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How much polygonal Masonry would survive without the great `Cataclysm 11,111 years ago?

>>16504908
>stupid
As some of you probably know, Tasmanian devils suffer from Devil facial tumour disease (It's blue board, I'll spare you pictures.) Years ago I read some scientist claimed that tumor evolved into a new species and even assigned a Latin name for it. The problem is right now I cannot find any source on that. Anyone's got any links and is willing to share? Thank you in advance.

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You start doing a spiralling pattern inside a square like in picrel so that the ratios shown are equal as the pattern continues.

If the square is a unit square having its vertices in coordinates (0,0), (1,1), (1,0) and (0,1), given the angle alpha, which coordinates does the spiral converge into if it continues forever?

>>16504988
Idk, but the leading hypothesis for the origin of the parasite that causes whirling disease is exactly that, but with jellyfish. Some cnidarian had cancer, and the cancer became free-living.

Find the vector [math]\vec{a}=(x,y,z)[/math] which has magnitude [math]\|\vec{a}\|=5[/math], is coplanar with vectors [math]\vec{b}=(2,1,0)[/math], [math]\vec{c}=(-2,3,1)[/math] and forms an angle [math]\dfrac{3\pi}{4}[/math] with the vector [math]\vec{d}=(-1,1,-1)[/math].

>>16505670
Do it yourself you lazy fuck

>>16505674
I can't, I don't know how

>>16505670
draw it

>>16505670
[eqn]\vec a \cdot (\vec b \times \vec c) = 0 \\
\| \vec a \| = 5 \\
\vec a \cdot \vec d = \| \vec a \| \| \vec d \| \cos \left( \frac{3 \pi}{4} \right)
[/eqn]

Those are 3 equations with 3 unknowns. (The three components of [math]\vec a[/math].) You should have learned how to do these types of systems in middle school.

Time doesn't exist right?
Time is just how we quantify things moving in the universe.
So does that mean if we implement a time machine, it's possible to make a machine that reverse the particles movement, which includes our memories.
Hence causing to stuck in a forever time loop where we thought we never press the button yet, and forever repeat the process of
press button - time reverse - forgot it happened - press button again - repeat

Why am I generating so much static electricity lately? Yesterday I reached to turn the computer on and a visible bright blue spark appeared between my finger and the computer case. It hurt more than usual too.

I've started using a wool blanket in my sofa lately because of cold but the static electricity problem has only started the last week. I've been using the blanket for a month.

I wear slippers, which insulate me from ground I suppose. But I've always done that.

>>16505730
Clocks tick therefore time exists. What is the nature of time – we don't know (obligatory reference to Plato's cave.)

>>16505804
Whenever I'm about to get shocked by a chair or
doorknob, I give my hands a solid clap.
This dispels the stray electrons from the hand and
so avoid getting zapped harder than I should.
Give it a try.

What's the average height difference between brother and sister?

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>>16504908
What's a no-nonesense, non-popsci Math book that will get a relative of mine interested in Mathematics? He's in his late teens. He hasn't given much thought about Mathematics (or school for that matter); he just does the bare minimum, but he passed Calculus 1, so he's at least capable of wrapping his head around this shit.

Should I gift him a College Algebra/Trigonometry textbook, or a Calculus textbook? I don't want to gift him a full-sized textbook because then I know it will be tedious for him to carry it around. The more easily accessible an activity is, the more inclined one is to do that activity. Mathematics proficiency is partially a matter of dedicated practice, another aspect being that of working through problem sets.

With that in mind, I think a book which is relatively small and portable, and has a decent selection of problem sets would be ideal. A problem book would work too, I guess.

>>16505730
Depends on which particles you move. Locally, you can move a handful of particles to the "past" without affecting the particles in your brain, so your memory stays intact. But depending on how particles from the unchanged present interfere with the rewound particles in their "past" state, the rewinding process could scramble the "real" past into a different "past-like state."
What we really need are concrete definitions for what makes a state past-like vs. future-like

I am a 30 year old NEET degenerate but I have ultimate metaphysical objectives. I maybe want to learn math or physics for ulterior philosophical motives but my IQ is 107, so it won't be a very fun experience due to the sheer attrition I will have to confront. Also it seems autistic and "gay" to sit in my room doing highschool math.

>>16504725

I believe >>16505206 is correct that the minimum length is a T of total length 5/3.

Firstly, it’s trivial to prove that for any amount of lines creating the three shapes, those lines can be reduced down to just three lines, and that in so doing, always shrinks their total length.

Then, to further reduce total length, the vertices should be as close to each other as possible, which forms (as a start) an equilateral triangle, inscribed within the square.

To further reduce the total length, you have to push the inscribed equilateral triangles vertices even closer together. But this is restricted to moving vertices along the sides of the square. In order to make any progress, you have to move two vertices identically towards a third, since on a square, moving just one vertice will reduce length in one direction, but increase the length in the other direction.

For such a reduction to work, it therefore demands that two vertices on the square be reflections of each other across the square, so that they can move in sync towards the third. There are two such inscribed equilateral triangles:

1: The Third vertice is in a corner, and the other Two are on perpendicular sides.
2: The Third vertice is in the center of a side, and the other Two are on parallel sides.

Painstakingly calculating both scenarios, and setting the areas of the created shapes to be 1/3, the first scenario gives total length 1.7415, and the second scenario gives a total length 1.6667.

The first scenarios isosceles triangle has the square’s-corner vertice’s wide angle be 0.83558 Radians, and the point where the lines meet is 0.647557 along the diagonal, bgeinning from the square’s-corner vertice, if anybody wants to construct this.

>>16505804
it's winter and the air is drier. I turn into a lightning mage come mid-november.

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>>16505004
When it’s turned sideways, it really seems to be a bunch of similar triangles stacked on top of each other, up until the point where the stack is tilted enough that anymore would fall down. It seems that it’s converging onto the point along the side of the final triangle, which is where the steepness becomes too great for anymore. The point on that side seems to be the point that divides that side by the common ratio present everywhere else in the pattern.

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Seven ducks are in random locations in a circular pond which has diamater of 50 meters. You throw a piece of bread somewhere in the pond blindfolded (it lands in a random point in the pond). The ducks all see the bread landing at the same time and swim towards it the same speed until the first one gets it.

What is the average time that it takes for one of the ducks to reach the bread after it hit the water? All the ducks swim at 1/2 m/s.

>>16506596
How big are the ducks? How big is the piece of bread? What happens if two ducks crash into each other?

>>16505004
Seems like there are multiple possible answers as the ratios could be equal to different values. You also haven't drawn this to scale, as:
e+f > a+b, e/f = a/b | e > a, f > b

>>16506373
>What's a no-nonesense, non-popsci Math book that will get a relative of mine interested in Mathematics?
There are many answers, because math students come from very different backgrounds. I got interested after reading Grossman's Linear Algebra after struggling with Axler's LADR.

>>16506643
No because the ratio is determined by alpha. If X is the angle alpha then the ratio is going to be tan(X)/(1-tan(X)).

>>16506596
ducks shouldn't eat bread. it's bad for them

>>16506643
lol this.

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I'm relearning math since I want to get into graphics programming. I already brushed up on all the types of arithmetic operations and am now reviewing algebra but there's something that's been bugging me and I'm not sure if i just missed the explanation somewhere in the book I'm reading.

Pic related is the book I'm using, and it doesn't format algebraic operations so problems look like this

4/3 - x/6 = 3x/4

And if I solve it

[math]
\frac{4}{3} - \frac{x}{6} = \frac{3x}{4}
[/math]

[math]
\frac{4}{3} = \frac{3x}{4} + \frac{x}{6}
[/math]

[math]
\frac{4}{3} = \frac{11x}{12}
[/math]

From here on I saw two options, one was to move the 12 to the other side

[math]
\frac{4}{3} * \frac{12}{1} = 11x
[/math]

[math]
\frac{48}{3} = 11x
[/math]

[math]
16 = 11x
[/math]

[math]
\frac{16}{11} = x
[/math]

The other was to move the entire fraction except x

[math]
\frac{4}{3} = \frac{11x}{12}
[/math]

[math]
\frac{4}{3} / \frac{11}{12} = x
[/math]

[math]
\frac{4}{3} * \frac{12}{11} = x
[/math]

[math]
\frac{48}{33} = x
[/math]

[math]
\frac{16}{11} = x
[/math]

Bsically what I'm asking is if there's a functional difference between

[math]
\frac{11x}{12}
[/math]

and

[math]
\frac{11}{12}x
[/math]

Can I just move the variable in and out of the fraction as I see fit or is this equation just coincidentally correct using both methods and only one of them is right?

>>16507239
>Can I just move the variable in and out of the fraction as I see fit
Yes. Your two formulations are fundamentally doing the same thing - multiplying by 12 and then by 1/11 - but the first is doing it in two steps whereas the second is doing them together. Which way you prefer makes no difference, besides perhaps your own accuracy/efficiency.

I'm doing a particle question (not for hw, just learning), where Proton_A + Proton_B -> Kaon_1 + Kaon_2 + Proton_A + Proton_B .
The original question is that, given the energy of P1, what's the minimum energy of particle A needed if A is colliding to B at rest? To me, it seems that the way I'm doing it is long af and I'm wondering if there's a better way.

I'm gonna refer it to A + B -> K1 + P2 + P3 + P4, where I don't know for sure what P2 (my guess is this one is Kaon_2), P3, or P4 are for certain.
I saw at it as two equations and 4 unknowns, which gave 2 freedoms to minimize, so I thought that setting P3 and P4 to be at rest. So
>1.) A (moving to the right) and B (moving to the left) collide together at equal speeds ----> 2.) P2 (moving to the left) and K1 (moving to the right) fly out at opposite momentum, P3 and P4 at rest
or we go to a frame moving to the left at speed V_B, so in this primed-frame (using ' for prime)
>3.) A (moving to the right faster) collides B (at rest) ---> 4.) P2 (moving to the left slower) and K1 (moving to the right faster) fly out at opposite directions, P3 and P4 moving to the right.
So, I interpret the question as given E_1', the energy of particle K1 in 4.), can you find E_A', the energy of particle A in 3.)?

>work
2.) tells us momentum of K1 and P2 are equal, which means we can find a relationship between E_1 and E_2. Then, 1.) tells us that E_A = E_B. Conservation of energy between 1.) and 2.) gives a relationship between all four (E_3 and E_4 are rest energies), so combined you get a loong relationship between E_A and E_1.

From 3.) to 1.), you get a small enough relationship between E_A' and E_A. The frame shift velocity V_B can be found by rearranging the velocity addition formula, so it's a function of V_A and V_A'. All velocities V can be found from energies E.

To get from 2.) to 4.), combine V_B and V_1 to get V_1', which gives us E_1'. Reverse everything to get from E_1' to E_A'

This insane?? Is there a better way?

>>16507389
>work
[math] \begin{aligned}
\tfrac{E_1^2}{c^2} - m_1^2c^2 & = \tfrac{E_2^2}{c^2} - m_2^2c^2 \\
2E_A & = E_1 + E_2 + m_3c^2 + m_4c^2
\\[10pt]
(\tfrac{2E_A}{c}, 0)^2 & = ( \tfrac{E_A'+m_B c^2}{c}, p_A' = \sqrt{ \tfrac{E'^2_A }{c^2} - m_A^2c^2 } )^2
\ \Rightarrow\ \tfrac{4E_A^2}{c^2} = 2E'_A m_b + (m_A^2 + m_B^2)c^2
\\[10pt]
\tfrac{V}{c} & = \tfrac{pc}{E} = \tfrac{\sqrt{E^2 - m^2c^4}}{E}\\
V_A' & = \tfrac{V_A + V_B}{1+V_A V_B / c^2} \\
V_1' & = \tfrac{V_1 + V_B}{1+V_1 V_B / c^2}
\end{aligned} [/math]

>>16507389
P2 should be wtv is lightest

So I think I might be like one of those people who benefits from listening to audio or watching videos. Can you guys make some recs for creators ? My field is geoscience but honestly it's probably good to have a good rounding in all of the sciences

>>16504908
are winds seasonal or do winds blow at any intensity regardless of time of year?

>>16507885
Hurricanes are largely seasonal

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How bad would a spent nuclear fuel pool fire be (contaminated area, impacts on people)?
Spent fuel rods require cooling for 1-2 years before they can be moved to dry-cask storage. This is usually achieved by storing them in pools and actively cooling them with water. However, if this process is interrupted, the water will evaporate from the pool within a week and the rods' zirconium cladding will catch fire, releasing large amounts of radioactive isotopes into the environment (I-131 which decays in 8 days, but also Cs-137 and Sr-90 lasting ~30 years). I looked up modeling studies about this, but the range of estimated radius of the contaminated area is rather wide - anything from 50 km downwind to 500 km - and the literature isn't really new.
So, how dangerous would it really be? And if so, then wouldn't it be better to dump spent rods somewhere remote (geological repository, ocean trenches)? If anything, this looks like a potential disaster in the making.

>>16507436
No it should be all 3 of them - should be heaviest, not lightest to move forward the most

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Hi, maybe not a stupid question, but I'm sure it at least qualifies for being dumb or idiotically inane.
So, computers use electric currents to do stuff, right?
I've heard people describe electricity similar to a hose with water.
I know analogies are just approximations, and don't typically translate to literal 1:1 analogies, but that's ok, it'll at least be able to communicate what I'm trying to say.

Is it possible to have a battery as a source of power -, that produces electric current towards the opposite side of the battery +? And then in the middle of that current, you have the computer hooked up, which basically shuffles the electricity through different switches and tunnels depending on what calculations it is performing, but then have the electricity leave through a single 'exit door', which makes its way to the + side of battery?

So it would be like a house, where there's one pipe that supplies to water to all of the facilities in the house(sinks, showers, toilets) -for sake of argument, pretend all of the water that is used is going to be recycled back down the drain(so you're not taking any water for drinking, watering plants, etc). So any water that is used will then exit down the exit pipe(sewer drainage), at an amount = to however much you used from the water supplying pipe. Use 100L of water, and you flush down 100L of water.

I know computers use energy because they radiate heat, but is there any extra loss of electricity that I'm not considering? Is there a specific phenomena that prevents "recycling" energy? If circuits are just - -> +, why couldn't that work for other electrical appliances?

Sorry, maybe this isn't just idiotically dumb, it actually is probably certifiably stupid.
>ty pls no bully

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>>16508253
Oh, and why don't we use large serverfarms to power generators?
Like, capture the used heat to boil water to spin fan?
Probably reasons, but just curious what the reasons are.

Why doesn't Elon just make a nuclear power plant and sell the energy to people?
Now that he's in with Trump he's above the law, so they can't stop him.

>>16508253
>Is it possible to have a battery as a source of power -, that produces electric current towards the opposite side of the battery +? And then in the middle of that current, you have the computer hooked up, which basically shuffles the electricity through different switches and tunnels depending on what calculations it is performing, but then have the electricity leave through a single 'exit door', which makes its way to the + side of battery?
yea thats how computers work.
>If circuits are just - -> +, why couldn't that work for other electrical appliances?
1. all electrical appliances are in fact circuits.
2. when an electron moves from +1 volt to ground (or ground to +1 volt, actually, since electrons are negatively charged), it loses energy, specially 1 electron-volt of energy. so when the electrons move back into the battery, you cant use them to power something else since theyre "out of energy". its like releasing a bunch of toy cars at the top of a track: the number of cars that end up at the bottom are the same as the number dropped from the top, but if you want to race them again you have to bring them back up to the top.
>Is there a specific phenomena that prevents "recycling" energy?
the second law of thermodynamics, mostly. once you spend energy, you cant use it again. at least not 100% of it. if you put an ice cube in lukewarm water, it will eventually melt and the temperature will become homogeneous. but if you set a glass of water out, an ice cube will never spontaneously form inside of it, even though that technically wouldnt violate conservation of energy (which is the first law of thermo).
its unclear at the moment whether or not you could theoretically build a computer that doesnt spend energy, but the computers we make right now out of MOSFETs definitely need energy to run. specifically, you need electrons to flow into the chip to switch gates on/off, and then they have to flow out of the circuit to switch them off/on again.

>>16508258
you cant boil the water because the chips dont get up to 100 celsius, ideally.

Am I dumb for not understanding anything in an introductory stats course?

>>16508258
The temperature is too low. But it can and is used for cooling and heating human occupied spaces with heat pumps.

>>16508438
>The temperature is too low.
>>16508427
>you cant boil the water
not with that attitude, no.
What if you used other liquids with a lower boiling point?
What if it was in a near-vacuum environment so the boiling point is dropped even more?
What if you used peltier cooling to increase the output temp- assuming that the additional energy used for the peltier cooling is less than the energy you can produce by being able to reach sufficiently high temperatures?

>>16508497
None of that would make a difference. Usable "work" from heat requires a temperate gradient (that's simple thermodynamics), the greater the difference the more you can do with it (like generate electricity). The excess heat from server farms isn't high enough to do much except for what >>16508438 says.

>>16508527
>the greater the difference the more you can do with it
I thought peltier coolers main use was to create temperature gradients by moving hot out and moving cold in- and they generate heat in the process.

Is there a reason you couldn't use some material that has a low boiling point, and just funnel the heat from a large server farm into a relatively smaller area that can self sustain peltier cooling?

>>16508585
Like vapour cooling they need energy to run, they don't move heat around for free. You would always use more energy than you could possibly gain, so what would be the point. Also the amount of heat flux they can handle is small, I can't think of any, even in series, that could handle anything the size of a datacenter.

Would someone with institutional access be so kind as to get this paper for me? Usual places turned up nothing although it's quite old.
>Whatever happened to organizational anthropology? A review of the field of organizational ethnography and anthropological studies
>https://doi.org/10.1023/A:1016961918626
Yes I know it's humanities shit, pls no bully

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>>16508910
its on scihub

>>16508945
oh thank anon apparently I'm retarted

>>16509071
np fren <3

>Astrophysicists find something in space that doesn't fit in their model
>They respond by fudging or tacking on to the model so that it fits whatever they just witnessed
Isn't this basically like writing a program with spaghetti code?

>>16509922
No, that's a wildly incorrect analogy. People seem to forget / ignore just how good the existing model is at explaining all the other observations we have and how well it works. You can't just make big changes to the model to fit new observations because that breaks it so much it no longer works for everything else we have seen & understood already (this is why stuff like MonD is a huge failure - you can't create a working model of the universe with it).

>>16508675
>You would always use more energy than you could possibly gain, so what would be the point
I figured it would make sense to try to at least use the heat generated from the server farm and the cooling apparatus to try and produce some energy from a generator- even if you're not "gaining energy", maybe you could at least reduce the total energy spent on the server/cooling?
As opposed to just using more energy to move heat outside of the server(and producing more heat with the cooling), you could recycle some of that heat by using it to power a generator, perhaps.

>>16510072
The Laws of Thermodynamics mean that is never going to happen. You would be better at looking at more efficient ways to keep the servers cool, that is why people are investigating technologies like submersion in mineral oil or simply creating more energy efficient hardware.

Apparently the fine structure constant (you know, [math]\alpha \approx \frac{1}{137}[/math]) is not a constant, but changes both in energy scale and in time. Could someone explain the implications of this phenomenon?

>>16510088
The definition of the constant is [math]\alpha = \dfrac{e^2}{4\pi\varepsilon_0\hbar c}[/math], which on the surface would appear to be a fixed value. However the strength of the electromagnetic interaction does change with energy scales (due to renormalization) which effectively means that the value of e changes, and hence so does the fine structure "constant".

>Cluster point, adherence point, accumulation point
What the fuck are the differences?
Does [math](B_\rho(p)\backslash\{p\})\cap E \neq \emptyset[/math] mean that [math]p[/math] is a 'what' point of [math]E[/math]? And what about [math]B_\rho(p)\cap E \neq \emptyset[/math]?

Will I do better on my math exam if I snort a fat line of coke before

[math](a+b)^n=a^nb^0+na^{n-1}b^1+n(n-1)a^{n-2}\frac{b^2}{2}+n(n-1)(n-2)a^{n-3}\frac{b^3}{1\cdot2\cdot3}+...+n(n-1)(n-2)...(n-(n-1))a^{n-n}\frac{b^n}{n!}[/math]
Did I did this right?

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>>16510080
>The Laws of Thermodynamics
I'm a sovereign citizen of the Universe, so I am actually not beholden to the same socially constructed laws of whatever country you hail from, but I respect your desire to oblige to whatever rules&regulations are required by whatever artificial social contract you are engaged in. But ty for your input.

>>16510349
>Cluster point,
Stupid question, but I'd rather ask here before I look dumb and make a fool of myself irl.
Is it pronounced "cl-uh-stir", or is it "cl-ooo-ster"?

>>16510464
>Is it pronounced "cl-uh-stir", or is it "cl-ooo-ster"?
cl-uh-ster.
If you can answer my question, I'd appreciate it

>>16510397
No.

>>16510349
Cluster and accum are the same iirc. The issue with calling them limit points (same thing) is that it might confuse you with other limits in analysis. I personally call em limit points.

An adherent point is either a limit point or an isolated point. A closed set is a set that contains all it's adherent points, so the limit and the isolated. An isolated point obviously aint a limit point.

First looks like a limit point, second looks like adherent.

hi. i have wondered about the processes used for studying test rat sacrifices. i do not understand a lot of the jargon used when trying to read a paper and so ill ask stupid quiestion in the meantime. i could at least grasp that there is many different ways this is performed depending on the focus of the study.
it has stuck in the back of my mind and i dont know where i got it from. when rat brain samples are prepared for metabolomic analysis by gcms (or lcms?), do they put the lil rat brain into a blender? i thought this up when wondering how we even analyze rat brains for levels of various molecules and macromolecules. so i then thought, to be able to more accurately gauge the concentration of a target substance, are blenders used in any point of any method to more evenly distribute the brain matter into a liquid solution? or use of solvents to dissolve the tissue? or am i entirely off the mark?

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>>16510476
>If you can answer my question, I'd appreciate it
I already asked a stupid question to your post, I doubt you want a stupid answer to go along with it.

>>16510723
Good point

Do I need to start bragging about my grades so shitbrains sit down and show respect when I tell them things?

>>16510732
enjoy your gay sex with them

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>>16504908
>>16504908
Hello /sci/, so my country ranks 13 in the most air polluted countries. So how bad is this and how would this affect me and what should I do in my home to have clean air.

>>16511573
It's really bad, this kind of pollution levels can decrease your life expectancy by 2-3 years. It's also linked to decreases in IQ. Get a HEPA air purifier.
https://dynomight.net/air/
https://dynomight.net/better-DIY-air-purifier.html

Is there a more rigorous way of handling mass-energy equivalence, [math]E = \gamma m c^2[/math]? Like with proper four-vectors and stuff?

>>16512950
Yes, you use the four-momentum.

If the sea level keeps rising why cant we just dig a big hole in the ocean to make the ocean deeper

>>16513112
It would have to be a very, very big or deep hole. The oceans cover 70% of the globe and have a surface area of ~360m km^2. A 1m rise in sea levels (well within the range of current predictions by end of the century) would require a hole the size of the USA dug to a depth of 100m. Alternatively if you could dig down to the earth's core you would still need a hole ~ 240km x 240km in size.

>>16513112
>If the sea level keeps rising why cant we just dig a big hole in the ocean to make the ocean deeper
This is super smart! We'll just heap up the dirt on the land to make it taller at the same time!

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Why isnt this working even when I add the scope to it?

If sin = opp/hypotenuse then why is it that when we input pi/3 radians, we get rt3/2 when 2 isn't the hypotenuse of the radius hypotenuse being investigated and the radius hypotenuse is nowhere to be found?
If anything it seems to be outputting a related triangle where the radius is a side length, and then somehow the ratio between the non radius sides is the projection onto the y axis for he component of the radius

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>>16513339
Like this I guess

>>16513339
If the hypotenuse is 2 then the opposite side is [math]\sqrt{3}[/math], it gives you the same angle. All you have done is scale down the size of the triangle by a factor of 2.

What to do if I want to go back for a PhD in physics but my bachelors is in EE and my masters is close to physics but not physics? I was a shutin retard at the time so I barely graduated and no great research experience, not even a thesis.

Apply to masters programs and work my ass off to get into a good PhD program?
Or transfer my credits and finish a physics bachelors and then apply to grad schools?

I have a great job it’s just boring as shit. They’ll reimburse education so I dont care about cost, just want to get into a good PhD program

>>16508073
Anyone?

Would approaching an object several light years away give you an accelerated timeline?
As in, if you were to launch a probe magically past the speed of light toward a massive star that went supernova, but is so far it's still a star to us, and started recording, what would we see?

Let [math]L[/math] be a chain of subsets of [math]X[/math] ordered by [math]\subseteq[/math], such that there is some cardinal [math]\forall_{A \in L} |A| < \kappa[/math].

Does this imply that [math]\sup_{A \in L} {|A|} = |\sup_{A \in L} A| [/math]?
(The supremum of sets is equivalent to the sum).

Where can I talk about nuclear energy?

>>16508073
>>16513962
Start an Oppenheimer or maybe a Chernobyl thread on >>>/tv/

Hi /sci/. I'm a non-science person and tourist on your beautiful board, and was hoping for a scientific insight on the following:
I am great at intuitively understanding mechanical systems, visualization, and logical and analytical reasoning. BUT, I'm only great at logical and analytical reasoning when it comes to words. I have no problem intuitively reading and understanding really complex philosophical abstract concepts.
I'm pretty good at math for someone who works in law, but only when I write it using symbols. When words get involved with math I'm retarded.
I'm really retarded when it comes to electricity and electronics. I've had more free time than I usually do and was hoping to get into a hobby. I was looking at electronics to apply my brain to something less abstract than what I deal with at work, but I'm retarded when it comes to understanding this stuff.
I did well in physics in high school and decently well in a mechanics 1 physics class in undergrad, but for some reason I could never "get" or apply the concepts in mechanics 2, which was about electricity, magnetism, and so on... Even after reading and watching videos about basic circuitry I feel like I'm retarded. And I enjoy learning and expanding my knowledge and skills.
Now get this, I'm decent at computer programming. (I was 2 credits shy of a CS minor.)

Is my brain just not wired to deal with the specific abstract concepts in electronics?

I contracted a cold 2 days ago after sleeping in a cold room with exposed neck. Got a family dinner on tuesday. Should I skip to avoid infecting others or is that not how it works?

>>16514251
it's the kind with runny nose, stinging throat, and it feels kind of pleasant otherwise, like some kind of drug

I know this is probably a brainlet question, but what is the general procedure to go from SI to natural units (hbar = 1, c = 1) and from natural units to SI?
For some reason I can't find any clear explanation

>>16514539
It depends what natural unit scheme you're using and what you're converting too. But tl;dr - just google a natural units conversion table.

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>>16504908
scientifically speaking, what happens if i cover a lamp's lightbulb with aluminum foil? idk if it's incandescent or not, but i'm assuming it is because of how hot it is. my lampshade lets too much light thru, so the easiest fix is for me to cover most of the bulb with this foil i have handy.
will the filament over heat and burn?

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>>16514674

>>16514674
Kys

>>16514678
no

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>>16504908
How do I prove this associative property of tensor products using only the information in the image? Presumably the author meant there is a canonical isomorphism that maps u⊗(v⊗w) to (u⊗v)⊗w.

This was my attempt:

The author has previously shown that all f in F(s) can be represented as a formal finite sum [math]a^(1)s_1 + ... + a^(n)s_n[/math] for [math]s_i[/math] in [math]S[/math]. The author has also shown that if [math]\{ f_a \}[/math] and [math]\{ g_b \}[/math] are bases for [math]V[/math] and [math]W[/math], respectively, then [math]\{ f_a \otimes g_b \}[/math] is a basis for [math]V \otimes W[/math]. So, if [math]\{ e_i \}[/math] is a basis for [math]U[/math], then we have [math]\{ e_i \otimes (f_a \otimes g_b) \}[/math] is a basis for [math]U \otimes (V \otimes W)[/math]. Likewise, [math]\{ (e_i \otimes f_a ) \otimes g_b \}[/math] is a basis for [math](U \otimes V) \otimes W[/math].

If we take [math]φ: U \otimes (V \otimes W) \to (U \otimes V) \otimes W[/math] as a linear map defined by [math]φ(e_i \otimes (f_a \otimes g_b )) = (e_i \otimes f_a ) \otimes g_b[/math], then we still need to show it is well-defined.

We have that [math]\{ e_i \otimes (f_a \otimes g_b ) \}[/math] and [math]{(e_i \otimes f_a ) \otimes g_b \}[/math] are bases of [math]U \otimes (V \otimes W)[/math] and [math](U \otimes V) \otimes W[/math]. They both have dimU dimV dimW elements so the vector spaces are isomorphic. For [math]u \in U[/math], [math]v \in V[/math], and [math]w \in W[/math] we can write [math]u \otimes (v \otimes w)[/math] as [math](u^{i}e_i ) \otimes ((v^{a}f_a ) \otimes (w^{b}g_b ))[/math] which, by bilinearity equals [math]u^{i}v^{a}w^{b}e_i \otimes (f_a \otimes g_b )[/math]. So [math]φ(u \otimes (v \otimes w)) = u^{i}v^{a}w^{b}(e_i \otimes f\_a) \otimes g_b = (u \otimes v) \otimes w[/math] which is unique.

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Is this correct?

Bump >>16514845

>>16514845
Which book is that from?

>>16515158
Szekeres, P. (2004) A Course in Modern Mathematical Physics. Cambridge University Press.

Why are stinkbugs suicidal?

>>16514539
Constants of nature go to the constant 1 or some other constant number. Instead of saying E^2 = p^2 c^2 + m^2 c^4, you say E^2 = p^2 + m^2 because it's annoying af to keep track of all the c's, and it's pretty much a waste of time to do so because in the end you can always put the c's back to make it dimensionally consistent.

For example, if your answer is something like E = [(m_1)^2 + (m_2)^2 - (m_2)^2 ] / [2m_2], you should notice that your answer has units of m, which means you're missing a c^2 that multiplies by everything in the end.

For whatever constant you dislike writing 20 times per calculation so you'd rather forgo it, replace with the number 1 and just re-add it in the end to make your answer dimensionally correct

I know you can use conservation of momentum along each dimension and conservation of kinetic energy to solve for the final velocities of 2 particles in an elastic, 2D collision, but what about more particles in 3 dimensions? It feels like there aren't enough equations. But then what happens?

My dumb ass did something stupid
I put a solution of hand sanitizer spray in front of an open flame just to see the sanitizer catch flames. The solution says the following
Isopropyl alcohol 75% v/v
Chlorhexidine Gluconate 0.5% v/v
Glycerin 1.45% v/v
Water q.s
From what I can tell, everything in here is just carbon and hydrogen, except for the second which has chlorine and nitrogen as well
The dumber part is that I did a few sprays in an enclosed room, although I opened the windows for some ventilation afterwards
Will this make me any more retarded than I already am? The worst short/long term combustion product is carbon monoxide no?

which is greater, the current gain for common-emmitter or for common-collector in a forward active bjt transistor? and why?
please the only thing I find on the internet is that common base is around 1 and both common collector and common emitter is much greater than 1.
I'll do anything for whoever helps me with this, I'll even send nudes if you want

>>16506596
Sounds like a jadar problem.

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Let [math]S={(x,y,z) \in R^3 : (y-1)^2+z^2=4,\ 2<x<3}[/math] a surface, for every orientation that S admits, give a parametrization of its border such that the Stokes' theorem hypothesis is satisfied.

I parametrize the surface S as
[math]\sigma(x,\theta)=(x,1+2\cos(\theta),2\sin(\theta))[/math]
The normal of this surface can go outwards:
[math]\hat n= (0,cos\theta,sin\theta)[/math]
or inwards:
[math]\hat n= (0,-cos\theta,-sin\theta)[/math]

For the parametrization of the borders, I would use the parametrization of S, replacing x by 2 or 3. But I'm not quite sure how to verify that the orientation matches with the one of the surface. I tried a couple of different parametrizations but they all seem to point inwards.

What happens if we allow infinite intersections in our axioms of topology?

>>16515615
How would you do two particles in 3 dimensions? They tell you to flatten it out so that they're confined to a 2 dim plane, but even if you don't flatten it, it should still be possible to solve for two particles in 3D. What is the action of "flattening" their 3D motion into 2D? Think about this.

...
...
...

>answer
You rotate your head (also rotational symmetry <--> angular momentum conserved).

>>16515615
Since there is no general closed-form solution with more than 2 particles involved you would solve it numerically.

>>16516094
Thanks Anon. I forgot about angular momentum conservation as well.
>>16516102
Is there only one solution, or are there multiple?

>>16516212
Multiple but the question is common enough. You probably want to go lookup n-body collision algorithms.

>>16515863
If all you got are the equations of the boundaries, B, there's an infinite number of surfaces that it can be a boundary of. The boundary itself won't determine the correct orientation to do stokes theorem on. The boundary AND the surface are needed.

At this point, teachers will just say use the right hand rule to find the correct equation + orientation of all the boundaries. It says (sigma_theta) cross (sigma_x) points outwards, so you want your boundary oriented such that (boundary derivative B') cross (dB = vector pointing towards the surface away from the boundary) also points outwards.

Being a boundary, B doesn't need to be in S, but there should exist some B + dB = B_2 that's always in S where dB vanishes nowhere, and as dB gets smaller, B_2 approaches B. In general, that means B is the limit as n -> infty of B_2 = sigma( alpha_n(t) ) where alpha_n(t) = ( theta(t), x(t) )_n, for a set of curves alpha_n(t) where t \in [0,1). If you want to reverse the direction of B, then reverse the direction of the alphas, or replace t with t' = 1-t. The t's and stuff is just to generalize - parametrize to a single variable however it fits best (in your case, keep x constant and parametrize by theta or -theta). Even as the limit of dB goes to 0, you should still be able to do the normalized cross product to see if it points outwards.

But orientability doesn't know outwards or inwards; the cross product only give a vector. So you'd have to see if the limit of the Normals of S as we get closer to B approach the normalized cross product of B and dB.

Or just use right hand rule like a sane person. If there's any other way to do this, I wouldnt know it

>>16516212
>forgot about ang. momen.
Oh just thought of it, you can also do frame boosts. If you're moving in a frame such that one object looks motionless and all others are colliding into it, then you got a new set of equations that work too. So not only do you got rotational symmetry, you have translational symmetry. Lots of overkill, but you choose wtv works best (like moving to a rotational frame where the ang momentum is zero or a translating frame where the momentum is zero). In relativity, you use frame boosts occasionally to make problems easier (doesn't always work, sometimes it's harder).

>>16516222
Thanks; I'll look those up
>>16516270
Thanks Anon, that makes sense.

>>16514251
>>16514252
If fixed it really fast with 4x dose of vit c and zinc. Just did the family dinner with no symptoms.

Someone tell me how to make 4chan into dark mode, please. There's gotta be some way to do it.

>>16516406
>>>/g/103525147

how much topology do you really need to appreciate analysis?
lots of analysis books either barely mention it or just enough to make a point but i never really got the impression you need a full on course in topology to do analysis, at least at thee undergraduate level

>>16516704
>how much topology to appreciate analysis?
Let's restrict ourselves a bit, how much topology do you really need to appreciate calculus? The following is an excerpt from right the beginning of professor Peter J. Olver's alternative calculus lecture notes (https://www-users.cse.umn.edu/~olver/ln_/cc.pdf):
>"I started thinking about the topological definition of continuity, [12]. In brief, a function is said to be continuous if and only if the inverse image of any open set is open. This sounds very simple — and certainly simpler than the limit-based definition used in calculus. And I started wondering why not try to develop basic calculus using this as the starting point, and, possibly, eliminating all references to limits, epsilons, and deltas while still retaining rigor. And, after some thought, I realized it could be done. Continuity is basic, and limits, including limits of sequences, and derivatives follow from it in a reasonably straightforward manner, while bypassing epsilons and deltas entirely! You will see the results of this line of reasoning below.
>
>Not only can the development be made completely rigorous, I believe it is more elementary and eminently more understandable by the beginning mathematics student, who will be better able to appreciate the rigor behind the calculational tools. Moreover, this approach introduces them to the basics of point set topology at an early stage in their mathematical career, rather than having to start from scratch in a later course in the subject or in preparation to study real analysis".
There's also honors calculus textbooks from the past like Thurston's which argue that it is more elegant and at the same time easier and more illuminating to think in terms of [math]\epsilon[/math]-neighborhoods instead of the traditional but dry full [math]\epsilon{-\delta}[/math] statements:
>>16515492
Let me finish saying that multivariable calculus rightly viewed has a much more topological (and linear algebra) flavour.

>>16516857
interesting read, thanks.

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The Definition of a Planet:
>1. It must orbit a star (in our cosmic neighborhood, the Sun).
>2. It must be big enough to have enough gravity to force it into a spherical shape.
>3. It must be big enough that its gravity has cleared away any other objects of a similar size near its orbit around the Sun.

Isn't #3 a flawed seeing as we are pretty sure Mercury can't capture a moon due to its proximity to the sun and also has nothing in its orbital path to have cleared as far as we know?

>>16516704
>how much topology do you really need to appreciate analysis?
I'd argue that exactly zero. You see, topology trivializes certain results of analysis. For example Weierstrass theorem (continuous real function whose domain is a closed interval is bounded and attains its extrema) can be simply expressed as "image of compact set in continous function is a compact set", while Darboux property of continuous function (if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval) in topology can be stated "image of connected set in continous function is a connected set".

How much does it cost to hire a broke Asian college student to teach me math over the summer

>>16517477
Darboux property? Where does that name for Weierstrass (and Bolzano) Intermediate Value Theorem come from?. I read somewhere that the IVT proof is more readable if instead of taking the least upper bound property as axiom one starts from the cut property (if one uses Tarski's version even more so). I now remember the source: https://faculty.uml.edu/jpropp/cut.pdf

>>16517414
Nothing in the definition says it has to be able to capture a moon, also you answered your own question. There are no other bodies of a similar size in Mercury's orbit.

How can I prove that
>Let [math](X,d)[/math] be a metric space. Every infinite subset of [math]X[/math] has a limit point [math]\iff[/math] [math]X[/math] is sequentially compact.

Math makes bank but why do so many math teachers (who dont typically make bank) expect clueless children to love it for its own sake?

Are rates of autism consistent across languages? One of the most prominent features of autism is interpreting language literally. Do less literal languages have higher instances of autism?

>>16504908
If you have one hydrogen atom and the electron is required to be in quantized orbitals, if a muon replaces the electron why is the muon's orbit closer to the nucleus? From what I have read it is because the muon's greater mass, but how would the increased mass change the quantized orbital?

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>>16517772
Now, here is a proper stupid question. You see, there is a formula for a distance between proton and electron in the atom of hydrogen (screenshot from Wikipedia because I refuse to code Bohr radius in TeX.). Now, look very carefully at denumerator. What do you see there? Yes, a mass of electron. And since muon is about 206.77 times heavier than electron, Bohr radius for muon will be 206.77 times smaller.
(Homework: read any article about Bohr model.)

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reviewing some math I haven't done in years I wanted to calc [math]\frac{\partia(T)l}{\partial log(T)[/math] and I get pic. That can't be right no?

>>16517928
>to calc \frac{\partia(T)l}{\partiallog(T)

[math]\frac{\partial(T)}{\partial log(T))}[/math]

>>16517928
It's correct
https://en.wikipedia.org/wiki/Inverse_function_theorem?useskin=vector

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Stupid question here.
I have a system full of a liquid, no air entrapped, like the pic. Say the pressure is 1 psi at port A because of the height of the liquid at the other end of the system.

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>>16518142
Now if I double the liquid in another pipe like the pic, will the pressure at A double?

anyone knows value and/or source to average heat requirement for warehouses?
Im talking about any type of warehouse but specific answers are also welcome.
aim: making up a rough estimation for [kWh/(a*m2)]

>>16518146
no, it will not double.
its the same liquid depth, so the static pressure remains the same.
as long as nothing moves (or flows) its
>liquid density x g x height difference

without flow its called hydrostatics.
as you see pressure is proportional to the height difference (depth).
buoyancy force is just the result of pressure applied to a body under 'water' from all sides.

Okay so google says centrifuging nuclear fallout out is a no go. But what about evaporative cleaning? Meaning like, you evaporate the water out of the mixture and then recondense it. Would that remove the fallout from the water?

>>16518331
Thanks

>>16518266
10 to 20 kWh per year per m2

From Griffiths, Introduction to Quantum Mechanics
>It is often said that the uncertainty principle means energy is not strictly conserved in quantum mechanics - that you're allowed to "borrow" energy \Delta E, as long as you "pay it back" in a time \Delta t ~ \hbar / (2 \Delta E); the greater the violation, the briefer the period over which it can occur. Now there are many legitimate readings of the energy-time uncertainty principle, but this is not one of the. Nowhere does quantum mechanics license violation of energy conservation, and certainly no such authorization entered into the derivation of [previous equation].

Also from same Griffiths, Introduction to Elementary Particles
>The Heisenberg uncertainty principle says that you may 'borrow' an energy \Delta E, provided you 'pay it back' in a time \Delta t given by \Delta E \Delta t = \hbar / 2... In this case, we need to borrow \Delta E = mc^2 long enough for...

So, which Griffiths is right, and why's he contradiction his own pedagogy?

>>16517928
if it's hard to look at, let y = ln x, and solve for dx/dy. It's the same thing

>>16518146
easy to understand that Energy/Volume is constant throughout. So (m/V)gh/ + P(h) + (zero kinetic energy since static) = Constant. The p=mass/volume of water is pretty constant since water isn't very compressible. g close to earth is pretty constant. At the top of the water, the pressure is 0. This means pgh + P(h) = pg*h_max, or that P(h) = pg(h_max - h).

I dont memorize this, it's a 10 second derivation.

>>16518397
eh nvm

Asking all healthcare professionals, and please be honest. My wife cooked some food for me (cauliflower, eggplant, etc). All was well until I drank the soup that came from the pot; there was a small piece of plastic in my bowl. The type of plastic you find wrapped around spice bottles, a very small piece of it seemed to fall into the pot whilst she was cooking this entire time.

I managed to remove the small plastic from my mouth but I need to ask; did I just infest toxic substances from said plastic piece via my food and soup? I ate the entire fucking thing and there wasn’t any plastic nor did it taste off. It wasn’t until I drank the soup from said cooking pot where I discovered it scraping my mouth. I’m asking here because google/webmd says everyone has cancer and AI doesn’t understand the question, giving me sources for aptly related things but not matters pertaining to accidentally cooking a piece of plastic with food. Please and thanks

>>16518561
Youre fine. Just dont do it often. People eat from "microwavable plastic" or hot foods with plastic or cook with teflon or wtv all the time, and while it isn't exactly healthy, one single incidence isn't a 2 year death sentence.

Just like sugar or fat, establishing healthy life practices that limit your intake of em and mitigate any negative effects is best. Cook with wood, bamboo, or metal; reduce or remove teflon use; dont microwave with plastic; try to use glass/non-plastic containers; etc etc.

>>16517877
>from Wikipedia
what is wikipedia?

>>16518599
>its only a little bit of skin off your penis
">.

>>16517642
Reciprocal one is quite easy, as by definition, every sequence of points in X has a convergent subsequence converging to a point in X, so use cluster points and definition.

Now suppose every infinite subset of X has a limit point. Let 𝑎_n be a sequence in X. Notice that {a_n} is an infinite subset of X, so {𝑎_n} has a limit point. Let x be a limit point of it. Then every neighborhood of x contains some term in {𝑎_n}. Choose 𝑎_nk∈{𝑎_n} so that 𝑎_nk∈N_1/k (x)∖N_1/k+1 (x). Then for all 𝜀>0,
there exists some K>1/𝜀 so that for all k≥K, d(𝑎_nk,x)<1/K<𝜀.

>>16518766
PS: Is there any mathJax tutorial for dumbasses like me?

Why does it make sense to refer to particles as “particles”? Take the photon as an example. Isn’t an individual photon best understood as a discrete quantized excitation in the electromagnetic field? Not as an object unto itself, but something like blip in this ever-present field?

I’m pretty new to quantum mechanics and especially quantum field theory. Am I simply thinking too classically? What the fuck actually is a particle?

>>16518769
There is in the sticky.

is it unhealthy to hear voices that seemingly come from nowhere just as you are falling asleep and just as you are waking up?

>>16518831
No.

>>16518800
> Why does it make sense to refer to particles as “particles”?
Simplicity and convenience. Also history and tradition.
> Isn’t an individual photon best understood as a discrete quantized excitation in the electromagnetic field?
Context matters. In some realms it is much easier to use the standard Maxwell wave formalism, in others photons. It's only in particle colliders that you really need to use QFT. Sure QFT may be more "correct" but it's kind of useless in everyday calculations.

>>16519041
Thank you for the answer! That makes a lot of sense.

>>16516002
There are examples of infinite intersections of open sets that aren't open. Exercise: find a trivial one using easy examples of topological space. (Hint. use open intervals on [math]\mathbb{R}[/math] indexed by natural numbers)

>>16519098
Not doing your homework.

>>16519166
It was an exercise for the anon i replied.

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Does anybody understand what is meant by the expression v_p(f)? I think it's got something to do with the prime factorization. But I'm not sure.

>>16519268
i know. it was a joke (I can't solve it)

>>16519300
>Unique factorisation domain
I make a guess that v_p(f) means an exponent of p in factorisation of f (for example v_2(2) =1, v_2(3)=0, v_2(4)=2, etc.)
>>16519302
Consider open domains (-1/n; 1/n) where n>0. What's their common part?

>>16518367
so you say 15 kWh/m2 would be a good all over average value?
or is your knowledge specifical?
whats you location or latitude?

How exactly is Brownian motion a continous function. I know that X(t)~N(0,t), but doesn't that mean there is chance that X(t) is like 100000 or something , even though it is very small? But every graph of Brownian motion I see depicts it as continuous?

A [math] \Delta^+ [/math] baryon decays into [math] \Delta^+_{uud} \rightarrow p^+_{uud} + \pi^0_{u\bar{u}} [/math]. Does this violate parity? Is this a possible strong force decay?

>>16519166
kek, I chuckled

>>16518800
To give an example, there are two types of neutral Kaons, one with an Down+antiStrange and another with a Strange+antiDown. As they move through time, Kaons can mix between each state, so as a result it's possible to describe Kaons as a combination of both in two normalized orthogonal eigenstates K_1 and K_2 (like the orthogonal K_1=a+b and K_2=a-b instead of just a and b). In these orthogonal states, it's possible to see that there are decay scenarios for K_1 and K_2 where K_2 tends to outlive K_1.

The original Kaons produced by the strong force don't decay like that, but the mixed states K_1 and K_2 decay by the weak force, so which is the "true" particle? The latter has a defined decay lifetime, so is it the combination of both that's the true particle?

>uesless rant
Doesn't matter. Actual particles are pointlike, and irl particles aren't exactly pointlike all the time anyway - it's just a name we call em that has some value but not 100% perfect. Kinda like how a whale isn't a fish because it's a mammal, but all mammals are fishes in the way all birds are dinosaurs, or that some cultures use the word fish to mean the animals that swim in the water. Language isn't rigorously perfect; what we refer to as irl particles is just how we refer to em. Their properties and behavior simply IS so it is us that follows their rules, not the other way around (like a bear and a dog or a male and female don't need a to be described as different or the same in a mathematically rigorous way for the objects to exist). Particles simply ARE, so as long as you got their properties and behaviors down, can predict their next move, and are able to communicate with other people the info in an understandable way, that's enough. This doesn't mean stop looking for anything more fundamental though (bears and dogs connect via DNA and evolution), just don't worry about exact terminology

>>16519437
ignore this

>>16519395
Why wouldn't it be continuous? It's a real world process (time is continuous). However a graph is just an approximation with finite time increments small enough to give the illusion.

> doesn't that mean there is chance that X(t) is like 100000 or something
Well, yeah, it's a normal distribution. But depending on the variance of the process the odds of that occurring could be greater than lifetime of the universe.

>>16519453
I have a Ph.D. in particle physics, but I actually know embarrassingly little... Tbf I only ever took one undergrad level particle course that didn't even include QFT.

What do you mean by "the original kaons produced by the strong force" vs "K_1 and K_2"? And is the fact that we say they're a+b and a-b instead of a and b just for mathematical convenience?

After 10 years of studying physics, I still feel like I know nothing. I didn't read any of the textbooks (or if I didn't, I didn't actually pay attention, I just thought about something else while reading), I didn't pay attention in class, I cheated my way through all my assignments by either looking solutions up or working with friends, I memorized a few things and got lucky on all my exams and got great grades but forgot everything after the exam was over. I feel like a fraud. Now that I'm a postdoc with no mechanical engineering skills or coding skills, I can barely do work that's given to the undergrads in my lab. The distance between me and a professor feels massive. I still fail to understand some stuff about high school physics and have so many misconceptions when it comes to the simplest things, like friction and fictitious forces. Do other people who graduated from physics feel the same, or is this just me? I have no confidence and have no idea how to get a job when I feel like I have zero knowledge or skills, even after all this time. Maybe I'm just too lazy to actually learn stuff for real, or at least remember it.

Are there any examples of objects visible one year that are no longer visible the following year (or any reasonable time frame) because they are so far away the expansion of space exceeds the speed of light and the light from the object can no longer reach us?

>>16519801
No. At those kind of distances everything is red-shifted so much we simply can't see them with current technology.

>>16519549
Im just reading Griffiths. It's fairly basic stuff. I feel if you've already taken the classes, it should be a breeze for you, and it's already a very nice read. These kaon systems were the first example discovered that demonstrated a difference between matter and antimatter, because it seems K_2 very slightly violates CP symmetry in that it has a very very small preference to decay into positrons over electrons.

If you feel you're missing stuff, just read through the basics. Griffiths really is a great teacher, and his intro books are good intros

>>16519867
Even there I kind of just get by with a passing knowledge, I feel like I don't internalize things very deeply. I'll never even reach the low level of those guys on fucking stack exchange saying things like "every explanation I've ever read online has misconceptions about this, here let me explain it the real way for once," or people commenting on Veritasium videos saying "you got this wrong and that wrong." Sometimes my friends ask me questions about stuff like Veritasium and 3Blue1Brown and if they're correct, and I just go "I guess so, yeah, seems fine to me, I don't know, I've never heard any of this before." Then they ask me questions I couldn't begin to answer. That's not the level someone with a Ph.D. should be at... I feel pathetic and like the past decade was a waste of time and money.

What's worse is physicists can't even do things. We're not mathematicians, or programmers, or engineers, or anything else. They do all the real work. We just sit back and get everything wrong, time and time again. It's the most unproductive useless job, and none of my friends that did Ph.D.s are any better off, none of us seem to know anything.

>>16520434
This /sqt/ so i will answer accordingly. It's simple, you didn't take the advice (repeated ad nauseam) "get a skill" seriously and now you regret it. I didn't, as well...

>>16510500
gonna ask once more, shorter and more legible.
after a test rat is sacrificed with the intent to analyze vital tissue, do they use little blenders at some point, in any case? i get that there are many multitude of different ways to go about specimen preparation, but i am convinced that test labs have a little blender for little rat brains. do they, researchers, have a little blender for rat brain amalgamation?

>>16520434
anon, i think its cool you chose physics anyways. it might mean nothing to you but i appreciate the thirst of knowledge. despite the coasting through, i am assuming you chose physics because you have some desire to try to understand the nature of reality. i think that makes you a pretty cool faggot so dont dwell in uncertainty forever and dont an hero over anything insignifigant in the face of vapid existence
t. retard

>Quarks and gluons are dimensionless pointlike particles
How can this exist in our universe where everything is made up of something?

>>16521561
Because our current best theory says that everything is made of quantum fields and as such every particle is a vibration in their associated field. That means every electron in the universe is a vibration in the single electron field. The same applies to those quarks and gluons.

Is it true: [eqn]F(Y)[X] \simeq F(X)[Y][/eqn][math]F(Y)[/math] is the quotient space of the ring of polynomials [math]F[Y][/math] over a field [math]F[/math].

So, I just had a stupid idea that I couldn't immediately think of a solution to.
Is explaining the integral as a 'continual sum' even correct?
If I look at the integral of x from 0 to 1, that should be roughly equal to a sum of numbers between 0 and 1. But that obviously diverges.
[math]\int_0^1 x \,dx \approx \sum_{0\leq x\leq 1} x \geq \sum 1/n = \infty[/math]
Is the 'continual sum' concept a lie?

>>16504908
libgen.rs is down, i use libgen.li

>>16521731
No, the concept with the sums makes sense. Google "Riemann sums". In your specific case, you have [eqn]\lim_{n\, \to\, \infty} \frac{1}{n} \sum_{\nu\, =\, 1}^{n} \nu = \lim_{n\, \to\, \infty} \frac{1}{n^{2}} \cdot \frac{n^{2}+n}{2} = \lim_{n\, \to\, \infty} \frac{1+\frac{1}{n}}{2} = \frac{1}{2} = \int_{0}^{1} dx\, x.[/eqn]

>>16521731
>that should be roughly equal to a sum of numbers between 0 and 1
No, it should equal roughly equal to the arithmetic mean of the values between 0 and 1, which is 1/2.

As a math student, what to do during study breaks?
I used to go out for a cig but I'm quitting smoking so that's now out of the question.
Please, don't bullshit me with "meditation" or "do the laundry". I'm not gonna meditate or do the fucking laundry at uni. Also, stuff like just pacing around the hallways and sitting idle outside won't do

>>16522090
Jerk off, a là Wittgenstein

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>>16504908
Someone on /x/ actually has a solid understanding of time-space physics and it seems anons will attempt actual timetravel via dangerous manipulation of electricity and I'll dare to ask how many will actually die attempting the process?
>>>/x/39491447

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>>16522432
It's troll bullshit. His mechanism to reverse time is to draw an arrow in a different direction.

[eqn]x \euqiv 1 \mod 200 \implies x = 200\mathbb{Z}+1[/eqn]

Is it true?

>Given a marker locus M/m and a disease locus D/d, how to use the Haldane map function to map the disease locus?
Biocucks explain?

Are there math books that teach math by trial and error and showing you the process of what you actually do to navigate your way through solving problems instead of just jumping to the cleverest solution from the get go?
I would think the latter would obviously be the way to do it since that's how solving shit actually works but for some reason books think just showing you the end product without explaining any of the pitfalls along the way.

>>16522731
Books are meant for reference. The trial and error is expected to be either taught in class or figured out by yourself. The huge portion of the audience wouldn't like a book bogged down by unnecessary fluff.

>>16522731
The closest a i can think is the situtation where the "trial and error" is done by the student, not the author. The latter would be a rare gem. Returning to the student, there's Inquiry Based Learning (look it up, e. g. https://www.ams.org/open-math-notes Notes Type: IBL) and Numbers and Functions: Steps into Analysis - R. P. Burn (2015)

>>16522752
>The latter would be a rare gem
It seems so. I was listening to a video where Terrence Tao said his students found exactly this sort of approach most useful, i.e. lectures where he would go and mess up and have to figure it out on the spot. With programming how you debug your code is something you learn early on when you see someone put print statements everywhere for example.
>>16522734
>huge portion of the audience wouldn't like a book bogged down by unnecessary stuff
I think it's not unnecessary and I think many people would like that approach in a introductory/beginner book, especially since a lot of them I feel like also advertise themselves are being autodidact friendly

>>16521561
"Dimensionless" and "pointlike" implies the existence of infinity, which is retarded and leads to retarded results.
And physishits wonder why they can't discover anything new

>>16522477
But anon, time IS a magic arrow. If you turn it backwards, the whole universe will go into reverse!

>>16518672
A miserable pile of obtuse math trivia

>>16522798
You've solved it! Give this man a Nobel Prize!

>>16522760
>I think it's not unnecessary and I think many people would like that approach in a introductory/beginner book, especially since a lot of them I feel like also advertise themselves are being autodidact friendly
You overestimate the number of beginners who use books for self studying. Graduate books generally do not need this level of handholding and undergraduate books generally do not have the audience for such handholding.

Nevertheless, there are undergraduate books for pretty much every subject that have this sort of handholding. Analysis, for instance has Abbott. AMS has its whole "inquiry based learning" series. If you are serious about mathematics, you should learn not to rely on such explanations since if you are going to do research on mathematics, you would be studying cutting edge papers which definitely won't have this stuff.

When I was first studying math, I enjoyed Abbott's approach, but now I would never refer to it and would much rather refer to Rudin. All the stuff in Abbott becomes quite frustrating when you reach a certain level of mathematical maturity. Nowadays, when I read graduate level books with the intention of learning, I spend a lot of time in the proofs, deeply understand what all the mathematical formalism actually means, often reading it partially and attempt to prove it myself. This is much more effective than just reading the thought process of someone else. You should really try the same, otherwise you won't get much far with doing any original mathematics.

You now remember that one post where someone in 2023 said "what no-lifes study during their Christmas holidays??"

>>16522855
I see. I'm mainly talking as a beginner so I might enjoy Abbott's approach like you did, will check out his books. As for the AMS series, I looked it up and is it just a bunch of articles?

Your explanation of how you show yourself part of the proof and then try to move forward yourself is something I remember doing in uni several times cause I found it easier to come up with the solution to a problem myself than understand what the lecturers were saying but that's just cause I think my brain is weird and has a neurodivergent way of encoding things lol.

Anyway, if you have any other advice for me let me know, I feel like the most useful math I should learn is statistics and probability, linear algebra, bit of set theory and for my own interest calculus. All of this to a pretty superficial level though (and maybe some geometry).

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I have some room with some air pressure that is connected to another room with a lower air pressure via a potentially limiting factor
How would I estimate the flow of air through the connection?

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>>16504908
Is pic related solvable for all three angles and sides using trigonometry? If not, is it solvable at all? By what methods? Law of sines and law of cosines does not apply, I do not think.
This is not for homework. It is for recreational carpentry and curiosity.

>>16523104
Not a single value, as the 14-5.5 angle can be altered to meet other points of the projected unlabeled side.

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>>16523109
So there are multiple values of the top angle and the unlabeled side which would satisfy the given informetion?
It seems like there could only be two? Is this correct? If I drew a circle from the top corner of r=5.5 and extended the unlabeled line to infinity, the line and circle would intersect at only two points right? If so, how would I find these?
Drawing is terrible and I am sorry.

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>>16523111
1. Your circle is tragically bad.
2. Your drawing isn't to scale.

>>16523121
I guess I will say that the circle proves that there is more than one possibility. By changing the radial angle of 14-5.5, infinitely many circles can be drawn. And its probably two triangles for each one except where the unknown side is tangent to the circle.

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>>16523121
I agree, I thought it was enough to illustrate my question, though. I allow I may have been mistaken.
>>16523131
>By changing the radial angle of 14-5.5, infinitely many circles can be drawn.
I am sorry if I am misunderstanding you but I only see how one circle can be drawn. We have a fixed center point and a fixed radius. The above responder is correct in chastizing my drawing because it could indeed be possible that the unlabeled line is a tangent (or even incapable of intersecting such a circle) but you cant really tell but a not-to-scale paint drawing.

>>16523142
If the drawing was to scale, then the angles and side lengths are known by definition.

How can I get a physical intuition for the covarient derivative in gr, given the sloppy or informal description of it describing the way a vector(tensor) changes in a certain direction along the manifold, taking into account the basis vectors in any old co-ords might be changing too

>>16523172
topology.org

>>16523179
>topology.org
thx anon, that seems like a hefty differential geometry book he's got going. Reconstructed(?). Anyway, I'll take a look. I must admit I did shamefully grin >: - ) when clicking on the website:
>ROBOTS ONLY:
>If you are a ROBOT, please click on this link
yeh not really funny is it. Would you recommended to have a adjunct math book along with physics texts? I'm trying to learn a bit of General Relativity on my own and I'm somewhat retarded. It's a tough game. The wind is against me.

Stats math teacher subtly tells me I'm not smart enough and a another student overhears and gives a quick laugh. Still got an A though.

Honestly have no idea why I work so hard if I'm naturally dumb

>>16523381
Is he Indian?

>>16523381
>Stats math teacher subtly tells me I'm not smart enough
What did you do, anon?

>>16523434
No

>>16523535
I can't give the exact quote since this a while back and I wanted to suppress that memory. But the jist of it was that I'm not really using logic to figure out problems.

The class is non traditional in the sense that the you're sorted into groups and you have to work together to figure out the topic with very little hints from the prof. Problem is i dont really know what the question is asking 99% of the time and i dont generally learn anything while im in a group since it takes me while to understand a topic. I had a lot of trouble with stats btw, for whatever reason it didn't click and it still doesnt. Calculus 1-3 was easy for me to grasp on the other hand.

>>16523728
You think everyone is good at every subject? I know math professors who can't do basic mental arithmetic. Just accept stats isn't for you and move on.

>>16523829
Not at all and I did actually enjoy stats. I can see how powerful it is and wouldnt mind taking a higher level class on it. But I can't help but compare when people just seem to get it.

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>>16504908
>stupid
Do you think there's a connection between Plesiosaurs and Nessie?

>>16523900
> Nessie
Do you think Santa is real too?

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Can this number be simplified any further?

>>16523929
Yes. You can write the sin and cos terms using the double angle formula in terms of tan. Then the inverse tan functions will all cancel. If the rest will then simplify ... I'm too lazy / on my way to being drunk to check.

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How to find the curve traced by the center of the circle (red point)? I know f(x) and the circle radius.

>>16522752
Oh nice skipped over your post but thanks for the link, I checked out the link and it looks nice. What's the story there, you made it sound like it's made by students and then hosted by ams? Do they check it?
And for the R.P Burn book, who would you recommend it to?

>>16523981
> What's the story there, you made it sound like it's made by students and then hosted by ams?
No, they are intended for courses that eschew the tradional lectures and meet instead to directly attack the problem sets by means of trial-and-error and teacher/teacher assistant advice. It's made by professors using the Moore Method:
https://en.wikipedia.org/wiki/Moore_method
>And for the R.P Burn book, who would you recommend it to?
Someone who would want to try to develop all the theory by himself, of course with many hints along the way. That is, i'd recommend it to someone who works better with problem books than with lecture notes/classical textbooks. But if you really want to know if this or any other book suits best your interests, you better read some of its reviews (the last is about a different book but from the same author and in the same style):
https://sci-hub.ru/10.1017/mag.2016.42
https://zbmath.org/0872.00009
https://old.maa.org/press/maa-reviews/a-pathway-into-number-theory

>>16523962
There wouldn't be a simple function as the answer. You are talking about using trig to know if the circle intersects the line in more than one point at the same time. It's more collision detection algorithm than math.

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>>16524004
If both the line and the circle have an analytical expression, intuitively I would expect that the answer could be a simple function. Someone else had suggested the parametric function in pic related, which seems to kinda work.

Simple function or not, what's the best approach to find the red curve? Collision detection algorithms seem a bit overkill, for example I wouldn't need any information about timing.

>>16514191
>>>/diy/ohm
Start by getting a generic electronic components kit (resistors, capacitors, transistors, LEDs, etc.), a breadboard, some wires, and some pliers. Build something simple, like a buzzer or a light-sensing circuit. Don't get too hung up on scientific laws or overly technical descriptions at first. Just focus on getting a feel for what each component does, and how it can be used as part of other circuits. Test stuff. Tweak it if you get curious about it. See how you can improve or worsen something.

If you're anything like me, you'll learn more about what transistors do through by, say, using them to build a motor speed control circuit than you would by just reading a description of them in a textbook. I'm not saying you'll gain the same knowledge that an electrical engineer would have, but you'd at least have some working knowledge that could help you understand more advanced equipment and learn about the theory behind this stuff.

When I take a shot of alcohol, or take a big gulp of wine, my body shudders mostly focused on my head for a second or two. Why? What is the mechanism that causes me to do this? I'm not an alcoholic and I'm in my thirties, I'm not looking for doom articles about how drinking too much can cause you get the alchy shakes. I just want to know in the moment why does my body shudder to something that feels like poison, is this helpful in some way?

I don't know how to ask the question so I'll just do an example. Suppose we have y = mx + b where b follows a random distribution parametrized by mean [math]\mu[/math] and standard deviation [math]\sigma[/math]. We know that [math]\frac{dy}{dx} = m[/math]. However, what happens if the mean and the variance of the distribution depends on x? In other words, what is [math]\frac{dy}{dx}[/math] when [math]b \sim D(\mu(x),\sigma(x))[/math]? Can the derivative be expressed analytically? How does the answer look? Has a similar problem been studied in mathematics? If so, how can I read more about it?

>>16524392
https://encyclopediaofmath.org/wiki/Stochastic_process,_differentiable

>>16524392
Your question makes no sense.

>>16524398
Thanks, I'll look more into that.
>>16524429
What I mean is the distribution of a random variable is usually a given. What happens if, say, the mean and the variance of a random variable depends on x? For example, the higher the x the higher the mean/variance. How would I then express the derivative of y with respect to x knowing that the distribution b is drawn from will be changed by x?

>>16524392
>However, what happens if the mean and the variance of the distribution depends on x?
that doesnt really make sense. the mean/variance cant change with each x because the mean/variance is supposed to be a function of ALL of the x's.
in any case, whatever your expression for b is, plug it in and take the derivative like you normally would. the derivative of an analytic function will always be analytic.

>>16524440
With some types of distributions, it should cancel out, but not all.

>>16524392
I don't know the answer, but I know you're looking for Malliavin calculus https://en.m.wikipedia.org/wiki/Malliavin_calculus

>>16524454
What is regression on this sort of model called?

>>16523279
Lee's intro to Riemannian manifolds is a standard reference that should be mostly accessible to a physics student except for some standard smooth manifold stuff. Pick up the thinner early edition, it has less extraneous material.

>>16523997
Thanks for the links, they seem like places that compile math book review, which is cool. Usually I don't put too much value in reviews on say amazon, since I don't know much about the person leaving the review and I also can't talk to them to pick their brains some more, also don't know where that sci hub review is, I'm guessing it's part of the book itself?
What do you think of the Abbott, the other anon recommended him?

>someone who works better with problem books than with lecture notes/classical textbooks.
I came to realize a while ago that doing I was learning and understanding the most while doing the exercises or while trying to solve the problem myself like mentioned here >>16522933. Do you do it any other way, like isn't "doing the thing yourself" an important part of getting the information integrated into how your brain works?

>>16524735
>also don't know where that sci hub review is, I'm guessing it's part of the book itself?
It isn't part of the book. It's on SciHub because it is an article from a scientific journal, the kind that publish expository but professional articles and reviews instead of research. The Mathematical Gazette iirc. The most famous journal in this category is the American Mathematical Monthly, look it up.
>What do you think of the Abbott, the other anon recommended him?
Haven't read it but i know it is very praised. Can't tell you anything you won't find in the same book review repositories, so use them. For example (seek at least three different reviewers), https://old.maa.org/press/maa-reviews/understanding-analysis
>I came to realize a while ago that doing I was learning and understanding the most while doing the exercises or while trying to solve the problem myself like mentioned here >>16522933. Do you do it any other way, like isn't "doing the thing yourself" an important part of getting the information integrated into how your brain works?
Naturally, i admit i said something slightly non-sensical because every good textbook needs good problems and exercises and it is by trying them that you do the learning. But R. P. Burns' text is nothing but problems and exercises, because he walks you through the steps for providing your own proofs of the theoretical results instead the usual, which is passively glancing at the tidy, finished and authoritative proofs you find in classical textbooks. This is not to say that it always should be done like that, i think both approaches are complementary.

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Why does x/3 become 1/3?

>>16524794
It doesn't, try reading the text again.

>>16524435
Holy shit you retard. Listen to yourself before blabbering something that sounds like a question. Your question literally makes no sense. You're just writing technobabble like an AI.

I'm starting to study math just to study my brain, after looking it up I decided to start with a pre algebra and algebra book, is this a good starting point?
Is there a math progression?

>>16524866
also
you think I should read math books or just straight up do the excercise sheets you can find on the internet and look up things as you need them?

>>16524392
I think we can find the answer for a normal distribution without any fancy math using the fact that [math]N(\mu(x),\sigma(x)) \sim \mu(x) + \sigma(x)N(0,1)[/math]. From here, [math]\mathbb{E}[\frac{dy}{dx}] = m + \frac{d(\mu(x))}{dx}[/math]. I'm guessing things aren't that simple with other distributions.
>>16524865
Why does the question make no sense?

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Can thermal radiation emit any radiation wavelength at any temperature?
I heard that the thermal radiation of an object is not a single frequency but a range. Does this mean ice cream can release a photon of gamma radiation from time to time even if its exceptionally unlikely or is there a hard limit to this range? I really want gamma ice cream to be a thing

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>>16525006
Technically thermal radiation is a spectrum that's well-defined for any wavelength, but a chance for an ice cream to emit a gamma ray is negligible.

>>16525034
There has to be a limit somewhere though, right? Theres only so much energy that ice cream contains
If the limit was the energy of the ice ceam, im wondering if its technically possible for an atom in that icecream to immediately drop to absolute zero by releasing one extremely high energy photon
If its technical possible, what frequency would that photon be?

>>16504908
What is going on in this video?

https://www.reddit.com/r/oddlysatisfying/comments/1hn8qg5/what_is_the_phenomenon_called/

>>16525177
Goddamn reddit mods can't leave anything interesting up.

>>16525177
For anyone who checked too late, it was a video of a champagne glass where bubbles were rising in a straight line in a spot and then creating a spiral when hitting the surface. It's hard to describe but it was a neat effect.
>>16525345
I don't get it either. Pretty much every commenter says it's just bubbles and there's nothing interesting going on. Do redditors have no curiosity?

I took two IQ tests, one gave 131 and the other 128.
During the second one, I had some mental health impairments (such as depression) and had my sleep schedule totally fucked up.
If I were to inform my IQ, would it be safe to say that it's "130 with a 2 point margin of error"?
Or would it be best to say 131, even though this result dates from my childhood?

>>16524866
>>16524870
>[...] or just straight up do the excercise sheets you can find on the internet and look up things as you need them?
The best exercise sheet you can find is on Khan Academy because you get instant feedback (they are interactive. And the videos are optional, it is better to look up thing as you need em like you say instead of listening to the jeet)
Also, see this thread:
>>16521972
and this post
>>16524956

>>16525065
The equation / graph for blackbody radiation is an idealized model. So yes, the "body" generating the radiation will in fact behave differently and have a physical limit to what it can produce, even if that is just a temperature where the body breaks apart (e.g. turns into a gas).

>>16525544
say 131 cuz it's the highest

Assume I was 14 (I'm 30-ish but I will have to talk about this stuff to 14 year olds). How would you explain to me why the work done by lifting something up or by sliding it to the same height using a ramp are the same??? Without saying stuff like "gravity is a conservative force" or stuff like that

>>16526514
Realistically it's not; you forgot about the horizontal force. If you ignore friction, by lifting the object up the ramp you give the object horizontal momentum that is never dissipated by friction, so it just keeps moving horizontally; this is extra work to move it sideways. If you add friction, then you add a ton of extra work to counter the friction trying to push against your motion. So, there's always horizontal work being done.

If you want to say that the "upward work" to lift something up vs the "upward work" to push it up a ramp - thus ignoring the "horizontal work" - sure, that's "correct". The issue is that work isn't conserved directionally, so there's little reason to talk about "directional work". An example of when this becomes an issue is when you talk about stuff like "electro-magnets never do any work", where one issue pertaining to this is mistaking energy to be directional, i.e., believing that
>Force x distance_in_the_x_direction = Energy_in_the_x_direction,
when this is in fact not a thing.

If we ignore the directional energy issue, back to you question, it's best to think about it in the kid's point of view: why is the opposite way of thinking (the possibly more intuitive guess) NOT true? It seems to be easier to walk yourself up a ramp than to go up the stairs - why should it be that going up a ramp or the stairs takes "the same work" (again, ignoring the directional energy issue)? The answer to this is the concept of
>POWER = Energy/Time.
Ignoring horizontal, it is simply the rate of change that is different between the two cases. Is it really surprising that running one mile in 8 minutes tires you out more than walking a mile in an hour? You're still going the same distance in each case though. Now apply the same logic to energy/time instead of distance/time.

>>16526731
Not part of your question, but for running a mile in 8 minutes or walking one in an hour, it's hard to tell which situation actually expends more energy. On one hand, you might think that the longer to move, the more energy you're using. Instead of it taking one hour, you can extend this to taking a year to walk one mile - does this seem somewhat inefficient? But if you try to run a mile as fast as possible, shouldn't there be a high energy cost for high speeds?

In normal cases, the higher speed = higher energy is way more important than longer time = more energy unless you take so long that basic metabolic processes consume a non trivial amount of energy. With this idea in mind, this means going up the stairs tires you out more because your body genuinely is using more energy to lift yourself up faster than if you went up on a ramp at a leisurely pace. But if we're going to count this, shouldn't we also count the "horizontal energy" it takes on the ramp too?

When you talk to the kids, be sure to mention ALL the things you're ignoring when you say "the energy going up the stairs is the same as going up a ramp", because it truly IS NOT TRUE if taken exactly.

Do electrons stop moving at 0 kelvin?

>>16527080
That's why it's impossible to get to 0 kelvin

>>16527118
>leaving out some crucial information
Fair, I'll answer you with another question. How different are electrons from other electrons? Are all electrons, protons, and neutrons created equal?

>>16527080
You can't assign a temperature to a single particle. Temperature is the statistical average of an ensemble.

>>16527146
They are all the same. Why was actual something of a mystery until quantum field theory was formulated. Each particle is a quantized vibration of a single field.

>>16526731
>>16526745
Thanks!!!! <3 I think I got it. Thanks so so so much and have a nice new year c:

Can someone who understands physics explain this to me (a retard)
In this video, they say they start a fire by "striking the iron"
They hit a rod of metal with a hammer, and then touch the rod to a paper, which lights on fire.
What is the physics of what is happening here?
https://www.youtube.com/watch?v=1S1FclIqWVs
It is at 2:05

>>16527080
Electrons are superluminal, they never stop

>>16527476
Energy comes in many forms.
>People can manipulate energy of physically moving around.
>Hammer has energy of inertia from being swung downward.
>Energy of inertia is transferred to metal rod by hitting it.
>Energy in rod is absorbed in multiple forms, through indents and heat.
>Heat can be extracted by touching it with paper.
>Paper has a low burning point.
>The heat causes the paper to ignite.
Im not the best at describing this sort of thing, perhaps looking up concepts about the conservation of energy and how energy/physics work together could find you a good youtube video.

>>16527476
It takes energy to bend or break something. When you're bending or morphing metal, you're putting energy into it, which makes it heat up. By slamming on the iron really hard, it heats up pretty quickly to the temp that it can light paper.

Look up the video about a guy who cooks a raw steak by slapping it with a machine. Or slap your hands a bunch of times, and notice it heats up some.

Why do people still use the "brain as a muscle" analogy when it's been so thoroughly debunked

Can an adult increase their working memory? If so, how, and if not, why not? Saying "bc it's fixed lol" is just begging the question.

>>16527980
>>16527967

>>16527352
I was using a crystalline solid in my example. It was implied but not stated. Sorry about the confusion.

>>16513945
No. Let L be the ordinals less than Aleph_1. Each one has cardinality at most Aleph_0 so the supremum of their cardinalities is Aleph_0. However, their union is Aleph_1 so the cardinality of the union is Aleph_1.

>>16527476
https://www.youtube.com/shorts/-hzue8KIS9M

>>16524764
>Naturally, i admit i said something slightly non-sensical because every good textbook needs good problems and exercises and it is by trying them that you do the learning. But R. P. Burns' text is nothing but problems and exercises, because he walks you through the steps for providing your own proofs of the theoretical results instead the usual, which is passively glancing at the tidy, finished and authoritative proofs you find in classical textbooks. This is not to say that it always should be done like that, i think both approaches are complementary.
Yeah I would imagine the latter approach where you basically see the answer proof is good after you make an attempt at it and basically can understand what is going on, so when you're shown the answer you know what is going on, but it has to be just beyond the boundary of your knowledge. People who learn languages call this i+1 learning.

>>16527080
No, if it was a free electron it would be sucked back in to the fabric of space.
If it's a valance electron the more you slow it the more it will blur into the BEC.

bump

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Here is a problem that has had me thinking a bit.

What if you have an infinite set of numbers, with each number having a random distribution of digits.

Also, the length of the numbers is strictly monotonically increasing, say the n'th number in the set has n digits.

Now for the 100,000,000'th number in this set (with length n=100,000,000 digits), we know the chance that this number contains, say, only 1's (or 3's etc) is infinitesimally small.

But since the set is infinite, my question is whether we guaranteed that eventually one of these numbers in the set (say, somewhere after the 100,000,000'th) will contain only 1's (or 3's etc)?

Keep in mind the digits are random, and that there is only one number in the set for each digit length.

>>16530807
shouldn't just be summing 1/10^n?

>>16530815
but since there are an infintie number of them, even though the chance is essentially 0 for each individual number to have this property, what if we add up all these individual infinitesimally small probabilities over an infinite number of them

>>16531213
It's what the other anon said, the probability a set contains only a specified digit is [math](1/10)^n[/math]. Then to deal with all the possible combinations of multiple sets matching the criteria it is easier to instead ask what is the probability of *no* set having that property and then subtracting that answer from 1.

So the combined probability of all the sets having at least one that matches the criteria would be: [eqn]1 - \prod_{n=1}^{\infty} \left( 1 - \frac{1}{10^n} \right) \approx \frac{1}{9}[/eqn]
So the answer to your question is no, the probability is non-zero but not 100% guaranteed.

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>>16531285
Thank you anon!

What would happen if we started n at some arbitrary point, say 10^100, instead of 1?

>>16531287
The probability would get (much) smaller, tending towards zero as k tends to infinity.

>>16531295
I see, thank you anon. That's what I am having some trouble with. I keep feeling like that since there is an infinite number of possible attempts, eventually one of them must be right, even though each individual one should get progressively less likely.

how do i neutralize acids or based in a way that minimizes the salty flavor that gets left over?

>>16531323
What you are describing is the topic of infinite series and if they converge or diverge. It's essentially Zeno's paradox. Also just because you have an infinite list of numbers doesn't mean that every possible set of numbers is included.

>>16531360
ion exchange resins

>>16531399
Given a digit string is merely representing the number, is there an infinite stringe that doesn't encode every possible number?
Consider 1111111111111111. . .
one could see it as: 1, 11, 111, 1111, 11111, . . .
And then it does encode every number.

>>16531653
Take a random segment from that string, what number(s) are encoded in that segment?

How do people actually get confused by AI? Lets say AI videos, images, music, etc. Boomers/etc (but not just them either) are truly and actually convinced by some of these pieces of AI-media.

What I am asking is: how is that even possible? Like if they listen to an AI generated religious song they just outright believe in it and say "amen!"? I mean how? Do they actually not understand it isn't "real"? Does that make sense? They see an AI generated image of a girl in a sexy outfit and they fully believe it is just a real image, a real person, real everything? I mean that seems so insane to me; right? They actually can't tell the difference? Or they choose not to? I mean that seems like such idiocy that I'm not sure I can even explain that? It makes me feel uncomfortable in a way; and I'm also not saying I'm some genius or something. It just feels like they are legit being completely fooled, shystered, but can't see that

>>16531672
bad eyesight probably. Your quality of senses decrease as you get older

>>16531672
>They actually can't tell the difference?
No. A lot of people actually cannot tell the difference. They have not learned to look for it, and the images look real to a lot of people on the surface. That's just how the brain works.
You too will be convinced by all sorts of stupid bullshit when you are old.

>>16531672
When you are older, you will find that passages of 5 years tend to feel like 1 year, mainly because you just aren't as involved in things.

Imagine for a boomer the jump between around 2015 up to now. That would have felt like 2 years for them.

How much advancement in deep fakes and AI generated images have occurred since then, especially in the last 5 years?

Now imagine if you were like 80, and your height of technology competency was back in the 80s or 90s, and you're also facing cognitive decline.

I think the real problem is it is becoming more difficult to prove that real videos/images are not AI. It must be very hard for boomers to know what is real and what isnt.

>>16531672
I've seen this a lot lately too. Jeets and trannies catfishing with obviously AI-generated images of women and boomers leaving comments like they were talking to a real person. Really bizarre. Hard to say who is the bot and who isn't.

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How do I solve this?
I was reading a chink manwha and came across a few problems.
I'm struggling on this one because of the fucking midpoint.
I was gonna cut the left one's obtuse angle into a 90° degree angle to see if I could make it easier afterwards but it's just putting me back into an awkward spot.
The red stuff's the ones I already figured out

>>16532795
Assume it's set of linear equations, a+b+c always equals to 180 for any triangle, like that you need to write them down, and commit equation stuff to find one angle.

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>>16532795
AB = BC. find BD in terms of AB, and then you have two sides and one angle of △BCD which makes it fully defined. solve for ∠BCD and hopefully the AB's will cancel out. google "SAS triangle" if you get stuck.

Is the ratio between the previous and the next Catalan number converging towards 1/4 if you use larger and larger numbers? I discovered this by trying it out with a calculator.

For example, the ratio between the millionth and the 1000001:th Catalan number is 0.25000037499981250009374995312502...

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>>16533048
In fact it is according to wolfram alpha

>>16531672
What the fuck are you talking about? Do you know someone that, even after being told something is AI generated, they still think it is "real"? Or do you think you can with no extra information distinguish between AI generated content and human? I mean, with text is nowadays virtually impossible if someone prompts the AI to hide some of the more evident stuff. With images if it is a simple enough image it is really easy to fool most people if you are just glancing at it. I mean, good Photoshop already does that and IG whores already massively altered their photos even before this new AI boom. Or hell if it is a cartoon or animation, how the fuck do you tell it appart from a human made?

>>16533123
>Or hell if it is a cartoon or animation, how the fuck do you tell it appart from a human made?
its easy to tell if you look at a lot of it. theres some easy tells like hair/eyelashes, fluids, and especially repeating patterns tile floors, fishnets, etc. but even if the AI nails all of that stuff (which isnt hard if you know what youre doing), the biggest tell is that AI has a very hard time with perspective, even in photo-realistic imagery. it just... kind of... mix-and-matches focal lengths. its really hard to describe, but its very noticeable once you know to look for it.

>>16533177
Well yeah, but the point is people are not going to inspect every single photo they see in facebook like that and it is well easy to be mistaken. So I don't understand if >>16531672
meant that people are really stupid to get fooled from time to time by AI generated stuff.

>>16532807
>>16532878
Thanks, i'll try again in a bit and see if I can solve it that way.

is libgen down? i am getting 502 bad gateway on libgen.is

Are there any gemstones that 1. are transparent, 2. are colourful and 3. the source of colour is not a contamination?

>>16533578
CuSO4, among others (cobalt, nickel, copper, iron, lead etc. salts)

>>16533580
I wouldn't really call copper sulphate a gemstone.

>>16533447
Try Anna's Archive

>>16533578
I can't think of any. Impurities are what give them their color. In some cases they wouldn't even be gemstones without them. e.g. Rubies. Pure aluminium oxide is a grey opaque stone.

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>>16533630
>>16534027
Chalcanthite (CuS04 • 5H20) looks nice.

Suppose you've travelled time. Given a telescope, can you figure out century/decade/year out of watching the stars?

>>16534127
Yes, in principle. Though the accuracy would probably be more like to the nearest thousand or tens of thousands of years.

>>16533630
Depends on how you define gemstone then. Purely silicates/aluminates/beryls? Then no, those are inherently colorless.
Also, I believe cinnabar was used as a gemstone in some cultures. Either way, transition metal salts are your best bet.

What is the physical interpretation of the relativistic term mc?
In the momentum 4-vector, the terms are [mc, mvx, mvy, mvz]. The xyz are obviously cartesian momentum, but what's the mc supposed to mean? "Rest momentum?"

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>>16534027
>>16534179
I hope nobody's insane enough to actually wear it, but realgar [math](\text{As}_4\text{S}_4)[/math]) makes nice gems.

Tea can be brewed as a concentrate, and then be watered down before serving. Does it change the tannin:fluoride:caffeine:theanine ratios?

>>16534381
Only if the compounds are in saturation, which I hightly doubt.
You might also want to look into the mechanism for how hydrophobic oils are extracted, as they're what carry most of your floral/aromatic components. Their extraction may or may not be more dependent on surface area or turbulence than actual solubility.

>>16533578
Amber?

is it a bad idea to heat glassware outside in the winter? i don't want to breath fumes, but i also don't want temperature differences to shatter things

New thread

>>16534688
>>16534688

>>16534186
>What is the physical interpretation of the relativistic term mc? In the momentum 4-vector, the terms are [mc, mvx, mvy, mvz]
It is probably clearer to write the first term it in its more usual form 'E/c' where E is then the relativistic energy.