Can anybody see where I’m going wrong here? I know $\omega$ has to be inter solution but seemingly it vanished when I calculate the eigenvalues and thus doesn’t show back up in the answer. Any help?

@cocomac if you carry out this experiment, at beginning the heat energy inside the can absorbed by the water is less but enough to vaporize, It exerts pressure on all the sides, if the can is wide open it will rise up as it is, but the vapor is directed to exit through a small hole in which the pressure builds up and in turn convert into kinetic energy, the vapor travels through the tube on left, which will hit the turbine.

it will definitely rise up, after it loses the gained kinetic energy

@KavinIshwaran Neat, thanks! Just wondering, if I make the tube smaller (not in length, but in interior diameter), will the steam come out faster, causing it to spin faster?

@cocomac A slightly less diameter than the one in the image should be ideal, remember that very less diameter will eventually slow the thrust, to make the turbine spin faster, keep it closer, and make the angle of attack of the turbine blades in an equilibrium.

Morning

@JakeRose When your matrix is time-dependent as you have there, just looking for the eigenvalues isn't going to cut it

while the eigenvalues are time-independent as you have found, the actual eigenvectors are changing

nlab is still stuck on that weird Amazon AWS server

yeah, what's up with that?

did they forget to extend their domain registration? :P

I guess not since the old URLs forward to the new ones

probably just some hiccups related to the "imminent" move to the cloud

Finally they are ascending to heaven

heh, I guess cloud migrations should really be called raptures

I wonder if they write their website in a language based on category theory like Haskell

the GitHub for the nLab is linked right there - somewhat anticlimatically it's mostly Ruby and Python :P

Sellouts

I can never remember what's the physics/math name of a normal neighbourhood v. a totally normal neighbourhood

People use those terms, or geodesically convex neighbourhood, or Cauchy normal neighbourhood

Isn't it ironic how evolution developed positive dopamine and serotonin releases on reproductive activities in humans to "encourage" reproduction, and for most of history it worked, humans reproduced because it felt good (positive neurochemical reinforcement) and now humans use condoms and in a way cheat the system to get positive neurochemicals while not reproducing (screwing up evolution) and yet it's evolution that developed the brain that developed the condom.

Not particularly ironic

And I understand that evolution has no "consciousness" and is just a process that happens

Evolution has developped ways to curb reproduction many times before

Reproduction isn't always a benefit

Species that can't control their births may have issues

yeah I get what u mean

what could those issues be?

Death by famine

For a fun mathematical perspective of the issue you may want to check out the Lotka Volterra equations : en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations

yeah too much people and too small of a forest

The classic trick is to eat the babies

@Slereah LOL

Less common with humans

I learned yesterday that left-handedness (I'm left-handed) is somewhat genetic and reflects the balance between competitiveness and cooperation in a society. Left-handed people have a competitive advantage (e.g. can confuse the opponent) and a cooperative disadvantage (e.g. tools are made for the right-handed majority) so in a society that has 10% left-handed people means that cooperation is a lot more present

Historically the most common ways was just to abandon them in the woods

I watched this on ted-ed for 5 mins, not sure how accurate it is

@Slereah is it that hard to realize that if you make the baby, and you can't feed it, it's better to not make it

positive neurochemical reinforcement is too strong I guess

Well for a start circumstances may change in between the conception and the delivery

also making babies is fun and abandonning babies is easy

It's not like they're gonna struggle a lot

just watch out for trails of breadcrumbs

lol evolution is weird

So many "bad" things have happened as you said above, and yet it's evolution that defines what's good and bad (moral and immoral)

Not really

Evolution just happens

whether it is good or bad is left up to whatever interpretation

yeah but it has defined good and bad in our human brains at least

[citation needed]

Only in pretty broad term, and even then the human brain tends to be too complicated for those to always stick

killing is bad and immoral because evolution has figured out that if you discourage such behaviour, you have a higher chance to pass those "peaceful" genes, no?

@JingleBells many people would disagree that "killing is bad and immoral"!

Well I invite you to look at all of human history to decide that

otherwise how do you explain wars :P

Killing your own kind is bad, that works?

killing the "others" (i.e. another tribe or a country) is acceptable

Also not a rule particularly followed historically

Some people even kill themselves!

@JingleBells that seems to be a lot more widespread, but still I contest the idea that this is somehow an imperative given to us "by evolution"

I mean kind of I suppose, but "evolution" just roughly gives "What kind of protein should be produced"

There's quite a lot in between that and "how people behave"

if people are (somewhat) rational agents, they can do enough game theory to reach states where they prohibit killing their in-group without any inherited propensity to do so

Also another thing to keep in mind is that humans live in groups and it's quite likely that on an evolutionary level, it's common for humans to evolve different personalities

Since different behaviours can be useful at different times

Yeah it's quite complicated, with multiple evolutionary forces pushing stuff in whatever directions

IIRC it's estimated that any personality type that's present in over 5% of the population is probably rooted in such things

and then you also get cultural ("memetic") evolution where you have ideological groups that prohibit killing members of that group, and which spread via systems mostly unconnected to genetic evolution

@Slereah what's ur 16 personality type thing?

@ACuriousMind hbu, have u taken it

we've talked about this before - the idea that all human behaviour can be viewed through the narrow lens of genetic evolution is at best overly simplistic, at worst pseudo-science

@ACuriousMind yeah I totally agree, there's cultural forces, environmental influences, and so on

@JingleBells all these personality types are essentially horoscopes

at least the ones for which you can take fun tests on the internet :P

@ACuriousMind the barnum effect does play a role in the sense that people fill in personal specifics in general statements

but it told me that I'm a rare type so I'm biased toward liking the test

I memorized 50 biases and 24 logical fallacies

im the new socrates now

The behaviour of people is roughly described by the structure of their neural net in their brain, with about 100 billion neurons and up to 10,000 connections for any given neuron, also each neuron is affected by the levels of neurotransmitters and also each individual has neurotransmitter receptors that are constructed differently

I should be making my roblox game what am I doing lol

It's a miracle that we're behaving at all similarly as it is

@Slereah Yeah but also evolution has carved out a bunch of boilerplate circuits in there

Not even

There's no map of the brain in the genome

You just have a bunch of proteins which will, hopefully, create something resembling a standard human brain

but this depends on the genes and on the conditions all around

well that's true for every part of the body, DNA indirectly shapes the brain (and it's connections) to an extent

@Slereah but there's a map of the proteins that go a build the brain, so indirectly, there is a map of the brain, no?

Sure, except it's chemistry fundamentally

It's gonna be affected by whatever other chemicals are around and temperature and whatever else

yeah I still don't know after those proteins get built in the ribosomes, how do they know where to go and what to do lol

also it's not a perfect process, it's gonna be slightly different everytime

@JingleBells had you read any Socrates/Platon, you'd recognize that more as the hallmark of a sophist :P

or a big dork

it is unclear to me whether there were any non-dorks in the Platon vs. sophists conflict :P

Thou shall not question, should I with path be lead to wisdom will be

mmm

The worst part of making a big broad spanning paper is finding enough symbols to not have possible confusions

How can I write the polarization vector of an EM wave

If I use $e$ I run the risk of confusing it with the tetrad field!

the classic choice is $\epsilon$

Well that could also be the levi-civitta tensor!

Although I haven't used it so far

Let's go with that

the number/form of indices should make it possible to distinguish it from the LC symbol

@ACuriousMind so I have to find the eigenvectors? How would I do that in this case?

@JakeRose no, finding the eigenvectors isn't the correct solution, either :P

or rather, it's not the end of the solution

The best way probably is just by getting a second order ode

This just felt much more natural

whenever you can avoid it, you should avoid getting into time-dependent Hamiltonians :P

there's nothing natural about them and solving problems involving them is always annoying, so if you have a different way of solving the problem you're actually trying to solve, take that one

What’s the alternative?

Ah I see. I think I’m just used to linear algebra being all powerful

the problem is that the time-dependence destroys all the power :P

you can still determine eigenvectors at every instant, but there's nothing nice about how they evolve, in particular they're not just evolving with a phase

Is there any other general techniques for solving them?

well, the "general" technique is writing down a ridiculous Dyson series that no one will ever compute in practice :P

for specific cases, you might get lucky, or you have to use (time-dependent) perturbation theory

I think Sakurai discusses this at some length

@ACuriousMind What if your quantum system is next to "The machine that generates a time-dependent potential"

ie most experiments

@Slereah I am surprised that you'd disagree doing experiments is annoying ;)

I mean yes, but less so than modelling every atom of the machine

"FOUN@ATIOkS OF DIFlf'ERENl%.AL GEOMETRY"

Ah, bad OCR

tomlr.free.fr/Math%E9matiques/Math%20Complete/…

What the hell did they scan it with

Are they trying to hide the location of a secret treasure

I think I found the theorem for guaranteeing that a spacetime has a non-bogus splitting

globally anyway

Although I think that doesn't guarantee that it's spacelike

yeah null surfaces are technically still achronal

I think you need stably causal to have the foliation

Though stably causal doesn't guarantee that all leaves are diffeomorphic

> This challengeable project is to accurately measure and evaluate gravitational acceleration with ultracold atoms and Bose-Einstein condensates for studying climate change.

Did they just add "climate change" to get funding? Or is there a real purpose?

Maybe the climate will get so cold that the atmosphere will condensate to a bosonic state

That sounds like "hell freezes over".

In Finland they call it "Wednesday".

Hey all! Apologies for the dumb question but if I start with the langragian (not its density) and add $L '= L + \int c dt$ where $c$ is a constant. How do I get the cosmological constant from this?

Can someone link me to explicit calculations?