12:29 AM
> Integration inverses differentiation
Trying to resist starting an integral vs. antiderivative debate again...
@NovaliumCompany Basically integration generalizes the concept behind multiplication

@SirCumference oh calm down it’s not that bad ;)
@NovaliumCompany yeah but a way of understanding the integrals is that they’re the opposite of derivatives. The derivatives make really obvious intuitive sense but the integrals take more thought.

Well that'd be antiderivatives...
@JakeRose Yeah I know, it's just a petpeeve of mine. :P Imo it's often necessary to separate the two concepts, especially in cases where the fundamental theorem doesn't apply
That, and the fundamental theorem becomes a lot more intuitive when antiderivatives and integrals are distinguished
@NovaliumCompany This is an excellent explanation on how integrals can be interpreted

12:46 AM
'repeated multiplication' in the sense that area is base times height i.e. area

The entire concept behind integration is that we're adding products. It's just that we're taking the number of products to infinity
Each one differs slightly from the other
So for example, let's say a man is initially moving at 5m/s, and then after 3 seconds he instantly changes to 10m/s and stays that way for 7 more seconds. How far did he travel in those 10 seconds?
To get it in meters, we'd take $3\cdot 5 + 10 \cdot 7$.
If instead he starts changing many times in that interval, we'd end up adding many products
If he is continuously changing, we'd basically be adding infinitely many products
Integration is basically like multiplying one number by another, except we bear in mind that one of the numbers changes while the other does

But you can't multiply those 5 m/s by 3 bananas and get the right answer

@bolbteppa I never understood why integration is so often associated with area. I mean yes it obviously gives you the area, but in elementary school you are not told "multiplication is defined as the area of a rectangle"
It's indeed the area of a rectangle, but it limits the way you can think of its uses

There's a reason integration is literally a subset of measure theory, measure = measurement i.e. area etc
How does this notion of multiplication explain probability and integration over those insane spaces
Or things like integrating that function which is 1 on the rationals and zero on irrationals

I'm giving a basic introduction on the motivation behind the Riemann integral
It's not as precise as more modern definitions, but it's helpful in gaining an intuition on the applications
At the very least it's much more general than "opposite of derivatives"

12:57 AM
Yeah, but why are you multiplying
It's because of area = base times height

Y...yes. But you never think in terms of area when using multiplication in physics
Either way, the Riemann integral is still basically the limit of adding a bunch of products
@bolbteppa You get 15 bananameters per second :P

Integration as opposite of derivatives is good in that $\int \frac{dy}{dx} dx = \int dy = y_2 - y_1$ makes sense i.e. you sum up the changes with respect to $x$ in $y$ as it changes with $x$ which is just the change in $y$ which is basically saying the change of the area composed of one side $dy/dx$ and the other side $dx$ after cancelling out $dx$ will just leave you with the changes in the $dy$ side with all intermediate changes cancelling out $(y_2 - y_1) + (y_3 - y_2) + ... = y_n - y_1$

@bolbteppa Well if we're gonna be precise you don't "cancel" the $dx$. I'd hesitate to rely to much on the classical notation
But yeah it's the sum of changes
Nonetheless it only matters if your integrand is the derivative of another function. Far, far more functions are integrable than antidifferentiable
The explanation in terms of multiplication is still more general

Referring to 'The limit of a sum of products where one term is the value of a function within some subinterval and the other term in the product is the difference of two functions at the endpoints of that subinterval over the subintervals as the subintervals shrink to zero' (Stieltjes) as just a sum of products, you might as well just call it a sum of functions and forget the multiplication

@bolbteppa Well yes you wouldn't be wrong to say that :P But you'd lose the intuition on when it's useful
At any rate my point is that the "opposite of derivatives" explanation technically only holds in extremely specific situations, i.e. when the fundamental theorem is applicable

1:09 AM
It's way way too general to say it's just a limit of a sum of products this is literally the definition of an infinite series the difference is that the terms in an integral are supposed to behave in a very specific way which a general infinite series need not satisfy
So in that sense you're right, because an integral is a limit of a sum of partial sums it is an infinite series and so you can view it as a sum of products but you're using the intuition of infinite series which extends beyond integrals so you're missing the thing that distinguishes an integral from an infinite series by taking this POV

@bolbteppa Yes, I should have been more specific when saying "sum of products". But the concept of "multiplication when one quantity changes with respect to the other" is far more useful when realizing when to apply integrals, compared to "area under the curve"
It's a looser and less precise explanation, but it's much more intuitive and nonetheless very general
Someone more awake than me should be capable of explaining my idea more accurately and still keeping that intuitive concept
@bolbteppa The most important thing imo is separating between the notions of integration and antidifferentiation. You give the intuitive explanation behind the FTC, but most people dismiss that and simply consider the two to be the exact same thing, aside from one having a constant of integration (which...should be called a constant of antidifferentiation)
This is how you get terminology like "indefinite integral"
Terminology in analysis is a complete mess tbh

1:27 AM
Yeah I get it but isn't there more to it than just being an infinite series - the notion of area, approximating areas of curved regions using non-curved approximations which become accurate only in the limit to infinity, distinguishing it from arbitrary infinite series. I don't really see how it's a useful way to view integration, e.g. you're basically multiplying one thing with another thing which actually goes to zero in the limit :p what's the spark to it vs. area

@bolbteppa It's just that if I was your elementary school teacher and the only thing I told you about multiplication is that "multiplying 3 with 5 gives you the area of a 3x5 rectangle", you wouldn't intuitively realize its uses in physics
You'd dismiss it as something primarily used by geometers
Even derivative is given a more intuitive explanation. The first time you learn about it, it's in terms of rates of change, rather than strictly the slope of a tangent line
I'm obviously not saying the area definition is wrong, just that it isn't sufficient for the sake of learning practical calculus

1:42 AM
Your example is not just multiplying apples and oranges though, you're multiplying things with the right units that let you use an 'area' to end up with an interpretation of one side of that area. If velocity is change of position per unit time then summing up change of position with respect to time times time leaves you with summing up changes of position, so that all intermediate differences cancel out leaving you with the overall change.
The sum of products idea is like summing areas and without specifying that one of the terms in the product has units that the other term has in it's 'denominator' so that the units 'cancel out' you'd be led even further away from physics :p
I agree it's not obvious and is unintuitive until you get it

@bolbteppa Your integrand doesn't need to be a quotient or derivative though

This is why people didn't discover calculus properly for about 2000 years, simple things like this

@bolbteppa I'm not really sure I understand what you're saying by "use an 'area' to end up with an interpretation of one side of that area"

"let's say a man is initially moving at 5m/s, and then after 3 seconds he instantly changes to 10m/s and stays that way for 7 more seconds. How far did he travel in those 10 seconds" in this example you're summing up the velocity times 'change in time' i.e. rate (= change in position over change in time i.e. a quotient) times time, leaving change in position, or rather change in position times the identity still giving you an area.

Again, I don't really understand what you mean by "change in position times the identity still giving you an area."
Oh wait, I think I get what you're saying

1:51 AM
Like you're cancelling the units, but formally that side of the area is still there, the units were never there to begin with mathematically

Wait, now I'm not sure I'm following. Is the problem that I specifically chose a case where FTC holds?
Or is it that my example was physical, so it used units?

In physics the idea behind this example is going to hold since velocity is always the derivative of position w.r.t. time i.e. we're always integrating a derivative...

Welp I'll be back in a few hours when I finished my essay.

I'm 95% sure that things like divergent series completely destroy the notion that integration is like a sum of products as well btw
e.g. the whole summing $1 - 1 + 1 - 1 + ...$ to any number

3 hours later…
4:51 AM
there's one odd way to think about integration when it comes to interpreting it as a sum. suppose for a second that $x$ is in meters, you could think of distance as an infinite number $n$ of "points" in space, $n\to\infty$, then in this case $f(x)\Delta x$ would mean that you now have $n*f(x)$. now, as usual, you think of $\Delta x$ as vanishing to $0$, and thenthink $f(x)dx[\text{meters}]$ as just one point times $f(x)$, and so summing all these would get you the sum of all $f(x)$s
in meters that is, so if the integral equals $5.36$, you consider it as the number of points in $5.36$ meters.
this is how I actually like to think about flux, work etc
"as just one point times $f(x)$", nearly that is, approximation.
"number of points in $5.36$ meters" infinite of course, but it's a way of "summing" infinity.
if you think of it this way, it kind of also makes sense that the average of $f(x)$ is $\frac{1}{b-a}\int_a^b f(x)dx$, you're diving by the "number of points" in $b-a$ meters, which corresponds to the number of $f(x)$s. again, infinite of course, but we're just manipulating infinities using names.

2 hours later…
6:43 AM
mornink

7:33 AM
Look at all those dumb ass problems
now to fill them with the worst possible formalisms

8:24 AM
@Slereah ew, your URLs have spaces in them!

As god intended!
All the site is programmed by hand
Handcrafted!

That doesn't mean you can't encode your URLs :P
I mean, it means one cannot copy-paste your URLs: samuel-lereah.com/db/problemdb/Static%20point%20charge
huh
Firefox automatically did that encoding for me!
It would appear browser developers have already programmed around people like you :P
Hm, maybe you have encoded it and Firefox is just decoding the displayed URL nowadays. I retract everything I said...

I think I did yeah
Lemme check the code
<a href="/db/problemdb/<?= $value['title']? >"><?php echo$value['title'];
?></a>
Nope!
So anyway
why is the basic epsilon in Latex the worst one?
Nobody likes using $\epsilon$
Everyone wants $\varepsilon$

8:50 AM
Some random thought:
Give me an example of a statement that does not use any of the following notions:
containment, hierarchy, category, describability, predictability, transcendence, limit, existence, relation, narrative, mysticism, logic

@Slereah Probably because Knuth liked it better

Damn that man
You could make an argument for $\phi$ versus $\varphi$
And everyone prefers $\pi$ to $\varpi$

I mean, he wrote TeX in his own homebrew literate variant of Pascal. That he's a bit eccentric is well-established :P

But varepsilon is objectively better
Also this is 2019
Computers have enough memory
You can add \Alpha and \Beta and such

You can't add that to TeX because it's finished, nor to LaTeX because the chance of breaking existing sources who also define these is rather high

8:55 AM
Not with that attitude certainly

Maybe LaTeX3 will do it, if they ever release

1 hour later…
10:14 AM
hm
What's another cute little physics problem
Electric conduction, perhaps

11:05 AM
Knowing all the angles of a triangle, you cannot know the sides, only their ratios?

11:15 AM
Well yes
Since you can expand the size of a triangle while keeping its angles
At least in flat space
It's actually equivalent to Euclid's fifth axiom
"There exists a pair of similar, but not congruent, triangles."

However, that's seventh grade math. You should have learned that in school.

They teach conformal field theory in seventh grade? :-)

11:31 AM
@Loong This is exactly the things they don't teach. I mean, I figured it out on my own since I am reading a math book. Our school builds buildings on loose foundations.
@skullpetrol We've learned about the similarity topic, but as I've said, Bulgarian school system is bad
I basically go to school to finish school. Most of my studies take place in home teacher - me.

@JohnRennie I mean they teach homothetic transformations, certainly
it's not rocket science
small shape becomes big shape

11:48 AM
nor brain surgery :-)

12:31 PM
Oh great. JD is backing up safesphere physics.stackexchange.com/questions/492477/… I suppose I could just delete all my comments in that thread...

@PM2Ring Just flag cases where comment discussions spin off into not discussing the actual post they're on like that.
Sometimes users with idiosyncratic views like to debate in comments instead of posting answers because they can't be downvoted in comments. Don't take the bait.

@Loong If not earlier. I'm sure we were at least introduced to the topic of similar triangles in 5th or 6th grade. I'm pretty sure I remember proving that a triangle on a diameter of a circle is a right triangle by 6th or maybe 7th grade.

moving it to a chat room where
> This user is suspended on the parent site and cannot chat for 192 days.

@ACuriousMind Yeah, sorry. I'm partly to blame, for continuing the discussion. I should've just posted the Wikipedia quote & bailed out.

sounds like solitary confinement to me :-)

12:41 PM
It's not

@skullpetrol How does that work? Clearly JD can now post on Physics, which appears to be his parent site.

@PM2Ring If you get suspended in chat because you get suspended on your parent site, you can change your chat parent, but the suspension and message remains the same
I.e. that suspension does not come from a suspension on Physics

@ACuriousMind Ah, right.
So does that mean that JD is suspended from all chats?

all chats on chat.stackexchange.com

Thanks

12:51 PM
so he is in a chat room where he can not chat

Excellent.

it happens all the time
they can go over to the stack overflow chat rooms and chat

@Loong I see your Barium-133 question still doesn't have any responses. Oh well. I don't know much nuclear stuff, but it looks like an interesting puzzle.
@skullpetrol Right. I don't expect he'll try to harass me in the SO Python room. :)

:-)

1:17 PM
yo @Qmechanic, what's with this edit? physics.stackexchange.com/posts/380525/revisions (v5 → v6)
I take it you wanted to change from "Michelson Morley" to "Michelson-Morley" but the title was taken?
adding extraneous non-rendering MathJax (and at the beginning, no less -- where it's most likely to be visible in external search engines and to mess up e.g. alphabetic listings of titles) doesn't sound like an appropriate solution to me
this should've been used to edit the title into something descriptive:
0

In the Michelson-Morley experiment, the light from a source is passed through a semi-silvered mirror from where a part of it moves horizontally towards a mirror (from where we calculate $t_1$) and a part vertically towards another mirror (from where $t_2$ is calculated). Now, $t_1$ is calculated ...

(no biggie, though)
> On a stainless steel part that was removed from a spent fuel pool of a PWR, we found ...
not one of the most common starting lines for PSE questions, that's for sure
@Loong ping me when the question is bountyable, if it hasn't received enough attention. I'm curious.

1:34 PM
@EmilioPisanty :D It sure grabbed my attention. My guess is that some unusual component in the concrete, or even the water, is the culprit. But even then, I can't figure out how you'd get to Ba-133.

@EmilioPisanty : Yes, you guessed it. Thanks for improving the title.

@Qmechanic =)

2:14 PM
(requires account but not payment)

2:25 PM
-2

Basically I’m attempting to design a time machine using a new model of physics which relies on the postulate that gravity is not cause by mass or rather that the weight that is supposedly the cause of space bending like a hole is actually caused by spin & electromagnetic forces by a torus energ...

he needs a better camera

@EmilioPisanty quick summary?

;-)
boy, I am annoyed
I saw this t-shirt on the street the other day
and, nerd-snipable that I am, I had to look
turns out, there's this
A Janus molecule (or Janus-faced molecule) is a molecule which can represent both beneficial and toxic effects. The term Janus-faced molecule is derived from the ancient Roman god, Janus. Janus is depicted as having two faces; one facing the past and one facing the future. This is synonymous to a Janus molecule having two distinct purposes: a beneficial and a toxic purpose. Examples of a Janus-faced molecule are nitric oxide and cholesterol. In the case of cholesterol, the property that makes cholesterol useful in cell membranes, namely its absolute insolubility in water, also makes it lethal...
which is an interesting enough concept
but no
turns out it's this idiocy: utopiatv.fandom.com/wiki/Janus
> It is split into two parts to avoid detection: a protein called GCHN1 which is added to all industrially farmed corn, and an amino acid put into the vaccine for Russian flu.
no it's not.
if you want to put a protein in your TV show, make it a goddamn protein
if you want it to be an aminoacid, make it a goddamn aminoacid

Unfortunately, protein formulae aren't so easy to draw :P

@ACuriousMind aminoacids are
bam, done
too simple?
bam, done

2:59 PM
I just saw physics.stackexchange.com/questions/492805/… It'd be interesting to know how common the belief is that there's no gravity in a vacuum, but I didn't have much luck with a few minutes of Googling.

@PM2Ring ugh. awful question.

@EmilioPisanty At least we now have a good dupe target for next time.

3:23 PM

3:35 PM
@Slereah cool nice work now how about something on (1) solitons (2) spacetime fabric :)

Sine-Gordon is a soliton
although I need to write it out

right. maybe that was my inspiration. you could include a brief footnote to the soliton TOE :)

"Many exactly solvable models have soliton solutions, including the Korteweg–de Vries equation, the nonlinear Schrödinger equation, the coupled nonlinear Schrödinger equation, and the sine-Gordon equation. The soliton solutions are typically obtained by means of the inverse scattering transform, and owe their stability to the integrability of the field equations. The mathematical theory of these equations is a broad and very active field of mathematical research."
@vzn the whole field of integrability is based on this soliton stuff in some sense, one of the most common approaches, maybe you just need to read up on classical and quantum integrability :p

4:01 PM
@bolbteppa understood theres a lot of material on the subj, have dabbled in it, but think it will expand in key, previously unforeseen areas. aka future of physics™ :) also think (right now) theres a too much emphasis on analytic approaches and not enough on simulations.

@vzn look at the 2D vs 3D ising model integrability stuff to see how both are used

almost nobody is talking about it as a TOE... talk about a glaring vacuum... (or "loud silence"...) to see it as a (mere) mathematical technique is a vast misapprehension...
...my feeling is no matter how much is already known (a respectable amt), its only scratching the surface™ + tip of the iceberg™...

@PM2Ring : As a general rule of thump, when asking about issues outside our universe (such as, e.g. multiverse, pre-big-bang, etc), Phys.SE requests extra validations/references, in order not to become primarily opinion-based and/or a soapbox for crackpots. If you think you can help improving the post, please edit it accordingly.

4:19 PM
@vzn not really the goal here
@bolbteppa you fool
You're assuming that vzn actually knows about physics

:( ... Solitons are basically some stability in an otherwise crazy medium like water etc how could they be a TOE, the TOE would have to first describe the medium those solitons exist in right

@bolbteppa We've had this conversation here with vzn at least half a dozen times. Do you really need to engage in it again?

@ACuriousMind all I did was recommend vzn read up on Ising, the last statement was simply a general comment

@Qmechanic Ok. That sounds like a sensible rule.

4:34 PM
Ron Maimon, New York City
1 1 9 17
Whoa. TIL 70 year bans exist

@EmilioPisanty Thank you :-)
The pool currently looks like this:

Aug 19 '18 at 13:21, by ACuriousMind
Why are y'all compulsively checking Ron's profile, anyway? :P

It's a mess; however, all the fuel has already been removed.

@ACuriousMind Lol I was wandering through meta and saw a complaint about him

Aug 18 '18 at 23:47, by ACuriousMind
@EmilioPisanty I've asked and it's indeed simply "as permanent as the system currently allows". As to what triggered the lengthening all I can tell you is that it wasn't a random act.

4:38 PM
But man, if 70 year bans exist why haven't we implemented them on some frequently banned people

@SirCumference more like 274 years

@Loong wait, what?

@Loong What part of the world is it in?

given this I imagine you're right, but where is this documented?

@EmilioPisanty You can see it e.g. on the chat account
That number of days corresponds to 274 years

4:41 PM
@ACuriousMind huh.
so the date-rendering code is completely out of step with the suspensions code?

Iirc JD had a similar length chat ban, but I guess it got reduced
Not sure who expects him to have a change of heart tho

@EmilioPisanty If I had to guess they convert all dates to display format with the same function, regardless of the context they appear in

'cause there's no way you can read The suspension period ends on Mar 18 '92 at 16:28 as meaning 2292

@SirCumference 1184050 days, but that was corrected

@Slereah lol! am learning it from your comprehensive site :P ps why dont you change the title of your blog to look at all these dumb ass problems :P

4:44 PM
And at the time that display function was written, no one imagined SO would have any need for displaying dates beyond 2099 :P

@ACuriousMind it's not that -- it's the fact that the dates display code has not been modified to accommodate for the possibility that it'll be asked to display dates after 2100

If you wish to learn more I would wait until I finish writing them

@Loong That's...over 3000 years

Guess there's no upper limit

4:45 PM
9 hours ago, by Slereah
Look at all those dumb ass problems

@Loong seriously?
was that somebody mis-typing in numbers?
did that come from a site suspension?

@EmilioPisanty I guess, probably more like gaming the system

@EmilioPisanty Well - almost all of the dates they display are time stamps of posts, i.e. dates between the beginnings of SO and today, so I can see why they didn't anticipate that

@Loong wait, what?
@ACuriousMind oh, for sure

@EmilioPisanty more like a mod being a bit overzealous

4:46 PM
but maybe this trigger is a good call to have a look now?

A lot, actually

@ACuriousMind is it known (/public/publishable) on which site this happened?

Probably a very annoying thing to do since you need to examine all layouts whether the additional two digits breaks them
@EmilioPisanty It wasn't on a site, it was a pure chat suspension

@ACuriousMind I agree =P

@bolbteppa everybody says they want a TOE but all possible candidates must be shot down with extreme prejudice ofc... aka all trespassers will be SHOT ON SIGHT™ :P

4:47 PM
@ACuriousMind OK, thanks.
@ACuriousMind and then this got reverted by a CM?

Yup

OK, thanks.

Meh, I personally don't see the point of banning someone every year
2
Might as well go for a several year ban eventually

Hey Mr. @Slereah your articles/Mathematics page is missing mathjax
@SirCumference it's like a holiday/special occasion!

@danielunderwood Yeah I know
Although I need to finish writing a few articles before I really care
Like have the site "officially open"

4:51 PM
@SirCumference Moderators cannot suspend for longer than a year on main sites; only CMs can do that, and, in truly exceptional cases, do.

@ACuriousMind so if I were one of those truly exceptional people, wouldn't I just make another account?

@ACuriousMind Yeah, but at some point it ought to be raised to the CMs that someone keeps receiving year-long bans
It's kind of comical at this point

@danielunderwood Many try. Few succeed

there's a whole bunch of half finished articles you can't even see
they are SECRET

@Slereah Please don't use @Secret's name in vain.
4
=P

4:56 PM
@EmilioPisanty Well at least he gave a correct answer for once
Albeit on a pretty basic question

@SirCumference No. This is a person abusing a weakness in the SE system, by posting on easy subjects to obtain rep and badges that are then used for cover when posting misinformation elsewhere.
there's nothing to "at least" here.

@ACuriousMind hmm how are you caught
can you see user's IPs?
or is usually manually, like poeple go back to the same shenanigans

@Slereah that's much better than the ton of blogs that I see that just throw everything out there without any thought...and lack references and use stolen figures