April 25, 2012 2:57 PM Subscribe

I'd really love a detailed explanation of the terms and humor in this math / science related XKCD cartoon.

I know it's probably a tall order, but hey, never hurts to ask! I'd love to have a basic summary of each of these terms and concepts, and why the "punch" in the right column is funny / specific to the concept.

Here it is.
posted by lazaruslong to Education (14 answers total) 9 users marked this as a favorite

I know it's probably a tall order, but hey, never hurts to ask! I'd love to have a basic summary of each of these terms and concepts, and why the "punch" in the right column is funny / specific to the concept.

Here it is.

Just plug the terms into Wikipedia. Are there any whose entries there don't make sense?

The middle and right columns aren't funny or specific to the left hand column entries except for the fine structure constant. The reference is explained in the Wikipedia entry.

The chart is just a bunch of silly, coincidental approximations. Another example is that pi seconds (i.e. 3.141... seconds) is a nanocentury to within less than one percent.

posted by jedicus at 3:09 PM on April 25, 2012 [1 favorite]

The middle and right columns aren't funny or specific to the left hand column entries except for the fine structure constant. The reference is explained in the Wikipedia entry.

The chart is just a bunch of silly, coincidental approximations. Another example is that pi seconds (i.e. 3.141... seconds) is a nanocentury to within less than one percent.

posted by jedicus at 3:09 PM on April 25, 2012 [1 favorite]

The overall humor derives from starting with some reasonable and useful approximations for basic physical constants or other common values, and becoming progressively absurd in both what is being approximated and how its being approximated. For instance its probably just easier to remember that Avogadro's number is 6.022 x 10^23 than remember the given approximation.

Another big chunk of the humor derives from basing some of these approximation on pi and e to imply that there is some deep connection between what is being approximated and these fundamental constants. My favorite in this category is "Jenny's Constant", which works out to approximately 867.53090198... (similar to the famous Tommy Tutone song "867-5309/Jenny").

That most of these are actually somewhat accurate, as shown by the third column of the table is just coincidental or more accurately, contrived to be accurate without really implying the connection that the approximation seems to make.

posted by Reverend John at 3:11 PM on April 25, 2012 [7 favorites]

Another big chunk of the humor derives from basing some of these approximation on pi and e to imply that there is some deep connection between what is being approximated and these fundamental constants. My favorite in this category is "Jenny's Constant", which works out to approximately 867.53090198... (similar to the famous Tommy Tutone song "867-5309/Jenny").

That most of these are actually somewhat accurate, as shown by the third column of the table is just coincidental or more accurately, contrived to be accurate without really implying the connection that the approximation seems to make.

posted by Reverend John at 3:11 PM on April 25, 2012 [7 favorites]

http://www.explainxkcd.com/2012/04/25/approximations/

posted by man down under at 3:13 PM on April 25, 2012 [3 favorites]

posted by man down under at 3:13 PM on April 25, 2012 [3 favorites]

lazaruslong,

For me, you will henceforth have MeFi user number 2^2 + 6^3 + 7^5.

posted by lukemeister at 3:17 PM on April 25, 2012 [3 favorites]

For me, you will henceforth have MeFi user number 2^2 + 6^3 + 7^5.

posted by lukemeister at 3:17 PM on April 25, 2012 [3 favorites]

Most of the humor here is derived from the fact that in the world of pure mathematics, there is often a "neat" relationship between two things, because there is the same underlying logic at work, whereas in system involving units of meters, feet, pounds, kilograms, etc., almost nothing relates nicely because a "foot" or a "meter" is a completely arbitrary made-up unit. So you end up saying things like "one foot-pound is 1.3558 newton-meters"

So, for example, the number of feet in a meter is given as 5/(pi^(1/e)), which is written as if there is some sort of deep relationship between feet and meters involving the mathematical constants pi and e when in fact no such deeper meaning exists, and the apparent accuracy of the approximation is just due to the fact that with a few constants (pi, e, and phi are I think the only ones he uses) and a large number of operators, plus integer or decimal constants, you can come up with an expression that is a fair approximation to just about anything.

posted by jcreigh at 3:20 PM on April 25, 2012 [3 favorites]

So, for example, the number of feet in a meter is given as 5/(pi^(1/e)), which is written as if there is some sort of deep relationship between feet and meters involving the mathematical constants pi and e when in fact no such deeper meaning exists, and the apparent accuracy of the approximation is just due to the fact that with a few constants (pi, e, and phi are I think the only ones he uses) and a large number of operators, plus integer or decimal constants, you can come up with an expression that is a fair approximation to just about anything.

posted by jcreigh at 3:20 PM on April 25, 2012 [3 favorites]

For instance, Euler's identity.

Think of the cartoon as the pure-maths equivalent of "dude, don't you see -- it's

posted by holgate at 3:26 PM on April 25, 2012 [1 favorite]

jcreigh has it spot on. It is sort of a parody of the quick reference physical constants and equations table likely to appear on the back page of any science textbook, in which there are inevitably all kinds of constants and equations defined in terms of one another; convoluted formulae involving e and pi are common. There is inevitably a physical/mathematical explanation to these formulae but the poor student has to accept it on faith until they have learned the material inside out. When your eyes are glazed over, it seems perfectly plausible that the fundamental charge is 3/(14*pi^pi^pi); why not?

posted by PercussivePaul at 3:29 PM on April 25, 2012 [4 favorites]

posted by PercussivePaul at 3:29 PM on April 25, 2012 [4 favorites]

And missed the most useful one of all (which was perhaps the point): π^{2}=10, for smallish values of ten.

posted by scruss at 4:08 PM on April 25, 2012 [1 favorite]

posted by scruss at 4:08 PM on April 25, 2012 [1 favorite]

What jcreigh said is a good explanation. As a physicist who works with a lot of these numbers, I started laughing at the cartoon because of what Reverend John said - normally you want an approximation to be something easy to remember, but a lot of these are hard to remember so it seems absurd.

For example, I learned in undergrad physics that the number of seconds in a year is approximately pi times ten to the seven= (60 seconds in a minute times 60 minutes in an hour times 24 hours in a day times 365 days in a year = 31,536,000 seconds per year), which is pretty easy to remember. Where as the xkcd suggestion of 75 to the four somehow seems less easy to remember. And why even bother to memorize something when multiplying 60 times 60 times 24 times 365 is so easy?

Even more ridiculous, in first year physics we use the gravitational acceleration at the surface of the earth, g=9.8 meters per second squared. The suggested xkcd approximation? 6 + ln(45), which is way harder to remember.

posted by medusa at 5:22 PM on April 25, 2012

For example, I learned in undergrad physics that the number of seconds in a year is approximately pi times ten to the seven= (60 seconds in a minute times 60 minutes in an hour times 24 hours in a day times 365 days in a year = 31,536,000 seconds per year), which is pretty easy to remember. Where as the xkcd suggestion of 75 to the four somehow seems less easy to remember. And why even bother to memorize something when multiplying 60 times 60 times 24 times 365 is so easy?

Even more ridiculous, in first year physics we use the gravitational acceleration at the surface of the earth, g=9.8 meters per second squared. The suggested xkcd approximation? 6 + ln(45), which is way harder to remember.

posted by medusa at 5:22 PM on April 25, 2012

Everyone above has excellent explanations. I laughed a lot, because I've seen and referred to such tables a thousand times. I'll add that the part that would troll a teacher would be using one of these on a homework assignment and somehow getting the right answer. "They're supposed to be calculating the number of molecules they got at the end of this synthesis--where'd pi come in, and *how the hell did they get the right answer anyhow*?" Pi doesn't have anything to do with chemical equations, normally, you see.

It's like saying "I was wondering how many steps it would take to walk two city blocks, so I weighed myself and multiplied that number by the number of kings of England named Henry," and getting the right answer.

posted by tchemgrrl at 6:27 PM on April 25, 2012 [1 favorite]

It's like saying "I was wondering how many steps it would take to walk two city blocks, so I weighed myself and multiplied that number by the number of kings of England named Henry," and getting the right answer.

posted by tchemgrrl at 6:27 PM on April 25, 2012 [1 favorite]

XKCD referenced a similar idea in one of the earlier strips:

http://xkcd.com/217/

posted by scose at 7:00 PM on April 25, 2012

http://xkcd.com/217/

posted by scose at 7:00 PM on April 25, 2012

Thanks, everyone. I'm not fluent enough in the language to have gotten the humorous juxtaposition of hard math and arbitrary assignations, and also didn't pick up on the humorous implication that these coincidental relationships could be used to convey a "duuuuuuuude it's all connected" sense either.

I really appreciate it, y'all! I'm gonna spend some time reading about the actual terms.

posted by lazaruslong at 6:32 AM on April 26, 2012

I really appreciate it, y'all! I'm gonna spend some time reading about the actual terms.

posted by lazaruslong at 6:32 AM on April 26, 2012

This thread is closed to new comments.

posted by Blazecock Pileon at 3:07 PM on April 25, 2012 [3 favorites]