Weird how magic and mystery stops being magic when scientists have words for it.
One day we’ll 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.
Cmon, you wanna tell me the world is purely material when our math literally uses imaginary numbers to make sense of things?
Imaginary numbers are merely a poorly named mathematical construct used to reconcile the empirically observable phenomena of nature (e.g., summations of waves). They’re the means by which we achieve mathematical closure under exponentiation. You could call them whatever the F you want, so long as they could be used to represent vectors in the complex plane.
What reason do you have to believe in anything outside of material nature?
Up to the introduction of quantum mechanics imaginary numbers where only ever a theoretical tool and any calculation in electromagnetism, mechanics or even relativity can be done without them.
Also, any measurement you can make will always result in real numbers because there is no logical interpretation for imaginary measurements (a speed of 2+i m/s doesnt really make sense)
I said that any calculation in electrodynamics CAN be done without imaginary numbers, I never said that it would be the most common or convenient way of doing things.
If you use a different form of solution to maxwells equations, electrical impedance can totally be expressed as just another real property. Fourier transform also is not necessary to solve maxwells equations or any other physical systems. It just might make it significantly easier and more convenient.
Obviously imaginary numbers existed and where used way before quantum mechanics was a thing but they werent technically necessary in physics because they never appeared in the equations of fundamental theories (Maxwells equations, general relativity, newtonian mechanics)
I was just trying to make an argument that imaginary numbers were technically not necessary and thus it makes historical sense that they werent seen as something ‘real’. Im not trying to get people to stop using them ;)
Well, in AC circuits, having √3̅+√-̅1̅ A of current makes as much sense as having 2 amps with a 30° phase shift. It’s just easier notation for calculations - Cartesian coordinates for what would otherwise be polar.
There’s a really good science fiction novel by Robert Sheckley called Immortality, Inc. where scientists in the future have discovered that there is an afterlife, but the only way to ensure you get there is a medical procedure and you can only do that if you can afford it. That’s just the beginning, there’s a huge amount of worldbuilding, but that’s the main theme of the book.
actual theoretical physicist here: “imaginary numbers” are just poorly named, there’s nothing imaginary about them. You might as well use 2D geometric algebra to do the exact same job (treating real numbers as scalars and imaginary numbers as pseudoscalars)
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.
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?
Yep, there’s an alternative, i.e. equivalent mathematical formulation that does everything complex numbers do: the geometric algebra introduced in the article I posted earlier.
The fundamental object of GA is the “multivector”, which is essentially a sum of scalars, vectors, bivectors and higher grade elements. For instance, you could take the unit x-vector and add it onto some number, say 2, to get the multivector M = 2 + e_x. (To be precise, the space of multivectors is the direct sum over the n-th wedge of the base vector space, n = 0 to dim V).
Another important concept is k-vectors, which are essentially k-dimensional volume elements. For instance, a bivector is an area with a direction, and a trivector is a volume with a direction (in 3D there is only one possible “direction” for the volume, but in 4D spacetime volumes itself can be oriented like surfaces can be in 3D).
Then, you introduce the “geometric product” for two vectors a and b:
ab = a·b + a ∧ b
where a · b is the normal scalar product between the two vectors, and a ∧ b is the wedge product between them. The wedge product essentially is the plane spanned by the two vectors, and is antisymmetric (a ∧ b = - b ∧ a, because the orientation of the plane is reversed when exchanging the vector). For instance, the unit bivector in the x-y plane is given by
B_xy = e_x e_y = e_x ∧ e_y
Notice how the scalar product part of the geometric product is zero, and only the wedge (i.e. bivector part) remains
In 3D, there are four types (“grades”) of objects: scalars, vectors, bivectors (also known as 3D pseudovectors) and trivectors (or also known as 3D pseudoscalars). It’s already a very rich subject and has many advantages over classical vector calculus, but for replacing complex numbers, we’re mainly concerned with the 2D case.
In the 2D case, there are three types of objects: Scalars, 2D vectors, and bivectors/2D pseudoscalars. There is only one possible orientation for a 2D plane in 2D, so we just denote a bivector with area A as B = A I, where I = e_x ∧ e_y is the only unit bivector/2D pseudoscalar.
A nice thing we notice about the I is that it squares to -1 with the geometric product:
I^2 = (e_x ∧ e_y)^2 = (e_x e_y)^2 = e_x e_y e_x e_y = - e_x e_y e_y e_x = -e_x e_x = -1
The first step works because the scalar product part between e_x and e_y is zero. The second step is just writing out the square. The third step is e_y e_x = e_y ∧ e_x = - e_x ∧ e_y = -e_x e_y, which again works because e_x · e_y = 0. We see that the 2d pseudoscalar I behaves just like the “classic” imaginary unit i.
Because the geometric product is associative, and commutative if only scalars and bivectors are involved, the geometric notion of scalars and 2D pseudoscalars can fully replace the notion of complex numbers by making the substitution a + bi -> a + bI.
If you want to learn more about GA, I can recommend Doran, Lasenby: Geometric Algebra for Physicsists :)
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.
On the other hand, I don’t think calling everything we don’t understand “magic” … and give god or anything else (like karma) credit for it would be more clever.
i think quite a few theologians would agree with that point
And it’s great. Though, as a religious person, thinking this way is no more than shooting yourself in the foot, which is quite sad because religion has only two choice: either cultivating the ignorance but going against science, which is wrong, or cultivating knowledge but overtime, disappearing as a religion. Either way, nowadays it’s doomed.
Religion and science are orthogonal. Science seeks to answer the question of “how?”, while religion seeks to answer “why?”
Understanding the Big Bang all the way through evolution doesn’t give an indication as to why all of this happened. Why are we here? What is our purpose? Science doesn’t have an answer for these questions because these questions are orthogonal to science. Any kind of answer to this kind of question would constitute a religion.
It’s really atheism (at least in the present iteration) that’s doomed to failure. It’s dependent on ignorance of basic philosophy, and attempts to derive any kind of morality based solely on science results in things like eugenics and an “the ends justify the means” kind of mentality. Atheist ethics have resulted in more deaths than all other religions combined. And yes, atheism is a religion, but the ignorance of atheists has resulted in them believing it isn’t a religion even when it exhibits all the properties of a religion. It’s just a shit religion, which is why it’s doomed to fail.
i completely agree with the first two paragraphs, but i don’t quite understand what you mean in the third paragraph. could you elaborate on what you mean by the present iteration of atheism, how its like a religion, and why you think it’s doomed to fail? it sounds interesting and i haven’t heard much about it.
Religion and science are orthogonal. Science seeks to answer the question of “how?”, while religion seeks to answer “why?”
Religion doesn’t try to answer anything: it’s just blind faith. You’re not gonna try to tell me religious people are “looking for” anything. The definition of religion is “belief in a deity”. It doesn’t try to explain or find out anything.
It’s dependent on ignorance of basic philosophy, and attempts to derive any kind of morality based solely on science results
Since when atheism prevents philosophy? Haven’t you heard of atheist philosophers? They exist, they’re not fairies, you know.
About morality, it’s still a subject and a lot of philosophers have different opinion, with the subjective or objective moral, relativistic moral, etc…
And whatever you mean by “derive any kind of morality based solely on science results”, it’s still better than arbitrarily define a moral based on a book written by some people a long time ago to then enforce it for centuries, with violence if needed, and then when the bad atheists come to clean all the mess by making moral laws to have everybody end up agreeing on after few decades, claim it was just a misinterpretation of the texts or whatever, which is the dumbest excuse I’ve ever heard of.
Atheism isn’t a religion either: atheism is a lack of belief in the existence of an unproven (and certainly unprovable) entity.
So a lack of belief certainly didn’t kill anybody.
And atheism was never the reason or the foundation of the sentence “the end justify the means”, it existed long before atheism was even a concept.
i don’t see how it’s shooting yourself in the foot. one of the ideas behind the argument i linked to is that pitting god against science isn’t good theology. science will offer more compelling explanations for material phenomena, but that doesn’t necessarily exclude the existence of a god. the idea is to see god as more of an architect: something that made a world that has all these wonderful scientific rules and complex systems that we can discover.
i should mention that i’m not a religious person but i do think it’s an interesting thing to think about.
Friend of mine (who is dead now ironically enough, and damn, I miss him), wrote a story about this. Where the dead show up on some random planet in the Andromeda Galaxy, in their prime, one that’s infinitely large and does the minecraft thing where it generates as you go, and contains the means to do pretty much anything except for leave… with them just showing up in the Capital City of the planet if they die again, which cannot be done of natural causes here.
The dead initially think it’s Heaven, but then they notice “Heaven” is being powered by a Dyson Sphere, eventually they connect enough of the dots to realize that their world is a simulation.
The protagonist is the grandchild of one of the deceased who wound up here after testing experimental teleportation technology, turns out the simulation brought him there to inform him why teleportation technology shouldn’t be invented.
Eventually the grandchild goes back to Earth, agreeing to keep this a secret, for fear that if people knew about this it would create “Dyson Sphere cults” and would encourage people to commit mass suicide, just “dying to get there”
My thought was more like, then there must be god, that god must have been created (since not naturally developed) so he must be there for a reason (administrator or something) so there must be a system behind it.
Weird how magic and mystery stops being magic when scientists have words for it.
One day we’ll 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.
Cmon, you wanna tell me the world is purely material when our math literally uses imaginary numbers to make sense of things?
Imaginary numbers are merely a poorly named mathematical construct used to reconcile the empirically observable phenomena of nature (e.g., summations of waves). They’re the means by which we achieve mathematical closure under exponentiation. You could call them whatever the F you want, so long as they could be used to represent vectors in the complex plane.
What reason do you have to believe in anything outside of material nature?
It’s called a joke
Idiotic joke
It’s fucking mindless.
I bet you’re a blast at parties.
You’re fun!
Up to the introduction of quantum mechanics imaginary numbers where only ever a theoretical tool and any calculation in electromagnetism, mechanics or even relativity can be done without them.
Also, any measurement you can make will always result in real numbers because there is no logical interpretation for imaginary measurements (a speed of 2+i m/s doesnt really make sense)
Bro, are you not aware of the Fourier transform?!? Electrical impedance? Wtf???
I said that any calculation in electrodynamics CAN be done without imaginary numbers, I never said that it would be the most common or convenient way of doing things.
If you use a different form of solution to maxwells equations, electrical impedance can totally be expressed as just another real property. Fourier transform also is not necessary to solve maxwells equations or any other physical systems. It just might make it significantly easier and more convenient.
Obviously imaginary numbers existed and where used way before quantum mechanics was a thing but they werent technically necessary in physics because they never appeared in the equations of fundamental theories (Maxwells equations, general relativity, newtonian mechanics)
Yes, and one CAN integrate by taking paper cuttings and dispense entirely with the idea of infinity.
I was just trying to make an argument that imaginary numbers were technically not necessary and thus it makes historical sense that they werent seen as something ‘real’. Im not trying to get people to stop using them ;)
Eh, this is not worth your time or mine to argue about. Let’s move on. Also, I take your point.
Imaginary numbers are indeed poorly named. They are not much more imaginary than members of ℝ.
It’s all fine… except for the part where reality has a √-1 component.
Well, in AC circuits, having √3̅+√-̅1̅ A of current makes as much sense as having 2 amps with a 30° phase shift. It’s just easier notation for calculations - Cartesian coordinates for what would otherwise be polar.
Yeah but quantum mechanics is just magic.
There’s a really good science fiction novel by Robert Sheckley called Immortality, Inc. where scientists in the future have discovered that there is an afterlife, but the only way to ensure you get there is a medical procedure and you can only do that if you can afford it. That’s just the beginning, there’s a huge amount of worldbuilding, but that’s the main theme of the book.
actual theoretical physicist here: “imaginary numbers” are just poorly named, there’s nothing imaginary about them. You might as well use 2D geometric algebra to do the exact same job (treating real numbers as scalars and imaginary numbers as pseudoscalars)
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.
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?
Yep, there’s an alternative, i.e. equivalent mathematical formulation that does everything complex numbers do: the geometric algebra introduced in the article I posted earlier.
The fundamental object of GA is the “multivector”, which is essentially a sum of scalars, vectors, bivectors and higher grade elements. For instance, you could take the unit x-vector and add it onto some number, say 2, to get the multivector M = 2 + e_x. (To be precise, the space of multivectors is the direct sum over the n-th wedge of the base vector space, n = 0 to dim V).
Another important concept is k-vectors, which are essentially k-dimensional volume elements. For instance, a bivector is an area with a direction, and a trivector is a volume with a direction (in 3D there is only one possible “direction” for the volume, but in 4D spacetime volumes itself can be oriented like surfaces can be in 3D).
Then, you introduce the “geometric product” for two vectors a and b:
ab = a·b + a ∧ b
where a · b is the normal scalar product between the two vectors, and a ∧ b is the wedge product between them. The wedge product essentially is the plane spanned by the two vectors, and is antisymmetric (a ∧ b = - b ∧ a, because the orientation of the plane is reversed when exchanging the vector). For instance, the unit bivector in the x-y plane is given by
B_xy = e_x e_y = e_x ∧ e_y
Notice how the scalar product part of the geometric product is zero, and only the wedge (i.e. bivector part) remains
In 3D, there are four types (“grades”) of objects: scalars, vectors, bivectors (also known as 3D pseudovectors) and trivectors (or also known as 3D pseudoscalars). It’s already a very rich subject and has many advantages over classical vector calculus, but for replacing complex numbers, we’re mainly concerned with the 2D case.
In the 2D case, there are three types of objects: Scalars, 2D vectors, and bivectors/2D pseudoscalars. There is only one possible orientation for a 2D plane in 2D, so we just denote a bivector with area A as B = A I, where I = e_x ∧ e_y is the only unit bivector/2D pseudoscalar.
A nice thing we notice about the I is that it squares to -1 with the geometric product:
I^2 = (e_x ∧ e_y)^2 = (e_x e_y)^2 = e_x e_y e_x e_y = - e_x e_y e_y e_x = -e_x e_x = -1
The first step works because the scalar product part between e_x and e_y is zero. The second step is just writing out the square. The third step is e_y e_x = e_y ∧ e_x = - e_x ∧ e_y = -e_x e_y, which again works because e_x · e_y = 0. We see that the 2d pseudoscalar I behaves just like the “classic” imaginary unit i.
Because the geometric product is associative, and commutative if only scalars and bivectors are involved, the geometric notion of scalars and 2D pseudoscalars can fully replace the notion of complex numbers by making the substitution a + bi -> a + bI.
If you want to learn more about GA, I can recommend Doran, Lasenby: Geometric Algebra for Physicsists :)
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
i think quite a few theologians would agree with that point
And it’s great. Though, as a religious person, thinking this way is no more than shooting yourself in the foot, which is quite sad because religion has only two choice: either cultivating the ignorance but going against science, which is wrong, or cultivating knowledge but overtime, disappearing as a religion. Either way, nowadays it’s doomed.
Religion and science are orthogonal. Science seeks to answer the question of “how?”, while religion seeks to answer “why?”
Understanding the Big Bang all the way through evolution doesn’t give an indication as to why all of this happened. Why are we here? What is our purpose? Science doesn’t have an answer for these questions because these questions are orthogonal to science. Any kind of answer to this kind of question would constitute a religion.
It’s really atheism (at least in the present iteration) that’s doomed to failure. It’s dependent on ignorance of basic philosophy, and attempts to derive any kind of morality based solely on science results in things like eugenics and an “the ends justify the means” kind of mentality. Atheist ethics have resulted in more deaths than all other religions combined. And yes, atheism is a religion, but the ignorance of atheists has resulted in them believing it isn’t a religion even when it exhibits all the properties of a religion. It’s just a shit religion, which is why it’s doomed to fail.
i completely agree with the first two paragraphs, but i don’t quite understand what you mean in the third paragraph. could you elaborate on what you mean by the present iteration of atheism, how its like a religion, and why you think it’s doomed to fail? it sounds interesting and i haven’t heard much about it.
Religion doesn’t try to answer anything: it’s just blind faith. You’re not gonna try to tell me religious people are “looking for” anything. The definition of religion is “belief in a deity”. It doesn’t try to explain or find out anything.
Since when atheism prevents philosophy? Haven’t you heard of atheist philosophers? They exist, they’re not fairies, you know. About morality, it’s still a subject and a lot of philosophers have different opinion, with the subjective or objective moral, relativistic moral, etc… And whatever you mean by “derive any kind of morality based solely on science results”, it’s still better than arbitrarily define a moral based on a book written by some people a long time ago to then enforce it for centuries, with violence if needed, and then when the bad atheists come to clean all the mess by making moral laws to have everybody end up agreeing on after few decades, claim it was just a misinterpretation of the texts or whatever, which is the dumbest excuse I’ve ever heard of.
Atheism isn’t a religion either: atheism is a lack of belief in the existence of an unproven (and certainly unprovable) entity. So a lack of belief certainly didn’t kill anybody.
And atheism was never the reason or the foundation of the sentence “the end justify the means”, it existed long before atheism was even a concept.
i don’t see how it’s shooting yourself in the foot. one of the ideas behind the argument i linked to is that pitting god against science isn’t good theology. science will offer more compelling explanations for material phenomena, but that doesn’t necessarily exclude the existence of a god. the idea is to see god as more of an architect: something that made a world that has all these wonderful scientific rules and complex systems that we can discover.
i should mention that i’m not a religious person but i do think it’s an interesting thing to think about.
If you think it to the end, existence of an aftlerlife would be evidence that we run in a simulation.
Friend of mine (who is dead now ironically enough, and damn, I miss him), wrote a story about this. Where the dead show up on some random planet in the Andromeda Galaxy, in their prime, one that’s infinitely large and does the minecraft thing where it generates as you go, and contains the means to do pretty much anything except for leave… with them just showing up in the Capital City of the planet if they die again, which cannot be done of natural causes here.
The dead initially think it’s Heaven, but then they notice “Heaven” is being powered by a Dyson Sphere, eventually they connect enough of the dots to realize that their world is a simulation.
The protagonist is the grandchild of one of the deceased who wound up here after testing experimental teleportation technology, turns out the simulation brought him there to inform him why teleportation technology shouldn’t be invented.
Eventually the grandchild goes back to Earth, agreeing to keep this a secret, for fear that if people knew about this it would create “Dyson Sphere cults” and would encourage people to commit mass suicide, just “dying to get there”
My thought was more like, then there must be god, that god must have been created (since not naturally developed) so he must be there for a reason (administrator or something) so there must be a system behind it.
But nice story!
How did you come to that conclusion?
Which part?