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Gödel, Escher, Bach (book by Douglas Hofstadter) actually touches on this topic. They are an abstraction, but they are isomorphic to reality. The big news here
by ko27 6y ago
Gödel, Escher, Bach (book by Douglas Hofstadter) actually touches on this topic. They are an abstraction, but they are isomorphic to reality. The big news here is that we thought complex numbers have no isomorphism with reality (physics) that couldn't be explained with real numbers only.
https://en.wikipedia.org/wiki/Isomorphism https://en.wikipedia.org/wiki/Isomorphism
- GoblinSlayer 6y agoComplex numbers themselves can be explained with real numbers only.
- ko27 6y agoYou didn't define what you meant by "explained". You are more then welcome to explain the results of the linked study (once its released) with real numbers only.
- GoblinSlayer 6y agohttps://news.ycombinator.com/item?id=26329883 https://news.ycombinator.com/item?id=26329883 - like this. AIU the article disproves a specific theory that threw away the imaginary part of wave function or something like that, so the result is kinda expected, but it doesn't mean that complex numbers are indispensable.
- ko27 6y agoThat doesn't explain complex numbers with real numbers (matrices are not real numbers). So the point of the article, and my comment still stands.
- GoblinSlayer 6y agoYou can say that about anything, like real quantum mechanics isn't just real numbers, but also functions, equations, operators and a lot of stuff like that.
- ko27 6y ago> Functions, equations, operators All of those are part of Peano and ZFC axiomatic systems, which were thought to be enough to explain all of physics (albeit not easily). Matrices and imaginary numbers are not part of those formal systems. Just ask yourself. If you are right, why didn't Schrodinger or the researches that are publishing this study just think of your idea of using matrices?