# There's definitely a method to my madness. Definitely.

December 19, 2007 7:37 AM Subscribe

Lightning calculator and "mathemagician" Art Benjamin goes through his paces in a 15 minute video.

(Though obviously he's a lot faster than that. Also, I only use tricks that are spatio-visual, because that's how I do math. Special tricks for certain numbers are not my "thing".)

posted by DU at 7:51 AM on December 19, 2007

posted by DU at 7:51 AM on December 19, 2007

Does he do square roots? "Mental square roots" was my workhorse party trick when I was in college. And if you don't think that's a good party trick

posted by escabeche at 8:01 AM on December 19, 2007 [3 favorites]

*you are going to the wrong parties.*posted by escabeche at 8:01 AM on December 19, 2007 [3 favorites]

Gah! I am math deficient and this kind of thing might as well be magic to me.

posted by Baby_Balrog at 8:02 AM on December 19, 2007

posted by Baby_Balrog at 8:02 AM on December 19, 2007

*Gah! I am math deficient and this kind of thing might as well be magic to me.*

At that speed, it's magic to anybody. The only thing that made sense (on first viewing, anyway) was his three parts. If you draw a square as a literal square on graph paper, you'll see why the binomial theorem works: (a +b)

^{2}= a

^{2}+ b

^{2}+ 2ab.

posted by DU at 8:08 AM on December 19, 2007

Usually he follows this "performance" part with a lecture on the tricks he uses, including a sketch of the mnemonic system he uses to help remember intermediate results. In a small room, he gives the impression of Calvin after a couple boxes of chocolate frosted sugar bombs washed down with extra hfcs. But he does seem to hold onto an audience for 30 minutes talking about arithmetic, and if that ain't magic...

posted by Wolfdog at 8:10 AM on December 19, 2007 [1 favorite]

posted by Wolfdog at 8:10 AM on December 19, 2007 [1 favorite]

Oh hey, here is like 1.5 hours of him, I assume explaining the tricks in detail.

posted by DU at 8:15 AM on December 19, 2007 [1 favorite]

posted by DU at 8:15 AM on December 19, 2007 [1 favorite]

That 5 digit square thing at the end is frankly amazing, not so much for the outcome as for the peek into his highly anomalous brain.

posted by The Bellman at 8:29 AM on December 19, 2007

posted by The Bellman at 8:29 AM on December 19, 2007

Bonus points for the Rainman reference. If that's what that was. If not, carry on.

posted by empyrean at 8:51 AM on December 19, 2007

posted by empyrean at 8:51 AM on December 19, 2007

*the peek into his highly anomalous brain*

My impression it is simply a skill he has learned, and not a "rain man". I know the Chinese have schools that teach kids to do stuff like this. First they learn on an abacus, then they learn to move a "ghost abacus", then they learn to do it all in their head. They get nearly the same results as autistic savants.

posted by stbalbach at 9:09 AM on December 19, 2007

Bart: Hey, Houdini! Why don't you saw Martin in half?

Magician: Oh, I'm not the kind of magician who does tricks. I'm a mathemagician!

[Kids groan]

Magician: Now, prepare to marvel at the mysteries of the universe, as I make this remainder disappear. [writes 7 goes into 28 three times]

Lisa: But 7 goes into 28 four times.

Magician: Uh, this is a magic 7.

posted by Astro Zombie at 9:41 AM on December 19, 2007 [1 favorite]

Magician: Oh, I'm not the kind of magician who does tricks. I'm a mathemagician!

[Kids groan]

Magician: Now, prepare to marvel at the mysteries of the universe, as I make this remainder disappear. [writes 7 goes into 28 three times]

Lisa: But 7 goes into 28 four times.

Magician: Uh, this is a magic 7.

posted by Astro Zombie at 9:41 AM on December 19, 2007 [1 favorite]

Amazing. The Rainman reference is at 13:01. Definitely. Definitely.

I linked to a couple of similar minds here. Daniel Tammet holds the record for memorizing the digits of pi, and Kim Peek (speaking of a peek into a brain) is the original Rainman. He was born without a corpus callosum to connect his left and right cerebral hemispheres, so he reads books two pages at a time (left eye left page, right eye right page), remembering about 98 percent of the info. I don't think we realize the extent to which "normal" people process huge amounts of information, except we do it mostly with sensual impressions and images rather than numbers and facts. Kim Peek can't function well in this "normal" sense.

posted by weapons-grade pandemonium at 9:49 AM on December 19, 2007

I linked to a couple of similar minds here. Daniel Tammet holds the record for memorizing the digits of pi, and Kim Peek (speaking of a peek into a brain) is the original Rainman. He was born without a corpus callosum to connect his left and right cerebral hemispheres, so he reads books two pages at a time (left eye left page, right eye right page), remembering about 98 percent of the info. I don't think we realize the extent to which "normal" people process huge amounts of information, except we do it mostly with sensual impressions and images rather than numbers and facts. Kim Peek can't function well in this "normal" sense.

posted by weapons-grade pandemonium at 9:49 AM on December 19, 2007

Except they aren't similar. Art himself explicitly says he's not a Rainman-type, it's just a bunch of tricks done at lightning speed. The amazing part is NOT that the bear can dance at all, the amazing part is how well he dances.

It's like a juggler who's spent years honing his craft--almost anybody could do it, if they were willing to invest the enormous time practicing. A little inclination and a lot of perspiration.

posted by DU at 9:57 AM on December 19, 2007

It's like a juggler who's spent years honing his craft--almost anybody could do it, if they were willing to invest the enormous time practicing. A little inclination and a lot of perspiration.

posted by DU at 9:57 AM on December 19, 2007

If he's so smart, why is he wearing that ridiculous outfit? HMMM?

The whole point is that it's

posted by delmoi at 10:08 AM on December 19, 2007

*That 5 digit square thing at the end is frankly amazing, not so much for the outcome as for the peek into his highly anomalous brain.*The whole point is that it's

*not*an anomalous brain. Normal people (well, normal smart people) can do this if they just practice enough. It's just not that useful anymore now that we have calculators and computers.posted by delmoi at 10:08 AM on December 19, 2007

*It's just not that useful anymore now that we have calculators and computers.*

Not for your average Joe, but it's very, very useful for calculations that don't even belong on the back of an envelope.

Also, I just realized that 17

^{2}is

**much**more amenable to being expressed as 10

^{2}+ 140 + 49. And it only took me 5.5 hours to figure that out!

/me gets invited to showcase "slow math".

posted by DU at 10:17 AM on December 19, 2007

We just discovered my son who is six can do the date-day thing for years between 2000 and 2010 so accurately that I don't check behind him half the time anymore. In the 80s, 90s, 10s and 20s he is right about three quarters of the time. When he is wrong it is by a day and his accuracy with those is improving. I was thinking that he has a programmer's head, but now I see a new career path....... mathemagician!!!

posted by spartacusroosevelt at 10:50 AM on December 19, 2007

posted by spartacusroosevelt at 10:50 AM on December 19, 2007

Doesn't everyone know the squares of one- and two-digit numbers?

posted by king walnut at 10:50 AM on December 19, 2007

posted by king walnut at 10:50 AM on December 19, 2007

Art Benjamin is also a professor at Harvey Mudd College and when I was there he applied his math skills to "recreational" endeavors as well. Not someone I would want to compete against in any game of chance!

posted by bgribble at 11:30 AM on December 19, 2007

posted by bgribble at 11:30 AM on December 19, 2007

Here's how to do the squares of numbers ending in 5 (ok, I only checked this for the first 10 or so, I'm sure someone will point out if it breaks down on larger numbers):

Take the number you would have if you removed the last 5, and multiply it by 1 more than itself. Then append 25 to the end of the number.

Example: 25 squared = 2 (the number without the 5) times 3 (one more than the number) =6 and then append 25, so 625. (25x25=625).

Example 2: 75x75 = 7*8 + "25" = 5625

Easy, right?

posted by Crash at 11:35 AM on December 19, 2007

Take the number you would have if you removed the last 5, and multiply it by 1 more than itself. Then append 25 to the end of the number.

Example: 25 squared = 2 (the number without the 5) times 3 (one more than the number) =6 and then append 25, so 625. (25x25=625).

Example 2: 75x75 = 7*8 + "25" = 5625

Easy, right?

posted by Crash at 11:35 AM on December 19, 2007

That was awesome. I thought, when he was moving his arms as people told him numbers, that he was using a spatial mnemonic. I used to do that, using a "memory house" and objects within it. It allowed me to get good grades on lots of tests where memory of facts was necessary, but it broke down when it came to things like art history classes.

posted by sonic meat machine at 11:40 AM on December 19, 2007

posted by sonic meat machine at 11:40 AM on December 19, 2007

Nice one, Crash. It works for all numbers ending in 5.

(Explanation/proof: These can all be written as 10k+5, and k is the 'number you would have if you removed the last 5'. Multiplying that by 'one more than it' gives k

posted by gleuschk at 11:51 AM on December 19, 2007

(Explanation/proof: These can all be written as 10k+5, and k is the 'number you would have if you removed the last 5'. Multiplying that by 'one more than it' gives k

^{2}+k. Appending 25 to a number effectively multiplies it by 100 to get the 1s and 10s places free, then adds 25, so we end up with 100k^{2}+ 100k + 25, which is the same as (10k+5)^{2}.)posted by gleuschk at 11:51 AM on December 19, 2007

A quick shout-out to all the Mudders in the house! I know you're out there...

posted by lalas at 11:57 AM on December 19, 2007

posted by lalas at 11:57 AM on December 19, 2007

My favourite bit is how he does 683^2:

683^2 = 700 * 666 + 17^2

Which is quite a useful little trick.

How the hell he does 700 * 666 so quickly I have no idea.

posted by snoktruix at 12:28 PM on December 19, 2007

683^2 = 700 * 666 + 17^2

Which is quite a useful little trick.

How the hell he does 700 * 666 so quickly I have no idea.

posted by snoktruix at 12:28 PM on December 19, 2007

I'm not super-fantastic at rapid mental arithmetic, but one thing I do that seems to help is allow myself some nonstandard representations of numbers (like "eighty-twelve" instead of ninety-two) in intermediate steps and then sort out the carries at the end.

posted by Wolfdog at 12:31 PM on December 19, 2007

posted by Wolfdog at 12:31 PM on December 19, 2007

I'm only disappointed that Feynman recognized 1728 as the number of cubic inches in a cubic foot, but not 1729 as the number of Hardy's cab.

posted by mr vino at 12:49 PM on December 19, 2007

posted by mr vino at 12:49 PM on December 19, 2007

*How the hell he does 700 * 666 so quickly I have no idea.*

I'd think the fastest way would be to regroup it as 100*111*42; multiplying by 111 is just 4200 + 420 + 42 = 4662 and multiplying by 100 yields 466200. Did I do that right? It seems not in the spirit of the thing to check. Oh, and surely he knows small squares like 17^2 = 289 by heart.

posted by escabeche at 1:14 PM on December 19, 2007

I might have done better in Mudd math classes if all that was required was to watch Prof. Benjamin do sweet tricks. :)

posted by adamk at 4:36 PM on December 19, 2007

posted by adamk at 4:36 PM on December 19, 2007

I thought he was going to be a superhero who liked Art. I momentarily forgot that Art is a first name.

I was wondering if perhaps his sidekick was Math James, or Music Doug.

posted by blacklite at 11:39 PM on December 19, 2007 [1 favorite]

I was wondering if perhaps his sidekick was Math James, or Music Doug.

posted by blacklite at 11:39 PM on December 19, 2007 [1 favorite]

Actually, he does 700 * 666 by reading (and calculating) from left to right rather than the standard right to left. The advantage to this is that he can start saying the answer before he has it completely figured out!

He says to himself, "Seven times six is fourty-two, so I've got three fourty-twos lined up, add the two and the four, the two and the four, and I get 4664, and then put on two zeros to get 466400." While this is going on, he's saying (or writing) the answer one digit at a time, quite rapidly.

(I saw this happen at one of his lectures, and he explained it to me afterwards. It's also in one of his books.)

Art Benjamin has his own website, too: http://www.math.hmc.edu/faculty/benjamin/

posted by math at 11:19 AM on December 20, 2007

He says to himself, "Seven times six is fourty-two, so I've got three fourty-twos lined up, add the two and the four, the two and the four, and I get 4664, and then put on two zeros to get 466400." While this is going on, he's saying (or writing) the answer one digit at a time, quite rapidly.

(I saw this happen at one of his lectures, and he explained it to me afterwards. It's also in one of his books.)

Art Benjamin has his own website, too: http://www.math.hmc.edu/faculty/benjamin/

posted by math at 11:19 AM on December 20, 2007

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posted by DU at 7:49 AM on December 19, 2007 [1 favorite]