It Must Be Beautiful: Great equations of modern science

My current reading is rather fascinating. It’s actually a reread. I picked it up, along with Deborah Cameron’s The Myth of Mars and Venus, in a bookshop in Naas. I was in Naas for a job interview (I’ve forgotten what the job was for, but this must have been a chemistry job before I got into writing code, so a couple of years ago now). I’d not heard of either book before, and both called out to me as books I absolutely had to buy. I’ve read both more than once, so the instinct was a good one.

The concept of “beauty” in a scientific equation is perhaps a tricky one, and not all the equations in this book actually are beautiful. The Drake equation stands out as an odd choice. (For a start, despite its name, it’s a formula, not an equation. Also, it is not, by any reasonable definition, beautiful. It’s an interesting subject, yes, and the article on it is very well written, but the formula is emphatically not beautiful: it’s an ugly kludge.) There’s a different author for each equation, and some talk quite a lot about mathematical beauty, while others seem uncomfortable with the concept the editor has chosen and skip over it quickly, with an embarrassed cough.

The essays on Dirac and Einstein (there are three essays on Einstein) all make a great deal about mathematical beauty, but then so did both of those physicists, particularly Dirac.

I quite liked David’s review on Good Reads and shuttledude’s review on I agree with both that the writing is uneven, and the style of the essays is very varied, with some focusing directly on the equations themselves and others being more biographical sketches. I also agree with both that Robert May’s article on the logistic map and how chaos theory is applied to evolution, “The Best Possible Time to be Alive”, is absolutely top class: science writing at its best.

I do have a background in chemistry, and perhaps it is for this reason that I disagree with the assertions by David and Helen Joyce that chemical equations don’t count. I think the essay on the ozone layer and the effects of CFCs is perfectly at home in this book, and well written to boot. (There is, of course, real maths in chemistry too, but that’s not what’s covered in this chapter. It is mentioned that the rates of certain reactions seemed inconsistent, which lead to further research, but the mathematics of reaction kinetics (which is calculus) was not explored.)

From reading the reviews, it looks like the chapters are ordered differently in different editions. A few state conclusively that the book opens with the famous E=mc2. My edition, however, begins with an essay arguing that E=hf was actually Einstein’s most important work, even if it was Planck who came up with the equation itself.

The review by William G. Faris of the American Mathematical Society is rather in-depth, and is actually more an expansion on some of the mathematical concepts treated in the book than a typical review.

The authors of the chapters in this volume do a remarkable job of showing how each of the great equations is situated in a broad cultural context. The equation itself is at the center. But the geometry is something like that of a black hole; the actual equation remains nearly invisible to the general reader. One of the privileges of being a mathematician is that one is allowed a glimpse inside.

Is it a strength or a weakness of the book that in many of the essays the equation itself is “nearly invisible to the general reader”? (The Dirac equation is relegated to the notes at the end of the book.) Probably a weakness. The strongest essays in the book tackle their equations head-on. Once again I’ll mention the logistic map, and add Igor Aleksander on the Shannon equations. Next to those two I’d place the other biological entry, John Maynard Smith talking about evolution and game theory. And then I’d put the essay that other reviewers felt was out of place, Aisling Irwin on the Molina-Rowland chemical equations and the hole in the ozone layer.

A review by American Scientist, quoted in the book itself, praises specifically Christine Sutton’s essay on the Yang-Mills Equation (an essay which managed to cover interesting historical and biographical detail, and also tackle particle physics in great detail) and Roger Penrose’s article on the Einstein equation of general relativity.


Were you there in the aspen grove?

I’ve always liked the name aspen. There’s something pleasing about it. And the trees are pleasing too. They’re related to the birch, and it was nice to see some real broad leaf trees when I was in Colorado: the dark pines were making me feel hemmed in: it was quite oppressive, really, and the scrub oak was no help: it served only to remind me that real oak trees didn’t grow there.

I didn’t get to see the Trembling Giant, which is in Utah. It’s an 80,000-year-old grove of aspens, which is actually one single colony (all the trees (roughly 47,000) share a root system), meaning that this is the oldest (and probably heaviest) known living organism. (Follow that link: it’s got more information, and some lovely photos.)

This beautiful aspen grove, is, of course, one of many proofs that the world is older than Ken Ham would care to admit. He wouldn’t accept that. Were you there?, he’d ask.

Well, no, of course not. And then again, yes. The past is ever-present, and we always see things as they were. Michael Busch reminds us that “what we perceive as now is a fuzzy stretch of time many hundredths of a second long”.

As PZ Myers says,

I pity those unable to see the grand arena they are a small part of, who want to deny that history is observable.


I believe: How it works

British pharmacists are allowed as a matter of conscience by their regulatory body to pretend they believe that contraception is an “abortifacient”.

A pharmacist who claims to believe that emergency contraception (or even regular daily contraception) is an “abortifacient” is either lying in order to justify imposing their religious views on other people, or is allowing their religious beliefs to overrule their scientific training.

Meanwhile, in America, Hobby Lobby thinks it should be exempt from covering medical care “they believe” causes abortion.

So Hobby Lobby’s legal claim is that a company has a “religious liberty” right to avoid anything they say causes abortion even if it does nothing of the sort.

If Hobby Lobby were to be granted such an exemption, then, what would prevent any other corporation from claiming that it believes minimum wage laws, OSHA regulations, nuclear safety rules and fire codes are also “abortifacient”?

What Hobby Lobby is seeking isn’t merely some legal permission to be exempt from providing health insurance. The corporation is seeking the “religious liberty” to redefine reality and to rewrite the laws of medicine, human anatomy, biology and chemistry.

The medical care they’re talking about is, again, emergency contraception, which (keep up) does not cause abortion. It doesn’t even cause abortion in the very narrow sense of preventing implantation, which most medical experts would not call abortion anyway:

There were studies done that show that overly huge amounts of estrogen can cause failure to implant in mice, so that warning was stuck on Plan B while they studied it in human vagina owners. But no proof has been found that it happens in human women.

Of course, this is actually all about sex:

If Hobby Lobby said that they believed cancer was caused by sinful behavior, and therefore they weren’t covering chemotherapy, they would be shamed so fast they wouldn’t know what hit them.

Except when it’s all about politics:

I note in passing that Hobby Lobby is neither passionately sincere or sincerely passionate.  They offered this coverage without any qualms until they found out that President Obama wanted to make them do it.


Monkey Chimeras

What is a chimera?

In Greek mythology, the Chimera was a fire-breathing monster–part goat, part snake, and part lion–borne of a half-woman half-snake mother, Echidna, and a part-viper part-dragon father, Typhon. Nifty, right? But in science, a chimera is a single animal formed from fusing at least two separate zygotes or blastocysts. That means at least two sperm and two eggs have all genetically contributed to one, fully-functioning, chromosomally normal individual. It might just be me–but I find this even more compelling than any mythological lion-goat-snake concoction.

Mouse chimeras are fairly common, but now researchers at the Oregon National Primate Research Center have announced a monkey chimera.

Their paper has many, many implications–but one of them is that primate development is critically different from mouse development.


Movement on Theology

Whenever we find ourselves concluding that a question is just too large to ever answer, I think it’s instructive to remind ourselves that we solved the biggest problem of them all.

Hold that thought. We’ll come back to it.

Theology has questions to answer. For example,

One of the vibrant issues across a number of academic disciplines, including theology, is the very broad area of ‘consciousness’.

This is a question theology addresses. It’s also a question addressed by neuroscientists, computer scientists, evolutionary biologists, and others. Where do you expect the answers to come from?

Science is what you know, philosophy is what you don’t know.

Bertrand Russell.

Theology has answered many questions. It’s answered a lot of them wrongly.