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View submission: Ask Anything Wednesday - Engineering, Mathematics, Computer Science
When we make changes to an equation, like 'cancelling', or resolving for a given variable, we're making new statements of truth, justified by the previous statement being true, and adhering to the rules of logic when making the change
Interesting approach. It seems reasonable to assume that people in ancient times understood the parts about stating a truth, and about balancing every adjustment..
What isn't obvious is why make specific adjustments purely for the sake of revealing or discovering an unknown, unsuspected aspect in a mechanical model of how nature works. Who came up with that? How did they figure out that canceling could reveal surprises?
The adjustments almost seem like playing around with the equation to see what unanticipated insights might pop out.
Comment by rmeredit at 14/12/2023 at 02:59 UTC
2 upvotes, 0 direct replies
What isn't obvious is why make specific adjustments purely for the sake of revealing or discovering an unknown, unsuspected aspect in a mechanical model of how nature works. Who came up with that? How did they figure out that canceling could reveal surprises?
Well that's the academic discipline of mathematics in a nutshell - it's not just the algebraic technique of changing equations that we're talking about here, it's the general aim of coming up with mathematical hypotheses and trying to prove or disprove them. It's solving puzzles, basically, and it's a creative process that uses insight, hunches, assumptions as much as anything else. The Greeks used geometry as their primary method. The Persians algebra. But it's all the same process, just different means of representation.