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> You can’t do math by measuring real-world objects. Don't we all start out doing math by counting/measuring real-world objects? It was all "Sally has x apples
by autoexec 2y ago
> You can’t do math by measuring real-world objects.
Don't we all start out doing math by counting/measuring real-world objects? It was all "Sally has x apples" and rulers when I started school but some kids do math using other tools like cubes and cuisenaire rods which are also used to do math through measuring/counting real world objects.
- xigoi 2y agoMathematics is a tool that can be used to describe the real world, and mathematical discoveries are often motivated by practital uses. However, mathematical structures are not directly influenced by the real world; they can just model it.
- autoexec 2y ago> Mathematics is a tool that can be used to describe the real world, And that's what the article says the Greeks believed they could do using whole numbers and fractions. In the case of a real world square with sides of length 1 it seems that you can get away with describing the length of its diagonal in those terms which made it seem odd that it was what caused them to abandon their belief/aspiration. Maybe the author just described their dilemma poorly/strangely. I'm not at all suggesting that math has to be limited to the real world or that irrational numbers don't have their place. We're certainly better off with them.