02:00 - 16:0016:00 - 00:00

@JohnRennie What does A level course mean?

In the UK students take exams called GCSEs when they are 16. Some students leave school at that age, but if you decide to stay on you take two years to study for exams called A levels. The A levels are meant to prepare you for starting at university.

@JohnRennie What do people who leave school do?
@JohnRennie What do they study in A levels?

So an A level course would be something children would do from age 16 to age 18. Typically at school, though there are specialist colleges that just do the A level courses.
@Sid work in MacDonalds probably.
@Sid Typically you do three or four A levels. I did Maths, Physics, Chemistry and Biology.
There are lots of A level courses covering all areas, not just sciences. There's probably a Wikipedia article on them.

@JohnRennie Wait, is that just extended high school you are talking about?

4:09 PM
The A Level (Advanced Level) is a subject-based qualification conferred as part of the General Certificate of Education, as well as a school leaving qualification offered by the educational bodies in the United Kingdom and the educational authorities of British Crown dependencies to students completing secondary or pre-university education. A number of countries, including Singapore, Kenya, Mauritius and Zimbabwe have developed qualifications with the same name as and a similar format to the British A Levels. Obtaining A Level or equivalent qualifications is generally required for university entrance...

What do they teach in A levels?

Anonymous
@Sid A levels is/are the British equivalent of classes 11 and 12.

@Sid we don't have high schools in the UK.

@Blue Oh. It just sounds fanciful

Primary school takes you up to age 11 and secondary school takes you up to age 18. Then you go on to university.

Anonymous
4:11 PM
Even here, the students who study in international schools take the A level tests instead of the Indian board examinations.

some even take the CIE or IB here

Anonymous
@PrathyushPoduval Yeah, that too

Anonymous
Depends on the school

Some UK schools do the International Baccalaureate
But A levels are the most common qualification
@Sid I've just looked on the web site of my old school, and these are the A levels they offer

What is Further Mathematics?

4:16 PM
They didn't offer a Computing A level in my day, but then they didn't have computers in my day :-)

@JohnRennie didn't you say you were a computer nerd back in the day?
how could you be that without any computers in those days? :P

Anonymous

@PrathyushPoduval for most of my undergraduate years I worked on mainframe computers
An IBM 370 then an IBM 3081

Punch cards?

the ones which took the space of half a room?

4:19 PM
The IBM System/370 (S/370) was a model range of IBM mainframe computers announced on June 30, 1970 as the successors to the System/360 family. The series mostly maintained backward compatibility with the S/360, allowing an easy migration path for customers; this, plus improved performance, were the dominant themes of the product announcement. Improvements over the S/360 first released in the S/370 model range included: the block multiplexor channels introduced on the most recent high end System/360 systems; standard dual-processor capability; "monolithic main memory" on the model 145, based on...

Anonymous
Must be nostalgic for you...going through your school's website :^)

@0ßelö7 yes, at first I used punch cards. They introduced VT100 terminals in my second year.

Anonymous
I wonder...do you still have contact with any of your school friends?

@JohnRennie based on my experience with fortran I imagine the suicide rate among STEM students was higher then

@Blue I've lost touch with all my school friends, though I still keep in touch with friends from university.

4:22 PM
@JohnRennie It must be a nice feeling, having worked with punch cards back in the day and now you're seeing small laptops with very high perfomance :-)

Anonymous
@JohnRennie I sort of expected that O:)

@0ßelö7 it's hard for students now to appreciate what it was like back then. Computers were so new and so amazing that even FORTRAN seemed amazing.

@JohnRennie actually I bet 90% of my issues come from the fact that I know Java/Matlab and they are 100% more logical
like you HAVE to declare variables at the beginning of the program
so if you want to read in some integer n you can't make an array with that dimension
you have to make a subroutine that does everything you need with that array

The modern version of FORTRAN is very different to the version used in the seventies. Back then you didn't have to declare variables at all.
When the compiler encountered a new variable name it just automatically declared it.

like python

4:25 PM
@JohnRennie How is it supposed to know that killMe is an integer array with length n, where n is a variable from before

So if you mistyped a variable the compiler didn't warn you - it just automatically declared it and initialised it to zero. The bugs that caused!!!

Is your doubt why in dimensional regularization we switch to $d-\epsilon$ and set $d=4$? The value for $d$ is just the dimension of spacetime. The $\epsilon$ has to do with isolating the divergence. — user1620696 33 mins ago

@0ßelö7 I can't remember how you declare arrays in FORTRAN IV ...

@JohnRennie well if it's like Fortran 90 you have to do it AT THE BEGINNING OF THE PROGRAM
ARGH

[FORTRAN IV](Language reference)
That's odd, why isn't that being formatted as a link?

Anonymous
4:30 PM
@0ßelö7 Since when have Portuguese people started talking about "doubts"?

@Blue Portugese?

he's in the Portuguese SO

Anonymous
@ACuriousMind Most probably... pt.stackoverflow.com/users/1917/leonardo

Anonymous
"Portuguese (português or, in full, língua portuguesa) is a western Romance language and the sole official language of Portugal, Brazil, Cape Verde, Guinea-Bissau, Mozambique, Angola, and São Tomé and Príncipe.["

Anonymous
Ah, maybe from those other countries too ^

4:33 PM
Or maybe just an Indian who knows Portuguese
you didn't see that coming, did you?

Since Brazil has far more inhabitants, concluding that a Portugese speaker is Portugese may be premature

Anonymous
I mentioned that :D

Anonymous
1 min ago, by Blue
Ah, maybe from those other countries too ^

Anonymous
@BalarkaSen That's ill-logical XD

Anonymous
But possible

4:34 PM
No it's not ill-logical, just improbable.

@Blue Wasn't Goa colonised by the Portugese?

@0ßelö7 looooooool
Point, John Rennie.

Anonymous
HaHaHa

The Portuguese of Goa refers to the Portuguese language spoken in Goa, India. == Background == The history of the Portuguese dialect began in Goa due to Portuguese rule in the region that lasted for over 450 years. During the existence of the Portuguese State of India, Portuguese was used extensively, in government or in the education system. In addition to the official government media, it was also used by [[missionaries in their missions, although the Portuguese language coexisted with other languages. == After 1961 == However, after the end of Portuguese rule in Goa, brought about by an Indian...

Anonymous
Or, maybe, it was a side-effect of colonizing Goa....the Portugese guys had to go back with "doubt"

Anonymous
4:38 PM
:'D

wao, mind blowing and cutting edge explanation of the phenomenon
such linguist much historical
wow

It's not often I find myself teaching Indian history to Indians :-)

Anonymous
@JohnRennie I'm sure most of us knew about the Portuguese colonization of Goa. It was just improbable that the OP is from Goa and also knows Portuguese. I do have some friends in Goa and I'm pretty sure that their families do not know the Portuguese language.

Improbable?
This whole situation is strange
@Blue maybe it's a shared account

Anonymous
4:54 PM
@0ßelö7 It's been a long time since the Portuguese rule ended

Anonymous
There has not been much considerable attempts at revival of the language

@Blue Brits haven't rule us for 250 years and we still speak their lingo

Anonymous
Perhaps the older generation knows a bit of Portuguese

@Blue In the grand scheme of things, 55 years don't seem very long. The point seems to be more that the language didn't spread through the population to begin with

Anonymous
@ACuriousMind Right. Goa is a small place

4:56 PM
@Blue Britain was colonised by the Basques, then the Celts, then the Romans, then the Germans, then the Vikings, then the French. Makes you wonder just what the adjective British actually means :-)

@JohnRennie At least the Vikings and the French are responsible for much of the vocabulary

@ACuriousMind are you a viking?

@ACuriousMind I'll resist the urge to post a list of words with Anglo-Saxon origins on the grounds I don't want to be suspended :-)

@JohnRennie Heh.

I don't get it

4:58 PM
@0ßelö7 Maybe?

Oh, all of the usual curse words are Anglo-Saxon?

aren't german dudes goth, not vikings?

ACM is indeed goth

@0ßelö7 when the Normans invaded all the posh people switched to speaking French, while the serfs carried on speaking old English. Inevitably a lot of the Old English words that survived covered the more, erm, basic aspects of life :-)

@JohnRennie hmm.

5:03 PM
@0ßelö7 for example the Old English word scītan just meant to defecate. It was only after the Norman invasion that it ended up as a swear word.
> In the 16th century an anonymous monk was reading through the monastery copy of De Officiis (a guide to moral conduct) when he felt compelled to express his anger at his abbot. O d fuckin Abbot, he scrawled in the margin of the text.
Wow, monks spoke hip-hop slang in the 16th century.

lool

@JohnRennie could you be any older?

There isn't that much difference between 56 and infinity really ...

has seizure
@Slereah well, looks like I bought this for nothing

Oh no
what book is this

5:15 PM
Wave equation on a curved spacetime by friedlander
It's supposed to be a prequel to HE

Damn prequels
Can't we just get fresh original GR plots

@Slereah what's the first thing to check in the references

Steenrod?

Not there
Incredible

Well it's not really topology related I guess

5:19 PM
Bottom of the page

Well it's not wrong
And you can prove that without Steenrod

@Blue "You can't make better things till you break things." Oddly enough Stack Overflow was built to differ from certain feature of the USENET and forum model. One of those thing was exactly the fact that in the then existing formats the same questions were asked and answered over and over again, making it hard to run down either all of the answers or a canonical answer.

Oh well, if we've finished talking about swearing I'm going to get back to my book (about a girl with sentient hair).

@Slereah "push zeros off to infinity" isn't a proof :P

IS IT NOT
Although that's the easy part
The hard part is showing that all vector fields have at most countably many zeros
Wait no
What was it
I forget
something like that

Anonymous
5:26 PM
@dmckee I don't disagree with that. I meant something else. I was saying that unless SE experiments with the site features, they'll never know what suits the site members best. Being stagnant is not a good sign. If something goes wrong with the experiment they can always go back.

Anonymous
I know it's not easy to make changes. Neither is it easy to avoid problems due to changes. But it can be worth a try.

@Slereah that you can have a vector field with isolated zeros I think

yeah something like that
and then
Woosh
the zeros to infinity
but proving the isolated zeros was the hard part IIRC

@BalarkaSen can I request a proof

of what

5:31 PM
proof of citizenship

@BalarkaSen I would really appreciate a reasonably detailed proof that a noncompact manifold admits a nonzero smooth vector field

pick a random vector field and bimbadabim the zeroes to infinity
$\blacksquare$

To be fair I've seen a loooot of bimbabadimming in things of read. Think @BalarkaSen might be onto something.

@BalarkaSen no seriously, I'm curious

5:36 PM
Let me think for a bit

@0ßelö7 There's a proper embedding of $[0, \infty)$ starting at a given point in any noncompact manifold, right?

@BalarkaSen Sure. Give it a Riemannian metric and then you can have a ray.

Don't you need a complete Riemannian metric
The ray might bimbadabim in finite time

@BalarkaSen any manifold has a compete metric

5:47 PM
Ahhh yes ok
So what I am thinking is, say $X$ is a vector field on non-compact $M$ with a single isolated zero $p$.
Pick a proper embedding $f : [0, \infty) \to M$ with $f(0) = p$
Take charts $U_i$ along $f$ with $p \in U_0$.

Are you trying to isotope the zero to infinity

"Push $p$ along $f$" in the following sense; let $i_1$ be the diffeomorphism isotopic to identity of $M$ which takes $p_0 := p$ to some $p_1 \in U_0 \cap U_1$ and leaves $M$ invariant outside a ball in $U_0$... fuck
yes that's what I am trying to do
Fixed.

@ACuriousMind Just like we can't conclude that an English speaker is English. =D
@ACuriousMind Oh I make this mistake often too. It is spelled Portuguese. =D

@BalarkaSen That seems reasonable. Why the Anglo Saxon word for fornication?
@user685252 no. What does that have to do with anything?

loool
@0ßelö7 I am a bit worried, though, because you have to take a limit of $i_1, i_2 \circ i_1, \cdots$.
Well, no, the limit of the vector field $X$ pulled back by those.
So you have to do this carefully so the limit actually exists.

5:55 PM
@BalarkaSen but the advantage is that you only change stuff inside of those neighborhoods

Right (which we can, by a lemma in Milnor's little book)

i know the lemma well

Yup, I just wanted to write that to be completely rigorous up to this point

Ok, but first. Why should there exist such an initial X?

Right, so I think if you have finitely many zeroes you can merge them to a single zero.

5:57 PM
I feel like that should violate some conservation of zeros theorem...

Nah, just the index of the merged zero would be huge
Think about merging two index 1 points to a index 2 point

Ok
So you want to keep one fixed and move all the others to it?

This should not be the hard part
@0ßelö7 Yeah along a path

How does that work. Your isotopy could move it when you get close

Hm, OK, that's a good point. Let's think

6:00 PM
(I'm in class right now)

Ok, fine, I'll do the thinking :P
So we have the following local problem; take a vector field $X$ on $\Bbb R^n$ with zeroes $p, q \in B_\varepsilon(0)$ inside a ball of radius $\varepsilon$ very small.
I am here to chew bubblegum and homotope $X$ to $Y$ so that $Y$ has a single zero.
And I am all out of bubblegum
Ah, locally a vector field is a function $\Bbb R^n \to \Bbb R^n$. This should be a stupid ass problem.

Too bad this chat only has smart asses :P

That jab hurts
Ok, hm but how do I work this

@ACuriousMind don't worry I'm usually lurkin' keepin' the average IQ down.

6:04 PM
Ok, look at $X + vt$ for some vector $v \in \Bbb R^n$.
I think for an appropriate choice of $t$ those two $p, q$'s should merge.

This is scaring me. Why can't you just push them all off to infinity individually

You probably can but I want to minimize le work

How do people measure the energy that they are supplying to a reaction? Like if someone says 380 kJ of heat was supplied for $A-> B$ How did he measure that 380 kJ?

It's probably easier to construct a vector field with finitely many zeros first and then push each to infinity
How to do the initial construction is what I'm primarily concerned about

Yeah me too.

6:09 PM
Math overflow says to just do it
Those people are either kidding themselves or just too smart

I did not know Shia Lebouf was in MO

@BalarkaSen who do you think Mariano is

but damn son
@0ßelö7 lolol

@Abcd A very simple way would be using $Q=mc\Delta T$
where $Q$ is the energy, m mass, c specific heat capacity and $\Delta T$ change in temp

But seriously, the kind of flippant answers people get on MO is unlike anything I've experienced from real life mathematicians

6:11 PM
@CooperCape where c is specific heat capacity of what? the container?

whatever's being heated
however that's only applicable to a few situations I should imagine

They probably know their shit

@CooperCape But there are so many reactants in our reaction .

I suppose you could use change in entropy.

I mean I can try to take a transverse section to the zero section in $TM$, but I can do that only upto compact support, which, uh, doesn't tell me anything about the zeroes outside the support
Ah wait

6:12 PM
@CooperCape Haven't studied entropy yet. That's in the next chapter.

On any noncompact manifold $M$ I have a proper smooth function $f : M \to \Bbb R$
That's a partition ze unity construction

To keep on listing ways if it's heated electrically you could use $E=itv$

@CooperCape What if people were supplying light energy? $E= h\nu$?

Do you not have an equation there?

@BalarkaSen si

6:13 PM
Just need to take into account energy loss - depends on the (type of) system of course.

@CooperCape $E= h\nu$ for 3 s? Would have to multiply by 3 right?
does energy supplied even depend on time?

Anonymous
@Abcd What is $E$ in that equation?

$E=h\nu$ describes the energy of each photon

@Blue Energy of photons.

you'd need to know how many photons/second

Anonymous
6:16 PM
^

Anonymous
@Abcd No

Anonymous
It's energy of 1 photon

You can work out photons/second from how many Watts the beam is

yes.

@0ßelö7 I am thinking of gradient $X$ of $f$ in a complete Riemannian metric on $M$.
I am not sure why

6:17 PM
@Abcd Do you have how many Watts the beam is?

@CooperCape What does energy in chemical cases mean? Does it still refer to the transfer of a "number" (I have started thinking of energy as numbers)?

So $g(X, Y) = Y(f)$ for any other field $Y$. If $X$ had infinitely many zeroes, $Y(f) = 0$ would happen infinitely often for any field $Y$.

@CooperCape I am not solving any question.

Well, uh, nothing is stopping that.
I guess I want $f$ to have finitely many critical points.

@Abcd Ahh in that case when heating with a beam one would just find the power of the beam $IV$ and multiply by time for the energy.

6:20 PM
Such a function might not actually exist. Take a surface of infinite genus; I'm pretty sure the topology at infinity bars such a function to exist
Why is this so hard.
I feel like I am overthinking this

Energy is a really horrid concept imo. It feels easy to manipulate mathematically and use but when some says what is it it kinda gets tricky. One sort of definition would be 'the capacity an object has to do work' that is the more energy an object has the more work it is able to do but I haven't really been happy with any definitions presented to me

@CooperCape We have had a discussion on that earlier.

The best way to think about it is energy is not a 'thing'

@CooperCape But even leaves have chemical energy, don't they? What work do they do?
and work is $$\int \vec{F}.d\vec{s}$$
I don't think photosynthesis is "work".

@BalarkaSen that's how I would do a similar construction for compact manifolds

6:24 PM
With chemical it's more how likely (bad way sounds like probability its not) a substance is to undergo a chemical reaction

For a Morse function
@BalarkaSen I will ask the topology people at the topology seminar

@CooperCape but that doesn't fit the definition of energy :(.
Where's displacement?

Yea the point is proper Morse functions on infinite genus surfaces typically should not have finitely many critical points

What's displacement to do with anything?

Because of "topology at infinity"
Handles accumulating at infinity, etc etc

6:26 PM
@CooperCape See the definition of work. It has displacement term.
And energy is the ability to do "work" (f* displacement).

That's a way for describing what is 'done' to an object
Energy is just a horribly defined thing

@BalarkaSen hmm, yeah
@Slereah this book has a nice proof of the existence of convex normal hoods

Anonymous
@Abcd After sugars are produced in photosynthesis, these sugars must be transported to other parts of the plant for use in the plant's metabolism. "Transport"....there's proof that energy denotes capacity to do work. There is lot of indirect stuff going on. That "sugar" is a condensed form of energy, really.

@Blue And leaves provide the force? (Energy = Force* s)
But I had studied that all this transportation stuff relates to concentration of water in plants?

Anonymous
@Abcd No. Not directly at least.

Anonymous
6:31 PM
That's a biology question

Osmosis is veeeerry much entropy related
And entropy has units of Joules/Kelvin

@Blue So you can't say that leaves have chemical energy unless you provide force from them and there's displacement after that.

Or at least bring this up in the math chat

@Abcd For chemical energy, the work it "can do" is e.g. if you enclose the substance in a piston and then trigger an exothermic chemical reaction, the piston gets raised by the pressure of the heated material. That's how engines work.

Anonymous
6:32 PM
@Abcd There is a force being applied. But the "leaves" are not the ones applying it.

@BalarkaSen I don't see why not

Anonymous
I can go into the details, but you better read a bio book for that

@Blue Then why do we say that leaves have chemical energy.

I've thought about it before but never got anything rigorous on paper
People like to throw around triangulations and stuff but that's hardly smooth and I don't know if I trust smoothing on a noncompact manifold.

Anonymous
6:33 PM
@Abcd It does not necessarily mean that they are the ones directly doing the work.

Anonymous
A leaf has many parts

No questions have been asked on philosophy.stackexchange.com regarding Energy. That's strange.

Anonymous
The phloem transports the food.

@Blue I know all that.

Anonymous
@Abcd Then I don't understand your question.

6:35 PM
@Abcd What about them? You can also burn leaves, they're just not a very efficient fuel.

@ACuriousMind what work do leaves do(/can do) if they have chemical energy?
@Blue ^

@0ßelö7 It seems Ted's not here

@Abcd Energy is the potential to do work. For instance, you can make them do work if you burn them as fuel.

23

After years of studying physics I am suddenly struck by the question - What is energy? Wikipedia defines it thus: Energy is often understood as the ability a physical system has to do work on other physical systems. (1) If that is the case, what is work? In physics, work is the amou...

Found it.

@BalarkaSen I can go to the math room you know :P
For a compact fold would one use the transversality theorem?

6:37 PM
@Abcd They carry out photosynthesis which is an endothermic reaction and then transport the products. All energy requiring.

yeah compact is easy
just find a section of TM transverse to the zero section

@0ßelö7 You can?
2 days ago, by 0ßelö7
I never go to the math chat

ROASTED

@ACuriousMind But how is work done when they are being burnt?

@Abcd If you burn them in a piston, it's done by raising the piston. Please read what I write.

6:38 PM
I don't like it, but I can go there. I guess reading comprehension is hard for Vikings.

@0ßelö7 Me no likey letters. Me smash puny beardless people!

Perhaps we need to stray away from setting the definition of work as only applicable to Force$\times$distance.

Anonymous
@Abcd Leaves don't necessarily have to spend all their energy. Some of the condensed energy produced is used to transport the sugars to other parts of the plant. So, there's work involved. If you really want to, you can think of a leaf pumping sugars to other parts of the plant. So, crudely a leaf does work while pumping sugar. But it is much more complicated than that.

@ACuriousMind Oh yes! If I am not wrong, the piston is raised due to two energies: 1) Chemical energy of leaves 2) Heat energy being supplied by the flame.
Please verify this^ . Is my understanding correct?

@Abcd External Energy? The energy given off comes from the exothermic nature of combustion.

6:41 PM
@CooperCape Um...work is literally defined as the force applied integrated over the path the object moves, how would you stray away from that?

@ACuriousMind no smash pls. Does a neck beard count?

@Abcd I don't know what you mean by external energy - once the leaves are ignited, the reaction sustains itself

@ACuriousMind By the word external I just meant "from outside"

I feel like in a definition of energy where types of energy are so variant it would be more plausible to go with a more linguistic approach to 'work'. Perhaps I am incorrect, however.

@Abcd Sure, but there is no energy from outside necessary after you have started the fire

6:43 PM
Lol, I was thinking of fire as "the energy from outside" @ACuriousMind

@CooperCape Energy is certainly more slippery, but work is...just work, $\int F\mathrm{d}s$.

@CooperCape yes, I feel that too.

@0ßelö7 Ugh, no

"Questioning the fundamentals is advanced stuff, that where you start to really learn."

Hi, everybody.

6:50 PM
@Blue Too many philosophical questions in my head...
@ACuriousMind Thank you. I understood your explanation.

@ACuriousMind can you please put a small space between integrand and measure?

7:08 PM
Apparently a flame thrower works well :-)

@ACuriousMind can u just give us the proof

"Energy of the collision must be greater than the activation energy". Is the physical chemist referring to potential energy or chemical energy?
I think he's referring to the conversion of kinetic energy to potential energy.
Which he later tried to explain using the "ball and hill" analogy.
Can anyone explain?
Does this mean that the product has tooo much kinetic energy as energy is always conserved?

7:58 PM
@BalarkaSen did the doubt get resolved?

8:42 PM
Who speaks Portuguese?

Anonymous
@BernardoMeurer Portuguese.

@Blue Sigh

Anonymous
(/◕ヮ◕)/

That had me laughing out loud. I am disappointed in myself.
DISAPPOINTED

Anonymous
Who speaks American? Americans. Who speaks Indian? Indians. Who speaks nonsense? Nonsensians.

Anonymous
8:53 PM
@BalarkaSen I hope you won't disappoint us by not digging up a meme for this situation (^_-)-☆

@BalarkaSen I had to leave class Monday because my professor said "Magnets, how do they work?!" unknowingly and I lost it
I couldn't stop laughing

lels in multi-kek

9:12 PM
In this day and age I simply assume that all the things are a meme. ALL OF THEM!

Memes are the art of the internet age
accept it or be destroyed

0

I believe some old questions would be quickly closed if asked today (e.g., What is sound and how is it produced? in my opinion is too broad and shows too little prior research effort). What should we do? always leave them alone, 5+ years is history; consider voting to close, but only if ther...

@PhysicsMeta Have you been talking to @WorldbuildingMeta?

1 hour later…
10:16 PM

10:28 PM
Why?!

11:02 PM
Somehow this is valid Python

11:15 PM
@BalarkaSen watching

11:38 PM
@BalarkaSen do you think Perelman looks nice?
in my mind you look like an Indian Perelman with a kek t-shirt

02:00 - 16:0016:00 - 00:00