I think this is exactly right. We have seriously misunderstood math. I don't know exactly what the "fix" is, but I think you're on the right track. If you want to come on my show and talk about it, I'd be honored to have you. https://linktr.ee/Adam_Haman
To address infinity being a philosophy notion and not a math notion: Applied math is presently restricted to finite numbers and organized into axioms of Group Theory. Because a development of force and energy equations for electromagnetism that are compatible with special relativity cannot be (cleanly/beautifully) discovered using only finite numbers of Group Theory, applied math must be extended beyond finite out to the infinite. This extension is accomplished in a counter-intuitive way because the axioms of Axiomatic Set Theory are modified to remove actual infinity. The removal of actual infinity removes illogical ambiguities. Without actual infinity, a real number is a rational number specified by a finite quantity of place-value digits both before and after the decimal point. Place-value digits beyond this finite quantity, which is the largest number yet counted-to, are unspecified and therefore unknown and unknowable. The zeros to the left (before) the decimal point only extend to a finite quantity, which increases with time. The unspecified place-value digits left of those zeros form infinity, but this infinity has different properties than previous notions of infinity, for example, it cannot be the quantity of a set. This infinity, which is large-scale imprecision of a real number, is added to the time/space hyperbolic angle in a special relativity Lorentz Transformation to model electromagnetism using the Dirac Equation. Post-processing using the complex conjugate and the Dirac Spinor result in the desired energy and force equations for electromagnetism, and these include the empirically discovered electromagnetic energy density and the momentum Poynting vector. That success in the hundred-year-old electromagnetic theory, to finally complete it, means that the modifications to Axiomatic Set Theory were correct, and finally Axiomatic Set Theory is moved from pure math into applied math. Infinity, with the derived properties from modified Axiomatic Set Theory, transitions from speculative philosophy into actual applied mathematics. What was just explained is the core idea in the book Special Algebra for Special Relativity - Paul Daiber
Math is relationships of quantity. IIt cannot be gotten rid of and there's nothing that can replace it. To get rid of it would mean to live in an insubstantial, ineffable universe.
That's a metaphysical category error, not math. Math is relationships of quantity. Quantity is when you can divide something into equivalent parts - equivalent boundary conditions. Infinity has no boundary conditions so you can't math with it. It's an instruction - keep going or etcetera, not a mathematical thing that can be manipulated.
Wonderful! Thank you. Are you familiar with Martin Heidegger's criticism of mathematics? "The mathematical is...a project of thingness which, as it were, skips over the things." -- Heidegger in "Modern Science, Metaphysics, and Mathematics."
> The proof is baroque and hard to follow.
That's good, because if it wasn't baroque, you couldn't fix it.
</deadpan>
I'll show myself out . . .
That is so terrible, it's beautiful.
Same. Have worked on this subject. One of the fellows at our organization works on it full time. Thanks for keeping the subject alive.
I think this is exactly right. We have seriously misunderstood math. I don't know exactly what the "fix" is, but I think you're on the right track. If you want to come on my show and talk about it, I'd be honored to have you. https://linktr.ee/Adam_Haman
To address infinity being a philosophy notion and not a math notion: Applied math is presently restricted to finite numbers and organized into axioms of Group Theory. Because a development of force and energy equations for electromagnetism that are compatible with special relativity cannot be (cleanly/beautifully) discovered using only finite numbers of Group Theory, applied math must be extended beyond finite out to the infinite. This extension is accomplished in a counter-intuitive way because the axioms of Axiomatic Set Theory are modified to remove actual infinity. The removal of actual infinity removes illogical ambiguities. Without actual infinity, a real number is a rational number specified by a finite quantity of place-value digits both before and after the decimal point. Place-value digits beyond this finite quantity, which is the largest number yet counted-to, are unspecified and therefore unknown and unknowable. The zeros to the left (before) the decimal point only extend to a finite quantity, which increases with time. The unspecified place-value digits left of those zeros form infinity, but this infinity has different properties than previous notions of infinity, for example, it cannot be the quantity of a set. This infinity, which is large-scale imprecision of a real number, is added to the time/space hyperbolic angle in a special relativity Lorentz Transformation to model electromagnetism using the Dirac Equation. Post-processing using the complex conjugate and the Dirac Spinor result in the desired energy and force equations for electromagnetism, and these include the empirically discovered electromagnetic energy density and the momentum Poynting vector. That success in the hundred-year-old electromagnetic theory, to finally complete it, means that the modifications to Axiomatic Set Theory were correct, and finally Axiomatic Set Theory is moved from pure math into applied math. Infinity, with the derived properties from modified Axiomatic Set Theory, transitions from speculative philosophy into actual applied mathematics. What was just explained is the core idea in the book Special Algebra for Special Relativity - Paul Daiber
Math is relationships of quantity. IIt cannot be gotten rid of and there's nothing that can replace it. To get rid of it would mean to live in an insubstantial, ineffable universe.
The fix to logic violations cause by Cantor’s countable and uncountable infinities is in the book Special Algebra for Special Relativity.
That's a metaphysical category error, not math. Math is relationships of quantity. Quantity is when you can divide something into equivalent parts - equivalent boundary conditions. Infinity has no boundary conditions so you can't math with it. It's an instruction - keep going or etcetera, not a mathematical thing that can be manipulated.
This is barely scratching the surface
Wonderful! Thank you. Are you familiar with Martin Heidegger's criticism of mathematics? "The mathematical is...a project of thingness which, as it were, skips over the things." -- Heidegger in "Modern Science, Metaphysics, and Mathematics."