How mathematicians see physics

Posted on 21 February 2013 by John

From the preface to Physics for Mathematicians:

In addition to presenting the advanced physics, which mathematicians find so easy, I also want to explore the workings of elementary physics, and mysterious maneuvers — which physicists seem to find so natural — by which one reduces a complicated physical problem to a simple mathematical question, which I have always found so hard to fathom.

That’s exactly how I feel about physics. I’m comfortable with differential equations and manifolds. It’s blocks and pulleys that kick my butt.

History of weather prediction

Posted on 19 February 2013 by John

I’ve just started reading Invisible in the Storm: The Role of Mathematics in Understanding Weather, ISBN 0691152721.

The subtitle may be a little misleading. There is a fair amount of math in the book, but the ratio of history to math is pretty high. You might say the book is more about the role of mathematicians than the role of mathematics. As Roger Penrose says on the back cover, the book has “illuminating descriptions and minimal technicality.”

Someone interested in weather prediction but without a strong math background would enjoy reading the book, though someone who knows more math will recognize some familiar names and theorems and will better appreciate how they fit into the narrative.

Are tweets more accurate than science papers?

Posted on 31 October 2012 by John

John Myles White brings up an interesting question on Twitter:

Ioannidis thinks most published biological research findings are false. Do you think >50% of tweets are false?

I’m inclined to think tweets may be more accurate than research papers, mostly because people tweet about mundane things that they understand. If someone says that there’s a long line at the Apple store, I believe them. When someone says that a food increases or decreases your risk of some malady, I’m more skeptical. I’ll wait to see such a result replicated before I put much faith in it. A lot of tweets are jokes or opinions, but of those that are factual statements, they’re often true.

Tweets are not subject to publication pressure; few people risk losing their job if they don’t tweet. There’s also not a positive publication bias: people can tweet positive or negative conclusions. There is a bias toward tweeting what makes you look good, but that’s not limited to Twitter.

Errors are corrected quickly on Twitter. When I make factual errors on Twitter, I usually hear about it within minutes. As the saga of Anil Potti illustrates, errors or fraud in scientific papers can take years to retract.

(My experience with Twitter may be atypical. I follow people with a relatively high signal to noise ratio, and among those I have a shorter list that I keep up with.)

Sun, milk, red meat, and least-squares

Posted on 26 October 2012 by John

I thought this tweet from @WoodyOsher was pretty funny.

Everything our parents said was good is bad. Sun, milk, red meat … the least-squares method.

I wouldn’t say these things are bad, but they are now viewed more critically than they were a generation ago.

Sun exposure may be an apt example since it has alternately been seen as good or bad throughout history. The latest I’ve heard is that moderate sun exposure may lower your risk of cancer, even skin cancer, presumably because of vitamin D production. And sunlight appears to reduce your risk of multiple sclerosis since MS is more prevalent at higher latitudes. But like milk, red meat, or the least squares method, you can over do it.

More on least squares: When it works, it works really well

Personalized medicine

Posted on 10 October 2012 by John

When I hear someone say “personalized medicine” I want to ask “as opposed to what?”

All medicine is personalized. If you are in an emergency room with a broken leg and the person next to you is lapsing into a diabetic coma, the two of you will be treated differently.

The aim of personalized medicine is to increase the degree of personalization, not to introduce personalization. In particular, there is the popular notion that it will become routine to sequence your DNA any time you receive medical attention, and that this sequence data will enable treatment uniquely customized for you. All we have to do is collect a lot of data and let computers sift through it. There are numerous reasons why this is incredibly naive. Here are three to start with.

Maybe the information relevant to treating your malady is in how DNA is expressed, not in the DNA per se, in which case a sequence of your genome would be useless. Or maybe the most important information is not genetic at all. The data may not contain the answer.
Maybe the information a doctor needs is not in one gene but in the interaction of 50 genes or 100 genes. Unless a small number of genes are involved, there is no way to explore the combinations by brute force. For example, the number of ways to select 5 genes out of 20,000 is 26,653,335,666,500,004,000. The number of ways to select 32 genes is over a googol, and there isn’t a googol of anything in the universe. Moore’s law will not get us around this impasse.
Most clinical trials use no biomarker information at all. It is exceptional to incorporate information from one biomarker. Investigating a handful of biomarkers in a single trial is statistically dubious. Blindly exploring tens of thousands of biomarkers is out of the question, at least with current approaches.

Genetic technology has the potential to incrementally increase the degree of personalization in medicine. But these discoveries will require new insight, and not simply more data and more computing power.

Cancer moon shots

Posted on 21 September 2012 by John

M. D. Anderson Cancer Center announced a $3 billion research program today aimed at six specific forms of cancer.

Acute myeloid leukemia and myelodysplastic syndrome (AML and MDS)
Chronic lymphocytic leukemia (CLL)
Lung cancer
Melanoma
Prostate cancer
Triple negative breast and ovarian cancer

These special areas of research are being called “moon shots” by analogy with John F. Kennedy’s challenge to put a man on the moon. This isn’t a new idea. In fact, a few months after the first moon landing, there was a full-page ad in the Washington Post that began “Mr. Nixon: You can cure cancer.” The thinking was the familiar refrain “If we can put a man on the moon, we can …” President Nixon and other politicians were excited about the idea and announced a “war on cancer.” Scientists, however, were more skeptical. Sol Spiegelman said at the time

An all-out effort at this time would be like trying to land a man on the moon without knowing Newton’s laws of gravity.

The new moon shots are not a national attempt to “cure cancer” in the abstract. They are six initiatives at one institution to focus research on specific kinds of cancer. And while we do not yet know the analog of Newton’s laws for cancer, we do know far more about the basic biology of cancer than we did in the 1970s.

There are results that suggest that there is some unity beyond the diversity of cancer, that ultimately there are a few common biological pathways involved in all cancers. Maybe some day we will be able to treat cancer in general, but for now it looks like the road forward is specialization. Perhaps specialized research programs will uncover some of these common patters in all cancer.

True versus Publishable

Posted on 13 September 2012 by John

This weekend John Myles White and I discussed true versus publishable results in the comments to an earlier post. Methods that make stronger modeling assumptions lead to more statistical confidence, but less actual confidence. That is, they are more likely to produce positive results, but less likely to produce correct results.

JDC: If some scientists were more candid, they’d say “I don’t care whether my results are true, I care whether they’re publishable. So I need my p-value less than 0.05. Make as strong assumptions as you have to.”

JMW: My sense of statistical education in the sciences is basically Upton Sinclair’s view of the Gilded Age: “It is difficult to get a man to understand something when his salary depends upon his not understanding it.”

Perhaps I should have said that scientists know that their conclusions are true. They just need the statistics to confirm what they know.

Brian Nosek talks about this theme on the EconTalk podcast. He discusses the conflict of interest between creating publishable results and trying to find out what is actually true. However, he doesn’t just grouse about the problem; he offers specific suggestions for how to improve scientific publishing.

Related post: More theoretical power, less real power

Flying to Mars in three days

Posted on 30 August 2012 by John

Richard Campbell brought up an interesting idea in his recent Mars geek out show. Suppose you could travel to Mars accelerating at 1 g for the first half the trip, then decelerating at 1 g for the final half of the trip. Along the way you’d feel a force equal to the force of gravity you’re used to, and you’d get there quickly. How quickly? According to the show, just three days.

To verify this figure, we’ll do a very rough calculation. Accelerating at 1 g for time t covers a distance is g t²/2. Let d be the distance to Mars in meters, T the total of the trip in seconds, and g = 9.8 m/s². In half the trip you cover half the distance, so 9.8 (T/2)²/2 = d/2. So T = 0.64 √d.

The hard part is picking a value for d. To keep things simple, assume you head straight to Mars, or rather straight toward where Mars will be by the time you get there. (In practice, you’d take more of a curved path.) Next, what do you want to use as your straight-line distance? The distance between Earth and Mars varies between about 55 million km and 400 million km. That gives you a time T between 1.7 and 4.7 days.

We don’t have the technology to accelerate for a day at 1 g. As Richard Campbell points out, spacecraft typically accelerate for maybe 20 minutes and coast for most of their journey. They may also pick up speed by slinging around a planet, but there are no planets between here and Mars.

Deniers, skeptics, and mavericks

Posted on 21 July 2012 by John

Suppose a scientist holds a minority opinion. There’s a trend in journalism to call him a denier if you think he’s wrong, a skeptic if you don’t care, and a maverick if you think he may be right. If this had been the norm in Einstein’s day, he might have been called a Newton-denier.

“Denier” is an ugly word. It implies that someone has no rational basis for his beliefs. He’s either an apologist for evil, as in a Holocaust denier, or mentally disturbed, as in someone in psychological denial. The term “denier” is inflammatory and has no place in scientific discussion.

Ancient understanding of tides

Posted on 15 July 2012 by John

In his essay On Providence, Seneca (4 BC – 65 AD) says the following about tides:

In point of fact, their growth is strictly allotted; at the appropriate day and hour they approach in greater volume or less according as they are attracted by the lunar orb, at whose sway the ocean wells up.

Seneca doesn’t just mention an association between lunar and tidal cycles, but he says tides are attracted by the moon. That sounds awfully Newtonian for someone writing 16 centuries before Newton. The ancients may have understood that gravity wasn’t limited to the pull of the earth, that at least the moon also had a gravitational pull. That’s news to me.

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