Math Hacks and Potato Sacks: Day in the Life of a Physicist

After Years
Today, from a distance, I saw you
walking away, and without a sound
the glittering face of a glacier
slid into the sea. An ancient oak
fell in the Cumberlands, holding only
a handful of leaves, and an old woman
scattering corn to her chickens looked up
for an instant. At the other side
of the galaxy, a star thirty-five times
the size of our own sun exploded
and vanished, leaving a small green spot
on the astronomer's retina
as he stood on the great open dome
of my heart with no one to tell.
—Ted Kooser

One of my favorite poems from many years ago. :) I recently remembered it after seeing an email The Writer's Almanac sent me saying that they'd interviewed Ted Kooser in celebration of National Poetry Month. Check out Ted Kooser's interview here: http://writersalmanac.org/bookshelf/ted-kooser/?utm_campaign=APM%20TWA%2020160401%20NPM%20interview%201%20Ted%20Kooser%20Email&utm_medium=email&utm_source=Eloqua&utm_content=An%20interview%20with%20Ted%20Kooser&elqTrackId=cf8aceae637f40ef83a45f543d53987d&elq=b13c7058852a4232829a4e21c10175f6&elqaid=21346&elqat=1&elqCampaignId=18492

But anyhow, let's swing back onto the SRP train. Choochoo!


So we finally got some results that make sense!

Like I said, we are calculating the error on the parameters using the inverse Fisher matrix method using a program called Mathematica to do all our calculations. We set B=6*10^-21 s^-1/3, f_h=75Hz, and f-l=50Hz and calculated the terms. However, when we were trying to find the inverse matrix, Mathematica kept producing an error message. Mathematica was having trouble calculating the inverse matrix because our matrix terms were very different in scale. For example, our first row first column term was 1.9258`*^43, our first row second column term was 4.6191*10^21, and our second row second column term was -.94581. Here's a screenshot of our matrix and inverse matrix calculations.

Woohoo, bleeding off the blog. I don't care.

Let me explain the matrix a little. So the diagonal values (1st row, 1st column; 2nd row, 2nd column; 3rd row, 3rd column) of the inverse matrix are the values that will give us the error on our parameters: amplitude (B), high frequency cutoff (f_h), and low frequency cutoff (f_l). The square root on the 1st diagonal term=the error on B, the square root of the 2nd diagonal=error on f_h, and the square root of the 3rd diagonal=error on f_l.

But anyhow, so after we got this error message, we had to get creative. How could we get our terms to be closer in scale to each other? So Dr. Zanolin created this math hack where we set B=e^c, c=-46.5625274836 when B=6*10^-21. This way, when we take the derivative with respect to B, nothing happens(!) because the derivative of e^c is just e^c.

When Dr. Zanolin showed us this, I thought it was kind of cheating. You can't just manipulate the equations like that. But time and time again, he shows us that you can just look at the math in a different way, do some manipulating, and get an answer where before you couldn't. That's one thing about physicists and mathematicians. They just create new math sometimes. I also noticed this in Physics C when we were learning how to use Gaussian surfaces to calculate the electric field of a 3-D object. It's such an out-of-the-box way to do it, you wonder how Gauss even thought it up. So, in order to be a good physicist/mathematician, you have to be a very creative problem solver. And, you know, understand math very well.

However, I feel like we don't really learn how to be creative problem solvers in math class. We only learn how to be problem solvers. And you don't really need to understand math super well to solve the problems, you just need to recognize the patterns and practice practice practice, and if you practice enough times, you don't really have to know what you're doing, you just replicate what you did before. Does that count as problem solving even? Well, you can probably develop creative problem solving skills just like you develop other skills, so maybe practice does help. We'll see.

Here is the new matrix and inverse matrix calculated using the e^c method.

Notice how close in value the second diagonal (2nd row, 2nd column) and third diagonal (3rd row, 3rd column) terms are in the e^c inverse matrix to their corresponding terms in the original inverse matrix. Crazy huh? But what about the 1st diagonal (1st row, 1st column)? Because we set B=e^c, the first diagonal=the error on c, not B.

So once we calculated the error on B based on the error on c, we got our results! Here they are:

Remember that B=6*10^-21, f_h=75, and f_l=50, so these values for error are reasonable. We still need to do checks to make sure these are correct, but many mistakes and math hacks later, we have results that make sense.

I think I'm done. I kind of want to talk about how quirky physicists are, but I'm tired. I'll tell one story.

Dr. Zanolin was telling me one day about how weird physicists are, and he gave me a bunch of examples from his own experiences. I think he was at MIT, and all the physicists decided to have a potato sack race. Who knows why. But there they all were, a bunch of old white guys lined up on the field, standing in their potato sacks. The race began. You wouldn't think these old white guys with their heads in the stars would be very energetic, but when it comes to potato sack races, physicists can get competitive. They may have Nobel Prizes and PhDs, but none of that matters in the sack. Some guy in the back of the pack started elbowing his coworkers to the ground to get in front. Someone gave the Director of the Physics Department a bloody nose. And all of them were fierce sack hoppers.

I have other funny stories, especially about how physicists dress, so if you enjoyed that one, I'll post more.

But I'm done for now.

Goodnight (or good morning or good afternoon, for whenever you read this).

With utmost sincerity,

Carissa