I was recently reminded of a beautiful paper by Tony Bracken and Geoff Melloy, Probability Backflow and a New Dimensionless Quantum Number (publisher subscription required, alas). What they describe is a marvellous (and too little known) quantum phenomenon that they dub “probability backflow”.

The basic idea is simple, although counterintuitive. Imagine a quantum particle moving in free space. It’s easiest if you imagine space is one-dimensional, i.e., the particle can only move left or right on a line. The discussion also works in three dimensions, but is a bit trickier to describe.

What Bracken and Melloy show is that it’s possible to prepare the particle in a state such that both the following are true:

(1) If you measure the velocity of the particle, you’re guaranteed to find that the particle is moving rightwards along the line.

(2) Suppose you fix a co-ordinate origin on the line, i.e., a “zero” of position. They prove that if you measure position then the probability of finding the particle to the right of the origin actually decreases in time, not increases, as one might naively expect from point (1).

So far as I know, this has never been experimentally demonstrated.

Bracken and Melloy also give a beautiful explanation of probability backflow in terms of “quasi-probabilities”. It’s been known for a long time, at least since Wigner, that you can reformulate quantum mechanics as something very much like a classical theory, but one with negative probabilities. Using this reformulation, Bracken and Melloy explain the phenomenon: sure, the particle is moving right, but it’s actually negative probability that is flowing to the right of the origin, and so the probability of being to the right of the origin decreases in time.

Inspired by the power of this intuitive explanation, I once worked for a while trying to use quasi-probability formulations to find new algorithms for quantum computers. Despite my lack of success, I still think this is a promising approach, not just to algorithms, but more generally to quantum information.

• Confessions of a Science Librarian: Google Scholar and the future of A&I databases
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  • People are odd: “Andrew Kellett, 23, was banned from boasting about his criminal activities on the Internet after posting videos of himself and others taking Class A drugs, racing cars at high speeds and trespassing and shouting abuse.”
• Open Library API: Cataloging 13 Million Books
  • Moving towards a webpage for every book every published. How about a wiki for every book every published?
• Bruce Schneier: Our Data, Ourselves
  • “In the information age, we all have a data shadow… Who controls our data controls our lives… We need a comprehensive data privacy law.”
• Secrets to smart decisions when you graduate from college » Brazen Careerist by Penelope Trunk
  • Good post on making big decisions (especially career decisions) in general.
• Find Similar Users on del.icio.us
  • Python script to find similar users on del.icio.us
• InFasta
  • An Open Science Experiment in Bioinformatics

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Anyone from the physical sciences on friendfeed? There are dozens of biologists, but not so many from the physical sciences.

Fascinating article earlier this year in “Current Directions in Psychological Science”, examining how the structure of communication in a group can affect the rate at which innovations occur. To quote the EurekAlert! story:

Good ideas can have drawbacks. When information is freely shared, good ideas can stunt innovation by distracting others from pursuing even better ideas, according to Indiana University cognitive scientist Robert Goldstone.

“How do you structure your community so you get the best solution out of the group?” Goldstone said. “It turns out not to be effective if different inventors and labs see exactly what everyone else is doing because of the human tendency to glom onto the current ‘best’ solution.”

[…]

This study used a virtual environment in which study participants worked in specifically designed groups to solve a problem. Participants guessed numbers between 1 and 100, with each number having a hidden value. The goal was for individuals to accumulate the highest score through several rounds of guessing. Across different conditions, the relationship between guesses and scores could either be simple or complex. The participants saw the results of their own guesses and some or all of the guesses of the others in their group.

In the “fully connected” group, everyone’s work was completely accessible to everyone else — much like a tight-knit family or small town. In the “locally connected” group, participants primarily were aware of what their neighbors, or the people on either side, were doing. In the “small world” group, participants also were primarily aware of what their neighbors were doing, but they also had a few distant connections that let them send or retrieve good ideas from outside of their neighborhood.

Goldstone found that the fully connected groups performed the best when solving simple problems. Small world groups, however, performed better on more difficult problems. For these problems, the truism “The more information, the better” is not valid.

“The small world network preserves diversity,” Goldstone said. “One clique could be coming up with one answer, another clique could be coming up with another. As a result, the group as a whole is searching the problem space more effectively. For hard problems, connecting people by small world networks offers a good compromise between having members explore a variety of innovations, while still quickly disseminating promising innovations throughout the group.

The original article is behind a publisher paywall, but here’s a link for those with access.

Many thoughts immediately arise:

• Mark Newman has shown that the structure of many scientific collaboration networks is a small world network, at least as of 2000.
• The “small world” classification is pretty coarse. It’d be helpful to say more precisely which network structures give rise to or inhibit innovation.
• The problems posed by Goldstone and collaborators were pretty artificial. What happens for more realistic problems?
• How does problem-solving effectiveness scale with the size of the group? I expect that the point of diminishing returns is hit pretty quickly even with very difficult problems. A good understanding of this would potentially have implications for science funding.
• Certain periods of intellectual history were especially fertile. What’s the pattern of collaborations look like for the founders of quantum mechanics (or insert your favourite topic)? Is it special?
• More generally, what predictive power does the pattern of collaborations (or citations, or any other type of linkage) have?

The last few weeks I’ve been experimenting with stickk.com. What stickk.com lets you do is pick a commitment – say, to exercise for 3 hours per week – and then sign a contract saying that if you don’t meet the commitment, a certain sum of money will be given to the anti-charity of your choice.

My anti-charity is the Bush Memorial Library. If I should miss making a commitment, I’ll be making an automatic 50 dollar donation. It’s a good choice for me personally, since even though I dislike Bush I won’t feel too bad if I strike out (it’s just a library, not a re-election fund), but find that thinking about Bush really motivates me to keep my commitments.

To keep you honest, you get to nominate an independent referee and supporters.

It works surprisingly well. When I get up in the morning, and just can’t stand the thought of going to the treadmill, I simply bring an image of Bush to mind. It gets me energized every time. So far I’m 5 from 5 – I’ve met every one of my commitments. I’m tempted to put a poster of the man up somewhere.

Psychologically, the effect is weird. In economic terms, I seem to apply a pretty steep discount factor to my future time. That is, the site exploits the fact that when I’m making my commitment, I put a much lower value on my future time than I actually do in the moment. It’s a clever trick.

One other oddity is that the effect seems to last. I’ve found that even when I take a week off, it seems to be a lot easier to keep the commitments anyway.

• Wired Campus: A ‘Frozen’ Wikipedia Could be Better for College, Founder Says – Chronicle.com
• ClimatePrediction.Net
  • Distributed computing effort aimed at modelling the climate. According to Wikipedia it involves 145,000 machines, and is the most computationally powerful modelling effort in the world.
• Clay Shirky interview on the social web
  • “It’s almost universally [true that social] software that launches with the fewest features is the stuff that takes off. The shift is from thinking about the computer as a box to thinking of the computer as a door, and nobody wants a door with 37 handle
• ivan krstić · code culture » Sic Transit Gloria Laptopi
  • Thoughtful comments on the “One Laptop Per Child” project, including the recent decision to ship it with Windows.

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• Clay Shirky interview on the social web
  • “It’s almost universally [true that social] software that launches with the fewest features is the stuff that takes off. The shift is from thinking about the computer as a box to thinking of the computer as a door, and nobody wants a door with 37 handle
• ivan krstić · code culture » Sic Transit Gloria Laptopi
  • Thoughtful comments on the “One Laptop Per Child” project, including the recent decision to ship it with Windows.
• Wendy’s Blog: Legal Tags » Sony BMG Sends YouTube Ads Instead of Takedown
  • Instead of taking down YouTube videos of their bands, Sony has been trialling a program to automatically insert links to Sony whenever a video is uploaded. This is promising, although the musicos ability to shoot themselves in the foot is amazing.
• The Day There Was No News
  • Eerie.

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Great interview with Clay Shirky in the Wall Street Journal. Shirky makes a particularly interesting comment about social software:

It’s almost universally the case with social software that the software that launches with the fewest features is the stuff that takes off. The shift is from thinking about the computer as a box to thinking of the computer as a door, and nobody wants a door with 37 handles. Twitter has six features, and it launched with only one. A brutally simple mental model of the software that’s shared by all users turns out to be a better predictor of adoption and value than a completely crazy collection of features that ends up being slightly different for every user.

Empirically, Shirky seems to be right. Email, Facebook, Usenet, Twitter, wikis, Blogger, Flickr, Friendster, del.icio.us – all were incredibly simple when they launched. They certainly had a “brutally simple mental model of the software that’s shared by all users”.

But I’m not sure I believe this is true, and I certainly don’t know why it’s true, if it is.

Maybe a partial explanation is that having a simple shared mental model makes network effects much more powerful. When we think about social software as a user, we don’t just think about the software, we also think about the network of other users, and it’s important to be confident that we have a shared understanding with those other users. If we’re not confident of that shared understanding, we won’t connect, and the value of the software will diminish.

Update: In comments, Clay Shirky replies:

“If we’re not confident of that shared understanding, we won’t connect, and the value of the software will diminish.”

I don’t think this is a partial explanation. I think this is *the* explanation. Given the competition all social software has, a simple and shared mental model is essential to elevating the eventual leaders over the competition.

There has been some great discussion in the comments on my post about “Open science”. One outcome is that Jean-Claude Bradley has created a search engine customized for open notebook science:

http://tinyurl.com/4multu

Fittingly, many people contributed to the discussion! 🙂