Math is a tool of the mind to describe our world, imaginary numbers is only a extension of that tool to allow us to go beyond what mathematical logic prevents us to do, while still getting in the end a real number. Math, despite being powerful, is a flawed tool, so getting around its flaws by creating things like imaginary numbers isn’t absurd and doesn’t make the result any less real at the end.
On the other hand, I don’t think calling everything we don’t understand “magic” or the new trending words “supernatural” and “a miracle” and give god or anything else (like karma) credit for it would be more clever.
Back then, we didn’t understood the concept of thunder and interpreted it as god’s wrath. Now, we understand it’s a transmission of electricity from the negatively charged clouds to the neutral ground through ionized particles in the air. I don’t think that scientists now, despite referring to the same phenomena, are talking about the same thing as we did a long time ago.
So no, no scientist will discover the afterlife “but we’ll just call them “Post-Human Conciousness Wells” or something, and insist it totally isn’t the same thing as that ancient superstition.” as it won’t be.
Stating mathematics is a tool doesn’t answer if mathematics are real or not.
But I would say, from my humble experience, that mathematics is both unreal and perfectly tangible.
Mathematics is totally a real thing as it obeys strict rule in logic that are true in our real world, axioms, on which everything else is based so that it can’t be used to state things as being true out of the blue, without any justification before using those axioms, which you can translate into our real world.
But math also has its limits and has been used to demonstrate that it itself is incomplete, undecidable and inconsistant (mathematically, of course, it’s not our common definition here). Meaning, as mathematics are imperfect, it can’t describe our world perfectly and therefore isn’t real.
Incorrect. You can construct an isomorphism between the even subalgebra of the 2D geometric algebra Cl(2) and the complex numbers that maps 1 to the unit scalar and i to the pseudoscalar: https://link.springer.com/article/10.1007/BF01883676
Are you interested in proving me wrong, or figuring out the right answer? If you actually read that article instead of just the title, you would have noticed at the end it says
This leads us to say a few words about the widely held opinion that, because complex numbers are fundamental to quantum mechanics, it is
desirable to “complexify” every bit of physics, including spacetime itself. It will be apparent that we disagree with this view, and hope earnestly that it is quite wrong, and that complex numbers (as mystical uninterpreted scalars) will prove to be unnecessary even in quantum mechanics
They literally say that “complex numbers are fundamental to quantum mechanics”. In other fields of physics complex numbers are just a convenient tool, but in quantum mechanics they are(as far as we know) fundamental, even if the author hopes that to be proved wrong at some point.
You seem like you know a bit about alternatives to complex numbers in other areas of physics, so it would be interesting to have a further conversation, as long as you stop being so defensive.
Complex numbers seem to be used either as 2d vectors or as representation of waves/circles in exponentials, is there an alternative that combines both of those uses?
Math is a tool of the mind to describe our world, imaginary numbers is only a extension of that tool to allow us to go beyond what mathematical logic prevents us to do, while still getting in the end a real number. Math, despite being powerful, is a flawed tool, so getting around its flaws by creating things like imaginary numbers isn’t absurd and doesn’t make the result any less real at the end.
On the other hand, I don’t think calling everything we don’t understand “magic” or the new trending words “supernatural” and “a miracle” and give god or anything else (like karma) credit for it would be more clever. Back then, we didn’t understood the concept of thunder and interpreted it as god’s wrath. Now, we understand it’s a transmission of electricity from the negatively charged clouds to the neutral ground through ionized particles in the air. I don’t think that scientists now, despite referring to the same phenomena, are talking about the same thing as we did a long time ago.
So no, no scientist will discover the afterlife “but we’ll just call them “Post-Human Conciousness Wells” or something, and insist it totally isn’t the same thing as that ancient superstition.” as it won’t be.
There’s actually some controversy on that one:
https://www.scientificamerican.com/article/is-the-mathematical-world-real/
Stating mathematics is a tool doesn’t answer if mathematics are real or not. But I would say, from my humble experience, that mathematics is both unreal and perfectly tangible. Mathematics is totally a real thing as it obeys strict rule in logic that are true in our real world, axioms, on which everything else is based so that it can’t be used to state things as being true out of the blue, without any justification before using those axioms, which you can translate into our real world. But math also has its limits and has been used to demonstrate that it itself is incomplete, undecidable and inconsistant (mathematically, of course, it’s not our common definition here). Meaning, as mathematics are imperfect, it can’t describe our world perfectly and therefore isn’t real.
There is an excellent video from Veritasium on the subject of the limits of math: https://piped.video/HeQX2HjkcNo
Here is an alternative Piped link(s): https://piped.video/HeQX2HjkcNo
Piped is a privacy-respecting open-source alternative frontend to YouTube.
I’m open-source, check me out at GitHub.
Man I really love Lemmy for that kind of shit. I’ll change the link right away
Quantum mechanics, as far as we know, requires imaginary numbers.
nope, they’re just one mathematical construct out of many (e.g. 2D vector calculus or geometric algebra), and they just happened to stick
Nope, you’re just wrong. Quantum mechanics without complex numbers(real quantum theory) is less predictive than complex(regular) quantum theory. https://www.scientificamerican.com/article/quantum-physics-falls-apart-without-imaginary-numbers/
Incorrect. You can construct an isomorphism between the even subalgebra of the 2D geometric algebra Cl(2) and the complex numbers that maps 1 to the unit scalar and i to the pseudoscalar: https://link.springer.com/article/10.1007/BF01883676
Are you interested in proving me wrong, or figuring out the right answer? If you actually read that article instead of just the title, you would have noticed at the end it says
They literally say that “complex numbers are fundamental to quantum mechanics”. In other fields of physics complex numbers are just a convenient tool, but in quantum mechanics they are(as far as we know) fundamental, even if the author hopes that to be proved wrong at some point.
You seem like you know a bit about alternatives to complex numbers in other areas of physics, so it would be interesting to have a further conversation, as long as you stop being so defensive.
Complex numbers seem to be used either as 2d vectors or as representation of waves/circles in exponentials, is there an alternative that combines both of those uses?