When I travel by airplane, I prefer to start my trip on foot, rather than car. There's an air of wonder about traveling when you step from your front porch, belongings in hand, headed for a destination thousands of miles away. When you do it by car, invariably encountering traffic, the whole affair feels like an inefficient commute. My trips usually involve walking just over a mile to the light-rail, taking the light rail about 10 miles to the airport, then getting on the plane. As I was sitting on the train today, it occurred to me that the first leg of my trip is at a velocity of about 3 miles per hour (if I'm taking it leisurely). Then, on the train, it's about 40 miles per hour, and finally, on the airplane, it's over 600 miles per hour. If I took a whole trip to the Coast on foot (as Louis and Clarke did), it would take months. Who needs jetpacks?
Speaking of crypto treasure-hunts and math circles...I just found these educational materials from the NSA. There are dozens of lesson plans for topics ranging from probability to geometry. They're very complete, including clear instructions for the teacher (or parent, or math circle leader for that matter), and nice activities to print out for the students.
Between this, Wolfram's recent re-dedication to K-12 education, and KenKen, this has been a fruitful month for me in the math education quest.
I was surprised to hear Audra wanted "codebreaking" to be the theme of her party this year. Maybe she missed math circle, or maybe there's cryptography in the air, maybe she knew it would bring Dad even more into the party preparation than normal (last year's Pirate Party was also
Codebreaking is pretty abstract, so I knew we'd need something to drive the activity. Treasure hunts are always fun (for parents and kids), so that seemed a natural combination. Over the days before the party, I thought of the collection of codes and activities we could put together. I knew it would be great to send kids home with something to remember the party by, so I designed a "secret agent ID badge", and a "Top Secret Code Breakers Manual". [pdf link]
Sally Browning, one of my friends and colleagues at Galois, had prepared a codebreaking tutorial for some visiting middle-schoolers, and as part of that, she prepared a "scytale" (sounds like s + "Italy") activity - a bunch of dowels with different diameters, with ribbons to wrap around. Heidi had found a simple substitution cypher for the invitation (some of our great attendees replied in code -- I love it!) And from there, I pretty much had a template for the activity.
The party started at 1:00. I started working on the final treasure hunt at 8 AM that morning. I finished just in time (!). All told, I think I spent 8 hours working on the treasure hunt activities. As often as possible, I tried to make the activities parallelizable among the 10 guests...this worked mostly, and it was definitely obvious when there was a one-person bottleneck to an activity.
Heidi and I agreed that we'd try to keep the tenor of help provided along the lines of "math circle", which is pretty much hands-off, but perhaps with a few Socratic questions thrown in to accelerate things if needed.
Here's the sequence of the treasure hunt:
Audra took a photo of each guest as they arrived.
- We put out puzzles and thinking-activities from our "games and puzzles drawer out for people to play with as the party gathered. We also left out a set of the "code books".
- When everyone assembled, we said "instead of a cake, all we have here is this empty-feeling box". Inside the box were two ribbons with letters on them. The kids figured out that dowels would be needed, and thought of wrapping the ribbons around chair legs or other cylinders around the house...not noticing the pile of 10 dowels against a wall. Eventually, the dowels were discovered, and one ribbon got decoded on the first try -- what are the odds? It took a lot more work to decode the second ribbon. Between the two ribbons, the message was "I have hidden your stuff in a secret location. You will find help where les oeufs are produced." The two French dictionaries were sitting next to where the empty box started ended up helping out. "The Chicken coop!" and they were off.
- Inside the coop was a plastic egg with two smaller eggs nested. In that was a tiny USB thumb drive. I created a bunch of directories (A-Z) and a "readme.txt". The file said "Look in directory "D" for the next clue". Inside directory D were another set of directories A-Z, and a readme.txt that said "What "are" you looking for". Inside directory "R" was another readme.txt: "what are "you" looking for, again?". Inside directory "U" were more directories, and a readme.txt: "mmmmmmmmmmm...I love cake." Finally, inside directory "M" was a file that said "you've found the right place."
- The innermost directory (note the path was "D/R/U/M") had a text file with morse code spelling out "The next clue is hidden inside an instrument you hit with your hands." as well as an .mp3 file with morse code spelling out "DRUM". I used this web site to generate the two files. The cryptographers broke into two groups, one group tried to decode the audio, the other asked me to print out the morse code for them to decode. Even though I slowed the morse code audio way down, that team finally switched to decoding the text as well. Nobody noticed the path spelled out DRUM. Interesting!
- Inside the drum was an envelope with a bunch of slips of paper in the original transposition code (I wrote a python program to generate this... see the bottom of this post). I wanted to allow this task to be parallelized, so I wanted to chop up the message into bits, and then added numbers so they'd know which order they went in. The slips decoded to the text "ONE LOOK", "TWO UNDER", "THREE THE THING", "FOUR THAT HANGS", "FIVE ON ROPE", "SIX FROM A", "SEVEN TREE AND", "EIGHT CHILDREN", "NINE PLAY ON", "TEN FOR FUN". They quite quickly decoded the individual strips, but had a dickens of a time figuring out the ordering of the slips. They were thinking the numbers were another level of code, or were part of the message, or formed a more complex pattern (like 2 4 6 8 ...). Finally, they got them all on the floor at once, and with a little Socratic questioning help, they figured it out. "The Swing!"
- Under the swing was an envelope with what caused the funniest moment of the party (for me, anyway). I wrote "Hermione shows up with fancy hair and a dress." With no time at all, the rushed into the house, grabbed the single volume (book four) of the Harry Potter series, and took about 30 seconds to find the right chapter. On that page was another slip of paper, this time with another book title, and a math problem (110 * 3 - 10). And so on for eight books. The last slip of paper was in an art book, on the page about Miro. They discarded the book before noticing the slip of paper said "look behind a painting that looks like this one." They dug it back out, found the page, and behind the painting was another envelope, holding a paper saying "four legs eats here".
-
"Cat bowl!" Under the cat bowl were two more scytale ribbons "Oh, no, not more?!?!". They were getting hungry for cake. The scytale ribbons had a little-bit-too obscure clue (I think I was getting tired at this point in the puzzle-making process): Ribbon one: "Your next clue is hidden inside a musical instrument on the West wall of the house" and "If you go to Hawaii you will hear my strings". It took way too long to find the Ukelele on the West wall of the house. I was busy upstairs laminating the ID cards, but heard the excitement of finding a slip of paper with the URL http://www.mecodegoodsomeday.com/secretCode. Heidi says she had to help them with the typing - theirs was too error-prone to get it right.
- They recognized bits of the car, and my car-key's bike-chain keyring. They finally found the cake in the trunk...but no goodie bags! Fortunately, the icing had morse code ("Not again!") that said "look under the bed" which is where they found their goodie bags.
Heidi heard more than one guest say "this is the best birthday party ever!" which blew me away, but totally reinforced the theme of a book I've been reading (
A Theory of Fun for Game Design, by Ralph Koster), which is that real "Fun" comes from the excitement of actually learning something new.
All told, it took 2.5 hours to solve the clues, and they just got to the cake as parents arrived to pick them up. It was an exhausting, but very rewarding, party.
As an aside, here's the shell script I used to create the maze-on-thumbdrive (watch out - it's slow, and the result takes up a lot of space!):
#!/bin/sh
export digits="A B C D E F G H I J K L M N O P Q R S T U V W X Y Z"
for i in $digits; do
mkdir $i
cd $i
cp /tmp/readme.txt .
for j in $digits; do
mkdir $j
cd $j
cp /tmp/readme.txt .
for k in $digits; do
mkdir $k
cd $k
cp /tmp/readme.txt .
for l in $digits; do
mkdir $l
cd $l
cp /tmp/readme.txt .
cd ..
done
cd ..
done
cd ..
done
cd ..
done
It's a common thing for folks to say "hey, it's 2009 fergoshsakes, where's my jetpack?" And to some degree, I agree. However, I think we take a lot of amazing stuff for granted. The Internet, for example, has evolved into a knowledge and collaboration source that I think exceeds most folks' wildest dreams (mine, anyway). And modern air travel is a marvel, etc, etc.
Back when I was a kid, flying on a plane was really a treat, and airports felt...really felt...like space ports. Today, it's much more of a mundane thing. However, the joy, exuberance and amazement that I felt as a child when getting on a big jet plane has never completely left me. I really relate to Louis CK's bit here on Conan (10/1/2008) - I think the folks who truly do take this stuff for granted are missing something big -- are somehow less than fully awake or alive.
Concretely, last Wednesday (beginning of March, 2009), my family and I returned from a vacation to Baja, California for a week. I'd never been to Baja, but was blown away. Friendly people, wonderful food, an amazing climate, and the wildlife! Watching pelicans dive for fish in the afternoons and evenings blew me away. We returned to Portland in Winter. It has snowed three times since returning, and just today, I took a wonderful bike ride up into Portland's West hills, riding upwards into snow, then riding through thicker snow, then hail, then sleet. When I got back, I was so cold that it took three hours to warm back up.
Here's where I was last Wednesday, and this morning:
I'm happy to be alive at a time when such juxtapositions are possible.
Galois moved downtown last week. I love it! Our new space is gorgeous, and conducive to both concentration and collaboration. Downtown is just so alive...it's invigorating.
On the trivial side of things, this sign is outside our window, and it's made me think...
Am I alone in parsing this sign as saying "Think Bank, Big Smart"? Maybe this was intentional: I kind of like it - bad translations from, say, Japanese are hip, edgy even. Is this what U.S. Bank had in mind? Nahh, that's over-thinking it...it's probably just incompetent design.
In the past few months, the seriousness of my "coffee hobby" has escalated. I bought a coffee roaster, a "Gene Cafe," and I installed a PID-controller, which is a computer-controlled thermostat. While I don't think that everyone I know should follow these footsteps, I certainly am getting mighty-fine coffee out of my setup.
A couple weeks ago, Heidi and I collaborated with our friend and neighbor David Griswold, founder of Sustainable Harvest coffee company, on an auction item for our children's school, Sunnyside Environmental. We hosted a coffee seminar: David described the origins of coffee, growing, harvesting, processing and importing. Heidi lead a cupping of coffee's from around the world, as well as a comparison of different roasts. Finally, I described brewing techniques, culminating in making espresso drinks for everyone. It was a blast.
Sometime soon I'll add photos of my PID controller and roaster at work...
Simplify Media is a tool that lets you listen to your home iTunes library from work (my "killer app") and it also lets you choose up to 30 people to share with as well.
You might think the RIAA will be all over these guys to shut it down, but they've done a couple clever things that I think will keep the RIAA at bay (even though I think it's going the way of the dinosaur soon anyway): first, the music is only streamed to your friends, they can't copy the files via the tool. Second, the 30-person-limit keeps you from sharing all of your music with everybody in the world (a-la Napster).
One concern I have is that it will saturate the uplink direction of my DSL connection if multiple people are listening to my library at once. Hopefully, someday, DSL bandwidth in the U.S. will start improving past 1.5MB/s, as it has done everywhere else in the world.
It makes me happy because this was the feature of TrueDisk* that I missed the most. It's also heartening because Simplify Media has a better interface than TrueDisk had, and it's a free service -- they're having "issues" with their business model, just as we were at TrueDisk.
* TrueDisk was a startup I spent an exciting three years working on with a great group of people...
I grew up admiring David Byrne and Brian Eno. From the great music they've made to the incisive social commentary to being consistently ahead of the curve in both technology and cultural trends (the good ones).
I found the audio clips attached to this Wired article charming -- you get to listen in on a casual lunch between them. This both brought them down from the stratosphere in terms of approachability, as well as bolstered my preconception that their signal-to-noise ration is higher than 99% of us achieve.
Great stuff. See the sidebar 1/3rd down, titled "David Byrne in Conversation with Brian Eno"
Oh, and it's not news, but I'm ever more convinced after listening to these guys that record companies, as we know them, are doomed.
It's been too long since I updated the blog with math circle news...quite a lot has happened:
Binary arithmetic
We did two days on binary numbers. Five students sat at the front of the room, each holding a card with dots. From the right, moving left, the first card had one dot, the second two dots, the third four dots, and so on.
I asked the students how to make the number Ten by selecting cards. I told them that the new way to say the number Ten was to name the students who were holding up cards. To make things clear, we said the names from left to right, and if a card was being left out, we said "blank" instead of the name.
We named a bunch of numbers in English, and translated them to "math circle-ese". This was great.
We then took turns adding one to different numbers, which was also great. Then we ran out of time.
The next week, a few students showed up who hadn't been there the week before, so we reviewed the activity, then we moved on to adding two different binary numbers. The big trick here is carrying, but quite a few students got it. Unfortunately, I think we went too fast for some, and I wasn't able to take the time to bring them back into the fold.
Probability
The next week I brought two dice for each student, and sheets of paper with number grids from 1-6 and 2-12. We all rolled first one die, then two dice, filling in a square each time a number (or sum) was rolled. I was amazed at the distributions. Finally we all reported our 2-12 sums to the front of the room and added those up. 8 won by a landslide, but 7 & 6 came in 2nd and 3rd. Interesting! Everybody enjoyed the activity, but I think the summing felt "forced", so the learning wasn't as effective. This could have easily been spread out over two or three sessions with lots of discussion and less dice-rolling.
Snowflakes
The next week we made paper snowflakes, and discussed the math of the activity. We talked about reflection, as well as "how many diamonds will my snowflake have if I fold my paper X many times and cut one diamond?" Some of the students delighted in the fact that this pattern brought back our binary numbers (woohoo!). If we had more time, and enthusiasm, it would have been good to bring everybody along for this, but the energy in the room was very scattered.
Code
Finally, yesterday I brought in a code (with key) for the students to decode. This was wonderful. The energy was subdued but interested. (Interestingly, a number of the students proposed they read instead of do math circle. I said that's fine, please do it at a table behind the others. Very quickly that whole table was engrossed in decoding the message. Neat!) Once the students finished this, I suggested they encode messages, and a number of them wrote long messages and handed them to me to decode. I showed them a quick way of decoding using a tree (left is ".", right is "-"). None of them thought it was faster (hmmmm.) I was flattered by the messages they sent me. Thanks! :) I finally told them this was Morse code, but not before Madi called it "binary code". Cool.
What's next?
I'm going to ask the parents to send me frank evaluations of what went well, and what didn't (both from their perspective and to ask the students). I'm planning on doing something in the Winter or at least by Spring, but it won't be exactly the same. I'd like to have fewer students per group, but figure out how to do multiple groups. So my work moving forward will probably be more volunteer coordination than direct student interaction. This is both sad and happy for me (less directly fun, but more impact).
We've had two more math circle sessions, and I (at least) enjoyed both of them quite a bit. The second session (which was really the first official session), I slightly repurposed an activity from "computer science unplugged". We took turns being, and then programming, "Drawbots". Initially we started with blank paper, and had the drawbot face away from the whiteboard, and the programmers face toward the whiteboard (but sitting on their hands). Then I drew various figures on the board, and the programmers described to the drawbots how to reproduce the figures using only words.
It was a hoot. I started with simple drawings: a rectangle with an inset square with an inset circle, and similar arrangements. Then (warning them I was doing to do something difficult), I drew two parallel wavy lines. Hilarity and mayhem ensued. One student was so frustrated, she started to cry. I assured them all that mistakes and frustration were the point of the exercise - that made her smile and she quickly recovered. (whew!)
Next I brought out some numbered graph paper, and had them draw points at specific coordinates and connect the dots to draw shapes. We did a triangle, then a simple face. I made a mistake transcribing the numbers to the whiteboard, which cracked the kids up.
The following Monday, as Heidi was dropping Audra off to class, a number of parents said how much fun their child had in Math Circle, and how they were disappointed there was no homework over the weekend. (woohoo!) So I drew one up and sent it out. As part of it, I wrote a program that plotted the homework to make sure I didn't make any mistakes (actually, so I knew where the mistakes were).
There was a week off, followed by this most recent meeting on Nov. 2nd. I decided to finally do some non-robot, mathlike exercises. I read the activity name "function machine" in the math circles book by Bob and Ellen Kaplan, and decided to design what it would be myself: I brought some empty cereal boxes and cut slots in them, and labeled one "input", the other "output". Once the group had settled down, I told them that this "number machine" took slips of paper with numbers on them, did something to the paper, and spits it out the output slot.
I started by being f(x)=x+2, then f(x)=2x. It was hilarious! The kids were really excited at first just to go through the process, shortly after when they realized the output was related to the input, and finally when they figured out the relationship between the input and the output. Next I tried f(x)=x/2. I knew I was out on a limb with this one...I got a 2, a 4, a 3 (1 1/2!), and at 10, everyone guessed correctly using different language than I'd have guessed - "Takes away half!"
Then we broke into groups of 4 or fewer, each with a parent volunteer (thanks!!). They first decorated their own number machines (this was a good break in the pace), then took turns being functions. The kids did great. It was amazing to see the excitement when they thought they had the answer, and sent in a number to test their hypothesis. When it was my turn, I did f(x) = 2x+1, and they were vexed. I could tell when they were frustrated with something when the numbers I got were over 20. 10,000 isn't going to tell you much about a number machine's function that 0 or 5 wouldn't. At that point, I suggested thinking about what a "doubler" machine would return. After four more tries, one girl got it, and was thrilled when she turned out to be right. I hope that wasn't too much of a hint. Given the chaos of the moment, I don't think a subtler hint would have gotten through.
For homework, I'm going to try doing some number machine activities around the breakfast routine for a while. Colin (our 4-year-old) likes participating just to see the machine do things. Generally his numbers have four or more digits. Awww.
Anyway, this has turned out to be a wonderful experience for me -- all of the kids seem to truly light up. I've got two weeks to come up with a good follow-on activity.
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Gromita said:
[this is good]=)is that the code that was on your computer's keyboard...?hugs read more
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Charles Pergiel said:
Or maybe it was some subversive in the art department surreptitiously thumbing his nose at "The Man". read more
on Is it just my weird brain...
What a Wonderful birthday party=)codebreaking rocks!!! read more
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