Category: Science
Quantum Game Theory
Let’s play a coordination game: You and I are each asked a single question, either “Do you like cats?” or “Do you like dogs?”. Our questions are determined by independent coin flips. We both win if our answers differ, unless we’re both asked about dogs, in which case we both win if our answers match.
Here’s a pretty good strategy we could agree on in advance: We’ll contrive to always differ. Whatever we’re asked, I’ll say yes and you say no. That way we win 3/4 of the time.
Can we do any better? No, if we live in a world governed by classical physics. Yes, if we live in the world we actually inhabit—the world of quantum mechanics.
All we need is a pair of entangled particles, easy enough to create in the laboratory. If I get the cat question, I’ll measure my particle’s spin (which is either up or down) and answer “yes” or “no” accordingly. If I get the dog question, I’ll do the same thing, but first I’ll rotate my measuring apparatus by 90 degrees. You do the same, but start with your measuring apparatus rotated 45 degrees from
mine.
The thing about entangled particles is that the outcomes of these measurements are correlated in a very particular way, and remain so forever, even if the particles are separated. In particular, our answers will differ about 85% of the time unless we both make “dog” measurements, in which case they’ll agree about 85% of the time. Overall, then, we’ll have about an 85% win rate. Those particular correlations would be impossible to achieve with any set of measurements if our electrons obeyed the laws of classical physics.
(More precisely, our win rate is cos2(pi/8).)
I took this example from a beautiful paper by Richard Cleve, Peter Hoyer, Benjamin Toner and John Watrous. (The paper has a lot of other cool examples too.) The moral is that game theory changes dramatically when players have access to quantum technology—which might sound very science fictiony at the moment but probably won’t in another couple of decades.
The Flu versus Anthrax
Annual U.S. Deaths Due to the Flu: approx 36,000.
Annual U.S. Deaths Due to Anthrax: ~1.
Spending on R&D to fight Flu: $283 million.
Spending on R&D to fight Anthrax and other biological agents: $5.6 billion.
The history of life, on a postcard?
Will your children see an exponential growth explosion? Here is Robin Hanson’s latest:
A revised postcard summary of life, the universe, and everything, therefore, is that an exponentially growing universe gave life to a sequence of faster and faster exponential growth modes, first among the largest animal brains, then for the wealth of human hunters, then farmers, and then industry. It seems that each new growth mode starts when the previous mode reaches a certain enabling scale. That is, humans may not grow via culture until animal brains are large enough, farming may not be feasible until hunters are dense enough, and industry may not be possible until there are enough farmers.
Notice how many “important events” are left out of this postcard summary. Language, fire, writing, cities, sailing, printing presses, steam engines, electricity, assembly lines, radio, and hundreds of other “key” innovations are not listed separately here. You see, most big changes are just a part of some growth mode, and do not cause an increase in the growth rate. While we do not know what exactly has made growth rates change, we do see that the number of such causes so far can be counted on the fingers of one hand.
While growth rates have varied widely, growth rate changes have been remarkably consistent — each mode grew from one hundred and fifty to three hundred times faster than its predecessor. Also, the recent modes have made a similar number of doublings. While the universe has barely completed one doubling time, and the largest animals grew through sixteen doublings, hunting grew through nine doublings, farming grew through seven and a half doublings, and industry has so far done a bit over nine doublings.
This pattern explains event clustering – transitions between faster growth modes that double a similar number of times must cluster closer and closer in time. But looking at this pattern, I cannot help but wonder: are we in the last mode, or will there be more?
If a new growth transition were to be similar to the last few, in terms of the number of doublings and the increase in the growth rate, then the remarkable consistency in the previous transitions allows a remarkably precise prediction. A new growth mode should arise sometime within about the next seven industry mode doublings (i.e., the next seventy years) and give a new wealth doubling time of between seven and sixteen days. Such a new mode would surely count as “the next really big enormous thing.”
Read the whole thing. Yes you should pay attention to these ideas; even if their chance of being right is small, their expected value in terms of importance is high. That being said, I sometimes tease Robin for offering us a secular version of Pascal’s Wager.
Note that Robin makes Arnold Kling look like a pessimist.
Private Space Travel Takes Off
The $10 million X-Prize has been won.
To win the X-Prize, a privately funded team had to fly a craft at least 100 kilometers high carrying a payload equivalent to three humans, successfully land and then repeat the feat within two weeks.
With this accomplishment, the SpaceShipOne team may have cracked more than space, as it appears that, just as planned, the X-Prize competition has cracked open the door to space tourism.
Sir Richard Branson recently announced plans to use the SpaceShipOne design for a space tourism company to be called Virgin Galactic.
Rutan, Allen and Branson attended the X-Prize’s victory flight.
Did life come from sugar in space?
A cotton candy-like cloud of simple sugar drifts in the unspeakably cold center of the Milky Way about 26,000 light years away, offering a remote, yet tantalizing, hint of how the building blocks of life may have reached Earth billions of years ago.
This frigid cloud is composed of molecular glycolaldehyde, a sugar that, when it reacts with other sugars or carbon molecules, can form a more complex sugar called ribose, the starting point for DNA and RNA, which carry the genetic code for all living things.
The simple sugar molecule glycolaldehyde was found in this dust and gas cloud, Sagittarius B2. The colors indicate radio emissions of different strengths.
Astronomers have known about sugar in space for some time, but new research reported last week in the Astrophysical Journal Letters showed that gaseous sugar could exist at extremely low temperatures, as are found in regions on the fringes of the solar system where comets are born.
Here is the full story. Here is the press release.
The Fable of the Cows
Here is a contrasting story about deforestation:
Do cows improve the view? That is a question which interests the Swiss government, given that it subsidises farmers heavily to graze their cows in the mountains. One justification for the subsidy is that cows eat young trees, and fewer trees mean better vistas of the sort beloved by tourists. But just how much do cows improve the view and where do they provide most value for money?
To help answer these questions, Kai Nagel and his colleagues at the Swiss Federal Institute of Technology, in Zurich, have developed computer models of the Alps and populated them with virtual tourists (or “autonomous agents” in computer-speak) that can wander the electronic landscape. The agents are programmed to behave, as far as possible, like real tourists, and to record their impressions as they go.
Here is the full story. I do not favor the heavy burden of Swiss agricultural subsidies, but it is rarely appreciated how much the “pristine” landscapes of that country owe to careful human planning. Thanks to James Barnett for the pointer.
New uses for flies
British scientists are developing a robot that will generate its own power by eating flies.
The idea is to produce electricity by catching flies and digesting them in special fuel cells that will break down sugar in the insects’ skeletons and release electrons that will drive an electric current.
“Called EcoBot II, the robot is part of a drive to make “release and forget” robots that can be sent into dangerous or inhospitable areas to carry our remote industrial or military monitoring of, say, temperature or toxic gas concentrations,” New Scientist magazine said on Wednesday.
Chris Melhuish and his team, who are developing the robot, have to manually feed the flies to EcoBot II because they are still designing some type of pump to suck the insects into it.
And here is an advantage to flies which perhaps you never thought of before:
“One of the great things about flies is that you can get them to come to you,” he said.
Hence the downside of the fully autonomous robot: it will have to use sewage or excrement to attract the flies and is bound to smell appalling.
Here is the link, and thanks to Yana for the pointer.
Science round-up
There are plenty of new science reports, here is a sample:
1. The Americas may have been settled by Pacific navigators in early times.
2. Global suicide takes more lives than war and murder put together.
3. Medieval man was almost as tall as modern American man, and the eighteenth century was a low period for height in the Western world.
4. Being out of shape is a better predictor of heart disease than is being overweight.
Thanks to Cronaca.com for the pointer on the third item.
Going up?
The X-Prize is close to being won and has been a success in motivating the research and development of private spacecraft. Ultimately, however, putting people into space by sitting them atop powder kegs or similar devices just seems too crude. As I wrote earlier, a space elevator would dramatically lower the costs of developing space. Elevator 2010 is sponsoring several new prizes for space elevator related technology.
Where are they?
The odds are small, but the expected value of this development is high.
Here is more detailed information. And here is a related piece on why aliens might instead prefer to throw rocks at us.
How to bet on physics experiments?
Betting on the greatest unsolved problems in the universe is no longer the preserve of academic superstars such as Stephen Hawking. From Thursday anyone will be able to place bets on whether the biggest physics experiments in the world will come good before 2010.
For two weeks, British-based bookmaker Ladbrokes is opening a book on five separate discoveries: life on Titan, gravitational waves, the Higgs boson, cosmic ray origins and nuclear fusion.
Here is the full story. The origin of cosmic rays is the big problem most likely to be solved soon, and bettors are more optimistic about nuclear fusion than are physicists.
Our colleague, Robin Hanson, has long argued that gambling could save science by encouraging scientists to more honestly reveal their true estimates of the likelihood of various theories. Here is some refreshing evidence that he may be right:
“I’d be tempted to take a bet on the Higgs [particle] at 6-1,” says Brian Foster who heads the particle physics group at the University of Oxford in the UK. “I’ve been quite instrumental in betting the taxpayers’ money on us finding it, so I’d better put my money where my mouth is.”
Maurice Allais is even smarter than you think
Remember Maurice Allais, one of the lesser-heralded Nobel Laureates? He is best known for his work on expected utility theory, more specifically the Allais Paradox. He also made significant though neglected contributions to macroeconomics, monetary theory, welfare economics, capital theory, and the economic history of civilizations. It now turns out he may have made a breakthrough in observational physics and general relativity, read more here.
Another proof that .999…=1
Jim Ward sends this nice proof:
1/3=.3333333…
  .33333333333333333333...
+ .33333333333333333333...
+ .33333333333333333333...
------------------------------------------
= .99999999999999999999....but 1/3 + 1/3 + 1/3 = 1
Of course this proof requires that we understand that 1/3=.333… but that at least can be shown by long-division. Steve Landsburg, who has a PhD in mathematics in addition to being a brilliant economist, writes to warn, however, that we haven’t defined what we mean by an infinite series like .999… nor have we proven that multipying by 10 (in the earlier proof) is equivalent to moving the decimal point. These are all valid points. As a lay consumer of mathematics, rather than a producer, I find these “proofs” helpful but do take them with a grain of salt.
Addendum: Here is more on Kakutani’s theorem for the mathematically strong of heart.
QED
QED: Beauty in Mathematical Proof by Burkard Polster is a short book with some elegant proofs (about 1 per page) from elementary geometry and number theory. Here are two that caught my eye. I know that .999…. =1 but I have always thought of this as something like a convention. Not so. Here is the proof.
Let x=.999…
then 10x=9.999…
now subtract x from both sides and we get
9x=9 or x=1
QED
And here is a just too lovely proof for the sum of the first n natural numbers.

How to spot a liar
By studying large groups of participants, researchers have identified certain general behaviors that liars are more likely to exhibit than are people telling the truth. Fibbers tend to move their arms, hands, and fingers less and blink less than people telling the truth do, and liars’ voices can become more tense or high-pitched. The extra effort needed to remember what they’ve already said and to keep their stories consistent may cause liars to restrain their movements and fill their speech with pauses. People shading the truth tend to make fewer speech errors than truth tellers do, and they rarely backtrack to fill in forgotten or incorrect details. [emphasis added]
“Their stories are too good to be true,” says Bella DePaulo of the University of California, Santa Barbara, who has written several reviews of the field of deception research.
Liars may also feel fear and guilt or delight at fooling people. Such emotions can trigger a change in facial expression so brief that most observers never notice. Paul Ekman, a retired psychologist from the University of California, San Francisco, terms these split-second phenomena “microexpressions.” He says these emotional clues are as important as gestures, voice, and speech patterns in uncovering deceitfulness.
And a (scant) few people can serve as super lie-detectors:
O’Sullivan now says that her further studies of federal agents, forensic psychologists, and other groups of professionals indicate that a very small percentage of people are extremely good at spotting a phony. “We always found one or two people who were very good,” she says.
Here is the full story.