Compass and Straightedge
by Jeff
Image text: The Greeks long suspected this, but it wasn't until April 12th of 1882 that Ferdinand von Lindemann conclusively proved it when he constructed himself the most awesome birthday party possible and nobody showed up.
This comic is funny because Cueball is a stick figure so technically it is possible to create friends with a straightedge and a compass. Just one circle with the compass and 5 lines with the straightedge.
There is also a possible reference the "Straight Edge" a movement that refrains from taking drugs or drinking alcohol. So, the alternative interpretation is that Cueball was straight edge in high school so therefore had no friends.
Ferdinand von Lindemann was a real German mathematician. In 1882, he proved that pi is not a zero of any polynomial with rational coefficients or a transcendental number.
February 28th, 2011
Your explanation is, I think, incorrect. The ancient Greeks studied compass and straightedge constructions a lot; in other words, they wanted to see what figures could be made using only these two tools (http://en.wikipedia.org/wiki/Compass_and_straightedge). They came up with 3 constructions which they suspected could not be constructed using these two tools: squaring the circle, trisecting the angle, and doubling the cube. In the beginning of the 20th century, these were all proven impossible, and von Lindemann’s proof that pi is transcendental is crucial to proving the first.
February 28th, 2011
You’re right, I think this comic is an obvious reference to the “squaring the circle” problem in particular.
Maybe you can improve the explanation I wrote here http://xkcdexplained.wikia.com/wiki/Compass_and_Straightedge
(shameless advertisement for an xkcd explanation wiki I’m trying to launch)
February 28th, 2011
http://xkcd.com/410/
http://en.wikipedia.org/wiki/Friendly_number
More likely this comic is a double pun on (1) the match concept of “friendly numbers” also mention in xkcd-410, and (2) the fact that mathematicians typically are nerds with few friends in the first place.
February 28th, 2011
I seriously resemble that remark.
February 28th, 2011
If at all possible, you need to change “Xkcd” in your wiki title to “xkcd” or at least “XKCD”. For why this is, I have quoted below an FAQ in the About section of xkcd.com:
How do I write “xkcd”? There’s nothing in Strunk and White about this.
For those of us pedantic enough to want a rule, here it is: The preferred form is “xkcd”, all lower-case. In formal contexts where a lowercase word shouldn’t start a sentence, “XKCD” is an okay alternative. “Xkcd” is frowned upon.
March 1st, 2011
Lowercase isn’t possible so I switched it to uppercase. Thanks for the advice!
March 19th, 2011
i’ve always said xkcd explained should be a wiki
i wanted to name it xplainkcd
March 1st, 2011
Perhaps we’re over-analyzing this one? There’s a universal human need to be connected, to have people who like and love us, to know that we belong. We also want to be smart, respected, recognized for what we’re good at. But the second doesn’t always lead to the first.
It feels good to be a nerd, to see the beauty of the universe through the crisp, clear lens of math and science, in a way our non-nerd classmates and co-workers will never fully understand. And yes, it’s great to have them go, “Wow! You’re so smart!” (Well, in our dreams, anyway)
But sometimes what we crave is simple human connection. And for that, our usual tools of evaluation and engineering don’t help. For that, our intellectual skills can utterly fail us in our quest to feel less alone. Thus, the poignantly humorous observations that you can’t construct friends with a compass and straightedge, and that the “best” birthday party in the world is meaningless if no one shows up.
March 1st, 2011
OK, the above sounds like it was written by a Liberal Arts major, sorry! (The NRC* is reviewing my membership in the Society of Nerds)
Of course, I didn’t mean to imply that the whole “things you can’t do with just a compass and straightedge” reference is over-analyzing. The incredible amount of effort that we nerds have put into squaring circles, trisecting angles, and doubling cubes over the centuries just because someone said it’s impossible is an important component of the humor, as is the idea that we might try to apply this same methodology to something for which it is obviously utterly un-suited.
But the poignancy comes from the fact that we might try (and fail) to “make a friend” in this fashion.
* NRC: Nerd Review Committee
March 1st, 2011
I think this comic is what makes xkcd so great. I have little knowledge of advance math so I don’t sete that side of the comic. I see humor in the stick figure pun, and the social reference. Different people get different parts of this one. Great comic.
March 2nd, 2011
I think this comic is simply using standard irony. It starts with a statement that makes one expect some reference to Greek mathematical discovery, and then switches directions in the middle and makes a joke about the stereotypical friendless mathematician. I don’t think this comic is any deeper than that.
March 2nd, 2011
Dude! It’s xkcd. . . it’s ALWAYS deeper than that.
And if it ain’t, it should have been.
March 3rd, 2011
I note that April 12th was his birthday and so in 1882 his birthday party should have had transcendental pi (pie) which sounds pretty awesome indeed
March 10th, 2011
http://tinyurl.com/4czu56y
Also, a straightedge and compass would create some awfully stiff stick figures. I don’t think you could create convincingly xkcd-like stick figures with a compass and straightedge >:(
March 11th, 2011
Not if they could move.
March 12th, 2011
Just a note that the last sentence of the explanation can be read two ways, one of which is wrong. The way I read the explanation first is that it says pi is not a transcendental number. Pi is a transcendental number, which means that it is not the root of any polynomial with rational coefficients.
April 10th, 2011
One thing that may have been over looked is the possible self-deprecation in the comic. The artist’s comics contain mostly circles and lines, which are the objects made with a straigtedge and compass. He may br saying it has gained him no friends…
April 13th, 2011
I think the explanation misses the bulk of the joke’s background. Trisecting an arbitrary angle and doubling the cube were proven impossible around 1840. The same methods proved squaring the circle impossible under the extremely plausible assumption that pi is transcendental. However, this wasn’t proven until decades later with Lindemann’s 1882 result, which then completed the earlier impossibility proof. That is, Lindemann’s result was essential in proving the impossibility of a certain compass and ruler construction, mirroring the impossibility of “constructing friends” for his birthday party in the same year. If I were to guess, I doubt Lindemann’s main intent was to complete the impossibility result, but oh well.
My inner mathematician has to make three remarks:
0. “Transcendental” here means “not a root of a finite length polynomial with integer coefficients”; “algebraic” is the opposite, like sqrt(2) or i.
1. Lindemann’s result is significantly stronger than just showing that pi is transcendental. It actually says that e^a for a algebraic is transcendental whenever a is not 0; plug in a=pi*i to get the result that pi must not be algebraic.
2. Weierstrass generalized Lindemann’s result in 1885. It says that if {a1, …, an} are linearly independent over the rationals, then {e^a1, …, e^an} are algebraically independent over the rationals–no finite polynomial in n variables and with rational coefficients has (e^a1, …, e^an) as a root.
3. A slightly weaker assumption that pi is not a root of any irreducible rational polynomial of degree a power of 2 would have sufficed instead of Lindemann’s result, though his result is of interest in itself.
December 6th, 2011
not because you want to do too much exaggerated to cover up defects the so-called overkill,mens uggs what should be just right, but not too far.