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/sci/ - Science & Math

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5317263 No.5317263 [Reply] [Original]

ITT: Concepts that are fascinating

>> No.5317267

<div class="math">\int_M \langle F\wedge e\wedge e\rangle</div>

>> No.5317947

so many things
Second Law of Thermodynamica blew me away the first time I learned it
Simpson's Paradox had me thinking of the -for me superunintuitive- example of the 2 boxes with white and black marbles for a long time
I remember the complete subject of Linear Algebra also opening my eyes to a lot of things

>> No.5317959

>>5317267
What does this mean?

>> No.5318832

>>5317267
>>5317959

bump 4 interest

>> No.5318844
File: 13 KB, 300x300, 41+-P-RfMLL._AA278_PIkin4,BottomRight,-26,22_AA300_SH20_OU01_.jpg [View same] [iqdb] [saucenao] [google]
5318844

quantum entanglement. chapter four of david mcintyre's quantum mechanics.

>> No.5318861
File: 20 KB, 293x73, Fourier.jpg [View same] [iqdb] [saucenao] [google]
5318861

>>5317263

Specifically how it can relate to crystallography.

>> No.5318867

>>5318861
Care to elaborate?

>> No.5318871

The holographic principle, and more specifically the AdS/CFT duality. Its a pretty crazy thing claiming that a theory of gravity in d dimensions is the exact same thing as a quantum field theory without gravity in d-1 dimensions, and it seems to really work.

>> No.5318874

triple integrals

>> No.5318879

Newton's first law of motion

>> No.5318892
File: 86 KB, 1000x398, ecuaciondecampo.jpg [View same] [iqdb] [saucenao] [google]
5318892

Gravity, by Albert Einstein.
One of the most beautiful formulas out there, which explains the behaviour of spacetime when you put a mass on it.

>> No.5318895

>>5318874
What's exciting about this... Simple and easy to grasp.

>> No.5318903

>>5318895
I think he meant it as a joke.

>> No.5318910

The graph of the iterations of
<span class="math">z_n = {z_{n-1}}^2 + z_0[/spoiler]

>> No.5318914

when suddenly math isnt numbers anymore and their are letters like x and y

i was all like whoa dude mind=blown

>> No.5318920

>>5318914
Stop ruining /sci/ with your inane trolling and share some actual concepts you find fascinating.

>> No.5318931

induction

>> No.5318936

Using phasors for circuits

http://en.wikipedia.org/wiki/Phasor

>> No.5318957

>>5318936
I don't know this and I don't really like reading Wikipedia because I feel it doesn't explain new concepts very well. Mind explaining what it's about? If you don't want to I understand, but it's worth a shot.

>> No.5318967

I'm fascinated by the concept of women's breasts.

Haven't got past the conceptual level, sadly.

>> No.5318987

>>5318967
Keep at it, soon you will have a breakthrough, I am sure of it.
Perhaps you need some more practical R&D?

>> No.5318996

>>5318987
I have already established several cohorts for a longitudinal study.

In my mind.

>> No.5319021

The concept and history of zero.

>> No.5319028

>>5317263
First time I looked at the double slit experiment with photons and then electrons I nearly shit my pants

>> No.5319042

>>5319028
I can relate.

>> No.5319059

This is my first time on sci and what the fuck is this even 4chan? I went on /g/ and thought I was smart for understanding things but I come here and feel retarded, i don't even understand a single thing :(

>> No.5319080

>>5319059
It's good that you realize that you still have a lot to learn and it's never to late to start. Don't worry either, /sci/ isn't as smart as you think it is.

>> No.5319094

>>5317959
Is anyone going to answer this?

>> No.5319143

>>5318957

basically it lets you solve AC (alternating current, ie: the current is not constant) circuits much easier using complex numbers (using euler's formula).

This lets you solve AC circuits using algebra instead of differential equations.

>> No.5319156

>>5319094
It's the action for general relativity. <span class="math">\int_M[/spoiler] is an integral over the flat Lorentzian manifold generated from the Poincare group (http://en.wikipedia.org/wiki/Volume_form#Relation_to_measures)), <span class="math">F[/spoiler] is the curvature form (http://en.wikipedia.org/wiki/Gauge_theory#Mathematical_formalism)) of the Poincare group <span class="math">\mathrm{ISO}(3,1)[/spoiler] (http://en.wikipedia.org/wiki/Poincar%C3%A9_group#Technical_explanation)), <span class="math">\wedge[/spoiler] is the wedge product (http://en.wikipedia.org/wiki/Exterior_algebra#Formal_definitions_and_algebraic_properties)), <span class="math">e[/spoiler] is the triad (http://en.wikipedia.org/wiki/Cartan_formalism_(physics)#The_basic_ingredients), <span class="math">\langle -\rangle[/spoiler] is the invariant polynomial (http://en.wikipedia.org/wiki/Invariant_polynomial).).

>> No.5319163

>>5319143
Ah ok, I understand that. Very interesting indeed. Thanks for answering.

>> No.5319170

>>5319028
I still don't get electrons. That plus Heisenberg's uncertainty principle. I can recite what sources have taught me, but I still don't have any idea why these are true.

>> No.5319200

>>5319156
Thanks.

>> No.5319227

>>5318910
>The graph of the iterations
full retard.
you don't even understand the definition of the mandelbrot set, you are just hippie popsci fan trash.
"lol dem fractals color, dem beautiful , proof god is lsd"
just fuck off

>> No.5319226

>>5319170
Heisenberg uncertainty principle is esentially a mathematical theorem so it is true as it is true that 1+1=2. However, from that principle you can derive very shocking consequences.. such as the need to abandon the idea of a path (in the sense of walkway) for quantum systems.

For electrons, if you really want to understand them in a very deep way you need to study quantum field theory and in particular the dirac field. So, keep up the hard work at quantum mechanics and you will eventually jump to quantum field theory which will allow you to understand the elementary particles in the most deep way that we know

>> No.5319266

>>5319226
Well I think I'm still a few years away from needing to learn quantum mechanics, but things I read about it isn't sticking well.

I can just reiterate that an electron can act as a wave and a particle, and the more you know about its position, the less you know of its momentum. Just have no clue why yet.

>> No.5319284
File: 8 KB, 200x200, 1353664341200s.jpg [View same] [iqdb] [saucenao] [google]
5319284

>>5317263
>triangle X times triangle P is greater than or less than h with a dash bar 2

I'm so glad that schools is a lot easier in America than anywhere.

>> No.5319305

>>5319284
>greater than or less than

It's clearly symbolism for an Alligator mouth.

>> No.5319299

Euler's Identity.

a.k.a. God's Toolbox

>> No.5319301

>>5319266
Well that's because you just can't learn or make proper statements about quantum mechanics without the mathematical formalism.

I've never thought very much about the wave particle duality.. any particle that can be treated by the means of quantum mechanics will exhibit particle like properties at some experiments and wave like properties at others, this is the point. For example, we know that electrons can have particle like properties. Well they can show wave like properties such as diffraction, i.e. you can see the diffraction pattern of a beam of electrons, and moreover, the wavelenght is given by the deBroglie relation! Q.M. is a very shocking but very well stablished part of physics.

About the Heisenberg principle it can be stated as you say, at least in a naive way. For example if you can calculate the wave function of the system under study, this principle says that the spread of the position and the spread of the momentum associated to that coordinate of position are related, and it's product has a lower bound, say hbar / 2. It can be used to stimate order of magnitude of position or momentum of the system.. Also it does apply to energy and time, but the proof here, as far as I know it's much more naive than in the position, momentum case (because energy and time are no operators, and the heisenberg uncertainty principle is a principle relating hte commutator of operators with the product of their spreads)

If you are interested in quantum physics, which is a very nice interest, you can prepare your way by learning some math (loads of linear algebra, some differential equations) and physics (esentially classical mechanics in the Hamiltonian formalism, but radiation physics in order to understand the historical development of quantum physics is nice)

>> No.5319344

>>5317263
If you took a bunch of sticks 2.5 yards long and threw them all over an american football field (lines every 5 yards), the number of sticks thrown divided by the number of sticks intersecting a line is pi.

>> No.5319370

>>5319344
You've got my attention. Why is that so?

>> No.5319376

I still find the fact that you can figure out the position of a ball thrown in the air at any given time fascinating.

>> No.5319378

>>5319299
Why aka God's toolbox?

>> No.5319381

>>5318867
Basically in an x-ray crystallography apparatus, you send the x-rays through crystal faces and then you get a diffraction pattern on the other side of the crystal. You take this signal and you reciprocates it sort of like a mirror using the Fourier transform into a readable graph. This is also used in wide arrays of spectroscopic methods, just like IR (hence Fourier Transform Infrared Spectroscopy)

>> No.5319382

>>5319344
Wait, nigga, what?

No. This can't be for every case.

Wait, seriously?

>> No.5319393

>>5319378
Because it is mind-blowingly magical O.O

>> No.5319405

>>5319378
It's a joke, because it's a relatively simple to understand equation that combines variables like Pi, e and i, that pop-sci faggots go crazy about.

>> No.5319412

>>5319382
I think he means if the sticks are thrown randomly, and if threw an infinite number of sticks.

>> No.5319743

>>5319412
Wich is actually impossible, so its not so fascinating, just obvious.

>> No.5319756

isn't it fascinating that the strongest metal on eath (diamond) is see through and lightweight??

>> No.5319764

>>5319756

Carbon is a nonmetal, try again.

>> No.5319767

>>5317263

Can someone explain what the triangles represent? Also the x, the p, and that underlined >. The h over the 2 as well.

>> No.5319779

>>5319764
who said anything about carbon??

>> No.5319781

>>5319767
>triangles

Well, I hope you are below the age of 16, otherwise this is just embarrassing.

>> No.5319785

>>5319779
Why do you go on /sci/? Please, go.

>> No.5319803

I'm still fascinated at the concepts grasped by mathematicians and scientists in the 1600s and 1700s with their extremely limited resources and little past knowledge.

>> No.5319808

>>5319781

I'm 22.

>> No.5319812

>>5319781
>>5319808
Its not about age.
Its error in spanish. (Im not good at english). The difference between the known valye and the real value.

>> No.5319854

>>5319382
Well if the lines are L distance apart and the sticks are L/2 long, theres a 1/pi chance that a stick will intersect a line.

http://www.youtube.com/watch?v=sJVivjuMfWA

And I know it's not the single most reputable source, but I made an excel program to do this and it's actually right.

>> No.5320034

>>5319803
this

>> No.5320629

>>5319767
Do you know statistics? And the statistical interpretation of the wave function? The triangle symbol is the greek letter delta (actually capital delta) which means <span class="math"> \sqrt{\langle x^2 \rangle}-\langle x \rangle^2[/spoiler] where <span class="math"> \langle f(x) \rangle[/spoiler] is <span class="math"> \int \psi^{*}(x)f(x)\psi(x)dx [\math][/spoiler]

>> No.5320638

>>5320629
epic fail at tex: <span class="math">\sqrt{ \langle x^2 \rangle - \langle x \rangle^2 } [/spoiler] and <span class="math"> \langle f(x) \rangle = \int \psi^*(x) f(x) \psi dx [/spoiler] and similarly for <span class="math"> g(p) [/spoiler] however we use the fourier transform of <span class="math">\psi(x), \tilde{psi}(p)[/spoiler] instead of <span class="math"> \psi (x) [/spoiler]

>> No.5320645

>>5319028
This

>> No.5320649 [DELETED] 

>>5320638
Furthermore <span class="math"> \Delta x = \sqrt{\langle x^2 \rangle - {\langle x \range}^2} [/spoiler] is the standard deviation of x! It's all connected baby!