0849: "Complex Conjugate"

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Re: 0849: "Complex Conjugate"

Postby Steroid » Wed Jan 19, 2011 11:42 am UTC

OK, I have to ask, was this an intentional pun or am I reading too much into it, that "physics" can also be medicine, possibly a laxative, so it is actually shit that just got real?

And am I wrong in thinking that this guy also once gave a math paper?

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Re: 0849: "Complex Conjugate"

Postby Monika » Wed Jan 19, 2011 12:09 pm UTC

Yes, you are reading too much into this.
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Re: 0849: "Complex Conjugate"

Postby Von Haus » Wed Jan 19, 2011 12:14 pm UTC

*reads comic* Oh, that kind of funny, not great but ok.
*reads title text* Again, ok but doesn't add much.
*comes back to check the forum an hour or so later and glances at comic - instantly gets the joke...* I'm an idiot. I blame not having had to use imaginary numbers for over a year now but still, god I'm an idiot.
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Re: 0849: "Complex Conjugate"

Postby SlyReaper » Wed Jan 19, 2011 12:44 pm UTC

I like appearing smart in front of people I'll never meet, so I'll just mention that I personally got the joke immediately.

But I think there are other names for complex conjugate, and if you've learned a different name by habit, I can understand not getting it.
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Re: 0849: "Complex Conjugate"

Postby dg8672 » Wed Jan 19, 2011 12:54 pm UTC

I'm a Long time reader (and math major), and just registered to say that I've never enjoyed a facepalm as much as the one I performed after reading this one :)

I got a hearty laugh out of it. Nothing beats a good math/science pun.

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Re: 0849: "Complex Conjugate"

Postby vmanivan » Wed Jan 19, 2011 1:11 pm UTC

... they'll eventually move the class to another room and tell everyone else except you.

It's either 'everyone except you' or 'everyone else'. It can't be both. </grammarrage>

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Re: 0849: "Complex Conjugate"

Postby xepher » Wed Jan 19, 2011 1:23 pm UTC

This comic would be funny, but the joke's been done before. For a loooong while. As someone said, there are t-shirts with this stuff on it. Sure, it's mildly funny when people first encounter it, but if you're catering to an audience of smart people, as Randall should be, they're not going to be impressed.

Alt-text was meh-ish. Better than the strip itself.

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Re: 0849: "Complex Conjugate"

Postby snowyowl » Wed Jan 19, 2011 1:33 pm UTC

I loved this one precisely because I knew enough complex arithmetic to get the joke instantly, but not enough to see it coming.
If they make T-shirts with this on, I want one. Or maybe a variation without the S-word, so I can wear it among people who don't get the joke and think I'm being offensive.
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Re: 0849: "Complex Conjugate"

Postby chrisk » Wed Jan 19, 2011 1:49 pm UTC

I enjoyed the pun - but if I were really a physics student in that class, I'd actually feel better able to handle it once 'the shit got real' and I no longer needed to worry what the imaginary/complex quantities actually meant. (Especially if there was any chance they meant that an octopus would start to emanate a death energy field that could devastate the planet - but that's imaginary numbers in psychology, not physics, and an old Isaac Asimov story to boot.)

I do find it funny that the various classes of numbers nearly all evolved because there are mathematicians who asked 'but what if you could' when told that they couldn't do something. The kind who want there to be answers to every possible problem:

"If I have three apples, and take two away, how many remain?" "One. Okay, if I have two apples, and take four away, how many remain?" "You can't take away that many." "Yeah, but what if we could??" - thus, negative numbers.

"If I have eight apples, and split them into two equal piles, how many are in each pile?" "Four. Okay, if I have seven apples, and split them into two equal piles, how many remain?" "You can't split an odd number into two equal piles." "Yeah, I could, if I used a knife to cut one apple up." - thus, rational fractions and decimals.

"Since three piles of three apples is nine apples, we say that three is the 'square root' of nine." "All right - what's the square root of two?" "You can't do that, because there's no way to set up the piles that way, it wouldn't even be a fraction." - thus, irrational roots.

"Okay, for a break, let's look at this circle. If we measure it this way across the center, that's the diameter, and if we measure it all the way around, that's the circumference. The larger the circle, the more both quantities increase." "Is there a way of determining one from the other?" "Sort of - it's a ratio, but one that's impossible to ever fully calculate, a bit like that square root of two thing you came up with." "Okay, let's call that ratio pi" - transcendental numbers.

"So, what's the square root of negative four?" "YOU CAN'T DO THAT! No matter if a number is positive or negative, the square will always be positive." "Okay, then let's come up with this new number i, so that if you multiply i times i, the result is minus one. Then, the square root of -4 is 2i - or -2i." - This gets you to imaginary numbers, and adding them to real numbers gives you complex numbers.


It's enough to make you wish that mathematicians would leave something alone, just once, right? Actually - once they had to. Division by zero is one case where the mathematicians had to accept that an operation was illegal and couldn't make it legal by inventing new numbers - because if you invent a number to stand for 1/0, then you can use that algebraically to prove that 1=2.

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Re: 0849: "Complex Conjugate"

Postby Coffee » Wed Jan 19, 2011 2:03 pm UTC

I don't have the imagination for that level of physics.
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Re: 0849: "Complex Conjugate"

Postby sylvos » Wed Jan 19, 2011 2:40 pm UTC

Byerley wrote:It may be moderately obscure math, but it's really common in physics. In electronics and quantum especially, probably other branches too that aren't coming to mind, it's much easier to work with the functions in imaginary space, but you need to take the projection onto real space at some point to get an observable value out of it. I do it all the time, but it still took ~30s of blank staring to finally get the pun :( . Maybe I'm just bad at puns.


I don't think its even that obscure, I remember quite clearly learning it in high school, so its part of the core curriculum. The only problem here is that while they teach you what complex number is, and they teach what a conjugate is, it isn't usually explicitly stated that this will result in i^2 which is real.

I didn't get the pun for a half second because i just skimmed the beginning part without thinking about what he was doing, once I read the punchline my reaction was, where's the joke? I thought it had to be some pun, so I re-read it and its good for a chuckle. My guess is most people just run to the forums rather than puzzle out what they know.

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Re: 0849: "Complex Conjugate"

Postby ChurchSkiz » Wed Jan 19, 2011 2:44 pm UTC

In Soviet Russia, complex numbers imagine YOU!

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Re: 0849: "Complex Conjugate"

Postby Max2009 » Wed Jan 19, 2011 3:17 pm UTC

Ronfar wrote:
Max2009 wrote:I hate complex numbers. I mean, calculus was hard enough to begin with, why the hell did they have to go and invent imaginary numbers? Were they deprived of imaginary friends as children and now want to get back at the rest of the world?


Amazingly enough, calculus actually gets easier when you introduce complex numbers. Trying to do calculus on functions of two or more real variables quickly becomes a real pain in the neck, but if you can use a complex function instead, things become much simpler. You don't have to worry about such things as curl, divergence, the del operator, or any of that other stuff - if the function has "is analytic" and has a derivative at all, you can find it the same way you find derivatives of real functions. And analytic functions have all sorts of other properties that make them easier to work with, too.

Also, to answer your other question, imaginary numbers were invented in order to solve cubic equations - when you plug numbers into the cubic formula, you sometimes end up having to deal with imaginary terms in the process of getting your answer, even if all three roots are real.


*headdesk*
Please don't take me seriously? I know why they invented imaginary numbers, and precisely how useful they are for solving equations, mostly in physics related stuff. I am a computers-physics geek. So I know exactly why one needs imaginary numbers, and how to use them.
But that doesn't mean I like them, or detract from my humorous statement.
And seeing as how you didn't realize that this was a humorous statement..., well, I probably shouldn't have dignified you with a response.
But I did.
I'm not sure why.
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Re: 0849: "Complex Conjugate"

Postby Vorticity » Wed Jan 19, 2011 3:30 pm UTC

Judging by the fact that the time-dependent Schrödinger equation appears at the top of the whiteboard, the most probable reason that the individual pictured would be multiplying the wave function by its complex conjugate is that they are deriving the quantum continuity equation for probability flow.

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Re: 0849: "Complex Conjugate"

Postby Monika » Wed Jan 19, 2011 3:34 pm UTC

Max2009 wrote:I know why they invented imaginary numbers

This was not exactly obvious. Your readers do not know your physics background. There is no voice or facial expression to make it clear. You chose not to use emoticons. Just because the "imaginary friends" part is obviously a joke it's not obvious that the question regarding the reason for the invention of imaginary numbers is one, too.
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Re: 0849: "Complex Conjugate"

Postby Diadem » Wed Jan 19, 2011 3:48 pm UTC

Terrible, terrible pun.

I propose that if Randall makes puns like this more often we'll move XKCD to a new site and tell everybody but him about it! :twisted:
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Re: 0849: "Complex Conjugate"

Postby rcox1 » Wed Jan 19, 2011 4:35 pm UTC

It was very early when I read this, and it took me a few minutes to process it, but when I did it was the funniest thing to appear on XKCD in a very long time. I know it is punnish, and that is usually bad, but when done right it can be very very bad.

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Re: 0849: "Complex Conjugate"

Postby Æshættr » Wed Jan 19, 2011 5:25 pm UTC

Finally my avatar becomes appropriate!

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Re: 0849: "Complex Conjugate"

Postby Aelfyre » Wed Jan 19, 2011 5:35 pm UTC

haha,, ok so that was great.. I actually got the punchline for once! I just *recently* learned what a complex conjugate was from Leonard Susskind's lectures on Quantum mechanics (btw itunes.stanford.edu is a gold mine of free education.. I am soaking up as much as I can as fast as I can)

shit just got real.. now thats funny.. [insertcheeseburnhere]
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Re: 0849: "Complex Conjugate"

Postby JohnTheWysard » Wed Jan 19, 2011 6:09 pm UTC

Good one... and I love the discusssion it generated.

alt-text: "if you say this every time a professor does something to a complex-number equation that drops the imaginary part, they'll eventually move the class to another room and tell everyone else except you."

so you'll be left in the classroom with just your imaginary friends.

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Re: 0849: "Complex Conjugate"

Postby uncivlengr » Wed Jan 19, 2011 6:53 pm UTC

I actually liked it better before picking up on the imaginary/real numbers pun... just a professor getting his hardcore lecture on.
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Re: 0849: "Complex Conjugate"

Postby 55redJDs » Wed Jan 19, 2011 7:55 pm UTC

Talk about timing...learned complex conjugate just an hour before reading this.

:)

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Re: 0849: "Complex Conjugate"

Postby Gazzaman » Wed Jan 19, 2011 7:55 pm UTC

I LOLed!

my GF just sighed when she saw what i was reading.

I am studying Electrical and Electronic engineering...I have to take complex conjugates all the time and thus got this straight away. Its that or use Eulier's theorum to calculate useful numbers. for reference, its used a lot in control engineering because everything is drawn on a complex plane.

I wish my lecturers would make jokes, even if they were as bad as this...It would make the lectures so much easier to bare!

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Re: 0849: "Complex Conjugate"

Postby Wybaar » Wed Jan 19, 2011 9:06 pm UTC

Ronfar wrote:
Max2009 wrote:I hate complex numbers. I mean, calculus was hard enough to begin with, why the hell did they have to go and invent imaginary numbers? Were they deprived of imaginary friends as children and now want to get back at the rest of the world?


Amazingly enough, calculus actually gets easier when you introduce complex numbers. Trying to do calculus on functions of two or more real variables quickly becomes a real pain in the neck, but if you can use a complex function instead, things become much simpler. You don't have to worry about such things as curl, divergence, the del operator, or any of that other stuff - if the function has "is analytic" and has a derivative at all, you can find it the same way you find derivatives of real functions. And analytic functions have all sorts of other properties that make them easier to work with, too.

Also, to answer your other question, imaginary numbers were invented in order to solve cubic equations - when you plug numbers into the cubic formula, you sometimes end up having to deal with imaginary terms in the process of getting your answer, even if all three roots are real.


You don't even need to go to cubic equations, just quadratic.

  • Natural numbers allow you to solve the equation x + a = b where a and b are both natural numbers and b > a. What do you do when b < a, for example x + 2 = 1? You extend the natural numbers to the integer numbers. [What happens when b = a depends on whether you consider 0 to be a natural number.]

  • Integer numbers allow you to solve the equation a*x = b where a and b are both integer numbers and b is a multiple of a. What do you do if b is not a multiple of a, for example 2*x = 1? You extend the integer numbers to the rational numbers.

  • Rational numbers allow you to solve the equation x^2 = a where a is a rational number that is the square of a rational number. What do you do if a is positive but not the square of a rational number, for example x^2 = 2? You extend the rational numbers to the real numbers. [This extension is a bit different than the previous extensions.]

  • Real numbers allow you to solve the equation x^2 = a where a is a nonnegative real number. What do you do if a is negative, like x^2 = -1? You extend the real numbers to the complex numbers.
Do you need to extend the complex numbers to solve any nonconstant polynomial equations with complex numbers as coefficients? It turns out you don't.

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Re: 0849: "Complex Conjugate"

Postby soren121 » Wed Jan 19, 2011 9:52 pm UTC

fenrir_darkwolf wrote:
soren121 wrote:Thanks to Randall for making me research my most hated subject at midnight.


What's your most hated subject? Quantum mechanics? Have you taken a quantum course? It's quite nice once you get over how much maths formalism there is (not that there is anything wrong with maths formalism :P )


I just meant mathematics in general.
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Re: 0849: "Complex Conjugate"

Postby cjmcjmcjmcjm » Wed Jan 19, 2011 10:11 pm UTC

Æshættr wrote:Finally my avatar becomes appropriate!

I think I may have to represent my mathematical neighborhood and use this is as my FB pic for a while someday
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Re: 0849: "Complex Conjugate"

Postby Ronfar » Wed Jan 19, 2011 10:41 pm UTC

Wybaar wrote:
Ronfar wrote:
Also, to answer your other question, imaginary numbers were invented in order to solve cubic equations - when you plug numbers into the cubic formula, you sometimes end up having to deal with imaginary terms in the process of getting your answer, even if all three roots are real.


You don't even need to go to cubic equations, just quadratic.



Perhaps, but that's not how it actually happened historically. For a long time, mathematicians were quite content to say that equations such as x^2 +1 = 0 simply had no solution. It wasn't until after they were shown to be important in finding real roots of cubic equations that mathematicians began to take imaginary numbers seriously.
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Re: 0849: "Complex Conjugate"

Postby Ogh_II » Wed Jan 19, 2011 11:22 pm UTC

Oh dear - I'm lost. Literature major (or whatever you Yanks call it) in tha house. Even my mild knack for natural science won't help me out, here.

Looking forward to Friday's comic, though.

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Re: 0849: "Complex Conjugate"

Postby mattholimeau » Wed Jan 19, 2011 11:38 pm UTC

chrisk wrote:It's enough to make you wish that mathematicians would leave something alone, just once, right? Actually - once they had to. Division by zero is one case where the mathematicians had to accept that an operation was illegal and couldn't make it legal by inventing new numbers - because if you invent a number to stand for 1/0, then you can use that algebraically to prove that 1=2.


Isn't this the perfect opportunity to mention limits and infinity? Not that what you said isn't true (well - I'd argue with the wanting em to leave something alone), but they may have said "but I want to divide 100 apple by *almost* zero, and thus ended up with more and more pieces of apples as the kept dividing by smaller and smaller chunks. Then we can start using apples for examples of stuff that they didn't wanna tell you in highschool, 'cause it'll confuse the rest of the class, heheh.

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Re: 0849: "Complex Conjugate"

Postby jophiel » Wed Jan 19, 2011 11:40 pm UTC

Perfect timing Randall!

I'm in my first year of college studying physics, and right now we're studying for our Linear Algebra exams on monday. The second year students are studying for their Quantum Mechanics exams, and the fourth year students are studying for some advanced Quantum exam. Needless to say, 'Shit just got REAL' was heard everywhere on campus today.

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Re: 0849: "Complex Conjugate"

Postby mattholimeau » Wed Jan 19, 2011 11:42 pm UTC

Belteshazzar wrote:I have a math professor who is in the habit of saying things like "... defines a real Banach space. (pause) A real Banach space, Daddy? Yes, son, a real Banach space."


Could someone do me a favor and explain this bit? It seems to me it's just a professor being odd, but based on the context of the comic, I have to assume there's a comparison or pun I'm not getting. What does "real Banach space" have to do with a father and son? Is there something about the pronunciation? I'd think I might be over-analyzing it... but this is xkcd, so I highly doubt it.

Thanks.

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Re: 0849: "Complex Conjugate"

Postby A_of_s_t » Thu Jan 20, 2011 1:27 am UTC

I lol'd so hard. Randall must make this into a shirt.
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Re: 0849: "Complex Conjugate"

Postby mnkyman663 » Thu Jan 20, 2011 2:10 am UTC

I just started my complex analysis course today! Coincidence???????

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Re: 0849: "Complex Conjugate"

Postby rho421 » Thu Jan 20, 2011 3:05 am UTC

First strip that has made me laugh aloud in some time. Good job, Randall.

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Re: 0849: "Complex Conjugate"

Postby AlejoHausner » Thu Jan 20, 2011 3:28 am UTC

It's not just a math joke, it's a PHYSICS joke. When you multiply the wave function by its complex conjugate, you get the (real) probability distribution of the system: you find out, say, the probability that particle is here, and the probability that it's there. It's a quantum thing, I learned it, but I was just a quantum mechanic, so I just learned to do the math without knowing the reality behind it. Had I been a quantum metaphysician, I would know what it MEANT.

Hence shit doesn't strictly get real: its reality becomes probable. Or maybe shit gets real, but you can't be sure exactly where the shit is. Kinda like walking into a room where the cat has peed: you know it's real pee, but you don't know its exact location.

Hmm... Randall could have said it better.

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Re: 0849: "Complex Conjugate"

Postby ConMan » Thu Jan 20, 2011 3:54 am UTC

mattholimeau wrote:
Belteshazzar wrote:I have a math professor who is in the habit of saying things like "... defines a real Banach space. (pause) A real Banach space, Daddy? Yes, son, a real Banach space."


Could someone do me a favor and explain this bit? It seems to me it's just a professor being odd, but based on the context of the comic, I have to assume there's a comparison or pun I'm not getting. What does "real Banach space" have to do with a father and son? Is there something about the pronunciation? I'd think I might be over-analyzing it... but this is xkcd, so I highly doubt it.

Thanks.

Like in the comic, the prof is punning on real/imaginary/complex numbers (or in this case real/complex Banach spaces) and real/imaginary things in the world - like the child who finds out his dad is getting him a bike: "A real bike? Wow!"
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Re: 0849: "Complex Conjugate"

Postby gmalivuk » Thu Jan 20, 2011 5:06 am UTC

Funniest comic in quite some time, imho. I feel like the comic itself was meant to appeal to those who hadn't heard the joke a thousand times already, and the alt-text was for those who had and were tired of it.

vmanivan wrote:
... they'll eventually move the class to another room and tell everyone else except you.
It's either 'everyone except you' or 'everyone else'. It can't be both. </grammarrage>
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Re: 0849: "Complex Conjugate"

Postby Linux0s » Thu Jan 20, 2011 5:37 am UTC

But when is show & tell? I brought a shiny red fire truck.
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Re: 0849: "Complex Conjugate"

Postby kr0n05 » Thu Jan 20, 2011 6:14 am UTC

I finally registered just to point out how terrible a pun this makes...

Shame on you Randal.

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Re: 0849: "Complex Conjugate"

Postby wrongusername » Thu Jan 20, 2011 7:41 am UTC

Awesome. My professor did this in physics class today! He said "Shit just got real." The class roared with laughter. I didn't get it, until I finally saw today's comic :(


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