The Critical Brain

We live in a world that is neither completely static and stable, nor completely noisy and unpredictable. As argued in previous blogs, we live a "complex" world between too stable and too random.

This is very similar to what is known as a "second order phase transition" in physics. Take ice, it's in a highly structured state with all atoms neatly organized in a lattice. When we heat it up, the molecules start to move around chaotically and break up the nice ordered structure: ice becomes water. The transition point is a phase transition and it is between order and chaos.

People have also argued that computation is best performed on the edge of chaos. A particularly outspoken figure in this respect is Stephen Wolfram. The idea here is that computation in the ordered regime can store patterns in memory but the system is so stable that it is is impossible to manipulate these patterns. On the other end of the spectrum there is large amounts of noise and/or chaos which simply prevents one to store any patterns stably. Again, we need something right on the edge.

Since brains are computing devices, one can ask if brains are also in a critical state. And indeed, evidence has been found that this is the case. In particular, if you take a patch of brain (from a dead animal but in a solution such that it still behaves somewhat "normally") and stimulate random neurons you will very often see very small groups of neighboring neurons respond. However, rarely you will also see the entire patch become active temporarily. It's just like earthquakes: there are enumerable small ones but rarely a really big one hits (note: a quake with magnitude 7 dissipates 10 times more energy as a quake of magnitude 6).

Researchers have argued that a critical brain is a wonderful thing to have. To name a few things: there are (optimally) many meta-stable states that it can represent. Moreover, this memory can be quickly accessed. Also, it maximizes the dynamic range of "senses", in the sense that it can respond to both very faint signals and signals that are many orders of magnitude larger. This "input gain control" is necessary because the world around is complex and thus in a critical state and therefore transmits signals with wildly varying magnitude. Finally, the brain needs to both integrate many parts of the brain but also allow for many different brain states (segregate).

A telltale signature of criticality is very long range interactions between units which are only locally connected. This is both in space (all regions of the brain are correlated with each other) as well as in time (very long memory). In fact, almost anything you measure, including these long range dependencies, follows a powerlaw distribution. Without technical details this means that there is no length scale that you can identify at which things are correlated. A good example of this the size of objects in an image. You will find many extremely small (perhaps even the size of 1 pixel) objects and few very large objects. You can't quite say: all objects have a size roughly between 90 and 100 pixels.

But for me, perhaps the most interesting point to make is this. By adapting to our environment we are forced to add new patterns in our brain and forget others. We are constantly maintaining the memory content of our brain. A brain that is sub-critical is too stable and it is very hard to erase memories and imprint others. A brain that is too chaotic and noisy will not hold memories at all. Moreover, this learning process is highly dynamic and needs to happen quickly. It seems our ability to adapt and learn and our need to predict the world around us is key to understanding why we have critical brains. A lot still needs to be understood here, but the outlook seems promising.

Anti-Islam Politics in Europe

Just type the work "Islam" in Google images and you get a good feeling for the current sentiment towards that word. Islam is slowly becoming the equivalent of the evil force that is trying to take over the world. This trend is global, it extend from the Western world though Russia and China. The world is polarizing.

In Europe this trend is very visible. In many countries ultra right political movements are gaining force. In the Netherlands the anti-Islam party PVV is now executing its political agenda by quasi-participating in Dutch government. But anti-Islam movements are on the rise in many countries in Europe: Belgium, Sweden, Denmark, Germany and so on.

Why do I believe this trend is so dangerous?

1) The economy is bad. People suffer and need a black sheep to blame. It's true that there are serious integration issues in the big cities in the Netherlands and a small fraction of Moroccan youths cause significant trouble. But so do other minority sub-populations such as Antilleans. These problems are caused by ignoring integration problems for far too long, but they seem to have little to do with Islam.

2) Al-Qaeda Terrorist attacks fuel the anti-Islam sentiments. Every time there is an attack all Muslims get to share in the blame. This is the annoying tendency of humans to over-generalize. We find one feature that holds true of the terrorist (they are Muslim), then the logic gets reversed to infer that all people who share this feature must therefore be evil to some degree. This is a well documented psychological phenomenon. But of course, the majority of Muslims want nothing to do with terrorists, they are law abiding citizens that value democracy and freedom as much as the rest of us do.

3) The problems are global. They span China, Russia, Europe, North America and Africa. Not to forget the Middle-East. Further escalation of the conflict between Iran and Israel may spread through the world like wildfire because the tensions are already high. And it seems inevitable that at some point Israel will strike against Iran's nuclear program.

Where have we seen the concurrence of these conditions before? In particular: a group of people labeled by their religious beliefs blamed for the problems in society? We must not follow gut-feelings, we must not generalize, we must remember the conditions that led to earlier conflicts and genocide. We must educate the population at large, broadcast the friendly and hospitable side of Islamic culture, foster tolerance and compassion.

Do we know what we don't know?

How good are we in estimating the uncertainty of our claims? Pretty bad in my opinion. And this may be particularly true for scientists, medical doctors or other experts. Since they have noticed that there are very few people who know more than them on a (very) particular topic they infer that they may actually know close to everything there is to know about it. I recently watched in interview with a renowned physicist about the possibility of EPS (extra perceptual sensation). This expert embarked on a long story about how all physical laws decay as one over the square of distance and that therefore the signals necessarily underlying ESP would have been detected. Problem is of course that his reasoning was solidly rooted in the physical laws as we know them and that the possibility of entirely new physics causing the phenomenon was simply denied. A clear overestimation of ones grasp of the unknown.

Ever tried to argue with a doctor why your child needs Tylenol for a mild fever? They will almost consider you criminal if you choose to deny them the medicine. But there is never a clear reason as to why they need it. It's simply the way it is. But do they have any clue as to the long term effects of poring medicine into these small bodies? Yes, of course, Tylenol was rigorously tested and approved but it's almost impossible to test for the increased risk of cancer after 20 years. They seem completely certain it's safe until a new study shows it's not (as was indeed the case with Tylenol). Why are doctors so certain about the effect of drugs or vaccinations: because they chronically overestimate their grasp of what is unknown.

Perhaps the clearest example is given by reviews of scientific papers where reviewers are asked to provide their confidence. It is very common to find two maximally confident reviewers with completely opposite opinions. Clearly one of the two must be wrong. And, this is of course very frustrating at the receiving end.

Bottom line, always keep an open mind and try not to underestimate what you don't know.

A Mosque at Ground Zero?

A new controversy is currently hotly debated in the press: to build or not to build a mosque at ground zero? I see two arguments, one against and one in favor. The argument against building such a mosque is that it may hurt the feelings of those who lost family, friends or loved ones in the 9/11 bombing. In fact, this seems a very strong argument because irrespective how we feel about the issue, these people will want to visit the site where their loved ones died and that experience can be severely affected by a clearly visible mosque. However, I am not sure the majority of the surviving dependents actually will be offended by a mosque. At the very least their opinion should be polled. And by the way, I am sure many moslims also died in the 9/11 attacks and wouldn't they need a place to mourn their loved ones?

Now the argument in favor. I believe the most appropriate monument we can build that expresses the tolerance of our western society towards other cultures and minorities, and expresses how much we value our constitutional rights (aka liberty of speech, liberty of religion etc.), is to precisely build a mosque at ground zero. It expresses the fact that we do not stigmatize a very large group of well willing citizens and accuse them of the crimes committed by a very small group of terrorists. It expresses the fact that we have learned from history and will not make the same mistakes again (and again). So, please let's build that islamic center at ground zero and use it to create mutual understanding and eradicate the hate that led to 9/11. Let's not think with our gut but with our head for a change.

The Efficient Market Hypothesis

The stock-market is a fascinating beast. It's the largest casino in the world, better compared to a huge online game for adults. If you are able to predict the future price of a stock you are in (big) business. When it rises, you buy that stock and sell later. When it drops you short-sell that stock (basically selling it now before you own it and paying for it at a later time when the price is presumably lower). But the view held by most academics is that markets are efficient, that is, unpredictable. Imagine there is some knowledge out there in the world that makes the price of a stock predictable, then the first person who knows about it will "gamble it away". It takes only a few people (or even one) to remove the predictable pattern (if it were still predictable, gamble some more until it is no longer predictable). And there is little delay in this process too (since potentially millions of dollars are involved investors will act very fast). And so the hypothesis is that the market is a random walk: utterly unpredictable.

So what are all these thousands of investors wasting their time on? A huge paradox is presenting itself here. An army of investors are presumably making money on the market every day, while an army of academics is claiming they can't. What's going on?

Hypothesis 1: the investors are seeing patterns where there are none. They believe they are beating the market but in reality they don't. Perhaps they gamble on more risky stocks which have a higher average return. It is well know that humans tend to see patterns in data where there are none (it can't be coincidence that I met my old friend in Lissabon during the summer). We hear about the successful investors who have survived but they represent 50% of the population. The other half can be found in the gutter.

Hypothesis 2: Any obvious patterns are absent, but there are hidden patterns that are not public on which you can make money. It is a well documented fact that once a pattern is made public, it will instantly disappear because investors will start using it. But it's rather stupid to post your successful trick to make money on the wall (unless you are an academic). So, we must assume investors are using their own secret rules to trade. Some figured out you should trade on the scale of seconds or less, others use complicated rules of thumb at the scale of days/months etc. The mere fact that publicized patterns disappear tells us that before they were made public they were still predictable.

To me, the markets represent an interesting collective artificial intelligence that determines the true value of stocks very efficiently. Markets have even been used to predict other facts. If you want to know the answer to an arbitrary question (i.e. who will be the next president) start a market and let people bet on it. The collective wisdom of the masses supersedes the wisdom of any knowledgeable individual. We should probably be thinking about how to use this idea for better purposes.

Japan

A brief blog about Japan. I have just been to Kyoto and Tokyo. Brilliant experience. I was most impressed with Buddhist gardens. And with Japanese hospitality. Japanese are among the kindest and most hospitable people I know. They go out of there way to show you around and help you in any possible way (thanks to Kazuyuki Tanaka and Kenichi Kurihara). I gave a talk at Tokyo University and the level of interest and the quality of questions was absolutely impressive. I don't know how they do it, but they give you more then anywhere else the impression that you are special and your talk was brilliant. They genuinely care it seems and that is a lasting experience. Our dinner at an Okinawa style restaurant was also very interesting. We had lot's of good conversations about topics that I might have thought were perhaps taboo (the war, their Korean ancestory etc.). And yes, the food is about as good as it gets anywhere on the globe.

Japan has a culture that is about as alien it gets (if we confine ourselves to earth). One in ten Japanse wears a face mask in public. It freaks me out a little I should say (but I got more used to it in the end). You feel like the plague has broken out. Nobody eats in the street (I started to notice it while eating my sandwich going to the bus). Tokyo is an anthill. Not because there are so many people packed together (there are) but because people are organized. They follow the rules. And there are many signs pointing out the rules. You pay your bus fare when you exit a bus and not when you enter (makes lots of sense). When buying a ticket or ordering your coffee (in English) the response is invariably in Japanese. Not just one word, but long sentences of unintelligible Japanse from very friendly smiling faces. I am sure they know I don't understand a word, but it doesn't matter. I think it is just polite this way and it doesn't bother me in the least (given a little more time I would have started to talk back in Dutch). By the way, Japanese is more like singing actually, where the last vowel is extended for a second or so. And lot's of bowing. In the beginning it looks a bit funny but after a few days I found myself bowing quite a bit as well. And then finally, there are the toilet seats... They are high tech devices. Preheated and with a few options to clean your bottom (couldn't figure out how to reduce the temperature though).

Boy, did I enjoy Japan. From it's cherry blossoms, via its temples to its friendly people. Thanks everyone for a wonderful experience.

Time

We take time for granted. It's simply there and flowing forward at a steady and unstoppable pace. In fact all of modern science is dependent on it because it is necessary to define causality: the notation that one things "causes" some other thing to happen. This apparently happens only in one direction. However, there is a huge paradox luring behind the corner, because all fundamental laws of physics are time reversal invariant. The reason for the observed asymmetry of time is the second law of thermodynamics which says that entropy can only increase. That is actually not quite stated correctly. It should say that there is an overwhelming probability that it increases but there can be random fluctuations that make it temporarily decrease.

Where does the second law of thermodynamics come from? Fill a swimming pool with a red fluid and a blue fluid separated by a wall. Now remove the wall and you will notice that the colors mix. The opposite will never happen. Yet the underlying laws are symmetric. What's going on? The issue is that there are very (very very) many more states with colors mixed up that look the same to us than there are states which separate the fluids. So we can imagine the state-space as being build up from cells where all states in a cell all look the same to us. As we randomly wander around in this space we will move from cell to cell but since some cells are so hugely much bigger than others we always tend to wander into those. So, perhaps surprisingly, the second law is "subjective", it depends on us not being able to to distinguish the many states with mixed colors.

How would the world look like if all possible states would look equally different? Imagine just looking at 2 marbles moving around in a box. They reflect off the walls and so now and then reflect off each other. If we play the movie backwards it looks exactly the same. In this world we would have no features available to tell the directionality of time. In such a world the concept time might not even exist for creatures living in it. Hard to imagine isn't it?

Let's go one step further. If entropy is increasing since the conception of the universe, it must have been very small to begin with. In fact, this is exactly, what Roger Penrose proposes in his book "the Emperor's New Mind" (in the less controversial chapters of it). The universe was in a very low entropy state when it was created and has been steadily increasing ever since. The notion of time and the reason we perceive it must be sought at the "time" of the Big Bang. Nobody knows why this is true. In fact, one can easily imagine an opposite scenario where (for some reason) the universe must end in a very low entropy state (perhaps a bizarre version of a Big Crunch) but started out in a high entropy state. In such a universe effects are followed by their causes. Broken glasses magically assemble themselves into whole glasses. In such a world the future looks much more certain then the past.

Try to imagine living such a world. My feeling is that time would be experienced in reverse, but we wouldn't really notice it, because time is all just an illusion anyway. The reality is that the universe is simply there from beginning to end. We occupy a small window of that universe and perceive it as flowing in a certain direction. Very Buddha.

Now for some very controversial experiments that cast doubt on how we might understand time. It seems that there have been quite a few experiments where an experimenter would repeatedly show subjects pictures that were either extremely disturbing or very nice and beautiful. The subject is hooked up to some device measure his/her level of excitement (say fMRI or simply resistance in skin). Disturbing pictures will evoke a much different response then nice pictures after you have seen them. That's not strange. What's strange is that the subjects seem to have a significantly different response before the pictures have been shown. In other words, they seem to anticipate whether a picture is disturbing or not.

I am assuming that the experimenters very carefully ruled out any learning effects (although I haven't actually seen this mentioned). This is important because people seem to be able to learn very complicated patterns completely unconsciously without even knowing it. It's easy to control for this though, because you simply produce a random sequence, or even better show a complicated correlated (i.e. predictable) sequence and then reverse the correlations. If the signal stays you rule out that the subjects were able to predict what image would come next based on correlations. I also assume they did their statistics right of course.

However, if all these things were done correctly it presents a huge puzzle. These subjects seem to know the future, i.e. they "remember" the future. This leads immediately to a paradox.
"suppose one can know the future.
Then one can take action so that that future will not happen.
So it doesn't happen.
Contradiction
So no-one can know the future"
Unless, one could not use the information to change the future.

Ok, all of this is really bizarre. And the first impulse for any scientist will be to reject this out of hand. But I think we should keep an open mind. The notion of time is very strange and paradoxical in itself. And there are other strange cracks in our scientific theories that concern causality. Take the quantum mechanical phenomenon of the collapsing wave-function. If you take two entangled particles with opposite spin and shoot them off in opposite directions of the universe and then measure the spin of one of them, the other one is instantly known on the other side. You cannot explain this by assuming that they already were in a certain spin orientation but that you simply didn't know which one. No, the spin direction is genuinely undetermined until you measure it.

Measuring the orientation of this strange entangled state implies that some kind of signal must be traveling from one end of the universe to other to inform the other particle that it must now be opposite to the value we just measured. If it travels faster than light however, it means that you can identify two observers in the universe traveling with high velocities in different directions for which the causal relationship between the events is reversed! For one observer spin A collapsed first and sent a signal to B, while for the observer spin B collapsed first and sent a signal to A. Now these signals (if they are indeed signals) can never be used by somebody to actually send information because it would result in causal loops again. And indeed, if you try to figure out a way to send information you find that nature is just a bit too smart and prevents this.

One things seems clear from these paradoxes. Our current theories are clumsy when we try to explain these quantum mechanical phenomena. Nobody knows why the wave function collapsed, yet it is ingrained in quantum mechanics and widely accepted. In fact, there are no good explanations for these paradoxes. So keep an open mind, even when it come to things that are at odds with everything you have learned in class. Be critical, but don't dismiss too early. Breakthroughs only happen when the unimaginable become reality.