Tuesday, December 30, 2008

Living in a Bubble

Cosmology is full of surprises and black holes are definitely one of them. Roughly speaking, a black hole is a tiny core with enormous amounts of matter packed into it. There are no known forces that can prevent the collapse of this core into a singularity, but then, we don't know all of physics, so there may be such a force after all. Another feature of a black is its event horizon, the mathematical line drawn in space beyond which there is no return possible to the outside, not even for light. Once in, there is no escape, everything will fall onto its core. However, the inadvertent traveller (or planet) moving through this event horizon may not notice a thing. For all we know, we may have passed through an event horizon of some black hole out there (I presume that we would probably have detected this but I don't know the details of this.)

Here is another one of those questions that kept me awake as a child: "is the universe really infinitely big"? The very idea seems absurd. However the reverse is not better; if there is an end, what's behind it that thing that marks the end? At any rate, the current wisdom is that the universe is infinitely big and expanding at an ever accellerating pace. The ramifications of this idea are far reaching. Imagine you are walking on a road made of rubber. You have reached the speed of light, but the rubber is expanding under your feet at a pace faster then you. You are trying to get to the end of the road, but will never make it. In fact, the endpoint is slowly receding while you are running at your top speed. The stuff nightmares are made of really.

The same fate befalls the light from distant stars and galaxies trying to reach us, perhaps carrying the messages of alien civilizations. As the universe is expanding, fewer and fewer of those distant stars can communicate with us and disappear behind a black curtain, forever invisible. And the bad news is that the black curtain is drawing nearer every minute. At some point in the future, there will be just us and a small cluster galaxies (see http://www.nytimes.com/2007/06/05/science/space/05essa.html?_r=1&pagewanted=2.)

The irony is that we will then be locked up in our private bubble of the universe. Even if it wanted to, the rest of universe cannot send its information to us, and reversely, we cannot send our information to them. We we live on "causally connected islands" floating in the middle of vast expanses of emptiness. Sending messages (in the form of light) into this void is futile since space is growing faster there than light can travel. Our messages will travel forever, never getting anywhere. Like the inhabitants of ther Easter island, we are locked up. Pretty claustrofobic idea really. But fortunately, we still have an odd trillion years to enyoy the stars in the sky!

Monday, December 29, 2008

Learning and Prediction

Our world is not merely random but has structure. Every day the sun rises and sets, quadrupeds with their eyes in front of their head want to eat me, fire is hot and will damage my body, and so on. Our, that is all living things, primary task is to discover as much structure as possible so that we can leverage it effectively and manipulate our world. In fact I want to argue that the primary goal of learning is prediction. If I can predict the world I can find food, defend myself, survive and ultimately bear offspring. Thus, "learning = prediction"

But learning is not just remembering what we see. Why? because we will never encounter exactly the same situation again. Instead we need to derive rules that can be applied (generalized) to new situations as well. A nice example is the "eye pointing forward rule". If I noticed it for tigers and lions, I can now apply it to panthers, wolves and bears. So, we need to connect the dots: interpolate between the things we have experienced. Another example: when a child sees her mommie appear and disappear she learns that out of sight does not mean non-existant. S/he can now apply this rule to cars being momentarily occluded which may save her life. Thus, "learning = generalization".

When we have learned to predict something well, we have a feeling that we have "understood" something. Perhaps the underlying causes. For instance, we might learn that all animals with bright colors are poisoness. We have learned a concept or an abstraction that aptly explains a class of events with an elegant rule. Most of modern science explains phenomena through powerful often mathematically driven abstractions. Thus, "learning = abstraction".

When you zip your files on your computer, you compress the number of bytes necessary to describe its contents but not the information (which can easily be reconstructed perfectly.) So the original format must have been redundantly encoded. Indeed, language is redundant in the sense that you can often predict the second half of a word given the first half. Similarly, photo's are highly redundant because if I would pay you 1 dollar every time you would predict the color of a pixel correctly given the pixels surrounding it, you would earn a lot of money. Hence, the better we can predict, the more structure is present, the more we can compress and in fact the more there is for us to learn. Hence, "learning = compression".

Evolution has heavily selected for creatures that predict well. Humans are the pinnacle of this process, the ultimate "prediction machines". We can now predict far beyond what seems evolutionary necessary, such as the mass of the electron, or the speed of light. We have run away with our ability to predict and as a result completely dominate the world (I guess in a certain sense only because one could argue that ants rule the world in a different sense.) But, being able to predict well does seem pays off.

Time Flies (faster when you are old)

We all know the saying: "time flies when you are having fun". The reverse is also true, when you wait out an hour it goes tantalizingly slow. Paradoxically, when after a year you recall these events, the hour wait seems like a minute, while the busy hour feels much longer. So our perceived sense of time is not the same as the time that actually passed. In analogy with a feel-temperature, let's introduce a "feel-time".

Many have proposed that one psychological effect has to do with the fact that you measure duration relative to the time you have already lived. Your yardstick grows over time and hence time intervals feel shorter. Assuming your yardstick (L) grows linearly in time, L = a*t, then a feel-time-interval as measures in units L is ds = dt/L = b*dt/t (with b=1/a.) If you didn't follow this, it says that time intervals feel shorter as the reciprocal of your age: a year at 20 feels twice as long as a year at 40.

A somewhat orthogonal explanation that one can find in the literature is that it has to do with the number of new events experienced in a time interval. If each new experience means an increment of 1 unit in your feel-time, then you spend a lot of feel-time in your youth and very little in your old age. In fact there are two effects at play: when you are young everything is new, while when you get older many everyday experiences have become routine and do not increment your feel-time as much. Add to that the fact that your memory is much better when you are young and thus many more experiences are stored (In fact, research has shown that you mostly seem to remember the time when you were around your twenties.)

The second explanation seems more plausible to me. I have worked out the math for the highly simplified case where there is a bag if N experiences from which the world samples experiences uniformly at random. The assumption is that after you have seen an experience once, it will no longer count as new and not increment your feel-time. This model predicts that feel-time-intervals become exponentially smaller with a rate of 1/N (with N the total nr. of experiences.) This exp(-t/N) form is very different than the 1/t predicted by the yardstick theory. Most importantly, if you have reached N, time stops! Of course, this model was too simple to be of any practical use because there is a very large amount of possible experiences and they are not at all uniformly sampled (e.g. going to the restroom is sampled thrice a day while marrying your spouse hopefully only once.)

In Orange County people seem to be obsessed with staying young judged by the number of plastically enhanced individuals. But perhaps a better strategy is to invent a pill that stretches out the perception of time. I have heard this possibility is quite seriously being researched. Take this pill before you go on an adventurous trip and you can buy yourself many years of life. Or maybe memory implants such as played out Total Recall will be the easier solution for the future.

Saturday, December 27, 2008

Cruel Evolution

The world is full of suffering. Humans seem particularly talented at inflicting suffering to others. We wage cruel wars, kill millions in gas chambers, burn so-called witches at the stake and so on. Think of the most cruel thing you could imagine and some person (typically male) will have committed it somewhere, someplace. Why do we commit these atrocities?

To answer this, let's make it less personal. A certain kind of parasitic wasp stings spiders into a sort of coma and lays her eggs inside it. By the time the eggs hatch the larvae eat the living spider inside out. An even more bizarre adaptation can be found in another kind of par­a­sit­ic wasp, Glypta­pan­te­les, who's larvae manipulate their host caterpillar into a bodyguard (see http://www.world-science.net/othernews/080605_glyptapanteles.) Pelicans usually hatch 3 eggs. In good times all three survive but usually one of the older brother/sister kicks the smallest baby pelican out of the nest which of course immediately dies. One more: when a lion becomes the new alpha-male of a group it will kill each and every infant lion to make sure it is his genes that get propagated into the next generation. Needless to say, this is but a small selection of a very large collection of examples of the cruelties one can find in the animal kingdom.

Back to humans. We evolved in social groups and have all sorts of fantastic social adaptations that let us function in groups. I have been told a very significant part of the brain is devoted to social interactions. Presumably, these groups were constantly in fierce competition. There may have been strong selection for the variety of proto-humans that were most effective in exterminating their competing neighbors. Peacemakers may simply not have had the edge in evolution. The recent genocide between Hutu's and Tutsi's may serve as a flashback to how things may have looked like in the stone-age (don't get me wrong: "we" -- white Caucasian males-- are no better.)

How deeply burried is the animal inside us. I believe it is not far away at all. What does someone have to do to you in order to fall back to your prehistoric self. How about someone killed your family? Personally, I cannot predict how I would react, but likely very aggressive and ready to march into war. Another unsettling example is the second world war. I grew up in the Netherlands and although some Dutch like to think of themselves as different from Germans, Dutch and Germans are virtually the same race. We all know what some Germans were capable of in WO-II, and I have no illusions about myself ending up fighting on the wrong side, given certain conditions were met (such as living in Germany in 1941, having patriotic parents and being influenced by the well oiled nazi propaganda machine etc.)

To study how easily people are manipulated into committing acts that border to torture Stanley Milgram set up some cunning experiments in 1961 (see http://www.world-science.net/othernews/080605_glyptapanteles.) He basically ordered students to administer electrical shocks to subjects that they could not see but could hear screaming. The pretend-professor only had encourage the students a bit and claim this was all for the good of science for these students to almost "kill" these pretend-subjects. Of course, there is nothing special about Yale students, and we should have no illusions that we can be tricked into similar acts.

I think we should admit to ourselves that a part of us is still governed by animal drives and instincts, perhaps inconsciously. This is what creates a lot of the suffering we see even today. We should guard ourselves against it by at least recognizing it, and hopefully one day taming this beast.

End of Science

At the end of the 19-th century physicist thought they had figured it all out. All of elctromagnatism in just 6 (Maxwell) equations. What a victory. Newton's laws of motion and gravitation describing how things move including all of the celestral bodies. But what a surprise when relativity and in particular quantum mechanics messed up that neat clean picture. Today there are many who believe all of physics can eventually be reduced to a few fundamental laws of physics. But even this extreme form of reductionism does not imply we can stop the scientific endeveaour there and then.

Perhaps the most canonical example of what some people called non-science is an attempt to describe the physics inside a black hole. Almost by definition, the black hole is an object from which nothing ever escapes, so it seems utterly futile to try and understand what goes on inside it. If only because one's theories can not be based on observations. That was before the modern insights that Hawking radion can eventually radiate out the information stored in a black hole. I guess the debate isn't settled yet, and the picture is somewhat more complicated (for observers that remain outside the event horizon nothing really ever falls into the black hole, instead it freezes in time on the horizon and so the information is more like stored on the horizon rather than inside of it.)

But there are other questions one can ask pertaining the possibility to even finish physics (and therefore science as physicist like to believe.) Can we ever find explanations for everything? Can we find explanations for why certain physical constants have the value they have? And if so, can we explain why the laws of physics are what they are? There always seem to remain questions unanswered. This infinite regression reminds of a child's game: "Dad, why is the sun warm?" "Well, because it consists of a big fire", "but why is the sun on fire dad?", "well because there is nuclear fusion that makes it really hot", "but dad, why is the there ...."

A different problem asserts itself when we try to explain how the first reproducing molecules came into existance. Any such theory will rely on a random, lucky first event that created such a molecule. Yes, all ingredient must be present but we still need to reason like: "there are X possible events per year, times Y years times the probability P of that event gives us Q=XYP% chance life came into existance in the 3 billion years available to the earth. How big must Q be before we are satisfied, is 0.0001% ok, or do we require more like 50%?

And then there is chaos, which presents perhaps the biggest blow to the cherished notion of predictability in science. It asserts that certain systems are unpredictable by any practical methods even if wee know the laws of physics exactly and know the initial considtionals to a *very* high degree of accuracy. It's a fascinating topic and it shows that even knowing the laws of physics at their most fundamental level may not be very helpful in understanding the phenomena that result from it. Instead, we ought to be looking at the problem on a larger, less "fundamental" scale. Ineresting structure can still emerge by changing the magnifying glass. The primary example is thermodynamics and its relation to statistical mechanics. The collective behavior of large quantities of chaotically moving particles can result in predictive phenomena described by quantities like pressure, temperature etc.

When can we say that we truly understand something? Take the brain. When can we declare victory? Even if we can replicate a brain in all its detail in a computer (including consciousness etc), do we understand the brain? How many levels and how much detial of explanation do we need?

And then there is this annoying mathematical theorem: Within any framework build on a finite set of axioms one can formulate questions that remain unanswerable within that framework (Godel.) I am not sure how relevant this turns out to be, but it ought to make us a bit humble.

So, were will science end up in the end? Never quite dead I hope. Perhaps, at a fundamental level we will end up with an infinite number of theories which are all consistent with the observations we have (it seems string theory is heading that way right now.) But I predict we will always be busy with improving theories at a practical level. Improving our ability to predict the weather, or earthquakes for instance. Up till now the mathematics we have used to describe physical phenomena has been surprisingly elegant (Riemannian geometry for general relativity, Hilbert space theory for quantum mechanics, etc.) and moreover it was almost always invented by mathematicians before its application to physics (modern string theory being the exception.) This to me seems highly suspicious. I see no good reason why the mtahematics describing physics ought to be elegant. It raises the suspicion there may still be a whole lot of "ugly" physics out there which has not been filtered through our "elegance sieve", the high hanging fruit so to speak. I predict there is much, much more of that than we can even start to imagine. No, science has not come to an end, it has just started.

Friday, December 26, 2008

Our Bigger Self

Most of us have a sense of "self". The boundary of "us" is our body. At least that is the boundary we are most aware of. It is also a natural boundary because its parts rely on each other for their survival. Loosing a limb will definitely diminish the chances of survival for all the constituant parts. So the self acts more or less like a queen over her hive, her primary role is to make sure the part peacefully cooperate to serve one goal: the survival of the unit and ultimately the reproduction of the organism.

It may be interesting to know that our body really is a pact between its cells. It was a major step in evolution when single cell organisms "decided" to join forces into a multi-cell organism. For most animals these cells are stuck together, but this distinction does not seem necessary. How about bees in a hive or ants in a colony? Do we consider the colony or the ant as the natural unit of organism? Also, even inside our body not all is peace. Sperm-wars and strong competition between chromosomes have been reported in the literature.

Even with humans it is not clear whether the body is the natural unit to claim a self. Interesting experiments have been conducted where researchers have measured the electric conductance of the skin of human subjects. These subjects were confronted with realistic looking mutulations of parts of their body. For instance, by using mirrors one can stage a situation where it looks like your hand is about to be hit hard with a hammer. This "would be" mutulation elicitated a stress reaction of the body which could be measured. However, similar reactions can be measured when virtual harm was done to one's direct family members, especially ones with which you share genes such as your children. Bizarrely, males also showed a reaction when their car was damaged (no kidding.) Researchers concluded that people also have an extended sense of self, or an "extended body" so to speak, which includes family members.

Reversely, some stroke patients seem to reject parts of their own body as belonging to "them". And then there are of course the patients with multi personality syndrom, where multiple "selves" claim a single body. It an illness allright, but it shows that the mechanism can break down. What we think as utterly normal may simply be one possibility out of many.

Perhaps we have many senses of self with a varying magnitude of commitment. From body via family or community to country. We can ask ourselves why people are willing to fight and die for "their country". What is inherently good about the country you happended to get born in? Isn't it odd that for every soldier on one side of the border that strongly believes in the cause s/he is fighting for there is another one on the opposite side of the border? Perhaps we have drawn another somewhat arbitrary line in the sand and created a "country level self". Maybe we should be working on a global sense of self, encompassing all of humanity. If only we would experience the suffering of 80% of humanity in underdeveloped countries as our own suffering, then there would most definitely be much less of it.

Visions of the Future

Walking over campus at UC Irvine I count about 50% of all students talking on their cell-phone. We routinely search the internet to figure out what or where to eat, chat with friends, watch a movie from netflix, look up trivia about the first world war and so on. We want to stay connected and we crave information from our collective memory "the world wide web". This is the information age. Developments are going so fast, that today's predictions are tomorrows reality. Where will this go? Let me try to sketch a picture of how the information age may look like a decade from now.

Right now, in the UK there is a surveillance camera for every 14 people. It's not hard to see that pretty soon we may cover every square inch of inhabitated space with one or more camera's. This creates a patchwork of life video footage that covers the "interesting" parts of the earth. Already, people shoot images with their digital camera's and upload them to websites such as Flickr, Twitter and YouTube. In fact there are so many images that from most interesting touristic landmarks one can synthesize a virtual environment by stitching together these images (see Microsoft's photosynth.) Imagine combining all video from surveillance cameras to create a life version of Google Earth where one can fly through the world and observe it realtime.

But, perhaps an even more fascinating development is the possibility to record everything you ever saw in your lifetime. By building a small camera and recording device in your glasses (or parhaps using an eye-implant) you can simply record everything your eyes see in their lifetime. You can then start asking things like: "show me the highlights of my 3'd birthday", or "show me every turtle I ever saw" etc. We can imagine projecting life feeds of our best friends "eye-cam" in a small corner of your visual field (using something akin to a "head-up display" used in modern fighter jets.)

In fact, one can easily imagine overlaying the real world with images from a virtual world. For instance, you could project the image of your best friend in front of you when you are talking to him/her. Or, you could make a virtual appointment in Rome. My point is that at some stage the distinction between the real and the virtual world may become blurred. When realistic enough, the experience of talking to a life virtual projection of a person might be as good as the real thing. Why paint my walls when I can virtually paint them and there is no visual difference? In the latter case I could even change the color every day. Why place traffic signs if you can place virtual traffic signs alongside a road (this can only work if a law is passed that obliges people to use their eye-implants and have updated the latest software)?

When we push this idea to its extreme we cannot help but think of the matrix. The real world may become an ugly concrete skeleton on which we project our fancy dressings -- a super projection screen of sorts. But what I find fascinating is the possibility that we may genuinely forget the distinctions between real and virtual. After all, isn't our brain doing the same thing? If we never get to see the "real world" (imagine we cannot switch off our eye transplant) how different is this really from our brain interpreting some light frequencies in terms of colors and adding a layer of interpretation over it?

Clearly, a system like this is the ultimate Orwellian nightmare if not controlled by strict privacy laws. However, I am not in the business of predicting what is desirable morally, rather of what seems possible or even inevitable.

I like to close this entry with the remark that all of these "science fiction fantasies" do not require much more new technology than we have today. Yes, we need faster computers, more storage capabilities, better computer vision and graphics algorithms, smaller cameras etc. but nothing really drastically different (for instance I don't think we need quantum computation.) Let's hope we live to see it!?

Thursday, December 25, 2008

Three Elements of Learning about the World

How do we learn? Or more ambitiously, how do we create a consistent view of the world? I am not talking about a religious view of the world, but rather a scientific "theory" of world. I believe there are at least three important mechanisms that help you build a consistent picture: 1) mental pictures, 2) paradoxes and 3) metaphors.

Of the three above the first one is undoubtedly the most important one. When you listen to, or read about some topic of interest you never remember the literal words. Rather, you compress the text into a mental picture that summarizes its content (at least that's how it seems to works for me.) I have read about famous scientists like Einstein, Poincare, Feynman etc. who build very elaborate mental pictures (see e.g. "the psychology of invention in the mathematical field by Jacques Hamadard.) The picture must represent an abstraction; in some sense the "essence" of what is being told. When one reads about new things either new mental pictures are build or old ones updated. In fact, I believe it is this collection of mental pictures with their interdependencies that defines ones world view. One tends to interpret new information in light of this existing framework. As an academic researcher I attend a rather large number of "talks", 90% of which are quickly classified as "abstract idea X with bell and whistle Y and Z". So now and then, I hear about an entirely new idea which does not resonate with anything else in my mental knowledge-base or is even in direct conflict with existing information nuggets. This makes my heart pound faster and forces me to pay close attention. In fact, a frustrating, somewhat stressful state of mind overtakes me that only subsides when a new picture is build or when the dissonance is resolved.

This brings me to the second mechanism: paradoxes. Sometimes we learn about things that are not consistent with what we know. The paradox that results is a very powerful singularity for learning. One should never step over these paradoxes as may be most convenient, but embrace them in order to update one's internal mental representation. Paradoxes almost always point to beliefs that are wrong and are in great need to be updated. Do not rest until you find out the cause of your paradox. It would be a missed opportunity.

Finally: metaphors. The real world is often so complex that creating mental pictures are a real struggle. It is of great help to first describe the problem in terms of elements that we are familair to us in our everyday lives. Metaphors are almost always simplifications and relying on them too literally will quickly lead to paradoxes. So, one ought to proceed with caution and refine one's mental pictures as one gains understanding. Nevertheless, metaphors a great way to make initial progress.

In this blog I will be (hopefully) describing a good number of interesting or surprising scientific ideas that may cause your mental picture of the world to slightly shift or even be somewhat upset. Keep and open mind, as will I with respect to your comments.

To Blog or Not to Blog

Never thought I would do this, but here I am blogging my first blog on Xmas day. Why? Well, Xmas vacation provides some time to reflect on issues other than work. Issues that dig a little deeper. I remember thinking about such issues a lot more often when I was a student back in the Netherlands. I also realized that many of the issues that kept me busy in those days, such as evolution, religion, physics, politics etc, define who I am now. Since then, I have had the opportunity to discuss and learn about many more new and interesting scientific pearls of wisdom. Why not share them? If nothing else, they can serve as a document for my children to read when they will be old enough to appreciate them. At any rate, I hope you may enjoy them as well.