/sci/ - Science & Math

I'm having difficulty formulating the integrals for the periods of an elliptic curve. Can anyone help me by walking me through an example?

This is the example wikipedia gives on
https://en.wikipedia.org/wiki/Period_mapping

I'm not sure how they come up with the paths for example.

do these analogies between finite abelian groups (denoted A in the picture) and endomorphisms between vector spaces have a concrete mathematical structure?

Retard trying to understand quantum mechanics here.
Can you confirm that the red line is just the wavefunction of ONE of the many energy levels available to an electron in a periodic potential? So there would be many other wavefunctions, each with a different shape, but they draw only one for clarity?
And if I select a point in a band-structure diagram (i.e., a momentum and an energy), then that point has its very own wavefunction associated to it, right?

>>16057008
They are both connected to module theory.

A finitely generated abelian group = A finitely generated module over the integers
A finite-dimensional vector space = A finitely generated module over a field

>>16057193
>Can you confirm that the red line is just the wavefunction of ONE of the many energy levels available to an electron in a periodic potential?
Wikipedia has some surprisingly good articles on these things as of late. Your answer is here https://en.wikipedia.org/wiki/Bloch%27s_theorem#Theorem

tl;dr yes. Also noted on the page, that solid line is a schematic of the "real" part. Naturally changes of "nk" mean a different behavior.

How are you supposed to set up this problem?

I'm programming a MNIST number recognizer using neural networks. I have a general understanding of the forward propagation and dot products where when I take a 10 number matrix and multiply it with another 10 number matrix I will receive a SINGLE summation.
Now after forward propagation is BACKWARDS PROPAGATION. This is whats really tripping me up right now. The python program I am looking at does a dot product between two 10 number matrices and returns a 10x10 matrix. Mathematically how the fuck is this happening!?

>>16057420
It's probably the outer product

>>16057542
No. Back prop uses standard matrix x matrix multiplications to perform all the calculations across the layers in a single pass.

>>16057420
Have you never taken a linear algebra course? There is a standard way to multiply a matrix by another matrix and get a result which is a matrix. A dot product is a specific case which only applies to vectors (a matrix where one of the dimensions is one).

>>16057598
No my highschool linear algebra never mentioned matrices it only occured in college Abstract Calculus class and I was either drunk or high. What is this standard multiplication you are talking about because google sucks, go figure when the AI search engine only knows how to give out popular answers.
>>16057542
Outer product looks exactly like whats going on when I print out the data. I will wait for the other anon to elaborate.

Are there any viruses/bacteria that are lethal to cockroaches but are mild or non-infectious to humans? They are masters of spreading diseases around so i think biological warfare would be really effective against them
I understand that if it was possible, it would probably be on the market already but its hard to imagine that there are no cockroach exclusive viruses that can be utilized to fuck their shit up

i dont know if remi still lurks around here but i found a remilia pop-up shop in akihabara today and i wanted to share it with him.

>>16057698
> google sucks
are you an idiot? search for 'matrix multiplication'. click any of the top results.

https://en.wikipedia.org/wiki/Matrix_multiplication

>>16057239
Thank you anon, that was exactly what I was looking for.

>>16058026
I do lurk sometimes. I didn't get bored or grow out of 4chan or anything, I'm just busier nowadays.
Have fun on your trip!

>>16057999
I'm sure funghi can kill them.

>>16057399
It tells you in the hint. This has nothing to do with radioactive decays per se, it is just a straightforward application of conservation of energy.

>>16058534
Glad I could help.
>>16058550
I know the feeling. I wish money could buy you more free time without costing you the ability to make money (e.g. promotions, job requirements, etc). Society's kinda screwed up that way in my opinion when you're just required to put your ass in a seat for no reason.

I recently came into a 5L plastic jerrycan that used to contain 70% ethanol. if I let it air out, wash it and let it soak with water it should be safe like new again? so I can store (drink)water or other stuff in it
the ethanol can't seep into the plastic making it unsuable or something like that? and even if it did it should be diluted so far it's neutralized?
It's really sturdy and it has a nice vertical shape which is handy, that' s why I want it

>>16058741
> I recently came into a 5L plastic jerrycan
There are better places to do that anon.

>>16058759
see my last line
also if by ''that'' you mean something I genuinely have no idea what you mean. I think it's a very handy bottle/jerry can

>>16058741
>drinking water
The worst that can happen from the ethanol is that you end up with 0.0004 proof vodka. I'd worry more about the 30% since it might have been denatured with something toxic. If it's just methanol and/or isopropyl alcohol and you wash it well you should be good.

>>16058765
It's a pun.

>>16058798
>I'd worry more about the 30% since it might have been denatured with something toxic.
I see, if it was denatured with water it should be fine? also what could the worst case scenario be?
>>16058805
forgive me... I guess this really is a thread for stupids like me

>>16058807
>I see, if it was denatured with water it should be fine?
Although water (probably) made up most of the other 30%, that's not what's doing the denaturing there. Nobody's denaturing with water.
Denaturing is adding some amount of other substances to ethanol not intended for human consumption to strongly discourage that. Methanol's the most common one and the main one you want to watch out for. Literally. Because it attacks the optic nerve and will blind you.
But, again, a few proper rinses should be enough to get rid of most of the stuff they'd put in there, be it methanol, isopropanol, whatever ketones, pyridine...

>>16058821
I see thanks, what I get is that if I clean it properly enough then it should be safe
also I checked the SDS (I know which manufacturer sold it) and it says it's a mixture made up of ethanol and distilled water (with ranges for both being very broad, but it averages to 70%).
I read through the entire thing (even the transport safety...) and found no mention of any of the other chemicals.
>Because it attacks the optic nerve and will blind you.
thanks a lot, I'll use some safety glasses when cleaning it then, I didn't know it was that bad

>>16058550
>I'm just busier nowadays.
thats funny, ive noticed i post less and less the more free time i have. the most i posted was when i was taking 18 hours and driving an hour to work every day after class. now im not in school, live in the city i work, and only work like 30 hours a week at that, but i somehow drifted away from here. sometimes i worry i didnt really know what it is i want.
>Have fun on your trip!
thanks <3

>>16058867
>thanks a lot, I'll use some safety glasses when cleaning it then, I didn't know it was that bad
No, no, not like that. That shouldn't be necessary.
It's only when consumed/inhaled in excess. I don't think there are any additives anyone would put in that'd fuck you up just from passive exposure while cleaning. Not that it'd hurt to use goggles anyway, of course, but it shouldn't be necessary.

>>16058867
nothing else? For a good time you could drink it as is then

>>16058061
>wikipedia

>>16058984
>baiting

>>16058950
oh okay, I thought it was a bit weird that a chemical that is used in the open air would need saftey goggles. I'll rinse it plenty and thoroughly
>passive exposure
I work in a food testing lab and have to routinely use it to clean so I get exposed plenty. not enough to start causing damage I figure, otherwise we would have precautions or other stuff. also I forgot to mention but even if the sds didn't say it contained anything, I'll just treat it like it has
thanks again

>>16058983
how do you think it came to be empty in the first place ;-)

How is quantized gravity even supposed to work?
Gravity can bend light, and we are told that it because gravity warps spacetime and bends the straight path light takes. But how would that work quantumly? How could a graviton affect the path of a photon when photons can't influence each others path? Why couldn't a photon influence the path of gravitons? Or could they?

I only ask because just about everyone's own theory of everything seems to treat quantized gravity as a given.

Why does this definition of the limit require S to be arbitrarily close to x_0? I haven't seen this in other books. Is this related to the completeness property of real numbers? Does the definition require that the domain of the function is an interval of real numbers?

As a side question. What is the property of real numbers that means you can always find another real number as close as you want to a given real number, i.e. that they form a continuum?

>>16059640
>Why does this definition of the limit require S to be arbitrarily close to x_0?
So that you can actually approach x_0. Otherwise you'd have a gap between x_0 and the closest point in S and the definition would not mean what we want it to mean. In other books they usually just assume S is an interval. This property is also called "x_0 is a limit point of S"
https://en.wikipedia.org/wiki/Accumulation_point
>Is this related to the completeness property of real numbers?
No completeness is related to convergence of Cauchy sequences but this definition doesn't rely on sequences
>Does the definition require that the domain of the function is an interval of real numbers?
No, you can have a function that is defined only on the rationals, or on a union of intervals, or an interval and an isolated point etc
Also you can generalize this to S being a subset of other spaces than the real line
>What is the property of real numbers that means you can always find another real number as close as you want to a given real number
Dense set (in the metric topology). But even rationals have this property. What makes reals special is completeness (every Cauchy sequence of reals converges to a real)

>>16059669
I thought a function f:N->R can be continuous. Why can't x just be the same as x_0 in this case? Like in this reddit thread: https://www.reddit.com/r/math/s/qCfk2EnAtq

>>16059671
>Why can't x just be the same as x_0 in this case
It's often useful to take the limit of a function as it approaches a point where it's not defined, but if we limit it to [math]x=x_0[/math], that possibility is no longer a possibility.=

>>16059640
well, part of the definition of a limit is that you need the x values in the neighborhood of x_0 need to get closer and closer to satisfying f(x) = L, and the “neighborhood” part means that delta has to go to zero, so S must approach x_0. and intuitively, surely you couldnt say anything meaningful about the value of f(3) by only looking around f(4), no?
>What is the property of real numbers that means you can always find another real number as close as you want to a given real number
“dense”, but you usually only use it to describe subsets of the reals and not the reals itself. saying a set is “dense on itself” is almost a tautology.

>>16059679
That makes sense, but what are they referring to there? Apparently any function f:N->Y (for some space Y) is continuous. It's mentioned here as well and now I'm confused: https://math.stackexchange.com/questions/1409364/continuous-functions-with-domain-in-the-natural-numbers

>>16059671
Yes in that case the limit at x_0 is always f(x_0) but that isn't really interesting
You are usually interested in the case where x_0 is not in S

>>16059680
For the definition in wikipedia they don't mention that f is defined on a set that is arbitrarily close to x_0: https://en.m.wikipedia.org/wiki/Limit_of_a_function

In general I just don't see the "arbitrarily close" qualifier mentioned much. Is it essentially assumed?

>>16057420
what kind of code are you looking at, backprop is usually done through computational graph...

>>16059690
Are phoneposters blind these days?

>>16059680
Why is it a tautology to say a set is dense in itself? Are the natural numbers dense in themselves?

>>16059640
>I haven't seen this in other books
What standard analysis textbook doesn't include this?

>>16059640
most other textbooks assume that |x-x_0|>0 where it makes more sense for x_0 to be an accumulation point of the domain

What fraction of a spheres surface area is covered between 60°S and 60°N?

>>16059671
If you have [math]x - x_0 = 0[/math] then it's trivial there's nothing to show. The definition explicitly says that the difference between x and x_0 is some delta that is bigger than 0.

>>16059559
> How could a graviton affect the path of a photon when photons can't influence each others path?
You are wrong. Photons do produce gravity, they have energy, it is just a very, very small effect. The reason it is rarely ever seen is that photons have no mass, only momentum, and almost all of gravity is produced by the masses involved ([math]E = mc^2[/math], [math]c^2[/math] is a very large number but for photons [math]m=0[/math]).

> just about everyone's own theory of everything seems to treat quantized gravity as a given
The other three forces can all be described by fields (the electromagnetic field being the most familiar). There is a set method (quantum field theory) that can quantize such fields so they obey the laws of quantum mechanics. Without having to manually add them to the theory, out of this method appears the force carrying particles (photons, W and Z bosons, and gluons) and quantum properties like spin. QFT is the most remarkably successful theory physicists have ever come up with.

Then you have gravity. Our current best theory of gravity (General Relativity) is actually a field theory (albeit a classical one). So the obvious assumption should be that we can quantize it.

> How is quantized gravity even supposed to work?
That's the billion dollar question. When we apply the usual steps of QFT of turning a field into a quantum field, when it comes to GR the math just does not work. QFT fails. So the only correct answer to your questions is that we do not know. Everything you've heard or read about how quantum gravity would work is with the assumption it would work in a similar way as history and the math showed us the other quantum fields did. It is a reasonable conclusion, we have no reason to believe otherwise, but without a working theory it's a best guess.

>>16059865
>the math just does not work. QFT fails.
Care to elaborate? Qft fails with qed and qcd as well. You just need to regularize it, renormalize it, subtract out infinities and reinterpret quantities in your lagrangian

>>16059893
I don't know what your definition of 'fails' is since each of those theories produce results that match observations. That makes them working 'good' theories.

> You just need to regularize it, renormalize it, subtract out infinities
So what? Each of the steps has been shown to be mathematically rigorous. The better question would be why do we have to do those steps to get a working theory? That is still an open question.

> Care to elaborate?
The reason QFT fails when applied to gravity is that those steps can't be done. The math of QFT assumes a fixed spacetime but once you add gravity that is no longer the case. Everything goes to shit. A simple analogy is that it is like trying to paint a picture but the moment your brush touches the canvas, the canvas warps and also changes where you applied the paint.

>>16059908
>So what?
So the original attempt failed and had to be modified multiple times. And for the record, resummation is a necessity in QFT and isn't mathematically rigorous in the slightest. It's an ad hoc explanation.
>Everything goes to shit.
You keep saying this vague, nebulous crap. What specifically is going wrong? In the case of qft, I was specific in saying infinities are being subtracted out, terms in lagrangian are renormalized, and so on. I could just as easily say "yeah the math just doesn't work in qft". Be specific motherfucker. And just to be clear when I'm saying to be specific I'm not saying to write a treatise with fifty pages of mathematical steps. Write a clear short paragraph saying what the issue is, like what I did with qft.

>>16059938
>So the original attempt failed and had to be modified multiple times.
Yes anon, that is how science works. Trial and error.

>>16059975
You're not understanding. What specifically is wrong with applying qft to gravity? What, specifically, is making the math not work? And how is it different from the original problems qft had in describing qed and qcd?

>>16059989
Quantum field theories are generally defined using a Feynman path integral measure. This means that you compute correlation functions of observables by summing over all histories of your system. In a field theory, these histories are functions on some spacetime manifold.

Just as you define the ordinary integral as a limit of Riemann sums, you define the Feynman path integral as a limit of "regularized" path integral measures. There are a lot of ways to do this; one of the most popular is the lattice regularization. We choose a finite set of points in spacetime, living on a lattice whose nearest neighbours are a distance a apart. Then we choose a "microscopic" action on our space of fields and discretize it, replacing derivatives with finite difference quotients, and approximate the path integral's weighted sum over histories with a sum over functions defined on the lattice.

We usually want to take a continuum limit, making the lattice spacing smaller and smaller. If we do this, while keeping fixed the coupling constants in the microscopic action we used to define our measure, in most cases, we run into a problem: the coupling constants in the classical equations of motion depend on the lattice spacing a, and become infinite as a goes to zero. So that's probably not the limit we want.

And indeed, in most circumstances, we know the classical physics, and are trying to find a quantum theory that reproduces it. So we'll try something else: make the coupling constants in the microscopic action depend on the lattice spacing, and hope that we can tune them in a way that keeps the classical physics fixed.

Sometimes this works; sometimes it doesn't. It can happen that there isn't any way of tuning the coupling constants so as to reproduce a nice classical limit; when this happens, the theory is said to be non-renormalizable. This appears to be what happens in General Relativity, if you use the discretized Einstein-Hilbert action as your microscopic action.

>>16059893
I''m not the guy you are replying to, but I think I can answer your question more clearly.

>You just need to regularize it, renormalize it, subtract out infinities and reinterpret quantities in your lagrangian
In renormalizable theories you can think of the "infinities" (I put this in scare quotes because the theory is regularized and nothing is infinite) as being absorbed into the bare parameters in the regularized Lagrangian, and crucially there are a finite number of parameters to work with.

When you try to do the same with a non-renormalizable theory like the Einstein-Hilbert action you can still regularize it, but you'll find you need to introduce additional terms in the action (for instance like the Riemann tensor contracted with itself) to be able to "subtract the infinities." Then the additional terms you introduced will lead to additional loop diagrams with their own infinities, and you need to introduce even more terms to cancel those. So in short, to get it to work out to arbitrary loop order you need an infinite number of parameters in your Lagrangian. This situation is actually considered okay nowadays, it is called an "effective field theory," but in any case that is what goes wrong with gravity that doesn't go wrong in renormalizable field theories.

>>16060065
So every time you add a counter term, a new infinity pops up that can't seem to be eliminated.

>>16060255
Yes, that's the distinction between renormalizable and non-renormalizable. But you are missing the effective field theory point of view which is that 1) these aren't really infinities since the theory is regulated at some UV scale that I'll call M, and 2) both the additional terms you add, and the loop diagrams themselves can be ordered in powers of M so that you only need to consider a finite number of terms at each order. This lets you make sense of a non-renormalizable theory, and we have plenty of examples like the Fermi weak theory, and the Euler-Heisenberg theory, where you can calculate something both the effective field theory way and a renormalizable way, and you get the same answer.

Why does it take me over 25 seconds to put together any trigonometric ratio from an image like pic related? This is very simple math and is literally elementary-tier compared to most of the stuff that passes through here, but if this image is rotated, numbers are substituted in for the variables, or if θ is moved, it can take me almost 40 seconds to figure it out.

I'm genuinely worried that I might have some sort of legitimate learning disability or something. What is wrong with me? In class, my professor handed out timed tests with various simple trig function questions like pic related, just like the old multiplication tables sheets, and I only finished three of them.

More than half the rest of the class finished at least one side.

What is the *exact* process one is "supposed" use to answer a question like pic related?

>>16060345
Do you know about https://en.wikipedia.org/wiki/Mnemonics_in_trigonometry ?

>>16060345
c is the hypotenuse (it doesn't touch the right angle, and it is the longest side). Of the remaining sides, a touches the angle theta and b does not. So a is the "adjacent" side, and b is the "opposite."

If you have enough intelligence to type your post, once you understand the paragraph above you should be able to identify the three sides in a short amount of time.

Then it's just
Sine = opposite / hypotenuse
Cosine = adjacent / hypotenuse
Tangent = opposite / adjacent

>>16060345
soh cah toa

>>16059764
kinda. the special part about the natural numbers is that they dont always have elements in between them, e.g. theres no natural number between 3 and 4, but thats not the same thing as being non-dense. i can think of sets that always have elements between any two elements but nonetheless arent dense in the reals.

How to prove that their is not more than 20 sidon sets from the set {1,2,3.......100} ?

Sidon set is a set in which {a+c /= b+d}

For example {1,2,3,4}
Here 1+3= 4 and 2+4=6
Hence it is a sidon set


Is this a pigeonholed principle type question ?

trying to figure something out i my head not sure wheher this makes sense
If i have an eccentric gear in this case a peg off centre with 4 ropes attached to the peg at 80 degres each and 4 equal weights attached to the ends of the ropes hanging over rollers

since the tension is balanced will the gear require the same force to move as when it was unladen ignoring friction obviously

2nd part that I'm struggling to figure out
if I place a spring underneath one of the weights so that everytime the gear rotates the it interacts with it what actually happens? will it exert its full downwards weight on the spring? what will the oher weight balancing it do?

this is my attempt to visualise the processes on old jerker line oil pumps systems and their bull wheels.
they mentioned balancing the loads with matched wells

one example of the system I'm thinking of and trying to understand
https://www.youtube.com/watch?v=TWYLAwmCgNc&list=PLqBpN9TbAq0HNmpdCWgu5T-uBJYHlEdGb&index=21&t=116

the rods connect out to a bunch of oil pumps lifting up a pump rod

for some reason I can't properly visualise

>>16060556
>Hence it is a sidon set
It isn't, though? sets are unordered, and 1+4=2+3
But in any case, you are correct about it being a pigeonhole principle problem.

>>16060350
>>16060360
>>16060366
Thanks lads. Surprised at how many of you responded.

I'm trying to get better at remembering them, but for whatever reason I seem to have a particularly difficult time. I realize I keep misremembering the mnemonics frequently; a memory trick is only as helpful as one's recall is accurate. I'm going to create some flash cards later tonight and see if some careful repetition hurts.

Trigonometry, for me, is a hard concept to grasp. Working on these problems feels like trying to parse a text written by someone from a higher dimension. I am very stressed because this is one of the first times in my life I have ever encountered something that I didn't simply "get" right away, and I think it's coloring my attitudes towards it and making it harder to learn than it really is.

>>16060669
There are still some people around here who want to answer genuine questions. Whether here, math, or rarely when it crops up as independent threads. The more people learn and are willing to seek learning, the better. Given how accessible information is online the state of ignorance, especially willful ignorance, is appalling. Please keep learning and please keep asking questions.
>Trigonometry, for me, is a hard concept to grasp.
It frontloads a lot of processes and jargon but it should "click" with a bit of practice. If you're having trouble with a particular resource use a variety of them, libretexts, youtube, khan academy, try to get at what you feel stuck on from multiple angles. The more diverse attempts at explaining you are exposed to the more likely you will understand what you were stuck on and why.

Exposure is the big thing.

>fell in love w/ a girl and had high hopes for 2 months
>no acne
>got crushed in early February
>acne came back with vengeance despite getting over her last month
Can someone explain to me what happened? I’m over her but my acne is back. When I was in love and had hopes over her, pining and what not, I cleared up 100%. What the fuck happened? I didn’t change anything about my sleeping or eating habits. Someone help

>>16060826
> correlation does not imply causation
the two events are not linked.

Bros
I'm training a neural net and measuring the metrics by taking the average precision
now this is all fine and it works but you can clearly see that from one save point to the next every like 10k iterations or so the AP can shift from 50 to 60.
So how should I report this? Like the uncertainty seems to be pretty large even though it shouldn't be as large? I'm pretty sure it's just the huge dataset with way too many classes fucking everything up but still
Should I just note the highest result? Or the last result? I know no one cares in ml about uncertainty, but what do you guys think I should do?

>>16061156
>you can clearly see that from one save point to the next every like 10k iterations or so the AP can shift from 50 to 60.
Not sure if you mean the precision varies up and down between 50 and 60, but that might just be your training method and your hyperparameters, Also a lot has to do with analysis of the data set before you start doing any training so you can understand the distribution of your classes. I would probably use a confusion matrix instead of precision if you have that many classes desu

>>16061157
>Not sure if you mean the precision varies up and down between 50 and 60, but that might just be your training method and your hyperparameters
sorry yeah my post wasn't clear. It does vary up and down. Basically it goes to 60 then drops down to 50 and kind of averages out to be 55.
Maybe the learning rate is the issue as it's just a constant during the entire training
My class distribution is total shit. Like 500 classes of which 400 have like 5 examples each and 100 have like 500 examples each. I did make a confusion matrix but obvi seeing things in a 500x500 confusion matrix is a bit shit. All I really saw was that the small classes that looked alike were often confused. I'll have to check again but I think a lot of errors came from a mistake in the dataset that couldn't be fixed without spending a large amount of time on it which I don't have. Basically 1/10 of the dataset is wrongly annotated :)
Is that what you mean with analysis or am I missing something? Thanks for your reply

>>16061161
try tweaking the learning rate or using an adaptive optimizer like Adam you are probably overshooting the optimum
what is your loss function? how does the training loss and validation loss behave?
you can also try training on a small fraction of the data and check if you can get >90 accuracy if not something is wrong

>>16061162
>what is your loss function?
I'm building on previous work so they've set this up and I'm adding new things to it. So I don't know the loss function we're using to be honest.
The validation and total losses do follow nice downward curves which are pretty smooth, no real up and down variations like the AP
>you can also try training on a small fraction of the data and check if you can get >90 accuracy if not something is wrong
That's a great suggestion, I'll keep this in mind.
What other suggestions do you have? Thanks for your help.

>>16060826
When you were in love, you may have changed your behaviour in a certain way, which affected your acne.

>>16059640
Rudin also requires that x_0 must be a limit point of the domain. Also, this definition is incorrect. |x - x_0| must be > 0.

>>16059640
Rudin also requires that x_0 must be a limit point of the domain, otherwise the "limit" can vacuously have multiple values. Also, this definition is incorrect. |x - x_0| must be > 0.

>>16061189
>Also, this definition is incorrect. |x - x_0| must be > 0.
What in the stated definition contradicts this?

let functions [math] f_{n}:X\to\mathbb{R},n\in\mathbb{N} [/math] be such that [math] \{f_{n}(x):n\in \mathbb{N},x\in X\} [/math] is bounded. Prove that [math] \\ \varliminf_{n \to \infty}\left( \inf_{x\in X} f_{n}(x)\right) \leq \inf_{x \in X} \left(\varliminf_{n \to \infty} f_{n}(x)\right) [/math]

>>16061281
For any [math]n[/math] and any [math]x[/math], [math]\inf_x f_n(x) \leq f_n(x)[/math].
Then also, for any [math]x[/math], [math]\liminf_n \inf_x f_n(x) \leq \liminf_n f_n(x)[/math].
Thus [math]\liminf_n \inf_x f_n(x) \leq \inf_x \liminf_n f_n(x)[/math] because your set is bounded.

> born in the wrong universe

>>>/fa/18038728
can anyone explain this

>>16061383
Nice. Hormones probably contributed, although I've heard there's historical cases of guys successfully breastfeeding even before them, when they needed to feed a baby and didn't have any other way. Suction on the nipples can trigger lactation. There's not really all that much difference between male and female nipples, the only reason men even have them is because it was simpler to evolve them for both genders than just one.

Let [math]A,B,C[/math] be events in a probability space. Suppose we are given [math]\mathbb{P}(A), \mathbb{P}(B), \mathbb{P}(C), \mathbb{P}(A \cap B), \mathbb{P}(A \cap C), \mathbb{P}(B \cap C)[/math]. Can we use this data to calculate [math]\mathbb{P}(A \cap B \cap C)[/math]?

>>16061465
https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle

>>16061161
What I'm saying is an assumption because I've not seen your data but 5 training example for 400 seems not enough to get a decent decision boundary unless your data is extremely different for each class. Is your model capable of classify any of those marginal classes at all? It's hard to help without the full context

>>16061468
But in order to use this formula I would have to know the probability of the union [math]\mathbb{P}(A \cup B \cup C)[/math] too - an assumption I can't make. Am I missing something obvious?

>>16060826
Maybe she made you less stressed? I've heard stress is linked to acne

>>16061485
That formula tells you the probability of the union since you know the individual terms.
Try to say P(ABC)=1-P(A^c or B^c or C^c) and then apply that formula to rewrite this second term in terms of stuff you know.

so normally when relating points we have to give them a position on an imaginary grid. this is fine for simple things that are close together (from a computer / floating point perspective) but it also means calculations aren't deterministic because the coordinates used have a precision level and different coordinates may lead to different results from a given calculation. even just translating 2 point from {(0,0), (0,1)} to {(0,0.3333), (0,1.3333)} can cause this despite being the exact same points related in the exact same way

so, why do we use this imaginary grid? shouldn't we be able to relate points to each other directly and do calculations based on that? For example, instead of saying point1 is at (0,0) and point2 is at (0,1), we can use the distance and say point1 is 1 unit away from point2 and point2 is 1 unit away from point1. If you add motion into the mix you can relate them as a distance equation d(t), and if you add more points (the 'grid' frame of reference points) you can solve a series of distance equations to move things around and relate them to each other right? This would also mean this system could be 'translated' anywhere in the original grid and calculations using it would remain deterministic because instead of positions updating, distance equations to other points in the grid get updated

I'm having some difficulty understanding that if f(x)=g(x) for all rational numbers and they're both continuous then f(x)=g(x) for all reals. I get that for all reals there exist a sequence of rational numbers that converge to it, but they're still not at x right? I get they converge do it, but they don't actually achieve the value of the real number.

>>16059773

>>16061562
You know that limits in Hausdorff spaces a unique right?
Take any real number p then you can find a sequence of rational numbers (a_n) that converges against p. Since f and g are both continuous, f(a_n) converges against f(p) and g(a_n) converges against g(p) but both (f(a_n)) and (g(a_n)) are the same sequence. So by the uniqueness of limits f(p) = g(p).

>>16061504
>>16061504
Anon forgive my stupidity but I don't see how this works out. We have [math]\mathbb{P}(A \cap B \cap C) = 1 - \mathbb{P}(A^c \cup B^c \cup C^c)[/math]. Now the formula expresses [math]\mathbb{P}(A^c \cup B^c \cup C^c)[/math] as a signed sum of stuff that I calculate *plus the probability of the triple intersection* [math]\mathbb{P}(A^c \cap B^c \cap C^c)[/math]. Computing this last summand in terms of the quantities that I am given is no easier task than the original one. What am I missing?

Imagine being from a respectable neighborhood

>>16061465
No.
Consider [math]A = \{1, 2\}, B = \{2, 3\}, C = \{3, 4\}[/math] and [math]A = \{1, 2\}, B = \{1, 3\}, C = \{1, 4\}[/math]
Then you can check that all of the values you gave are the same for both cases but [math]P(A \cap B \cap C)[/math] changes.

>>16061594
Ah whoops I had a senior moment. You can't do it without some extra information.

>>16061197
The fact that its not stated at all

How do we know that black holes have a "singularity" inside them? How do we know matter isn't just spun around the horizon like layers of an onion?

>>16061707
> How do we know that black holes have a "singularity" inside them?
We don't "know", the math of our best current theory of gravity says so. However no physicist actually believes there is a singularity, instead it's a region where the math no longer applies and we need a new better theory.

> How do we know matter isn't just spun around the horizon like layers of an onion?
We have no reason or evidence to think that is the case.

>>16061606
Thanks anon. Something seems odd, though. In the first case we have [math]A \cap C = \{1,2\} \cap \{3,4\} =\emptyset[/math] whereas in the second one [math]A \cap C = \{1,2\} \cap \{1,4\} = \{1\}[/math]

>>16061744
Right, terribly sorry, should be [math]C = \{ 3, 1 \}[/math] in the first one.

>>16061803
Yeah I'm totally convinced. This checks out. Thanks again

thinking of famous textbook
It has the Great Wave as a cover
I think it was a Princeton (or Cambridge?) book, university published anyway

it was about Chaotic Systems or something
Undergrad level I think

>>16061693
Why would it be?
It's implicit in the definition of absolute value. Why specify it again here?

>>16056951
I'm under the impression that this is wrong, but I am well aware that this could be due to my own stupidity

any anons know how the hell i1 leads i2 by 210 and not by 30 degrees?
Why would they additionally shift by 180, when the point of changing i1 into a cosine term was to create a workable equivalency

What branches of science/engineering should I study to become like Jinx ?

>>16062395
hormone therapy and gender transition, extensively

>>16062370
Because the amplitude of i1 is negative which means a 180 degree phase shift.

>>16062407
ahh ok, for some reason I thought the original amplitude direction was irrelevant
thanks anon

>>16062409
It comes from the fact: [math]\sin(-x) = -\sin(x) = \sin(x + 180^{\circ})[/math]

>>16062412
>degrees
fag

>>16062416
the original question used degrees...

>>16062412
thanks for the clarification
I was operating on the assumption that
-sin(A) = cos(90-A) which in a sense is true but I suppose ignores the context of the amplitude

thanks again anyway

Where can I find practice problems for subjects like GR and QFT? Especially for GR, I just want to get some practice applying the mathematics to different physical situations to gain familiarity with the process and computations. Most questions I've come across in textbooks for physics (and math) at this level is more proofs, derivations and explaining conceptually what's happening.

>>16062057
|x-x_0|=0 iff x-x_0=0

>>16062500
For GR, Sean Carroll—Spacetime and Geometry has a lot of exercises like this

>>16062543
But in that case, they're the same point, so continuity between a point and itself is trivial.

>>16062556
It's a definition of limits, not continuity. The problem isn't that it says the wrong functions are continuous, it's that it's wring about when discontinuous functions have limits.

Does coiling wire mean you have to increase the current proportional to the number of turns?

>>16062913
Faraday's Law of Induction has no explicit dependence on resistance, only on the number of coils. However the resistance of the wire will depend on its total length so that will affect the amount of current you can use.

is it possible to know it all + 1?

>>16063268
yes, take me for example

Is it a bad idea to do a double major in compsci and math?

I’m 28, and technically a senior double major in comp and math, like the retard above me wants to do. I haven’t been to school in a couple years, but have thought about completing it recently. Would it be a good idea?

I don’t know what I want to do professionally, currently run my own business and like that but don’t feel accomplished or like I’m intellectually fulfilled. I kinda wanna finish and go to grad school, but worry about just being annoyed with beaucracy. But I wouldn’t be financially dependent so maybe it’d be more chill.

I feel very stupid now that I don’t study so will be gettinf back into it.

>>16064390
Finish up your degree and get an internship somewhere. Stop approaching things with a defeatist. You aren't a retard. Think about what you want in life. Do you want a chill life? Go into a networking/sys admin or even web dev if you want a little bit of challenge. Do you want more challenge? Try to find an internship that would eventually transition into a.i or some other shit

>>16064409
Why do you call me a defeatist?

>>16064409
To be clear, I currently make more money than what those positions would offer me at entry level. Unless I was the meme 300k starting or work from home software dev position. I make about $100-150k between USPS wagie and business right now.

And I don’t think I’m ‘defeatist’, if I complete the credits the university must award me the degree. And if I’m a good candidate for another job, they’d higher me. I just don’t know if it’s a good move or worth it vs self studying.

I’ll probably do it though anyway, only a few grand anyway.

>[The Bosen-Einstein-]condensate entities were mass-produced by scientists working for the former regime, from molecular copies of the human test subjects' remains, whose peripheral nervous systems were hooked up to a central machine that keeps the functioning condensate copies alive.
>en.wikipedia.org/wiki/Spectral?useskin=vector#Plot

Scientifically speaking, how feasible is this?

>>16064166
No it's based
>>16064417
If you have only 1 year of courses left I'd complete your undergrad but idk about grad school
If you're self-employed it's ultimately about your own ego

>>16064532
It's meaningless technobabble

>>16064711
Why is it about ego? I want to work on more interesting stuff personally.

So hold up colour is just the wavelength of light after it hits molecules based on the arrangement of electrons? So when we see colour we are seeing what, energy/electrons? That's what it is? I know I sound like a dudeweedbro but it sounds so weird to me we're just seeing electrons and some arrangements of electrons like red freak us out.

>>16064868
Light is photons not electrons

>>16064905
Right, but my presumption was that the photons were interacting with the electron field and the electrons were sending the photons back. Or is it the nucleus

>>16064907
Yes with the electrons
The thing is though the atom is like 100 pm while visible light has a wavelength of 100s of nm, so you can't resolve the atoms at all, it's a complicated scattering process

>>16064916
>ough the atom is like 100 pm while visible light has a wavelength of 100s of nm,
This is the opposite of what I expected. I would've guessed atoms were far wider.

>>16064916
>so you can't resolve the atoms at all,
Do you mean individually as in how each photon interacts with each atom or?

>>16064931
yeah for these effects it makes more sense to view the light as a wave

>>16061330
Can you slap the limit inferiors/and superiors to both sides of an inequality like with a normal limit?

>>16064939
Yeah, if you already know it works for limits this follows since [math]a_k \leq b_k[/math] implies for any [math]n[/math] and any [math]k\geq n[/math], [math]\inf_{k \geq n} a_k \leq b_k[/math] so also [math]\inf_{k \geq n} a_k \leq \inf_{k \geq n} b_k[/math] and then you take limits.

>>16064936
So is it correct to say colour is seeing some quality of the energy configuration of the electron field or am I just missing something? I guess I view protons and neutrons as being 'hard' and electrons as being energy, so seeing a colour of energy seems weird to me because I view colour as a part of the physical properties....

>>16064956
Electrons aren't any more "energy" than protons/neutrons they are particles with mass just more delocalized

>>16064965
how the fuck do particles that exist in a probabilistic field have mass unless probabilistic field is a euphemism for 'we have no idea where they are exactly at any given time'.

>>16064968
> how the fuck do particles that exist in a probabilistic field have mass
having one such property does not negate also having the other.

> we have no idea where they are exactly at any given time
and you have essentially discovered why a theory of quantum gravity is so hard to come up with. how can you write an equation for gravity when you are uncertain where the mass that produces it is located or the other masses that interact with each other?

>>16065069
>here the mass
what is mass?

>>16064711
Why is it based?

>>16065145
why would it be a bad idea

>>16056951
what do i need to know to start learning brownian motion? I assume thermodynamics

>>16065537
Sure but actually almost all of the theory is based upon the probability of random variables.

Is there a simple group that is quasi-isometric to an extension of an infinite group by an infinite group? Is there one that isn't? Is there a non-simple group that isn't quasi-isometric to an extension of an infinite group by an infinite group? Is there an extension of an infinite group by an infinite group that is quasi-isometric to a simple group? Is there one that isn't?

If you wanted to hit the triangular arrangement of balls two times so that in both times the end result would have no visual difference, how accurately would all the variables need to be the same?

Things like, the position of the balls in microscopic scale, the force and angle of the hit, so on and so forth.

>>16065663
You have sort of answered your own question. All the variables have to be within the parameter range to produce the accuracy you desire.

>>16063268
No

I don't know anything about math so question about integrals in picture.

So my understanding there is a plane wave in here.

This article here has picture example of "bivariate joint distribution" in the second section on "conditional continuous distributions".

Now I know that the image is not about probabilities, but my question is whether the plane wave is analogous to how they talk about conditional probability distribution in that picture (yes, they use word plane there which is unrelated and coincidental).

Then this integral thing in image is telling you to sum all of the plane waves from all different points it is conditioned on (which not same as probability sum yes but the plane wave itself is obvious related to conditional probability since all the points on it are equal like equal probability distribution?)

So just question is if my intuition here is correct or way off.

>>16067083
shit forgot to link the article

https://en.m.wikipedia.org/wiki/Conditional_probability_distribution

Let me get this straight....
A magnetic "flux quantum" is a single line of mangetic flux, is that correct? Not just an abstraction, but an actual line of flux?

>>16067599
> A magnetic "flux quantum" is a single line of mangetic flux, is that correct?
No. Magnetic field lines aren't physically real, they are just a device for you to visualise the strength and direction of the magnetic field at any point. It's only in those specific superconducting structures that the amount of magnetic flux is quantized, otherwise it can be any value at all.

>>16056951
i want to get a head start on a linear algebra class by self studying over the summer. What books or youtube resources do you guys recommend?

>>16068481
Gorodentsev's Algebra books cover lots of linear algebra.

>>16068481
Proof-based or computational linear algebra?

>>16068508
thanks. Admittingly i did have to take a year due to some personal family issues so is there anything i should brush up on, before i took a break i did up to calc 3
>>16068573
proof based

anybody have the old /sci/ sticky image by any chance?
for nostalgias sake

>>16068584
The book is relatively self-contained and closer to linear algebra than just algebra (it only somewhat diverges in the second volume once you're done with representation theory). You should be fine even without much exposure to proof-based math (it'll be very hard in the beginning). Note that the author is Russian so you'll either hate or love the style, it's nonetheless a very rigorous book and probably even moreso than most linear algebra books. The exercises have hints at the end of the book, the problems don't and are also significantly more difficult. Coming from Calc, you should probably get used to leaving a few problems for later and continue reading (they are massive time sinks); the exercises, especially with the hints, should be doable and mostly enough. Feel free to ask questions about the contents on /sqt/, that's what I did (and still do) whenever I'm self-studying

When did 4chan stop showing poster counts in threads? What is this supposed to improve?
>>16068587
>>/sci/thread/3709882
>>16061963
https://bookstore.ams.org/gsm-197

>>16068662
>Feel free to ask questions about the contents on /sqt/, that's what I did (and still do) whenever I'm self-studying

appreciate it.

I also found this book through google, do you think i should just start with this just to get basic ideas down before attemping the russian book?
https://textbooks.math.gatech.edu/ila/

>>16068663
thankss

>>16068481
Linear Algebra Done Right
>>16068663
Today

>>16056951
>100 iq supposedly represents average IQ
>majority of world sub 100 IQ
Why

>>16068679
You can supplement whatever you like, as long as you learn linear algebra in the end. No need to read through any book linearly, cover-to-cover either. I personally just prefer having one or two main texts. One thing I forgot to mention though is that you should probably brush up on/learn basic mathematical logic, that is, basic proof methods, predicate logic, etc. since Gorodentsev only covers set theory. I also recommend studying proofs in-depth or else you'll have no way of knowing if yours are rigorous enough.

>>16068724
>basic proof methods, predicate logic

welp i was not taught any of this in my schooling. Maybe some basic geometric proofs when i was in highschool. Ive wanted to learn proofs for a while though so i dont mind spending a couple hours a day on them

>>16068699
>Today
Went on /g/ to see if there were any threads, checks out. Thanks.

What tools do you use to make pretty figures or diagrams ? I use matplotlib, tikz and powerpoint but I would like to know of other alternatives

>>16069088
• ggplot2 is hands down the best tool. Used to use Matplotlib for some niche cases but not anymore. If I needed that much manual control, I'd rather just use an image-generation package like Javis.jl or Pillow.
• Makie.jl (for 3D and especially 3D animations, https://beautiful.makie.org, though recently I've been using rayshader & rayrender with ggplot2 instead, but Makie.jl is much faster).
• draw.io
• Inkscape & Scribus (for complex visualizations with text).

>>16069088
>>16069131
See these examples of what is not very difficult to do in ggplot2 (if you have the visual taste) and would be annoying in Matplotlib:
• https://www.christophenicault.com/pages/visualizations/
• https://www.cedricscherer.com/top/dataviz/

>>16068663
thanks!
don't think it's the one I want tho, it definitively wasn't AMS :(
just the Wave

>When wind turbine blades get old what's next?
https://www.bbc.co.uk/news/business-68225891
>Made of fibreglass they are covered with a tough epoxy resin, designed to withstand years of hammering by the elements.
>These durable qualities make breaking down the blades for recycling a tricky process.

Why not cut them into "planks" and use them to build houses?
Would this be feasible?

I have a question for physicists: Is the solar system an inertial reference frame? Technically, gravitational forces are exerted on it by the heavy objects in the center of the galaxy, which do accelerate it. On the other hand, it moves in a circular trajectory around the center of the galaxy, which causes a constant velocity. So what is it?

>>16070145
>it moves in a circular trajectory around the center of the galaxy, which causes a constant velocity.
...in a constantly-changing linear direction, meaning that the velocity is in fact not constant

>>16070153
Disregard the forces form objects nearby and treat the center of galaxy as a point mass. In this idealized picture the velocity should be constant, even though there's an acceleration.

>>16070157
It's in a circular trajectory.
There is no point at which its velocity is constant. If it were, it'd fling off into the abyss.

This thread is now a Barkon Approved Thread.

>>16070159
The absolute value of the velocity is constant is constant. So how do you explain conservation of the angular momentum in the solar system, for example? Necessary condition is that the solar system is an inertial reference frame, right?

>>16070163
>So how do you explain conservation of the angular momentum in the solar system, for example?
Properly speaking, it's non-inertial, but the acceleration is small enough that it is by-and-large negligible. Especially if we're considering gravitational influences from other nearby objects as being negligible

>>16070171
Thanks

>>16069671
Asking for too much there, anon.

Let [math]f: \{0,1\}^\mathbb{N} \to \mathbb{R}[/math] be continuous. For all [math]N \in \mathbb{N}[/math], define [math]a_N = \frac{1}{2^N} \sum_{s \in \{0,1\}^N} f(s_1, s_2 \dots s_N, 0, 0, 0, 0\dots)[/math].

Is [math](a_N)_{N=1}^\infty[/math] Cauchy?

>>16070750
Here is a fun idea (bit sloppy maybe): take an infinite sequence of independent Bernoulli(1/2) random variables, [math](B_n)[/math].
Then, writing [math]X_N=(B_1,...,B_N,0,...)[/math], you have [math]a_N=\mathbb E f(X_N)[/math].
Now, any number [math]x\in[0,1][/math] has a unique (if you ignore infinite repeating decimals of measure 0) binary representation as [math]x=0.b_1b_2...[/math].
Then we can write [math]\frac{\lfloor2^n x\rfloor}{2^n}=0.b_1b_2...b_n[/math].
So, we can just as well look at [math]f:[0,1]\to \mathbb R[/math], and [math]a_n=\mathbb E f(\frac{\lfloor2^n U\rfloor}{2^n})[/math], where [math]U[/math] is uniform on [math][0,1][/math].
Your function is cts on the compact interval [math][0,1][/math], so attains a maximum [math]M[/math].
By dominated convergence and continuity again [math]\lim_n a_n = \mathbb E f(\lim_n \frac{\lfloor2^n U\rfloor}{2^n})[/math] and note that this inner rv converges almost surely to [math]U[/math], so that [math]a_n \to \mathbb E f(U)[/math], so it must be Cauchy.

>>16070171
To put some numbers on this anon's answer:

The Milky Way has a diameter of [math]9.5 \times 10^{17}\ km[/math] and spins at around [math]200\ km/s[/math]. The magnitude of the centripetal acceleration is given by [math]a = v^2/r[/math], so plugging in the numbers for Milky Way gives you the quoted range for the acceleration of [math]10^{−8}\ m/s^2[/math] to [math]10^{−12} m/s^2[/math]. To put that into perspective the centripetal acceleration of the Earth's rotation is [math]3.39 \times 10^{-2} m/s^2[/math] at the equator and that is ignored in calculations too.

What speed would a 160pound/72kg guy riding an unlimited speed motorcyle on a P60 sandpaper platform have to be, to completely disappear after the motorcycle comes to a sudden stop but he continues onward onto the sandpaper thus being erased?

anyone got videos like this:
https://www.youtube.com/watch?v=rJKmc4PVdh4&t=521
but for the scales beyond C and D?

>>16070809
Thanks very much kind anon, I'm sure your solution works, it's just that I don't know much about all the stuff you mentioned. I would love to see an elementary approach to the problem if you happen to think of one.

let [math]f:\mathbb{R} \to \mathbb{R}[/math] be a continuous function with a period of 2 so [math]f(x)=f(x+2)[/math]. Prove that [math]\exists x_{0}[/math] such that [math]f(x_{0}+\pi)=f(x_{0})[/math]

>>16071765
Are you sure that's the question? You can't have a doubly periodic function only using reals.

>>16071801
that's the question

>>16071765
Set [math]g(y)=f(y)-f(y+\pi)[/math].
Then [math]\int_0^2 g(y)dy=0[/math].
If [math]g[/math] were always 0, you'd have your equality.
Else, if [math]g[/math] were always strictly positive or negative, the above integral wouldn't be 0.
So then there must exist distinct points where [math]g[/math] takes positive and negative values, so in between it must be 0 by continuity.

why in the scalar product we multiply the projection of a vector to another one, with that one magnitude's? what does this mean geometrically?

David J. Griffiths - Introduction to Elementary Electrodynamics, page 62: where does the cos θ come from?

>>16072674
It shows you where the angles comes from in diagram (b). You have to sum the strength of the fields produced by the two charges at the intersection point.

>>16071765
[math]g:= x \mapsto f(x +\pi) - f(x)[/math] is also 2-periodic and continuous so if it doesn't vanish it has a constant sign (wlog >0) and besides there is [math] m \in [0,2][/math] such that [math]g(m) = \min\{g(x) \mid x \in [0,2]\} = \min\{g(x) \mid x \in \mathbb R\}[/math]. For every integer [math]n[/math], [math]f(x + n\pi) - f(x) \geq n g(m)[/math] which is impossible because, being continuous and periodic, [math]f[/math] is bounded.

>>16070750
What do you mean by continuous over {0,1}^N? It's a discrete domain

>>16072696
I don't get it. What is the connection between cosθ and the unit vector?

>>16072674

Seems like it is demonstrating the electric field equation by using it as part of a simple trig equation. If you are still struggling to understand the trig part, then, well, I don't know how to tell you this, but you are ngmi cuh fr fr

>>16056951
Thanks for using my thumbnail OP, cool to see that someone remembers my shitpost

>>16072653
<a,b> = |a||b| cos t

cos t = adjacent / hyp
so adj = hyp cos t

then the projection gets multiplied by the magnitude of the other (if the other was unit length you would get just the projection without the extra multiplicaiton)

lazy/fast explanation but...

>>16073344
as for why
I think it is to make the dot product take into account the length of the other vector somehow

>>16072973
> What is the connection between cosθ and the unit vector?
The two unit vectors are along [math]\boldsymbol{E_1}[/math] and [math]\boldsymbol{E_2}[/math]. You want the vertical electric field vector pointing along [math]\boldsymbol{E}[/math]. Hence the angle [math]\theta[/math] between them.

>>16072788
[math]\mathbb{N}[/math] denotes the set of natural numbers. The space [math]X = \{0,1\}^\mathbb{N}[/math] of infinite binary sequences is given the product topology, which is compact (and definitely not discrete). It's induced by the (ultra)metric [math]d(x,y) = \exp(- \min \{n : x_n \ne y_n\})[/math] if [math]x\ne y[/math] and [math]d(x,y) = 0[/math] otherwise.

How do you prove that the function f(x)=1, when x>0 and f(x)=-1 when x<0 is an elementary function?

>>16068723
>he doesn't understand what average means
I'm sorry anon, but I think you're sub 100 IQ

>>16074006
[math]sgn(x) = \frac {x} {|x|} = \frac{x} {\sqrt { x ^2 } }[/math]
since it can be represented as the composition of elementary functions, it is elementary

>>16068663
Probably they want to save on storage.

What's cheaper:

12 x 355 ml @ 7% alcohol content for $30

or

6 x 473 ml @ 5.5% alcohol content for $13

?

>>16072775
I get that f(x+pi)-f(x)>=g(m), just not how you can stick that n to both sides. And how does this imply exactly that f(x+pi)=f(x)?

>>16077306
in terms of fluid in general, the former is about 1.5x the per-unit price of the latter
in terms of alcohol content specifically, that goes down to being about 1.2x

>>16077340
Which one is better value tho?

>>16077346
there's more to quality than just how much you're getting
...That being said, if that's all you're interested in, the second one is your better option

>>16077349
Thanks. I'd drink horse urine if it was cheap and got me drunk.

Not really, but still.

>>16077349
I ended up getting the FANCY whiskey. A whole $2 more, I'm almost broke.

>>16056951
[topology][metric]
What does a induced metric topology mean? I don't even understand the information given in this question. Is there any video or pdf I can read understand?
And any hints on the a)?

Where do you find communities of people who discuss intelligent things instead of jerking off over whether free will exists all day?

How to isolate a drug from a bunch (read few hundred) transdermal patches? Like how to get rid of all the other crap? It's just for fun with my spent estrogen patches

>>16078408
If only there was a tool that existed where you could search for things on the internet, like forums for the topics that interested you.

>>16078724
That doesn't work. That's what the likes of you do to find such communities, and as a result they're full of tedious morons.

>>16078408
Your best bet is to find blogs by competent programmers or mathematicians who also like to blog about economics and history, and pick those who host small Discord groups. Naturally, you already have to be interested and competent enough to read such blogs, but if you aren't, you have no place diluting such communities.

How many stars would you say are in our local bubble? 200K, 1B?
https://en.wikipedia.org/wiki/Local_Bubble

>>16078728
> find blogs by competent programmers or mathematicians who also like to blog about economics and history
> you already have to be interested and competent enough to read such blogs, but if you aren't, you have no place diluting such communities
> and as a result they're full of tedious morons
oh the irony

>>16078740
Just estimate the number of galaxies in the bubble then use the fact there are 100 million stars in the average galaxy.

>>16078208
This is in your textbook (Munkres, section 20 page 119 on metric topology)

>>16068742
most introductory analysis books (Amann Escher, etc.) contain an intro to proofs and set theory. You should know how to express arguments in predicate logic, useful equivalences, like [math]\neg (\forall x \exists y: P(x,y)) \Leftrightarrow (\exists x \forall y: \neg P(x,y))[/math], etc. Imo, there's no reason to specifically go through a book on proving stuff, you'll learn more than enough proof techniques from carefully deconstructing proofs in textbooks. Just knowing why a proof works from a logical standpoint and being capable of working out the logical statements in one is very helpful. What's also often the case is that you're confronted with a complex problem that you can break down into many easy-to-prove statements or cases, or find an equivalent or sufficient claim to the problem. I think Frege once described logic as "mental hygiene" and he couldn't be more right

How much differential calculus and analysis can be transferred over to unitary commutative rings?

im extremely bored

>>16078942
>¬(∀x∃y:P(x,y))(∃x∀y:¬P(x,y))

so this means : Not every x exists for all y's in set P(x,y) which is the same as saying every x for all y does not exist in set P(x,y) ?

>>16079583
NTA
You missed the IFF "if and only if".

Not all x where y exists are points (x,y) "if and only if" there exists some x for all y such that there is no point (x,y)

So "it isn't raining if and only if it isn't wet" or something I'm bad at forming analogies. Pretend it's analogous. Point is "thing doesn't exist if and only if property doesn't exist".

>>16079583
"It is false that for every x, there exists a y such that P(x,y) is fulfilled" is equivalent to "there exists an x such that for every y, P(x,y) is false". The point I'm trying to make is that negation switches the quantifiers.
Also useful to know are formulas like [math]\big(\forall x\in X: P(x)\big) \Leftrightarrow \big( \forall x: (x\in X)\Rightarrow P(x)\big)[/math] but [math]\big(\exists x\in X: P(x)\big) \Leftrightarrow \big( \exists x: (x\in X)\land P(x)\big)[/math]. From that, you can, for instance, derive [math]\neg\big(\exists x\in X: P(x)\big) \Leftrightarrow \big( \forall x: (x\notin X)\lor \neg P(x)\big)\Leftrightarrow \big( \forall x\in X: \neg P(x)[/math] (because [math] (A\Rightarrow B) \Leftrightarrow( \neg A\lor B[/math]. You can show that by comparing their truth tables, for instance) and similarly [math]\neg\big(\forall x\in X: P(x)\big) \Leftrightarrow \big( \exists x: (x\in X)\land \neg P(x)\big)\Leftrightarrow \big( \exists x\in X: \neg P(x)\big)[/math]. Note that [math]x\in X[/math] can be replaced by any arbitrary set property, so effectively, we've shown that negation also leaves any additional property of the quantified element alone.

>>16073353
this is actually my question. For example, if a=b then the <a,b>=a^2=b^2 but what does this mean?? Why not divide by |b| if we wanted to know how much of a is projected to b?
To my understanding the scalar product only makes sense when you're projecting on the normal vector since |n|=1

>>16080815
You can turn definition into one only about the unit vectors.

[math]\mathbf{a} \cdot \mathbf{b}
= \|\mathbf{a}\| \mathbf{\hat{a}} \cdot \|\mathbf{b}\| \mathbf{\hat{b}}
= \|\mathbf{a}\| \|\mathbf{b}\|\ \mathbf{\hat{a}} \cdot \mathbf{\hat{b}}[/math]

And given geometrically the projection of one unit vector onto another is simply the cosine of the angle between them, then you get:

[math]\mathbf{a} \cdot \mathbf{b}
= \|\mathbf{a}\| \|\mathbf{b}\|\ \mathbf{\hat{a}} \cdot \mathbf{\hat{b}}
= \|\mathbf{a}\| \|\mathbf{b}\|\cos{\theta}[/math]

>>16080950
let me explain better what i mean.
i understand all the projection stuff, i want to know what kind of physical/geometrical meaning can we give to the scalar that we get as a results. I want to understand if this quantity is just a number derived by observations or if it actually measures something.
in my example above, if a = b then the scalar product is a^2 (or b^2) which is a square, what does this figure mean in this context?

>>16080962
Well you can _define_ the length of a vector as the square root of the scalar product of the vector with itself. That is a general definition that also applies to higher dimensions and also complex numbers (with a slight tweak - the vector and its complex conjugate).

>>16080987
a bit circular innit?
so in conclusion i have to accept the scalar product as it is

>>16080997
> a bit circular innit?
Not really. As long as you understand the projection stuff then it simply follows from that. [math]\mathbf{a} \cdot \mathbf{a} = \|\mathbf{a}\|^2[/math].

> so in conclusion i have to accept the scalar product as it is
Yes. It is a definition. Like much of math it is a tool with many useful properties.

>>16080962
>or if it actually measures something.
it measures similarity in directions while taking into account magnitudes

some vague intuition I have of what taking into account magnitude means (it may be wrong) is
>turn the measurement unit for the similarity into the unit of lengths of the projected-onto vector
and because of the symmetry of the dot product this works in both "choices" of projected-onto

>>16081014
>Yes. It is a definition. Like much of math it is a tool with many useful properties.
if i were to learn math like this i would feel like a monkey, but it would be much easier.
actually i think i should change approach. i always have trouble starting studying because of the immense stuff i have to know everything about before.
it's just that i have a feeling of discomfort when i'm reading/doing something without fully understanding the fundamentals of it.

>>16081023
You aren't that unusual thinking that way. However you are trying to purely look at the scalar product geometrically, which I'm not sure works. To fully understand it you also need to look at the component definition and then why both definitions are equivalent.

>>16081036
>You aren't that unusual thinking that way.
what should i do about it, ignore the holes in my knowledge and redefine concepts as needed? for example i took a linear algebra course but i didn't think much of it and i just studied to pass it. only now that i see what's it used for i want to study it all over again.
of couse i will study it faster but you can see that i can be a massive waste of time if i do it for all the subjects i am intersted in.
>However you are trying to purely look at the scalar product geometrically, which I'm not sure works
all this questions came to me after a physics lecture where we derived the scalar product in some integral (i don't remember which one).
maybe that's why i have this stubborn idea that there's must be some meaning under it.

>>16081045
> all this questions came to me after a physics lecture where we derived the scalar product in some integral
That wouldn't happen to be quantum mechanics would it? The inner product / dot product / scalar product features heavily in that.

>>16081052
lol no i'm much dumber. undergradute class mainly about electromagnetism.

i solved physiques :D

>>16056951
Why is lseast squares method called least squares method?

>>16082024
>lseast
least*

>>16082024
Because you're minimizing some square function. Instead of minimizing the total distances of your points to a line, you're minimizing the area of the squares with as endpoints the points and the line, as in picrel.

>>16082034
oh as in geometical square distance?

>>16082039
It's not the usual distance between two points, but rather an area, like a square, that you're minimizing, yes.

>>16082042
Oh is its not necessarily tied to a graph plane?

>>16082053
I don't know what you mean by that.

>>16082058
The square are their own entity that shrink or enlarge as the point travels closer or farther away from the mean line. They don't correspond to a graph.

>>16082034
That's not quite right. It's minimizing the squared error from the regression line, which is the vertical distance squared.
There's another regression technique that uses the perpendicular distance, but I don't know one that works based on least diagonal distance
https://en.m.wikipedia.org/wiki/Deming_regression

Do any chemists out there know what kind of powder is used for pH testing? I got pic related and it came with 10 little power caplettes. I'd like to do more testing and not have to run out and buy another fucking kit for $15.

>>16082098
colours just look like ordinary litmus

how fucked am I if I have a history of ADHD, severe depression and stress issues and I start hearing noises before going to bed?

I think its over, at least i wont feel bad about not having friends i guess

>>16082507
>how fucked am I if I have a history of ADHD, severe depression and stress issues and I start hearing noises before going to bed?
When you're tired you can experience hallucinations that also keep you stressed and awake more. So, regressing to a more survival state where sleep is bad which tends to be a bit of a downward spiral. It probably isn't schizophrenia or anything like that since it superficially sounds sleep related. I don't know what you can do to help yourself out any, anon, but you don't want it to spiral out of control. Worst case scenarios are things like nightmare disorders. So if you couple that with the ensuing insomnia, the nightmares torturing you, the depression, and making ADHD far worse from the added lack of sleep and quality sleep, shit sucks bro.

If you can get any kind of treatment or help finding treatment at all, do so. You've got to care about yourself enough to care to get better if you can, and if you've nothing else. If the social problems are ADHD related sometimes medication can fix that on its own, other times there's an adjustment period. If coupled with other comorbidities, like childhood abuse or neglect, you may have CPTSD (more recognized outside America) compounding all of your problems.

I don't see many people who are "worst case scenario" in that area, but when I do they also tend to be childhood abuse victims. So I'm just shotgunning "here's where you likely are, to here's where the worst end result can get, and here's who is most likely to experience that without help". So, no help and no medications. Alcohol or other substances will, of course, make all of that infinitely worse.

>>16082191
Cool! Thanks anon!

>>16082098
>10 pH strips for $15
damn, what a steal

1. Does pressure (such as a sub undersea) continue to weaken and damage a "hull" of something overtime and eventually implode it given enough time even if the hull is strong enough to withstand the given pressure? Or will it be able to withstand the pressure eternally (ignoring factors like water/air degrading a hull or other things, all variables but pressure ignored)?
2. Since the moon is tidally locked to the earth, would that theoretically make it easy to lower or heighten its orbit by putting boosters on its retrograde side? I assume the amount of power needed to do something like crash it into the earth would be absurdly unpractical. Putting Mars in a closer orbit to the sun even less practical due to higher mass and no tidal locking.
3. In calculating a translunar or transplanetary path of a ship from earth orbit to the moon or say mars, how much does the gravity influence of the sun, other planets, and other bodies factor into the math of calculating an accurate path? I assume most things, except perhaps the sun, would be negligible?

>>16082799
1) Ignoring all variables you state then yes, it would last forever.
2) The amount of tidal acceleration causes the rotation speed of the moon to change by nanoseconds per day. If you have enough rockets to move the moon that is going to be an insignificant effect, essentially zero in any calculations.
3) You are talking about chaos theory. Over short periods of time or distances the perturbations from the other bodies will have negligable effects and they might be perfectly fine to ignore. Translunar journeys wouldn't care. But as you project the calculations further forward those errors will just keep increasing until they dominate so you have to factor in as many bodies as you can.

>>16082077
The perpendicular distance is the least diagonal distance from a straight line.

>>16056951
What does 26 + 6 equals?

I have my thesis presentation tomorrow
it's not even finished lol
I have a script and I know what to say and I'll finish up the presentation now
I'm actually very nervous
I've done a reasonable job, my advisor trusts that I'll do fine, my story is more than enough to fill the time maybe even too much, and I've been tacitly informed that the committee members are kind and will probably let me pass no matter what
still though I feel nervous as hell
do you think I could fail?

>>16083095
It doesn't matter what the outcome is. The important thing is why the outcome is.

>>16083095
in STEM fields 99% of thesis presentations result in a pass, if they want to fail you they won't allow you to present

how many references is too many for a publication? most of the articles im reading in my niche have between 130 to 170 references per article.

Im taking comp sci for the first time in a few months. The language we will be using is java. What books do you guys recommend so i can selfstudy before classes start?

Also what would be the best way to approach programming? I ask this because i attempted to teach myself in the past but nothing really clicked

>>16083216
I vaguely remember reading a PhD thesis with over 1000 references and there's a genre of huge comprehensive literature reviews with 50+ authors that also easily can have like 1300 references
Most venues will have a page limit, how much of that is references is up to you

If Maxwell's equations predicted the speed of light is constant, what other predictions are there like this from quantum physics and general relativity? Or most of them?

>>16083749
General Relativity predicts that building time machines is possible.

>>16083777
Are there any that we haven't observed yet that it should be possible to test? For example Maxwell's equations only require being able to move to test the speed of light being constant. We don't know there should be a way to test if time machines can exist since we don't know there is a possible way to construct one.

What do I read to recognize when I can apply integrals to questions I'm curious about? Is there like a compendium of estimation questions à la "Street-Fighting Mathematics" or "Guesstimation" or "The Art of Insight in Science and Engineering" but about integration specifically, in biology, chemistry, and so on? Like, I don't want or plan to find antiderivatives, I just want to be able to recognize when I can shove a function or probability density into a numerical integrator or Monte Carlo sampler and get an answer back.

debunk the idea that the "observer" or the act of "observation" or "having of information" is what causes wave function collapse
I know the universe is neutral and uncaring but people present these ideas as if our act of observing or knowing information (IE which way information on a delayed choice quantum eraser) rather than being a result the measuring device or measurement in the first place

>>16083858
i like many worlds because theres no wave function collapse.

I've been using Professor Leonard for learning my math material up until Calc III. I have one last math class I will need to take next semester: Linear Algebra. Professor Leonard has been basically carrying me through this, so not having him as a resource for my last math class sucks.

Are there any good Linear Algebra lectures on YouTube?

>>16083892
3b1b

>>16083892
https://www.youtube.com/playlist?list=PL44B6B54CBF6A72DF

What am I in for?

>>16056951
What would happen if we sent an air fryer 2 millennia back in time?

>>16084008
Everyone would end up gay.

>>16084002
unironically a good show. They don't make them like that anymore...

Could someone help me understand why the sum turned into (24*36)-54*||B||2?

>>16084188
Are you sure that isn't a typo as I have no idea where that (24.36) term comes from?

What are the best things to do to increase baseline testosterone and IQ / executive function? My anecdotal evidence, which I trust above all, suggest that lots of math/problem solving, fasting, reading (and avoiding scrolling), adequate high quality sleep and exercise are totally yuge here. Also it's sort of nebulous but in general keeping a tidy environment and staying on top of basic things like cleaning my room etc are equally important.

I assume those are the basics, based on my experience, but am open to any suggestions.

>>16084229
>keeping a tidy environment and staying on top of basic things like cleaning my room etc are equally important.
I guess I mean to say that 'habits' let you abstract over that mundane shit, to free up your executive function worry about more important things. I've been habitfying what I can. But the lack of an automated and generative agenda system has been a real bottleneck.

>>16084223
https://www.stumblingrobot.com/2016/04/28/compute-length-vector-satisfying-given-relations/

I got it from here.

Say I have a rod of length L free to move in space and I apply to forces at its to ends, of equal modulus and direction. So, the rod won't rotate because M (sum of torques)=0 but it will move at a certain speed. How do I write F=ma in this situation to find this speed?

>>16084008
No one would be able to power it. It would probably end up lost and broken, but possibly someone would keep it as a decoration.

>>16084257
Ah, that makes it clearer. You did not post all the information, specifically the first line of the question which states: [math]\|A\| = 6[/math].
[eqn]\sum_i^n \left(24 a_i^2 + 36 a_i b_i - 36 a_i b_i - 54b_i^2\right) = 0 \\
\sum_i^n \left(24 a_i^2 - 54b_i^2\right) = 0 \\
24\sum_i^n a_i^2 - 54\sum_i^n b_i^2 = 0 \\
24\|A\|^2 - 54\|B\|^2 = 0 \\
24 \cdot 36 - 54\|B\|^2 = 0[/eqn]

>>16084257
Ah, that makes it clearer. You did not post all the information, specifically the first line of the question which states: [math]\|A\| = 6[/math].
[eqn]\sum_{i=1}^n \left(24 a_i^2 + 36 a_i b_i - 36 a_i b_i - 54b_i^2\right) = 0 \\
\sum_{i=1}^n \left(24 a_i^2 - 54b_i^2\right) = 0 \\
24\sum_{i=1}^n a_i^2 - 54\sum_{i=1}^n b_i^2 = 0 \\
24\|A\|^2 - 54\|B\|^2 = 0 \\
24 \cdot 36 - 54\|B\|^2 = 0[/eqn]

>>16084380
Simply sum the vectors of each force. In this case that would be the same as a force twice the magnitude pushing at the centre of the rod.

>>16084002
this book doesn't fuck around
there's a lot about soft matter, if you want to do semiconductors or something electronics related I'd recommend Kittl instead

>>16084468
Thank you :)

>>16084188
You know that by definition sum{a_i^2} = ||A||^2 = 36 and so from the first term you can factorise the 24 out of the sum to get 24 * sum{a_i^2} = 24 * 36. The second and third terms cancel. The 4th term becomes 54 * sum{b_i^2} which is 54 * ||B||^2. Send more context next time.

I have a Ti-84 with python on it. i never really bothered using the python abilities on it, as its never really been neccessary. But recently i realized. My school doesn't allow CAS calculators, but it does allow this one for tests. Couldn't I theoretically program or (more realistically) import what is effectively a python powered CAS to cheat on exams? Has this been done before? Where can I learn more about this?

>inb4 dont cheat
I really dont have to. I havent cheated once so far. But it would certainly make tests less stressful/easier. At the very least as a way to skip the easy filler questions. A lot of the quizes are really just activites in endurance and meticulousness rather than a challenge of your theoretical knowledge

I'm getting ready to expose my first hologram. My setup is using a prism as a beam splitter for the laser, and one of the beams is significantly more luminous than the other. Should I use the brighter beam to hit the object being imaged and the dimmer beam as the reference beam? Considering that not all of the light from the object beam will even hit the holographic film (since some will scatter) I would think that using the brighter one might be better off, so that way there will be closer to an even mix of light from the object beam and light from the reference beam hitting the holographic plate. Thoughts? Anybody have any experience making holograms?

>>TLDR: Im making a hologram and one of the 2 beams is significantly brighter than the other, should I use the brighter beam as the object or reference beam?

>>16084827
back in the day i programmed my ti-83 to calculate basic shit like the quadratic formula so i have an easier time checking my answers. So i dont see why you couldnt program it

Ti has some python guide books on their website:

https://education.ti.com/en/guidebook/details/en/1424CF4F539A4DBB9145E2AA89F0FF54/ti-84-plus-ce-python

>>16084827
Well you would have troubling installing standard packages like sympy since the Ti-84 only has a few MB of flash. That is nowhere near large enough. You would need at least 1 or 2 GB as a minimum.

>>16084853
Theres a language called micro-python designed to run on small microcontrollers like a microbit or an arduino (although the arduino doesnt use it natively, Im sure you could make it work somehow). Its basically the same thing as python, but stripped down in some ways and designed specifically for devices with very little memory to spare, so that might be useful?

>finished my masters thesis
>got told during evaluation I was subpar because I took too long for my results and I had a bad planning
>they did tell me my results weren't bad and I did most things okay but just not great
How bad is it to have a below average thesis?
It kind of feels like I failed

>>16084862
> micro-python
That looks to be just the basic interpretor. It doesn't include (or maybe even support) other 3rd party libraries or packages.

>>16084901
You either pass or fail. As long as you pass it does not matter to anyone else.

>>16084915
Dats rite. I blind of that. But I have what to do in code now I just do that code. Let's see if it works. I know I'm doing all of it now.

>>16084901
You have a master's degree now, and no one will ever know the evaluation comments except you and the people who gave them. If you do go on to a phd just take those comments as constructive criticism. If you don't, just forget about it

>>16084921
-He kisses us like Billy kisses him-

>>16084924
You don't know you know that you cannot know nuffin

>>16084919
Yeah I guess
on the one hand it feels so good to be done
on the other hand their criticisms were fair
all I can do is do better
>>16084921
yeah you're right
Although my grade wasn't the best
will a company care if I get a below average grade you think?

>>16084970
Not sure what country you are in but all the ones I know a master's thesis isn't graded. You get the degree, or not. That's it.

>>16084992
huh in Europe everyone gets a grade for their thesis

I have a couple of basic questions. If I have a homogeneous rod of length L, free in a vacuum, and I apply two forces of equal magnitude F perpendicular to the rod at its ends, it will translate as if a force of 2F were applied at its center of mass, correct? And if the two forces have only the same direction perpendicular to the rod and the same direction but let's say the magnitudes are F1=F and F2=0.5×F, and are always applied at the ends, can we say that (ignoring rotation around the center of mass) the center of mass moves as if a force of 0.5F were applied to it?And if the two forces are not perpendicular to the rod, can I always decompose them into parallel and perpendicular components and treat them as if they were applied to the center of mass? (In all these cases, I am not considering rotation).

>>16085098
> the center of mass moves as if a force of 0.5F were applied to it?
No. It will move as if as force of F_1 + F_2 was applied to it, so 1.5 x F. The amount of linear momentum has to be conserved.

>>16085151
Yeah sorry im retarded. But now consider this case; on one end I apply a force = F (perpendicular to the rod etc), on the other end I apply a force of 0N, and now the rod is only rotating and its center of mass is still. Or am I wrong and does it still move while it's rotating?

>>16085161
It will move and rotate. You will generate torque but that does not change the amount of force you have applied perpendicular to the rod.

>>16085169
Okay thanks, so to sum it up if I only care about how the center of mass of a rigid body will move I can treat all forces on the rigid body as if it was a point mass positioned in the center of mass of the rigid body, correct?

>>16085180
Yes. I think your confusion partly arises from the fact it will take more energy to produce the same perpendicular force in the second scenario since it will be split between the kinetic energy of the linear motion and the rotational kinetic energy.

>>16085202
Thanks dude

>>16085151
nta but how can linear momentum be conserved under a force..
F = dp/dt
I would say both sides have 0.5F so that's a forward motion
then on top of that one side has a 0.5F motion which should result in a rotation
>>16085169
why would it move at all?
>>16085202
>it will take more energy to produce the same perpendicular force in the second scenario since it will be split between the kinetic energy of the linear motion and the rotational kinetic energy.
>take pen
>lay flat on table
>push one side and keep pushing harder
>aka F
>rotation occurs
>center of mass moves in rotation
but there's no linear motion afaik
only rotation of the mass around the other edge of the rod
there's only angular momentum

>>16085923
>>16085923
>>16085923

new thread