'Previous thread is actually here >>16131491';

'I dont understand the concept of complex manifolds or manifolds with metrics that are not euclidean. For me, everything must be euclidean and embedded in some higher dimensional space. I dont understand intrinsic curvature';

'I've got some stupid questions.

Is there any experimental proof of space expansion/hubble constant? or do we just assume it with seemingly linear redshifting of galaxies?

Why are there no live-feeds of orbiting satellites of other planets/moons? Is it because the shitty data transfer? Isn't the moon close enough for it to be possible? or is energy usage an issue?';

'>>16159237
>Is there any experimental proof of space expansion/hubble constant? or do we just assume it with seemingly linear redshifting of galaxies?
I'm not sure if I understood your question right, but redshift is a direct indicator of velocity so this is how Hubble's law is determined, because it's very hard to directly measure the velocity of a distant object

>Why are there no live-feeds of orbiting satellites of other planets/moons? Is it because the shitty data transfer? Isn't the moon close enough for it to be possible? or is energy usage an issue?
both factors come into play but data rate is the most restrictive one
your typical spacecraft transmits data at a rate of two-digit bits per second, it would take at least a year to get a single second of video footage
I suppose the Moon could be feasible given the distance but that would require big enough antennas on both ends of the transmission link';

'>>16158770
I'm looking for some free software that can display a graph of the relationship between different authors and their publications to find citation rings.

I've been looking into the work of a particular author which I'm considering using, but nearly all the papers on the topic, it seems, are coauthored by him. And I'm a bit skeptical and don't want to waste my time in the long run.';

'>>16159276
Thanks for answering
>but redshift is a direct indicator of velocity
Is there experimental proof of velocity induced redshift/blueshift? or is it again something we assume to be true because of the doppler shift with sound?
>>16159276
>your typical spacecraft transmits data at a rate of two-digit bits per second, it would take at least a year to get a single second of video footage
sheesh';

'If I know these two quantities:
[math] \langle \alpha |\hat H| \alpha \rangle[/math]
[math] \langle \beta |\hat H| \alpha \rangle[/math]
Is it possible to calculate:
[math] \langle \beta |\hat H| \beta \rangle[/math]
? If so, how?
[math] \alpha [/math] and [math] \beta [/math] are wavefunctions and [math]\hat H[/math] is a regular Hamiltonian.';

'>>16159338
no, think about H as a matrix and these quantities as matrix elements, knowing some doesnt tell you what the others are. To a point, because if H is Hermitian then there must be some relations among the matrix elements, and knowing enough might tell you what the others are';

'>>16159305
>or is it again something we assume to be true because of the doppler shift with sound?
doppler shift works the same way for both electromagnetic and sound waves, and in fact the relativistic Doppler effect has been tested in laboratories a number of times
https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment?useskin=vector';

'>>16159346
>https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment?useskin=vector
great, thanks.';

'https://www.youtube.com/watch?v=sLYazynm_1M
https://www.youtube.com/watch?v=6Ew3wiP4BNw

How do these things work? They somehow made one run along a string';

'could the reason the universe is expanding be because we are inside a black hole which is 'eating'?';

'I've done a little research on this question but can't find a specific answer. I suspect climate, geography, weather, botanical issues would lead to various different answers.
>How loud (decibels) can a forest fire get if the observer (human and/or recording equipment) is within 150ft of the closest flame
Live on the west Coast, always have. Fires destroy everything each summer, but twice in my life I got trapped close to the front lines and once worked for the Oregon Department of Forestry during a fire. The sound was insane. Like 100 jet engines at full throttle. A roar that can not be shouted over. Always wondered the sound decibel radiation.';

'is this proof right?';

'Lets say you're a professor/researcher at a university and your university is really excellent and so you aren't slaving away every hour of your life
You have an interest in a field that is not your own, say biology or physics
How exactly do you indulge in your interest? I'd assume this hypothetical person wouldn't read pop science but actually I wonder if they actually would

Also I'm curious about how inter-disciplinary work occurs
Basically my question is, are researchers able to have their team essentially split between those who are experts in field A and those who are experts in field B or do they inevitably require researchers who are familiar with both fields at a certain point?
Do they ever send a certain researcher with a very valuable skill to do a masters in order to acquire competency/knowledge?';

'>>16159345
I see, thanks';

'>>16160850
As an example, imagine H is diagonal, and the first quantity would be some number... the second would be zero since its off-diagonal. The third quantity would also just be some number..
Knowing an element of a diagonal hermitian matrix, doesnt tell you what the others are. Just thought its less abstract when you consider H as a diagonal matrix, which it can totally be in a base or eigenvectors.';

'>>16160868
Also, in this basis, all the diagonal numbers would be eigenvalues. Knowing one doesnt tell you the others';

'>In fact, it is consistent with ZF that [math] \mathbb {R} [/math] is a countable union of countable sets, so that any subset of [math] \mathbb {R} [/math] is a Borel set.
What does this mean? I read this in the wikipedia article for Borel sets. The reals are already a countable union of countable sets, e.g. take sets [0,1), [1,2) ...
Also, I've been looking for a simple example of a non-Borel set. I'm trying to solve the exercise in this probability book that says something like:
Show that if X is a random variable, and f: R -> R is a Lebesgue measurable function, then f(X) may not be a random variable.
Since random variables here are just Borel measurable functions if I understand correctly, this just requires a non-Borel measurable function and e.g. some identity function for the random variable. But I've never actually seen a set that is Lebesgue measurable but not Borel measurable and all the examples seem pretty tough.';

'>>16161078
>What does this mean?
If you don't add the AoC to ZF you can get such results. I'm not a logician but see https://mathoverflow.net/questions/32720/non-borel-sets-without-axiom-of-choice
In short you need AoC to show a countable union of countable sets is countable, so if you drop this axiom then you could, in principle, write an uncountable set as the countable union of countable sets.
>The reals are already a countable union of countable sets, e.g. take sets [0,1)
[math][0,1)[/math] is not countable because any countable set has Lebesgue measure 0.

For your exercise, I'm not sure you need to construct a Lebesgue-but-not-Borel measurable set, as long as you show one exists. Iirc you can show by transfinite induction that you have [math]2^{|\mathbb R|}[/math] Borel subsets but [math]2^{|2^{\mathbb R}|}[/math] Lebesgue measurable ones.
In fact by your starting remark you'd need the AoC to find such a subset, so it's probably complicated to construct one `from scratch'.

For what it's worth, none of this stuff is very important for probability theory. Usually all probability spaces are standard and output spaces Borel, and all this goes away nicely. Completeness is not very important, most people being content with showing a property holds almost surely.';

'I got too far away from my computer (I was upstairs) and my headphones lost connection. When I came back the bluetooth app couldn't connect to them. Even when I reset the headphones to pair they couldn't connect. So I restarted my computer and instantly it found my headphones and paired them.

Why does that work? Why does simply restarting my computer fix problems?';

'Calculate the radius of convergence of each of the power series [math]\sum_{n=1}^{\infty} \frac{z^{n}}{1+(1+i)^{n}}[/math], and study the behavior on the boundary of the convergence disk.

I tried applying the ratio test, and I got that [math]\left| \frac{a_{n+1}}{a_n} \right| = \frac{1+(1+i)^{n}}{1+(1+i)^{n+1}}[/math], but I don't know how to keep going from here.';

'I don't understand this';

'>>16161551
The majority of the time it's software related - operating system / firmware / driver / app. Doing something unexpected puts the software into a state it doesn't know how to handle so things stop working. Essentially you trigger a bug. Reinitialising all the software fixing everything, performing a restart is the simplest method to do that.';

'>>16161575
Which part don't you understand?';

'>>16161551
Everything that uses bluetooth is overpriced garbage coded by indians to sell to retarded gaymers. Bricks and softlocks happen, frequently.
Not /sci/ence or math';

'>>16161605
I understand that multiplication of 7 by itself cycles through 4 different last digits, but I'm confused at the next part where they start substituting. I don't grasp how knowing that the last digit of 7^(1000) is 1 in mod 4 means you know 7 is the last digit of the entire expression, it's weird because in the exponent they're substituting mod 4 but the base stays as 7';

'>>16160269
>How exactly do you indulge in your interest?
In private. Research positions don't tolerate experimentation.';

'>>16161605
>>16161612
to continue my post, are they saying that 7^7 mod 4 is -1 so it can be rewritten as 7^7^1000, and doing that gives 7^1?';

'>>16161614
Sorry if it wasn't clear I was asking what they'd do in their spare time';

'>>16158770
it seems clear to me that all behavior is driven by biology, in a deterministic fashion and there is absolutely no reason to believe otherwise as all behaviors have biologically identifiable causes.

and yet, it seems like we are designed AS IF there is an agent making choices; we are oriented towards good sensations and away from bad ones (and these sensations can't be by coincidence, because the qualitative factors are necessary for their reaction. for instance, it is possible to feel pain without suffering it e.g. in the case of pain asymbolia, so clearly the negative experience is explicitly generated, for some purpose).

what gives? any insights into this? it seems contradictory: there is no need for biological things to have agency, and yet they clearly do. what the fuck?';

'>>16160097
looks right to me, nice';

'So, everything in the universe is matter even waves are matter & matter can turn into waves also?';

'>>16161627
matter isn't waves, and waves aren't matter
it's both at the same time';

'>>16161555
don't really care at the moment what 1+i is, just call it 'x' for now (which you will turn into Re^{i\theta} later). Btw your result for the ratio test is missing something very important. It's also missing very important absolute value signs.

You should write your work out, missing two things in one step is pretty bad.

For the ratio \frac{x^n+1}{x*x^n+1}, just factor out the 1/x so that the numerator and denominator are polynomials with the same power of n. Now you can blow n up to infinity.';

'>>16161627
>everything in the universe is matter
Light isn't matter. Look up its definition

>matter can turn into waves
Matter can already be described as waves. If you want to convert them to pure energy, combine them with antimatter and you've turned them into radiation that can be described by light waves.';

'>>16161639
Thanks a lot!
Yeah I didn't miss the absolute value in my paper sheet, but I didn't paid much attention when rewriting it here, sorry.';

'Source Article: https://www.tandfonline.com/doi/full/10.1080/01621459.2020.1758115

Pop Source: https://towardsdatascience.com/a-new-coefficient-of-correlation-64ae4f260310

A new metric for correlation

Premise:
In a pair, (X, Y), ranks all elements of X and sort from least to greatest.
The average difference - or other functional relation - between Y_n and Y_n+1 in X-sort 2-tuples relates to how correlated 2 events are.

This really doesn't seem to make sense.
The bummer is the implicitly packed into ranking. Suppose we were to compare correlation between guns and deaths. It seems that there are many different ways to rank cities or counties and we could tease out preferred results by ranking across arbitrary parameters.
Do you guys think that if we have a complex correlation case and a complex ranking system, that the highest correlative rankings, according to the article, are valid or even most likely?
Basically, is this even real? It seems like BS where they can just push whatever and call it science.';

'>>16162031
I only skimmed the article (the real one) but it looks quite interesting, to me. I wonder why I've not seen it before.

I'm not too sure what you're after with your example. There might be arbitrary ways to rank cities or countries, but here there'd be one way that the coefficient uses: the numeric value of either guns or deaths (it's not a symmetric measure).
I also don't get what you're trying to say with a 'complex ranking system' or why it'd be valid or not.

It's definitely not a nonsense article. I've read some of Chatterjee's work on Stein's method and that was very good, this looks to be as well.';

'>>16162081
1. List all gun deaths by city.
2. Rank city by any given metric to get X-sort that confirms bias of guns le bad or guns le good.
One example would be gun deaths by republican population size, as a knock-on effect of gun deaths always because of more opportunities. But specific tangibles aren't really what I am worried about. It is more like ranking where some functional abstraction that requires digging into fifty different cummie articles to break and tease out the actual implicit assumptions to realize their rankings are bogus.';

'>>16162096
That's not what the correlation is doing. It'd be
1. List all gun deaths by city
2. List something else by city
3. Sort either by gun deaths or by the second variable from step 2
4. Further calculate the coefficient.

I think what you're missing is that _in this article_, which is all I've read, there is no arbitrary sorting of the data, but only one predefined way, and furthermore the coefficient is defined in such a way that it takes this sorting into account and produces a meaningful measure of dependence.

If you have a specific dataset in mind, which I suspect you do, you can always calculate the 'usual' correlation and compare it to this particular one.
He makes a somewhat big deal out of the fact that it's meaningfully different in some cases, but I'd be surprised if the correlations wouldn't be close.';

'>>16162104
I am payblocked so i only got the Pepsi. According to that, If X can be sorted from least to greatest than the metric. holds for some coefficients. If it is a tuned value for specific datasetsx then i am not even worried about it.
I am more concerned with it being a test for correlation itself, on whether that is true or false. For one reason, if it were true i can see a jumber of ways to employ it but they would br a waste of time if it is something bogus. But from what you have said that doesnt seem to be the argument.';

'>>16162178
https://arxiv.org/abs/1909.10140';

'Question:
Say I have some (tensorflow) neural network. Given some linspaced values x, how can I make the initial weights/state of the neural network mimic some function f(x)?
I suppose one way to do it would be to train a network to mimic f(x), and then use those weights as the initial weights of the real network, but surely there's a better way to do this?
Basically what I want is for NN(x) in its initial state to look close to f(x), if plotted for some continous variable x. Like an ansatz, if you will';

'https://youtu.be/2qhmxpfv620?si=5kKZ1718sn_LVm0T

Anyone writing simple and easy to understand math textbooks that are still correct?';

'>>16162031
>The bummer is the implicitly packed into ranking. Suppose we were to compare correlation between guns and deaths. It seems that there are many different ways to rank cities or counties and we could tease out preferred results by ranking across arbitrary parameters.

Putting aside your /pol tier question, That isn't even close to how this statistic works.

You are not ranking cities. You are ranking the ordered pair of (number of guns in an area, gun deaths in an area), BY the order of the number of guns in an area, so as to create a ordered ranking of the gun deaths by area to see if they are out of order, and by how much. If the ranks of the gun deaths were perfectly in order in both monotonicity and difference, then the new function would return a 1. If they are out of order, the new function would return some value from zero to one that is closer to zero.

So if you are asking if you could pick samples or populations to fit your prior conclusions, that is true of every statistical measure, but the order of the rank of Y is set by ordering the X, which is monotonic increasing.';

'I was sent a video of someone who supposedly built a pyrolysis process that used microwaves to heat the plastic. Now I know how pyrolysis works, but would the microwaves actually be able to heat the plastic? As far as I understand the only reason microwaves work on water is because of its polarity, and plastics are (essentially) non-polar.';

'>>16162917
Microwaves definitely work on non- and semi-polar molecules. Many plastics also have significant amount of C-O bonds, so are far from pure grease.
From what I've read, fats can reach some pretty insane temperatures too, often enough to fry bacon and scorch the food if they dry out (try microwaving a slice of sausage or pepperoni for too long, it gets toasty)';

'>>16162982
but would it be more efficient than just, say, heating it with fuel or electric heaters? seems like you'd lose a lot of heat.';

'>>16162639
which subject?';

'>>16162187
This is the part that makes me nervous.';

'Anyone familiar with this notation for spin-orbitals in quantum mechanics? It seems inconsistent to me, and the halved indices confuse me. For example, why, when the spatial integral is compacted back in bra-ket notation, are the indices not halved?';

'ok how does the fact that the universe is expanding make EM wavelenghts stretch? isn't this just ether with extra steps?';

'>>16163969
The wavelengths only change from the perspective of the viewer - this is the Doppler effect, which applies to all waves and is pretty easily observable if you happen to be standing around while some emergency vehicle passes by while blaring its siren.

Imagine an object at point A emitting continuous, repeating, unbroken waves (of any sort, not just light), while you are observing it from point B. The frequency and phase speed are constant, and so the wavelength will also be. Easy enough.
Now, start moving that object from point A towards you at point B, maintaining a constant velocity. From the object's perspective, nothing has changed - you're moving towards it. Hence the wavelength, frequency, and phase speed are all unchanged. From your perspective, the phase speed may have changed when it started moving, but it's constant throughout the motion.

What is not constant is the position of the object relative to you. Because it's getting closer and closer as it emits those waves, they're taking less and less time to get to you, which in turn drives the frequency up. And because the frequency is going up while phase speed is constant, the apparent wavelength drops from your perspective, even though nothing has changed. That's blueshift - redshift is just the opposite, where the frequency decreases because each wave takes longer to get to you, so the wavelength appears to increase. Of course, I said to assume a constant velocity just for the sake of simplicity - the effect still applies with acceleration, and can become more pronounced in that case.

The expansion of the universe is just causing that increase in distance to begin with.';

'>>16163994
guess the main point I forgot to make is: none of this requires any specific medium. sure, a medium might change the phase speed, but the effect happens anyway, aether or no';

'>>16164006
If there is no medium, what is waving?';

'>>16164009
the light itself just kind of vibes on its own I guess';

'>>16163994
let's say i hold a ruler in my hand
is the ruler expanding ever so slightly because of the expansion of the universe?';

'>>16164020
not really
the forces keeping the ruler bound together (chemical bonds and the like, and even the ruler's own gravity) are significantly stronger than the expansion of empty space';

'>>16164021
but it does have an effect? the idea being that the ruler's particles are in spacetime, and spacetime is slightly expanding. the bonds you mentioned hold the ruler together, to the completely cancel out the stretch effect, or just make it even less notocable? how could this be described by dopplers effect? if the ruler stretches, it would be detectable from all reference points';

'this doesn't make any sense, why would the torques be the same if one is further out and applying perpendicular force further away';

'>>16164057
The angle of the force relative to the radial line changes.
Draw a line from the center to B, then calculate sin of the angle between that line and F. It should be half of the sin of the angle at point A.';

'>>16163220
I think there can be a market for math and (mathematical) physics where theres no proofs being given except plenty of redundant examples and everything is explained in simple english, with no ambiguities because everything would have redundance and examples, which ought to dispel any subjectivity in the written text.
It could allow people to advance rapidly through the material, and then whoever wants to can always check the actual proofs and abstract definitions in the "professor" textbooks. Think about it as a pedagogical aid.';

'>>16164009
>what is waving?
Electric and magnetic fields. Its a model';

'>>16164172
Supposing these fields exist, what makes them wave about an equilibrium position?';

'>>16164193
>what makes them wave about an equilibrium position?
Different laws of physics like the law of induction, i forgot the name, basically the time-dependent Maxwells equations';

'>>16164199
I thought induction was Faraday's law. Induction of what?';

'>>16164481
I think you already know these equations, theres nothing else i want to tell you as you just want to be a contrarian';

'>>16164494
Not at all. Such laws only describe behaviors of the fields as it relates to derivative phenomena and not as they are. The proposed question is something like this: why are the fields interacting in a coaxial circuit, magnetic and electric, what binds them so they transform between each. If E and B are maxed, why should they ever return to zero?
The basic premises being is Newtons third law and left hand rule. Instead of force, like in the case of a motor, it is 90 degrees in some other direction. There must be some restorative element; however, the problem is that it isn't just the dipole bleeding back out to a neighbor because radio interference would inhibit the whole premise of broadcast.';

'Any pharmacists here?
How come when I go to pick up a prescription it takes me 1 minute to speak to the pharmacist and get my script but 90% of the time when I have to wait in line behind somebody that take at least 10 minutes, and often more to do the same thing?';

'>>16164171
im sorry, were you trying to answer my question?';

'What's an example of a square matrix which isn't congruent to a diagonal matrix?

(Definition: two nxn matrices B,C are "congruent" if there exists an invertible nxn matrix P with [math] PBP^T = C [/math].)';

'>>16164762
What have you tried?';

'>>16163058
Doubt it, but I've been surprised before.
Look up whether it's been tried before, chances are an efficiency calculation already exists
https://www.uspto.gov/patents/search';

'>>16164762
>>16164887
Nvm I think I got it: if A is a square matrix, then
(A is congruent to a diagonal matrix) iff (A is congruent to a symmetric matrix) iff (A is symmetric)';

'>>16164968
(At least when A is real)';

'so yknow how spheres pack inefficiently, like 72% of the space is used?
would smaller spheres waste less space, or is there just more spots to lose space';

'>>16165085
Take your packed spheres then shrink the radius. The packing efficiency in that reduced volume would be unchanged.

However if you then packed multiple of those smaller volumes together the packing efficiency of the new volume might differ to the original value, but remember you would not be comparing like for like.';

'>>16165085
Not anon, but tangently related. Does space expand like a sphere since it is expanding everywhere at the same moment in time?';

'>>16164537
>Such laws only describe behaviors of the fields as it relates to derivative phenomena and not as they are.
Then why did you ask me about what Faraday's law was about? If you know about Faraday law you already know the equations of electromagnetism, yet you play dumb asking "but why" like a baby. I would talk more to you if you were sincere in your questions, but instead what you want is to convince others of some idea of yours. Why are you so dishonest?';

'Ok so gravity..
What the FUCK is it???
How is it so strong yet they call it the weakest force?? How can it exert so much force on objects even across huge distances??? It's like spooky as fuck.
Like I can jump out a plane at thousands of feet and yet I just instantly start plummeting down at huge rates of speed because of this force. And that's weak?
I get that it's like relative to the size of the earth vs the size of me but still.
And what is it about "objects" that give them this magical ability to just pull stuff to them across vast distances? How does that even make sense?';

'>>16165996
I'll try a simple-ish answer.

>How is it so strong
Contrast it with electromagnetism (EM) since both are inverse square laws (Coulomb's Law). In EM, unlike charges attract. But, for most macroscope objects, positive and negative charges cancel out - EM is really only relevant at small scales (like the nucleus) and specific niches. By contrast, all mass attracts all other mass - it doesn't cancel out or attenuate, so gravity affects everything all of the time. And there's some big stuff in the universe (planets, stars etc.). In short: Earth doesn't really have a net positive or negative charge, but it does have tons of mass.

>Jumping out of a plane
Your experience with gravity is basically everyday objects versus the entire Earth (6x10^24kg). Your instinct for gravity is skewed by that.

>What is gravity?
Newton's model is that mass attracts all other mass. You could sort of think of it like other attractive forces (e.g. magnetism), except all matter can attract itself.

But why? Well, Einstein's model is that the "attraction" we see is fictitious. In fact, matter is bending space and other matter is moving according to that bending - the macroscopic appearance of this is mass being attracted to other mass c.f. https://www.youtube.com/watch?v=MTY1Kje0yLg.

Of course, that just substitutes a new question - why does matter bend spacetime; what does that mean? And one might argue that this is (part of) the definition of what matter is! The "mass" of an object might be thought of as (related to) how much an object bends spacetime, a priori. "That's just how the universe is."

It's bordering on a question for philosophy. And probably there is a deeper, quantum understanding of gravity to come. But these are just models. The easiest takeaway is that all mass attracts all other mass. And because there's no attenuation or "cancelling out" like other forces, gravity takes over any appreciably large scale.';

'>>16166031
Part of what trips me up about it is how contradictory it seems
Like imagine a force that is powerful enough to grab me and pull me across thousands of meters, but also a force that is so weak that I can easily resist it by just using my legs to stand up. Intuitively it would seem like we were talking about two different forces but they're really the same thing.';

'>>16165996
its pretty shrimple';

'When predicting earthquakes, is there a simple relation like "total pressure released" that can predict the next big one?
Like if a magnitude 3.0 is 100x weaker than a 5.0, does a 3.0 hitting mean the next 5.0 will be delayed by 1%?';

'what are some good books for learning basic technical mechanics for dummies, no fluids or anything like that, simply:
>newton laws
>static axioms
>forces, moments, couple, reducation
>bonds and bond reactions
>center of gravity of the figure, body and line (practical tasks)
>friction
>kinematics of particles and rigid bodies
>dynamics of particles, dynamics basic laws, dynamics of particle systems + moment of inertia
so basically, classical mechanics from what i see
i'm really struggling, i failed it last semester and i pretty much have all summer to figure it out and go out to the exam in early autumn before the winter semester begins';

'>>16166381
openstax';

'>>16166155
No. A small earthquake could actually be a precursor indicating a larger one was about to happen. In general predicting earthquakes is an incredibly difficult thing to achieve and depends on the geology of the local area, so any method that works in one region may not work elsewhere. However there has been a lot of research done in the last few years trying to use AI that seems to be producing some interesting results - still a long way from accurately predicting any earthquakes though.';

'>>16161575
can anybody help me on this
i guess i'm shamelessly "bumping" my post';

'>>16166606
That given explanation is fucking atrocious. It completely skips over what it's actually doing and why it's doing it.

Trying reading this pdf. The third section is all about powers of 7 and finding their last digits, and it covers why mod 4 is used.';

'>>16166638
You know Euler's theorem, right?
https://en.wikipedia.org/wiki/Euler%27s_theorem

[eqn]\varphi(10) = 10(1 - 1/2)(1 - 1/5) = 4[/eqn]
So [math] 7^{4} \equiv 1 \pmod{10}[/math]

Now just using this you get that [math]7^n \equiv 7^k \pmod{10}[/math] if [math]n \equiv k \pmod{4}[/math].
Basically you can reduce the exponent mod 4.

It's northing special about powers of 7. It will work with powers of all numbers that are coprime to 10.';

'How the fuck does gravity work?
None of this curvature of spacetime bullshit.';

'>>16166715
> None of this curvature of spacetime bullshit.
That's the best theory we have. Just because you don't like it doesn't make it wrong.';

'Looking to purchase a microscope (trinocular for picture taking). Will use it for bacteria/fungus and I'm eyeing the euromex iscope compound 40X-2500X. Is this the way to go or is there something better? Also how much would I need to spend for something like this? Found one for $2,066.99 with a 18MP cam. I could also attach to my mirrorless cam but figure it would be too much of a bitch rather than having a builtin cam.';

'>>16166779
>Will use it for bacteria/fungus
Bacteria are hard to see, even with the right resolution. They're practically invisible. You'll either want some dyes or one of those polarizing lens microscopes
>2500X
Optical limit is 1500x, smells like a scam
>how much would I need to spend for something like this? Found one for $2,066.99 with a 18MP cam.
Also smells like a scam, this is 1700's technology. Just nigger rig a cheap digital camera to a cheap used scope, you could probably do it for less than $500';

'>>16166381
youtube';

'>>16166715
>>16166721
its just a force. if you calculate lagrangian of electric field you get the same results. and if you calculate lagrangian of strong force in 8 dimensions you get the same results. thats the whole idea of the higgs field
but it just reframes the question: wtf is a force?';

'>>16166796
My dentist had a setup where I could see all kinds of shit in my mouth. Even some spirochetes.
Do you know of good models to get?';

'>>16166803
> if you calculate lagrangian of electric field you get the same results. and if you calculate lagrangian of strong force in 8 dimensions you get the same results.
that's gibberish, wtf have you been smoking?';

'>>16166670
How does that apply to [math]a^b^c[/math]? I don't understand how to use that logic to a ladder of exponents.';

'>>16166810
idk
https://www.youtube.com/watch?v=aZzRygip5XY';

'>>16166823
danke';

'>>16166822
>>16161575
The last digit [math]d \equiv 7^n \pmod{ 10}[/math] where [math]n = 7^{1000} [/math]
Now we use the fact that the powers of 7 form a cycle in mod 10: [math]7^0 \equiv 1, 7^1 \equiv 7, 7^2 \equiv 9, 7^3 \equiv 3, 7^4 \equiv 1 \pmod{10}[/math] and so on and this cycle repeats with a period of 4 (which is [math]\phi(10) [/math])
So to find [math]d[/math], all we have to do is find what [math]n = 7^{1000} [/math] reduces to modulo 4. Because [math]7 \equiv -1 \pmod 4 [/math], [math]n \equiv (-1)^{1000} = 1 \pmod 4 [/math]. Plugging this back in we get [math] d = 7 [/math]';

'I don't get this proof. How can we form such a subsequence and why does sqrt[k]{u_{k}} \leq q for all k>= N then?

The series[math]\sum_{k=1}^{\infty}u_{k}[/math] converges absolutely when [math]c=\limsup \sqrt[k]{|u_{k}|}<1[/math]. Proof: Assume that c<1 anf fix a random q \in (c,1) . Notice that the inequality [math]\sqrt[k]{|u_{k}|}[/math]
can only hold for a finite amount of indexes k otherwise we could form a subsequence [math] \sqrt[k_{i}]{|u_{k_{i}}|} [/math]
that converges to a number greater than c. Therefore there exists an index N such that [math]\sqrt[k]{|u_{k}|}\leq q[/math] for all k>=N';

'how do i teach? I am going to be a teacher assistant soon and have no clue where to begin';

'I'm getting ready to start on a project about robot ethics (aka AI ethics), but considering it's a niche field, I find myself kind of at a loss for good sources. Anyone know any good books/publications to recc? Books about the history of robots and AI also welcome for a short preface.';

'>>16167181
>How can we form such a subsequence
Use Bolzano-Wierstrass.
>why does sqrt[k]{u_{k}} \leq q for all k>= N then
You simply pick N bigger then the biggest index where the inequality doesn't hold.';

'>>16167512
How do we get from Bolzano-Weierstrass that that subsequence's limit is bigger than c?';

'>>16167726
Firstly the sequence [math]\sqrt[k]{|u_k|} [/math] is bounded since by the definition of the limsup for epsilon=1 you can find an N such that [math]\sqrt[k]{|u_k|} < c + 1[/math] for all [math]k > N[/math]. The first N terms are bounded by [math]\max{\{\sqrt[k]{|u_k|} \mid k \in \{1,2,...,N\} \}} [/math].
Call an upper bound of this sequence K.


If there are infinitely many elements in the sequence that are between (q,K] then you can find a subsequence such that all elements of the subsequence are in (q,K]. Then by Bolzano-Weierstraß this subsequence has another subsequence which converges against a limit L in [q,K]. Since the limit is bigger or equal to q it is also bigger than c. A subsequence of a subsequence is also a subsequence of the original sequence.';

'Which branch of physics research can lead to a development of "new" tech-commercialised industry ?

Is it condensed matter physics, solid state physics, optics, photonics ?';

'>>16167798
semiconductors unless you think making transistors smaller and more power efficient isn't "new" tech, but it's the biggest in terms of investor funding
imo the biggest gamechanger for industry that seems somewhat realistic in the next decades would be an advance in power storage that's a step beyond lithium ion batteries, maybe using some organic material
or a method to mass-produce graphene
so my answer would be material science/nanophysics
>>16167491
https://www.aisafetybook.com
https://course.aisafetyfundamentals.com/alignment
these are very biased to the "effective altruist" cult thinking but there's a lot of interesting links in here
also read a couple of these:
https://scholar.google.com/scholar?q=responsibility%20gap';

'>>16166970
nta you were talking to.
Why does \phi(10) = 4 matter? If we were using 5^x instead of 7^x, 5*5=25 so it has a cycle of just 1 instead of 4.';

'>>16168025
nvm i got it, cant delete post either idk why';

'>>16167974
There are lava batteries on the horizon. They are much more cost efficient.
Let me get that company name for you... Ambri.
Would you say transistors are more important than photonics for computing. How far in the future would you estimate for photonics to take over?';

'For the chembros
I came across a little 17th century alchemy textbook see what you make of it
https://archive.org/details/TheCompleatChymist/page/n5/mode/1up';

'>>16168351
This looks comfy.';

'>>16168351
I'm confused as to why some 's' are written as 'f' and some as 's'';

'>>16167347
keep it clear and simple. most people don't give a fuck about the subject, and want a clear list of things they'll have to know by the test/lab day.
plan your lectures beforehand, and practice them 30 minutes before class.';

'>>16168375
Might've been a form of saving space?';

'what the hell is this supposed to mean';

'>>16168375
Because the f represents a 'long s' and the other s is a 'short s', only the short s is used today. You could think of it as a kind of accented character. Fun fact, it's actually still used in one common place today, it's the basis for the integral symbol.';

'So I have been on this problem for a long time, and seem to continuously be solving it the wrong way. I wrote down the way I have been going about it, but trying different distances (9.11 cm, 1.36cm, 7.75cm).
I would appreciate help.';

'>>16160097
No idea.';

'>>16168132
before any move from semiconductors to photonics I think there's gonna be mixed technology with silicon logic and optical interconnects
>Ambri
filed for bankruptcy this month, too soon';

'Are the surfactants and other chemicals in fragranced soap likely to be aerosolized at room temperature?
I ask because I've been vigorously huffing the scented hand soap at work for around a month now and only just realized that it's probably not just the fragrances that are being released into the air since my respiratory tract has started feeling irritated 24/7 and I'm making stupid mistakes more frequently.
Bros...did I give myself lung cancer and brain damage?';

'>>16168620
nvm (:';

'>>16168531
what's a long s?';

'>>16168765
The grammar rules when it was used were kind of ad-hoc but it's essentially the length of the 's' sound. e.g sweat vs spoon ('f'poon). It was also almost always used in double 'ss' endings like success or excess (succefs & excefs)';

'>>16168531
https://www.historyofinformation.com/detail.php?id=2344

>According to R. B. McKerrowOffsite Link, An Introduction to Bibliography for Literary Students (1927), the effective introduction of the reform in England was credited to the printer and publisher John BellOffsite Link who in his British Theatre of 1791 used the short s throughout. "In London printing the reform was adopted very rapidly, and save in work of an intentionally antiquarian character, we do not find much use of [long] s in the better kind of printing after 1800" (McKerrow p. 309). Though it would be amusing to do so, there seems to be no reason to accept the legend that Bell initiated the change in his edition of Shakespeare because of his dismay at the appearance of the long s in Ariel's song in The Tempest: "Where the bee sucks, there suck I."
>"Where the bee sucks, there suck I."';

'How am I supposed to sketch parametric surfaces with pen and paper? I can visualize most of them pretty accurately but I don't know what to do when they get more complex.
a) [math]\bf{r}(s, t)=\left(s, t, s^2+t^2\right), \quad 0 \leq s^2+t^2 \leq 4[/math]
b) [math]\bf{r}(s, t)=(\cos s, \sin s, t), \quad 0 \leq s \leq 2 \pi, \quad t \in \mathbb{R},[/math]
c) [math]\bf{r}(s, t)=(1, s, t), \quad(s, t) \in \mathbb{R}^2,[/math]
d) [math]\bf{r}(s, t)=(\sin s \cos t, \sin s \sin t, \cos s), \quad 0 \leq s \leq \frac{\pi}{2}, \quad 0 \leq t \leq 2 \pi.[/math]';

'Is this right? Do vaccines actually cause autism?
https://kirschsubstack.com/p/why-every-scientist-should-agree';

'>>16168874
No. It just another conspiracy theory / complete falsehood.';

'>>16168531
Neat, so a german ß holdover? Old languages are so cool';

'What happens to liquid soap chemistry after the expiry date? Should I not use it? What's the proper way to dispose of expired liquid soap?';

'Is there a place online where I can navigate through the data of all known living species? I mean, if they are registered, where can I find the register?

I want to see the whole tree of life or at least all animals. It's weird that I can't find that online easily.';

'>>16168848
The best way is to allow one parameter to be constant,
like r=0, while the second parameter can be free.
Draw each level curve for a select few choices.
Then, change places and let s=0 and r free.

In pic related, the torus is made up of two parameters
which control the shape of a part of a torus. The phi
angle as it varies makes the small circle at some spot
on the main ring of the torus. The theta angle as it varies
swings that small circle around the x-y plane. Together,
they both make the whole torus.

Here's a short video as an example for graphing surfaces
by looking at level curves. The idea works about the
same way in Cartesian coordinates as in parametric
coordinates.
https://www.youtube.com/watch?v=f2KsJBClJ1g';

'>>16169049
Also this video:
https://www.youtube.com/watch?v=uaHiAxFESc4';

'What is intrinsic curvature of a surface/manifold?
How does something have curvature on its own, without being embedded in a bigger space?
For instance a 2 dimensional spherical surface, not embedded in a 3D space although it would be really easy to do. What does it mean to say it has curvature?';

'>>16169069
I mean, i can understand curvature only in reference to a flat reference.. what can intrinsic curvature mean?';

'A visiting senior prof from a top 5 university who's a major big shot in my field recently came to give a talk at my low-ranked university. I spoke to him about my research and he was very interested. Any way I can leverage this into having me visit his university for a year and join his lab? How should I approach him?';

'>>16168878
Would you be so kind as to look over this and point out the problem with it because I'm too naive on the topic to properly understand the deception.
https://kirschsubstack.com/p/two-verifiable-anecdotes-are-the#%C2%A7our-autism-anecdote-is-also-impossible-if-vaccines-arent-causing-autism';

'>>16169142
>The chance of that happening if autism is happens randomly to kids [sic] is less than 1.66e-13.';

'>>16169182
oh, and another thing. the woman being somewhat old looking and the fact that she had TRIPLETS (have you ever seen triplets before in your life?) leads me to suspect she was pumped full of weird fertility drugs, or underwent in vitro fertilization, and/or something else that likely increases the chance of autism.';

'>>16158770
How to scientifically reconcile with the fact that God and afterlife don't exist? Every other waking moment of my life I experience terror at the indifference of the Universe and the eternal oblivion. Maybe I should take medication or something.';

'>>16169203
meds dont work. I would take them if they worked, like i take ibuprofen for headaches, however medicine is just not advanced enough.
Psych meds of all kinds cause brain damage that will make your life much worse that what would already be. They are only justified for extreme schizos that are trying to kill themselves, since they can increase their lives for a few more years. In such situations theres really no "long term". Like taking meth in a combat situation where survival is measured in hours, who cares about "long term" brain damage?';

'>>16169193
so why did all three get autism only after taking their vax?';

'>>16169203
god exists, but not all conceptualisations of god are god
determine what god actually is';

'>>16169237
repeat after me, "correlation is no causation", "correlation is no causation", "correlation is no causation" ...';

'>>16169241
absence of correlation is absence of causation but correlation is a good indicator of potential causation
Until you can explain these cases to a satisfactory degree other than repeating that mantra you don't know anything.';

'>>16169241
causation is just a special case of extreme 100% correlation';

'>>16169237
they didnt all get autism right after the vax, they were diagnosed right afterwards, likely because they were in a clinic where such a diagnosis would be possible in the first place.
>After age two their walking and talking difficulties came sharply into focus. The triplets were examined by child psychiatrists at ages two and a half and three and a half. At two and a half they were described as smiling, though completely aloof and uninterested in people. They could only say certain single words which they would keep repeating sometimes for hours on end. They were hyperactive, resisting body contact, clinging to certain objects such as wheels of toy cars and sticks of wood. A woman social security helper working three hours a day in the childrens' home when they were aged from three years and four months to five years described them as much the same during those years.Resistance to body and eye contact gradually lessened, but all the triplets still demanded that they themselves be the ones to decide when and if contact could be accepted. The helper found the three boys extremely alike in looks and behaviour.
the triplets were identical, so it makes sense that all three would have autism. they were born premature, and the mother was experiencing considerable stress during her pregnancy.';

'>>16169203
if youre having trouble functioning day-to-day then i would suggest getting medicated.';

'>>16169203
> How to scientifically reconcile with the fact that God and afterlife don't exist?
Why is that a bad thing? Believing there has to be either is simply your feeble human emotions at work. Accept the truth and realise you might as well make the best of life for the short amount of time you have it.';

'>>16158770
My thread got jannied. I think maybe it was because janny wanted it here?

>jannied thread
https://warosu.org/sci/thread/S16168337

Does anyone in here know where to see more PILOT code?';

'>>16169286
>Accept the truth and realise you might as well make the best of life for the short amount of time you have it.
I did and it doesn't work. Still getting borderline panic attacks.
I think I worry more about my loved ones rather than myself. Understanding that there is no salvation for them and that the only constants are suffering and oblivion takes a toll on your psyche. Honestly I would cease to exist myself if it spawned an all-father into existence to care about them. But alas.';

'>>16169323
> the only constants are suffering and oblivion
not true, knowledge and understanding lead to wonder and enlightenment.

https://youtu.be/ZbFM3rn4ldo';

'>>16169024
As far as I'm aware, there isn't one singular database. It seems like whenever they refer to large amounts of species for a tree, they just pull data from multiple databases. Some good ones I've seen are
>catalogueoflife
>iucnredlist
>ncbi taxonomy';

'>>16169069
>>16169076
on an intrinsically curved surface a triangle's angles won't add up to 180 degrees for example, euclid's 5th postulate won't hold, geometry will be all wonky
basically the intrinsic curvature defines geodesics which are like straight lines in that they're the shortest path between 2 points but if the surface is curved they have different properties from straight lines';

'Where can I find abacus practice sheets and resources?';

'So are wormholes irl impossible or not? I mean the ones we could never travel, but still exist outside of pure theorem?VYV8';

'>>16169658
Which type of abacus?';

'>>16169762
Soroban';

'>>16169775
Can you speak japanese or leverage mtl well enough to find japanese problem set pdfs?';

'>>16169783
No.';

'>>16169743
They're possible in the sense we've never found one and have a model that supposes their existence if that's what you mean.';

'>>16169793
paste this into a search engine
そろばん filetype:pdf';

'Can someone please baby steps walk me through d)? I genuinely just don't get it.';

'Throughout the million years of life on earth we have seen completely different types of animals do:

1.) Crocodile type water ambush
2.) Aquatic
3.) Flying
4.) Crabs
5.) Tyrannosaurus-style jaws.

You know, Convergent evolution.

Why is it that only one time in Earth's history an animal figured out that walking on two legs and good dexterity was a good idea (Human-like animals and primates)';

'>>16169906
>Why is it that only one time in Earth's history an animal figured out that walking on two legs and good dexterity was a good idea (Human-like animals and primates)
Do most maniraptoriforms not count?';

'>>16169906
Consider that primates evolved from what was essentially a furry lizard.';

'Suppose the normal calorie intake is 2000kcal per day to keep your weight steady. Fat people are fat because they constantly eat more than that, let's say 3000kcal per day. So the excess difference is 1000kcal per day, making you gain fat.
So my question is, why don't they get fat indefinitely? At some point they reach a new balance of steady weight, which sure, is more than they should eight, but it's not like their weight is approaching infinity. And it's not like they self regulate and eat less all of a sudden. So that would mean, their bodies start burning more calories or their bodies are becoming less efficient at absorbing energy from food.
Does anyone know what mechanism is behind this?';

'>>16169960
Hormones. Different tolerances for different people, some have faulty hormone production and that leads to a higher chance of the indefinite slide you're talking about with morbidly obese people.';

'>>16169960
first challenge, what causes puberty?';

'>>16169889
use conservation of energy
W=Fd
K=1/2mv^2';

'>>16169960
Kcals burned is related to current body weight. Say you burn 13 kcal/lb/day and are eating 2000 kcal/day. Then you'd eventually be 2000/13 lbs or around 153.85 lbs. 3000 kcal/day gets you to around 230 lbs. From a cursory look at google it seems like the kcal/lb/day can be anywhere from 10 to 15 depending on age, sex, body composition, exercise.';

'im trying to perform the substitution v into the following equation

v = y^2 + y
(2y + x)y' + 2 = y^2 + xy - y

Performing it should turn the equation into a linear non-homogeneous ODE, but I just cant seem to do it.';

'Are there any studies about changing the strong beliefs of others? I always believed that no matter how strong someones belief in something was, if you used the right words, you could atleast form a crack in their confidence that would widen overtime.
Ive never been able to prove it to myself though so im wondering if there is any studies explores methods of changing the beliefs of others';

'Why do scientists pretend like time is an actual, physical thing and a law of nature when time doesn't actually doesn't exist?';

'>>16170409
It's the only rational position to take if you're going to be dealing with it all day in your work. You can pretend it doesn't exist, but that doesn't make your work go away.';

'>>16169617
So all the definition of curvature can be summed up to the local angles of a triangle? Over 180? Less than 180?';

'>>16170409
Because shut and calculate.
Scientists try (or used to) try to understand real problems, you are not deep by saying nothing exist durr durr the matrix';

'>>16170409
>doesn't actually doesn't exist?
good to see you admit it does exist.';

'>>16170397
> if you used the right words, you could atleast form a crack in their confidence that would widen overtime.
I don't know about any studies but that part is patently not true. Some people will never change their beliefs. Logic and rational argument means nothing to them especially is they are around others (online or irl) that support those baseless beliefs.';

'>>16170397
Look into psychology. Therapist have some things about this too, but it's not any sort of study. It's more like self control tips that work empirically.';

'Are there any fields which actually use Bayesian methods as their primary approach for problem solving? I appears to me as if Bayesian statistics is just a conceptually interesting framework which is rarely used outside academia.';

'>>16169960
energy theory in nutrition is bunk check zoe harcombe's research';

'>>16170608
Not sure about primary but anywhere that statistics is used Bayesian methods is frequency part of the analysis tools that are applied.';

'>>16169417
thanks!';

'Real science do not require daily updates';

'>>16166803
>its just a force. if you calculate lagrangian of electric field you get the same results. and if you calculate lagrangian of strong force in 8 dimensions you get the same results. thats the whole idea of the higgs field


r u ok anon?';

'>>16169658
There is an abacus game app for mobile which helped me understand how to use it. I forgot the name though, look it up, should be easy to find.';

'>>16170437
I was reading more about this and.. i figure that if i was located in some huge sphere (like a planet durr) i could measure the curvature by measuring triangle angles.
Locally the effects would be null, as these curved manifolds are locally flat by definition, but by drawing ever bigger triangles one would start to notice that the angles dont add up to 180, and the effect if bigger with triangle size.
So this would indicate a scale of how big the sphere was, hence the radius hence the curvature. Very good.';

'>>16158770
Is nuclear power used in starships, rockets, and whatnot?';

'>>16171617
https://en.wikipedia.org/wiki/Nuclear_power_in_space';

'What's the difference between Atomic Physic, Nuclear Physics and Particle Physics?';

'>>16172975
>Atomic Physics
Study of the atom.
>Nuclear Physics
Study of the things that make up the atom.
>Particle Physics
>Study of the the things that make up the things that make up the atom.';

'>>16172975
atomic physics: study of the entire atom as a system. electrons, nucleus, everything.
nuclear physics: study of the atomic nucleus specifically.
particle physics: study of individual elementary particles. more quarks than nucleons, for example';

'>>16172978
Ok, but what's the actual difference? They're all microscopic entities, shouldn't they follow the same quantum laws or something?';

'>>16172980
The only one that studies the quantum effects is the last one because it's subatomic.';

'>>16172982
Do I need to study atomic physics and nuclear physics before studying particle physics?';

'>>16172980
>They're all microscopic entities, shouldn't they follow the same quantum laws or something?
Different scales, its like you saying i biology is just chemistry. Maybe at some abstraction level but not in practice.
Atomic physics deals mostly with electron transitions. Nuclear with the nucleus part of the atom. Elementary with all kinds of particles that dont even have to be in atoms.';

'why don't we genetically alter an organism, preferably a human, to express telomerase throughout its life like a lobster or similar creature that can theoretically live until it can't feed anymore? it seems like a simple thing with a possible huge upside.';

'>>16173321
An experiment like that would never be able to be concluded, how would you prove it works without waiting out the entire lifespan of hundreds of years? How would you create ideal conditions where the experiment isn't tampered and fails due to some random event?';

'Did the Covid shots really erase genes from your DNA?
Were the Covid shots some sort of population control psyop by kikes?';

'>>16170382
You followed the instructions wrong. The sub is supposed to by v = y^2 + xy.';

'>>16173393
No and no.';

'>>16169049
>>16169054
Thanks man, this helped a lot!';

'>>16169317
>My thread got jannied
Because it's not math or science related. Just post on /g/ for fuck's sake. It's embarrassing to witness you try to make technology threads "on-topic" by adding some schizobabble on homotopy type theory. You're clearly not interested in any of that so just stop posting here';

'>>16169203
I'm an atheist, maybe agnostic I suppose - I always say that if God exists, then it is impossible to prove it's existence. If believing in God helps you get over existential dread, then don't stop believing.';

'>>16173426
>>16169049
Of course, anon. I hope to see your surface drawings soon from your attempts!';

'>>16169203
God exists (in our heads, therefore has a chance to manifest and become the true God of all existence and rewrite all laws of the universe).
The afterlife exists (you just don't get to experience it because you are dead).
It's that shrimple.';

'>>16158770
In a month of exactly 28 days and given all periods last exactly 7 days, what is the probablity that in a group of 3 women, exactly zero/one/two/three is in her period';

'>>16158770
so do resistors convert electricity to heat in a one to one ratio?';

'>>16174045
https://homepage.divms.uiowa.edu/~mbognar/applets/bin.html
>>16174097
not sure what this question is asking. one unit of electricity = one unit of heat? electricity doesnt have units. the power dissipated by a resistor is proportional to voltage squared, and also current squared.';

'>>16174133
i guess how much heat is created in joules when 1 volt or 1 amp is put into a resistor';

'>>16174160
formula is current squared times resistance equals power, and its all heat
meaning, to drive a current of 1 ampere through a 1 ohm resistor, will take a power of 1 joule and will create 1 joule of heat';

'>>16174167
gotcha thanks.';

'>>16173349
well, you could use mice. it's aggravating that it's handwaved away as "well, there are other components to aging," like no shit, but why not isolate telomeres and at least gauge the effects of long, beautiful telomeres for life?';

'Please someone help me understand Electric Potential and Electric Potential Energy. I know that Potential Energy is the energy "stored", but sometimes this doesn't seem to be the case at all for the Electric Potential Energy. I don't get how the Electric Potential Energy can be negative, I thought all energy should be always positive, but apparently when two charges have opposite signs will alway have negative Electric Potential Energy. And what the fuck even is Electric Potential? Like, at first I thought it was the "Electric Field" or the Electric Potential Energy, but everything about it just feels too different from the properties of Electric Field, it also doesn't help that when an Electric Field is zero at a certain point that doesn't mean that the Electric Potential will also be zero at that point, so they're not interconnected concepts at all and I have no idea why, but then it's strange because the formula for the Electric Potential has the Electric Field in it, what the fuck?';

'>>16174471
1/2
imagine youre standing on the side of a hill and you roll a ball uphill (ignore friction). the ball leaves your hand going some velocity, so it has some amount of kinetic energy. as the ball moves up the hill, it goes slower and slower until it reaches its apex and momentarily has a velocity of zero. what happened to its energy? in order to comply with conservation of energy, we say that the all the kinetic energy of the ball converted into potential energy. if the ball had 100J of kinetic energy when it left your hand, it now has 100J of (gravitational) potential energy *relative to where it left your hand*. it only makes since to talk about energy potentials relative to two different points in space.';

'>>16174471
2/2
now consider a positive charge in a uniform electric field. say the charge is one coulomb and the field is one volt per meter (volts are joules per coulomb, so the whole thing is joules per coulomb per meter). moving the charge with the field by one meter causes the charge to gain one joule. the voltage between the starting and ending position is one volt. its often helpful to talk about absolute voltage, but since all potentials are relative, we need to pick a reference point, and we usually do this by picking a point (usually the cathode of a battery) and manually giving it a voltage (usually zero). then all voltages are calculated relative to that. for our charge in a uniform field, lets give the starting position a voltage of zero. that means the end position as a voltage of one. but what if we moved the charge *against* the field by one meter, starting from zero voltages? the charge will have lost one joule of energy (or perhaps we would have lost the energy, if we were the ones pushing it). that position would have a voltage of negative one. theres nothing special about negative voltages, since its all relative. its kind of like the ball and the hill: when the ball first leaves your hand, it has no potential, when it hits the apex it has high potential, when it rolls back to you its back to zero potential, but if you dont catch the ball and keep letting it roll downhill, it will keep gaining kinetic energy and keep losing potential energy, so its potential is going negative. does that mean we're storing negative energy? not really, the negativeness is just a consequence of us defining "ground" to be our location on the hill, and we let the ball roll past that point.';

'>>16174097
resistor heating is 100% efficient, the amount of electrical power you put in is perfectly converted to heating power';

'What are some molecules which would have a huge impact on the world if we were able to manufacture them in a cost effective way?';

'If I rotate a point around the origin by an arbitrary angle, is it possible to do a series of scales/shifts to ensure all points that were integers before the rotation are integers after the rotation+scales/shifts, and all points that weren't integers before are also not integers after?';

'>>16174837
No.

First off, note that any net scaling at all will cause your condition to fail automatically. Consider a point 1 unit away from the origin; rotation about the origin will not change this distance. Then if you scale the grid down, this point will be less than 1 unit away from the origin, in which case it cannot be at integer coordinates. If you scale the grid up, then whatever ends up at 1 unit away started at less (and thus could not have had integer coordinates to begin with). In theory you COULD scale if you really wanted to, but you'd have to unscale by that amount later on, rendering it completely redundant.
Since we can't do scaling (at least not meaningfully), any two adjacent integer-coordinate points will remain separated by 1 unit. The origin remains an integer-coordinate point for any angle of rotation, so the adjacent integer-coordinate points must be mapped to integer-coordinate points by the rotation itself.

So such a transformation is not possible in general, and in fact is only possible if the angle is some multiple of π/2 radians (in which case the rotation on its own suffices).';

'>>16158770
Is doing math something you can learn to enjoy?';

'>>16174877
if you enjoy doing puzzles and games, yeah';

'>>16174984
I mean real math.';

'>>16175240
That's what he means
It takes a specific kind of person to truly enjoy math and they unfailingly like puzzles';

'>>16172982
>The only one that studies the quantum effects is the last one because it's subatomic.

Now thats a brainlet statement. All of them have quantum features and are quantum systems. Particle physics deals also with relativistic effects, so it uses QFT.

>>16172987
Not necessarily, but usually people get exposed to these before particle physics (you learn some atomic physics in high school even, if I'm not mistaken).';

'Is there a real nxn matrix [math] A [/math] and a column vector [math] x \in \mathbb{R}^n[/math] such that all the following hold:
(1) [math] A^n = \mathbf{1} [/math] and [math] A^k \neq \mathbf{1} [/math] for integers k with [math] 1\leq k < n [/math]; here "[math]\mathbf{1}[/math]" is the nxn identity matrix
(2) [math] x \neq 0 \in \mathbb{R}^n [/math]
(3) [math] x,Ax,A^2x,\ldots,A^{n-1}x [/math] are linearly *dependent* (over [math] \mathbb{R}[/math]) in [math] \mathbb{R}^n [/math] ?

(If no, does the answer become yes if we change "real" everywhere to complex?)';

'>>16175742
Nvm just realized the answer';

'I am trying to understand how a many-body wavefunction of [math]N[/math] particles can be expanded as:
[eqn] \Psi(x_1...x_N,t)=\sum\limits_{E_{1}^{'}...E_{N}^{'}}C \left(E_{1}^{'},...,E_{N}^{'},t \right) \psi_{E_{1}^{'}}(x_1) ... \psi_{E_{N}^{'}}(x_N) [/eqn][math]x_i[/math] includes the coordinates of the i-th particle and also stuff like spin. The [math]\psi[/math] are single-particle wavefunctions and [math]E_k[/math] represent a complete set of single-particle quantum numbers.
I have studied standard quantum mechanics in my bachelor but I am at a loss looking at this formula. I am not even sure I understand what the summation over all those indices is actually doing. Pic related is an extract from the book this formula is from. The books pretty much starts off by writing this formula so I have no idea where to look for an introduction. Any help or directions is much appreciated, thanks.';

'>>16175791
I didnt read the screenshot but basically you have an enlarged Hilbert space. Your quantum system with many particles can be described as just another quantum system, with its own Hilbert space.
The formula is just a system state, just a linear combination of basis vectors of the hilbert space. The Cs are just coefficients';

'>>16175870
>>16175872
[math]\displaystyle
\sin(\frac{\pi}{6}) = \frac{1}{2}
[/math]
?';

'>>16175880
Right, sorry my mistake.

Instead: for [math] x \in \mathbbb{Q}\setminus ( \{ 0,-1/6,1/6,1/2\} + \mathbb{Z} ) [/math] , can we say [math] \sin(\pi x) [/math] is irrational?';

'>>16158770
is this digivolution really just the number line?
think i'm descartes';

'>>16175798
>The formula is just a system state, just a linear combination of basis vectors
I can't see how that's a linear combination. A linear combination is just one sum, but here there appear to be [math]N[/math] different sums';

'>>16175909
Sorry messed up the latex: [math] x \in \mathbb{Q}\setminus ( \{ 0,-1/6,1/6,1/2\} + \mathbb{Z} ) [/math]';

'>>16175912
What do you mean N sums? The very formula you posted is one sum. I mean theres many things being summed, but its just a sum of state vectors times an amplitude, i.e a state of a hilbert space';

'>>16175791

>>16175798 basically covered it. This sum is expressing that for every single-particle wavefunction, you have the expansion in the complete eigenbasis of a well defined quantum number, remember [eqn]\psi(x_1,t)=\langle x_1 | \psi(t)\rangle =\sum_{ \left\{E_1\right\} }\langle x_1 | \psi _{ E_1} \rangle \langle \psi _{E_1}| \psi (t)\rangle=\sum _{\left\{E_1\right\} }C_{E_1} \psi _{E_1}(x_1) e^{-i\lambda _{E_1}t/\hbar}[/eqn]
where [math]E_1[/math] is denoting the set for quantum numbers of this particle and [math]\lambda_{E_1}[/math] is the eigenvalues of the basis. In the case of the free particle they would be the energy. You also get a different set of constants from the expansions of each wavefunction and that he denotes as [math]C(E_1,\cdots,E_N,t)[/math].';

'>>16175913
https://proofwiki.org/wiki/Niven%27s_Theorem';

'>>16175920
I interpreted that notation to mean:
[math] \Psi(x_1...x_N,t)=\sum\limits_{E_{1}^{'}} \sum\limits_{E_{2}^{'}} ... \sum\limits_{E_{N}^{'}} C \left(E_{1}^{'},...,E_{N}^{'},t \right) \psi_{E_{1}^{'}}(x_1) ... \psi_{E_{N}^{'}}(x_N) [/math]
Where [math]E_{i}^{'}[/math] is the index that runs over the possible values of [math]E_{i}[/math]. If it was just one sum why would they use the primed [math]E_{i}[/math]?

>>16175928
Sorry if it's obvious but I can't quite map that equation into the situation at hand... What is [math]\psi(x_1,t)[/math]? There are only the various [math]\psi_{E_{i}}(x_i)[/math], which are not time-dependent, or the total [math]\Psi(x_1...x_N,t)[/math].
Btw I love that picture';

'>>16175953
Well all the Eis there are primed, the prime doesnt seem to do anything. Yes, its one sum
This is called a tensor space, or something like that. When the particles are bosons (when theres no pauli principle) then the dimension of the new space is the product of the dimensiones of each space
So say you have 2 particles with hilber spaces of dimension 3, each of 3 states
You have then 9 states in the combined space
(1,1),(1,2),(1,3),(2,1).. etc, and of course any combination is also a state
For fermions the space is smaller because you cant have some repetitions of states';

'>>16175953
>What is ψ(x1,t)

yeah sorry I was a bit vague, in what I wrote I took [math]\psi(x_1,t)[/math] (or more correctly it should be [math]\psi_1(x_1,t)[/math]) to be the wavefunction of a single particle, eg particle "1" at "x_1". So imagine you have only one wavefunction, this would be the expansion in the complete eigenbasis. Now what you wrote is exactly doing this for the wavefunction of the N-particle Hilbert space (you can absorb the time-dependent exponential in the constant to be consistent with notation). If you want, this is the general tensor decomposition of the basis on [math]\mathcal{H}^{\otimes N}[/math] to each egenbasis of the one particle spaces.';

'I've been out of school for over two years and am going back to start a physics PhD in August. How do I get caught back up?';

'>>16175992
>Yes, its one sum
Then I really don't understand what the sum means. For example, what does the first term of the sum look like? To write it, I would have to substitute the value of [math]E_{1}^{'}[/math] inside [math]C \left(E_{1}^{'},...,E_{N}^{'},t \right) \psi_{E_{1}^{'}}(x_1) ... \psi_{E_{N}^{'}}(x_N)[/math]. But what about all the other [math]E_{i}^{'}[/math]? What values do they take in the first term of the sum?


>>16175998
Ok, then what happens in this passage?
[math]\langle x_1 | \psi(t)\rangle =\sum_{ \left\{E_1\right\} }\langle x_1 | \psi _{ E_1} \rangle \langle \psi _{E_1}| \psi (t)\rangle[/math]
Where does the sum come from, and why is [math]E_1[/math] in curly brackets whereas in my book it isn't?';

'>>16176137
>what happens in this passage?
you use that your basis is complete, ie:
[eqn]\mathbb{1}=\sum _{\left\{E_1\right\}}|\psi_{E_1}\rangle\langle \psi_{E_1}|[/eqn]

>curly brackets
I chose to write [math]\left\{E_1\right\}[/math] in the sum to emphasize that there might be more than one quantum number in the sum. Eg in 3d the particle in a box has 3 integers etc';

'>>16176137
>>Yes, its one sum

(I'm >>16176197) but don't get too confused about this (one sum with many indices == multiple single index sums) you got it correctly here I would say >>16175953';

'>>16176083
If you're going to do a PhD you should be able to work that out yourself.';

'>>16176083
depends on the type of PhD program and the research area.';

'>>16176356
I'm just concerned with making sure I nail the standard graduate level coursework';

'What’s the evidence that there were no humans in the Triassic period, the time of dinosaurs?';

'If three random points are picked inside a square (uniformly) and connected by lines to form a triangle, what is the probability that the triangle covers more than 1/3 of the surface area of the square?';

'>>16176482
I tried doing this is google sheets to brush up my skills but I'm getting bad answers, can anyone check my work
RAND() in A2 to F2
=0.5*ABS(A2*(D2-F2)+C2*(F2-B2)+E2*(B2-D2)) in G2
=if (G2>=1/3,1, 0) in H2
And then do as many trials as possible
Or if everything's good maybe I'm not doing enough trials? I did 10000 (Row 2 to 10001, fencepost error haha) and I get everything for 0.0035 to 0.0040)';

'>>16176548
What's more interesting is the so called closed form solution';

'>>16176548
Seems to be about right. I used Desmos with 10 000 trials and got 0.0041.';

'>>16176482
>>16176560
https://mathworld.wolfram.com/SquareTrianglePicking.html';

'>>16176548
And 100 years ago, everyone “knew” that the world was flat. >:D';

'>>16176761
100 years ago was 1924. WWI ended in 1918. America had pilots fighting in fighter planes in that war. You think they thought the world was flat?';

'Say you have a square with vertices in coordinates (0,0), (1,0), (1,1) and (0,1). You put seven points inside the square and connect all of the points to each other by straight lines. Now, clearly any set of three points out of the seven points form a triangle because any set of three points are also connected by lines. What are the coordinates of all those seven points if the area of the smallest such triangle is maximized?';

'>>16176472
Again, it depends on your field and the type of program. If you are taking courses then just recap some things and study a lot during the course. If its more like doing research from day 1, you probably have to start reading papers from now.';

'what happens if you use a portal gun to connect the bottom of the mariana trench with the moon?';

'>>16176946
It depends entirely on how the Valve devs coded it in
Real answer, portal guns don't exist (yet) so it's a meaningless question in here
>>>/x/';

'>>16176197
>>16176205
Thanks for the extensive help but I don't get it. Using the formula here >>16175928, if for instance [math]E_1=\{m,n\}[/math], I would have:
[eqn]\psi(x_1,t)=C_{m} \psi _{m}(x_1) +C_{n} \psi _{n}(x_1)[/eqn]But what if I have two particles, with [math]E_1=\{m,n\}[/math] and [math]E_2=\{p,q\}[/math]? How can the following make sense?
[eqn]\Psi(x_1,x_2,t)=\sum _{\left\{E_1\right\}\left\{E_2\right\} }C_{E_1,E_2} \psi _{E_1}(x_1)\psi _{E_2}(x_2)[/eqn]The only way I can think it would make sense is if it meant:
[eqn]\sum _{\left\{E_1\right\}\left\{E_2\right\} }C_{E_1,E_2} \psi _{E_1}(x_1)\psi _{E_2}(x_2)=
\sum _{E_1=m,n}\left[ \sum _{E_2=p,q} C_{E_1,E_2} \psi _{E_1}(x_1)\psi _{E_2}(x_2)\right]=
C_{m,p} \psi _{m}(x_1)\psi _{p}(x_2)+
C_{m,q} \psi _{m}(x_1)\psi _{q}(x_2)+
C_{n,p} \psi _{n}(x_1)\psi _{p}(x_2)+
C_{n,q} \psi _{n}(x_1)\psi _{q}(x_2)
[/eqn]But then:
[math]\sum\limits _{\left\{E_1\right\}\left\{E_2\right\}...\left\{E_N\right\} }[/math]
cannot be called a "single sum", because a single sum has a single set of indices. Unless of course [math]\left\{E_1\right\}\left\{E_2\right\}...\left\{E_N\right\}[/math] is taken to mean all the possible combinations of the different sets of quantum numbers, but that seems crazy as a notation choice.';

'My apartment recently started vibrating or something late at night, like at 3AM or something, and it keeps waking me up. It's not like earthquake tier, it's like there's a car turned on or something some distance away in the way it sounds. The frequency is around 33-37hz (or was it khz?) making it barely audible, but its the level where it's super annoying. Is there some way to cancel this out cheaply? Because it's probably the building, I don't think just sticking foam boards up will actually do anything, though I guess I could try.

I've already tried countering it with a fan, but, the fan just oscillates with the vibration after a while, making it louder and more annoying.';

'>>16177026
>if for instance E1={m,n}, I would have

No, you would have (you also ignored time):
[eqn]\psi(x_1,t)=\sum _{m,n\in\mathbb{N}}C_{m,n}(t)\psi_{m,n}(x_1)[/eqn]
Take the simplest example of a 2d box, there you have (take [math]\vec{x}_1=(x_{1},y_{1})[/math]): [eqn]\psi_{m,n}(\vec{x}_1)=\mathcal{N}\sin\frac{m\pi x_1}{L_{x_1}}\sin\frac{n\pi y_1}{L_{y_1}}.[/eqn] So for two particles with two integer quantum numbers you would get:
[eqn]\Psi(x_1,x_2,t)=\sum_{m,n,p,q} C_{m,n,p,q}(t) \psi_{m,n}(x_1)\psi_{p,q}(x_2)[/eqn]
This is what you wrote in the first equality after
>it would make sense is if it meant:
I do not understand what you wrote after the second equal sign (your sums dissapeared, you have free indices etc).

>>16177026
>cannot be called a "single sum"
I do not know why you get so confused about the sum, you can see in (1.3) that you have a *single* sum of N sets of quantum numbers. So its just a matter of language or notation if you want to break it into N sums of [math]E_k[/math]s.';

'>>16177048
(I do not know why this did not compile, here is another try (I checked with the TeX box))
>Take the simplest example of a 2d box, there you have (take [math]\vec{x}_1=(x_{1},y_{1})[/math]): [eqn]\psi_{m,n}(\vec{x}_1)=\mathcal{N}\sin\frac{m\pi x_1}{L_{x_1}}\sin\frac{n\pi y_1}{L_{y_1}}.[/eqn] So for two particles with two integer quantum numbers you would get:
>[eqn]\Psi(x_1,x_2,t)=\sum_{m,n,p,q} C_{m,n,p,q}(t) \psi_{m,n}(x_1)\psi_{p,q}(x_2)[/eqn]';

'>>16177048
>>16177050
TeX on this board bugs out a bit from time to time if you don't use enough whitespace. I assume it has something to do with the auto-wrap function or whatever? I'm not a web page designer, I just know that the problem (usually) goes away if you dump more spaces into things
[eqn] \psi_{m,n} (\vec{x}_1) =\mathcal{N} \sin \frac{m\pi x_1} {L_{x_1}} \sin \frac{ n\pi y_1}{L_{y_1}}. [/eqn]
>[eqn] \psi_{m,n} (\vec{x}_1) =\mathcal{N} \sin \frac{m\pi x_1} {L_{x_1}} \sin \frac{ n\pi y_1}{L_{y_1}}. [/eqn]';

'>>16177057
oh, good, the opposite end of the problem. now it works when I don't want it to.
I hate this site.';

'Sorry I'm retarded. So let's see if I finally understand. You wrote the sum over [math]\mathbb{N}[/math] because you are assuming they are principal quantum numbers? So for example if there was also an electronic spin quantum number [math]s[/math] then I would have [math]\{E_1\}=\{m,n,s\}[/math] and:
[eqn]\psi(x_1,t)=\sum _{m\in\mathbb{N}}\sum _{n\in\mathbb{N}}\sum _{s=-\frac{1}{2}}^{\frac{1}{2}}C_{m,n,s}(t)\psi_{m,n,s}(x_1)[/eqn]?
While if I had just a principal and an azimuthal quantum number then I would have [math]\{E_1\}=\{n,l\}[/math] and:
[eqn]\psi(x_1,t)=\sum _{n\in\mathbb{N}}\sum _{l=0}^{n-1}C_{n,l}(t)\psi_{n,l}(x_1)[/eqn]?
So basically the notation [math]\sum _{\{E_1\}\{E_2\}...\{E_N\}}[/math] is telling me to sum over all the quantum numbers in the set [math]\{E_1\}[/math], each on its specific allowed range, then to sum over all the quantum numbers in the set [math]\{E_2\}[/math], each on its specific allowed range, and so on until the set [math]\{E_N\}[/math]?

>>16177060
Eh I know the TeX can break randomly here. I just slapped everything into the preview box anyway';

'>>16177086
>because you are assuming they are principal quantum numbers?

I wrote the sum in [math]\mathbb{N}^2[/math] because I had in mind the 2d box (no other quantum numbers) but what you wrote is fine.

>>16177086
>So for example if there was also an electronic spin quantum number s then I would have

yes, what you wrote is correct. You have one set [math]E_k[/math] for each 1-particle eigenbasis, of course this set as you wrote can contain more than one number ranging in a different domain, and then you have N such sums.';

'>>16177097
Thank you very much';

'Suicide suicide suicide';

'>>16177036
Use earplugs.

It's cheap and cancels out the vibrations passing through the air and to your ears.';

'>>16177144
No problem anon';

'Suppose I want to solve a system of linear equations but I am only interested in the first value. Is there a computationally more optimal way to solve.';

'>>16177161
Not him, I doubt it will help. There used to be construction work going on in a building next to mine, with jackhammers and such, and I'd get woken up by the vibrations despite wearing the best foam earplugs I could buy (and that was 150-300 Hz).
Best course of action is to find out the source and tell them to stop. Low frequency noise is especially detrimental to human health and there are special laws that set upper limits. These laws are usually made with wind farms in mind but their limits should apply to everything.';

'>>16177179
>>16177161
You're right. When the building shakes, so does the person.
I guess the next cheapest option is to make a noise complaint.';

'>>16177170
LU is faster to factorize than Gaussian-Jordan, and since the final computation solving step is greatly reduced since you only need 1 value instead of all, seems like the way to go.

Might be talking out of my ass here, but to be more specific, LU factorization is O(n^2/3) with obvious O(n^2) solving, and GJ factorization is O(n^2/2) with obvious O(n) solving, but we're ignoring the solving step so they're now constant.';

'Does anyone have a guide for the physics like pic?';

'>>16177286
There's a chart in the OP which was made by a theoryfag, it has no nuclear physics and 1 condensed matter (Simon) which is too shallow: Kittel or Ashcroft & Mermin are better
This is better but also very theory focused and heavy: https://math.ucr.edu/home/baez/physics/Administrivia/booklist.html. If you start with Feynman lectures or Landau & Lifshitz instead of something easy like Serway you will get filtered immediately

Imo in terms of topics a chart would have to look like this (for a lot of stuff I can't recommend a textbook because I only read 1 or just used course notes)

Warmup:
>Serway
>calculus
>linear algebra

Common basics:
>analysis esp. Fourier theory
>differential equations
>Classical mechanics
>Quantum mechanics (Sakurai)
>Thermodynamics
>Statistical mechanics
>Electrodynamics & special relativity (Griffiths)
>Condensed matter (Kittel)
>optional: Intro nuclear physics (Krane)
>optional: Optics
>for theorists: groups and Lie algebras, differential geometry
>for experimentalists: statistics, numerical methods, Python scripting

With this you should be decently prepared for graduate level courses, but there's no point having a common chart for all the subfields. I'd welcome any additions.
t. physics MSc, currently a code monkey';

'Doing some world building for a personal project, what would be some interesting metals to have as a planet's core besides iron? The inhabitants of these planets can be extremophiles. I'm experimenting with what civilizations and cultures might be or develop like in foundationally odd or extreme environments.';

'>>16177423
Some book refs:
>analysis esp. Fourier theory
>differential equations
Hassani
>Classical mechanics
Arnold
>Thermodynamics
>Statistical mechanics
Kardar I&II, Pathria, Kubo

>for theorists: groups and Lie algebras, differential geometry
Hassani, Hall, Lee, Nakahara

Also, may I add to this:

>General Relativity
Weinberg, Zee, Wheeler, Wald, Carroll, Hawking&Ellis

>Particle physics
Halzen&Martin

>QFT
Zinn-Justin, Peskin, Bjorken, Tong notes, Weinberg I,II,III, Srednicki

>Quantum information
Preskill

>String theory and Supergravity
Zwiebach, Polchinski I&II, Kiritsis, Freedman, Schwartz';

'>>16177497
Also, forgot:

>Electrodynamics & special relativity
Jackson';

'>>16177504
>>16177497
>>16177423

Thank you anon. Love you';

'Is number sense real?';

'>>16178058
You mean like intuition? That's definiteky real.';

'If you are given the low-rank approximation of a matrix K*Q that was obtained by training a neural network to minimize the loss function, if you take K*Q and then take the SVD = U*S*V^T does that imply that K = U*S1*B and Q = B^-1*S2*V^T and S1*S2=S? If so, how can you find B?';

'>>16177161
>>16177189
>>16177179
>>16177189
Yeah it's basically the vibrations that are the annoying part. I've taken a walk around and can't pinpoint the source which is why I was hoping to just cancel it out somehow. I mean, it should be possible right?';

'>>16178344
>>16177189
It's possible. Just strip the walls down to their
foundations, throw on real foamy material that can
absorb the vibrations in all directions, put the walls
back on and you can have a restful sleep.

Not that the landlord would approve of it, of course...';

'>>16178381
jojokes on you I am the landlord; though, it's an apartment so I'm not sure if I can just remove the walls or if I need body corporate approval';

'>>16158770
I have a very elementary understanding of calculus and linear algebra and want to understand how they are connected. One of my mathematically inclined friends said that calculus can be generalized to linear algebra and from what I remember it had something to do with functions and derivatives being vector space and subspace respectively. Can someone help me understand in clearer terms?';

'>>16178414
https://people.math.harvard.edu/~knill/teaching/math22b2019/handouts/lecture25.pdf
The set of all functions is a vector space. The derivative operator is a linear operator on that vector space.';

'>>16178414
He is talking about functional analysis, but saying that calculus can be generalised to linear algebra is a pretty absurd thing to say. Also, linear algebra is foundational to multivariate calculus. In univariate calculus derivative represents the slope of the closest straight line approximation of the function. In multivariate, you'd deal with closest multivariate linear approximation of the function, and linear functions are what's linear algebra is all about.';

'Why isn't citric acid considered a vitamin?
I just ran an effective 3 year experiment in avoiding citric acid and i tried fucking everything to replace it and failed. Vinegar consumption was almost good enough. I think it's necessary to balance oxidative stress.';

'>>16178432
>>16178454
Thank you. So it's an oversimplification, but a relationship still exists... I ask because I would really like to pursue a degree in applied mathematics and it feels like a conceptual grasp of calculus and linear algebra (and their relationship) would be great to have, as they are the two subjects which seem to be taken for granted or serve as the foundation for other areas. Do you have any advice on being able to grasp the ideas in an intuitive, conceptual way while also being able to deploy them in models of real world phenomena? Thank you for the good responses.';

'How to profit from the upcoming paradigm shift of a multipolar world? China investing heavily in high tech and BRI
>inb4 chink shit
don't care, they're dominating and US is afraid, hence 100% tariffs on EV's.

On a more concrete level: I am a technician, so I troubleshoot electromechanical processes on various machines. How do I take this job and turn it into making money? Automation engineer? Project management? Consulting?';

'>>16178566
Do lots of exercises. It's normal to not fully understand a mathematical concept the first time you read it. You need to get familiar with it by using it. If you are stuck with a problem, it can help to look up worked solutions, lecture notes or stackexchange questions. In my experience this is true even for more abstract pure math subjects like analysis or topology if you want to understand the objects in themselves.
It's a bit different in statistics, physics and applied math, there I've actually gotten insights from reading textbook chapters and blogs that I wouldn't have gotten just from mechanically doing the exercises. For example, confidence intervals and p-values are often taught in a very misleading way, and it took me a long time to figure out what a density matrix is. Talking to more experienced people is good but they can often be very partisan or narrowly focused on their own research.
Applied math is a very good degree imo, especially if you also learn to code.';

'Hey /sci/, pretty sure I know the answer to this but wanted to see if some smarter folks had any insights.
I’m writing a (hard-ish) science fiction story with a focus on human settlements out in the Jupiter / Saturn area.
By and large permanent settlements are cylinder space stations (think Gundam or Policenauts). But that said I have major Ice mining going on with the various moons such as Callisto and Europa.
Is there a non-retarded way to have 1g settlements on the surface of these moons (thus creating long term quarters for miners - something like moon with Sam Rockwell)?
I have a scene in mind where the POV character goes down to such a habitat only to find that things have gone awry…but realized that it might just be idiotic for such a settlement to even exist at which point I’d have them go to some sort of satellite instead.
Open to any and all thoughts! I know the ‘fi’ stands for fiction but I want it to at least be grounded in reality.';

'>>16178663
>1g settlements
you mean like earth gravity simulation? the only way to do it is through spinning, and spinning in space is a lot easier than spinning on an axle thats bolted to the ground.';

'>>16178686
Yes and yes.
That’s what I figured - like the moving parts alone would make that a nightmare right?
And the alternative is living with 1/3rd gravity and getting boneitis or any host of awful complications.';

'What does this mean? Why are there two x's? Where does the z come from?';

'>>16178706
they're dummy variables with scope confined to the set definition';

'>>16178691
i mean, its not like earth gravity is 100% critical for supporting life, it would be okay to have it break down every so often, and its not like frequent rocket launches up to an orbital station would be any less error prone (which would, in fact, be a threat to supporting life).';

'>>16178663
> major Ice mining going on with the various moons such as Callisto and Europa
As long as the miners aren't living there full time it's a non-issue. They can return to 1g environments after 6-12 month shifts just like astronauts do today. Also since it's sci-fi, have them take some supplements / medicine that reduces bone degradation etc.';

'>>16178739
>>16178773
Fair enough! Glad I asked then.
I was thinking a space elevator as an alternative to rockets but it’s not like that’s a simple thing either.';

'>>16158770
Is it possible to do ochem, phys, and genetics simultaneously or will I fail in all three if I do them together?';

'>>16158770
are quantum mechanic effects the proof that we live in a computer simulation ? Or the opposite ?';

'>>16159237
that bird could just fly away when the trap opens';

'>>16179221
The opposite. Various quantum mechanical systems can't be simulated because the computational resources required scales exponentially. So even a universe size computer could not simulate another universe (or even a portion of it).';

'I have an initial velocity, final velocity and distance and want to find acceleration that will change the velocity over the given distance. Finding constant acceleration is pretty easy using basic acceleration equation. However I would like to ease the movement a bit by applying most of the acceleration only on the end or beginning of the path. Initially I used some easing functions with constant "area under graph"(integral?) but the problem is that same final change in velocity does not imply same displacement.

What kind of functions could I use for a(x) so that v(t) remains at v2 and disp(t) at d? Are there any functions like that except for constant value? I can change the equation for t too if needed.';

'>>16167974
Thanks anon.';

'>>16179188
They use different parts of the brain. Normally when you multi-class a semester, you want the subjects to be similar (like calc heavy, bio heavy, etc.) in some way.';

'Are all particle interactions mediated by photons?';

'>>16180143
No, just those involving electromagnetism.';

'>>16180150
>just those involving electromagnetism.
All of them? Would it be possible to detect, say, an electron, without photic interactions?';

'>>16180194
Depending upon precisely what you mean, sure.
https://en.wikipedia.org/wiki/Electron_capture';