Posts by chris
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My months of self-monitoring

The final month of 2011 was approaching and I was brunching with a friend in Inman Square. We hadn’t seen each other in a couple of weeks, so we spent some time catching up. At some point in the pedestrian conversation, we both remarked on the importance of having health goals. Both of us would be turning thirty in 2012 and wanted one last stab in our twenties to get into peak physical shape. We both had been rock climbing for years, but had recently struggled with a lack of motivation. We needed a game plan. I reached back into my childhood of growing up in the dirty south and latched onto some lessons learned from a rich history of riverboat gamblers–we would need to hedge our bets if this was going to shake out. But how exactly?

I stared blankly at my friend as we sat in awkward silence. A couple of minutes passed and then suddenly a flash of brilliance: the answer was right under my nose and had been filling my nostrils with a beautiful hoppy bouquet for the last fifteen minutes. What’s more, we were sitting in the mecca. The plan emerged. We were simultaneously going to climb harder than we did as teenagers and drink as much beer as possible. If we couldn’t achieve our lofty climbing goals, we would at least have a chance at our drinking goals.

On February 6th 2012, we sat down at Bukowski’s Tavern in Inman Square, the same place where we had devised the original plan, and kicked off our quest to join the Dead Author’s Club. For those of you unfamiliar with the challenge, the rules are relatively simple. You have 180 days to drink 134 bottled beers. They range from 12 oz. domestics to 25 oz. Belgian quadruples. If you complete the challenge within the allotted time, you are awarded with a mug with the name of the dead author of your choosing–good for a lifetime of discounted draft beer.

Like any other health challenge in my life, I took this one seriously. I rigorously collected detailed notes about what I drank and when, inspired by the recent trend in self-monitoring.  Meticulously, I studied the annual reports produced by Nicholas Felton for design inspiration.  And I drank.  Aggressively.

And without much further ado, I present you an infographic about beer or as I like to think about it, a beerfographic:

So if you feel compelled to take on the challenge yourself, just remember one thing: you will be spending a lot of time with the bartenders at Bukowski’s. They will get to know your face and, more importantly, your tipping habits. Remember, the challenge is an investment in your health.

 

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Interns, integers, and complexity

For the week of May 14th, I had the pleasure of having my very own intern. This wasn’t just any intern, but Dana Fry, an intern excited about mathematics—rare, I know. After spending some time thinking about a project that (a) would have a relatively low technical barrier to entry, (b) would be open-ended enough to allow exploration (like a freeform jazz odyssey) and (c) wouldn’t require too much cobweb dusting on my part, I decided upon the relatively simple question:

In a finite integer sequence, for example {1, 2, 3, 4, 5, …}, what comes next?

Bad news is there isn’t a unique answer, as it depends on how complex the function is that generated the sequence.  Good news is that you have a better chance of guessing blindly.  To demonstrate, here are three simple generators and their sequences.  Note how all three generators agree up until the sixth integer, then diverge quite quickly:

G1(n) = n; {1, 2, 3, 4, 5, 6, 7, 8, 9, 10,…}

G2(n) = n– 15n+ 85n– 225n+ 275n – 120;  {1, 2, 3, 4, 5, 126, 727, 2528, 6729, 15130,…}

G3(n) = n + DIGIT_SUM(n) – MOD(n, 6); {1, 2, 3, 4, 5, 12, 13, 14, 15, 7,…}

With the initial problem ill-posed and open-ended, we embarked on a journey exploring the degeneracies and intricacies of integer sequences.  The first step: a problem set, because I needed to buy myself a bit more time what’s a math class without a problem set?  So on Monday morning I gave my intern her first problem set pertaining to integer sequences, finite differences, and Newton’s expansion.  This would keep her busy. Meanwhile, I’d have plenty of time to formulate a real game plan for the week. But much to my horror, Dana finished by lunch time and was now sitting in the intern pen with a polite look of “what’s next” in her eyes. So I did what any mentor would do: I feverishly scrambled and chalked my lack of preparation up to the problem at hand.

Thankfully I had spent the better part of the previous week compiling different tools that we could use for the project.  The first tool was a small library of Java code that could be used to fit arbitrary integer sequences using genetic programming, the second was an extensive list of curated integer sequences housed at the Online Encyclopedia of Integer Sequences (OEIS), and the final tool was visualization—that’s what we do.

Dana spent the next three days investigating integer sequences using a combination of genetic programming, the OEIS, and Processing, and started to uncover interesting connections between seemingly simple functions and complex sequences.  Below is an example of a function that finds the greatest common divisor between a number and the remainder of the same number upon division by ten.  The entire sequence is plotted in the upper right panel, while each row in the lower left triangle shows the sequence broken up into multiple subsequences.  For example, the third row shows the sequence broken up into three interleaved sequences, where the first plot is every third integer starting with the first, the second plot is every third integer starting with the second, and the third plot is every third integer starting with the third.  Notice what happens when you divide the sequence up into ten interleaved sequences.  The tenth subsequence is perfectly linear (i.e. the plot in the lower right corner).

 

GCD(n, MOD(n, 10))

 

Interestingly, this highlights a way to compare and contrast sequence complexity in terms of how easy it is to build them up from simple interleaved sequences.  The more interleaved sequences that are required, the greater the algorithmic complexity of the generating function. Here are a few other plots to compare and contrast different generators:

 

DIGIT_SUM(N2)

 

The decimal digits of pi.

 

And like most short projects, this isn’t as much where the story ends but really where it begins. In the course of the project, we certainly learned a lot about integer sequences, but we left many unanswered questions in our wake.  The most obvious open questions regard the use of interleaving sequences to generate more complicated sequences.  Is this a particularly interesting way to define algorithmic complexity?  Are there sequences that don’t have closed-form equations where interleaving sequences are useful?  Is there any precedence in the literature regarding interleaving sequences, and if so with pertinence to what fields?  These will be left to future inquiry, but all in all it was a really successful week and great having a motivated intern like Dana around.

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MacRecipes is born

When I was forced asked to write a blog post, naturally I did what anyone would do when looking for inspiration: I went home, opened a beer and started streaming old episodes of MacGyver. There is something truly marvelous about combining a few simple household items and getting yourself out of a near-death situation. As MacGyver put it himself,

“It’s kinda interesting how you can put one thing with another and cook up the right formula for stayin’ out of trouble.” – For Love or Money (Season 2 Episode 22)

After a few days of collecting data, sketching some ideas, and staring deeply into the eyes of a massively oversized picture of Richard Dean Anderson, I think I have created a utility that gets at the underlying brilliance of MacGyver. Call it amazing, call it magic or perhaps just call it MacRecipes.

Chris shares a moment with RDA.

Founded in 2010 by Ben Fry, Fathom Information Design works with clients to understand complex data through interactive tools and software for mobile devices, the web, and large format installations. Out of its studio in Boston, Fathom partners with Fortune 500s and non-profit organizations across sectors, including health care, education, financial services, media, technology, and consumer products.

How can we help? hello@fathom.info.