Sunburn Science

Introduction

The diversity of skin types in Homo sapiens gives rise to a wide variety of responses to exposure to sunlight. This study aims to investigate the responses of a particular specimen, a 21-year-old female named Kate, whose sensitivity is distressingly binary. The vast majority of her existence is spent with an extremely pale skin tone. However, after a certain threshold of sun exposure, she becomes violently, painfully bright red. The anecdotal evidence of her history of sun exposure does not include any episodes where she can be described as the desirable “tan” – it’s albino or lobster for Kate.

The purpose of this study is to characterize the point at which the specimen switches from pale to burned, and to methodically determine if there’s any window for her to be tan in between. The study was prompted by the novel situation of being in sunny California for an entire summer, and also partially by being bored on a Sunday afternoon. By investigating a variety of circumstances under which tanning might occur via natural sunlight (no tanning salons!) the goal is to understand Kate’s skin’s sensitivity, and by the end of the summer, somehow engineer a tan.

Methods

The experiment took place by the pool of the Stanford Park Hotel, between about 1 pm and 3 pm on Sunday, June 16^th.  The subject was exposed to sun and shade in alternating 15-minute intervals. A smartphone was used as a timer. After each fifteen minutes, she switched between the lounge chair on the sunny side of the pool and the lounge chair in the dappled shade on the other side of the pool. The experiment lasted for 4 sun periods (a total of 1 hour) and 3 shade periods.

The temperature was about 70 degrees, and there was no wind in the shelter of the hotel courtyard, so it felt frickin hot! The sun was almost directly overhead. There were no clouds whatsoever. The weather record for that afternoon can be found on this shiny site: http://weatherspark.com/#!dashboard;a=USA/CA/Menlo_Park

The subject was provided with 40-inch size 1 circular knitting needles and 100g of Three Irish Girls McClellan Fingering (30% bamboo!) in the colorway Pixie Hollow, because sitting around by the pool would be boring if she didn’t have socks to knit. The subject was also provided with Cherry Coke. Duh.

Attire was shorts and a t-shirt. The subject did not turn because lying on her stomach sounded boring and she wouldn’t have been able to knit. While the subject’s face, arms, and legs were exposed to the sunlight, only the legs’ sensitivity was measured. Measurements were taken by photographing the subject’s legs three times during each sun period: at the beginning, about halfway through (this was not very consistent), and at the end. The photos were all taken on the sunny side of the pool to attempt to control the lighting. One shady-side picture was taken to show the dappled nature of the shade:

Against all her instincts born of a lifetime of dealing with painful sunburns, the subject did not wear any sunscreen whatsoever. These are the sacrifices you make for science.

Data

Sun Data 06-16-13

Observations

(Okay, abandoning the third person thing because it’s getting awkward.)

The sun is really hot when you’re sitting in it on purpose. Usually when I get a sunburn I’m out playing, on the boat or somewhere else, doing something to keep my mind off how hot it is. This methodical business, by contrast, tends to focus me in on how hot it is.

I should have done this in a bikini–I will probably have an awkward shorts tan after this afternoon.

And one final data point: as I write this, the tops of my thighs hurt as though they are burned. Aaand… yes, I have a burn line where my shorts were:

 Conclusion

I believe I just spent two hours methodically getting a sunburn.

Future Work

It’s possible that sunburn only appears a while after you sit in the sun – even if you get out of the sun, it takes some time for the burn to appear. Anecdotally, this seems about right. However, it’s a harder theory to test – in order to have the duration in the sun as a variable, I’d have to spend multiple different days testing different amount of sun exposure before I get out of the sun and wait to see if a burn develops. This would present the problem of recovery time, too: suppose I burn myself in one trial. Obviously my next trial should be shorter, but how long do I need to wait for my burn to heal before trying again, to be sure that it won’t affect later trials?

Another possibility would be dipping in the pool every 15 minutes when I switch – and this would probably make it more comfortable. It would cool off my skin temperature, but would this affect the UV exposure, and eventually the color/tan-ness/burned-ness of my skin? This is also a more relevant test to engineering a way for me to get tan in real life, because most of my sunshine activity involves swimming or boating in some way.

Then, there are the obvious questions to answer. What if, instead of 15 minutes off, 15 minutes on, I went with a different schedule? 20 minutes on and 10 minute off? A longer or shorter period than 30 minutes?

The entire experiment is also victim to issues of controlling all the variables. I can control for things like the time of day, and probably even cloudiness, but I have a feeling that things like temperature have a pretty big effect, and I can’t control the temperature (that is, if I want to stick to only natural sunlight, which I do.) I’ll have to accept simply recording the temperature for all my data and trying to draw conclusions that way.

What if different parts of my skin tan differently? While I’m pretty sure at this point, given the pain they’re in, that my thighs are burned, and my face doesn’t feel so great either, my arms feel totally fine. As far as I know they were in just as much sunlight as my legs, so perhaps the skin there has different sensitivity? It would be interesting to investigate the relative sensitivity of my legs, arms, face, belly, etc. One possible application of this would be learning which parts need the most sunscreen or most frequent reapplication.

Speaking of sunscreen… how do different brands and SPF rating of sunscreen affect the tan (okay, time to stop kidding myself, burn) I eventually get? There are so many variable to investigate here: how long before sun exposure do I apply, when do I allow myself to get in the water, reapplication timing. And that’s not to mention all the brands, strengths, application methods (spray-on, aerosol, lotion), etc. (I’m kind of experienced at sunscreen.) In the other direction, they make tanning oil I could try—but I think I know better than that. It would be so fun to paint myself in stripes of different brands/strengths of sunscreen and see what happened. It would also be very dorky-looking the next day.  Oh well. For science!

It’s SuperFreaky

The way I grew up, I was just as likely to become an English nerd as I was to become a math nerd. For one thing, I used to read books 24/7. For another, my mother’s own English prowess figured prominently in my childhood. My entire family encouraged this: the common endpoint of many dinner table conversations was “Let’s go get the dictionary!” (Yes, a paper dictionary. See, I grew up in a time when people didn’t keep their laptops a few steps from where they were at all times. We didn’t even have laptops!)

Tonight’s dinner table conversation made it clear that those days are not over. At issue: we know ‘uncouth’ is a word, but is ‘couth’? Turns out it’s an archaic past participle of ‘can’. While the dictionary was out (picture my mother precariously trying to keep the 4-inch-thick unabridged Webster from falling into her marinara-smothered calzone), my brother John claimed that the word ‘ain’t’ isn’t in the dictionary. Mom claimed that it is.

My sister and I, having learned through experience not to bet against the Language Guru, let it drop, but John pushed the issue. He bet mom the dishes duty that she wouldn’t find ‘ain’t’ in the trusty, as-old-as-I-am dictionary. John would do the dishes if it was in the dictionary, Mom would do them otherwise. (Laura and I won this bet before it was even decided!) Needless to say, John ended up doing the dishes.

One by-product of having my mom for a mom is that interesting books appear on the counter or the coffee table at seemingly random intervals. That’s one thing I’m going to miss when I move out (in 10 days! Whoa!) The latest instance of the phenomenon took place a few days ago in the form of SuperFreakonomics, by Steven D. Levitt and Stephen J. Dubner.

I’d heard of Freakonomics, by the same authors, but I’d never been particularly intrigued. Something about the picture on the cover, of an apple sliced open to reveal that it was in fact an orange, didn’t really attract me.

The cover of SuperFreakonomics, by contrast, has the same orange-disguised-as-an-apple…exploding!

Need I say more? I was hooked, and it turned out to be really good. Judging a book by its cover? Guilty as charged.

The authors claim the book is about economics, but it was unlike any economics I’d ever experienced. Granted, my exposure to economics consists of AP Macro and Micro, two semester-long high school classes which were clearly trying to teach us applications of calculus without saying so. I remember the first time I started jotting down integrals and derivatives in the margins instead of whatever formulas the book was trying to get me to use, and everything suddenly became clear.

Just like my introductory economics class, this economics book is mostly math, specifically statistics. Steven and Stephen (would you co-write a book with someone if they had virtually the same name as you?) essentially look at data about things like prostitution or hospital deaths and try to make sense of it, no calculus involved.

The style of writing reminds me a little of what I’ve done in this blog, trying to figure out why my duct tape calculations were wrong or whether there was a secret code on Vassar street. They look at problems, knock down common assumptions about them, and let the numbers show what’s actually going on. If that’s what microeconomics is really about, then count me in!

Fermilab!

Disclaimer: This post is not about math. However, it is about antiprotons and collision detectors and cancer treatments, which are almost as awesome as math.

I visited Fermilab today. I’ve visited Fermilab before, with my cousins, and it mostly consisted of driving around in search of buffalo and eating Chewy bars. But now, I know a guy (Ike Swetlitz) who knows a guy (Brendan) who has access to the D-zero detector. And right now, they’ve shut down the detector for maintenance, so you can get inside it! And Ike invited me and Alexander Hinch to do just that.

But first, we went to a talk about Fermilab’s cancer treatment center. Usually radiation therapy for cancer shoots photons at the cancer cells, which interact with the atoms and change their electric properties. If instead you shoot neutrons at the tumor, they actually cause the carbon atoms to break down into other elements, which means it’s much harder for them to regenerate. This is what Fermilab is trying to do.

As far as I can tell, they take their proton beam that’s going around in circles really fast underground, divert it away from the circle, and smash it into some beryllium. They get the neutrons that come out and direct them through a hole in a concrete wall to where a patient sits, strapped into some device to position the tumor so it’s right in the way of the neutrons coming through the wall. And then the tumor goes away! After four weeks of treatment, that is.

After the lecture, we wandered around the Wilson building, the biggest building at Fermilab, which is actually quite pretty.

Apparently, there are people at Fermilab who control the LHC when it’s nighttime in Switzerland but daytime around here! Apparently most of the stuff over there was “Idle” today (tonight?).

Then we made our way over to the D0 detector. The point of Fermilab is to make proton and antiproton beams, run them around in circles really really fast, and then smash them into each other. The smashing takes place inside the D0 detector, which is in a very blue building pretty far from Wilson.

Our tour guide, Brendan, showed us a model of what we were about to see, and explained the safety precautions:  waivers, radiation sensors and hard hats.

Then we went past a locked door, and we were climbing around inside the detector! We went up and down stairs past huge tanks filled with uranium and argon, truckloads of fiber-optic cables, and enormous red magnets.

The outermost shell of the detector was made of muon detectors. Apparently, the designers won some sort of art award for their circular design of the detectors, which they modeled after fish scales to efficiently fill the space.

It was pretty cramped in there—I was bent double in some places trying to get through. We went all over: around the sides, inside the outer shell, and we even got a peek in between the uranium tanks. Some of the parts looked like they were just duct-taped to the walls!

Next, we headed over to the anti-proton source, a triangular-ish loop where they make the antiproton beam and run it around.

It’s an underground loop full of magnets and detection/correction devices to keep the beam on track. The coolant they use for their machines is 95 degree water, so guess how hot it was in the underground tunnel? 95 degrees! And I was wearing jeans!

The really cool part is that the people at Fermilab had to build this all themselves. You can’t just order parts for a collider online! Brendan was saying the only thing more exacting than designing a detector or an antiproton source would be designing things to send into space. Apparently, in the early stages of construction of the antiproton source, aluminum foil was an essential building material:

Eventually, they replaced those pieces and welded them together. The  antiproton source has been up and running for a while now, and at best it produces 2 nanograms of antiprotons, per year! Apparently they just had a celebration for getting to 11 nanograms total in the entire life of the source!

Ike works at Fermilab this summer, analyzing data they get from the D0 detector, when it’s up and running. He showed us around his cubicle, which had an awesome view of the concrete wall behind which was the detector. Thanks, Ike, for this awesome opportunity!

Pi(e) in the Middle of the Night

I’ve been very excited about coming to MIT ever since I made my decision in late April, but so far I’ve mostly been exposed to the aspects of housing and pre-orientation programs.  I haven’t really thought much about what my math studies will be like, beyond assuming that they will be totally awesome. This past week at RSI has changed that.

I spent a lot of my time in the Athena cluster (read: computer lab) helping students out with their papers and presentations, often until late in the night (early in the morning?). One night, Kartik Venkatram, the head math mentor for all the MIT math students this year, came up to me and asked, “Do you like pie?” Thinking in the context of the math papers I was reading, I replied, “Of course!” –and then Kartik asked, “Key Lime pie or Pecan pie?”

Yes, Kartik had bought pie from a delicious bakery, and he gave some to me because I was the math TA.  So, let me get this straight: in the math department at MIT, you support each other by giving each other pie?! Can I go there? (Oh wait, I’m about to!) And by the way, thanks, Kartik!

I’d never been a part of the MIT math community like most RSI math students who have on-campus mentorships: I had a project with a chemistry professor over at Boston College, so I’d never experienced the awesome community atmosphere that the MIT math department brings to the summer math students. Aside from the pie, students have weekly breakfasts together (I missed those) and cookie breaks, as well as a delicious closing lunch at Legal Seafood. It’s not just the food though;  I can’t wait to join that community full time because of the people there and the support they have for each other.

Apparently, in every summer camp that I’ve ever heard of, it’s a tradition to stay up for the entire last night. I found myself in the company of some awesome RSI alumni, and we sang along to Dr. Horrible and played ninja for a few hours before deciding that staying up all night required some math. We found an air-conditioned lounge in Simmons Hall, and Zach Abel gave a “lecture” about category theory.

What on earth is category theory? The way I understand it, it’s a mathematical theory of everything: almost every kind of math can be described in category theory. In practice, it consists of drawing a bunch of pretty dots and arrows, which sometimes look nice and simple, but they mean a lot more than you might think.

“Lecture” is in quotes because I mean it in the loosest possible sense of the word. Zabel was the source of the information, but I think a majority of the time was spent with me saying, “Wait, back up, say that again.” Apparently, this was perfectly acceptable and in fact encouraged, and I actually feel like I understand most of what was going on. Speaking of the time, this talk occurred from 2:30 until 6:30 am. We watched the sun rise as we proved Yoneda’s Lemma, and we didn’t stop there.

In fact, according to Zabel, we covered the equivalent of almost two weeks of Harvard’s Math 55 freshman math class, in four hours. However much Math 55 intimidates me, I’d describe our nocturnal category theory explorations as nothing other than fun! At one point Zabel asked for a variable to use so he didn’t have to keep putting subscripts on π. I suggested a cherry, and before he realized my pun, a bunch of arrows on the board were labeled with little drawings of cherries. If every night in college is like that last night, I’ll be a very happy (very sleep deprived) mathematician.

The icing on the cake (or the cherry pie?) is that both Kartik and Zabel will be around at MIT next year!

Counting Tiles on Vassar Street

When I first visited MIT during Spring Break of my sophomore year of high school, the tour guide pointed out that there’s a code spelled out in black and white tiles on the first floor of buildings 16 and 56. This captivated my imagination so much that last summer, I took some friends and copied down the code so I could bring it back to my dorm and solve it. Thanks to the computational wizardry of my friend Ben Horkley, it only took about an hour to crack the code. I won’t spoil the fun by revealing what it says—go solve it yourself!

However, this memory has been fresh in my mind lately, since I’ve been on campus for the past week. I’m staying in Simmons Hall, which is a good long walk down Vassar Street from the rest of campus, so I’ve made the trek past Briggs field and the Steinbrenner “Stadium” several times a day. I’ve noticed that the wide sidewalk is tiled with approximately 1-foot square tiles in one of three colors: light-ish tan, dark-ish grey, and orange-ish yuck (orange is my least favorite color).

Maybe I just have secret codes on the brain, but is it possible that there’s a secret code in the tiles along Vassar Street the same way there is on the floor of Buildings 16 and 56? The black and white tiles represented some sort of binary system (I shall say no more!), so couldn’t the three colors encode some base-3 representation of messages? Could the sidewalk-layers be trying to tell us something important or profound or hilarious?

Of course, the sane answer to all these questions is “No, you crazy conspiracy theorist!” In fact, in almost every setting this discussion would end here. But this is MIT, and this is exactly the sort of thing you’d expect from those crazy engineers (us crazy engineers? It still seems so surreal that I’m going to be a student here!)  Anyways, I guess I’m going to fit in well, because I decided to investigate.

The easy answer is, “No, Kate, of course there’s no secret code, the colors of the tiles are random.” However, I don’t think this is the case, because you never see 4 tiles in a row. Wouldn’t you think that that would happen at least once or twice? What are the chances that, given a row of several hundred tiles randomly assigned to one of three colors, there are absolutely no blocks of 4 or more in a row?

I puzzled over this for about a day, trying to come up with some way to calculate this probability. I tried small cases, doing casework for 5, 6, and 10 tiles in a row (.913, .860, and .822, respectively). For small numbers of tiles, at least, it seems pretty likely that there could be no four-in- a-rows of one color. But after doing a page’s worth of casework for n=10, I was ready to abandon this approach.

Perhaps inspired by all of the RSI projects I’ve been reading about, I decided to try a simulation. This required dusting off my Java skills (which turned out to require downloading Java onto my new (and 2-month-old) laptop) but I managed to program a simulation for my problem, taking a suggestion from Jacob to make it run faster. I’d planned to brute-force everything; this is why I am a mathematician, not a programmer.

My program runs 100,000 trials for a given length of the row of tiles, each time randomly generating the colors and stopping if it finds four in a row.  Then it gives the number of trials out of 100,000 that had no four-in-a-rows of a single color. I ran this for row lengths of 10 through 500 and, amazingly, was able to put them into Excel and make a pretty graph!

For reference, everything past a 171-tile-long row has less than 1000 successful trials, or less than 1% success. Everything past 353 is in the single digits: less than .01%! It’s unbelievable that a chain that long could be devoid of 4-in-a-rows completely by chance. Or in other words, the p-values for rows of 353 or more tiles are less than .0000, which is less than any reasonable alpha-level, so we have evidence against the claim that random rows of tiles of this length contain no strings of 4-in-a-row. (A context statement! Ms. Free, my AP Statistics teacher, will be so proud of me!)

So, how long of a chain is Vassar Street really? Well, I measured (using my newest best friend Google Maps) and the distance I usually walk along Vassar, from the edge of the athletic center to the edge of Simmons, is about 1120 feet long. The tiles are about 1 foot square, so we’re talking a row of 1120 three-colored tiles, in which there are no 4-in-a-row sequences of the same color! This row length is twice what we simulated, so it would be even less likely to have no 4-in-a-rows!

My little experiment has thoroughly convinced me that the colors of the tiles on Vassar street are certainly NOT random in the slightest. However, I’m not rushing out to decode the hidden message just yet. It’s entirely likely that the lack of 4-in-a-rows is due to some aesthetic tendency of the tile-layers; perhaps they were instructed not to put too many tiles of the same color in a row, or maybe they subconsciously avoided this.

I think reading too many scientific and mathematical papers in the last few days has seriously affected my thought processes, because I’m going to conclude by suggesting avenues for future work. I greatly simplified the Vassar Street Problem by considering only one dimension of a two-dimensional tiling. I looked at blocks of adjacent color in one row, but there are many rows in a square tiling of the sidewalk. What if there were pentominoes of the same color, but no 6-ominoes, or n-ominoes with n>5? I’m not sure whether this is the case, but how likely or unlikely would it be that it could happen by chance? (And why stop at two dimensions? Consider a hypercube tiling of d-dimensional space, where each hypercube can have one of c colors…)

Well I’ve been busy!

In the just-over-a-week since I last posted, I have compacted 5 days worth of vacation into 26 hours, flown on both my smallest-ever and my largest-ever airplanes, attended a prom in a duct tape dress, and, most notably, read 13 technical math papers in various states of completion. I think it’s fair to say I’ve been a little swamped.

The vacation was to Lake Shellbyville, IL, where I waterskied, jetskied, and tubed as much as daylight would permit. My entire family heads to the lake, which is four hours downstate of Naperville, for five days every summer. I had to leave for RSI the day after arriving, but Thursday morning I spent some quality time with my cousins and a bin of Duplos:

(My cousin Timmy later rearranged the letters to spell I ❤ Tim, somewhat ruining the effect.)

When it came time to leave for RSI, my mother drove me to the Champaign airport, about an hour away. It was quite surreal finding “20-minute parking” signs along an airport drive-through– at places like Midway and O’Hare it seems like the security guards yell at you if you so much as put your car into park. I was very excited to be asked to take my laptop out of my bag—it was my first time through airport security as a laptop-owner. Also, I seem to have successfully smuggled a plastic water gun through airport security, a fact that dawned on me when I saw it inside my bag at the gate and freaked out, expecting to be momentarily tackled by intimidating security guards. Thank goodness the Champaign airport is so chill!

I boarded the plane and found my seat, which turned out to be both an aisle seat and a window seat. No, I didn’t have two seats: there was only one row! It was definitely the smallest plane I’ve ever flown in. The refreshment service consisted of the single flight attendant walking down the row offering everyone a cup of water. When I got to O’Hare and transferred to my flight to Boston, it was on my largest plane ever—I guess Airtran never felt the need to use 757s.

Eventually I got to RSI, and prom was Saturday night, complete with a photo booth with fake backgrounds:

I used the leftover red duct tape to make a hat band and tie for Jacob, after which the black and red rolls had about the same diameter, so I used them as a pair of complementary bangles. I also decided on a red purse with black trim, which was big enough to hold a backup dress (that I didn’t need to use!) and scissors in case I needed emergency repairs (which I did use).

RSI prom was a break from what has been a weekend of hard work reading papers. I am proud to report that I have read all 13 of this year’s math papers, though not all of them were finished or polished at the time. And that’s just for the first time! I’m looking forward to sticking with these papers as they evolve into the finished product over the next two days.

This year brings a pretty diverse bunch of math papers. From finding adaptive versions of Newton’s Method that are significantly better than the original, to using lower triangular matrices to encode information about braids, to exploring paradoxes that arise in different voting systems, the students have been very busy for the past 5 weeks. Though I know what I’ve been reading are works in progress, I’ve been very informed and, yes, I’ll say it, entertained.

And then, I read a biology paper. My headache is still in the process of subsiding. I have all confidence that it was an excellent paper, but this confidence is based more on pure idealistic optimism than any impression I got from reading it. I think from this point forward I’ll try not to stray too far from mathematics.

This blog entry had 666 words, so I felt compelled to add this sentence, because I am not evil.

Marbles

I went to Marbles (“The Brain Store”) in downtown Naperville today to buy a birthday present for my boyfriend Jacob. Marbles is probably my favorite store in ever. They sell brain toys, and the business model, so far as I can tell, is “We want people to buy our games. Let’s set up chairs and tables and get all the games out and let people play them!” I could spend (I have spent?) hours in that store playing brain games.

On one table they had X-balls and Y-balls. It sounds like something to do with chromosomes, but actually they’re kits of a bunch of magnetic “X” or “Y”-shaped magnetic pieces that go together to form nice, pretty, geometric, sphere-y… things. The Y’s were more like >–< though: they still had 4 magnetic attaching spots. I picked up the box for the Y-balls, and one of the features was “plays nice with X-balls.” Though this conjured up images of little children fighting and then learning to share, I decided to test it out.

There was one assembled ball of each type on the table, and I destroyed them both for parts. It turned out they did fit together nicely, but due to the polarity of the magnets they only fit in certain ways. At first this was irritating, because all I could really get was a planar checkerboard pattern of red X’s and blue Y’s. But after a little tinkering (I told you, I spent hours in that store!) I got to a nice circular arrangement with 5 blue Y’s and 10 red X’s holding them together. I went on to try for a torus, and it ended up looking pretty neat, but the ends didn’t all connect to each other the way they do in the ball form, so I considered myself a failure and went off to play with the Rubik’s Cube.

A while later, one of the employees walked up to my creation, and apparently she thought it was so cool. She was asking people if anyone knew who’d made it. By a complete coincidence, my next-door neighbors were in the store at the same time, and they’d seen me making it, so they gave me away. The lady was very impressed with me, and all of a sudden, she decided to put the little donut in the window of the store, next to some of the other most popular games. She was even talking about putting my name with it, but I managed to get myself out of that one, although I did get a picture of the model sitting in the window (sorry it’s so bad, I took it with my phone through a window):

If I didn’t already have a wonderful, mathematical job, I would totally want to work at Marbles! I overheard one of the employees talking about some sort of designated play time, where the employees have to take a break to play one of the games in the store so they understand the rules and can explain them to customers. Required playtime! Though if I worked there, I would have a hard time not completely neglecting my customers in favor of playing all the games myself!

I eventually decided on the perfect birthday present for my boyfriend … and of course I’m not going to say what it is in my very public, diligently-read-by-boyfriend-in-question blog! I’ll let you know once I give it to him :p

Duct Tape Dress

RSI (http://www.cee.org/programs/rsi) is having a ‘prom’ while I’m going to be there next weekend, and I decided to take the opportunity to fulfill a long-held goal of mine: to make a duct tape prom dress. Surprisingly, I was able to bring my mother around to the idea, and she suggested I actually get a pattern, so we went to Hobby Lobby and picked out a nice sheath dress with the advantages that it was not made of too many pieces and did not have much surface area: less duct tape cloth to create.  Then we stopped by a Home Depot and found red and black duct tape. If I’m going in a duct tape dress, it may as well be in bold colors, right?

After a solid day of cutting and taping, in which I had to de-gunk the scissors at least 3 times, the dress is done! It’s sitting in a corner of my basement where my fashion-conscious sister won’t find it, so I won’t have to face her shame. It actually fits, and my plan for getting into it on prom night is to have someone tape me into it. I would include a picture, but that would spoil the surprise for my boyfriend!

I was talking to Lauren about the process, and she recommended I find some way to mathify it. I was skeptical—duct tape dressmaking is basically just a bunch of cutting and taping and trimming. But this evening I wondered, how much duct tape did I actually use making that dress? So, in Lauren’s honor, I plunged ahead.

I didn’t even try to measure the duct tape on the dress itself. The pattern pieces were irregularly shaped, the tape had several layers in places where I put seams together, and the curves on it precluded any kind of linear measurement. I turned to the rolls of duct tape themselves, but these only showed what was left, not what was gone. (Why, oh why, didn’t I anticipate this and take preliminary measurements?)

I found the discarded shrink-wrapping that was on the rolls. It is shrink wrap, so it’s not exactly the best for measurements, but it was the best I had. Both packages looked to have a diameter of about 7 inches, which was encouraging. The width of all the tape was 1.875 inches. The diameter of the remaining black tape was 4.25 inches, and for the red tape it was 4.825 inches. I used these numbers to find the cross sectional areas of the missing, used-up-by-the-dress duct tape (24.298 sq. in. for black, 20.199 sq. in. for red).

At this point I figured if I could find the thickness of a single layer of duct tape, I could divide the area by this thickness to find the length of tape, and then just multiply that length by the width of the tape to find the area of tape used. There’s a flaw in this, of course: when wrapped around the roll, the duct tape is curved, so it doesn’t seem right to divide by nice linear lengths. Oh well. To find the thickness of a single layer, I stacked up 10 small squares of the red (of which there’s more left) and measured that. The cm side of my ruler worked better for this, and I calculated 10 layers = 2 mm, which is 0.2 mm per layer, or .00787 inches pr layer.

From here it was a short step to calculate that I’d used 3087.42 inches of black tape, for 5788.91 sq. in., and 2566.58 inches of red tape, for 4812.3375 in. I was ready to accept these numbers triumphantly…until I found the words that had been on the package. The manufacturers had printed specs, including the length, width, and thickness of all the tape on the roll (1.89 in. wide by 60 yd. long, 11 mil thick). Smart one, Kate.

The 60 yards of tape came out to 180 feet or 2160 inches total. Something stank here. I’d calculated the lengths of the black and red tape as 3087 and 2567 inches, respectively! My math had told me I’d used more tape than was on the rolls to begin with, when really there was some leftover! Sure, I expected some error, but that’s close to 1000 inches off! I realized my method of finding the tape’s thickness was not all that great—what if I’d put air bubbles between the layers or measured wrong? (2 mm is not so very different from 3 mm or 1 mm with the naked eye, but it could make a huge difference in my calculations.) The package said the tape was 11 mils thick. What the heck is a mil?

Ah, my best friends Google and Wikipedia! According to http://en.wikipedia.org/wiki/Mil_%28unit_of_length%29, a mil is one thousandth of an inch. So my .00787 before should have been .011. (Out of curiosity I calculated the percent error: 28%, which is not bad, given my measuring technique.) I recalculated the lengths with the new number and found I’d used 2208.91 inches of black tape and 1836.27 inches of red. I’d still used more black tape than the package said there was supposed to be on the roll! Something was still wrong.

With the numbers from the package, I had more information. I found the diameter of the innermost circle of the duct tape rolls, where they stopped being duct tape and started being cardboard (3.1875 inches). I used this and the original diameter of 7 inches to find the total area of duct tape at the outset, which was 30.50 square inches (whew! greater than 24.298 and 20.199, thank goodness!). That meant that, according to the manufacturers, there were 2160 inches of duct tape in 30.50 square inches of cross sectional area, for a multiplier of .0141, instead of our earlier .011 or .00787. I guess this means we’re assuming that the length of duct tape is proportional to the cross-sectional area, but not necessarily to the thickness.

Using this number and the areas from before, I found I’d used 1720.77 inches of black tape, for 3252.25 square inches, and 1430.48 inches of red tape for 2703.61 square inches. This seems a lot more reasonable to me, at least in terms of the length of tape used. I calculated the percent error of our initial method—78% for both. At first I was surprised that the percent errors were almost exactly the same (.7799 precisely) but then I realized I’d used the same area calculation in both methods and just manipulated it differently–I would be worried if the percent errors weren’t this close.

Note that the area I found includes the scrap tape that isn’t included in the dress: stuff I had to cut off the edges or pieces that folded over on themselves while I was cutting them off the roll. It’s more of a measure of how much duct tape it takes to make a dress than how much actually ends up on the finished product.

Nevertheless, I have a sizeable amount of both colors left. Enough to make accessories? I think yes! So… red purse or black purse?

Note: sorry for the more technical post. I included all the data I gathered so you can follow along if you like, and point out any mistakes…

Finished!

I spent most of my day doing this, plus a few hours Sunday and last Friday. I cut out 12 pieces, each with 5-fold symmetry. There are 300 little slits, making 150 places where two pieces slit together. These 150 come in groups of 5 along one line, so there are 30 edges, like an icosahedron. It definitely looks like an icosahedron when I hold it in my hand, but it obviously has some sort of dodecahedral structure too, because it’s made of 12 five-sided pieces!

This is probably one of the prettiest ones I’ve constructed. I’d planned to make “Windmills” in a pretty orange and yellow, but it turned out that my printer ran out of colored ink just as I was printing, so I got this lovely gray. Windmills is surprisingly dense, and in comparison Tangled Reindeer seems pretty flimsy, but it’s loads better than Deep Sea Tango, my first attempt (which is hanging half-dissembled in my bedroom .)

As I’ve said, I’ve made Tangled Reindeer before, but I found that the second time making the same design just wasn’t as fun. I had already developed a sense for how the pieces fit together, so it was more busywork than challenge.  I guess in the future I will try to keep constructing ones that I haven’t made before—but there are only 8 in George Hart’s modular kirigami paper! I’ve tried to make some of his other designs (i.e. not from that paper), with limited success.

However, it may be pretty tricky to get through all 8 to begin with. For the 8^th one, George writes, “With some bravura, I’ll wager a beer that no one else in the world would have the obsessive-compulsive patience to assemble it at all!” Well, if it takes me 3 years to construct it, maybe I’ll actually be able to drink my winnings!

In other news, yesterday Sammy gave me a starter for this Amish Friendship Bread. It’s a plastic bag full of yeasty-smelling goo, which I mush for 10 days and then bake. Actually the concept is interesting: I add to the mush, and then just before I bake it I split it evenly into 4 parts, use one to bake with, and give the other three to three of my friends so they can make bread too. (Sammy let me try some of the finished bread, and it’s to die for!)

The downside is this: I did the math (addition! Yay!) and day 10 falls on the day my family leaves early in the morning to go on vacation. How am I supposed to bake the bread in an Army Corps of Engineers cabin in downstate Illinois?! Apparently the baking of the bread is pretty time-sensitive–you have to do it exactly on day 10. Oh well, at least I’ll be able to take the three new starters with me when I go to Boston for RSI. Rickoids: holler if you want one!

Waterskiing: it’s all about the angles.

Don’t you hate it when your legs get sore unevenly? Waterskiing on one ski will do that to you. The past two Fridays, my dad has taken me and some friends to the Illinois River for a boat trip, and I’m perfecting the art/science of getting up on one ski. My aunts and uncles have always acted like this is the ultimate in waterskiing fun. I guess they forgot to mention the fact that one leg kills while the other one is just fine. It certainly makes getting up the stairs interesting.

I’ve been continuously learning how to waterski since I was about 6 years old. First you have to spend hours on the tyke-sized trainer skis, and then learn to manage two skis in the water and balance on them as the boat accelerates. When you get comfortable with that, you can start weaving in and out of the wake. Plenty of people just leave well enough alone when they get to this stage, but watching my dad whiz around behind the boat on one ski, throwing gorgeous, perfectly rounded sprays of water into the afternoon sun, made me want to try for more.

The next step is to drop one ski (hopefully leaving it boot-side-up so you can find it later), wiggle your free foot into the extra boot on the back of the other ski, and balance precariously with half the surface area. I have not fully mastered this, but I’m moving on to one of the last steps: getting up with just one ski. Even my dad can’t make this part seem effortless. My past few trips, though, I’ve been able to manage it after a few tries. This may be because I’ve had a lot of practice lately: two boat trips in as many weeks? That’s unheard-of—and highly awesome.

Now, after spending paragraphs gushing about waterskiing, I have to admit: I’ve never been very good at sports. Sure, I ran cross country and track for a while, but it really doesn’t take much coordination to run in a straight line. When it came to things that required coordination, or any kind of ball, I was hopeless. My ineptitude was not for lack of trying, though: I played on a subdivision soccer team for 5 or 6 years. (I scored two goals, total, in my entire soccer career. Both were accidents.)

I blame my failure at soccer on my love of math, or more accurately, my tendency to read math into everything I do. I was convinced that soccer was all about the angles. My thought processes while on the field consisted of, If he kicks the ball that way, it will bounce off the defender and go over there, so I should run to intercept it, etc. By the time I’d figured out what to do, the players would have made completely different decisions than I’d counted on and I’d have to reevaluate. And on the rare occasions when I actually got possession of the ball, half the other team would have descended on me to steal it by the time I figured out what to do with it.

I think the same over-analysis that served me so poorly on the soccer field is one of my strengths in waterskiing. When getting up, on one ski or two, I’ve discovered that it really is all about the angles: the angle between the water and your ski(s), your ski(s) and the rope, the bend of your knees, and the fin in the water. Experiment a little bit to find a range that works, and you can get up every time. This is also why one ski is so much trickier than two: eliminate one ski, and there’s a whole new degree of freedom. You have to get the right angle between left and right, as well as in all the other directions. Mostly I figure the right angle is, well, a right angle… unfortunately this is easier said than done. (Easier proved than constructed?)

Speaking of construction… blogging about the George Hart I was making on the airplane inspired me to make another one. I chose one from the modular kirigami page linked from George Hart’s website. I’ve actually made this one before (on a plane, no less!) and I like it because it holds together very well–there are a lot of tabs so it doesn’t really come undone. But the first time I’d made this one (its name is “Tangled Reindeer”) I’d used regular-weight paper, and the pattern had printed out in an unattractive grey. This time I figured out how to make it a nice purple color, and I printed it out on cardstock so it should be sturdier. Here’s a picture of the pattern I’m using:

Why am I not showing you a picture of the finished product? Because it’s not finished. I guess I forgot how long it takes to cut out all the pieces. I mean, look at that thing! I have to cut out 12 of those! It gets pretty annoying. On the website, George Hart talks about using some sort of laser cutter to cut out his pieces. I want!

The design looks enough like a snowflake that you’d think I could just fold it up and cut it out the way little kids do paper snowflakes, to save time. Unfortunately, it doesn’t have any lines of reflective symmetry (it’s all rotational symmetry) so that won’t work. Someday I’d love to design one of my own, and if I do it will definitely be easier to cut out, but I don’t think I understand the ones my friend George created well enough to go out on a limb and create my own. Yet.

Finally, apparently George Hart was “artist-in-residence” at MIT in 2003? Oh, if only I were ~8 years older. Also, the sculpture he and his students created is hanging somewhere in the Stata center. This I’ve got to see!