The h Bar

@GPhys why was a physicist doing set theory?

user228700

@MAFIA36790 -___- Why have u also started this tamasha? That curve is in the 11th std NCERT textbook.

*discrete time means a specific $*point*$ in time.

I received an honors bachelors of science in mathematics in undergrad, @0celo7

5:01 AM

@Kaumudi Honestly, Indian high school is more advanced than most American universities.

user228700

Anyhoo, @JohnRennie: I'm sorry I keep pinging you! >.< My doubtS have been cleared, so never mind!

which required writing a thesis

@GPhys Yes, I can read

But why set theory?

user116211

@GPhys WoW.

You clearly went for physics in the end

5:02 AM

internal set theory isn't as much set theory as it sounds like

@GPhys Hanging out with a different crowd I see.

you add some axioms but you don't have to touch ZFC

@BalarkaSen Hi

@0celo7 It is often said the same in China, China high schools are more advanced than most US colleges

user116211

Hey @balarka.

5:02 AM

and once you derive the basic results of those axioms you don't have to touch them much

but I found it kind of nonsense

hi, hi

it's mostly about learning to use the formalism after that

the China colleges all in all still produces nearly none nobel winners

it's much more nonstandard analysis than set theory, but that doesn't really justify it over physics

@BalarkaSen I mean, I am getting a Physics PhD to be fair

5:03 AM

@0celo7 not sure about that

user116211

@GPhys is a philosopher.

@Shing This is what I'm so confused about

@Kaumudi honestly knows way more than 99% of American high schoolers. Of that I am sure @BalarkaSen

But I doubt for all her hard work she'll be any better off than the average American...

user116211

Trump is also copying the Indian PM now.

I don't want to hear about Trump

user116211

Trump is wise.

5:05 AM

for sure. not sure that implies Indian high school curriculum is better; some individuals are smart, I guess, yeah

@0celo7 at any rate, the idea of breaking it up into finitely many pieces is standard NSA proof pizzazz

@BalarkaSen That was an exaggeration

My observation is: in China, they use a highly spoon feeding way to educate. the problems with that:
1.) Students "remember" a lot, but understand few.
2.) Students are discouraged to make their own mistakes, such that they have no idea how to trial and error

@GPhys seems wrong

3.) Students are generally much less motivated

5:06 AM

@Shing I have seen 1) a lot in this chat.

@Shing Bullcrap.

Studying for the JEE seems to be a life and death situation.

once they have gotten over JEE, they'll lose motivation

@0celo7 You mean 3.) is nonsense?

@BalarkaSen Why?

No, it's correct. "I want to rank in IIT/JEE" doesn't count

Hmm, looks like it's been a lively night's chatting :-)

5:08 AM

@0celo7 While NSA does justify much of previously hand-wavy use of infinitesimals, its use for giving dramatically unrecognizably different simple proofs for various standard analysis theorems is fairly underrated

well, let's say in my physics department, only about 5% undergrad students "interested" in physics (not saying "love")

user116211

Morning @JohnRennie.

Morning

whereas, eg., any of the questions you'll find on Math.SE always want to know about derivatives or limits or integrals

user116211

@JohnRennie ACM was alive all the night.

5:08 AM

@0celo7 hell if I know.

which it can do perfectly fine with infinitesimals, but the process is recognizably identical to the standard analysis one

@GPhys Can nonstandard analysis do calculus on Banach spaces?

NSA versions of topological properties I also found more intuitive

@MAFIA36790 Maybe he was possessed by an evil spirit. It was Halloween after all :-)

@MAFIA36790 lol

@GPhys example?

5:10 AM

@0celo7 That's different/ I am not familiar with JEE. but there is a essential different between external motivation, and internal motivation

@Kaumudi just as well really. It's been a long time since I looked at a PV curve :-)

in short, internal motivation is much better

@0celo7 a set $E$ is open if $x^*\in E\implies x\in E$ for all near-standard $x$

$x^*$ is the unique standard number that differs from $x$ by an infinitesimal

(provably unique for metric spaces)

it's not actually unique for topological spaces, but this definition still works when you generalize it to all of those points

@BalarkaSen I think they are externally motivated

so it's worth noting where it fails

5:12 AM

external motivation often destory interest. in human language: rewards punish

user228700

@BalarkaSen You are generlazing. Grossly.

$[0,1]$ is not open because the infinitesimal $-\epsilon$ has $-\epsilon^*=0$ which is in $E$ despite $-\epsilon$ not being

user228700

@JohnRennie Ah, OK :-)

and that's a rigorous proof by contradiction in internal set theory

Whats wrong with "[0,1] is not open because its closed"

5:15 AM

I am writing down my opinion and impression. Feel free to disagree with it.

@Rodolvertice because that's false

sets can be open and closed

How?

sets are not doors

@BalarkaSen I think I understand that. The same thing happens here.

(I'm only a highschool student, sorry for my ignorance)

5:16 AM

@0celo7 the converse of the open property gives the property for closed

even in medical schools (the elite in general in the eastern asia), students are not motivated.

for compactness you drop the requirement that $x$ be near standard

yah, such is my impression of what happens around this part of the world too

@GPhys If $[0,1]$ were open, $\Bbb R-[0,1]$ would be closed. It's not, take sequences.

user116211

@Rodolvertice $\emptyset$....

5:18 AM

@Rodolvertice (0, 1]

@BalarkaSen That's not clopen.

@BalarkaSen that's sad for those are interested in science. Environment are very important for learning science (e.g. how the copenhagen circles really excel back in history)

user116211

Just check the first property of topological space.

@0celo7 is this supposed to be refuting something?

@GPhys No, I'm just telling you how I would prove it

5:19 AM

oh

@0celo7 I never said it was

So far you've given me some examples of stuff

But I can prove them in standard analysis with the same brevity

Mike Miller

@ACuriousMind arxiv.org/pdf/1610.09836.pdf

the intent was not to give a proof with more brevity in NSA, but rather to illustrate what the definition meant @0celo7

the empty set, to my understanding, is not closed or open, not open and closed simultaneously

Right?

5:21 AM

The empty set is both open and closed.

user116211

^^

@0celo7 the usefulness is in proofs

@GPhys OK, so what's something that NSA does better?

for example, if you want to prove the restriction of a continuous function to a compact set is uniformly continuous

the proof is basically just "obvious"

(since it consists of nothing more than writing down the corresponding NSA definitions of continuous and compact)

It is obvious in all metric spaces by the Lebesgue lemma

5:23 AM

without relying on any lemma at all!

@GPhys Does NSA generalize to other types of spaces besides $\Bbb R$

@GPhys But I can prove it on metric spaces, and in particular $\Bbb R$

That's what's so nice about topology

internal set theory is completely general set of modifications

@GPhys You can prove it by contradiction and not use Lebesgue

I went out of my way in my thesis to prove everything in a way that generalizes to topological spaces

although the generalization to metric spaces is more obvoius

and requires no work at all

the generalization to topological spaces just requires some thought since the standard part function is no longer unique

(so, in particular, no longer a function)

So just send me the thesis and I will give it a read

I'm intrigued

But I have to go to bed now

5:25 AM

other than making proofs like that restriction just completely effortless, the actual interesting stuff is still things like the intermediate value theorem

Well now wait a moment

Don't you have to prove your definition of compactness is equivalent to the standard one?

Stuff like that?

user228700

@JohnRennie: Are u familiar w/ the definition of the vapour of a substance?

indeed, as is contained in my thesis

for the finite subcover definition

@GPhys upload it!

this was actually probably the most nontrivial part of the thesis

the proof is completely trivial for a metric space

5:28 AM

So the complement of a closed set can also be a closed set

but proving its equivalent to the topological definition of compactness was nontrivial in one direction

If you're not going to upload it, this conversation was a waste

@0celo7 en.wikipedia.org/wiki/…

user228700

Ah, never mind :|

note that's not the internal set theory formalism, but a different one that can make the same arguments

in IST you don't have to deal with the collection nonsense :P

5:30 AM

that proof is nonsense without background

since you modified ZFC so that the infinitesimals and "infinite" numbers literally exist in R

I'm out

@0celo7 it's kind of amazing when you get the background though

you literally just list the points and pick the correct one

@Kaumudi yes ...

user228700

Oh, um, I was just wondering what it meant, really. It says below its critical temperature and I didn't know what that was supposed to mean. I guess it just means that the vapours can be liquefied without decreasing temperature, yeah?

user228700

5:43 AM

BTW, are u sure u wouldn't be able to make any sense of P-V diagrams? It turns out that I have one small question...(?)

user228700

Aah, one definition is just pointing to another, which is pointed to another, which is pointing to the original definition!

user228700

Eg: Saturated vapor is defined as vapour whose temperature and pressure are such that any compression of its volume at constant temperature causes it to condense to liquid at a rate sufficient to maintain a constant pressure.

user228700

This is illustrated in the P-V diagram that I uploaded before...

user228700

And I don't understand what is happening >.< I think I'm gonna have a stroke any time now, at this rate.

6:00 AM

@Kaumudi Sorry for the slow response, I got distracted reading the chat log.

Vapour just means the gas phase as far as I'm aware.

I'm fundamentally confused about how electricity works.

Does anyone have a go-to source or reference on it?

@Rodolvertice Ohms law is pretty much all there is to it. What's confusing you?

user228700

@JohnRennie OK. Thanks anyway :-)

Well, Im trying to understand what exactly a 1 ohm resistor does. How can I know how much energy is lost in the form of heat given a resistor ohm value

@Rodolvertice The power dissipated in a resistance R when a current I passes through it is P = I^2R.

You can rearrange this in various ways by noting that the voltage drop across the resistor is related to the resistance by V = IR.

Using this we can write also the power dissipated as P = IV and P = V^2/R

6:16 AM

Isn't P = IV a measure of how much power is going through a wire?

No, power doesn't flow. Current flows, and the power is the amount of work the current does.

user116211

@Rodolvertice It's the amount of energy dissipated through the resistance per unit time in this context.

Oh, ok. So If I know the amps and volts, then I know how much power is being dissipated, in watts?

user116211

yes.

@Rodolvertice If you have some voltage source with a voltage V, and that source is producing a current I, then you must have a load of resistance R = V/I connected. The equation P=IV is telling you how much power is being dissipated in that load.

6:23 AM

5 volts at 3 amps would lose 15 watts every second? So whats left?

I need to do more reading on this, I'm wasting your time with basic questions, sorry.

@Rodolvertice Watts are joules per second so you wouldn't say 15 watts per second, just 15 watts.

Oh ok. I guess I am confused on how a circuit can lose joules of energy and yet the same amps and volts arrive at the other end.

Is it just a result of the volts and amps doing work?

Or is my assumption false

user116211

Potential drops.

Suppose you're pumping water through some pipework. The current is like the flow rate of the water, and the voltage is like the pressure of the water.

Christia Hall

Holy cow, they let me in! Hello everyone. I'm very excited to have found this.

6:37 AM

The power dissipated is the work the water does while it's being pumped.

Hi Christia

What casual physics research do you dabble in?

So If I insert a water turbine (work) in the system, the pressure and flow rate remain unchanged?

Wouldnt I be able to insert an infinite amount of turbines, if they dont affect the pressure and flow?

or does the pump need to pump harder (what would that mean in electricity terms?)

Christia Hall

Well, my highest level of math is only trigonometry and my technical knowledge of physics is really low, but nevertheless, I have an undying interest in it. I can't be more specific than that until I learn more terminology, etc.

@Rodolvertice If you insert a turbine then you need more pressure to keep the same flow rate. Just like in an electric circuit if you insert a resistance you need a higher voltage to keep the same current.

Alternatively if you keep the water pressure/voltage constant then when you insert a turbine/resistor the flow rate/current will decrease.

So, resistors do not affect voltage, only amps?

If the voltage is held constant, I mean

You're running into a common source of confusion for beginners.

When you talk about a voltage something must be producing that voltage

If I have a 12V car battery then it produces a voltage of 12V and that voltage is fixed. So when I connect different resistances I get different currents.

It is possible to get power sources that produce a constant current though these are more complicated than a simple battery.

And if you keep a constant current then increasing the resistance increases the voltage that your constant current source has to produce.

Christia Hall

6:46 AM

Makes sense.

Would an RTG produce constant voltage

(Ignoring isotope decay)

RTGs are complicated beasts. They work by producing a temperature difference, and that temperature difference creates a voltage using a phenomenon called the Seebeck effect.

They normally include lots of complicated electronics to control exactly how they work.

I'd guess most RTGs are designed to produce a constant voltage, but I'm not sure i'd say that's a fundamental property but rather a result of the way they have been designed.

If you're struggling to understand the basics of electricity I'd steer well clear of RTGs for now! :-)

Q: Rendering of the double surface integral, Tex

I'm a game developer working on a sci fi game, and I only wanted to be physically correct, mostly because I am interested in this, but also because I want those who play my game to be exposed to correct concepts :P

Physics Meta

0

It has recently come to my attention that the double surface intregral, namely \oiint, does not work for this site. How can we fix this? Example: How to infer what integrals and derivatives signify and when to take them?

feature-request mathjax tex

I'm pretty much hoping to abstract this to a point where its easily managable, but still correct. Could I assume a constant voltage, and work from there?

6:54 AM

If you want to introduce an RTG into your game then you should probably treat it as a constant voltage source.

Thank you for all your help, by the way.

If its a constant voltage source, then could I model the gradual decay as a drop in amperage?

You're most welcome. Most of us here enjoy chatting about physics :-)

user116211

We should ban physics here.

@Rodolvertice RTGs will have lots of complicated electronics to keep the voltage constant. I don't know exactly how they deal with the decay, but I'd guess they have a current limiter i.e. they have a maximum current they can supply. That limit will fall as the radioactive source decays.

user116211

@PhysicsMeta 2 hrs earlier? WHY SO LATE ._.

6:57 AM

But be cautious about treating the RTG as a simple device.

Don't worry, I'm not making a simulation for NASA. Just a game. ^.^

I'm willing to accept approximations

Is decay of the source a critical part of the game? If not I'd just treat the RTG as a constant voltage source.

Well, yeah, sort of. These RTGs are arcadified versions of the real ones, accepting any radioactive fuel source (pure only, not mixes), and should create different amounts of power and last different durations based on halflives and decay chains of the isotope.

Ah, OK.

Im probably going to treat it as a constant voltage, and just vary the amperage.

user116211

7:01 AM

@Jolenealaska?

user116211

Why external mod here?

user116211

What happened?

user116211

stares with horror...

I am not here as a mod. I never go into any chat room but my own as a mod.

Someone flagged us for discussing physics. Apparently we're only allowed to discuss video games and the German language :-)

7:03 AM

XD

user116211

You people are Grim Reapers. Must be ArtofCode in the conspiracy.

user116211

0celot can't flag now ;/

@MAFIA36790 Moderators don't wear a black cloak and have a raven on their shoulder. Well, not all of them :-)

Do electric motors function identical to a resistor, aside from the fact that they spin an axle instead of producing heat?

@Rodolvertice Ah, I'm afraid that's a whole new world of pain :-)

7:05 AM

Ignoring all the circuitry that modulates the pulses and all that

Electric motors have a resistance that changes depending on how much work the motor is doing.

Oh gosh

Hold on, that makes sensd

sense*

user116211

Well, Master @loong comes here daily; but I'm noticing two new mods here. Coincidence?

So pretty much if it does more work it 'spends more watts'

An ideal motor, i.e. no friction, would have an infinite resistance if it wasn't doing any work. Then as you start loading up the motor it draws more and more current.

7:07 AM

is it linearly proportional? (in an ideal motor)

In effect if the motor is producing a power P then the current it draws is given by P=IV.

Ok, same formula, thats cool.

So if you hold the voltage fixed then yes the current the motor draws is proportional to the power it is producing.

I have an interest in physics, my dad graduated from Caltech in physics, and he passed the interest on to me. I visit the main site upon occasion. I have popped in here a few times with a physics question in mind, but every time I do, I am immediately viewed with suspicion.

So, i could theoretically treat anything that uses electricity as a variable resistor

user116211

7:08 AM

@Jolenealaska WoW!!

@Jolenealaska how exactly were you viewed with suspicion?

Look at it this way: your voltage source is producing a power VI, and that power must be going somewhere. With a simple resistance the power ends up as heat. With a motor the power ends up as the work the motor does.

user116211

@Shing He is a mod.

@MAFIA36790 a mod?

@Shing it's the black cloak and the raven on the shoulder :-)

7:09 AM

It's not easy being blue.

Ok, so the RTG turns the heat to electricity, and everything else eventually turns it back into heat or work somehow.

Thanks for all the clarification, I understand much better now.

@Rodolvertice Basically yes. Energy is conserved so it has to go somewhere, and it goes into either heat or work.

All of this assumes that everything operates at equal voltage. What does a transformer do, then, to change voltage?

user116211

@Shing they are Sith Lords who like to use The Force to banish guys like poor Voldefield.

user116211

@JohnRennie yes.

7:12 AM

@Rodolvertice Are you asking exactly how a transformer works i.e. how does it change the voltage. Because that starts getting complicated.

user116211

@Rodolvertice, I will advise you to read a good book first; then if you have queries, ask. Otherwise this is going to be a lengthy discussion.

I don't need it for the game, I just got curious. I will google it.

Oh, any recommendation for a book?

user116211

@Rodolvertice Take Purcell.

the black cloak & raven thing and the sith lords makes me more confused. analoy for a self-righteous dude?

user116211

@Rodolvertice I don't remember if it covered transformers; anyways, there is also an elaborate discussion on transformers in Feynman lectures Vol2; but I'll not recommend this as it will be a show-off to recommend Feynman to a beginner (learnt a lesson earlier).

7:17 AM

@MAFIA36790 lol just ignore that kind of comments.

Will read. Thank you all for your time! Good night.

Q: How to infer what integrals and derivatives signify and when to take them?

oh damn

I think I get it now

"the one who we shall not speak of"?

user116211

@Shing yes.

Qmechanic

2

So I have very little background in physics since I'm a mathematical sciences major, but upon being exposed to some physics I've had some difficulties in understanding how to infer the derivatives and integrals (and specifically, why are they used and when), because I assume that in physics they'...

education mathematics differentiation integration unit-conversion

Should this be put on hold? E.g. as too broad?

user116211

Why? Because it is too broad?

7:38 AM

I am trying to describe a particular phenomenon. Imagine you have a clear basketball sized hollow ball, and another ball the size of a softball inside of that one. Magnets keep the inner ball centered. There are bullseyes on both balls that line up when the whole thing is at rest. Somebody comes along and jiggles the whole contraption and then suddenly holds the outer ball still...

The inner ball moves towards its natural position, but it takes a while to get there and be still.

What word describes that state of unrest?

Danu

@ACuriousMind arxiv.org/abs/1610.09836

I want some help from mathematicians here.

Does e^-dt have any meaning?

If it does, how do I differentiate it?

7:53 AM

@Jolenealaska We'd probably say that it a damped oscillation. The inner ball has an equilbrium position (at the centre of the bigger ball) and if you displace it from that position then let go it will oscillate around and gradually settle back to it's equilibrium position.

This is pretty common in physics. For example if you displace a pendulum then let go it will swing around then gradually settle back to hanging straight down.

@JohnRennie Greetings, Sir :)

@JohnRennie That works for my purpose. Thanks!

@SwapnilDas Morning. Are you asking how to differentiate $y = e^{-dt}$ ?

Oh yeah. I asked this in the channel sometime ago.

@SwapnilDas d is just some dimensional constant

in dt

7:57 AM

@Shing is it the second d?

I think a lot of things are missing in the problem...

is c also a constant?

Yeah!

d also a constant?

v is unlikely to be infinitely large.

One side yes, but it looks like the differential

It must be the constant d. Thanks @shing

no problem. but the question looks very strange to me. Did you just make up that question?

8:28 AM

I know the answer

but it loks like it is a homework problem

what will you give me in return for the solution

Tip of the day: Stupid questions DO EXISTS, and they are actually a big deal
Too many stupid questions can cause a person to question permaban you thus you can NEVER be able to ask them questions anymore for the rest of your life

Therefore, question ban does not just apply to SE. What's more:

Question ban in real life is permanent, as long the person still remember their past encounters with you, thus you can never appeal for the ban

How can you have "too many stupid questions" though when stupid questions don't exist

stupid questions don't exists in an objective form

but specific to a person and the community involved

if a question end up causing visible emotional disturbance when they are answering it, then it is highly likely you are screwed

Ok

I agree that there are stupid quesitons

but at the same time I agree when instructors lie to their students and tell them there are is no such thing

In practice , in an education environemnt, it is very hard to hit stupid questions, thus most don't need to worry

8:40 AM

What's the stupidest question you've been asked?\

Also emotional disturbance is not straightforward: A person can look very frustrated, but he/she actually enjoys it because it is a good question. It takes quite some experience to noticed if they are annoyed

I guess it might be my entanglement nature question, being too wordy and too full of my half baked understanding and such, might have disturbed the professor so much that he question banned me

there's also a possibility on that night having dinner with him and his students, he got the wrong idea of my personality due to some body language I unconsciously or semiconsciously did, which over time lead to his question banning

But what are the details I have no idea yet. I need to check the logs

what body lagnague did you do?

As for you, I believe you don't need to worry about this question banning business. Your personality is not pushy and enforcing enough as I am to make people felt uncomfortable

Mate I asked you a question!

8:48 AM

I said I am not sure about the details yet, I need to check the logs

just joking dude, you said i wasn't pushy so i became pushy

how much did everyone win at the melbourne cup?

Government Bureaucracy sketch

it's not like that, and you seriously do not want to learn this pushiness from me, it can hurt interpersonal relationships over time for people who don't think in the way I do

However, I do have a very good analogy:

When I am asking a question, I am no different from the determination of this woman in this video clip:

►

how come

yeah, it is more or less how it feels

This attitude in science research itself, is a very powerful asset, but using this on people = you are dead