Issue #25 ~ I’ll start this blog in a roundabout way, but – if you stick with me – I will hopefully arrive at something you’ll find exciting (of course, it’ll be quantum). I personally think it’s mind-blowing, though I’ve got no idea what to do with it 😊.
This post and Bertrand Russell's endorsement got me to read Laws of Form.
It is a shame that book has been ignored. I think it can be applied as a superposition compatible logic. And I note that superposition compatible logics might be related to the logics developed separately by Nagarjuna and possibly Hegel. Although Hegel's science of logic is could generously be interpreted as obfuscating sophistry, I think it can with enormous efforts be formalised symbolically. But I think the fruit of that effort may result in something that would be the equivalent of Laws of Form.
When my soul stares at the self referential equation x = 1/(-x), it cannot help but notice that x is very mysteriously intertwined & equated to its own additive inverse (-x) and its own multiplicative inverse (1/x) It is speaking to our souls in a language we cannot comprehend yet! :-)
Cardano & friends considered the equation x**2 = -1 (or equivalently x = -1/x). They called the solution i and interpreted it as an "imaginary" number.
Suppose they had reasoned like you and interpreted i as a superposition |+1> + |-1> of 1 and -1.
Then they would have considered complex numbers z = |x+y> + [x-y>. Complex analysis would have developed as it has, with this interpretation of i.
Then they would have said OK, perhaps physical quantities can be complex numbers (that is, superpositions)?
Would they have derived quantum mechanics this way?
There is a more ambitious solution to the paradox, which is to change the fundamental dimension of the problem. It must no longer be located in space and time but in the complex dimension. The self-reference paradox is an unresolved conflict between two equally unsatisfactory solutions, which alternate. This loop makes the paradox a stable element in itself at a level of complexity higher than the constitutive mechanism. To return to your example of hydrogen, the molecule resulting from the interaction of the two atoms is recognized as a stable element by the other constituents of the molecular level of complexity whereas it is a superposition of unstable states at the level of the atomic constituents. The higher level of complexity is an approximation of the previous level. Complex level changes are frequently hidden in the sign ‘=’, which explains paradoxes such as 1 = -1. Mathematics, in its current form, is not adapted to the complex dimension. They do not grasp the qualitative aspect and flatten reality.
This post and Bertrand Russell's endorsement got me to read Laws of Form.
It is a shame that book has been ignored. I think it can be applied as a superposition compatible logic. And I note that superposition compatible logics might be related to the logics developed separately by Nagarjuna and possibly Hegel. Although Hegel's science of logic is could generously be interpreted as obfuscating sophistry, I think it can with enormous efforts be formalised symbolically. But I think the fruit of that effort may result in something that would be the equivalent of Laws of Form.
When my soul stares at the self referential equation x = 1/(-x), it cannot help but notice that x is very mysteriously intertwined & equated to its own additive inverse (-x) and its own multiplicative inverse (1/x) It is speaking to our souls in a language we cannot comprehend yet! :-)
Thinking aloud:
Cardano & friends considered the equation x**2 = -1 (or equivalently x = -1/x). They called the solution i and interpreted it as an "imaginary" number.
Suppose they had reasoned like you and interpreted i as a superposition |+1> + |-1> of 1 and -1.
Then they would have considered complex numbers z = |x+y> + [x-y>. Complex analysis would have developed as it has, with this interpretation of i.
Then they would have said OK, perhaps physical quantities can be complex numbers (that is, superpositions)?
Would they have derived quantum mechanics this way?
This is very interesting. Digesting it...
There is a more ambitious solution to the paradox, which is to change the fundamental dimension of the problem. It must no longer be located in space and time but in the complex dimension. The self-reference paradox is an unresolved conflict between two equally unsatisfactory solutions, which alternate. This loop makes the paradox a stable element in itself at a level of complexity higher than the constitutive mechanism. To return to your example of hydrogen, the molecule resulting from the interaction of the two atoms is recognized as a stable element by the other constituents of the molecular level of complexity whereas it is a superposition of unstable states at the level of the atomic constituents. The higher level of complexity is an approximation of the previous level. Complex level changes are frequently hidden in the sign ‘=’, which explains paradoxes such as 1 = -1. Mathematics, in its current form, is not adapted to the complex dimension. They do not grasp the qualitative aspect and flatten reality.