Calculus from Washington

The White House is talking about derivatives again!  As in Calculus, though that’s not the word being thrown around.  Christina Romer is the Chair of the Council of Economic Advisers, and a week ago she was quoted in an article in the Christian Science Monitor (from the October 22 JEC hearing) as saying:

Most analysts predict that the fiscal stimulus will have its greatest impact on growth in the second and third quarters of 2009… By mid-2010, fiscal stimulus will likely be contributing little to growth.

That article apparently caused some confusion, so she clarified the situation in The White House Blog:

As a teacher, I should have realized that many people have trouble with the distinction between growth rates and levels….When we go from no stimulus to substantial tax cuts, increases in government spending, and aid to state governments, this has a large effect on the growth rate of real GDP – just as when you press hard on your car’s accelerator and go from 0 to 60, you have a great change in your speed. This sense of acceleration is exactly what we have been experiencing since the start of the year. Fiscal stimulus has been steadily increasing, raising GDP growth by between 2 and 3 percentage points in the second quarter and between 3 and 4 percentage points in the third quarter….. We expect that stimulus will continue to have a positive effect on growth in the fourth quarter of 2009 and well into 2010, though, by design, not by as much as it did in the second and third quarters of 2009. As a result, we expect the largest effect of the stimulus on the levels of GDP and employment to occur well after the largest effects on growth rates.

At some point, the stimulus plateaus at a high level. That is important too. Such continued stimulus may not add much to growth, but it is keeping the levels of GDP and employment much higher than they otherwise would have been – just as keeping pressure on the accelerator keeps the car going at 60 mph.

So here’s another kind of situation to discuss in those calculus classes!  And presumably the words “point of inflection” could also be brought into play, since that is apparently where Christina Romer thinks we are at right now.

*”again” referring to Hugo Rossi’s quote “In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection.” from the October 1996 Notices of the AMS.

HT:  smb

CSI: Calculus

Via xkcd:

Eat your heart out, David Caruso.

Math Careers: Astronaut

Additional training required.

Witness Lieutenant Colonel Robert Shane Kimbrough (who goes by Shane). He’s heading up into the sky Friday on the Space Shuttle Endeavor with Colonel Eric Boe and flight engineer Sandra Magnus. Lt. Col Kimbrough didn’t get his undergraduate degree in math (it was in Aerospace Engineering), but he got his MS in Operations Research from Georgia Tech and taught math at West Point. He’s given talks to school kids about how important math and science were in his being able to become an astronaut. And most recently he recognized his high school Calculus teacher (Sandy Sturgeon) in an official NASA letter because she was “instrumental in helping him get where he is today” and made calculus both real and fun.

For more information, see his official NASA biography or this recent article on ajc.com.

This is the premier post in a new series inspired by the common question, “What can I do with a degree in Math?”

Elvis does Calculus

That’s Elvis the dog, not Elvis the person. Elvis belongs to Tim Pennings from Hope College and likes to play fetch on the beach. When he went to catch a tennis ball, he’d run along the beach for a while and then swim. So his owner checked, and it turned out that he was using the nearly optimal path for reaching the tennis ball.

The video above is from CNN and a friend just sent it to me (thanks Ginny!). In doing a search I discovered that although I hadn’t heard it before, it’s been around for a while: Ivars Peterson wrote about it in Math Trek five years ago. Still, a story that features both calculus AND an Elvis? I couldn’t resist.

Line Rider Fun (or McDonald’s does Calculus)

Last year a few of our students discovered Line Rider — a computer game in which they could draw paths and a little sledder guy slides down and up. It’s a fantastic application of tangent lines (and therefore calculus with perhaps some vectors and physics), because in the version that I saw them doing last year they would simulate a curve by drawing lots of straight lines, as in this 83-second video:

It looks like Line Rider has gotten all fancy now (or maybe the artists are just more experienced) and you can draw curvy lines for the little guy to slide on. This inspired the following 30-second McDonald’s commercial:

Because calculus is so important, Line Rider has also been released for phones (Mobile in August and, according to a news release this past week, the iPhone and iPod Touch this month). No need to be without it ever!

Have you ever noticed how mathematicians count pretty much everything as applied mathematics? Yeah, I know, looking at the world through math-colored glasses!

Worms Do Calculus?

Well, according to this MSN story, they do. This will really make my students happy: “Come on! Even worms know how to differentiate!”

From John Scalzi, via Making Light.

The Calculus of Crabbing

TwoPi and I, still traveling around visiting family, were just on the Oregon coast for a few days. While we were there, my brother-in-law Ken took us out crabbing. The crabbing turned out to be a wash dinner-wise since they were too small, but the day was beautiful, the beaches calm, and as a bonus there was some cool math.

It seems that the best time to go crabbing is when the currents are weakest. To find out those times, Ken used a Tide Predictor:

The weakest tides are right at High Tide and at Low Tide. Why? That’s when the change in sea level — the derivative, in other words, is close to zero. Calculus in action! (Indeed, I imagine that current could be viewed as a kind of derivative of the sea height, since it is strongest when the slope of the water levels is changing the fastest.) As an aside, high tide is apparently better for catching crabs than low tide, but that has less to do with calculus and more to do with crustaceous personalities.

Edited 7/2 to add: I just realized that the second derivative also plays a role!  If the second derivative is closer to zero as well, it means that the current isn’t changing as quickly (in addition to not being very strong) so that gives a longer time period to check the traps and put them out again before the current gets strong enough that the crabs run back to the river sides or ocean.

If we hadn’t had the tide charts, we could have used this fancy Tide Clock on the wall:

Except it wasn’t working.

The tide itself leads to all sorts of other math problems. One of the neatest has to do with the cycles of the tides. The high tide peaks changed by almost 25 hours each day, not 24, so high and low tide cycle through different times of the year. It turns out that it takes 18.6 years for the pattern of high/low tide times to repeat itself. Apparently people used to be hired to take careful measurements of the tide and once the record stretched back 18.6 years, it was considered complete for that particular area. Not the most exciting job I suspect, but certainly important.

Friday Software Review: Maxima

This week we’ll look at Maxima, a computer algebra software (CAS) program. From the website:

Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors…Maxima can plot functions and data in two and three dimensions.

It has many of the same functions and capabilities as Maple and Mathematica and costs several hundred dollars less.