4 ms·

> But that depends on what particular people find meaningful or interesting Yes. That’s why I said it’s a matter of taste. My claim is that what makes things

> But that depends on what particular people find meaningful or interesting Yes. That’s why I said it’s a matter of taste. My claim is that what makes things meaningful is how they relate to reality, and by reality I mean things like the three dimensional world and the passing of time we perceive. Whilst most of pure mathematics seems ridiculously abstract on first glance, I don’t believe there is a single topic that truly has no connection to reality. > it's important not to confuse "reality" with our models of it This is a frequently repeated point and I’m inclined to agree, but any such model also exists in reality and so it’s hard to know where to draw the line.

pdonis 3y ago
> any such model also exists in reality Yes, but there's still a distinction between the model and the thing modeled. A map of your city is not the same as the city, even though the map is a real object in the same reality as the city. Similarly, real numbers are a model that is instantiated in the brains of mathematicians, papers in the literature, etc. Those things are of course real objects. But real numbers are used to model lots of other real things.
- xanderlewis 3y ago
  Of course there’s a distinction between a map and the thing it’s a map of. But they’re both parts of reality.
  - samus 3y ago
    It's also perfectly possible to draw maps of places that don't exist in reality, i.e., that only exist in somebody's brain.
    - xanderlewis 3y ago
      A good point. So the real numbers exist in the same sense that anything else they might describe does. My original point was really a comment on the way that the subject is often taught: the real number system is not introduced as some arbitrary set of rules that is as good as any other (though of course it is); it is introduced as if it were as incontrovertible an idea as, say… integer addition. I don’t think it is. It can perfectly well be argued that it makes sense and is useful, but its naturality is another matter. I personally find the leap from R to C less controversial than that from Q to R.
      - samus 3y ago
        Yes, I agree. Real numbers are a quite nebulous construct for which the need is a bit hard to see. Complex numbers are basically a hack to solve quadratic equations in all cases.

pdonis 3y ago

> any such model also exists in reality Yes, but there's still a distinction between the model and the thing modeled. A map of your city is not the same as the city, even though the map is a real object in the same reality as the city. Similarly, real numbers are a model that is instantiated in the brains of mathematicians, papers in the literature, etc. Those things are of course real objects. But real numbers are used to model lots of other real things.

xanderlewis 3y ago
Of course there’s a distinction between a map and the thing it’s a map of. But they’re both parts of reality.
- samus 3y ago
  It's also perfectly possible to draw maps of places that don't exist in reality, i.e., that only exist in somebody's brain.
  - xanderlewis 3y ago
    A good point. So the real numbers exist in the same sense that anything else they might describe does. My original point was really a comment on the way that the subject is often taught: the real number system is not introduced as some arbitrary set of rules that is as good as any other (though of course it is); it is introduced as if it were as incontrovertible an idea as, say… integer addition. I don’t think it is. It can perfectly well be argued that it makes sense and is useful, but its naturality is another matter. I personally find the leap from R to C less controversial than that from Q to R.
    - samus 3y ago
      Yes, I agree. Real numbers are a quite nebulous construct for which the need is a bit hard to see. Complex numbers are basically a hack to solve quadratic equations in all cases.