There are three technological developments that I’ve been waiting for that could actually improve my life.  The first is a letter-sized electronic reader that can hold every book and paper that I’ll ever need.  Amazon Kindle is not it but a company named Plastic Logic is promising something like this soon.  The second thing that I’m waiting for is a program that will read and sort my emails.  It will know how to prioritize them, delete the ones I don’t need anymore, update my calendar for events and meetings, and save keepers in the correct folders (including creating folders for new topics when expedient) when I’m done reading them.  (Actually, there is something like this already, known as an administrative assistant but I’m waiting for an electronic one.)  It may be a (long) while before something like this is available. The third thing I’m waiting for is a remote collaboration tool.  This would be something to interact with collaborators remotely that mimics the experience  of standing together in front of a blackboard.  Thus far, none of the things I’ve seen that are supposed to do this have gained traction with me.  However, Google is coming out with something called Google Wave that may be closer to what I’m looking for.  It is an online communication tool that will support latex.  Terry Tao has a nice summary of how it could be useful for scientific communication on his blog.

# Strogatz on the Wild Side

Steve Strogatz is the guest blogger on the Wild Side on the New York Times today.

# Snowbird conference

I’m currently at the SIAM Dynamical Systems meeting in Snowbird, Utah.  I gave a short version of my talk on calculating finite size effects of the Kuramotor coupled oscillator model using kinetic theory and path integral approaches.  Here is the longer and more informative version of the talk.  I summarized the papers on this talk here.

# The collective conscious

The materialistic view is that consciousness is an emergent property of a large number of interacting cells in the brain. The question we would all like to have answered is what is it exactly about these cells and interactions that give rise to consciousness. Does the number of cells matter?  Neuroscientists have shown that primates, dolphins and elephants possess self awareness and most would believe that they also have some form of consciousness.  I haven’t done a survey but perhaps a smaller set of scientists believe that this extends to all mammals and some birds. However, if you believe that not all animals have consciousness then what sets the cutoff scale? What is the difference between the animal with the smallest brain that has consciousness and the one with the largest brain that does not.

I think it is safe to say that most people don’t think that insects have consciousness. While an ant is, in the words of Utah mathematical biologist Fred Adler, “stupid but persistent”, an ant colony can seem quite “intelligent”. They are adaptive to changing conditions and some species of ants domesticate other species. Would an ant colony have a form of consciousness? How about a colony of bacteria? The Australian radio show “All in the mind”, had a fascinating episode on bacteria recently (see here).  Philosopher Pamela Lyon talked about the predatory soil bacterium myxococcus xanthus, which hunts in packs, lures and traps E. coli,  and exhibits division of labour.  Colonies have a self identity and individual mobs will war with other mobs.  Hence a colony of myxococcus could be said to have some form of self awareness, but does it also have a form of consciousness?

# Revised version of paper

We’ve just uploaded a revised version of our paper: Systematic fluctuation expansion for neural network activity equations, by Buice, Cowan and Chow to the arXiv. Hopefully, this is more readable (especially the path integral section) than the previous version.

# Why most published results are false

John Ioannidis published a very interesting paper in PLoS Biology in 2005 entitled “Why most published research findings are false.”  In it he argued that most affirmative results in biology papers that are based on a statistical significance test (e.g.  p-value less than 0.05) are probably wrong.  His argument was couched in traditional statistics language but it is really a Bayesian argument.    The paper is a wake up call that we may need to look more closely at  how we use statistics and even how we do research.

The question he asked was Given some hypothesis, what is the probability that the hypothesis is true given that an experiment confirms the result (up to some level of statistical significance)? Let $P(T | Y)$ be the probability that the hypothesis is true given a “yes” answer by an experiment, $P(T)$ be the prior probability that the hypothesis is true, $P(Y|T)$ be the probability of getting a yes answer if the hypothesis is true, and $P(Y)$ be the probability of getting a yes answer under all conditions.  Then by Bayes theorem $P(T | Y) = P(Y|T)P(T)/P(Y)$ where $P(Y)= P(Y|T)P(T)+P(Y|F)P(F)$, and $P(F) = 1-P(T)$.

We can then compute $P(T|Y)$ if we have $P(T)$, $P(Y|T)$ and $P(Y|F)$. $P(T)$ is the prior probability that is based on everything you know or don’t know. Ioannidis writes it as $P(T)=R/(1+R)$ where $R$ is the odds that the hypothesis is true versus it being false. In these terms, the likelihood $P(Y|T)$ is called the power of the experiment or study and is usually written as $1-\beta$, where $\beta$ is the false negative probability or the Type II error  rate. $P(Y|F)$ is the false positive probability or the Type I error rate and denoted by $\alpha$. Putting this all together gives

$P(T|Y)=\frac{(1-\beta)R}{(1-\beta)R+\alpha}$.

Often it is more convenient to consider the odds of being true versus being false: $P(T|Y)/P(F|Y) = (1-\beta)R/\alpha$. So the odds of a hypothesis being true given a “statistically significant” result requires that $(1-\beta)R>\alpha$, so  increasing power and lowering false negatives are always a good thing. But the interesting thing to me, (which is obvious in retrospect) is that even if you have infinite power, you can still get a wrong result if your false negative rate is higher than your prior odds of correctness.  This is made even worse if you have biases and Ioannidis gives typical parameter values to argue that most published papers must be false.

What was most illuminating to me is that many independent labs working on the same topic actually makes it less likely to be correct.  The reason is that if many labs are working independently than $P(Y|T)=1-\beta^n$ (i.e. false negative rate goes down) but also $P(Y|F)=1-(1-\alpha)^n$ (i.e. the false positive rate goes up). If many labs work on the same thing and don’t cooperate than the probability of getting a yes result goes up since the probability that everyone gets a negative result goes down. (This is the same problem you have if you do an experiment and don’t control for the number of effective hypotheses tested (for example, see here.)  Hence the odds in the multiple labs case is $(1-\beta^n)R/(1-(1-\alpha)^n$, which goes to $R$ as $n$ goes to infinity.  Thus, an infinite number of labs working on the same problem does not improve on the prior odds.   So the next time you get rejected by a high impact journal because your work is not of sufficient interest, you can take consolation in the fact that your probability of being wrong just decreased.

# Extraterrestrial Life

There is a pervasive belief  that there must be extraterrestrial life and in particular intelligent life in the universe.  In fact, that  is usually presumed to be so true that the only question people tend to ask is why haven’t we heard from anyone yet.  The celebrated Drake Equation, which tried to estimate the number of civilizations in the galaxy that we might be able to communicate with ended up with the number 10.  One of the factors in the Drake equation is the fraction of earth like planets that eventually develop life.  In 1961, when Drake wrote down the equation he assumed this fraction was one.  After all, the earth is teeming with life, so it must be easy to develop life anywhere, right?

Actually, we have no idea what the probability of forming life is. We do not know how life developed on earth.  There are several competing theories but we have no empirical evidence to support any of them.  The probability of forming life could be very high or it could be close to zero.  It is as equally likely that there are lots of civilizations out there to talk to or there are none.  The possibility that there is no life whatsoever in the visible universe beyond earth is as likely as any other hypothesis.  We really could be alone in the universe.