2028: Complex Numbers

2018-08-03T16:52:55Z

TrueBoxGuy: Transcript

{{comic
| number = 2028
| date = August 3, 2018
| title = Complex Numbers
| image = complex_numbers.png
| titletext = I'm trying to prove that mathematics forms a meta-abelian group, which would finally confirm my suspicions that algebreic geometry and geometric algebra are the same thing.
}}

==Explanation==
{{incomplete|Created by a MATHEMATICIAN - Do NOT delete this tag too soon.}}

The complex numbers can be thought of as pairs <math>(a,\,b)\in\mathbb{R}</math> of real numbers with rules for addition and multiplication.

: (a,b) + (c,d) = (a+c, b+d)

: (a,b) . (c,d) = (ac - bd, ad + bc)

As such they are 2d vectors, with an interesting rule for multiplication. The justification for these rules of multiplication is to consider a complex number to be an expression in the form a+bi, where <math>i^2 = -1</math>, ie ''i'' is the square root of negative 1. Applying the common rules of algebra and the definition of ''i'' yields rules for addition and multiplication above.

Regular 2d vectors are pairs of values, with the same rule for addition, and no rule for multiplication.

The usual way to introduce complex numbers is by starting with ''i'' and deducing the rules for addition and multiplication, but Cueball is correct to say that complex numbers are really just vectors, and can be defined without consideration of the square root of a negative number.

The teacher, (Miss Lenhard) counters that to ignore the natural construction of the negative numbers would hide the relevance of the fundamental theorem of algebra (Every polynomial of degree ''n'' has exactly ''n'' roots, when counted according to multiplicity) and much of complex analysis (the application of calculus to complex-valued functions), but she also agrees that mathematicians are too cool for "regular vectors"

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[Cueball (the student) is raising his hand and writing with his other hand. He is sitting down at a desk, which has a piece of paper on it]
:Cueball: Does any of this really have to do with the square root of -1? Or do mathematicians just think they're too cool for regular vectors?

:[Miss Lenhart (the teacher) is standing in front of a whiteboard, replying to Cueball's question]
:Miss Lenhart: Complex numbers aren't just vectors. They're a profound extension of real numbers, laying the foundation for the fundamental theorem of algebra and the entire field of complex analysis

:[Miss Lenhart is standing slightly to the right in a blank frame]
:Miss Lenhart: '''''And''''' we're too cool for regular vectors.
:Cueball (off-screen): I '''''knew''''' it!

{{comic discussion}}

Talk:2021: Software Development

2018-07-22T13:19:51Z

TrueBoxGuy: Comment

It seems to me that the cannon is a metaphor for powerful hardware. The drill is a metaphor for elegant and efficient code. The computer is so powerful that the fact that the elegance or efficiency of the code is irrelevant to how it is actually used.[[User:Zeimusu|Zeimusu]] ([[User talk:Zeimusu|talk]]) 15:48, 18 July 2018 (UTC)

Hi, first time posting ;)
To me it seems that the Title text is an example how after some time and many updates the original solution becomes some kind of abomination. Used in abstruse ways for something it was never intended for just because it works and is a quick and simple fix. After some time one always ends up doing unnecessary and arbitrary things in order to get what you actually wanted to achive. Like loading projectiles into a cannon just to use it as a battering ram. {{unsigned ip|162.158.91.137}}

:Agreed. The current rush to monetize distributed crypto-token ledgers smacks of this to me. Rather than focus on refining the protocols involved (which is hard) many projects seem to focus merely on implementing the protocols in any half-@$$ed way that appears legitimate enough on the surface to attract investment capital & turn a profit for some insider. [[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 16:49, 20 July 2018 (UTC)

Don't forget the fact that no one wants to figure out how to use the elegant drill, but instead use it for its most obvious if least elegant piece--the stationary pointy bit. -Todd 7/18/2018 17:32 UTC {{unsigned ip|172.69.69.88}}

The way I understand this, Hairy had the cannon done already to make holes in the wall, the typical brute force solution to the problem. But he needed ammo of a certain weight and gave that task to Cueball. Cueball then made a drill, an elegant solution that would do the job better than the canon. Hairy sees the drill and doesn't care about all the fancy functions, all he needed was an object of the proper weight to put 500 of them in the already built cannon. In programming, this shows either a reluctance from Hairy to adapt to the better solution and insist on using the brute force approach. Or, it shows how often programmers tend to make things way more complicated than is needed. Cueball went to remake a new solution for the problem when all he was supposed to do was make a cannonball of the proper weight.-Vince23 17:46, 18 July 2018 (UTC) {{unsigned|Vince23}}

This also shows the results of not clearly defining terms. Cueball interpreted 'drill' to mean 'a hand held drilling machine' whilst Hairy toolkit to mean a 'drill bit'. So when Cueball delivers his component, Hairy just uses it as a 'dumb' piece of ammo. [[User:RIIW - Ponder it|RIIW - Ponder it]] ([[User talk:RIIW - Ponder it|talk]]) 22:31, 18 July 2018 (UTC)

I have a slightly different take. You develop a tool (drill or accounting application) that solves the problem. Then you develop a meta-tool (cannon or cloud-based services or Container software) that bundles simple tools and throws them at the same problem. The comic is not too effective in making the point. [[User:Rtanenbaum|Rtanenbaum]] ([[User talk:Rtanenbaum|talk]]) 14:43, 20 July 2018 (UTC)

Automatic-Drill Cannon is my new favorite impractical weapon. [[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 01:44, 19 July 2018 (UTC)

::Sorry if this is amazingly off topic, but is that an automatic-drill cannon or an automatic drill-cannon? Like a Gatling gun for power tools? -Milliways 3:38, 19 July 2018 (UTC)

:::Not off topic at all; It's a cannon which fires automatic drills, therefore it's an automatic-drill cannon. An automatic drill-cannon would automatically fire drills. While it's possible (especially given the motorized base) that the cannon is automatic, we ''know'' that the drill is automatic.
::: Nice name, by the way.
:::[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 16:41, 20 July 2018 (UTC)

It is so fitting that this comic came out on the same day as Minecraft 1.13, an update that was incredibly rushed due to a stupid deadline. An update that contains many amazing features and code cleanups and rewrites, but also crashes, save corruptions, lots of bugs and lag, etc. An update that was meant to mainly fix bugs and clean up code, but ended up getting merged with another feature update, which caused most of this mess. [[User:Fabian42|Fabian42]] ([[User talk:Fabian42|talk]]) 08:22, 19 July 2018 (UTC)

Definitely seems make more sense if you consider the person on the left to be the software developer and the person on the right to be the user, doesn't it? But equally valid if the person on the left is the hardware developer and the person on the right is the programmer. [[User:Swhitlock|Swhitlock]] ([[User talk:Swhitlock|talk]]) 18:20, 19 July 2018 (UTC)

:It makes most sense if these are two software developers who each have been given part of a task, with ill defined boundaries between the parts. --[[Special:Contributions/162.158.134.34|162.158.134.34]] 06:27, 20 July 2018 (UTC)

:I think it also makes sense if the left is a software developer & the right is a hardware or UX developer. [Develop innovative code process -> Ignore finer points of process -> Implement a crude solution using brute hardware power & a kludge] seems to be a pretty common scenario. Modern computers running Windows™ or Linux could be considered an example of this, as both contain brilliant snippets of code implemented in cumbersome, inelegant, or less-than-efficient ways. (Mac might do this too, but I wouldn't know.) [[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 16:41, 20 July 2018 (UTC)

Example: Automatic drill <=> database. Cannon <=> foreach (var row in db.execQuery("select * from customer")) if (resultRow["name"] == searchTerm) return true; [[Special:Contributions/141.101.77.248|141.101.77.248]] 23:45, 19 July 2018 (UTC)

I think that this comic represents how programmers put time above cost. Having 500 drills would be expensive but it would significantly reduce the time taken, as they are synchronous. This arguably isn't a bad tactic, but it stops programmers from worrying about cost at all in some cases.

I think this also represents front end Vs back end. If you consider the drill as the front-end and the cannon as the back end. The drill is elegant while the cannon is ugly, the same thing often happens in programming. [[User:TrueBoxGuy|TrueBoxGuy]] ([[User talk:TrueBoxGuy|talk]]) 13:19, 22 July 2018 (UTC)

explain xkcd - User contributions [en]

2028: Complex Numbers

Talk:2021: Software Development