Saturday, October 15, 2011

Microscopic Black Holes and Cosmic Censorship

There is nice an argument that combines general relativity and quantum mechanics to show that our ideas of space and time start to break apart at the Planck scale (1E-35 meter). Imagine I try to constrain anything (say an elementary particle) inside a box of size 1E-35m x 1E-35m x 1E-35m (a *very* small box I will call a Planck box).

According to quantum mechanics, if we want to contain anything inside a very tiny region of space, then its momentum (mass x velocity) becomes highly uncertain. The more we try to constrain space the more uncertain the momentum becomes (the Heisenberg uncertainty principle). This means that if I would actually measure the momentum, then the outcome could be extremely large. Since momentum carries energy the energy could become so large that, just like stars, they can form black holes. This happens exactly when the box is a Planck box.

What does this say? To me it seems a really nice argument to show that at this scale the concept of space starts to break down. We can simply not contain anything inside a Planck box, for if we do, nature closes the box and we will not be able to peek inside it! A black hole is in a real sense the boundary of the universe, so if we try to look at scales smaller than the Planck scale we will be looking at the end of the universe. (As a kid I always tried to imagine how the end of the universe looked like -- maybe its all around us).

Roger Penrose has introduced a name for this trick that nature plays with us: "cosmic censorship". This principle says that anywhere where there are singularities in our theories a horizon will form around it so that we may not see it! Maybe mother nature doesn't want us to see something :-)

Sunday, June 19, 2011

The Illusion of Free Will

We like to think that every decision we make is made out of free will. While the concept of free will seems to make some sense at an intuitive level, it seems rather slippery when trying to define it. What entity other than our brain is making the decision, and on what grounds, based on what input? And what are the laws that determine how that entity is making a decision?

It seems rather dreadful that decisions are made according to "an algorithm". In particular, a *deterministic* algorithm is rather unappealing because it implies that our genetic make-up, in combination with everything we have experienced
in our lifetime plus the environmental factors that are in play right now are input to a function that deterministically outputs a decision:
It seems to imply that we cannot be held responsible for our actions: they are simply a deterministic function of our history and the decision was predetermined anyway. We have no free will to change that outcome.

Despite its unattractive philosophical implications, I think this is exactly what is going on. We have no issue accepting this point of view for plants, in which case the FUNCTION is rather simple. Even lower animals such as fish or even crocodiles seem highly predictable in their responses to the environment. In the case of humans this is definitely not true. Our responses are (fortunately) partly predictable
but also partly unpredictable. There may be a good reason for a certain amount of unpredictability in nature. Imagine a cheetah chasing a gazelle. If the swerving movements of the gazelle were predictable for the cheetah then the cheetah could anticipate them and easily catch the gazelle. It is therefore likely that the gazelle has developed an algorithm that is very hard to predict for the cheetah, i.e. a seemingly random strategy to swerve left or right. Also apes living in large social communities were probably prone to similar evolutionary pressures: predictable responses can lead to exploitation and manipulation by others and thus have negative fitness value.

Seemingly random behavior does not mean this behavior is not deterministic. The decision process can become so complex that the tiniest changes in the environment can cause a completely different decision. This sensitivity or instability is the definition of "chaos" and according to some, unpredictability should be the correct definition of randomness, irrespective of whether something is deterministic or not. It is not even quite clear what true randomness means to be honest. Perhaps quantum mechanics is the only theory that claims randomness at a fundamental level (e.g. not caused by chaos), but even here the jury is still out. Even if our behavior is partly random, then what does that solve in terms of free will? A decision does not become more free if it is random.

To me the only logical conclusion is that our behavior is deterministic albeit in a very complex and unpredictable way. There is some interesting evidence for such a
theory. Experiments show that decisions are made in the brain even before we become aware of them. This means that at the very least a significant fraction of our decisions we make are made completely unconsciously and our body only fools ourselves into thinking that we made this decision consciously.

Predicting human behavior (decision making) may turn out to be impossible even with the fastest supercomputers. This feels like good news, because it would be
very unsettling to have a clone build after you that can perfectly predict what you will do 1 second from now. But ultimately we may have to accept that we can build
robots that can display equally complex behavior that are in no way inferior to us.

Finally a word on the legal implications of a theory of this kind. Does this mean we cannot send anyone to prison anymore because s/he committed a murder?
Of course not! Whether actions are predetermined or not has nothing to to do with this. The reason we send people to prison is because we don't want this person to
do it again and to scare other from doing it. These functions of punishment remain perfectly valid. We should never punish out of revenge or retribution. It is useless and serves no function to society.

Saturday, March 5, 2011

An Imagined World

Over the past centuries science has pushed humankind from its pedestal several times. First Copernicus showed that the earth is not at the center of the universe, then Darwin showed that humans are the product of evolution and direct descendants of the apes. What else awaits us? With the advance of fast and more intelligent computation we will see the realization that computers can be far smarter than humans. We passed a few thresholds: Deep Blue beating Kasparov in chess, and now Watson becoming the new champion in the television show Jeopardy. As time goes on, we will see many more of these landmarks happen. There will be a time when we will be second to computer systems in almost any imaginable task. Are there even stranger revolutions that await us?

Although it is exceedingly difficult to look in a crystal ball, there are signs that an even bigger philosophical shock awaits us. Physicist believe that the true ontological degrees of freedom are far fewer than the ones we usually entertain to describe our world. In fact, there are signs that we could pack all the degrees of freedom on a two-dimensional plane, instead of in a three dimensional world. What then are these surplus unphysical degrees of freedom? My claim is that they are imagined: they live in our head in order to make sense of our world. Remember that all our brain is concerned with is predicting the future. If you can predict better you have an edge in survival. Now imagine that the ontological degrees of freedom have very complicated laws of dynamics, i.e. their future is very hard to predict from the past. Then lets imagine that by introducing a bunch of auxiliary variables this prediction task may become easier. This is not such a far fetched thought. In fact in statistics people do it all the time. Adding variables can simplify the description of a problem. However, in physics this is also a well understood phenomenon. Almost any modern theory has so called "gauge symmetries". These are transformations that change one description of the world into another description of the world without changing the actual state of the world. For instance, Einsteins general relativity allows one to transform between two frames of references (observers) that accelerate relative to each other. One observer interprets the state of the world as "gravitational pull" while the other as acceleration.

These symmetries lead to conservation laws (Noether's famous insights). Conservation laws are constraints between variables. They simply express that we have have used too many variables to describe the state of the world and hence some variables can be solved from other variables (and in fact removed). So there are two types of variables in a theory: variables whose state can only be solved from the world state in the past and variables whose state can be solved from the state of other variables at the same time. The second type is redundant, but often very useful in writing down nice concise equations to describe our world. What I predict will happen is that we have completely underestimated the number of these spurious variables in our theories. I believe, supported by the holographic principle which states that all real degrees of freedom can be stored on a surface, that there are vastly more unphysical degrees of freedom in our theories than physical ones.

Now let's take this one step further. Our brain is also in the business of making models of our world. Everyone of us is a physicist, if you like it or not. I now propose the following leap of faith: the way we view the world is also largely made of unphysical degrees of freedom. We have evolved to use these over-parametrized models because they lead to easier prediction at the macroscopic scale in which we live and survive. But they are largely an illusion, a fantasy of our minds that we all share (like the ability to speak language this illusion has been hardwired in our brain through evolution). This is the new revolution that I anticipate: we will come to realize we live in a fantasy world.

What are the potential consequences, if what I propose is true? While the auxiliary variables may work well at the macroscopic level, they may not work all that well at the microscopic world. I believe the brain has introduced new variables that follow simple laws of dynamics themselves. In particular, together with the real degrees of freedom they make up a consistent system where (usually) cause precedes effect. However, for the unphysical degrees of freedom there is no reason why this should be enforced. In general, there may be glitches in this framework in situations that are not important to survival. These glitches in consistency may for instance involve apparent reversed causality for the unphysical degrees of freedom, but in such a way that they will not affect the strict causality necessary for the physical degrees of freedom. We should not be able to receive a message from our yet to be born daughter who instructs us to kill ourselves so she will not be born (unless all the degrees of freedom that govern this daughter are unphysical of course).

All of this is compete speculation, and I make no claims that there is evidence for it. But oftentimes, a half true story might help one to keep an open mind to explore or embrace new ideas.

Saturday, January 29, 2011

Salaries of Charity CEO's

Ever given the salaries of CEOs of well known charities a second thought? Well it came as a shocker to me. Here are a few almost random picks from "charity navigator":

Amnesty International: Larry Cox, Executive Director $210,000
American Red Cross: Gail J. McGovern, President, CEO $446,867
Food for the poor: Robin G. Mahfood, President, CEO $345,245
American Cancer Society: John Seffrin, Chief Executive Officer $685,884
:Donald Thomas, Deputy CEO $1,027,306
Children International: James Cook, Chief Executive Officer: $423,114

Do I need to say more? This maddens me. Why would I support these salaries with my gift? How can they ask people with small incomes to give when at the same time there are CEO's leading these organizations with these outrageous salaries. The figures heading these organizations should lead by example. Clearly, they do not invest their time because they care. Very disappointing. Next time they call you for a pledge first ask what their CEO earns.