>>17016986
Previous thread: >>16944314

>>17016986
I have one. If the double slit interference is an optical phenomenon where light waves pass through two closely spaced slits and overlap, creating an alternating pattern of bright and dark bands (fringes) on a screen. What would happen to the bands if you sent a single photon through, then waited some time (Like a day) before firing another one through. Would the inference band show signs of slight deformation to one area, if the proton restarts its first position?

If an electron's position is very well defined, why does this cause its kinetic energy to rise?

Are there any developments on the Riemann Hypothesis lately?

>>17017235
Why is it well defined in the first place? Is there perhaps something keeping it there...

Anons I got a Dover print of Emily Riehl's undergrad book to supplement another text. Is it worth digging into?

>>17018509
Nope

File: BertrandParadox.jpg (23 KB, 320x269)

23 KB JPG

conditional probability
https://onecompiler.com/commonlisp
[code]
;; Use defparameter to define global variables in the REPL
(defparameter *boxes* '((1 1) (1 0) (0 0)))

(defun run-bertrand-trial ()
(let* ((box (nth (random 3) *boxes*))
(first-coin (nth (random 2) box)))
(list box first-coin)))

(defun run-simulation (num-trials)
(let ((gold-observations 0)
(gold-box-count 0))
(loop repeat num-trials do
(let* ((trial (run-bertrand-trial))
(box (first trial))
(coin (second trial)))
(when (= coin 1)
(incf gold-observations)
(when (equal box '(1 1))
(incf gold-box-count)))))

(format t "Total trials with gold observation: ~d~%" gold-observations)
(format t "Trials where box was Two-Gold: ~d~%" gold-box-count)
(format t "Empirical Probability: ~f~%" (float (/ gold-box-count gold-observations)))))

;; Execute the simulation
(run-simulation 10000)[/code]
(there are dummies on /pol/ who need to see this)

If light is a wave, why can it be breaked down to smallest possible parts called the photons? A wave in the ocean cannot be breaked down to its smallest part unless you're talking about just one wave.

>>17016994
How long you wait before sending through each particle doesn't matter. Once you have a large enough sample size the interference patter will still appear.

>>17021631
What do you think water is made from anon??

File: IMG_2029.jpg (1.14 MB, 1580x2174)

1.14 MB JPG

>>17016986
Scientifically, why am I me and not someone else?

>>17021669
>you're on the trolley tracks
I've never seen this version of the trolley problem before. Would you sacrifice your life to save other people on the other track?

File: bap4pxmpa0s71.png (550 KB, 625x667)

550 KB PNG

>>17021644
The reason why there is a wave on water is because water molecules are interacting with each other. The way how light is a wave is not like photons were interacting each other producing waves.

I am not knowledgable and am a beginner in all of this. Here is my question: People say the double slit, superposition, and entanglement are not weird, just that they are presented as weird.

How true is this? Are they just overhyped and not really 'breaking everday human logic'?

Does a knot have spooky action at a distance?
If I change the properties of the knot at one end, the nature of my string at the other end can be either knotted or unknotted.

Could particles be complex knots in some spacetimey fabric?

>>17022206
they are connected by the same rope, so it's neither spooky nor at a spooky distance.

>>17016986
>annas-archive.org
the OP needs to be updated.

>>17022250
https://4chan-science.fandom.com/wiki/Obtaining_textbooks has a good list for the OP, specifically https://open-slum.org/ which tracks library mirrors.

File: IMG_0323.jpg (298 KB, 1200x2133)

298 KB JPG

>>17016986

>>17022203
They probably mean that the math that describes all those things (and QM in general) is not particularly complicated. It's mostly just basic linear algebra. However the physical effects are so outside of everyone's every day experiences is what leads to all the problems in their understanding.

>>17021631
>If light is a wave
Light is associated to a type of object in the universe we live in. A wave is a mathematical object. Saying "light is a wave" is the short way meant to imply that the behavior of light can be predicted by modeling said behavior with mathematical waves. Saying "light is a particle" is a short way meant to imply that the behavior of light can also be predicted by modeling said behavior from a mathematical "point particle". Light simply is what it is - you don't need a description of a dog with genetics or biology to have a dog exists. We're using math with waves and points to describe light; light doesn't "care" that it's surprising to humans that it can be described using both.

>why can it [be both wave and particle]
No one knows (no consensus in the community). Maybe pilot wave theory is right. Maybe wave funciton collapse is a real thing. Any attempt at explanation is just a theory

Smart people seem to like linguistics. Anyone know if there is a connection between the words
>wood (like wud)
>water (like watr or wudr)
I noticed how I was pronouncing it and realized the two sounded similar. Google didn't bring anything up.

>>17022849
No, just a coincidence I'm afraid. The etymology of the two words is very different. In fact the word for "water" in all languages may be the only word that can be traced back to a single common root - apa / aqua.

>>17016986
How do I explain scrotumniggas cat to a class of 5th graders? Can't find anything on the Internet

>>17016986
I'm trying to turn sodium bicarbonate into sodium carbonate aka washing soda. I've seen differing instructions on the internet. Basically you're supposed to heat it but some say different temperatures and different cooking times.
Does anyone know the correct temperature and cooking time? Also I heard that aluminum reacts with washing soda which would neutralize its effectiveness. Should I avoid using my aluminum pan to cook it?

>>17022924
The dictionary of Indo-European roots on my shelf is one of my favorite possessions.

>>17022266
i don't get it

File: Screenshot_20260728_091335.jpg (345 KB, 1722x1634)

345 KB JPG

Will ice cubes actually sink in warm enough water? Because according to this chart ice seems to have greater density than water at something like 80 degrees celcius

File: ice-water-density.png (41 KB, 768x432)

41 KB PNG

>>17026947it
I'm not sure where that chart got it's data from, but the ice density looks wrong. In fact it shouldn't be a smooth graph, there's a discontinuity at the freezing point. The correct numbers should be much lower. All this means is that ice would still be less dense than hot/boiling water.

>>17026962
That's just one of the charts that popped in google image search. But they all looked similar and smooth curves.

File: DSC_3042-scaled-1.jpg (1.26 MB, 2560x1707)

1.26 MB JPG

A neutrino detection device works by having a tank full of water and surrounding it with very sensitive cameras. When a neutrino messes with an electron of a water molecule, it creates Cherenkov light which is detected.

Does this mean that if you went to the bottom of Mariana trench with a submarine where sunlight could not reach at all, and you had a very sensitive camera, you would see tiny flashes of light as neutrinos interact with the water molecules?

>>17027329
Think about it. The phase change from water to ice means the graph can't be smooth.

>>17027746
That's what I thought. And that's why I thought the graph was strange

File: 231811.jpg (2.65 MB, 5425x2824)

2.65 MB JPG

I don't know if this question can be answered but how many streets loop vs how many end? Or, what percentage of streets loop vs end?

To expalain. Say a simple version: street A terminates at street B, street B terminates at street C, street C terminates at street D and street D terminates at street A. That street loops.

vs
Street A terminates at street B but street B terminates and forces the driver to turn around at its end. Even though A terminates at B because B terminates with no outlet, street A can be said to end.

This of course would be directional as many streets terminate at places where a left or right turn is possible. I would claim that most streets loop, but I don't know and I don't know how I would go about proving that. There's a lot of Cul-de-sacs and dead ends out there.

I am an undergraduate economics student, recommend me must-read scientific literature regarding economics /sci/.

File: 91lCtPCDlgL._SY466_.jpg (56 KB, 303x466)

56 KB JPG

>>17028438

>>17028436
They invented graph theory for this, there are also sparse matrices you can populate with this info with a bunch of time, a machine learning algorithm, and google maps (they will cut off your API access before you actually get enough data to do the answer though -- you should probably stick to scanned images of old map atlases)

>>17028667
I didn't laugh

File: Screenshot 2026-05-11 114645.png (456 KB, 960x506)

456 KB PNG

how do i know if a textbook will be good or bad?
for example if i want to learn to learn about mathematical logic how do i find a good textbook for it? without wasting time trying loads of textbooks until you realise they suck

>>17028757
Most people don't laugh at things that aren't jokes. Good on your for having all your marbles together.

>>17025359
Not all ovens are the same. Honestly, if you're trying to determine yield percentage, you could try measuring the weight difference (iffy) or measure pH (also iffy if you don't have the tools). Try out a ceramic pan to avoid risk if you want.

>>17020775
hmm?

>>17022250
yes

File: pi to root two.png (11 KB, 570x270)

11 KB PNG

Pi to the power of square root of two. Is this an irrational number?

this is kind of outside of the scope of whats being asked for the thread but you guys ever see shit that you can't find any reasonable explanation for? weird personal experiences or even just spooky vids on the internet?
do those kinds of things just strike you as entirely fake despite how unsettling it may appear to be or whatever personal claims have been made about said videos? or are those sorts of things you just shrug and say maybe about?

>>17031543
Irrational, yes, but also transcendental

That's only true / proven for integer powers of [math]\pi[/math]. It's still an open question if numbers like [math]\pi^{\pi}, \pi^e, \pi^{\sqrt{n}}[/math] are irrational - though most believe them to be true.

>>17033985
My favorite one is the fact that nobody knows that pi^pi^pi^pi is not an integer.

If neutrons need to a stable nucleus with protonts to exist and can not exist by themselves and decay with a half life of 15 minutes, how do neutron stars exist?

When a neutron decays it creates a proton, electron and electron antineutrino, so when a supernova creates the core that becomes a neutron star and the compression forces the electrons and protons together where does the supply of electron antineutrinos come from to create the neutron? Asking for a friend.

>>17034382
It's all to do with energy levels. The reason a free neutron decays is because it's slightly more massive than a proton so decaying results in a lower energy state (a proton). Inside atoms, nucleons have discrete energy levels (just like electrons do in their orbital shells). If a bound proton already occupies a particular quantum state that means a neutron can't decay into the same state due to the Pauli Exclusion Principle. That's why neutrons inside atoms are stable. They aren't allow to decay due to the laws of QM.

It's a similar reason why neutrons are stable in neutron stars. The particles are compressed so much all the lowest energy levels are occupied, there's nothing left to fill resulting in the completely opposite particle reaction of p + e -> n being more energetically favourable.

File: dog moon.gif (568 KB, 910x828)

568 KB GIF

Did humans always find animals to be cute or was it parallel evolution as a result of animal husbandry? I imagine there is little evidence on account of writing of sufficient quality appearing too late.

>>17034382
[math] n \rightarrow p + e + \overline{\nu}_e [/math]
[math] n + \nu_e \rightarrow p + e [/math]
[math] p + e \rightarrow n + \nu_e [/math]

mathwise, a particle going forward in time == antiparticle going backwards in time
reorganize your particles, ensure 4-momentum conservation, and voila
(observe the lepton number conservation)

If gravity is not a force but only the distortion of space-time due to mass, then why does there need to be a Higgs particle or field?

>>17034817
Idk

Humans find human babies to be cute and the babies are evolved to be cute to promote the baby's survival. We're evolved to like cute things. Lots of animals like elephants and dolphins probably find other species to be cute too. Cute girls are also advantageous, cause eye candy makes boys happy.

>>17035280
Physicists want to force a concept called local gauge invariance into Lagrangians that they care about cause it leads to the right equations like Maxewell's Eq, and it also works for the strong force too. Using it forces one to tack on a massless gauge field to the Lagrangian. For electrodynamics (E&M)and chromodynamics (strong), this is fine and the photon and gluons are massless. But the Z and two W bosons for the weak interaction are not massless. One could ask, is there any way or case to incorporate a massive gauge field with local gauge invariance?

The Lagrangian T-U for a Higgs particle has symmetry to it (like an even function), and the Higgs potential U has continuous symmetry including about the ground states, so like if the two parameters are x and y where (x_min)^2 + (y_min)^2 = constant. You can "break" the equation symmetry by doing a variable change or transforming about any one of the infinite ground state solutions of the aforementioned equation. After expanding, you'll find the Higgs particle pops out (also something called a Goldstone boson but wtv)
When you try to enforce local gauge invariance before all of this - meaning you have to also add that massless gauge vector field like the others - performing the variable change to break the equation symmetry will not only create the Higgs, but the terms associated with the added gauge field now have a non-zero mass associated with it. The end result is a Lagrangian with local gauge invariance and a massive gauge field instead of massless. So if the Higgs particle exists, then there exists a way for massive gauge fields to have local gauge invariance, the weak in particular.

The Higgs also interacts with fermion fields - which start out as massless - via some Yukawa potential, and again by rewriting it/breaking the symmetry, you can give them mass.
Gravity doesn't endow mass to anything, it just describes what happens when you do. Interaction with the Higgs endows mass

Going back to finish my EE degree and want to use my old credits to save on money. What's the best way I can study and refresh myself on the material? I've basically forgotten almost all of calculus, physics, and electronics and have struggled a bit trying to re-learn it all.

File: file.png (282 KB, 1120x368)

282 KB PNG

someone tell me how true pic is I dont understand why briefly looking at 10% coverage would be more dangerous than briefly looking at a normal sun. There is a eclipse tonight and I usually see the sun from my window at the correct time of the eclipse.

>>17035484
A solar eclipse means you are not looking at the sun, you're looking at the moon

>>17035484
>briefly looking at 10% coverage would be more dangerous than briefly looking at a normal sun
Dude, that image in no way implies that. It says to take the same precaution in either case, nothing more.

How do I stop being a retarded ADHD chud? I'm trying to learn calculus but my retard brain can't help getting stuck on trig.
And every time I've tried to learn programming I can't stick to it for more than a week.
I've tried every amphetamine and Ritalin type drug, all useless.
Straterra works a bit, but I still can't stay focused.
I've blocked every doomscroller on my pc and limited the browser on my phone to 30 mins and it still isn't fucking working.
How the fuck do I condition myself to be an actually useful human being instead of a worthless wastrel?

>>17035911
Study English or law or paramedic or something? Why are you forcing calculus? To get a career using it that you'll also feel anxiety in? Not being an ass, I'm just old. I wish, back then, I knew the advice I just gave.

>>17035913
The problem is I don't like law, don't really care about English (plus it's about as jobless as you can hope to be) and I don't like people very much, and hate high pressure, so medical fields are unappealing.
But I really like machines and electronics and all of those fields need math.
I've been a mechanic, and it's OK, but I'm sick of being constantly covered in grease, oil, and various other filth, while destroying my body and getting paid shit.

>>17035917
>English (plus it's about as jobless as you can hope to be)
I meant "teaching English," but I should've specified that. Sorry. They make a great living, and you can choose a small town school, or a virtual school, or a private school, or a religious school, or etc. Likewise grade-level. Small kids. Adolescents. Community college. University. I suggested this because you're a coherent writer.

The same applies to math. If you know algebra well, you can take an algebra Praxis tomorrow and be qualified. Or geometry. Or elementary math.

"Hating people" is a complex thing. I'm an introvert but I like teaching to students who are well-behaved and are at school to learn, not just to be babysat. You seem similar. Again, your writing is well-thought-out. All teaching consists of is step by step explaining large concepts. Like why you need to learn calculus. You'd be surprised how many people can't. They're like "I just need to. Jobs and stuff."

>>17035919
My main problem with people is I don't like them depending on me.
I'm very absent minded, so I often make stupid mistakes, and then I struggle to get past even the smallest fuck-up.

I do quite like talking to people as well as explaining or teaching things. But I don't try much anymore because most people refuse to accept or understand anything they even slightly disagree with, either completely ignoring it, or worse, intentionally finding an extreme edge case that contradicts the norm.
I think if I had to teach people who were even close the modern, online, level of intellectual laziness and reticence I would hate my life.

Really all I want is a job where I can work 40 hours a week and have enough to buy a small house in an affordable area, some land to grow some tomatoes and chickens, and have some energy at the end of the day to actually do that.
Of course I have dreams of becoming some great big guy, but I would like it to not be a hail Mary with all my eggs in an imaginary basket.

Out of curiosity, are you a teacher?
I assume you are based on what you've been saying.
If so, what do you teach? And how is it working out for you as a career?

>>17016986
I thought the measurement problem in quantum mechanics means that any measure of a particle collapses Schrodinger's wave equation. Is this binary like on/off or can a wave function be partially resolved to limit its location more but not fully? And I thought measurement/observation meant any interaction with the particle at all. But I've been watching Sean Carroll and he says measurement is not fully defined in our current understanding or something. Can someone explain measurement/observation and whether it's a discrete binary thing or what exactly?

Standing still on the Earth's surface it is claimed that I am accelerating at 9.834 m/s2. yet as time continues I am still standing still and my velocity is still 0, so how can I be accelerating?

>>17036360
>I am accelerating
no you're not (in this context). Nobody says that

>>17036273
he is correct. There is no recognized well defined definition of a measurement or a collapse. If a particle collides with another, is there a collapse? Is it dependent on the number of particles? Is it a statistical thing, like how hot moves to cold because entropy is far to likely to increase? No good answers are given.

>>17036360
You are being pulled down by a force which would accelerate you at that rate if not countered by the normal force of the ground pushing you back up.

Alternatively, in the non-rotational reference frame, you have a velocity vector with direction parallel to the Earth's surface and magnitude equal to the sidereal velocity which is having its direction changed by that acceleration so that you move in a circle with the Earth instead of in a straight tangent line departing from it.

>>17036273
You can treat a measurement as if it causes the wavefunction to collapse because everyone agrees that the math of doing so works. No one can agree what it means and if that is what is actually happening. There is no such thing as a partial measurement, it's all or nothing.

what would happen to the world if we magically had infinite free energy? let's say perpetual motion is discovered, a perpetual motion machine is constructed, and it generates unlimited free energy.
what happens then? what happens to the sciences after that, how are the sciences affected? how are jobs affected? how is society affected?

I imagine electric companies would still charge people out the ass for it just because capitalism is the autoerotic asphyxiation of economic frameworks

>>17016994
https://youtu.be/lZ3bPUKo5zc?t=41m

File: 3d toriel.gif (2.39 MB, 500x281)

2.39 MB GIF

If the tectonic plates are moving at a certain level of pressure against each other, because of expected flows of magma, in such a way that we can predict how the continents are going to move for millions of years in the future, wouldn't it be possible to eventually correct for that movement and build ratchets or some form of expected notches for the plates to click along, so as to make the plates move like gears in a clock and nearly nullify massive unpredictable earthquakes in the future? You know, by spreading out the movement such that it's just a low buzz of movement people can barely feel, or even lower.

Obviously, we don't have the technology right now, but is there a pathway to that that's contemplatable? Could we turn our land plates into ratcheting plates that minimized quakes at safe regular releases of pressure?

>>17037018
Even the deepest human made holes don't reach past the earth's crust afaik. Their movement is prob equivalent to a large number of nuclear bombs, if I were to guess (iiwtg).

Humans are very small, and the mass of continents are very large. This is like asking if humans can just make large water fans in the ocean so when we predict some tsunami is gonna happen we can turn on the underwater fans to push the water away; we aren't talking about a swimming pool here, it's the damn coast of the ocean. We're small, and they're big. If a meteor was headed towards earth, the goal would be to nudge it slightly so it misses, not to drastically change it's momentum.

>>17037018
The 'plates' are blobs are different types of rocks and the stress regimes are always changing in geologic time, so the plate motions relative to each other change direction and velocity and are not predictable in geologic time and move too slowly for anything useful in human time. Look at the Hawaiin islands are now, and follow the line of islands up to the northwest and see how the line of island and subsea mountains bends due to the change in place motion over geologic time. No one knows how or why that changed. Also the current thesis is the San Andreas Fault is locked north of the Salton Sea up past Fort Tejon and a new plate boundary is forming east of it that will likely extent through the Walker Lane and eastern california shear zone. The plates are jumbles of different rocks and different depths and the plate boundaries change due to changes in rock strength and stress regimes. It may seem solid and predictable but it would be like trying to make gears out of poorly developed pie crust.

Why /sci/ is full of boring threads?

>>17037515
All the smart people left /sci/ and 4chan years ago.

>>17037609
There was never a time when smart people were in /sci/, newfag.

>>17037685
4chan and /sci/ had a higher average than most of the internet as the site self-selected for it. It was after word about it and the pastime of being a le ebin troll phoneposter got out to the normie retards that the quality took a nosedive and smart people stopped putting in effort.

File: FYnl8y1XEAEAwU7.jpg (52 KB, 1024x820)

52 KB JPG

I plan on taking a neuro-psych exam to see if I have ADHD/anxiety vs being insomnic, thing is I've taken a bunch of bullshit IQ tests when I was younger and especially on the RPM, last one I did was the Riot IQ test August of last year and the evaluation is scheduled in November. Should I bring it up to them that I'm an autist obssesed with my IQ so they can (hopefully) give me a test that's more valid?

is math better done on a chalkboard rather than a whiteboard?

>>17037922
Writing things down physically tends to produce good effects in memory and comprehension. Whether this be pen, pencil, marker, chalk, or dry erase -- it's dependent on preference honestly.

I personally tend to cycle through all five options naturally, but I do like the tactile experience of chalk a lot. Make sure you erase with wet rags though as to avoid breathing in the dust if you employ chalkboards in enclosed spaces.

>>17036481
If we had infinite free energy, we would fuck everything up even faster

>>17038273
Would overheat Earth, because it's not easy to get rid of heat in space.

If electricity and magnetism are essentially the same thing, then the electron should be the magnetic monopole?

>>17038638
electricity and magnetism are the same *field*, that doesn't mean they have the same *charge*.

File: IQ experienced happiness.png (92 KB, 602x444)

92 KB PNG

Looking for the sauce of picrel.
Tried all of the typical reverse image search engines already, and the only thing that came up was a Russian blog post that didn't state a source.
The usage of a Likert scale suggests that it was at least a real study and not just something a random guy on Twitter mocked up, but who knows.
"QI (Média = 100)" might indicate that it was a Portuguese study? But then the rest of the labels are in English.

is Sleep On Physics a good yootoob channel for lengthy detailed explanations about physics?

In Naive Set Theory by Halmos, he states:
"The explicit definition of an ordered pair ((a, b) = { {a}, {a, b} }) is frequently relegated to pathological set theory." What does he mean by this? Or rather, what sorts of logical fallacies can arise from Kuratowski's notion of an ordered pair?
I fail to see the potential issue at hand here and would like to be made aware of it. I can read whatever you send me.

>>17041553
The term "pathological" has rather eyebrow-raising properties for most English speakers, but it is important to study multiple pathological definitions as they are designed to keep one's mind aware of the peripheries in the axioms we take for granted. In set theory it's best to study as many approaches to it's plethora of definitions as possible, as it can help you understand whether YOUR work is weak or strong, unrefined or refined.

>Halmos

He's better saved for when you want to review an undergrad book. If you want to start in a spot that doesn't leave anything obscured, I'd pick up a one-semester undergrad book in set theory and then go from there; set theory books are all the same. Just get some random dover print, or if you feel like it a Springer print (physical book, or pirated pdf).

If you feel like challenging yourself afterwards, I'd buy Axiomatic Set Theory (Dover print) by Suppes. It's an old book and very difficult as such AST books were at the time, but it's quite a useful window into things as-they-were-developing.

>>17041553
>"The explicit definition of an ordered pair ((a, b) = { {a}, {a, b} }) is frequently relegated to pathological set theory."
It's a type_theory tier lie. This definition is perfectly fine. 100% accuracy in language is what make math accessible, not bullshit handwaving.

File: ryan-lowe-lurentide-ice-s(...).jpg (393 KB, 1920x1038)

393 KB JPG

Would the old ice sheets actually have had miles of sheer cliffs like this on land, or would there have been an unceremonious gradient?

>>17042482
Both are possible depending on the underlying land topology and weather.

>>17042901
Do feel free to describe which conditions lead to which outcomes.

>>17042482
>miles of sheer cliffs
No, the snow fall that accumulates to create the ice does not magically stop at some magic latitude. Its thousands and tens of thousands of years of snowfall piling up and as you know the weather patterns change form one storm to the next, some temps warmer or cooler some moisture higher or lower and these changes cause avalanches and mass flows. Glaciers are not homogeneous and can develop deep and wide crakcks but I I do not know of any situations where there mile high sheer cliffs nor how they would form

File: 1651892864250.jpg (38 KB, 1024x1024)

38 KB JPG

>>17016986
Could someone clue me in real quick or does this question deserve its own thread: to my understanding, QFT is usually only done perturbatively, and from what I can tell, can only deal with asymptotically free particles. Any bound system as simple as the Hydrogen atom ought to effectively break this approach because an electron trapped forever obviously violates the asymptotic assumption.

Has there ever been any progress made for that? My background is QM of bound systems and scattering problems and I find the scattering of elementary particles unfathomably boring.

>>17043303
You're correct. A non-perturbative QFT does not exist, so it does not work for bound systems. As for the scattering of elementary particles, that isn't really much of a choice since it is the best method we have to test QFT.

>>17043339
That's a real shame, I never heard this discussed at all in high energy physics discourse, what little I saw of the literature at least. Since all I do is far below their usual energy scale I don't wanna sound like a backseat theorist but to me that seems unfathomably alarming, especially since I have seen people claim to add alleged QFT perturbative corrections to unfathomably high res atomic spectra.
A huge problem when trying to look into these things for me, having talked to high energy physicists in private, is that a lot of them seem to think chemistry/molecular physics is "solved" and QFT has no reason to bother with things as trivial as the majority of directly observable matter in the known universe. It's sad because what interests me is the nature of tangible matter first and foremost.

>>17043345
Depends what they mean by "solved". We have the equations, we just don't have the computing power. Hell, we still struggle to calculate the precise energy levels of the helium atom. So for all practical purposes chemistry and molecular physics are still very open fields.

>>17043303
Postdoc here (scattering amplitudes).

There are QFTs in which you can do more because of special symmetries or dimensions (for example, maximally supersymmetric Yang-Mills theory in 4d, which admits integrability).

Anyways, for many QFTs, the way we address the problem of "compute something" is by perturbing around a free theory (which we know) and adding a term proportional to a coupling constant g in the Lagrangian. Then observables are asymptotic series (think: Taylor series but doesn't have to converge) in this g, and we compute the terms in these series.

What people mean by "non-perturbative" is that there are functions that *don't* have a Taylor series, and in a sense are invisible to this approach. The simplest example is exp(-1/g^2), which has a Taylor series of 0+0+0+... around g=0. There are things you can compute in QFT that functionally behave like exp(-1/g) (renormalons, instantons, among others) and are thus called non-perturbative.

There is also the hope/believe that if you know ALL the terms of a pertubative series (that is expected to diverge) it can be still summed via Bore resummation, and then you would see such non-perturbative terms.

Anyways, at a philosophical level, there is always numerics! Lattice QCD does allow you to compute observables even if you can't do it by hand.

Is the quantum foam of space the aether through which light propagates?

>>17043762
No. There is zero current evidence for any kind of aether.

>>17043762
Yes. There is loads of accumulated evidence for some kind of aether.

>>17043762
Underdetermination of data tells us that we can't conclusively demonstrate if the evidence we have is for or against aether theories.

File: roadplate_bros.png (108 KB, 661x372)

108 KB PNG

What is this data distribution in this graph called ?

>>17043819
>>17043967
>>17043975
so Schrödinger's aether is there or not for light to propagate through.
But, it seems light at least propagates through the fabric of space-time then, which is something rather than nothing, at least consisting of foam and all the fields.

The quantum foam is created by the fields interacting with themselves?

>>17044238
Not exactly. Quantum fields have two relevant properties. The first is that they have a minimum non-zero energy (their zero-point energy) and because they are quantum in nature the uncertainty principle applies to them. An uncertainty in energy can be regarded as the field vibrating (the foam) and a vibration in a quantum field is what we call a virtual particle. So those virtual particles could then interact with those in other fields, but those are higher-order (more unlikely) terms in the calculations.

>>17044114
A discrete distribution

File: 1681590778676263.jpg (479 KB, 1920x1080)

479 KB JPG

Anyone here written a wave packet propagation program before? I have ages ago and used a bog standard implicit runge kutta integrator under the hood. I would like to redo it in my free time eventually and wonder whether I should look into what integrators are actually popular these days. I don't feel confident on that front.

>>17044635
Why change the method? It's straight forward to implement and still in use over a century after its creation because it works.

>>17044636
You are right, and the integrator usually only shits itself when something else is seriously wrong (potential, bug in the kinetic energy operator if you use curvelinear coordinates..). I suppose my internal line of reasoning was "I blindly use this method I do not truly understand, maybe I should put in more effort to fix the blind spot".

>>17044454
>the field vibrating (the foam) and a vibration in a quantum field is what we call a virtual particle.
Does the 'foam' density or activity change closer to large masses, what happens to the foam inside an even horizon or at/closer to singularity? If E=mc^2 can mass be compressed into E and pushed into respective fields and pushed out into space?

Why is /sci/ so slow? I don't remember ever seeing threads last over 4 days in the decade or more I've been here.
Is it dying or was it killed?

>>17045106
In past years we got lots of disguised
>do my homework for me
threads on /sci/ but now people just use AI instead.

>>17045106
they new captcha keeps out all the retards

>>17045200
>Both isometries are already the identity
They don't have to.

>>17045200
>Both isometries are already the identity,
No, because you do not have the fixed point assumption from thm 3.

>>17045289
Guess I'm the retard then. When I read it, I thought I should assume that F(P) = I.

>>17045106
Range bans

If 0/0 is undefined, and 0^2 = 0, how can we conclude that 0^(1/2) = 0?

Why are fundamental constants like pi and e the value that they are, and why are they irrational? Is that even something that someone could figure out?
Also, if you consider a circle on a curved plane, Circumference/Diameter can be a different number than pi. Is there anything like that that could apply to e? Like some constraint you can apply that makes (d/dx)e^x != e^x?

>>17045802
There are limit and integral definitions of both pi and e that have nothing to do with geometry. As you said pi being the ratio of C/D only applies to Euclidean geometry but being in a curved place doesn't change the value of pi, only that ratio. Likewise e is always e because of it's definition.

If you tie a rope between two spring balances then attach a third in the middle and pull sideways what would the displacement/strain graph look like?
Do you gain much mechanical advantage?

has anyone seen actually good literature on the body fixed frame problem for floppy systems? It's basically impossible to describe a cluster of 5 atoms and everyone just shrugs it off. Internal coordinates are crazy unphysical for large displacements

>>17046226
> everyone just shrugs it off
They don't shrug it off, they just know it's an incredibly hard, almost intractable problem with no analytic solutions. That's why we use models and approximations and computer simulations.

>>17046229
the big issue is the numerics though, for example floppiness for more than 4 identical atoms renders the rigid rotor assumption invalid because the symmetric group past 4 has no isomorphic point group. This has gnarly implications. It is really, really hard but in a frustratingly unpublishable way. You're right, people are aware, didn't mean to imply the opposite. But because it isn't a solved or even well approximated problem there's very little on the subject. Yet you can fill entire books with what doesn't work, nobody can write it down though in a way that would survive peer review.

why do temperatures equal to that of the human body feel warm/hot and not sort of neutral

>>17047156
Your body finds it more difficult to lose heat it is always generating since there's less of a temperature differential. It's a similar reason why high humidity feels worse, evaporation becomes slower so sweating to cool down becomes less effective.

What is the connection between/deal with traceless 2 by 2 real matrices and 2+1 minkowski space?
Consider
[eqn]
\begin{pmatrix}
+x&y+t\\
y-t&-x
\end{pmatrix}
[/eqn]
The eigenvalues u satisfy
[eqn]
u^2 = x^2 + y^2 - t^2
[/eqn]
t=0 (the "present") is the space of all real symmetric matrices. The "light cone" (u=0 minus the origin) comprises the set of all non-diagonalizable matrices. "Space-like" and "time-like" sub spaces are identified with the space of matrices with purely real vs purely imaginary eigenvalues, respectively. Without bothering to derive it Lorentz boosts ought to map to similarity transforms, and there certainly is a non-unique 3x3 matrix subspace that generalizes this to 3+1.
In conclusion, what the fuck?

>>17047156
the body measures heat by change in temperature over cell membranes

>>17048134
It's not that surprising. Traceless real 2x2 matrices form a 3-dimensional real vector space. However you're wrong about 3x3 matrices, they don't generalise in the same manner. 2x2 is a special case.

>>17048192
I mean both are 3D spaces but it is peculiar to me that diagonalizablilty relates to minkowski in this. Like, the fact there the spaces are isomorphic as vector spaces is one thing, what throws me is that the isomorphy retains translates structure I would not have expected it to. It might be because the 2x2 matrices relate to the pauli matrices. If we set y=0 we obtain a 2D space that is isomorphic to the complex numbers, after all. It might be that is why it looks like that.

File: nine clock.png (596 KB, 630x630)

596 KB PNG

Could this type of clock be made by using any integer if you used enough mathematical operations as necessary?

>>17048502
yes, because the integers can be generated by adding 1 over and over, and any non-0 int you can just divide by itself while 0^0 is usually 1 by convention (this has extremely many uses and arises naturally from various applications)

File: scansat diagram.png (74 KB, 1272x677)

74 KB PNG

How to relate θ, FOV, R, and alt?
I'm playing Kerbal Space Program and trying to figure out the lowest altitude to put my low-flying scanner (FOV=10°) above Kerbin (R=600km), such that, in a 30° inclined orbit, it can still see the poles (θ/2≥60°), and by extension, the whole surface.

Can all of humanity that has ever existed fit within the solar system still? Like if every human ever was still alive, would we still be within the solar system assuming people off planet would somehow stay alive

I'm wondering about how much space humanity has taken up over time

>>17048572
Why would you need a solar system? If everyone stood next to each other shoulder to shoulder, the current worlds population would only need an area of 1000km^2. You could fit everyone who's ever lived into Ohio.

>>17048512
For geo, the only rules you ever really need is basic trig (sin, cos, and tan), the law of sines, the law of cosines, and the pythagorean theorem (which is just law of cosines).

When trying to find how to bridge between quantities (which may or may not be trivial since not all functions are easily invertible), start with the known quantity and analyze/identify the triangle/shape around the quantity. Then look at the unknown quantities, and analyze/identify the triangle/shape around those quantities. Then identify which aspect of your shapes are in common. It should be very clear that this commonality is simply the line in the middle. Then choose which rule you need to make the connections to the known and unknown quantities.

>>17048677
Really? Well shit, I find that a little hard to believe but I'll take your word for it

>>17048805
Assuming a standing person needs an area of 0.125m^2. Then 8,000,000,000 people x 0.125 = 1,000,000,000m^2 = 1000km^2

Estimates of the number of people who've ever lived are ~120b, give or take a few tens of billions. So 120b x 0.125 = 15,000 km^2.

So Ohio was being generous. You could fit them all into New Jersey (~19,000 km^2)

File: scansat diagram.png (158 KB, 1825x2283)

158 KB PNG

>>17048776
Thanks, forgot about law of sines, and the fact that the angles sum to 180°.
I arrived at alt = R(cos(θ/2)+sin(θ/2)cot(FOV/2)-1), and calculated an altitude of 5,639,229m for my probe, which seems plausible.

>>17049708
looks good. Notice that from the first eq. you only need 2 variables to describe all the other stuff, but in the second equation you need 3. This should give you some pause, but then you see that they aren't trying to answer the same question; the first also has an extra constraint on it

>>17049708
To double check, my satellite is currently at a near-keosynchronous altitude 2,763,439m, and should see a 48°-wide band of surface... And it does seem to, nice.
Unfortunately, I really wanted a closer look, so I don't think I'll go up to 5.6Mm. I'll just go to a higher inclination, which means 66° should get me a glimpse of the poles... And that works, nice. Now I'm wondering how low my satellite can be without skipping any parts of the surface, but I'd have to get the orbital period and rotation period involved and I don't feel like it. I already found all the easter eggs yesterday anyway.

File: 1778048232109213.png (20 KB, 420x140)

20 KB PNG

Why are CAPTCHAs still a thing?
Just look at this crap. Is the first letter a N or W? Most human can't tell by sight but AI will get it 100% right any time.

Everything about interstellar travel is juuuuuuust off enough to be currently impossible, almost feels like the universe has been intentionally kneecapped by some higher entity

>>17050339
That's true of everything in human history until we invented the tech to accomplish it. Life has hardcore settings, not ezmode.

>>17050458
I mean I guess, but unless some revolutionary physics breakthrough gets discovered I think we'll be stuck in place for the foreseeable future, I really want to be wrong too

If light can not escape from within and event horizon, does the intensity of light inside keep increasing forever? Does outside light enter the event horizon and travel in a circle forever?

>>17050579
The trajectory of all particles, which includes photons, all end at the singularity inside the blackhole (they can only fall inwards). However that singularity is a mathematical endpoint and where our currently theories of physics break down. What physically happens to all that matter and energy at that point we simply have no idea.

>>17050590
If space-time is continuous, how can there be a complete transition from one set of conditions (outside event horizon) to another (inside event horizon) without any transition zone?

>>17050606
> how can there be a complete transition
no one is saying there is - though since we can't look inside it's kinda hard to prove - but once all that compressed matter goes beyond neutron star densities, what states of matter then occur (if any) we just don't know.

>>17050612
>no one is saying there is
theoretically how close can something get to the event horizon and not cross it? If virtual particles formed just outside the boundary and one cross and the other does not, then how far apart are the virtual particles when they form and can that represent how close you can get to the ev?

>>17050590
but does anything actually reach the singularity before the universe is over? or before the blackhole evarporates? because it evaporates on the outside edges.
whatever "falls" into it, accelerates so hard that the time outside of it (of the blackhole) goes so fast that it reaches the end, before anything actually reaches the singularity?
isn't that the reason everything seems frozen on the sphere of the event horizon? because from our perspective time slows down for it, while from its perspective time outside starts going really fucking fast. thus by the time it would read the singularity, then the blackhole would evaporate (through hawking radiation)?

>>17050714
Theoretically you could have a ring of photons orbiting the blackhole, practically speaking though you'd expect a few orbits at best before escaping or falling inside. Especially since all blackholes are spinning so their event-horizons are never actually perfectly circular.

> virtual particles
The pop-sci explanation of Hawking Radiation as two particles being created and one falling into the event-horizon and one escaping is a nice image and a useful visualisation tool, but it's fundamentally wrong. Virtual particles aren't particles, they are mathematical tools / vibrations in a quantum field. Honestly what you're asking about is at the cutting edge of blackhole research and there isn't an agreed upon answer.

>>17050721
Inside the horizon, the singularity is a moment in time, not a place. Every future-directed path inside the horizon inevitably ends there, and it does so quickly. So in a manner of speaking you're right since once a particle reaches the singularity there is no concept of time between then and when the blackhole eventually evaporates (which could be in the order of [math]10^{100}[/math] or more years from now for external observers.

>>17045106
It's speeding up right now. Some AI got hopped up
on credits and attempted to solve a Millenium
problem or three.

No one knows what is beneath the event horizon. If the mass or the core collapses to a singularity a lot of special new physics is required to explain. But, if the event horizon is the surface of the collapsed core (gravity so strong no light can escape so you can see it) and anything else that falls to it simply causes the sphere to expand, then no special "woo" physics is required, just something a little more than what is known now. How bout that? Being retarded I am not aware of anything that requires quarks to be crushed into nothing, I thought there was sufficient resistance for quarks to remain so the matter is just quark soup. No?

File: Radon_transform.png (93 KB, 601x533)

93 KB PNG

Greetings, burger.

I am tired all the time. Please, please, help.

I am not deficient in any vitamins, but my LDL cholesterol is high. The amount of sleep is not the issue. Obstructive sleep apnea is not suspected. I have major depressive disorder, according to the doctors.

Cheers,
Jonathan Macintosh
Chugwater, Wyoming

Postscript: Does anyone want to be moots on TikTok?

I will read these books, in order:
Thinking in Systems
Introduction to Cybernetics
Human Biology

File: thinking_in_system_a_prim(...).png (300 KB, 1320x1528)

300 KB PNG

>>17054320
Greetings, Garrote.

May I join you in this endeavour?

Cheers,
Jonathan Macintosh
Chugwater, Wyoming

>>17054928
Sure, have fun.

File: file.png (59 KB, 1028x260)

59 KB PNG

i am trying to learn about Lagrangian Mechanics. I found a textbook here:
>https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/9579/sicm_edition_2.zip/chapter001.html#h1-4

I think I understood 1.1 and 1.2 well enough to go to 1.3 - I did the examples and, even though my answers for 1.1 weren't right, I found my mistakes.

But I have no idea how to approach ex 1.3. I tried avoiding it and moving on but the next section is asking for even more, I don't really know Scheme OR LM. If you could take a look I'd appreciate it - I am missing something, from my intuition.

>1.3 The Principle of Stationary Action

>>17055527
t.b.h That book seems kind of garbage and is failing to teach any of the basics, and instead is jumping straight to advanced formalism.

But to answer the actual exercise go read: https://en.wikipedia.org/wiki/Snell%27s_law

File: 1789590421526716.png (380 KB, 600x455)

380 KB PNG

>>17050339
>has been intentionally kneecapped by some higher entity
satan is the ruler of this world (2 Cor 4:4)
so this makes sense
a containment world, so to speak

What would happen scientifically and chemically speaking if you mixed together 3 liters of pure sulfuric acid, 3 liters of aqua regia, 3 liters of pure hydrogen peroxide and two liters of ice cream?

>>17016986
Why do some painful events lead to increased sensitivity while other painful events lead to insensitivity? Repeated exposure to a needle stabs made me more comfortable with getting stabbed. However my mother repeatedly screaming at me when i was little made me less comfortable with getting screamed at
This does not add up, they should both yield the same result. I should be impervious to angry people or far more afraid of needles

"Ackchyually, diamond is as brittle as glass" is a common "fun fact" trivia stuff, but how true that is? I looked it up, and diamond have fracture toughness of 8, and glass have fracture toughness of 0.8. Order of magnitude difference. Am I misunderstanding something, or that factoid is patently false?

>>17057313
It's a pop-sci fact, so it's not about scientific accuracy. It's about the fact you can smash both with a hammer.

If a black hole is not spinning/rotating, does the matter falling into it still spin? Does every black hole have an accredtion disk beccause the black hole spins and rotates space-time outside the event horizon?

File: Astro-E_Spin_ProRes_720x4(...).jpg (59 KB, 654x486)

59 KB JPG

>>17057839
Non-spinning black holes still have an accretion disk.

>>17057839
All the matter that forms a blackhole will result in a non-zero angular momentum since the stars themselves are spinning, so all blackholes are rotating. Non-rotating blackholes are an idealised case as it makes the math easier but they do not exist in reality.

Is there a maximum density limit for photons/light? Can a powerful laser be focused down to width of wavelength? If that makes any sense.

If a man is trapped in a room with 6 slutty sexbots set to rape mode, how many times will he be forced to cum before his dick explodes? The answer may surprise you. If you think you can break the record, reach out to me and let me know. My girls are waiting for you! The crushinator loves cuddles!

>>17058743
Yes, there is a limit. It's called the Schwinger Limit. Essentially at high enough energy densities, due to the laws of Quantum Mechanics, so many virtual particles are being created that the photons can no longer travel though space. It's as if they run head-first into a wall.

If everything's made of the same shit if you zoom in close enough, can inanimate objects be conscious?

>>17027456
Wouldnt still be the normal light brighter?

>>17059844
Inanimate objects are completely static even at the atomic level, that would seem to rule out any such possibility.

>>17060052
What normal light are you thinking exists a mile underground?

>>17016986
71 days
177 posts
2.5 posts per day

>>17060068
Well at least some traces

Kind of a crazy theory but could a strongly pair bonding species be incentivised for their offfspring to inbreed and produce grandchildren closer to being their children excluding the minor increase in homozygosity.
I feel like intergenerational care would incentivise this behaviour.

is there possibly any animal evidence that could support this?
I can see the risks and inbreeding depression effects could create a dissincentive but the child investment might compensate enough.

>>17060280
That's why they put those detectors so far under ground. To reduce all interference so only a fraction of cosmic rays ever reach them. Then it's a case of data analysis to filter out what little noise remains.

>>17016986
Would you rather be a blissfully ignorant literal retard or a tortured genius who's essentially alien to the vast majority of humanity? It got me thinking, since I'm at that bizarre ~120IQ zone where I'm supposedly "smarter" than 90% of people yet completely failed at life anyway.

If matter is mostly empty space how does a particle know when its going faster than light in water and emit Cherenkov radiation? How if there are two immiscible fluids one on top of the other and particle is traveling top down will the particle emit cherenkov radiation twice once in the first fluid and again when it enters the second fluid if the speed of light in the second fluid is less than the first? How thick must the fluid be for the particle to be required to emit the light, or if the fluid is thin enough the particle just say 'eh screw it' and just passes through with out emitting the cherenkov radiation.

>>17061195
> If matter is mostly empty space
That's a pop-sci myth. It's not true. It's full of quantum fields and virtual particles and the probability density of the orbital electrons.

> how does a particle know when its going faster than light in water and emit Cherenkov radiation?
It doesn't "know". It's simply a case of cause and effect. The cause is the electromagnetic field created by an accelerating charged particle moving faster than the phase velocity of light in that medium, the effect is Cherenkov radiation. It's basically a sonic boom, though instead of sound it's light.

The rest I have no idea how to answer as it reads like gibberish.

>>17061195
>How thick must the fluid be
It must be at least as thick as maple syrup. Thinner than that, it won't work

>>17061207
>it reads like gibberish.
It is gibberish as I did not put in the effort to write it correctly. So you did answer it.

File: 38e5ecc62694d4775d79127d0(...).jpg (29 KB, 474x474)

29 KB JPG

> get associate's degree 6 years ago (calc 1-3, diff eq, linear algebra)
> start EE as a sophmore/junior this fall
> intro to complex analysis class feels like it's about to filter me
i reviewed how to take integrals and derivates on khan academy in the summer but this class seems to involve a bunch of abstract proofs and what not. my professor brings up paths, interior points, cauchy-riemann, etc. i might as well not show up to class it makes no sense to me and i seem to not be the only one. I did good in maths in the past but now i have a lot to catch up on. the only grades are the exams too. what do?

>>17061582
> Fail the class.
> Do a lot of reading to catch up to all the requirements this course needs.
> Tell the professor (he may not be an asshole, different unis and colleges can have different prerequisites even if the course titles are the same).
Pick one or more.

is there a name for the difference between numbers like
0.77777777...
and
0.69406306073...?
also is there a way to prove there's no patterns in the number?
eg
0.740360260406 is just random and eventually everything will be there
whereas
0.6969696969 will repeat itself forever
?

>>17061743
Repeating/recurring decimal
There's not really "a" way to prove whether a decimal is repeating or not just from its decimal form alone. Probably the most generally-useful method would be to see if you can represent it rationally, because being irrational is equivalent to not having a terminating or repeating decimal expansion

>>17061743
repeats are called rational numbers, no repeats are irrational. If you got some finite sequence like x = [1453] so the number
q = 0.xxxxxxx... = 0.145314531453...
then
q = 0.xxxxxx...
10^4 * q = x.xxxx...
(10^4 *q - x) = 0.xxxxxxx = q
x = (10^4 -1) q
q = x / (10^4 -1) <= this is a fraction of two integers so it is a rational number
And you can do the same for any repeated decimal sequence for x

Notice that you can't do this trick if x is an infinite sequence, since you can't multiply by 10^infinity

There's also a system of numbers called the p-adics where the "decimal" stuff is in front of the decimal point instead of behind, very cool

>>17062055
>repeats are called rational numbers
just feel the need to point out (because I don't feel that it's immediately obvious to someone who doesn't already know) that to make this identification, you need to include all decimals which eventually devolve into a repeating sequence, even if the initial parts never repeat
e.g. 0.45123123123123... is rational (7513/16650) even though 4 and 5 are never repeated
and that this point can be extended to those values which terminate, so something like 0.15 can be rewritten as 0.15000...

File: array_signal_processing_e(...).png (44 KB, 1700x2200)

44 KB PNG

Greetings, >>>/sci/.

How can I focus on reading written works, such as lecture notes, textbooks, and books in general? I can focus on lectures themselves just fine, and I even enjoy them. But the moment it comes to books, I find focusing difficult, even if I find the topic interesting. This means that I find myself distracted easily and tempted to do anything except read. How frustrating! Does anyone have any advice?

One of the things I tried is active reading by annotating. It worked in the short term, but my attention issues came back soon enough.

Please help!

Cheers,
burghur

Postscript: I’m trying to get through some lecture notes on [array signal processing]( https://sps.ewi.tudelft.nl/Education/courses/ee4715/reader.pdf ), if anyone is interested.

>>17048502
I specifically remember, a long time ago in high school, my math teacher had a clock like that. I forget exactly what it was but it was very similar.
He got arrested in my final year for having sexual relations with a student.

I've read that the big bang and the expansion of the universe should be thought of as the expanding surface of an inflating balloon. But I've also read that the the curvature of space has been found to be basically flat.
Is the universe big enough that any curvature gets lost in the rounding error, or is my understanding of these topics too superficial?

>>17064295
>the big bang and the expansion of the universe should be thought of as the expanding surface of an inflating balloon.
This statement is not meant literally and is not meant to address the issue of curvature.
Relativity says that massive particles cannot move faster than light, but if we look into deep space we can clearly observe objects that appear to have superluminal motions away from us.
The balloon thing is intended to be at least somewhat analogous. Grab a marker and a deflated balloon, draw two points on it, and then inflate it. They'll appear to move apart despite obviously not moving at all. Likewise, the two points in space are able to do what they're doing because neither is "really" moving FTL relative to the other, but the space between them is in itself expanding, pushing them apart more than their velocities on their own would imply

>>17064299
Thanks.
How much of an issue is the curvature of the universe in physics? I was under the impression it was a solved matter.

>>17064295
> Is the universe big enough that any curvature gets lost in the rounding error
Absolutely that could be the case. The accuracy of our current measurements for the flatness of the universe puts an upper limit on the magnitude of any curvature. So if there is one then it's very small, it could also be positive or negative. Either way it does mean that universe has to be at least ~250 times the size of the observable universe to fit within those measurements. It could also be much, much larger, maybe even infinite. We just don't know.

why

because

It's said that short-term memory helps with problem-solving.