explain xkcd - User contributions [en]

Talk:2117: Differentiation and Integration

2021-11-03T12:53:16Z

162.158.62.96:

Darn, I have no idea what this comic is about. Randal has eluded my yet again. [[User:Linker|Linker]] ([[User talk:Linker|talk]]) 17:43, 27 February 2019 (UTC)
:Calculus. [[Special:Contributions/162.158.79.143|162.158.79.143]] 18:16, 27 February 2019 (UTC)
::Basically, differentiation is easy to do by hand, but integration, even of things that look simple on paper, can be very difficult, as well as easy to mess up or get lost in. [[User:Glassvein|Glassvein]] ([[User talk:Glassvein|talk]]) 01:52, 6 March 2019 (UTC)

And Calc 2 is why I stopped being a Computer Science major and moved (eventually) to majoring in English. Consistent 4.0s in math through Trig and Calc I ... 1.6 in Calc II, retook and got a 1.8. Without the Calc, couldn't do the physics; without the physics, couldn't get my 2-yr degree and move on from community college to a full university. I don't know what all the integration stuff in the flowchart is (since I didn't do well in Calc and it was a long time ago), but there's so very many things that become [https://en.wikipedia.org/wiki/Nonelementary_integral nonelementary integrals] that all sorts of special tricks have to be employed for things that look like they should be easy. It's like having a problem that's very easy to do division on, but requires special advanced mathematical tricks to use multiplication upon.[[Special:Contributions/108.162.216.208|108.162.216.208]] 19:07, 27 February 2019 (UTC)

Going to start learning integration in 3 weeks... Wish me luck. [[Special:Contributions/162.158.62.96|162.158.62.96]] 12:53, 3 November 2021 (UTC)

Basic ideas:
Integration by parts is the reverse of the Product Rule.
Substitution is the reverse of the Chain Rule.
Cauchy's Formula gives the result of a contour integration in the complex plane, using "singularities" of the integrand.
Partial fractions is just splitting up one complex fraction into a sum of simple fractions, which is relevant because they are easier to integrate.
Stokes theorem is the relationship between an integral over an area, and an integral over the boundary of said area.
Riemann integration was the first rigorous definition of integration. This has been superseded by Lesbesgue integration.
Bessel functions are like 2d versions of sin and cos, and turn up sometimes when doing integration.[[Special:Contributions/162.158.89.61|162.158.89.61]] 20:14, 27 February 2019 (UTC)
:"Lesbesgue integration." Best. Freudian. Slip. Ever. SCNR :P [[Special:Contributions/162.158.91.59|162.158.91.59]] 08:28, 28 February 2019 (UTC)
I know what you mean ;). After all, Gen 8 Pokemon was announced the other day, so you read it as "Pokemon League Integration". Completely understandable. [[Special:Contributions/172.68.78.28|172.68.78.28]] 14:40, 28 February 2019 (UTC)
Shouldn't Wolfram Alpha be somewhere in that flowchart? [[Special:Contributions/162.158.255.142|162.158.255.142]] 20:54, 27 February 2019 (UTC)

Glad to see I'm not the only one who is too dumb to integrate [[Special:Contributions/162.158.90.36|162.158.90.36]] 21:02, 27 February 2019 (UTC)
:Symbolic differentiation is just going through algorithm ; there are few functions which don't have it but they tend to be constructed in complicated way, and if function have differentiation it's usually easy to find it. Symbolic integration requires lot of thinking and trial and error ; even very easy function may lack primitive function and even if they don't, you may be unable to find it except randomly. If it's exercise in book, the ones for differentiation are done by thinking about some interesting function and putting it there. The ones for integration are done by thinking about some interesting function and putting it's differentiation there. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 23:38, 27 February 2019 (UTC)

Oddly enough it mentions Riemann integration, but that is the integral most people know how to use. Turns out there are a lot more (e.g. lebesgue and generalized riemann integrals). I'm halfway through a second semester of real analysis and was floored by how involved integration can be. [[Special:Contributions/172.68.34.106|172.68.34.106]] 21:36, 27 February 2019 (UTC)

One of my professors once said: "Never try to integrate a function. Almost all (in a strict mathematical sense) functions are impossible to integrate, so there is no reason why you should even try." --[[Special:Contributions/162.158.88.128|162.158.88.128]] 07:52, 28 February 2019 (UTC)

How is there no "+ C" joke in there [[User:Blagae|Blagae]] ([[User talk:Blagae|talk]]) 13:16, 28 February 2019
(UTC)

Probably because he put a +C joke in 1201:_Integration_by_Parts. [[Special:Contributions/108.162.219.160|108.162.219.160]] 13:48, 2 March 2019 (UTC)

== Risch algorithm ==

I thought I could contribute to the article with a better explanation of the Risch algorithm, since I have a bit of expertise here -- I've read all the original papers, plus the Cherry papers that add the extra features like Li and erf. I pulled out some of the old papers to review my knowledge of symbolic differential algebra (it's been a while!) then typed up a careful explanation which corrected some errors in the original description and fleshed out many more details... possibly excessively, but hey, that's kind of our calling here.

Then I saw that Glassvein completely removed my version for what appears to be the original without so much as a mention in the edit description. What gives? I

[[User:CRGreathouse|CRGreathouse]] ([[User talk:CRGreathouse|talk]]) 04:59, 28 February 2019 (UTC)
: Probably due to simultaneous editing. I've restored your definition. [[Special:Contributions/162.158.88.128|162.158.88.128]] 16:52, 28 February 2019 (UTC)

:: OK, wasn't sure if it was intentional (if somehow it was worse). Thanks! [[User:CRGreathouse|CRGreathouse]] ([[User talk:CRGreathouse|talk]]) 01:34, 1 March 2019 (UTC)
That was indeed an accident due to simultaneous editing. My bad!
[[User:Glassvein|Glassvein]] ([[User talk:Glassvein|talk]]) 02:47, 5 March 2019 (UTC)

== Numerical Integration ==
Better still...plot the graph - cut along the line - weigh the part under the line. :-) [[User:SteveBaker|SteveBaker]] ([[User talk:SteveBaker|talk]]) 20:46, 28 February 2019 (UTC)

[Anonymous: I understand mathematically that integration is much more difficult than differentiation, but is there a possibility that Randall is making the comment that the same is true for Society? Integration has proved very difficult, and has led to riots, but experience shows that dividing our society up into small subgroups (that then argue with each other, but don't spend enough time together for riots) is relatively easy.]{{unsigned ip|108.162.219.112}}

:Good luck plotting {{w|Weierstrass function}}. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 00:05, 9 March 2019 (UTC)

== overstates the case? ==

Current summary says that the comic overstates the case of how difficult integration can be. I'm not sure that's true. Sure, you can use numerical integration to get a specific area under the curve, but that's not what the comic is referring to. Unless some mathematician can show here how integration can be done by repeatedly following a set of fixed rules, Ithis comic is actually completely accurate. And that's why it's funny. :-)

2496: Mine Captcha

2021-07-30T22:23:29Z

162.158.62.96: Please learn that vision classifiers exist, can outcompete us, and we trained them to with captchas, and continue to use the same captchas.

{{comic
| number = 2496
| date = July 30, 2021
| title = Mine Captcha
| image = mine_captcha.png
| titletext = This data is actually going into improving our self-driving car project, so hurry up--it's almost at the minefield.
}}

==Explanation==
{{incomplete|Created by a LIVE MINE THAT ONLY EXPLODES IF DOUBLE-STEPPED ON. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}

This comic, like [[1897: Self Driving]], references the approach of using {{W|CAPTCHA}} inputs to solve problems, particularly those involving image classification, which are all solvable by computers now, specifically {{W|reCAPTCHA}} v2's fallback puzzle which is based on identifying road features and vehicles. A reCAPTCHA version of this puzzle might ask a user to "check all squares containing a STOP SIGN."

The CAPTCHA in this comic, however, asks the user to "Click all the pictures of MINES" by, ironically, clicking on squares that do not show anything more than a gray square, with the understanding that some of those gray squares are hiding 'mines' in a {{w|Minesweeper (video game)|Minesweeper puzzle game}}, hence the title Mine Captcha.

Furthermore, the CAPTCHA in this comic asks the user to click on the squares containing mines themselves, which is the opposite of the traditional goal in Minesweeper, which is to click on all boxes where there are ''no'' mines, and solving the puzzle is usually (although not in this case) impossible without revealing the information in those squares without mines. So the CAPTCHA in this comic would be especially difficult for a user who is familiar with how to play Minesweeper, in addition to being difficult for a user who is familiar with the normal CAPTCHA image-selection puzzle. But would be impossible for anyone that have never heard of the game/know the rules.

A captcha (also spelled CAPTCHA) is a challenge designed to be solvable by humans, but not by computer programs. It is used to protect websites from automated software. For example, editing the explain xkcd wiki without being logged in requires the user to solve a Captcha.

The captcha depicted in this comic is similar in layout to one of the challenges of ''reCAPTCHA'', a captcha system owned by Google. reCAPTCHA requires the user to click on several of 16 tiles laid out in a 4x4 grid.

The comic combines this with the game of Minesweeper, a logic puzzle game where the player must uncover tiles in a grid by clicking on them. Some of the tiles contain "mines", clicking on those means immediate defeat. When uncovering a tile without a mine, it shows how many of the (up to 8) adjacent tiles contain a mine.

This comic expects users click on the mines in a minesweeper puzzle to proceed with their task. 6 of the 16 tiles has a colored number, in blue font for the three number ones, green for the single instance of two and red for the two number three. Each number used a different font style disregarding the color. As the goal in minesweeper is to click on boxes where there are NOT mines, the puzzle would be especially difficult for anyone used to playing minesweeper. In addition, as long as a computer could be made to read and understand the task (presuming there is no obfuscation of the instruction or grid), a logic puzzle such as this is a case where an automated spambot could actually be prepared to more easily solve the puzzle than most people.

The comic shows a 4x4 grid with mostly grey squares, and a few tiles showing colored numbers. The setup and colors suggest a gaming board of the popular minesweeper game, with a few tiles uncovered. Numbers would then show the number of mines in adjacent squares. Given the current board configuration, one can deduce that there are four mines (in squares A2, B2, B3 and D3, where letters (numbers) mark columns (rows)), see [[#Trivia|trivia section]]. For example, there are two mines within the squares A2,B1,B2, as signified by the 2 in A1, but only one of those can be in B1 or B2 (because of the 1 in C1). Therefore, A2 has to be a mine. The title suggests this as a CAPTCHA, where proving to be human involves first recognizing this as a minesweeper simile, and then solving for those squares with mines.

<pre>
A B C D

1 2 . 1 .
2 * * 3 .
3 3 * . *
4 . 1 . 1
</pre>

Traditionally, the goal in minesweeper is to click on boxes where there are NOT mines, and solving the puzzle is usually (although not in this case) impossible without revealing the information in those squares, so the puzzle could easily trip up anyone used to playing minesweeper.

The title text is similar to [[1897: Self Driving]] where the CAPTCHA solver is asked to "answer quickly – [the] self-driving car is almost at the intersection", as a parody of the current tendency for CAPTCHAs to apparently be used to provide training information in order to improve automatic identification of traffic signals, pedestrian crosswalks, bicycles, buses and other potential road hazards. In this case the car is apparently driving into this minefield and can only avoid the mines if the user solves this CAPTCHA fast enough for immediate application of the input. Where the first would be realistic, although very dangerous, this time it is of course just a continuation of that old joke. Even if the car drove into a mine field, there would be no way to have the limited 'clue' information (with typically just the one complete and unambiguous solution) and yet somehow not already be able to have more knowledge of the 'answer' than the CAPTCHA user.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

[A "CAPTCHA" box.]

To proceed, click<br>all the pictures of<br>MINES

[A 4 by 4 ''Minesweeper'' field, with some cells revealed with numbers. Each number is drawn in a different font/style.]

<pre>
2 . 1 .
. . 3 .
3 . . .
. 1 . 1
</pre>

==Trivia==
*Here is where the mines are in this comic, and thus the fields that needs to be pushed in this Captcha to prove you are human:
:[[File:2946_Mine_Captcha_With_Bombs.png]]
*Here are the solved puzzle as it would look if played as a real minesweeper game, except the mines would be represented by flags. (The empty square top right corner has 0 bombs next to it. This is not written in the game but indicated as this field has been pushed down):
:[[File:2946_Mine_Captcha_Solved.png]]
*The original game can be played here: [https://minesweeper.online/ World of Minesweeper]
**It is possible to build a 4x4 CAPTCHA game there:
:[[File:2946_Mine_Captcha_Example_of_4x4_game.png]]

{{comic discussion}}

[[Category:CAPTCHA]]
[[Category:Self-driving cars]]
[[Category:Comics with color]]