An element(ary) building block analysis

Scientists are often known for our tendency to let our professional lives intermingle with our home/family lives. One classic portrayal of this in fiction is Dr. Murray (the mother of the main character in Madeleine L’Engle’s A Wrinkle in Time), a microbiologist who is not yet done with her experiment when it’s time to start dinner . . . so she just cooks the stew on a bunsen burner in her home laboratory. (When I first read the book, many years ago, this struck me as a eminently reasonable approach, and it did not cross my mind for an instant that there might be any potential downside to this arrangement — e.g., worries about the stew contaminating her experiment, or vice versa.)

Dr. Murray’s kids were already school-aged, though. When your child is a baby, and you are spending time at home with it, there’s decent likelihood that — amidst all the feeding, soothing, diaper-changing, general mess-management, etc. — you will not have sufficient resources (time, energy, and/or access to antimatter or high-voltage power supplies) to make much progress on your real research projects. Thus, you might instead find yourself re-directing your “usual methods” to your current situation.

This might mean recording every time the baby is asleep, for an entire year, and then producing a plot of the data (broken down into 15-minute increments) that nicely illustrates how your newborn’s many shorter naps gradually coalesced into fewer, longer periods. Or it might mean meticulously charting breast-milk production, so as to test the frustrating and often contradictory claims that various experts have made to you about this process. Perhaps you merely ponder whether the not-quite-yet-fussing baby’s gradual motion/rotation on the floor can be well described by a random walk model. Or maybe you find yourself analyzing the color choices on your child’s wooden blocks that are decorated with the elements of the periodic table:

When you see this, what question(s) spring to mind?

I personally didn’t do all of those when I was home with my baby — just most of them. And although the baby in question is now 4.5 years old (but still loathe to let me focus my attention on complex physics questions in her presence), I recently found out that 2019 is the International Year of the Periodic Table of Chemical Elements, so I figured it was a good opportunity to dig out some of those old results. Continue reading

Turning through the years

A new year usually means it’s time for a new calendar. One can opt for 12 months of natural parks or scenes from a favorite film or TV show, 365 days of political cartoons or origami projects, or so many others. The possibilities are nigh endless.

But what if you really liked last year’s calendar? Maybe it already had the perfect mix of paintings from your favorite artist, or maybe there was a different classic family photo on each month, and you’d be happy to see them all again. Suppose you just used the calendar for keeping track of which date fell on which day of the week (rather than, say, writing down appointments on it), so that it’s still pristine. Why not just hang onto it and hang it up again the next time it’s accurate? How long will you have to wait? Continue reading

Push-up calculations: Feline facilitation, quantified

Not everyone thinks of cats as being big helpers, but mine seems to very much enjoy helping me with my workouts — with push-ups especially:

push-up partnerSome might say that she is actually hindering the doing of push-ups, which is technically true . . . but since the whole point of the exercise is, well, to exercise, the extra weight is ultimately helpful.

And it actually makes a difference! At least, it feels like it makes a difference. Despite her affinity for cookies (among other things), she only weighs about nine percent as much as I do; yet, push-ups feel more than nine percent harder when she’s up there. Is that just my perception? Or is there something about how the weight is distributed that gives her contribution a disproportional effect?

I decided to investigate the matter, breaking it up into three key questions:

1. How much force is actually required to do a push-up?

2. How does the addition of a medium-sized feline passenger increase the required force?

3. How much does additional force change the difficulty of the exercise — or, relatedly, the number of push-ups that one should expect to be able to do?

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The “problem” with Pi Day, and why I celebrate anyway

I confess, I’m a fan of \pi, the transcendental and irrational number that is the ratio of a circle’s circumference to its diameter and when written out in base 10 starts 3.14159 . . . Somewhat amusingly, I’m honestly not sure if this is confessing that I’m too much of a nerd/geek or not enough of one; we’ll get to that later, though.

I’m also a fan of pie, the dessert.

So is my cat. That is, she is a fan of pies, especially those with meringue on top. I don’t know how she feels about the number pi.

Last but not least, I’m a fan of puns and word play in general. Thus, it seems clear that I should be pulling out all the stops when when it comes to celebrating Pi Day (March 14th), especially this year (2015). As you probably already know, the best way to celebrate Pi Day is with pie.

So what’s the problem? Continue reading

What makes a thesis?

The second anniversary of finishing grad school seemed like an appropriate time to try to get this blog going again. This might go without saying, but writing a Ph.D. thesis* can really interfere with a person’s recreational science blogging. (Not that the time thereafter is necessarily much freer, at least not when starting a new job in a new sub-field, on a new continent, in a new country that speaks a different language . . . but that’s another matter.) Similarly, the topic of the Ph.D. thesis seemed like an appropriate one with which to start.

“How long will it take me to write my thesis?” is a question that every grad student must wonder at some point along the way — probably several points, in fact. I was wondering it just as I was starting** to write mine in February 2012, and I decided that strictly tracking the number of hours I invested in the project might both A.) be an interesting factoid, and B.) help me to better focus on the task.

Looking back at the data I’d taken and adding it up, the answer, it turned out, was approximately 283 hours — i.e., the equivalent of 11.8 24-hour days, 15.7 18-hour days, 23.6 12-hour days, or 35.4 8-hour days.
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Cookie calculations

Every time I bake cookies, I wonder if I’m making the most of the space on the cookie sheet. I finally decided to stop wondering and figure it out.

Experimental methods

My investigation involved circular cookies of two different sizes:

cookie sizesTwo examples of large cookies and three examples of small cookies. There was some standard deviation in the size of each group, but it wasn’t too bad.

They were arranged on cookie sheets of two different sizes:

cookie sheet sizesThe sides are, in fact, straight. It’s just the camera that makes them look curved.

Now, the most common way to arrange cookies is in equally spaced rows and columns. This is called a square lattice; when you draw a line from the center of a cookie to each of its four “nearest neighbors,” you end up with a pattern of squares.

Another option is, instead of putting the cookies in row two directly under the cookies in row one, to arrange them in the “gaps” between the cookies on the first row. If you do this, you get a triangular lattice, also called a hexagonal lattice; when you draw a line from the center of a cookie to each of its six “nearest neighbors,” you get a pattern of triangles.

proto-cookies in square latticeproto-cookies in triangular latticeCookie dough arranged in a square lattice (OK, so this one is a slightly rectangular lattice, but you get the idea) versus a triangular lattice.

As you can see, the cookies are more densely packed when they’re in a triangular lattice, even though they’re the same distance away from the cookies closest to them. If you work out the geometry problem, it turns out that cookies arranged in a triangular lattice take up 86.6 percent as much space as cookies in a square lattice. In other words, you can fit 15 percent more cookies into the same amount of area.

Well, problem solved! Triangular lattice it is.

But wait! What if your cookie sheet isn’t wide enough for an offset second row? Is the triangular lattice still the way to go? Is it still worth it to get the rows closer together, when it means every other row is a cookie short?

To find the answer to these questions, I first tested the four different set-ups in my kitchen (small cookies on a small cookie sheet, small cookies on a large cookie sheet, large cookies on a small cookie sheet, and large cookies on a large cookie sheet). Then I used equations and graphs to generalize the answers.

Continue reading