## Can You Recognize Random?

December 13th, 2011 by Dan Meyer

Brit Cruise has a mind for math and a talent for filmmaking. This is a net win for math educators and math students alike. We should all be grateful for videos like this one, in particular, through which he’ll either tell you something you don’t know about random numbers or visualize beautifully what you already knew. In under two minutes. I’m impressed by the concision most of all.

He’s been trickling out these videos out every few months. Encourage him to keep up (and speed up) the good work.

on 13 Dec 2011 at 7:07 pm1 Franklin ChenNice! Thanks for sharing this. I’m going to explore his other work.

on 13 Dec 2011 at 8:11 pm2 Frank NoscheseI’ve read the following in a book (though I don’t recall where and my Google-fu isn’t working tonight), but…

***

There is a math teacher (college prof?) who, on the first day of class, splits the class in half. Each student in one half flips a coin 20 (30? 50? 100?) times and writes down the H/T they get. Each student in the other half is has to write down H/T (without using a coin) in order to fool the prof so she can’t tell which students used coins and which students didn’t.

The prof leaves the room while all this flipping is going on. Students collect the papers and mix them up. When the prof returns to the room, she quickly sorts the papers by coin/not coin and the students are ASTOUNDED. How did she know?

***

Which do you think works better…live in person, or video?

on 13 Dec 2011 at 8:42 pm3 Dan MeyerI did that for a few years. It was homework. If your mom’s first name starts with A-M, flip a coin 200 times. Otherwise, fake it. They brought the papers back in and I was able to pick out the fakers pretty well. It was all a bit too magical, though. I wasn’t able to turn it into understanding or an activity or something for the students to

do. I think Brit’s videoteachesthe math better than I did by just gesturing at student papers. So I’d use both. What I’d love now, from Brit or anyone else, is something for students do with that knowledge. Like catch tax cheats or something.BTW. Mr. K brought this up in the comments once [link].on 14 Dec 2011 at 8:40 am4 BritHi Guys,

Thrilled you are interested in this video.

Regarding application of this new knowledge, I’m working on a full length episode on Cryptography at the moment which uses this idea to explain why randomness is the key to strong codes. The uniform distribution makes each “message” equally likely (I compare this to a weak code where you get a very non-uniform distribution and can figure out the original message).

I also think a whole video series on the power of random algorithms would be nice. Even explaining the power of a “random sample” is useful to know.

I should have this up within the month!

Please keep in touch with class feedback if you ever try these videos out in class!

Thank you kindly,

Brit

on 14 Dec 2011 at 8:51 am5 Paul WolfDo you think students have the intuition to make a guess as to which are real and which are fake themselves?

I mean, the reveal as to which are which can come from the people that made them anyways, so you can have the students discuss and argue and all that without even really interjecting your own opinion at all.

on 14 Dec 2011 at 9:02 am6 Paul Wolf*You might have to prod them to justify and all that, so maybe some interjecting might be necessary.

on 14 Dec 2011 at 9:25 am7 Jason DyerQuick, classroom-ready version:

Have them pick a “random” number from 1 to 1000.

Plot the class distribution.

It will (if random) be linearly distributed, but it will instead (due to psychology) be logarithmic.

on 14 Dec 2011 at 2:01 pm8 LLThat is a really interesting way to look at whether the flips are random or not. You would also find that most people will not write 5 heads or 5 tails in a row, but this will almost always happen at least once when you fip a coin 100 times. Another thing to look at is the conditional probabilities: I think you would find that tails is much more likely to follow 2 consecutive heads if a person is writing the list.

on 14 Dec 2011 at 2:11 pm9 Jared DerksenI used this video in my AP Stats class. I feel that it has some flaws. The random mechanism isn’t clear. A little switch, as shown in the video, toggles a light between on and off. But the implication of the string of 1’s and 0’s seems to be that heads you leave the light on and tails you turn it off. Or is the rule: heads you toggle the switch and tails you leave the switch in its current state?

I think the video would be improved it made the connection between heads/tails and on/off more clear.

on 14 Dec 2011 at 7:36 pm10 Bowen KerinsHey, I love this. (Seems like the video could use some pauses or “Act 1 / 2 / 3″ breaks, but those are easily added when playing the video with students.)

We used a similar task to lead off the Park City Math Institute course back in 2007:

http://mathforum.org/pcmi/hstp/sum2007/morning/bowen/day1handout.pdf (top of page 2)

This was a big hit and really needs a lot of flips! (We used 240 flips so we could break it up into chunks like this video does.) Other strategies included counting the number and distribution of “runs” (fake data tends to have more, shorter runs, since how could it come up heads 8 times in a row amirite) and the distribution of heads and tails when the data is grouped (by 2s, 3s, 4s, etc).

The overall course directory (http://mathforum.org/pcmi/hstp/sum2007/morning) includes several groups’ real and fake data, some labeled, some unlabeled.

on 16 Dec 2011 at 12:53 pm11 Carl MalartreThat video is awesome!

I like Mr. K’s idea:

http://blog.mrmeyer.com/?p=6359#comment-258308

What I like in the video is that it focus on 1 and 0, on/off.

I’m trying this story line:

“There’s a new government program to screen people at the airport. A machine is randomly picking one out of two people to be searched on. Some people complain that they are searched on more often than other. Your group is selected to independently prove this. Unfortunately, the only data the airport keep and can share with you is a series of 1 and zeroes.”

By the way, they do that in Mexico. You press a green button, and it’s pseudo-random, but better than nothing. I was looking for a reference and found that article by Keith Devlin:

http://www.maa.org/devlin/devlin_05_02.html

Carl

on 03 Jan 2012 at 5:33 pm12 Stephen CastledenHi,

I like the videos by brit. Interestingly when I first clicked on the link from here to brit’s site there was a strange video (not by brit) on his site, the youtube link is

http://www.youtube.com/watch?feature=player_embedded&v=4jL2f-2vY1Q

I think brit may have removed the link…(hopefully).

It generates an interesting question about mathematics and propaganda…(I am a vexed athiest by the way!!!)

Thanks for all the good work,

Steve.

on 11 Jan 2012 at 8:17 am13 Brit CruiseHi Jared,

Thanks for that point. The video doesn’t explicitly say that heads = 1 and tails = 0 vs heads = toggle, tails = no toggle. I’m about to publish this full chapter and will make that distinction in the voice over.

Good day!

Brit

on 13 Jan 2012 at 12:29 pm14 dy/dan » Blog Archive » Khan Academy Is On Some Kind Of Spending Spree[…] Now Brit Cruise, whose exemplary work with videos and math instruction was featured in these pages a couple of weeks ago. For me, this has all the drama of some kind of skin graft or organ transplant where no one has any […]

on 09 Feb 2012 at 6:54 pm15 Themes | 5 Megapixels[…] are horrible at making random numbers. If you ask students to flip a coin 200 times and record the results, you can tell who cheated or […]

on 22 Nov 2012 at 10:19 pm16 7 Quick Takes (11/23/12)[…] in how one relates to every person one meets, man or woman. — 7 —And, finally, via dy/dan, a nice video on our intuitions about randomness: For more Quick Takes, visit […]