The h Bar - 2020-02-27

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1:48 AM

@bolbteppa the nCat stuff? Is there a non-category lecture that explicates bundles -> orbifolds -> supergeometry -> prequantum field theory -> QFT?

5 hours later…

7:18 AM

@alexchandel Almost certainly not, since "prequantum field theory" is not a concept outside of texts with the "npov". The "standard" parallel is any text on quantization, which you find in extremely varying degrees of rigor/mathematical sophistication.

2 hours later…

9:20 AM

One day I will learn category theory

And finally read nlab

Is there a baby's first category theory class?

Like category theory for number objects

Where all categories are sets and functors are functions

Novalium Company

9:38 AM

Where can I find people who are interested in AI? I need people with whom I can discuss AI topics, machine learning...

There's a bunch of AI-related Stack Exchange

Novalium Company

Yeah, I'll do that

Oh no

Reading things and now he's using the morphisms of one category as the objects of another

and functors as morphisms

10:03 AM

And now they're mapping a category to SET, implying that the functor maps the morphisms of the category to a set of those morphisms

But then that implies that those morphisms are themselves sets!!!

unless SET isn't the same as ZFC set theory

2 hours later…

Yuvraj Singh...

11:45 AM

I have a small question,it may look childish but yes.

Actually I have two cases once I throw a ball straight vertically, or at angle an angle theta, from the ground

Into space.

Since earth has large curvature so I defined my anger like that.

Ball has sufficient speed to put that in earth orbit.

So question is does the both cases are similar, similar mean throwing ball at angle will make no difference? (except 0, and 180)

1 hour later…

1:04 PM

Urs Schreiber - Introduction to higher supergeometry

youtube.com/playlist?list=PLcLi_mHOmW2LWTG7WHn4wDvsTwM5g0Sx8

1:19 PM

Hm

Riddle me this, Batman

A projective spacetime is a spacetime equivalence class $(M, [g])$ such that geodesics of each $(M,g)$ are invariant under change of metric

If I extend the connection to the general gauge connection, will any charged particle path be invariant

Although of course, those would be test particles, therefore unaffected by each other's charge

aaaah

why is everything bad

1:43 PM

How do you extend a connection to a gauge connection

Connection of gauge $\mathrm{SO}(3,1) \times \mathrm{U}(1)$ something something

2:15 PM

Apparently there's a whole rigamarole to deduct the exact spacetime you are in from measurements called the EPS construction but it is filled with equivalence classes

Where you get the topology, affine structure, conformal structure, projective structure and metric structure from the measurements

2:48 PM

Hi. There is a proposal for a Material Modeling SE which is currently in the commitment phase in Area51. If anyone is interested, you could support the proposal by committing to it.

There were many questions regarding DFT, basis sets, computational modeling packages etc. proposed in the example questions for the site. Do check them and if interested do commit to the proposal.

3:00 PM

"It should be realized that the representation of light in special relativity by means of ordinary cones rather than by hypersurfaces of hour-glass shape depends partly on a particular choice of differential structure."

@Slereah Do you remember Helmholtz theorem that any vector field can be determined if it's curl and divergence is given? I don't why on internet I can't find any links of it

@YuvrajSingh... Whom are you angry on?

Helmholtz decomposition

In physics and mathematics, in the area of vector calculus, Helmholtz's theorem, also known as the fundamental theorem of vector calculus, states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field; this is known as the Helmholtz decomposition or Helmholtz representation. It is named after Hermann von Helmholtz.As an irrotational vector field has a scalar potential and a solenoidal vector field has a vector potential, the Helmholtz decomposition states...

Yuvraj Singh...

3:40 PM

@Knight me?

3:55 PM

Let's say one has a spacetime model $S'$, equivalent to a nonlinear transformation on the original spacetime $S.$

Is there any obvious motivation to study $S'$ on the outset

Wouldn't this just be a coordinate transformation? So it would just be the same geometry in a different coordinate system.

@Knight sorry, I hadn't realised Slereah had already posted a link to the Helmholtz deomposition.

@JohnRennie Sir I’m looking for the way I have used it here

0

A: How to find the magnetic field of a current using the differential form of Maxwell's equations?

Biot-Savart law gives us magnetic field completely in steady current situations. So, why do we developed the differential form of equations? The Helmholtz Theorem (it is given in the form at the back of Griffiths Introduction to Electrodynamics) states if we are given the curl and divergence if a...

@YuvrajSingh... Yeah, just click on the arrow before my reply you can see which message of yours I have replied to.

Yes @JohnRennie Thanks for that insight. So just to clarify, the spacetimes would be completely equivalent?

Those proofs of Helmholtz are awesome

Which proofs?

4:05 PM

On the wiki page

@geocalc33 well what you describe sounds like a coordinate transformation. I'm not sure how you'd go about actually transforming a geometry into a different one e.g. Schwarzschild into Kerr.

@bolbteppa I’m looking of the form of Helmholtz theorem which I have used in my answer above. It is given in Griffiths but on internet I’m unable to find it

@JohnRennie okay, thanks. So you could in principle, map say, Minkowksi space under a nonlinear operator and strictly study the geometry of the transformed spacetime?

I don't know how that would be done or if it's possible.

and I must say a bijection between the geometries is necessary...

@JohnRennie Do you know who I could ask about this?

Yuvraj Singh...

4:10 PM

@JohnRennie hi.

@YuvrajSingh... hi :-)

@geocalc33 @Slereah is our resident GR guru. He hangs out in this room so he'll see this post.

Yuvraj Singh...

@JohnRennie can you see a question which I posted two three hours ago.

About launchng a particle from the Earth's surface?

Yuvraj Singh...

Yes

@JohnRennie

An orbit can be described by the angular momentum and kinetic energy of the orbiting body. If you launch the body at a different angle (and the same speed) you change its angular momentum so you change its orbit.

Likewise if you keep the angle constant but change the launch speed you get different orbits.

Yuvraj Singh...

4:15 PM

Which one is more efficient in fuel consumption.

Maybe you're thinking of the escape velocity? If you launch an object at the escape velocity then it doesn't matter what angle you launch it at - it always escapes.

Yuvraj Singh...

Straight up.

No I am talking about velocity to keep the object in earth orbit

Orbits are closed, so you can't throw an object into orbit from the ground. Because the orbit it closed it will always return to the point you launched it from.

Rockets go up in a curve when they put satellites into orbit.

Yuvraj Singh...

OK.

1

A: In what direction should you throw a 1Kg uniform sphere in order to put it into lower earth orbit?

If we ignore air resistance for a moment, then all orbits in an inverse square force like gravity are closed. this means that if you throw something hard enough it will complete one orbit then return to its starting point i.e. your hand. So if you throw the object downwards it obviously hits the...

4:25 PM

@geocalc33 whate are you mapping, exactly

And precisely what kind of nonlinear transformation are we talking about

@Slereah $f:\Bbb R^{1,1}\to N.$ s.t. that $f$ is an isomorphism

and

a lipschitz continuous map, $(u,v)\mapsto (u',v')$ , where $u'=e^u$ and $v'=e^v$

I'm not sure about the geometry, I think you'd need to investigate submanifolds of $N$

so just to be a little more clear..

$f$ only maps a pseudo-euclidean space to $N$ another pseudo-euclidean space. To get some geometry, one needs to consider lorentzian submanifolds of $N.$

Using $\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = \mathbf{b}(\mathbf{a} \cdot \mathbf{c}) - \mathbf{c}(\mathbf{a} \cdot \mathbf{b})$ which is easy to prove we have
$$ \mathbf{k} \times (\mathbf{k} \times \mathbf{\mathbf{G}}) = \mathbf{k}(\mathbf{k} \cdot \mathbf{G}) - \mathbf{G} (\mathbf{k} \cdot \mathbf{k}) $$
so that
\begin{align}
\mathbf{F}(\mathbf{r}) &= \int \mathbf{G}(\mathbf{k}) e^{i\mathbf{k} \cdot \mathbf{r}} d^3 \mathbf{k} \\
&= \int \mathbf{G}(\mathbf{k}) \frac{\mathbf{k} \cdot \mathbf{k}}{||\mathbf{k}||^2} e^{i\mathbf{k} \cdot \mathbf{r}} d^3 \mathbf{k} \\

4:41 PM

@Slereah sorry to bother you, I'm not sure if it's a good question

We can find separate equation for $\Phi$ by taking the divergence of $\mathbf{F}$, $\nabla \cdot \mathbf{F} = - \nabla^2 \Phi + 0 = D$ (since the divergence of a curl is zero), and a separate equation for $\mathbf{A}$ by taking the curl, $\nabla \times \mathbf{F} = 0 + \nabla \times (\nabla \times \mathbf{A}) = \mathbf{C}$ (since the curl of a gradient is zero). Solving these PDE's gives $\mathbf{F}$ uniquely.

Novalium Company

5:23 PM

If you remove the suit from Iron Man, it's basically Superman.

I mean, the Iron Man suit is used to make Tony Stark like Superman. Ultra-durable, shooting lasers, flying... nvm... I have no idea what I'm talking about :D

6:01 PM

@bolbteppa I have seen your profile and found that on one question you have got 109 upvotes, what are you currently doing in mathematics and what that question was about? I saw it but couldn’t understand nothing.

109

Q: Solving Special Function Equations Using Lie Symmetries

The Lie group and representation theory approach to special functions, and how they solve the ODEs arising in physics is absolutely amazing. I've given an example of its power below on Bessel's equation. Kaufman's article describes algebraic methods for dealing with Hermite, Legendre & associate...

ordinary-differential-equations representation-theory special-functions

It's just about differential equations

Novalium Company

6:25 PM

Can we infer that emotions are chemical processes that evolution has carved in the limbic brain for the sake of promoting reproduction where every emotion can be classified as a reward or a punishment? For example, when someone insults you, you feel a "punishment" emotion (sadness, maybe anger) because the insult is putting you onto a lower hierarchical social status which decreases the chances of reproduction...

If you get paid a compliment or something repoductionally beneficial happens, a "rewarding" emotion is released.

@NovaliumCompany Evolution does not place traits "for the sake" of anything anywhere.

Emotions have many roles

It's hard to be quite sure, because the brain doesn't necessarily work simply, but overall emotions are classified along a few axis

There is no guarantee that any specific trait an organism possesses is there because it increases its fitness, it might just be fitness-neutral and widespread due to gene drift, or it might even be harmful to fitness but caused by the same mutation that causes another extremely beneficial trait.

Or it might just be harmful but not harmful enough so that the selection pressure would be high enough to eradicate it

A common model for emotions is the PDA model

Positivity, dominance, arousal

Positivity is whether they are good or bad (reward/punishment system)

Dominance is whether you feel like you are in control or not

Arousal is whether or not you need to take action

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This doesn't answer my question about emotions.

Emotions exist to make us f*ck. Prove me wrong.

6:34 PM

Well only in the sense that people who do not fuck don't reproduce, although remember that genes don't need reproduction to pass down

@NovaliumCompany I'm explaining why such an inference is much harder than telling a just-so story of how certain emotional responses might have increased reproductory success in our ancestors

ie if you don't fuck but you help someone in your family fuck, your genes still pass down

Saying that everything in evolution is related to fucking isn't really a great analysis

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I understand that evolution is a complicated process. A lot of factors play in.

Evo psych is really hard to do well because at the end of the day, evolution is a blind idiot god - fitness is always relative to your competitors (i.e. evolution seeks local fitness maxima, not global ones), and genetics is hopelessly complicated once you step beyond monogenic traits like Mendel's peas

Ultimately, kind of (although not taking into account genetic drift or lack of optimality)

But this is like

"Eating is helpful for reprooduction because dead animals don't reproduce"

True but not really helpful to analyze the behaviour

Also see above about what I said about helping members of your family

Members of your immediate family have about 50% the same genes

6:38 PM

It's called "kin selection"

If a gene makes some people not reproduce, but help other people reproducing, then it will still be selected

Classic example being eusocial insects like bees that form hives where only the queen and a few drones get to reproduce

The worker bee certainly does not work in order to get some bee-on-bee action going!

Also of interest wrt psych evo : there is some idea that if a behaviour is present in over 5% of the population, it was probably selected because it is useful sometimes

But those may also be detrimental because they are also unhelpful other times!

Novalium Company

The core idea of evolution is that if you reproduce, your genes get passed on. Doesn't it that by itself tell us that most of our features have formed because they contribute to passing on the genes?

@NovaliumCompany well, see above

Genetic drift, genetic load, also evolution isn't that great

There are many unhelpful strategies that stick around just by statistics alone

6:43 PM

@NovaliumCompany Not necessarily, see everything we've said above. The idea that most variation within a given population is caused by drift of neutral mutation is called neutral theory of molecular evolution

Also a single gene never has a single function

And the crucial point about things like kin selection is that the gene can be passed on even if a particular carrier does not reproduce, but merely acts in such a way that another carrier gets to reproduce.

A given protein may contribute to some positive trait, but also to some negative ones

ie some features of evolution can be side effects

Maybe consciousness is just a byproduct of better banana seeking methods

Novalium Company

I'm sorry, I'm really tired of school and I can't understand anything. I'll read it tomorrow.

I read the words and they bring no meaning.

I'm tired, will read tommoroah

In conclusion evolution is a lie and God is great

Novalium Company

6:47 PM

If evolution was perfect, it wouldn't have given us the ability to oppose it xD

user image

Another system of emotional axis btw

Dopamine is probably related to the arousal from the PDA model (there are many reasons to believe that)

Novalium Company

I feel like this is just overcomplicating simple stuff

I'm afraid nothing is simple

Sorry

Novalium Company

Don't be afraid, it's good thing.

Otherwise, it would be very boring.

There's also a neat possible axis that is being research which is like

Emotions as it relates to the brain as a neural network

ie part of the emotional spectrum is the confidence in the outcome

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7:01 PM

What happens if we remove emotions? Can the brain still operate? Can I still make decisions?

Depression for bad outcome with high confidence, anxiety for bad outcomes with low confidence

Depends what you mean by emotion

But

There is a condition which affects the decision center of the brain

Novalium Company

If I can't make decisions, wouldn't that infer that every choice I make aims to get the most rewarding chemicals?

Well it is complicated

Abulia is the condition

In severe case, someone with abulia will just sit there and do nothing

Novalium Company

oh.

But for some reason

If asked, they will perform tasks

Although not great

ie if you tell them to eat, they will continue even after there is no food left on the plate

Also some patients, when asked what they are thinking about or what thzy are feeling, just say "nothing"

Novalium Company

7:06 PM

That is surprisingly interesting. If we were to make superintelligence, I suppose we must add some type of reward/punishment system, otherwise it could end up doing nothing

Reinforcement Learning baby

Well an AI doesn't have to be structured like a human brain

Novalium Company

True.

"Jim was suffering from a rare disorder called abulia, which is Greek for “an absence of will”. Patients who suffer from abulia can respond to questions and perform specific tasks if prompted, but they have difficulty spontaneously initiating motivations, emotions, and thoughts. A severely abulic patient seated in a bare room by himself will remain immobile until someone enters the room. If asked what he was thinking or feeling, he’ll reply, “Nothing”…"

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Is abulia the absence of emotions (or reward/punishment chemicals) that results in indecision?

It is complicated

That's just a single case

And as it's from brain trauma usually, multiple things can be wrong

Novalium Company

7:11 PM

The future will be exciting.

LET'S GOOOO

This is what wakes me up in the morning.

I'm happy to know that other people in the world exist that know and can converse about such topics.

School is a pretty locked-up misearble place where people are forced to sit next to each other and talk without having any common interests. It's even harder when you are introverted.

Glad it ends soon.

@Slereah just to follow up with you about my question a few hours ago...Would you mind taking a look at my post and editing it if you wish?

@NovaliumCompany Bad news. This is actually an elaborate computer simulation that you've set up for yourself to simulate conversation with other beings. You've been self-pranked!

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@JMac Wait... so you're saying that all people in existence are as dull as those in my school? Ah.. I'm doomed

@geocalc33 due to work being done in my house, I'm on my phone, not my PC

Hard to look at big equations

fair enough :)

7:19 PM

My advice is to be gooder at math

@Slereah okay I know I suck at math. Glad to know that's apparent :))

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@Slereah and english

Grammar is important but math is importanter

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I couldn't agreerer more

@NovaliumCompany Even worse, I'm saying the dull people in your school are a consequence of your own simulation. Along with me trying to convince you that you're in a simulation.

7:22 PM

at least in my case, because my first language is english and I got a B^+ in my college english classs

#flex

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@JMac Yeah, I agree. We actually could be living in some type of simulation. The Matrix.

Why would I put myself in a simulation tho?

And who is answering my question right now? A computer or myself?

both

@NovaliumCompany You were bored and had no one to talk to, since in reality you're the only person who exists, obviously.

Novalium Company

@geocalc33 that made it even deeper

@JMac I would be looking for answers tho. Why am I the only person in existence...

@NovaliumCompany No idea, I'm part of your simulation. You tell me.

Novalium Company

7:25 PM

I'm getting out.

* throws himself off the window *

JMac sued.

xDDDDD

@NovaliumCompany That's fine. Just don't turn the power off and we'll be okay.

Novalium Company

@JMac I'll come by to see how you're doing.

Don't eat all the cheeseburgers

@NovaliumCompany you can't. Someone generated this virtual reality world for you. They wrote a program s.t. if you indeed did the action of jumping and the action of out the window, the program will return "dead" and proceed to upload your consciousness to a parallel universe

a historical question which I just had: How old are ray-tracing diagrams?

they're one of those tools I take for granted in intro physics (even if I don't use them much) but I actually have no idea about their lineage

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@geocalc33 damn it. so I'm stuck here... great...

7:29 PM

Come to think of it, if I were a simulation anyways, I don't know how much I would care if you turned it off. It's like vacuum collapse, it's the type of thing that is pretty scary for my own existence, but I wouldn't be able to stop it, and presumably I wouldn't notice much either. So like it sucks that I wouldn't exist; but since nothing would be around to experience that suckness, it practically doesn't matter, except to me; but I wouldn't exist anymore.

Novalium Company

true.

death in a nutshell.

@NovaliumCompany Yeah, it's not really death itself that worries me. It's everything leading up to it and following it (for others) that I'd rather avoid.

Novalium Company

@JMac True. But you fear a future you wouldn't exist to experience. That's weird.

Thinking about it, if you worry that the people that love you will miss you and will cry... that's just a projection of your brain, a thought. When it happens, you wouldn't exist to experience it so you're basically fearing nothing.

huh, ray diagrams apparently go back to around the time of Galileo onward: google.com/books/edition/Springer_Handbook_of_Microscopy/…

makes sense given Galileo's use of the telescope, i suppose

this is neat: "Kepler appears to have been the first to draw the correct ray-diagram for image formation, with rays leaving an object point over a wide angular range and gathered to a focus by a lens."

@NovaliumCompany I worry now about what will happen to myself and others in the future. I'm not saying I will be worried when I'm dead, I'm saying that the events around dying does have some worries associated with it, because of those effects on others any myself which I can already think about. I'm not expecting to be worried myself once I'm dead, I'm worried now for any potential consequences on myself and others should I die.

Novalium Company

7:45 PM

@JMac Yeah but you are fearing a future that you wouldn't be here to experience... that seems kinda weird to me. I mean, I guess it's plausible.

To give an extreme example: Suppose a pilot were to die of a heart attack while flying a plane. From their perspective, you could argue that there's no difference between that and dying of a heart attack at home: they're dead either way. But I think they'd be more anxious about the former possibility, since then you have a plane with no pilot.

You can argue about whether that's strictly rational, but it's certainly a natural enough reaction

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@Semiclassical That is true. It just seems kind weird. That we care what happens after we die. Maybe the simulation shuts off... who knows.

@Semiclassical I agree 100%.

@NovaliumCompany I think it might be the difference between a healthy and unhealthy worry. I'm worried about the future after my death because as a person, I know what it is like to experience things and have empathy for the experiences of others. I'm not going to spend all my time worrying about what others will do once I'm dead and how it affects them; but I think it's fair and important to spend some time concerned with the impacts of my own death on others.

I think it comes to us valuing other human beings and their well-being, regardless of whether we're around to see it

Novalium Company

yep

7:50 PM

By the same token, you could argue that to die for the sake of others is meaningless since you're not around to experience the outcome. but people do sacrifice themselves

Novalium Company

True.

It's basically the golden rule. Treat others how you would want to be treated. If I'm dying, I want to minimize the negative impacts of my deaths on everyone else, the same way I would hope other humans act. People can indeed choose to live as if when they die, nothing else matters. Typically this is frowned upon because people recognize that if everyone thought like that, it would be horrible.

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That's true... I really hope to get out of this simulation some day tho.

doesn't the golden rule work perfectly if one's thoughts are golden

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@geocalc33 yeah, the neurons are physically made out of gold atoms.

7:52 PM

haha

Novalium Company

i know, i'm fun

I have been in this chatroom for 2 years. Time flies.

I remember the early days, when that guy Blue was around

Honestly, I've learned so much here.

1 hour later…

9:21 PM

What have you learned most?

@NovaliumCompany

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