/sci/ - Science & Math

[Anonymous No.12784151]

>physicists actually got paid to say that (-1)^0.5 is useful
So this is what non-engineers are up to these days

[Anonymous No.12784220]

>>12784151
>what if we make TWO entangled pairs instead of one?
>let's publish this amazing idea
>experiment? no way lol
Physics has become such a meme it's embarrassing.

[Anonymous No.12784326]

>>12784151
How do you calculate anything electricity related without them?

[Anonymous No.12784554]

>>12784326
I’m an EE so that’s why I posted this article since it was extra ridiculous to me

[Anonymous No.12784764]

>>12784151
Most scientists should just admit that they are corrupt people trying to sell seomthing instead of deluding themselves into believing they stand "for truth".

[Anonymous No.12784793]

If you actually have a problem with imaginary numbers then you are a retard.

[Anonymous No.12784909]

>>12784793
Not retarded. A lot of mathematicians hated them but knew that they made a lot of things work. They are a necessary evil. Descartes called them "imaginary" as an insult.

[Anonymous No.12784919]

>>12784151
>new thought experiment ... strange numbers that turn negative when squared
i (j for my EE chads) was like 10th grade math. Do journalists not even pass highschool

[Anonymous No.12785881]

>>12784909
Brainlet here. Redpill me on imaginary numbers. I understand that they can be written on a 2d axis, and the basic properties of them, but I don’t know why they’re useful.

[Anonymous No.12785890]

>>12784326
You can do it. Just harder to take derivatives. Take the real part of your answer before talking to brainlet EEs who can’t into complex analysis

[Anonymous No.12785894]

>>12785881
Impedance in electical circuits, is what I remember

[Anonymous No.12785900]

>>12785881
They are particularly useful for brainlets who, while not so brainlet they can’t into complex analysis, nevertheless can’t into Schwinger’s approach to QFT and have to rely on perturbation theory of Feynman the king brainlet. Also complex analysis makes real integrals easier sometimes.

[Anonymous No.12785908]

haven't imaginary numbers had applications in electrical engineering for over a century? outside of that, even the basic de moivre's is very useful for proving a bunch of trig identities.

[Anonymous No.12785913]

No need for wacky numbers, just use matrices.

[Anonymous No.12785919]

>>12785881
They are useful for the same reason that the rationals are. There really isn't any justification for the rationals being any less imagnary since they are all just abstract consepts to begin with.

[Mohan No.12785940]

>>12784151
>noooo you can't use this number it's imaginary it does not exist
you are, in fact, retarded.

[Anonymous No.12785958]

can you show me a single instance in physics where you have to use """"imaginay"""" numbers and the same relationship can't be expressed with trigonometric functions or power series or matrices?

[Anonymous No.12786392]

>>12785940
Congrats, your take away was the complete opposite of what I was saying in my post

[Anonymous No.12786460]

>>12785908
Yes they are extensively used in power analysis as somewhat of a measure between energy removed into an unusable magnetic field. Same in signal analysis. Essentially i (j) is just the magnetic axis for an electromagnetic wave

[Anonymous No.12786470]

>>12785881
>why they’re useful
rotations turn into multiplications, waaay easier

[Anonymous No.12786482]

>>12785881
The same reason anything in math is useful. It makes doing something easier

[Anonymous No.12786485]

>>12784151
Is i really even useful? What does working in C give you that working in R^2 doesn't?

[Anonymous No.12786489]

>>12784326
Are you stupid? Trick question: the answer is yes since all EEs are retarded. You use complex exponentials as solutions to your ODEs. Sines and cosines work just as well. All you need are two linearly independent oscillatory functions.

[Anonymous No.12786494]

>>12785894
Faggot you can handle impedance without imaginary numbers.

[Anonymous No.12786524]

>>12786494
Retard

[Anonymous No.12786532]

>>12786524
Spoken like a true EE student.

[Anonymous No.12786548]

>>12784151
Journalists should hang from trees. This reminds me of the time ieee spectrum made this sensationalist article about a groundbreaking technology company that would stagnate the free clean water problem. It was a solar panel with a dehumidifier. I emailed them pointing out how such a thing makes no sense, and they never replied or deleted the article. Journalism ethics my ass. They are a bunch of monkeys with slightly above average writing skill who are absolutely ignorant about anything, but that can organise their incoherent thoughts in a way that sounds credible to the layman.

[Anonymous No.12786567]

>>12785958
Right? You know what else? Fuck writing pi, anytime I want pi I will write the infinite series.

[Anonymous No.12787291]

>>12784151
what kind of target audience has interest in quantum mechanics and calls imaginary numbers "strange"?

[Anonymous No.12787300]

>>12784151
Calling them imaginary was a mistake.

[Anonymous No.12788135]

Sqrt(-1) is undefied even in Complex Analysis.

[Anonymous No.12788150]

>>12785913
[math] \displaystyle
a+b \, \text{i} \leftrightarrow
\begin{bmatrix}
a & -b \\
b & a
\end{bmatrix}
\\
\begin{bmatrix}
0 & -1 \\
1 & 0
\end{bmatrix}
\begin{bmatrix}
0 & -1 \\
1 & 0
\end{bmatrix}
=
\begin{bmatrix}
-1 & 0 \\
0 & -1
\end{bmatrix}
[/math]

[Anonymous No.12788179]

>>12785958
allegedly quantum mechanics, the complex wavefunction

[Anonymous No.12788182]

>>12787291
IFLS

[Anonymous No.12788196]

>>12788179
You mean the solution to Schrodinger's equation? Nah. Totally doable without complex numbers.

[Anonymous No.12788204]

>>12784151
What a fascinating idea. I can’t belive no one realized imaginary numbers are useful for modeling physical phenomenon until 2021! It was so obvious, why didn’t we realize this sooner?

[Anonymous No.12788221]

>>12785881
You can represent sine and cosine using I.
I forget the proof, It's linked to the machlaurin series, but the result is:
cos(θ) = (e^iθ + e^-iθ)/2 & sin(θ) = (e^iθ - e^-iθ)/2
If you take out I, you get the hyperbolic functions, which are very important in calculus, allowing you to der/int forms of e^x +/- e^-x

[Anonymous No.12788227]

>>12788221
Pseud. If you don't know the answer, don't make shit up. While what you wrote is accurate, it has nothing to do with the question.

[Anonymous No.12788230]

>>12788196
Really? Ok.

[Anonymous No.12788232]

>>12785881
they are all over the place in quantum mechanics when describing wavefunctions

[Anonymous No.12788236]

Someone redpill me on Grassman numbers. How do you actually do calculations with them?

[Anonymous No.12788257]

>>12788196
Now do the time-dependency

[Anonymous No.12788264]

>>12785881
Back when Indian-Arabic mathematics were making rounds into Europe, Europeans didn't like concepts many of the concepts. 0 and negatives were thought to be heretic math by the Christians of Europe because Christians didnt invent them.

[Anonymous No.12788269]

>>12788264
>0 and negatives were thought to be heretic math
They are

[Anonymous No.12788273]

>>12788257
If you honestly don't see how you can rewrite this without using i, then you're a pseud.

[Anonymous No.12788300]

>>12788196
how about
https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect
" an electrically charged particle is affected by an electromagnetic potential (φ, A), despite being confined to a region in which both the magnetic field B and electric field E are zero"

[Anonymous No.12788320]

>>12788300
Mathematically it arises from the phase, right? That's completely treatable via a real sinusoidal function. Asin(wt + p). I don't see the difference. Physicists really need to lose their hard-on for how phases only exist in complex exponentials

[Anonymous No.12788338]

>>12784151
I don't even understand this shit. As a mathfag, I have to say, these guys are philosophically illiterate.

You can't perform a test to determine if complex numbers are real or not. It's a meaningless question. Don't get me wrong, I'm a Platonist and I believe mathematical truths are objective and not dependent on humans, but at the same time, it doesn't make sense to ask whether complex numbers "really" exist in nature. Nor does it makes sense to ask whether real numbers "really" exist in nature. The physical world is not made up of number. It's made up of physical objects that can instantiate numerical properties relative to purpose or conceptual scheme, and we can make true or false claims on the basis of that, but there is not fact of the matter as to whether a physical system is real, rational, complex, etc. It's either all of those things at the same time, or none of them, depending on how you want to look at it. What matters is that any of these systems can be used to describe pretty much the same physical theories.

[Anonymous No.12788353]

>>12788338
>It's made up of physical objects that can instantiate numerical properties relative to purpose or conceptual scheme
that's the measurement apparatus which does this and of course its output is not really a number until a human converts whatever mechanism happens in the apparatus into a readable number

Anyway, scientific realism is indeed bogus.

[Anonymous No.12788360]

>>12788320
>both the magnetic field B and electric field E are zero
show the math big boi

[Anonymous No.12788368]

>>12788360
I mean I scanned the mathematical section of the article and it appears they struggle to formalize it even with complex numbers. Their argument is heuristic. I'm not sure a formal mathematical argument exists. If you're familiar with one, do share and I'll reproduce it without using complex numbers.

[Anonymous No.12788381]

>>12788368
how surprising

[Anonymous No.12788399]

>>12788381
How? What do you think was my original position, and what is my proposed new one? My claim is that you can handle all of QM without complex numbers. You bring up an effect that's usually explained to be caused by complex phases. I argue that phases can be handled with real sines or cosines. You tell me to show the math, I claim I'm willing to. I'm not going to derive an effect if no derivation exists, since I'm probably incapable of that. If such derivation already exists, and uses complex numbers, I can trivially reproduce it using sines and cosines.

[Anonymous No.12788410]

>>12788399
>I'm probably incapable
agree

[Anonymous No.12788420]

>>12788410
Don't pretend like you're capable of it. You're not.

[Anonymous No.12788447]

>>12788399
Brainlet here, how does one turn something complex into just sines and cosines?

[Anonymous No.12788607]

>>12788447
exp(ix) = cosx + i sinx