Why is the Universe Mathematical?

Why is our scientific description of the universe based on mathematics? If you've taken physics or chemistry classes, it might seem obvious that the laws of nature are mathematical, but in fact it's a very deep mystery. I should admit right from the start that I am not a particular expert on this subject, but since this is a blog, I am entitled to spout off about all sorts of things that I know nothing about. Caveat emptor. By the way, I also don't speak Latin. I just use it to make myself appear smarter than I really am.

Eugene Wigner, who was one of the great figures in quantum mechanics, was one of the first people to think about this problem. He wrote a famous article on it:  "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," which you can read here.  But why is this even a mystery? The way we learn mathematics in school obscures the true nature of math. In grade school and high school, math is firmly embedded in physical reality -- it's a way of solving real-world problems. We learn arithmetic in order to balance our check books (does anyone besides me do that anymore?) and we learn algebra in order to determine the age of our friends, like Suzy, who is twice as old as Jim was when Jim was as old as Suzy is now.  But "real" mathematics, as practiced by professional mathematicians, is nothing like that. Mathematics involves the construction of increasingly complex mathematical structures, which seem to have no basis in physical reality. If you doubt my view, take a look at a random entry at the Mathworld website.  And yet abstract mathematical structures frequently turn up in physical theories, often decades after they were first invented. Differential geometry, which examines curved spaces that seem to have no relation to the physical universe, turns out to be the basis of general relativity (whose centenary we are celebrating this month). Abstract algebra (not the algebra you learned in high school, but things like group theory and linear algebra) lies at the foundation of quantum mechanics. So why do these inventions of mathematicians turn up so reliably in physical theories?

Woodrow Wilson Trivia Question

Some of you might have noticed the recent kerfuffle about the position of Woodrow Wilson at my alma mater, where it seems like every other building is named after him. The reason for all of this Wilson hagiography is that Wilson was not merely a graduate of Princeton who became president of the United States, but that he was also a faculty member at Princeton and, ultimately, president of the university itself.

As I was contemplating the fact that Wilson was the only university president ever to become president of the United States, I realized that his career path was not unique. There is one other man who served as a university president before being elected president of the U.S. Can you name him? (Hint: like Wilson, he was the head of an Ivy League university).

Could We Still Exist if the Constants of Nature Were Different?

Physics is characterized by a handful of "fundamental constants."  For instance, the gravitational constant, G, tells us the force of gravity between different masses.  Similarly, the "fine structure constant" gives the electric force between two charges.  Does our existence depend on the values of these constants?  If they were different, could life still exist?

Probability and Statistics in Science Fiction

My previous post on mathematics in science fiction had a serious omission -- I ignored probability and statistics. These two subjects are often lumped together, but they are, in a way, opposites. In probability, you know the rules of the game ahead of time (I roll a die, and each number from one to six is equally likely) and you have to calculate the odds of various outcomes (how likely is it that I will roll three sixes in a row?)  Statistics is just the opposite:  you are given the outcomes and are trying to figure out the rules of the game. If you have a bunch of "data", what is the likelihood that they were produced from a particular model of the universe? In his book Numerical Recipes, Bill Press and his collaborators describe statistics as "that gray area which is surely not a branch of mathematics as it is neither a branch of science."  I couldn't agree more.

Probability is clean and precise, and I really enjoy it.  I've written several papers about the pattern of galaxy clustering in the universe (technically, this is called the "large-scale structure" of the universe) based largely on different aspects of probability theory.  Probability is my friend.

Statistics, on the other hand, is not my friend.  It's a necessary evil, like a decennial colonoscopy. Statistics is the Norse trickster god Loki -- it's slippery and untrustworthy.  There are even different sects within statistics whose members base their analyses on completely different fundamental assumptions.  For example, you can be a Bayesian or a frequentist -- these two groups fought an inconclusive war that devastated Germany in the 17th century.  (By the way, don't believe everything you read on the internet). For a less jaundiced and undoubtedly more accurate view of statistics, read the various posts on Michael Flynn's blog, such as this one.

Our Linguistic Debt to Chickens

There are four chickens living in my back yard. How did they get there? What road did they cross to get to my yellow slide? It happened in much the same way that I ended up with a dog: I returned home from work one day and discovered that we had adopted a small flock of chickens. So I am now the proud owner of a Metro Public Health Department Domesticated Hen Permit.

Once, after asking my kids if the chickens were "cooped up" for the night, and thinking about the "pecking order" that the chickens had established, I realized how many everyday English words and expressions we owe to chickens, and how accurately they describe the actual behavior of chickens.

No Radio Signals from KIC 8462852

Well that didn't take long. The SETI folks used the Allen Telescope Array to look for radio emissions from the star KIC 8462852 -- that's the star I discussed last week that shows an unusual pattern of dimming and brightening. You can read the scientific paper here. (They've got to find a shorter name for that star. How about KIC MEE?). So what did the SETI investigators hear over the radio?

Sailin' Through the Solar System

I first encountered the idea of solar sails in the Arthur C. Clarke story, "Sunjammer."  Yesterday, Les Johnson came up from the Marshall Space Flight Center in Huntsville to give an excellent talk on this topic -- I learned a few fun things I hadn't known before.  But first, a trivia question:  Do solar sails operate by catching the solar wind?

Mathematics in Science Fiction

Are there any examples of science fiction in which math plays the central role?  Before examining that question, let me pose a simpler one: is mathematics a branch of the sciences, like physics or astronomy?

Have We Discovered a Dyson Sphere Under Construction?

Many of you have probably seen this article over at The Atlantic.  The basic story is that the Kepler mission, which is designed to look for planets orbiting other stars, has turned up something very strange.  And no one is exactly sure what it is.

Best. Comic Book. Superhero. Ever.

Many years ago, when I was still working at Ohio State, I had the opportunity to have lunch with Steven Weinberg.  For those of you not familiar with his work, Weinberg is one of the towering figures of 20th century physics.  He shared the 1979 Nobel Prize for his role in the development of the unified theory of electromagnetism and the weak force, a key component of what is now known as the Standard Model of particle physics (yes, it's capitalized).

During lunch, the conversation turned, as it so often does among Nobel laureates, to the subject of comic books.  Weinberg opined that when he was young, parents wouldn't let their kids read comic books, because they were "trash," but these days most parents would be thrilled if their kids read anything at all, including comic books.

So are comic books a form of science fiction?  Of course they are, because they draw on many of the same ideas and themes as mainstream science fiction.  And of course they're not, because a science fiction snob like me will never admit that books with pictures and conversation bubbles should be placed among the pantheon of science fiction.  Yes, I know that comic book conventions regularly outdraw science fiction conventions by factors of 10 or 100 in attendance  Let's not talk about that.

Random Thoughts on The Martian (the Movie, not the Book)

I saw The Martian over the weekend and enjoyed it a lot. I particularly appreciated the fact that the plot did not lurch from one heart-stopping crisis to another. I won't belabor the science issues in the movie, since those have already been widely discussed on the Internet. The biggest one has to do with the Martian "storms." The atmosphere on Mars is so thin that it wouldn't be capable of the kind of death and destruction you see at the beginning of the movie.

Also, the gravity on Mars is much lower than on Earth, but this only becomes apparent near the end of the movie, when Matt Damon begins bouncing around a lot more. Or maybe he just lost a lot of weight from his starvation rations.

Fantasy Physics League

Fantasy sports leagues have been in the news lately, and not in a good way. There have been scandals involving "insider trading," and Nevada is in the process of classifying fantasy sports as gambling. So what should you do if the Feds shut down your fantasy sports league? Try fantasy physics instead!

College Admissions: A Story

I have an Op-Ed out in today's Wall Street Journal on the subject of college admissions -- I was driven to write it by my experiences with the admissions process as child number three has reached that stage. When my oldest child applied for college, my exasperation took the form of a short story, "The Common App", that was published in Nature.  If you'd like to read it, follow this link.

Physics Nobel Prize Trivia

The Nobel Prize in physics was announced today, so this is a good time for Nobel Prize trivia.

What Nobel laureate was sentenced to prison for war crimes?  Hint: he has an "effect" named after him.

Gregory Benford Talk at Vanderbilt this Thursday

I wanted to remind those of you in the Nashville area that noted science fiction writer and scientist Gregory Benford will be presenting our physics colloquium this Thursday, Oct. 8, at 3:00 in Stevenson 4327. The title of his talk is "Our Next Century in Space." The talk is free and open to the public.  Parking at Vanderbilt, however, is very much not free and barely open to the public. There are pay parking spots on the ground floor of the 25th Avenue Garage, and also metered parking on the street in front of the VA hospital (both a short walk to Stevenson Center). The metered parking has a two-hour limit. I believe that there is also free on-street parking once you get far enough east of campus, but I don't know how far east you have to go. Maybe Knoxville.