One day, a farmer called up a mathematician, a physicist,
and an engineer and asked them to fence the largest possible area with the
least amount of fence. The engineer made a circular fence and proclaimed he had
the most efficient design. The physicist made a long, straight fence
proclaimed, “We can assume the length is infinite…” and pointed out that
fencing off half of the earth was certainly a more efficient way to do it. The
mathematician laughed at them. He proceeded to build a tiny fence around
himself and said, “I declare myself to be on the outside.”
Those crazy mathematicians. I like to think of myself as
a mathematician, a scientist, and an engineer. I am a graduate student in
mechanical engineering, which makes me an engineer, though not yet a
professional one. As for mathematician and scientist, well, I just really like
math and science. I know liking math sounds crazy, but there are really fun
things it can do if you get past the nasty stuff.
Like prove that your friends are more popular than you. That may not be an appealing thought, and it
seems counter-intuitive but on average it is true. For example, a survey by the
Pew Research Center found that the average number of friends a Facebook user
has is 245, which makes me seem rather unpopular. They found that the average number of friends
that a Facebook user’s friend has is 359. The average user has 245 friends and
their friends have 359 friends on average. How can those numbers be different?
Well, this is a well-known phenomenon called the
friendship paradox. It isn't really a paradox if we just examine the math. We
are dealing with averages here, so it would help to review. When you take an
average, you add up bunch of numbers and divide the sum by how many numbers you
added together. The average of 8, 23, and 17 is (8+23+17)/3 = 48/3 = 16.
Easy peasy. In the Pew survey, they added up how many friends each person in
the survey had, and divided by the number of people in the survey. The number
of friends of friends is a little different. We add each person’s number of
friends into the total every time they are someone’s friend. So imagine there
is someone on Facebook with 10,000 friends. That means he shows up on 10,000
people’s friend lists and puts his 10,000 friends into the average 10,000
times. Then think of the guy with two friends. He only brings down the average
with his two friends twice. Popular people show up more in the average and pull
the number up. Thinking about it this way, I’m surprised the real numbers aren't farther apart.
Speaking of friends, doesn't everyone have at least one
sarcastic friend? For example, when I am trying to lift something heavy through
a small opening and it doesn't fit, there is a loud thump (and hopefully not a
crash) and someone makes a comment about how I must not understand physics. I
think square peg and a round hole is preschool material at the latest, and that
is what we are really dealing with when something doesn't fit through an
opening. Is that even physics?
It is, if we realize this problem boils down to why solid
objects can’t pass through each other. What is it that makes objects solid? The
answer is of course, science. Physics, specifically quantum mechanics.
Basically, when the electrons on something come really close to the electrons
in something else, they repel just like two negative magnets. Except that
electrons are really tiny, so the range over which they repel each other is
also tiny, and it looks to us like the objects touch. (Henry over at minutephysics has an interesting discussion on whether or not this is actually “touching.”) So it turns out that
it is physics stopping me from getting the square peg in the round hole, even
if my two-year-old knows it won’t work.
Math and science may be my hobbies, but engineering is my
livelihood. I came across an interesting article (autoblog.com article from 1/18/13 on the McLaren P1) recently that proves that my graduate
research is relevant (always a plus). My dissertation is on crashworthiness of
composites, basically designing carbon fiber so that it performs well in a
crash. McLaren, who made the mighty F1 supercar in the 90’s, is coming out with
a successor to that car, the P1, seen below. It is going to be an extremely expensive and
fast carbon-fiber wondercar. The interesting bit for me is that the crash
structures are made of aluminum, because “carbon fiber is lighter, but it
doesn't crush and absorb energy as well.” I don’t know if that statement came
from a McLaren representative or not, but I beg to differ. Carbon fiber is
lighter, yes, but it can also crush and absorb energy much better than any
aluminum alloy when it is well designed. And that is just it: designing carbon
fiber for crashworthiness is hard to do. It has to crush in a certain way in
order to perform well. If it crushes in the wrong way it will be terrible. I am
researching how to design carbon fiber so that it crushes well. My research matters!
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| 2014 McLaren P1 (http://www.desktopmachine.com/framepic.php?id=28324) |
It takes all three parts of me to be a good engineer.
Science is really just math applied to the world around us, and engineering is
just science applied to making things. I was inspired to write a blog by two of
my cousins, Jonathon who writes an excellent grammar blog (way more interesting
than it sounds) and Logan, who writes a sports blog using his background in
statistics that has an amazing predictive track record. I could just write
about engineering, but I love math and science so much that I couldn't leave
them out. Which kind of makes me sound like a joke.
