Continuous quantum

David Tong argues that quantum mechanics is ultimately continuous, not discrete.

In other words, integers are not inputs of the theory, as Bohr thought. They are outputs. The integers are an example of what physicists call an emergent quantity. In this view, the term “quantum mechanics” is a misnomer. Deep down, the theory is not quantum. In systems such as the hydrogen atom, the processes described by the theory mold discreteness from underlying continuity. … The building blocks of our theories are not particles but fields: continuous, fluid-like objects spread throughout space. … The objects we call fundamental particles are not fundamental. Instead they are ripples of continuous fields.

Source: The Unquantum Quantum, Scientific American, December 2012.

Pure math and physics

From Paul Dirac, 1938:

Pure mathematics and physics are becoming ever more closely connected, though their methods remain different. One may describe the situation by saying that the mathematician plays a game in which he himself invents the rules while the physicist plays a game in which the rules are provided by Nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen.

How to double science research

Scientists spend 40% of their time chasing grants according to some estimates. Suppose they spend 20% of their time doing something else, such as teaching. That means they spend no more than 40% of their time doing research.

If universities simply paid their faculty a salary rather than giving them a hunting license for grants, the faculty could spend 80% of their time on research rather than 40%. Of course the numbers wouldn’t actually work out so simply. But it is safe to say that if you remove something that takes 40% of their time, researchers could spend more time doing research. (Researchers working in the private sector are often paid by grants too, so to some extent this applies to them as well.)

Universities depend on grant money to pay faculty. But if the money allocated for research were given to universities instead of individuals, universities could afford to pay their faculty.

Not only that, universities could reduce the enormous bureaucracies created to manage grants. This isn’t purely hypothetical. When Hillsdale College decided to refuse all federal grant money, they found that the loss wasn’t nearly as large as it seemed because so much of the grant money had been going to administering grants.

How mathematicians see physics

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

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.

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Are tweets more accurate than science papers?

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

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

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.

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Cancer moon shots

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 1970’s.

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.

Related links: