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Greece

June 26, 2009 at 7:26 am · Filed under Uncategorized

For the first 4 nights of the trip, we stayed in Volos, a major port city where I attended a workshop on Information Theory. The following day, we took a bus to Kalambaka.

Natalie and I spent two days in Kalambaka hiking on Meteora, which might be the most amazing natural landform I’ve ever seen. Kalambaka is small town nestled up against some gigantic rock protrusions. Several of the rocks are topped with ancient (but still active) monasteries.

It’s a striking view and in fact one of the monasteries was used in the James Bond film, “For Your Eyes Only.” Here is a picture Natalie took of that monastery with me in it

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I can’t overstate how awesome Meteora was. I love mountains, views and nature. And I got it, for example, here is a mountainside meadow
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and the city of Kalambaka seen from an outcropping
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This was one of the best hikes of my life. Other pictures can be found here.

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AFCEA Fellowship Award Ceremony

April 6, 2009 at 2:35 pm · Filed under Uncategorized

From the fellowship awarding ceremony this morning. From the left: me, AFCEA Director of Scholarships and Awards Norma Corrales, my advisor Yuan Xue, EECS department chair Dan Fleetwood and Dean of Engineering Kenneth Galloway. Dean of Research George Cook was present, but not pictured.

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Update: the Vanderbilt School of Engineering has published an article.

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Submarine Parking Only

April 6, 2009 at 8:40 am · Filed under Uncategorized

We got a lot of rain this week. On the way home from the office, I saw some firehoses leading out of a parking garage. On one end they were spewing water into a sewer drain. I went to see what was on the other end. This is what I found.
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I’m not an auto or insurance expert, but I’d say some of these might need a lot of work.
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Update: I returned two days later and found out the water had been a half-foot or so higher than shown in the pictures.  I deduced this from the high water marks on the green van, which was still parked there (ominously).

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The Biggest Box Fedex Will Take

March 10, 2009 at 5:12 pm · Filed under Math, Uncategorized

My friend Megan Goering asks what is the largest volume box you can send through Fedex given that length + twice the width + twice the height must be less than 165 inches. It might seem odd to care about only the volume instead of the dimensions, but it makes sense if you’re shipping walnuts, balloons or bows for Christmas presents. Anything pourable, that is.

Here’s my solution. Say that the dimensions are $x$, $y$ and $z$. Then we can write the problem as

\begin{eqnarray*}\textrm{max } & & xyz \\\textrm{subject to} & &x + 2y + 2z \le 165 \\& & x,y,z \ge 0 \\\end{eqnarray*}

First, observe that if $x + 2y + 2z < 165$, then the product $xyz$ can be increased by increasing any one of the dimensions. Therefore, the maximum will occur when $x + 2y + 2z = 165$. Thus, we can eliminate $z$ because


$\displaystyle z$ $\textstyle =$ $\displaystyle \frac{165 - 2y -x}{2}$ (1)

Here is the problem

\begin{eqnarray*}\textrm{max } & & xy\left(\frac{165 - 2y -x}{2} \right)\\\textrm{subject to} & &x + 2y \le 165 \\& & x,y \ge 0 \\\end{eqnarray*}

The constraints impose that the maximum be achieved in a triangular area with one vertex at the origin and the other two each on one of the $x$ and $y$ axes. Notice that if we use a point $(x,y)$ on the border of this triangular region, the product $xyz$ will be equal to 0, so this is clearly not the maximum. Therefore, the maximum occurs on the inside of the triangle. This is important, because it means that the maximum is some sort of “bump” which means the problem can be solved directly with calculus.

We want to maximize $xy\left(\frac{165 - 2y -x}{2} \right)$. The choice of $x$ and $y$ that achieves the maximum is unaffected by multiplying that product by a positive constant, so use this opportunity to get rid of the $\frac{1}{2}$. Let $f = xy(165 - 2y -x)$. Then

\begin{eqnarray*}f & = & 165xy - 2xy^{2} -x^{2}y \\\frac{\partial f}{\partial...... -2xy \\\frac{\partial f}{\partial y} & = & 165x - 4xy -x^{2}\end{eqnarray*}

Thus, in order for the maximum to be achieved, we need both derivatives to be equal to 0. Thus, we need

\begin{eqnarray*}165y - 2y^{2} -2xy & = & 0 \\165x - 4xy -x^{2} & = & 0\end{eqnarray*}

Which is, conveniently enough, two equations in two variables, so we can probably solve this. First simplify as

\begin{eqnarray*}165 - 2y -2x & = & 0 \\165 - 4y -x & = & 0\end{eqnarray*}

Then as

\begin{eqnarray*}2y + 2x & = & 165 \\4y + x & = & 165\end{eqnarray*}

And finally

\begin{eqnarray*}x & = & 55 \\y & = & \frac{55}{2}\end{eqnarray*}

and we get

\begin{eqnarray*}z & = & \frac{55}{2}\end{eqnarray*}

from Equation (1).

Thus the maximum volume you can send using this Fedex rule is $55 \times \frac{55}{2} \times \frac{55}{2} = \frac{166375}{4}$ cubic inches, or about 24 cubic feet. This many walnuts weighs over 300 kg, so presumably the problem was motivated by something lighter.

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Why Web Comics are Better

March 10, 2009 at 2:56 pm · Filed under Uncategorized

A friend of mine, Brian Lewis, recently asked on Facebook why Web comics are better than printed comics.  My guess is that it’s a combination of factors:

Selection Bias.  Webcomics allow a reader to be much choosier.  You only keep up with the ones you like the most out of thousands (and you forget about the rest).  In the paper, the selection is smaller and you are still constantly reminded of the bad ones.

Audience Focus.  This is related to the above point.  To stay in paper, a comic needs to appeal to at least a few percent of the papers’ readers, probably at least 10%.  Thus, you don’t have niche comics about specific games, jobs or hobbies.  However it’s just these comics that develop the most devoted fans.  You heard about ones that are appeal to you from members of your peer group and you came to love them.  Your favorite comics are ones that other people wouldn’t like.  To be fair, you would probably dislike their favorites just as much.

Fearlessness.  Webcomics can take risks and offend people.  Print comics will get ejected from the paper.

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Hypnocake

January 3, 2009 at 4:59 pm · Filed under Uncategorized ·Tagged ,

The Hypnocake is an Internet phenomenon so I had to try it out. So far we’ve made 6.

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IEEE Mentorship Dinner

November 19, 2008 at 9:30 pm · Filed under Uncategorized

This is me at the IEEE Mentorship Dinner on Tuesday of last week.
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Blogging Fringe Benefits

November 10, 2008 at 6:20 am · Filed under Uncategorized

Blogging pays off in ways you don’t expect. Two years ago I wrote a tongue-in-cheek way to cancel fractions. Early this year, book publisher Wiley Australia asked if they could put it in Maths Xpress 7 for VELS Level 5 Student Resource Book and eBookPLUS. Here’s the scan from my free copy.

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They changed a few of the words. I’ve never said “Cool, hey?” in my life. Nevertheless, it’s an honor.

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MRI Images

November 7, 2008 at 5:41 am · Filed under Uncategorized

I recently volunteered for an MRI study at Vanderbilt. I got to lay in the machine for 90 minutes while it made loud rattling and humming noises. It used a supposedly ultra-powerful magnet: 7 Tesla. The superpowers haven’t kicked in yet, but while we’re waiting, click the picture below for the rest of the slices.

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WKU Math Symposium ‘08

November 5, 2008 at 8:21 am · Filed under Uncategorized

Saturday morning, I gave a keynote at the 28th Annual Mathematics Symposium at Western Kentucky University.  My talk, “How Big Can You Think?” began with a simple problem whose answer is so large it cannot be written down, even approximately, with elementary notation, such as towers of exponents. I tried to follow by saying that this inexpressability can be resolved with more powerful notation that greatly extends our ability to concisely describe numbers. I finished with an example (the “Harvey Friedman number”) which defies even the arrow notation used for Graham’s Number.

I met many interesting people, including

Dr. Peter Hamburger
Dr. Molly Dunkum
Dr. Dominic Lanphier
Dr. John Armstrong
Dr. Jason Rosenhouse
Dr. David Benko
Dr. Peter Lax
Dr. Peter Dragnev
Dr. Claus Ernst
Dr. Barry Burnson

Finally, here’s a picture Natalie took of me just after I spoke.

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