maths, so it is applied maths, nevermind how often this operation had to be repeated until the result would be substantiv?
There are two approaches to answering your question.
Firstly, what makes you think that mathematicians are unaware of the trail back to "the real world"?
Secondly, I'd be interested in knowing what you think this real world issue this problem might be descended from:
Dissect a circle into congruent pieces,
such that the centre point is contained
in the interior of one of the pieces.Re: Some Musings on Mathematics
#10Meaning is not something that is particularly an end goal. That is why there is specific differenciation between the syntax (structure) and its semantics. Once you isolate them, one could think of the structure itself and manipulate its related symbols, without worrying about their meanings. Sometimes surprisingly, some of these results map back to the meaning of the structure, but that is purely a byproduct.
> Meaning is not something that is particularly an end goal.
No, of course it isn't. The goal is where meaning gets you to.