What's the "fastest" way to learn Noether's theorem? What's the "best" way to learn Noether's theorem?

Tl;Dr do any of you guys know of any existing research concerning the measuring/imaging/mapping the electromagnetic field of living creatures?
I know this already sounds like some /x/ tier bullshit, but I'm just interested in the actual science of the matter.
Like, if I grab my radio antenna, in some physical arrangements I weaken the signal, and in other arrangements it seems to be the opposite.
I'm interested in studying this interaction to better understand theremins, and related technology.
I can't be the first person to consider this, but I'm not sure what keywords to search.

What are the safest and easiest to synthesize drugs that are similar to coke? I imagine being similar to, but safer than, many amphetamines would be fine too.

>>16235576
Not exactly what you're after, but if xanthines are acceptable, Chifir is a thing.

>>16235578
>xanthines
I'm not really sure what I'm after. I have a hard time focusing when I do coke, it just gets me super extraverted or something, it's not something I take to do 'deep work'. I've tried but it's not that kind of drug from what I've observed. But I've only done it a handful of times, usually drinking too. I'm just frequently fatigued but also wanting to do more intellectual stuff like learning piano and reviewing real analysis, or hobby programming. Lately I've just had a lot of fatigue and brain fog, and yeah I'm lifting/exercising, sleeping and eating well too.

I've bookmarked your suggestion, thanks. Why wouldn't they be acceptable though?

>>16235586
Well, it's a different sort of stimulant than the ones you mentioned.
Seems to be a thing where some people dig it and others don't.

>>16235350
why do some non-fat women have round heads/faces, just like fat women?

If I flip the coin N times and repeat the experiment 10000 times, then the resulting binomial distribution will look exactly like the normal distribution. Is it the consequence of CTL? But CTL is about sampling an existing distribution and calculating the means and we are not sampling anything, just tossing the coin.

>>16235494
There is no "fast" way. It requires a bunch of prerequisite knowledge, mainly: functionals, the calculus of variations, Lagrangian mechanics, and optionally Lie algebras. Each of those you can't really learn in isolation and require various other topics in math and physics you would have to study first.

>>16235690
For the central limit theorem you just need independent and identically distributed random variables. It's not specifically about sampling.

Is there a website with a fuckton of math problems? I feel my course literature don't fully let me put my knowledge into practice in some parts, for instance, identifying injective, surjective and bijective functions and proving them

>>16235754
OK but isn't it about the means of those variables being normally distributed? But when we are flipping the coin, we are not averaging anything, we are just counting the number of, say, tails, and still get the normal distribution.

>>16235639
>Genetics
>Medications
>Poor diet

>>16235987
There are apps for that.

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>>16235494
>What's the "best" way to learn Noether's theorem?
MOMENTUM MAP
O
M
E
N
T
U
M

M
A
P

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Any hope, any hope for a life after death at all, in any way or form, scientifically speaking? Been going through some tough times in life recently, where myself and those around me could be in danger of dying, and the anxiety and sadness has been eating me alive from the inside. I just want to know if theres any reason to believe beyond pure belief itself.

>>16236464
Scientifically speaking, absolutely no hope at all. The logical reductionist explanation is that everything is physics, all that can ever be is the interaction of particles. So, as such an afterlife is not possible. No law of reality allows for one. A belief in anything else is simply wishing thinking by the meat sacks we call our human mind and body.

>A ladder of mass m = 8kg and length l = 10m is leaning against a wall at the heigth of h = 8m from the ground. Find the ground and wall reaction forces.

Now, it is obvious that Fgy = mg = 78.48N. I know two ways to solve the rest but I get different results:

>the torque method
We'll take the point where the ladder touches the ground as the point of rotation.
Tw = Tm (torque caused by the wall is equal to the torque caused by the mass (weight))
Tw = Fw x h = Fw x 8m
Tm = 3m x mg = 3m x 78.48N = 235.44Nm (3 because we have a 3-4-5 triangle but scaled by 2, so the center of the weight of the ladder pulls toward the half of the leg of length 6)
Solving all of this we get that Tw = Fgx = 235.44Nm / 8m = 29.43N.

>the sine theorem method
We know that sin a = h/l = 0.8, so a = 53.13°. b = 90° - a = 36.87°. Now, we can construct a similar triangle with angles a and b but with legs of Fgx (opposite of b) and Fgy (opposite of a). Hypotenuse would be Fg then. Using sine theorem, we have that:
Fgx / sin b = Fgy / sin a = Fg.
Now, simply solving for Fgx, we get that Fgx = Fgy (sin b / sin a) = 78.48N x 0.75 = 58.86N.

So you see that using these two methods we get two different answers that are different by exactly the factor of 2. Where am I going wrong here and which is the correct answer?

>>16236380
If the mean number of tails (approximately) follows a normal distribution then so does the total number of tails, as the total number of tails is just 10,000 × the mean. A constant multiple of a normally distributed variable also follows a normal distribution.

>>16236464
There is a chance if you get into philosophy. Science just works with models, not reality as such, so you won't find what you essentially need there.

>>16236380
>>16236560
Sorry I slightly misread this >>16235690 post. I should have said the total number of tails is N × the mean.

>>16236556
I'll give you a hint. Without friction, the ladder will fall. Calculate the forces at any point. Then integrate over the displacement of the ladder in both dimensions. Compare with the total potential energy available at the start. This will tell you If your answer is correct.

>>16236597
Man, I don't know how to do any of that.

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Buying a new laptop, they're giving me a choice of chargers. Left or right.

While the form factor of right is comfier, I'm wondering if there are any benefits to the traditional type on the left? What are the benefits of 3-pin plugs/power supplies? Right clearly has a plastic ground pin. Is 3-pin better for safety or something? For the machine, or the human user, or both? I dunno much about electricity, but I know that all trends in the world are bad and so if they're moving away from 3-pin and pushing everyone to use ungrounded appliances, there must be an evil reason for it.
I just don't know what they are because I don't know science. Enlighten me, electrobros.
The laptop will have a metal body btw.

Can silver ions released into brine form silver chloride? According to the metal reactivity series, silver should not be able to displace sodium, but since they are all in an aqueous solution, and since silver chloride is insoluble, will the silver chloride form?

>>16237050
yes. it's pretty common to make it that way using silver nitrate as your cation source

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so i have long hair right, and i started wearing a headband like pic related. but theres a big fat vein on my forehead, so wtf happens if i use the headband?

What would negative energy look like?

>>16236383
thanks for your answer.
>>Medications
so it can be a chemical thing? what medications can do that? someone suggested elsewhere that cortisol can do it. is that true?

Why does water simply evaporate in normal room temperature conditions?
If I leave a glass of water out, all the water will be gone in a few days.
Even if I leave some food sitting out, it will get shriveled up and shrink and dried up as all the water someone escapes and goes somewhere. How can this happen if I'm not boiling it? And how does water exist outside if this is always happening in my room?

>>16236511
Physics makes no claims on the ontological basis of reality. That's just your ignorant impressionable midwit mind parroting popsci materialist midwit YouTuber/writer. Physics deals with how things move/behave, not what things are.

>>16236464
Death is not the end for you. You got born once, you will be born again. If you have no consciousness after death, then time will be instantaneous. It doesn't matter if 1 day passes or 10 quintillion years, you wouldn't perceive any of it. And then just like you popped into existence this time, you will do so again. The action of being born is clearly possible because it happened once so it will happen again given enough time. I don't personally believe that consciousness simply disappears on death, but rather expands. Brains are more of a filter/computational device and not the source of consciousness. Drugs that induce incredibly rich vivid states of mind usually decrease brain activity and metabolism while drugs that increase it result in states or blankness. Best of luck with your anxiety.

Is energy just a measure of entropy? >degrees of freedom of a system always decrease over time
And is time just a measure of entropy?

I have a divergent series of strictly positive reals [math]\sum_{n=1}^\infty a_n[/math]. Can I find a (necessarily infinite and co-infinite) subset [math]S[/math] of the natural numbers so that both sub-series [math]\sum_{n \in S} a_n , \sum_{n \notin S} a_n[/math] diverge?

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>>16236556
Is this so hard anons?

>>16237392
no but it's tedious and i don't wanna do some undergrads homework

>>16237401
Just explain where I'm going wrong.

>>16237371
Evaporation is a surprisingly complicated process. There are a lot of factor involved, for example: humidity, air flow, (vapour) pressure, and surface area.

> normal room temperature
> How can this happen if I'm not boiling it?
However to answer simply, temperature is the average kinetic energy of all the water molecules. In reality the thermodynamics of the system is a distribution, some molecules at the surface are moving faster than others and have enough energy to escape into the air.

>>16237372
> Brains are not the source of consciousness.
Take your meds schizo. >>>/x/

>>16237493
>moving particles cause only moving particles, and consciousness is obviously not moving particles
duh is it so hard to understand?

>>16237387
Not necessarily. For example, look at the depleted harmonic series (Kempner series).

>>16237387
Just realised I misinterpreted what you said when I made this >>16237559 post. Disregard.

As for your actual question; yes there is such a set.

Need some advice, MATH anons.

I'm planning to learn ML and I want get my math foundations right: Linear Algebra, Calculus, and Stats

I found the rentry ml roadmap that recommends the KA linear algebra, calculus, and stats sections. Is this comprehensive enough? I want to have a good foundation so I can understand what's behind the frameworks, not be some data janny.

I'm doing a CS degree and already took LA and Calc1&2 last year (but don't remember anything). I can alternatively do Strang's LA YouTube series and prof Leonard Calc 1-3.

What do you think is the best way to go? I want to have enough math down to read and understand research papers.

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>>16237387
Just force it.
Put [math]a_{n + 1}[/math] in S if [math]\displaystyle \sum_{k = 1}^n \chi_S (k) a_k < \sum_{k = 1}^n (1 - \chi_S (k)) a_k[/math] and do the opposite otherwise.

Figuring out what the chi means is left as an exercise to (You).

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>>16237784
Wondering now if you even need third removed to prove it like this.
Fucking intuitionists messing with my head.

Hey, since the number of ancestors goes up at 2^n, does that mean that 100 generations ago, just 2000 years if it's 20 years per generation, wouldn't you have over a nonillion (hopefully) different ancestors? Within just 2000 years? What am i radically misunderstanding?

How many generations would you have to go back until you have as many ancestors as the whole population size at the time?

Wouldn't it basically be all incest after that generation point?

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>>16237848
You're missing that not all of our ancestors are unique individuals. The same individual can appear multiple times in your family tree, and this becomes more likely the farther back in time you go.

>>16237857

Then see this:

>>16237855

I'm looking at the US population right now. And looking for when the 2^n equals the population. It's less than 20.

>>16237855
>Wouldn't it basically be all incest after that generation point?
No. There is a certain amount of consanguinity required for adaptive fitness.
https://en.wikipedia.org/wiki/Outbreeding_depression
Too much genetic variety can be just as harmful as too little.

>>16237861

Uhh, that just says we need it, not whether we have it.

Okay, here is what will probably answer the spirit of the question.

How many generations until it's over 50% incest?

Though that's not really a stupid question, that's a pretty good question.

Suppose we have a container with a gas under pressure p. It exerts a normal force F on the surfaces of the container such that F=p*S.
1) is there a specific term in english for that force F? I'm a bit confused because I've seen the word "pressure" used both for p and F, while in my language there is a clear distinction between those two and they have different names.
2) suppose the thermodynamic equilibrium of the system is disturbed. As I understand it, in such a case pressure p can't be defined until it reaches some state of equilibrium again. Is the normal force F acting on the surfaces of the container defined, even though pressure p is undefined?

>>16237943
The normal force is a vector, pressure is a scalar - the magnitude of the normal force.

>>16237955
>pressure is a scalar - the magnitude of the normal force
Wait, what? Those are different things tho.
So how do you call "p" in english in the F=p*S formula?

how is babby formed

>>16237982
I don't even know what that formula is.

>>16237982
Oh, wait, is S meant to be surface area?? Then p is the unit of pressure, typically a Pascal. So the total amount of pressure (F = P) is "the pressure per unit area" x "the total area".

>>16236556
bump

>>16236556
im pretty sure you have to consider only the portion of the torque that’s tangent to the point of rotation. for example, the wall pushes against the ladder with a force thats parallel to the ground, but the ladder is at an angle. you multiply the normal force by a couple factors of sin/cos of whatever and im pretty sure thats where the extra factor of 2 comes from.

>>16238871
>portion of the torque
portion of the normal force*

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>>16238871
>>16238873
I think that's what I'm already doing; here is the picture. You see my Fw is just the portion parallel to the ground (for some reason we usually ignore the component of the wall force pushing downward).

>>16238924
okay, just tell me am i dumb :/

>>16237986
i was legit watching frog spawn videos the other day, that shit is mind blowing
how to the cells just KNOW to put a leg, or an eyeball, or a spinal column there? how do you start with one cell and get billions??
https://www.youtube.com/watch?v=gmlaclb3K2o

>>16235722
I disagree. There is an order on this prerequisite knowledge and it's not as dense as you are portraying it. Functionals is not a topic on its own, it's just a definition. Calculus of variations can be studied in isolation very well, and will inevitably include Euler-Lagrange equations. This is enough of a basis to learn Noether's theorem.
Lie algebras can be studied on their own as well, though they are usually covered in the context of representation theory. You usually do that much later though and then revisit Lagrangian mechanics from a more abstract point of view.

>>16237372
>Physics makes no claims on the ontological basis of reality.
Interpretations of QM are still physics. And they are anti materialist.

>>16239167
> And they are anti materialist.
What makes you think that? They are still material interactions and follow the rules of QM.

>>16239216
Consciousness is inherently different from the material world. We haven't even identified the interaction mechanism yet.

>>16239236
> Consciousness is inherently different from the material world.
And where is the scientific proof for that? It's kind of idiotic to say just because you don't understand something we have to resort to magic.

>>16239246
And where is your scientific proof that you need a scientific proof?

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>>16239257
Why are you even on /sci/ if you don't believe in science? Or are you just here to shitpost?

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>>16239236
>interaction mechanism
If it exists, it can be reduced to a Markov model, and if it can be reduced to a Markov model it might as well be matter.
This is the issue with things like Cartesian Dualism, you end up just inventing new forms of matter that still function as gears in a clock. You don't escape materialism, you just dislocate it.
>>16239257
Kek.

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Dumb question
Why isn't the length OC here just 2?
If O is the midpoint, isn't any line to the edge just 2?

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>>16239719
>If O is the midpoint, isn't any line to the edge just 2?
You're thinking of circles. Probably. I don't know.
This is a square.

>>16239724
Now I see my mistake. I don't know why I thought this was the case for squares too.
How silly. I feel silly.

Is my intuition wrong? If a 100kg object falls from a height of 1 meter, I reckon much more force is generated than simply 2*(the 100kg object falling from 0.5m).

Concretely, I am interested if the object does more damage to some impacted surface if it's being dropped from that height of 1m, than being dropped twice from half the height.


I ask because I want to guesstimate the damage my body's joints would incur if I fall (jump) from twice a height onto some hard surface. I am trying to justify my logic that it DOES make a difference if I include an inbetween step.

Can we express complex numbers in radians or degrees of an angle with x coordinate line as its ray

>>16240749
https://en.wikipedia.org/wiki/Complex_number?useskin=vector#Polar_form
>>16240520
Yes, I can think of several effects that cause a single fall from twice the height to be more damaging than 2 falls.
First, the kinetic energy of the body at impact is [math]E = mgh = \frac{1}{2}mv^2 [/math] (neglecting air friction). This scales linearly with starting height. During the impact this is converted into a force [math]F = E/\Delta t [/math] where [math]\Delta t [/math] is the duration of the impact. This duration scales inversely with the fall velocity, so overall the impact force will scale as [math]F \propto h^{3/2} [/math].
Second, irrespective of the magnitude of the force, materials are more brittle at shorter timescales, because the molecules have less time to rearrange themselves.
Third, materials generally have a nonlinear stress response (https://en.wikipedia.org/wiki/Stress%E2%80%93strain_curve?useskin=vector): there is a certain point at which they go from deformation to catastrophic failure.
Finally, damage is not cumulative between falls: the body is elastic and between weak impacts it can relax into a strain-free configuration again.

>>16236464
Be careful what you wish for, pal.
You may desire life after death because you implicitely assume it's going to be similar to what you know (that you'll meet the same people, be human etc.), but this doesn't have to be the case.

Is there are any consumer (everyday life) technology that would specifically require any other sets of numbers other than of natural numbers and some positive fractions?

>>16240813
>infinite life in a void of space after the heat death of the universe
fun!

Do changes in atmospheric pressure have any effects on plants?
I'm not talking about precipitation and temperature changes - they obviously have influence and are more or less caused by changes in pressure - but strictly about direct effects of pressure changes. From what I understand they may have influence on humans (I may be wrong, but aren't migraines caused by them?), but what about plants?

>>16235350
Is a NiZn ferrite simply a macroscopic composition of Nickel ferrite (NiFeO) and Zinc ferrite (ZnFeO)?

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This is the trajectory of a bouncing ball. The bounces are a "perfect" shape in the sense that the peak of each one is exactly half-way between the bounce points, right? So like, the peak of h1 is exactly half the distance between t0 and t1.

What I want to know about is a situation where there's some sort of bouncing mechanism on the surface, like a trampoline, such that each bounce is exactly the same height.

In that case, the peak of each bounce would NOT be half the distance between the bounce points, but closer to the first point than the second one, right? Is there a formula for this or anything? Basically I need to know the "perfect shape" of a "perfect bounce" (i.e. one that doesn't diminish in height on each consecutive bounce).

I don't know shit about science so I hope this didn't come out TOO retarded

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>>16238924
sorry, looks like your torque method is right. something must be up with the other method.

>>16241845
https://en.wikipedia.org/wiki/Coefficient_of_restitution

Did the Dinosaur Extinction have anything to do with the Ice Age coming? I'm trying to think of plausible ways to make an Ice Age happen sooner because I hate this heat.

>>16241932
Yeah this is way over my head ... I just want to know about a situation where the bounces are the same height

>>16241964
No. There was a more than 60m year gap between the two.

>>16241976
in the real world, on macroscopic scales, balls cant bounce at the same height because the ball loses energy to non-conservative forces on each bounce, e.g. friction. a trampoline will not fix this. if you just want to know the shape of the bounce, its the same shape regardless other whether or not it bounces as high: a parabola.

>>16241928
is this your handwriting? looks really nice.

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>>16242100
no its not, its pretty sloppy or me. here's some old statics homework from college.
i wrote down the first chapter of lolita and posted it on here one time, not sure where it is, maybe remi has it saved.

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>>16242114
found it
https://warosu.org/sci/thread/12332227#p12335360

>>16242119
>if the field in a parallel plate capacitor flows from plate A to plate B, then the voltage from A to B is negative
what the fuck was i smoking

>>16235722
>functionals, the calculus of variations, Lagrangian mechanics, and optionally Lie algebras.
What do I need to know about funcionals?
I feel confident I can teach myself the basics of calculus of variations and lagrangian mechanics. Lie algebra would take more work, I think.

>>16235350
lol

>>16239164
I will study Gelfand's Calculus of Variations.

>>16242081
Yes I know that, I should have I meant more like a trampoline with a human jumping on it, such they consciously make the bounce a stronger than a "natural" bounce so they can get the same height each time

Would that really be the same shape? I would have thought if the bounces are the same height each time then the force going upward would have to be a bit stronger

>>16242081
>>16242434
Nvm I think I've grasped why it would be the same shape

>>16242436
You know nothing of shape. You're a leftist weak and confused troll who just mirs words and has no grasp of his mind.

>>16242438
Grasp this dick faggot

>Let [math]G[/math] be a finite group, [math]N\trianglelefteq G[/math] and [math]H<G[/math]. Suppose that [math]\gcd((G:N),\rvert H\rvert) = 1[/math]. Prove that [math]H\subseteq N[/math].
Any help is appreciated

>>16241439
Any botanist ITT?

>>16242454
[eqn] (G:N) |H \cap N| = (G:HN) |H|
[/eqn]
Since [math](G:N)[/math] and [math]|H|[/math] are coprime you must have that [math]|H|[/math] divides [math]|H \cap N| [/math] which implies [math]|H \cap N| = |H|[/math] so [math]H \subseteq N[/math].

>>16242608
This first equality follows from what?

>>16242614
Lagrange's theorem and second isomorphism theorem

By Lagrange's theorem:
(G:N) = (G:HN) (HN:N)
By the second isomorphism theorem:
(HN:N) = (H:H \cap N) = |H|/|H \cap N|

>>16242620
Got it. Thank you anon

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>>16242114
>maybe remi has it saved.
Actually don't even remember that happening.
>>16242119
Man I wrote weird back then.

>>16242114
>no its not
*not nice, that is. it is in fact my handwriting.

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Where should I look if I just want to do ~30 minutes of basic-intermediate maths per day to activate my neurons?

Something like this must exist in some form, right? I know there are millions of brain training games out there, I figure there must be one that leans heavier into maths, or even if it's not a game but just a web page

We cannot draw bijection of the infinite set elements to its power set elements. Is this conclusion correct according to the Cantor's theorem?

>>16243109
Yes

How do I go about calculating stuff like this, or what specific thing should I go and study?
>Every time X doesn't happen, its chance increases by Y (bonus resets after it succeeds)
>How many attempts does it take in average for X to happen Z times

>>16243260
Also what's the best programming software/language for shit like this?

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Does water temperature affect fire in any way? If I throw boiling water at a fire, will it make no difference whatsoever compared to cold water, or is there a measurable difference, no matter how tiny?

How do I learn to build machines/electronics? Or at least design things. I don’t want to go back to school.

>>16243360
Fire requires three things: oxygen, heat, and fuel. So water does two things to put out a fire, it reduces the amount of oxygen the fuel can burn and it's main role is to reduces the amount of heat. So yes, hotter water would impair that last effect but I doubt to a noticeable amount. The fire would be many hundreds of degrees C, maybe even more than a thousand, so a few tens of C difference between luke-warm water and boiling isn't going to be much of a factor overall.

Can we say that "the product of negative numbers is positive" is decided by the convention rather than by firm logical proof. If we thought that product of negative numbers is negative, would it contradict the concept of complex numbers and quaternions?

>>16243081
khanacademy
>>16243260
>>16243281
simulate in Python or R
>>16243727
>if we thought that product of negative numbers is negative
this would break division and the distributive property
-1 * -1 = -1, -1 * 1 = -1, now -1 / -1 can be either 1 or -1, division is no longer unique
-1 * (2 + -1) = -1 * 1 = -1, but -1 * 2 + -1 * -1 = -2 + -1 = -3, distributive property fails
negative times negative giving positive follows logically out of the distributive property and the addition rules for negative numbers

>>16243260
>How many attempts does it take in average for X to happen Z times
Since the chance of X resets each time it happens, this will be Z * "the expected number of attemps for X to happen once".
>Every time X doesn't happen, its chance increases by Y (bonus resets after it succeeds)
I'm assuming you know precisely what changes?
In this generality there's very little to say.
How do I go about calculating stuff like this, or what specific thing should I go and study?
This is called elementary probability theory, and as >>16243873 says it's probably easiest to just simulate what happens.

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Can someone help me with this? I think a,e are correct but don't know if they are and if the others are correct too.

>>16244194
your intuition is correct
think about:
>can any function be a pdf? what about a cdf? what are the restrictions?
>what shape is the graph of an exponential, binomial, normal pdf? cdf? what is the support (allowable x values)?

>>16244194
>>16244214
I don't think it's a pdf because the scale is wrong (doesn't sum/integrate to 1).

I don't exactly get why the Maclaurin series for e^x stands for all x in R. I get how it is derived and it does work for all x, but I'm trouble understanding it intuitively, since isn't the taylor polynomial at a point very accurate to the describable function at some surrounding of that point, but not for all x?

>>16244194
a) obviously yes. considering the definition of a PDF, that graph basically *is* one. pointing out that it doesnt sum to 1 is a bit nit-picky i think.
b) obviously no, considering the definition of a CDF (or simply the intuition the CDFs cant go down).
c) no, exponential distributions dont look like that.
d) this one is tricky. binomial distributions can definitely have that shape, but the problem is that some of the values of X are negative, and if you use the regular definition of a binomial distribution, you cant have negative values. you could always just do a change of variables to slide the whole thing over, but negative values in binomial distributions in the real world dont make a lot of sense (binomial distributions are usually used to calculate the expected number of successes given n trials, and you cant have a negative number of successes). im leaning towards no, but you could argue either way.
e) yep, right shape.

>>16235350
Wtf does Landau-Lifschitz equation describe? Does it describe how the domain wall motion rotates the magnetic moments in the shrinking Weiss domain to the direction of the magnetic moments of the growing domain or does it describe how in paramagnetic and ferromagnetic materials the spins align with the external field?

t. EEfag in need for help from physicists

>>16244230
True, you'd need to normalize it but informally I'd still say it approximates the pdf.
>>16244273
The radius of convergence can be found by using the ratio test on the series coefficients. An alternative way that might be more intuitive is to consider it as a complex function: the radius of convergence at a point in the complex plane is equal to the distance to the closest singularity. e^z has no singularities so it converges everywhere.
>>16244371
Not an expert but I think it can be either, it describes the time-dependent spin dynamics in the continuous limit (magnetization and H-field as continuous fields) as opposed to the lattice-based Ising model and Heisenberg model. This can include an external field but doesn't have to, and includes solutions with domain walls including moving domain walls, but doesn't have to. It would be quite pointless to use it to
>how in paramagnetic and ferromagnetic materials the spins align with the external field
unless you cared how the spins respond in time to the field being turned on. Fundamentally it's just an equation of motion for magnetization with a Larmor precession term and a damping term, like the Bloch equations for nuclear magnetization.

>>16243873
>khanacademy
Do they have general maths questions at random at a certain level or do you always have to go into specific topics?

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Baby maths, can someone explain to me in absolute basic terms why this works in determining the number of pupils with both. I get the method but can't seem to get the reasoning and it's bothering me.
why does adding the tally of both then minusing the number who have either give you how many students have both?

>>16244626
cat + dog = the maximum number of pupils that could own a pet if they had only one each.

but the first number calculated is the actual number of pupils with a pet, and it is less than that value. so there was be an overlap (venn diagram) where one of more pupils has both.

subtracting the two totals then tells you how many pupils have both.

>>16244626
okay so the question is how many dog owners have cats, out of all dog owners
so that's (dog owners with cats) / ( (dog owners with cats) + (dog owners without cats) )
we know that 125 = 23 non pet owners + X pet owners
so X is 102 pet owners and we can ignore the 125 and the 23 non-pet-owners

we know that (dog owners without cats) + (dog owners with cats) = 68
and (cat owners without dogs) + (cat owners with dogs) = 61

let's say dogs-only is A, dogs and cats is B for BOTH, and cats-only is C for CATS
A+B=68 students with dogs or both
B+C=61 students with both or cats
A+B+C=102 students with dogs or both or cats

102 - (A+B) = C
102 - 68 = C = 34
C = 34

102 - (B+C) = A
102 - 61 = A = 41
A = 41

A+B+C=102
41+B+34=102
B=27 where B means BOTH

so given that a pupil has a dog (sample size 68) what percent has a cat (so both a dog and a cat)
B=27
so out of 68 dog owners 27 own both a dog and a cat so the answer is 27/68

>>16244626
125 people total
23 have neither cat or dog
Therefore 125-23=102 people have a cat or a dog or both
Of those 102 people, 61 have a cat, so 102-61=41 do not have a cat.
Therefore, 41 have a dog and no cat.
68 have a dog, so 68-41=27 have a dog and a cat.

>>16242009
Prove it.

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>>16244683

If you have 360*N or 360/N, and the N is a positive integer, you get a number. Call that X. When you represent X in the decimal form and you sum up the digits, the sum is divisible by nine. How do you prove that this is the case for all N?

>>16244693
>look mom I posted a picture of a graphic some random person made on a 4chan thread! this proves it!

>>16244695
Oops I made a mistake. X needed to be 360*2^N or 360/(2^N). Obviously the sum of the digits would be infinite for 360/7 for example, that's not what I was talking about lol.

>>16244695
>360*N
This works only in base 10, not all bases, I believe. 360*N is necessarily an integer divisible by 9 because 360 is divisible by 9. Any integer divisible by 9 has digits that sum to something divisible by 9; this is a property of 9 being the highest single-digit integer in base 10.
So you could simply say 9*N instead of 360*N.
>360/N
But it doesn't hold true. N=9, for example. 360/9=40. 4+0=4. 4 is not divisible by 9.

As for a proof that the digits of 9N will always sum to something divisible by 9? Not sure, but it does hold true.
Also, the digits of 3N will always sum to something divisible by 3.

>>16244706
360*2^N: 2^N is an integer and 360 is 9*40 and 9 times any integer will have the property you describe
360/2^N: I believe this, again, applies to 9 or any multiple of 9, not just 360.
Another way of looking at 9/2^N is taking 9 then dividing it by 2, N times. I.e. 9/2^4 is 9/2/2/2/2. Another way to write this is 9*.5*.5*.5*.5. Furthermore, we could write it as 9*5*.1*5*.1*5*.1*5*.1. Or, 9*5^4*.1^4. Or in the more general sense (not using the N=4 example), 9/2^N=9*5^N*.1^N. We already know that 9*5^N will have digits that sum to a multiple of 9, since 9 times any integer will have digits summing to 9. And then the .1^N factor is trivial since it will just be of the form .000...0001. And multiplying something like that won't change any of the digits, it will only change the position of the decimal.
So your questions ultimately can be simplified to: "Why is it that 9N will always have digits that sum to a multiple of 9?" And again thats a property of us working in base ten and 9 being the highest single digit integer, but I dont have a proof beyond that

>>16244710
Yeah because I made a mistake and I explained it on an earlier post. The right formula was 360*2^N and 360/(2^N).

For example, 360/(2^21) = 0.000171661376953125

and 0+0+0+0+1+7+1+6+6+1+3+7+6+9+5+3+1+2+5 = 63

and 63 = 9*7

>>16244703
What would even count as proof for you? A time machine?

>>16244728
>since 9 times any integer will have digits summing to 9
*summing to a multiple of 9
(though they would sum to 9 itself if you keep summing them recursively til you have only a one digit number)

>>16244732
no because time travel doesn't real
what would count as proof is meeting some ayy lmaos who were there and videotaped it

>>16244735
> no because time travel doesn't real
prove it

>>16244729
360/(2^21)=9*40*(5^21)*(.1^21)
40*5^21 is an integer so 9*40*5^21 has digits that sum to 9
multiplying by .1^21 doesnt change those digits
So to answer the root question of "why does taking 9, and multiplying it by an integer, result in a number whose digits sum to a factor of 9?"
A quick web search turns up:
https://math.stackexchange.com/questions/1221698/why-is-the-sum-of-the-digits-in-a-multiple-of-9-also-a-multiple-of-9
https://math.stackexchange.com/questions/207122/why-is-everything-multiplied-by-nine-when-the-digits-are-added-the-result-is-a-m

>>16244736
'travel' is a process
a process is by definition a change that takes place during a positive change in time (a change that takes place over a negative change in time would be a reverse process)
To travel back in time is for a process (travel) (positive change in time) to occur during a negative change in time ('back in time')
Therefore, to 'go back in time' is for time to simultaneously progress and regress
That is to say 1=-1
But 1=-1 is not true
Therefore time travel doesn't real

>>16244749
Thanks for the answer ChatGPT.

>>16244753
That's not chatgpt dumbfucktard

Does anyone use Jupyter notebook with Python/sympy/etc ? I also realized that sympy makes it is so much easier to produce latex code instead of typing raw Latex. Just type an equation and then convert_to_latex. Done!

I love opening up that catalog and being greeted by Dr. Danielle Twum's smiling face

I found that skin exhibits a bi-linear elasticity because of collagen and elastin.
Elastin takes much of the load in the beginning, then at one point, the strain begins to affect collagen fibers who get orientate in the direction of the stress, up to a point where they are mostly parallel to each other.
Now, the skin is under tension all the time because of something called Langer's lines and once you cut the skin of and look at it ex-vivo, skin will retract and lose the form it had under its natural applied stress.
From what I understand, that would be something you find in viscoelastic materials.
Then, when you take an ex-vivo skin sample and apply stress repetitively in the same direction you will notice residual strain adding up, up to a certain point, likely because the collagen network have rearrange to accommodate this deformation.
Now, also from what I understand that more of a viscoplastic characteristic.
So would the skin behave more like a viscoplastic or like a viscoelastic material?

>>16244652
I get that bit, but I struggle with why subtracting the two total tells you how many have both

>>16244679
>>16244667
Oh, thanks, breaking it down like this makes a lot of sense, I appreciate it.
Both your methods to work out the total number of pupils with both a cat and a dog make more sense to me, but they use a different method and it's not presented as something that should take much time to figure out. I don't know why but I still struggle with it. It just doesn't seem to flow in my head to where I feel I'd recognise this pattern quickly again. If I broke it down this way it does flow a lot better but it feels like i should be more instantaneous to me, especially to understand the bit highlighted in the pic.

test
[math] \frac{\sqrt{2} \sqrt{\pi} \left(x \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)} + \frac{\sqrt{2} e^{- \frac{x^{2}}{2}}}{\sqrt{\pi}}\right)}{2}
[/math]

>>16245009
I tried for about a week before I realized Python was broken garbage and whitespace languages are shit-tier
Not only do you have to install some new whatever notebook, but also create new workspaces for every project so they don't brick your install? Stop using shitty languages

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>>16245952
what an interesting coincidence. i just posted a test from notebook seconds ago: >>16245945
what languages are not shitty?
for example, if i am trying to solve an integral, and i need help, i could type it in Jupyter note book, make sure the set up it is correct, then solve it, and the convert the solution to latex and post it here. brilliant. imagine the pain having to type
\frac{\sqrt{2} \sqrt{\pi} \left(x \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)} + \frac{\sqrt{2} e^{- \frac{x^{2}}{2}}}{\sqrt{\pi}}\right)}{2}

wtf is a "whitespace language" anyway?

Or for example imagine I was trying to understand how to solve this equation[math] \frac{t + x}{\sqrt{y + 1}} = y [/math].
And I didn't realize it was a cubic equation so I could just type into Python and get this result that I could post here
and ask a question about it.

[math] \left[ - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 t^{2}}{2} - 27 t x - \frac{27 x^{2}}{2} + \frac{\sqrt{\left(- 27 t^{2} - 54 t x - 27 x^{2} + 2\right)^{2} - 4}}{2} + 1}}{3} - \frac{1}{3} - \frac{1}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 t^{2}}{2} - 27 t x - \frac{27 x^{2}}{2} + \frac{\sqrt{\left(- 27 t^{2} - 54 t x - 27 x^{2} + 2\right)^{2} - 4}}{2} + 1}}, \ - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 t^{2}}{2} - 27 t x - \frac{27 x^{2}}{2} + \frac{\sqrt{\left(- 27 t^{2} - 54 t x - 27 x^{2} + 2\right)^{2} - 4}}{2} + 1}}{3} - \frac{1}{3} - \frac{1}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 t^{2}}{2} - 27 t x - \frac{27 x^{2}}{2} + \frac{\sqrt{\left(- 27 t^{2} - 54 t x - 27 x^{2} + 2\right)^{2} - 4}}{2} + 1}}, \ - \frac{\sqrt[3]{- \frac{27 t^{2}}{2} - 27 t x - \frac{27 x^{2}}{2} + \frac{\sqrt{\left(- 27 t^{2} - 54 t x - 27 x^{2} + 2\right)^{2} - 4}}{2} + 1}}{3} - \frac{1}{3} - \frac{1}{3 \sqrt[3]{- \frac{27 t^{2}}{2} - 27 t x - \frac{27 x^{2}}{2} + \frac{\sqrt{\left(- 27 t^{2} - 54 t x - 27 x^{2} + 2\right)^{2} - 4}}{2} + 1}}\right]
[/math]

>>16246011
Otherwise I'd have to type by hand:

\left[ - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 t^{2}}{2} - 27 t x - \frac{27 x^{2}}{2} + \frac{\sqrt{\left(- 27 t^{2} - 54 t x - 27 x^{2} + 2\right)^{2} - 4}}{2} + 1}}{3} - \frac{1}{3} - \frac{1}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 t^{2}}{2} - 27 t x - \frac{27 x^{2}}{2} + \frac{\sqrt{\left(- 27 t^{2} - 54 t x - 27 x^{2} + 2\right)^{2} - 4}}{2} + 1}}, \ - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 t^{2}}{2} - 27 t x - \frac{27 x^{2}}{2} + \frac{\sqrt{\left(- 27 t^{2} - 54 t x - 27 x^{2} + 2\right)^{2} - 4}}{2} + 1}}{3} - \frac{1}{3} - \frac{1}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 t^{2}}{2} - 27 t x - \frac{27 x^{2}}{2} + \frac{\sqrt{\left(- 27 t^{2} - 54 t x - 27 x^{2} + 2\right)^{2} - 4}}{2} + 1}}, \ - \frac{\sqrt[3]{- \frac{27 t^{2}}{2} - 27 t x - \frac{27 x^{2}}{2} + \frac{\sqrt{\left(- 27 t^{2} - 54 t x - 27 x^{2} + 2\right)^{2} - 4}}{2} + 1}}{3} - \frac{1}{3} - \frac{1}{3 \sqrt[3]{- \frac{27 t^{2}}{2} - 27 t x - \frac{27 x^{2}}{2} + \frac{\sqrt{\left(- 27 t^{2} - 54 t x - 27 x^{2} + 2\right)^{2} - 4}}{2} + 1}}\right]

fucking hell.
What other math package can help you with this? None but not Python + Sympy + Jupyter.

>>16245963
nta
>wtf is a "whitespace language" anyway?
its a language where white-space (spaces, tabs, newlines) are syntactically significant. try not indenting the lines after a function declaration or an if statement in python and it'll complain. basically, python replaces the brackets of something like C with newlines and indents. i dont think its a big deal, if you dont either then its not a problem. the fact that youre asking makes me think you didnt even notice it anyway.

>>16246243
yeah i am well aware of that, i just didn't think of it as a "whitespace language" but i did find it a bit i annoying compared to most other languages that use curly brackets. i agree it is not a huge deal especially if you use a proper IDE that does proper indentation for you in case you forget. vs code has an extension for that i think.

The mean score for a test is 45.7. Highest somone scored is 50, lowest is 40. The test is out 50 points. There are only 6 students in class. What are the test scores for each of the students?

>>16246452
Oh and each question was worth 2 points each so 25 questions in total

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>>16246452
>>16246455
theres no solutions. an integer (the sum of all scores) divided by 6 (the number of students) will never result in a terminating decimal of 7.

>>16246499
Unless someone rounded 45.6... up to 45.7 like a sociopath.
in that case the total of the scores is 274

>>16246518
even then the solutions arent unique
(46, 46, 46, 46) is one
(44, 46, 46, 48) is another
etc.

>>16246518
Of course that's what they've done. All you can say about the other 4 students is they have an average score of 46. There's not enough information to say how their scores are distributed.

If shorter wavelengths are more heavily scattered by air, does that mean, in practical terms, that UV lighting would be more greatly attenuated by distance to a measurable degree, say, in 0.5m to 2m from the source?

>>16246556
Yes though note that a large part of the UV spectrum is actually absorbed by the atmosphere rather than undergoing scattering.

>>16244325
great answer >>16244194

>>16246575
Let's say hypothetically you're some gay photographer using a UV lamp setup to take pictures of the patterns on flowers in the UV, and you are finding it difficult to light the flowers adequately unless the lamps are so close that they are almost in the way of the shot. You think back to using normal flashes for visible light photography, and feel surprises the light attenuates so dramatically, still considering the inverse square law. Would scattering be the likely explanation in the situation of this haplessly mathematically illiterate faggot?

>>16246583
In this scenario you would be dealing with light at 365nm.

>>16245841
>If I broke it down this way it does flow a lot better but it feels like i should be more instantaneous to me, especially to understand the bit highlighted in the pic.
People with cat 61 people with dog 68
people with cat and/or dog 102
The sum of (people with cat)+(people with dog) will differ from (people with cat and/or dog) by the amount of overlap there is between (people with cat) and (people with dog)
That is, the group of 68 and the group of 61 have to have exactly the amount of overlap that the total of the groups together is 102
So when you add 68 and 61, you're including the overlapped group of people twice, so you have to remove that overlap to arrive at 102
so 68+61-x=102
x=27

>>16246877
careful, i got b& for saying the nigger word on here the other day. mods are such jerks >w<

>>16246583
> still considering the inverse square law
Rayleigh scattering actually scales to the fourth power of the wavelength, so shorter wavelengths after affected vastly more than longer ones.

>>16246583
>>16246556
>>16246584
So purely due to geometry, the flux of light falls off with the inverse square law.
When considering only scattering/absorption light falls off exponentially (exp(-l*sigma*N)=exp(-tau)).
Here l is the path length through the atmosphere, N is the number denisty of particles and sigma is the cross-section. Whether or not the scattering/absorption is a dominant effect depends on what regime of the exponential you are in. If tau<<1, then the amount of light lost is small and basically linear with distance. When you have tau>1 most of the light is lost by scattering. Tau is the optical depth, the number of mean free paths between the source and observer.
I cannot find exact numbers, but given that light at that wavelength (365nm) makes it to the ground from space (from the Sun and other sources) we cannot be in exponential part. The mean free path must be many kilometers, not meters. So the photographer wouldn't notice any difference.

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>have chem degree
>PhD in physchem
>still only ever took chemistry-oriented quantum courses
Now I need to do a lot of electron spin resonance data analysis. Textbooks look like alien language to me. What quantum courses do I need to take to deeply understand topics relevant to electron spin resonance research?
Is there any point of me doing the intro qmech courses for physicists at this point, or should I just read a textbook? I don't get credit for taking courses anymore

>>16247896
>research?
why the fuck are you doing research in something you've never studied lmao

>>16247896
name of textbook you're struggling with?
read a qmech textbook for physicists (it's pretty shocking to me that a chemistry degree doesn't include a dedicated qmech course but what do I know)

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>>16235350
what the FUCK are eigenvectors and eigenvalues i CANNOT grasp these concepts at all. could somebody please link a moron-friendly explanation?

>>16248156
what have you tried?
do you understand / can visualize shearing?
there are like a million links on how to visualize eigenvectors. try 3Blue1Brown videos

>>16248223
i was reading the linear algebra textbook by serge lang and didn't understand the eigenvalue explanation. i looked up a couple explanations on the math stackexchange site but i still didn't get it.

3blue1brown's videos look great, will look for any linear algebra videos he's done. thanks a lot anon.

>>16247205
Thank you, this is very detailed. I guess there might be something wrong with my lights. Perhaps they are not adequately cooled and they have degraded in output over time.

>>16246583
you sure it's the right band of UV? A, B, and C all behave very differently

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>>16248077
chemists do a lot of this type of shit. We make the systems and perform measurements and model the data. You don't have to have a deep understanding of all the background in order to do applied research in the subject. But it would be nice. That's why I'm asking about it.
>>16248125
So, I'm mainly trying to get through
>Principles of Pulse Electron Paramagnetic Resonance by Schweiger and Jeschke
>EPR Spectroscopy Fundamentals and Methods by Goldfarb and Stoll
and some classic quantum chemistry shit like
>Modern Quantum Chemistry by Szabo and Ostlund
>(it's pretty shocking to me that a chemistry degree doesn't include a dedicated qmech course but what do I know
My degree had two. But they are quantum chemistry, not quantum mechanics. The subject matter is a little bit different, but I think our courses might be a bit easier. It's not that I don't understand these books at all. I just want to obtain a deeper understanding.

>>16246011
Skeptical at best . . .

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>>16235350
Okay, I managed to get this optimization down to one equation that
is a reasonable compromise between given variables and direct
access to a solution. This equation is:

[eqn] \left(\sin(\alpha) + {h\over2vt} \right)^2={1\over 2}+\left({h\over2vt} \right)^2 [/eqn].

It has height and (nonzero) velocity accounted for, but there's a "t"
in there that represents the time of travel of the ball from start
to the furthest distance possible where it lands. Gravity is also
assumed from "t", and I have the complicated expression that
optimizes this "t" if you wish to see it.

The range for [math] \sin(\alpha) [/math] and the angle is contained
in the first quadrant only, so use the positive square root. Then, you
will have the critical angle needed for the ball to travel the furthest.
If alpha breaks outside the first quadrant, adjust v, h or t as needed.

[math]e^{iπ}=i^2[/math]

Is this expression legit?

>>16249438
Yes, it's just another way to write Euler's identity.

>>16249417
I am having a hard time wrapping my head around where this 1/2 comes from. Is this just some sort of horrid averaging technique on sin(a)? At the same time, angle significantly impacts distance traveled. Basically, this looks nothing like a trajectory solution.

>>16249417
You haven't a question for us to answer, also what you wrote just looks flat out wrong.

Go watch: https://www.youtube.com/watch?v=M8xCj2VPHas

>>16249544
>>16249417
The 1/2 came out from completing the square on an intermediate solution I had,
[math] vt-2vt\sin^2(\alpha)-2h\sin(\alpha)=0 [/math]. When height and velocity are
kept constant, alpha does change the distance traveled by the object's horizontal
component, that is [math] d(\alpha)=vt\cos(\alpha) [/math]. The main part of the
problem is to have the maximal distance traveled by some specific alpha [math] d(\alpha') [/math].

I used some calculus to find out that this maximal distance at alpha prime is
[math] d(\alpha')=h\tan(2 \alpha') [/math] and used some trig identities to get
my solution to a manageable form.

>>16249560
>>16249417
The question came from here >>16245907 . It was a take on the projectile
problem where I attempt to find the maximal distance possible for some
height and velocity.

>>16249738
By maximal distance, I mean max horizontal range.

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>>16236511
epic cap thanks

I'm a brainlet and I want to teach myself math starting from trig up. Is there a general curriculum that people learning math should follow, or a starting point?

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Should I just kms if I can't understand the concept of negative numbers (and the set of integers) in any way other than considering them as complex numbers? -a is (i^2)*a, so it is rotating the section [0;a] by 180°. I can't accept the explanation of debt, because it has very narrow application. But with complex numbers I understand it just fine. And the negative times negative equals positive can be done much easier (i^2*i^2=i^4=1).

>>16236464
I wouldn’t know why it would bring you happiness to know if anything happens after you stop living. As if whether or not it’s true, will ever effect your life?

But if it’s hoping for a future with your dead loved ones: instead of hoping that they somehow made it to a better place after dying, you should try to make the World into a place which they would’ve wanted to live in.

>>16250447
Cancel the rope order, you're alright. Although your concept of
negative numbers involves what others might think of as advanced
notions (or may care to understand it), it is a valid idea since
complex numbers are an extension of real numbers anyway.

Perhaps you can think of negative numbers as an extension of
whole numbers, especially when it comes to addressing
solutions of certain equations (ex. 3 - 4 = x). Or maybe, in an
abstract algebra direction, the idea of subtraction being
an anticommutative operation which justifies their existence
[that is, a - b = - (b - a)].

>>16248644
If you've done orbital theory then a QM book like Sakurai shouldn't be that hard, you should only need to learn spins and fine structure for now I think, no quantized EM fields or density matrices or whatever
QM is conceptually weird, it's normal that it doesn't make intuitive sense the first time.
>>16250447
This is fine but you should also be able to understand notions like additive inverse or negative numbers as vectors with a direction. Equivalents to negative numbers also exist in other mathematical structures like groups that don't have natural extensions to complex numbers or easy geometric interpretations.
>>16250020
https://4chan-science.fandom.com/wiki/Mathematics#Precalculus khanacademy is your friend

is the computing cost per prompt for a big LLM like chatGPT only dependent on token count and exec time, or is there something more, like the content of the prompt?

>>16251085
I'm not sure it makes any noticeable difference since it's just feeding tokens to the model. >99.99..% of the compute cost is building the model in the first place.

>>16251093
>99.99..% of the compute cost is building the model in the first place.
ofc I'm aware, I meant apart from this, obviously.
I have the theory that prompts of free users are answered more generally and less precise, but longer, in order to make the answer longer to parse and delay additional prompts. A friend argued, that token count relates directly to computational cost, therefore openAI has no advantage of making answers longer.
I disagree because I think that the complexity of the prompt also plays a role.

Funnily enough chatGPT suggested that different attention weight distributions might have different computation costs. This seems plausible and exactly what I thought was additionally happening
I want to confirm this with other humans now

>>16250720
>Sakurai
okay I'll check it out. I'm gonna try to go on a long hike after I defend, so maybe I'll put it on an e-reader and bring it with me.
>QM is conceptually weird, it's normal that it doesn't make intuitive sense the first time.
As I said, it's not really the first time, since I've been doing the qchem classes for years (and TAing them too), but I think they are definitely dumbed down a bit. Most students in our programs are destined to be lab techs for oil companies, so they really don't need it. Fortunately, we got this Russian guy who still teaches it pretty hardcore to them. He has to make it very easy for them to anticipate the exam questions so the grades don't get too low, but he does teach the subject matter in pretty good detail in the classes.
>density matrices
They do seem to come up a lot in pulsed (Fourier-transform) EPR, which is mainly what I am doing. As far as I understand it, it's just a matrix that represents the current state of an evolving quantum system? It is kinda like a Bloch sphere, but it is a language to generalize it to arbitrary systems?

>>16251260
>As far as I understand it, it's just a matrix that represents the current state of an evolving quantum system? It is kinda like a Bloch sphere, but it is a language to generalize it to arbitrary systems?
Pretty much, the thing is it can represent both classical uncertainty and quantum entangled states. So you can have points in the interior of the Bloch sphere.
Good luck with your defense!

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>>16240796
I am a week late, but this has helped me so much.
That you not only correctly analyzed what I was asking for AND provided 4 different dynamics really betrayed a comprehensive M.O like I also prefer.
It feels great encountering actual intelligence after spending a little bit too much time on 4chan/Lebbit/or trying to wring something useful out of ChatGPT

does anyone have the pepe wojak meme with phd, masters, undergrad and hs dropout?

>>16235350
who is this black goddess

>>16251226
You're asking questions only OpenAI can answer. How they've implemented the front-end and back-end systems, and what - if any - differences exist between the subscription tiers, only they really know.

>>16235350
Is there an analytical or empirical equation that calculates the mutual inductance of two different-sized coaxial square/rectangular loops with circular wire cross-section?

How does one work-ethic /discipline maxx?

As a challenge mode: the person work-ethic maxxing is a sperg who gets upset easily by interruptions and differences in activity

>>16252043
stop burning yourself out like a retard

>>16239719
Squares are longer from vertex to vertex (corner to corner) than they are from side to side. AD is 4cm so you have to use the Pythagorean theorem to figure out the length of AC then half it to get OC. The length of OC is 2.83cm.

best computer program for solving exercises, writing math symbols and doing big dick shit like graphs and columns?
t. carpal tunnel

I went swimming today and cracked my toes by tugging on them while my body was submerged and my head sticking out of the water. I could hear the crack sounds clearly. How is that possible? The water should've muffled or silenced those sounds.

>>16252222
> The water should've muffled or silenced those sounds.
Water is actually an excellent conductor of sound waves - whale song can be heard thousands of miles away from thee source - but it very frequency dependant. However the muffled sound underwater is primarily because of water in your ear canal stops your eardrum vibrating, your head was in the air.

Would it be possible to treat my sunken eyes with this procedure http://www.rexresearch.com/becker/becker1.htm (silver iontophoresis)??? Could the current I'd need to apply be potentially dangerous to my eyes?

>>16251977
>You're asking questions only OpenAI can answer
I mean, I wasn't solely refering to chatGPT, but LLM models in general, like e.g. llama. Does the computation cost per prompt only depend on token count there?

>>16246623
thanks, it's getting clearer in my head
If I think about it as just the overlap then I think I can make it make more sense quicker in my head
I just still don't get why I don't seem to have that inherent "grasp" over what should be something basic

>>16235494
yes =t"heoreo", i learned ova 140 million tactical movement patterns which i can rotate agains 2 language wheels
>>16235535
mixx an human wiht 10 billion terra tessla in an text chamer

>onstrained optimization is adopted for estimating the tapers, i.e., windows. Explain why we use constrained optimization in the multitaper algorithm.
I dont understand the question, because for me, estimating the slepians is the exact reason why we use constrained optimization. What am I missing here?

>>16252546
do they want me to expand on, why slepians are good for spectral estimation?

like that they are orthogonal guarantuees that there are is no redundant information?

Viewing the Mobius strip (without boundary) as a real line bundle L on the circle,
what's the most straightforward way to show [math] L \otimes L [/math] is a trivial bundle (again on the circle)?

>>16253385
Nvm figured it out

>>16235350
Is it the maillard reaction that crisps up apple skins? I know it does the whole sweet and dry and shit, but does it also crisp up the skin or is that a different reaction caused by the heat?

>>16252511
I actually found a book on the topic.
Bioelectromagnetism: principles and applications of bioelectric and biomagnetic fields

What the hell actually is a 'foot pound'? I thought it was something similar to PSI, like a measure of how many pounds of force over a foot of area but when I looked it up it was some arbitrary measurement like horsepower.

>>16254100
>It is the energy transferred upon applying a force of one pound-force (lbf) through a linear displacement of one foot.
seems pretty intuitive to me

>>16254100
Nah, it's a pound of force moving one foot in distance.
Yes, it's as retarded as it sounds.
Welcome to murrican units.
(Just substitute it with 1.356 joules. It's used anywhere a sane person would use joules)

I recently smoked cream cheese and it added excellent depth of flavor to a dish. I want to use it in more dishes. What is the current scientific basis for flavor? I don't want to waste time trying recipes to find what works. I want models I can use to modify any dish.

>>16254611
You probably want to read up on molecular gastronomy, which is a fancy name for the science of cooking.

>>16239134
https://en.wikipedia.org/wiki/The_Chemical_Basis_of_Morphogenesis

>>16254100
torque.
Science uses force-acting-at-distance, i.e. Newton-meters, Nm
Turns out that force*distance = energy
so Nm can be replaced by J, usually people just leave it as Nm tho

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Smartbros...

If you were stuck with 95IQ tomorrow, what would you do to improve your life that's not committing suicide?

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>>16235350
Can someone explain what the authors mean here, regarding the ergodic hypothesis? How can some trajectories in a phase space reach all states and some don't. I thought trajectories themselves are part of phase space, or that being in a given state dictates where you'll go next necessarily.

>>16255473
There's a map from the space of initial conditions to trajectories. Almost all initial conditions lead to ergodic trajectories but there's a set of measure zero that leads to non-ergodic trajectories.

>>16255488
I thought initial conditions include velocity of particles. So a given initial condition inevitably moves in the phase space a certain way. So if the x axis is some measure of position and the y-axis is some measure of velocity, then the states available at a given energy necessarily lie on a certain curve and those states don't lie on any other curve for other energies. I'm probably misunderstanding the concept here, but I'm picturing those phase space representations you see like of a pendulum with elliptic trajectories and stuff.

>>16255516
Yeah OK you are right. I think the textbook fails to emphasize that even an ergodic trajectory only explores a part of the phase space with constant energy.

>>16255303
Maybe some Ashwagandha?

>>16255303
Why don't you ask the of the world that are also average like you.

>>16255626
I did. Answer? Watch netflix, and don't worry.

I'm going to start physics in uni soon, I've always dreamed of living the uni research worker life.
Due to severe family issues I was unable to continue going to highschool and now am self studying to finish off highschool diploma (we have a program that allows u to self study and do exams at some gov building)
How doomed is being someone who hasnt had a job and finished highschool at age 22 for ur resume in these kinds of fields? (Mainly reffering to STEM research jobs)

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>>16235350
What are the scientific implications of female mating behaviour being entirely Chad-focussed?

No matter what you say, I just don't like your conduct.

Add it up

>>16237108
nothing

>>16256263
Only your last degree matters. High school performance matters for undergrad admissions but once you have a BS no one cares about how you did in high school. Your age also does not matter much.

>>16256263
I think your perspective is slightly skewed. 22 is still young as fuck. Plenty of people do degrees in their 40's and even older. You are never to old to educate yourself.

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Can anyone confirm this? >>16255473>>16255516
Here's the rest of the discussion in the book. I don’t get how the rational trajectories can be ignored. As I understand it, the ergodic hypothesis is that the time average over a trajectory is equal to the 'space average' over possible states. Well, clearly the time average over a given rational trajectory is not equal to the average over all possible states as that includes trajectories starting from anywhere in the square and these will all fill the grid.

I think my confusion is about what exactly comprises the state space here? Are the slopes of the trajectories part of the state space? What counts as a possible state? I mean, how can you say that a given trajectory doesn't explore all possible states when it literally just does what is dictated by the laws of physics?

Bump

>>16235350
Alright, stupid question inbound...
If gravity cancels itself with opposed accelerations, then why the center of stars are so violent? One would say that gravity would cancel itself...but instead we see the typical vectorial behavior with force sources all around doing compressive and expansive deformations.

>>16256799
Because gravity is not the only force involved. You have the inward force of gravity and the outward force from radiation pressure due to fusion. You are correct though, at the center of mass of the sun the net-gravitational force would be zero.

Bump >>16256472

>>16256472
>I don’t get how the rational trajectories can be ignored.
Because they form a set of zero measure, therefore under any non-pathological distribution a trajectory chosen at random will be irrational almost surely.

>>16257189
Is there a way of formalising that to fit the ergodic hypothesis, or is it just an informal way of saying almost all trajectories satisfy the hypothesis?

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>>16256472
you world is definded by your knolwedge,

>>16256472
that a given trajectory doesn't explore all possible states

well you cant this is why manny programms are either obsessed wiht history or immortality.
you can as part of an mathematical agument, this doesnt prevent history from repating it self, like if you hate to get boiled, a fracal doesnt solve this you jst get biled wiht lower enrgy but it hurts as much, this is why manny proghramms obesss with history or immortality. :D

and yes you can solve everything whith relativity alltought they are also other theories who allow for a faster movement in space.

>>16257498
What

>>16257296
For almost all (in the technical mathematical sense) initial conditions, the average along the trajectory is equal to the average over the phase space.
https://en.wikipedia.org/wiki/Almost_all?useskin=vector
https://de.wikipedia.org/wiki/Ergodenhypothese?useskin=vector#Definition_und_Einschr%C3%A4nkung
https://en.wikipedia.org/wiki/Ergodic_theory?useskin=vector#Ergodic_theorems
You can prove this for certain kinds of systems (this is called the ergodic theorem) but the proofs go over my head.

>>16257881
Does the phase space include the slope of the trajectories or is it just positions in the square? Because any given slope will only stay on that slope and won't visit any of the other ones. So I'm wondering, what constitutes the phase space here?

>>16257986
just the positions

>>16258024
The ergodic hypothesis is about possible states, right? But it's not possible for a rational trajectory to explore the entire square, and thus it explores all that is physically possible. Or is it that it is possible for rational trajectories to hit everywhere in the square, just not for one starting position? So for irrational trajectories it doesn't matter where the ball starts, but for rational trajectories it can't reach everywhere no matter where it starts.

>>16258033
>The ergodic hypothesis is about possible states, right?
No, it's about the phase space
>But it's not possible for a rational trajectory to explore the entire square, and thus it explores all that is physically possible.
No, it only explores a part of the phase space. The square is the phase space. Your notion of "physically possible" is not how those words are normally used (it's identical to "on the trajectory")
>Or is it that it is possible for rational trajectories to hit everywhere in the square, just not for one starting position?
Yes, you cannot explore the phase space with any *single* rational trajectory
>So for irrational trajectories it doesn't matter where the ball starts, but for rational trajectories it can't reach everywhere no matter where it starts.
Yes exactly that's what the theorem is about. And there are infinitely more irrational trajectories than rational trajectories, so a random trajectory visits the entire phase space with probability 1

>>16258507
What was confusing is that when the authors introduced the notion of state space they said it encoded the positions, velocities, angular velocities etc. of every single particle (in a gas, for example) as a single point in some gadzillion-dimensional space. So I thought the slope of the trajectory would be part of the phase space. In that case, I wonder what constitutes a trajectory in a state space that includes velocities of the particles. Like how could a particle go through such a space and attain every velocity.

How does a battery know to stay on?

>>16258729
what do you mean by "on"? how does it know to keep a potential difference across it? same reason a ball at the top of a hill wont move unless you push it, its just conservation of energy.

Dumb question but what if the universe is moving in a donut shape(torus)? If we are at one side of the donut seeing the other side then it would like something is red-shifting away from us but in reality the space is just going to loop around again

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I need help with this y'all(ML/AI/data sci PhD advice )
>>16258416
>>16258691

P(N) 1) {1}, 2) {2}, 3) {1,2}, 4) {3}, 5) {1,3}, 6) {2,3}, 7) {1,2,3}, 8) {4} and so on. Why won't it be countable?

>>16259408
The set of finite subsets of N is countable. The infinite ones are uncountable because of the diagonal argument

What do you do when an expression in a Latex align environment doesn't fit on the page. This drives me crazy. Any solutions?

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>>16258838
Look up cosmic topology.

>>16259555
I usually put a linebreak in the middle, before a +, say, and \quad to indent it somewhat, like so:
[math]\begin{align*}x&=verylongexpression\dots\dots\\&\quad+nextpartofsamelongexpression\\&=anotherpart...\end{align*}[/math].
There's also multline but that only looks nice for one expression imo.
If there's no suitable operation in your multiline expression then I feel sorry for whoever is supposed to read it.

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Night train, passing through...

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>>16235350
1. How do I solve a relation equation?
In this equation I can't have x or y on one side of the equation so I put it on a graph program and realized it is not a function. I thought of swapping the x and y axis but that knot in the negatives means it would still be a relation.
2. Is there a way to solve this thing algebraically?
3. Any lessons or books to know more about this type of equations?

>>16260697
You can solve that expression for y, but since it's a quadratic you will get two results. Draw a line for each and you will produce that graph.

>>16247896
read Landau Lifshitz, vol. 3. Also read up on representation theory

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>>16235350
How can I prove that if a set of measure zero has well-defined volume (its indicator function can be integratee) then that volume is zero?

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>>16260864
Just to be clear, this is the definition of integral I'm working with.

Bump >>16260864 >>16260865

Let
[eqn]
L = \frac{m}{2} \dot x^{2} - \frac{k}{2}\, x^{2} - kx\dot x t.
[/eqn]
be the Lagrangian of a mechanical system. Is the energy conserved?

I would have said no, because the Lagrangian is not invariant under time-translations. So by the Noether theorem, the energy should not be conserved, right?

i have zero idea about electricity
no idea what the fuck is watt and shit
would going through physics middleschool+highscool on khan academy good resource?

>>16261002
Correct. Energy is conserved in the system when the Lagrangian doesn't depend explicitly on time. You could explicitly prove it using the Euler-Lagrange equation.

Why can't we apply Hilbert hotel to Cantor's diagonal argument.

In the double slit experiment, if you erase the which-way information after measurement the interference pattern reappears, right? What would happen if you first fed that information to an AI, and then deleted it? Or if you let someone know the result and then shot him in the head?

>>16261023
thank you

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Okay, this been on mind fr.

How come dogs that have curly hair are the best dogs for swimming, but the opposite is true in humans. I'm not trolling, I'm legitimately confused why picrel is a "water dog", but people of African ancestry aren't natural swimmers.

Why do complex numbers solve differential equations?

im a software dev and i want to learn more about engineering (not software engineering).
are there any books that explain engineering methods in a way that a layman like me can understand it?

>>16261097
Why not?

>>16261031
> if you erase the which-way information after measurement
And how do you do that?

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>>16261097
Wdym? There are situations in which you can turn ODEs into polynomials, then complex numbers help you because they give roots to those polynomials. I'm not sure what you're thinking of otherwise.

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Experimental particle physicists and CERNheads, what does the [math]\sqrt{s}[/math] and [math]\int L dt[/math] (guessing this is the action of something but I have no idea what the units mean) mean in this figure?

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How would you go about figuring out what the counterweight would need to be for this?
What kind of material would even be used that would weight enough and also be transportable? Would it make more sense to temporarily drill it into the ground or what?

>>16262101
[math]\sqrt{s}[/math] is the CM energy, which is the total energy of the particles being collided, as perceived by an observer stationary relative to their joint centre of mass.
The L is luminosity, the number of events detected over time in a certain cross-section. Integrating with respect to time gives you the inverse of the cross-section, which here is measured in femtobarns (1 barn being about the area of a uranium nucleus)

>>16262208
>The L is luminosity, the number of events detected over time in a certain cross-section.
Ohhh, I thought L was Lagrangian, thanks.

How the fuck do I identify the characteristic of quadratic form Q(h,k)? I'm not getting any of these problems correctly. Why the fuck for instance is h^2+hk+k^2 pos. definite but h^2+2hk+k^2 semidefinite????

>>16262767
[math]h^2+2hk+k^2=(h+k)^2[/math], so it has real roots wherever [math]h=k[/math], and since we have roots for nonzero real vectors, it is semidefinite.
On the other hand, if you fix [math]h[/math] and use the quadratic formula to solve for [math]k[/math] in [math]h^2+hk+k^2[/math], you'll find that there are no solutions where both are real besides [math](0,0)[/math]. As such, it is not semidefinite.

>>16262784
*wherever [math]h=-k[/math]. pardon me.

>>16262784
So testing for non-zero roots will reveal whether the quadratic form is definite or semi-definite, what about indefinite? How do I tell if something is positive or negative definite?

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>>16262767
Gram-Schmidt lmao.
How else would you do it?

>>16262904
>>16262767
Can't you calculate eigenvalues of the relevant matrix? [math]h^2+hk+k^2=v^t A v[/math] for [math]v=(h,k)[/math] and [math]A=\begin{pmatrix}1&1\\0&1\end{pmatrix}[/math], and all eigenvalues are >0 so it's pos def. For your other case one eigenvalue is 0 so it's pos semidef.
This is probably equivalent to whatever the other suggestions are but I thought I'd mention it.

>>16262997
Nowhere in the book does it mention using eigenvalues, I barely know what they are I haven't had linear algebra yet. I'm just gonna learn this method because googling trying to find how to do it just sends me back to these fucking eigenvalues

>>16263026
What the fuck are you doing studying quadratic forms then

Explain how I'm wrong without sounding mad >>16262939
else you conceed that I am right

>>16262997
Oh actually this might be retarded because there can be multiple matrices corresponding to the same quadratic form. I think it should be symmetric as well, so the off-diagonal elements should be 1/2 here.

In a theorem my textbook differentiates between a module (over a commutative ring) being free or finite dimensional. Aren't they the same though?

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>>16263040
...no?
Remember that ideals are always modules and that that's the single easiest way to construct non-free modules.

>>16263030
Dunno, it's part of the course book, like I said, it doesn't mention much linear algebra, especially not eigenvalues, save for determinants, scalar and cross product. With quadratic forms they just tell us to look at it and try some values, I don't think this is sufficient

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I'm a fa/tg/uy who is about to play in a game of Dungeons and Dragons. For our six attribute scores, our GM made us roll 18 d6 and replace four of the lowest with sixes, leaving us with a following pool:

1x0
2x3
3x4
4x2
5x2
6x7

We would then divide the dice to sets of three. Repeated values and sums are fine but we of course can't use the same dice more than once.

My question is that how many combinations can we get from that pool of dice? How about non-repeating combinations? Could I print out the combinations in some program or website?

Thank you for your patience and sorry for being a brainlet.

>>16263080
idk i sloved it age 11 pseudeo and age 16 close to i can do it for you if you want. 6^18?

An optics question:
Apochromatic lenses focus three target wavelengths to the same depth. As a result, there is a focus shift when using these lenses to photograph in light significantly outside of the visible range (UV and infrared). Would this focus shift be a static number, no matter the distance of subject to camera?

[math]\mu[/math] is Lebesgue measure on [math]\mathbb{R}[/math]. Assume [math]T: \mathbb{R} \to \mathbb{R}[/math] is measure preserving, ergodic and invertible. Let [math]A \subset \mathbb{R}[/math] have finite measure and denote [math]A_n = T^n A \setminus \bigcup_{j=0}^{n-1} T^j A[/math] for all [math]n \ge 0[/math].

Claim: [math]\lim_{n\to \infty} \mu(A_n) = 0[/math] and [math]\mathbb{R} = \bigcup_{n=0}^\infty A_n[/math] up to null sets.

Why? I cannot see it. I imagine I should prove that [math]\widetilde{A} := \bigcup_{n=0}^\infty A_n[/math] is [math]T[/math]-invariant to conclude that [math]X = \widetilde{A}[/math]. I see why [math]T\widetilde{A} \subset \widetilde{A}[/math] but I don't see why must [math]\widetilde{A} \subset T \widetilde{A}[/math]. I also don't understand why [math]\mu(A_n) \to 0[/math].

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>>16263871
No, in general the focus delta has a non-linear dependence on the wavelength (e.g. the shift for UV would be different to IR). The lens are designed so they bring the three specific colors to a common focus and its why the lens configuration is so complicated since each of those wavelengths has a different shift.

>>16263932
Thanks for responding. Sorry, I improperly phrased my question. What I mean to ask is, assuming you are shooting at one specific wavelength outside of the visible, let's say 850nm, does the focus shift at 850nm change with the distance of the camera to the subject? If I am 2m away or 0.5m away, is focus shift always going to be the same at a given wavelength?

>>16263937
I'm unclear why you think the distance matters? At some fixed wavelength the light going through the lens will be refracted by some fixed amount.

>>16261449
look up quantum eraser experiments I don't understand any of that stuff

I'm supposed to prove that [math]I_{xx} + I_{yy} > I_{zz}[/math] for the diagonal entries of the inertia tensor [math]I[/math] assuming that the rigid body is not a disk in the [math]xy[/math] plain.

Isn't this false? Imagine a object of negligible volume located on a disk in the [math]xy[/math] plain. In this case, the [math]z[/math] components would be a null set and we'd get an equality instead of an inequality.

What do you think, am I supposed to do here? Do they low-key want me to assume that the object has to have an non-negligible extension in the [math]z[/math] direction?

>>16264349
> I don't understand any of that stuff
It shows. The original explanation for that (by the experimentalists who first performed the experiment) is now regarded as wrong - but that hasn't stopped all the pop-sci myths from still existing. There's no delayed-choice / effect-before-cause going on. All that is taking place is the filtering of information.

>>16261728
I took a physics 2 class and the teacher was going over LRC circuits which I remember dealing with a little in ODE class but I didn't understand how you can just handwave away all the calculus and turn it into a simple problem where you just sub in the complex numbers.

new thread
>>16264698
>>16264698
>>16264698
>>16264698

Non-avatarfag new thread:
>>16264745

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Can someone double check this for me? My book claims that it doesn't have extreme points in origin but I'm vehement on the fact that it does, I might be doing something wrong.

>>16264827
It does not.
Fix [math]y=0[/math] and check the behaviour of [math](1+\sin{x})\ln(1+2x)-2x[/math]

>>16263983
It was unclear to me as well. I was finding my photos out of my focus despite using a flat focus shift (film, so can't check work on the fly). I had the same thinking as you, and felt like it must be me being retarded. Apparently not, at least not in that case. I must be making a mistake somewhere else. Thank you for the help.

>>16264876
I believe there is something I don't fully comprehend, I'm assuming it has something to do with being an inflection point and not an extreme point? I can't comprehend it, I just do derivative test, get derivative = 0 and say that it is an extreme point... Multivariable calculus seems so convoluted, I must've missed something in my studies...

>>16265024
When I say derivative test, I of course mean that I set the gradient to be 0

>>16265024
>I'm assuming it has something to do with being an inflection point and not an extreme point?
Your assumption is correct, yes.

>>16265071
How do I discern them in multivariable? Do I make a table of 2nd p. derivative? I thought the entire point of the quadratic form I've learnt is to avoid the table and figure it out more methodically