Equations That Rhyme?

This space recently reviewed a book by a German physicist who spends a lot of time on issues connected to the concept of mathematical beauty. Most of us didn't encounter that idea when we took math, unless we really got into the subject. A mathematician has a slightly different view of beauty when he or she refers to an equation instead of a painting, natural scenic view or a person.

Turns out math can do a lot of things, like be a limerick. Math blogger "zorn-lemon" created the following equation:

The equation, when read in words, can be made into a limerick poem:

The integral of inverse two z
Taken over a circle, size e
Divided by i
Times square root of pi
Gives you gamma of one-sixth times three

My appreciation for this particular move does not mean I in any way understand the equation in either format.

Target Acquired

New Horizons, the unmanned spacecraft that gave us our best look at Pluto, took a look at its next target, a small body nicknamed Ultima Thule, in preparation for a flyby at the first of the year.

Because New Horizons is moving pretty lickety-darn-split out there, the course has to be the next best thing to perfect or better. If it's off, there's no chance to steer it quickly enough to adjust before the probe is well beyond the missed target.

Ultima Thule is what's called a Kuiper Belt Object -- a small body that's part of the Kuiper Belt of faraway solar system objects. In order to determine exactly where it is, observatories have to watch it pass in front of a star and block out the star's light. It wasn't actually discovered until 2014, eight years after New Horizons was launched.

So in other words, scientists are aiming a tiny probe flying at 29,000 miles an hour at a small piece of rock more than 46 times as far from the sun as we are. That's some precision work, I believe.

Getting Into the Music

The above pic is one taken by photographer Adrian Borda and while it might look like it's the first steps inside some centuries-hidden catacomb, it's actually from the inside of a cello. Some more images can be found here at Twisted Sifter.

Say Goodnight, Gracie

And then came the day that The Babylon Bee had to shut down because there was no room left for satire:

"Pope Says He Will Address Sex Abuse Scandal Once He’s Finished Talking About Climate Change"

-- Babylon Bee satire site

"'The Pope Has a Bigger Agenda': Cardinal Cupich"

-- NBCChicago

Worth Pondering

I had thought of digging through some internet news to make a post like this, but since Jim Geraghty gets paid and has more time for research, I'll just link to this piece by him on what he calls "the fair-weather admiration of John McCain."

The senator, who died Saturday, is being lionized by many who, at different points during his career, said other kinds of things about him. Some of that may be a case of people deciding to pay proper respect to someone who has passed so as not to add to the family's grief, which is an honorable choice. And I'm inclined to give the benefit of the doubt to many who now praise Sen. McCain after  damning him when it was more convenient to do so. I think they mean their condolences and tributes to his courage and decency.

Which would lead me to suggest they didn't mean their comparisons to fascism and jabs at his supposed wealth and insinuations he had an affair and hints that he had anger-management issues and questions about whether or not he would survive his term if he had won the White House, and so on. That's the kind of thing that should make one upset with those folks, but they had shouted, "Monster!" so many times at so many different people who weren't monstrous that when the real monster showed up with his bizarre hair and minimal depth and lack of character, people no longer listened. They now live and work in the situation they warned against, largely due to their own efforts. That's revenge enough.

Baby Numbers

The Teaching Company is the organization that sells video and audio lecture series called "The Great Courses." They're lectures by university professors based on courses that the professors may teach during the year. The lectures are usually altered a little bit to make up for the fact that there's rarely any supplemental reading material and certainly no assignments or exams, but most of the content is the same that they would teach a regular classroom of students.

I'm a customer, finding among the many and varied course offerings something now and again that's worth the cost of the download (The DVD's are often quite pricey). One was Dr. Dennis Kung's How Music and Mathematics Relate, which showed exactly that: The many ways in which things we see in music represent mathematical concepts and relationships. It didn't require expert level knowledge of either field, which is good because I have neither.

But the knowledge that I do have may have come hard-wired into my brain, or at least picked up at a very early age. This excerpt from one of Dr. Kung's lectures in the course describes experiments in which babies were shown to grasp simple arithmetical relationships like addition. Babies as young as five months showed they knew what should happen when they saw a second object added to a first object: they should see two objects. If they didn't, they stared longer trying to figure out what went wrong (I have had the same response when listening to elected officials describe how they will offer free stuff. And sometimes even other responses common to babies, such as shrieking and throwing things).

Dr. Kung also notes that experiments showed babies understood music as more than a string of random noises, well before they had begun to process the idea that certain sounds represent certain things. If they turned their heads one way, they heard one song, but if they turned their heads the other direction they heard a different song, and they were able to exhibit preferences early on. If they spit up, they heard Nickelback, and if they had filled their diapers they heard Kanye West. That last phase of the experiment was canceled when the babies in the tests developed constipation.

The temptation, of course, is to ask why elected officials seem unable to grasp certain things about math that are evident to us at the earliest stages of our development, such as what happens when numbers are added together and what happens when they are subtracted. But they understand it quite well: They take your money and my money, and then add it together and call it their money. It's not math they don't get; it's pronouns.

Mutually Assured Ick!

In today's reprint, Calvin demonstrates to Hobbes the perils of conflict escalation.

A lesson unheeded by the current administration and by too many of those who cover it professionally.