>What about RSA encryption, and the former US export controls thereon?
That's exactly the point.
>Also, what about more exotic mathematical objects, like finite fields for example, that have a lot of structural properties but don't seem to model much of anything in the real world, but are still useful theoretically?
If that theoretical use applies to physics then to my mind the theoretical objects are as real as anything else. I have a friend who likes to say that electrons don't "really" exist (because they can't be directly observed), they're just a theoretical object that makes our calculations easier. I guess if you pressed me on philosophy I'd say that the only "real" things are sensory observations - we posit objects such as "that table" because they make the explanation of our visual perceptions easier. If positing a finite field makes some part of physics simpler, that seems to be the same thing.
Now for areas of mathematics that are isolated from the rest it's much easier to say they don't represent anything real. But one of the things I was trying to say in the grandparent post is that there's an uncanny tendency for these areas to not stay isolated for long.
That's exactly the point.
>Also, what about more exotic mathematical objects, like finite fields for example, that have a lot of structural properties but don't seem to model much of anything in the real world, but are still useful theoretically?
If that theoretical use applies to physics then to my mind the theoretical objects are as real as anything else. I have a friend who likes to say that electrons don't "really" exist (because they can't be directly observed), they're just a theoretical object that makes our calculations easier. I guess if you pressed me on philosophy I'd say that the only "real" things are sensory observations - we posit objects such as "that table" because they make the explanation of our visual perceptions easier. If positing a finite field makes some part of physics simpler, that seems to be the same thing.
Now for areas of mathematics that are isolated from the rest it's much easier to say they don't represent anything real. But one of the things I was trying to say in the grandparent post is that there's an uncanny tendency for these areas to not stay isolated for long.