One way of thinking about cancer is that it refers to cells that are separated from the bioelectric system that coordinates the individual cells into a collective self.
This is an interesting thought (and timely, since I was lecturing today about the axioms of measurement theory). But I think in this case, there's a sense in which the problems that exist aren't problems for the elements in the system, but for the user from outside the system. I don't quite see how this particular type of system can get the elements of the system to have goals or desires in the way that cells and organisms can. But it would probably work with some more complicated sort of mathematical system.
One other thing I was thinking when you talk at the end about functions, is that the obvious way to deal with this element is to extend the rules to it, and that's how you get fields of polynomials over R. The fact that the math does well with this extension suggests that whatever's going wrong here is importantly different from cancer and other externalities.
Also, the example strikes me a bit like the extended reals (which a student asked about in class today), where all the rules for addition, multiplication, and subtraction work fine for the finite elements, and sorta work for +\infty and -\infty, but only in somewhat broken ways. But the system still has some advantages that make it sometimes the right system to use.
I'm not a mathematician, so this is all just amateur speculation and guesswork. It does indeed seem like math can get rid of externalities much more easily than organisms and economies can. Though I do also have amateur speculation and guesswork about how normativity enters mathematics, check this out and let me know what you think: https://www.youtube.com/watch?v=Z8u26lpx-5E
I don't know enough to say, but I doubt that any mathematician would deliberately construct something as pointless as the example I gave. Mathematicians can get rid of externalities by being like "go away you dumb thing", so I'd be surprised if there turned out to be any significant examples in existing mathematics.
This is an interesting thought (and timely, since I was lecturing today about the axioms of measurement theory). But I think in this case, there's a sense in which the problems that exist aren't problems for the elements in the system, but for the user from outside the system. I don't quite see how this particular type of system can get the elements of the system to have goals or desires in the way that cells and organisms can. But it would probably work with some more complicated sort of mathematical system.
One other thing I was thinking when you talk at the end about functions, is that the obvious way to deal with this element is to extend the rules to it, and that's how you get fields of polynomials over R. The fact that the math does well with this extension suggests that whatever's going wrong here is importantly different from cancer and other externalities.
Also, the example strikes me a bit like the extended reals (which a student asked about in class today), where all the rules for addition, multiplication, and subtraction work fine for the finite elements, and sorta work for +\infty and -\infty, but only in somewhat broken ways. But the system still has some advantages that make it sometimes the right system to use.
I'm not a mathematician, so this is all just amateur speculation and guesswork. It does indeed seem like math can get rid of externalities much more easily than organisms and economies can. Though I do also have amateur speculation and guesswork about how normativity enters mathematics, check this out and let me know what you think: https://www.youtube.com/watch?v=Z8u26lpx-5E
Do you consider non-standard models of the Naturals to have externalities?
I don't know enough to say, but I doubt that any mathematician would deliberately construct something as pointless as the example I gave. Mathematicians can get rid of externalities by being like "go away you dumb thing", so I'd be surprised if there turned out to be any significant examples in existing mathematics.