The Dark Side of Scientists: A Tale of Complex Networks

I'm not citing names, first because they would be meaningless for most people, second because I'm not stupid and my future job may in one way or another depend on those involved some day. Besides, it wouldn't be either elegant or very professional. The tale I'm gonna tell is anyway very funny and clarify a bit of the human nature.

I've just got accepted for publication by PLoS ONE this nice paper, which I wrote with Joerg Reichardt and David Saad. Joerg, by the way, deserves all the merit as the computer expert behind some of the best tricks involved in the algorithm, which as I'm going to explain, is the main point of the paper. 

The paper is this:

The interplay of microscopic and mesoscopic structure in complex networks, J. Reichardt, R. Alamino, D. Saad - arXiv:1012.4524v1 [cond-mat.stat-mech]

The link above is from the preprint in the arXiv, the final version being a bit different in the end, but not very far from it. It's not traditional physics, it's a very interdisciplinary paper mixing ideas from physics and information theory and with applications to sociology and biology. Okay... It's fundamentally a paper on Bayesian inference and, being a mathematics paper, it's naturally interdisciplinary. But it's always nice to use that word. :) 

Let me talk a bit of the paper. That may be a long talk, so if you are more interested about the tale itself, I suggest you to scroll down. I will start by telling what we mean by a complex network. A complex network is basically a bunch of things, that may be equal or different, interacting among themselves in any kind of way. Looks like everything is a complex network, right? Well, it's very much like that. But it is much easier to visualize it with a picture, and so I'm putting one I found the internet here.

Each dot, or edge, or node, in the above network is an author of a scientific paper. Each connection, link, edge, means that two authors shared a paper. And that is a complex network. Mathematically, it's a graph. Now, in this graph it's not easy to see, but if you pay attention you will see that are some structures in these graph. Some groups of nodes are more interconnected among themselves than with other nodes. Finding out the rules by which this happens is called community detection.

It's interesting to note that this group structure is what we call a mesoscopic characteristic of the network. It means that it happens in an intermediary level between the macroscopic and the microscopic phenomena in the graph. By macroscopic you can imagine things like paths, cycles and cliques. By microscopic, you can think about characteristics of individual nodes or of small groups of nodes, two or three usually.

The interesting thing is that community detection is usually done by trying to infer how one group connect to another one, completely ignoring any node specific characteristic. What we've done was to include this microscopic information in the inference and, voila, our algorithm was capable of modelling the network structure better than the others!

Our algorithm is a Bayesian one, full of tricks I must admit, but it works anyway. What it effectively does is to define a general model for a network that depend on two hyperparameters: the group structure and the tendency of a node to link to another one. Then, we feed the algorithm with the observe adjacency matrix of the graph representing the network and the algorithm give back a classification of each node into a different group, how the groups link to each other and what is the propensity of a node to link to another one! 

You may say: Of course, give me enough points and I can fit an elephant! But first, we did not add as much parameters as we could, we did it by thinking about the best structure. Each one of our parameters has a "physical" interpretation. Second, we compared it with an algorithm with more degrees of freedom (more parameters to adjust) and we still performed better.

How do you know you're better? Well, there are some networks that were studied by specialists in their area and the group structure was inferred and studied by them. In out paper we give one example from sociology and two from biology. In these cases, we had what we called the expert classification. So, we run our algorithm and others on the network and compared with this classification. As I said, our algorithm agreed much better in ALL three cases. 

Now, I will ask you something. Isn't that clear that, in order to know if the algorithm was good, we had to compare with a case where the classification is known? Isn't it obvious that there can be cases where the expert classification may be difficult, may be not available, or may take a long, long time to be obtained? And after all, even if we always had the expert, isn't that interesting to have a program that is as good as the expert? That would certainly tell us something about how the expert works and, as I have been writing in this blog for a long time now, pure knowledge is also a good thing.

And finally we come to the climax of the tale. I explained all of that, except for the last paragraph above simply because I thought it was too obvious for an audience of scientists. After I finished my talk, there were few questions from the public, which is a sign that either no one understood what I said or that nobody liked what I said. The second turned out to be the case as one of the members of the audience asked with a sarcastic tone of voice:

"Why don't you always ask the classification for the expert?"

The audience was pleased with the question and many smiled and nodded in agreement. I answered that it was a test and the guy asked me for an example where the expert could not give the classification. I'm a terrible debater, so it took me some time to think about a specific example and the one I came with was not very convincing. But I guess that it's clear that the more complex the network is, the more difficult is to a human expert to analyse it. Note that these people were not stupid. But they were nonetheless arrogant enough to think that if they could not see the importance of what you're doing, it's not important at all. In fact, I could say that many of the talks from those who were smiling were actually very devoid of any short term practical application, what for me is irrelevant as, I'm saying again, knowledge for the sake of knowledge IS IMPORTANT no matter what politicians and businessmen say.

This kind of attitude is unfortunately very common in the scientific community. Not everyone is like that, but a lot are. Be it because we are competing for funding or for awards, or because we want to be the brilliant rising star, that's not what science is all about. I guess that this kind of disunion just make us more vulnerable to the attack we have been suffering from the governments around the world. The utilitarian philosophy, which is just a means of mass control, is already rooted into our community. On the other hand, maybe we were always like that. Newton seemed to be like that. Others as well. But it is, anyway, regrettable.

Talking about Time, Mach and Information

Two weeks ago, I had the pleasure of receiving Julian Barbour here at Aston for a seminar. Julian is a singular physicist and I really admire him. Specially for the path he chose after getting his Ph.D. in the University of Cologne, Germany. Instead of finding an academic position, he decided to finance himself by translating Russian texts part-time. He said to me that he knew he could not fit into the publish or perish academic environment. Well, his first published paper took him many years, but was published in Nature. In addition to that, he's a very nice and very polite person.

When I invited him to Aston, he promptly and kindly agreed to give us a seminar about his work on Mach's Principle. As probably most of you know, Mach's Principle is the idea, first expressed by Ernst Mach, that all movement should be relative. Newtonian physics is based on the assumption that a non-accelerated movement is relative, but whenever acceleration comes into play, there must be a sense in which we can talk about absolute movement. For instance, circular movement should be absolutely accelerated, no matter the referential. Mach, and many philosophers including Poincare, did not like that. They thought, as indeed I think as well, that all movement, accelerated or not, should be relative. The problem is that it doesn't seem that the universe agrees with this point of view.

Well, actually that's what I thought was the content of Mach's Principle before Julian gave his talk. What Julian taught us was that this is only part of it. It seems that the relational point of view has problems that appear even before acceleration comes into play

Another thing that Julian showed was how using Mach's Principle you are able to deduce very interesting physics like gauge theories. You should notice, however, that his work until now is just about classical physics, but Julian also works with quantum gravity and one of his objectives is to attack the problem from that perspective.

The details of all of this can be found in this paper, freely available from the arXiv:

• The Definition of Mach's Principle, by Julian Barbour

Julian has a book on his ideas about time as well, which I should have read before he came. That would have made our discussions much more fun. Yes... I am buying it now and I am eager to read it. I'll try to post some comments when I finish. Julian idea is the one of the block universe and he also shares David Deutch's enthusiasm with the multiverse idea.

After the seminar we had, as it is usual, a lunch on the Business School and afterwards we spend the rest of the afternoon discussing about his new interest on information theory. He was writing his essay for the Foundational Questions Institute contest whose theme was "Is reality digital or analogue?". His essay is quite interesting and can be read here:

• Bit from It, by Julian Barbour

Basically, he argues against the present fashionable position that information is a concept more fundamental than others, for instance, fields. "It from bit" is the famous aphorism created by Wheeler in his phase when he thought that everything should be originated from information. It's a quite enjoyable paper and we here already are planning to discuss it. I would recommend it's reading, as the mathematics is not very difficult. You can also vote for him in the contest. ;)

Fortuna Imperatrix Mundi

This very illuminating paragraph is a comment to the blog post Bloodbath for Science, posted in the Cosmic Variance blog, that talks about the huge cuts in science funding in the USA:

Understand, John: The people proposing these cuts believe that research scientists and staff are not doing any real work *by definition* unless they are employed by the private sector. If your work doesn’t contribute tangibly to some company’s bottom line, and ultimately to the profit of the CEO and shareholders, then your work produces nothing of actual value. In this view, any job that exists as a result of federal funding is, as a matter of principle, disposable and can be cut with no real loss of productivity. If your work is valuable to the private sector, you’ll be hired by some company anyway. If not, it has no value and you shouldn’t be getting paid to do it.

This is probably the most concise and clear explanation about how the mind of politicians not only in the USA, but also in the rest of the world, think. Very depressing. Most depressing yet is that many people will find that absolutely logical.  

Molecular Random Tilings

I am still organising the seminars in our group every Friday. In the last one, we had a very interesting one given by Prof. Juan Garrahan, from Nottingham University. The title was the same as in this post, Molecular Random Tilings. Although I don't have the version of the talk he gave, you can access a very similar previous version on his webpage through this link. 

The idea is a very interesting and beautiful one. The chemical problem is related to an organic molecule which is called TPTC or p-terphenyl-3,5,3’,5’-tetracarboxylic acid. It has the form below:

These molecules are adsorbed onto a substratum of graphite and bind together by means of hydrogen bonds in one of two possible relative configurations. After the deposition process, they cover the substratum forming an hexagonal molecular lattice. In fact, you can associate to each of these molecules a rhombus and, in doing so, each configuration of the molecular lattice can be associated a tiling of the plane (also known as a tesselation) by these polygons, which is a classic mathematical problem. It's also equivalent to another well known statistical mechanical problem, which is called the covering of the lattice by dimers, the simplest one being that on the regular lattice.

The way to associate the rhombus to the molecule is quite interesting. There are three directions for the rhombus in the plane and to each one a colour is associated (guess which...): red, green and blue. The picture in the top of this post, taken from the paper Molecular Random Tilings as Glasses by Garrahan et al., shows how the model is and the figure below, taken from an article in the AMS site (and property of Peter Beton) shows on the left an image of the molecular lattice taken by an scanning tunneling microscope and on the right the associated tiling.

The interesting thing in statistical mechanics is always to analyse phase transitions. In models like these, what is interesting is to study how the system passes from a phase dominated by random tilings, meaning tilings which are not ordered in the obvious way, to an ordered phase where the tiling is regular as we vary the temperature of the system. The basic quantity we need to calculate turns out to be the free energy, which will allow us to calculate everything else we want to know about the system. The beautiful thing about this model is that the free energy is proportional to the integral of the squared gradient of a field called the height field that can be defined for each point of the tiling. The cool thing is that this field can be seen in some sense as the height of the pile of 3-dimensional cubes you will certainly see when you look at the tiling! 

Another very interesting aspect of this model is that it supports fractional excitations, which are very much like the anyons we already discussed in some previous posts. While the anions have fractional statistics, these defects in the tiling are triangles which are a result of imperfect matches. Two triangles form a rhombus, but then they can divide themselves and run free through the tiling. This amounts for a fractionalisation of the degrees of the freedom of the model and, as you can imagine, charges can be associated to these defects.

The details of the model are in the paper I linked to in the beginning of the post. It's worth to take a look at it as there are a lot of beautiful images and much more information about the phase diagram of the model. After the seminar, I took Prof. Garrahan to have lunch in our Business School (one of the advantages of giving seminars in our group). A friend called also Juan, which is again also Argentinian as Prof. Garrahan, accompanied us. It was a nice lunch and I would like to thank Prof. Garrahan for an excellent talk and a pleasant conversation afterwards.

A Note about Footnotes

I know this seems completely off-topic and unnecessary, but one of the advantages of having a blog is to be able to make your complaints available for a wider audience. However, I believe that this will not be so useless as it seems and I would use it as an advice when writing documents, specially reports and thesis. It's simple: do not overuse footnotes!

Footnotes are devices that should be used with care, which in many books (some very famous) and articles they are not. I don't mind when the author use the footnotes to place the references, for instance. In fact, in some journals this is part of the articles standard format. I do prefer when the references are at the end of the paper, but that is just a biased opinion and there is not much difference. The biggest and most annoying misuse of footnotes is to add "extra information". I have an opinion about that. If you have any relevant information, just put it on the main text. If it's not relevant, almost all the time it's better to just keep it out of the document. There are very rare occasions where a footnote is okay, but they are really rare.

When should you consider the information worth of a footnote? Well, you must use your own common sense, but there are some tips to see if you are not abusing them. For instance, if every page of your thesis has a footnote, you actually have more than one thesis. Also, if your footnotes are longer than two lines, maybe the information should be written with slightly larger characters in the main text. Believe me, I have seen books where the main page had just a few lines of text and the whole rest of it was filled with footnotes!

Another thing, there is nothing more distracting for the reader than a long sequence of footnotes that keep interrupting the flow of the text all the time. It's absolutely disrupting and I gave up reading some books because the footnotes made it look like a jigsaw puzzle. And to give just one example of a brilliant person who abused too much of footnotes, think about the Landau & Lifshitz books (it's a famous series of physics books for those who are not physicists). Beyond all the other issues that make those books difficult to follow, on top of that the footnotes keep interrupting the reading over and over again. And Landau is surely in the pantheon of physics gods.

When I wrote my Ph.D. thesis, I used just one footnote. I kept it because, in fact, I wanted to look smart about a topic, but I regret it. The rest of the 150 pages has no footnotes, except for the references but they were at the end of the document, not of the pages. At the end, I received many compliments for the clarity of the text.

So, my advice is: include every relevant piece of information in the main text. Use parenthesis, comas or whatever other trick you may need, but don't force the reader to make a detour to the end of the page unless you really, really, really think there is no other way. Your readers (maybe me one day) will thank you. (Of course, that's only MY taste...)

Anthropic Principle

All definitions of the Anthropic Principle can be classified into two groups: the trivial and the wrong.

I know that the above assertion can be criticised for being too strong and too careless, and in some sense I must admit that there is a sort of radicalism in it. However, given that the probability of it being precise is high, it's worth the risk. I would expect that such issue would be longer settled, but over and over again I end up reading about the Anthropic Principle as if it is a really great and brilliant idea. In fact, I only decided to write about it because I was reading Richard Dawkins's The God Delusion and he talks about it at some point. So let me explain the reasoning behind my point of view.

The detailed definition of the Anthropic Principle, with all technical terms and such, can be found in a summarised form in the Wikipedia Article about the topic. Technically, there are basically two versions that can be afterwards subdivided according to extra details. They are the strong and the weak versions.

The strong version says that the laws of the universe are such that at some point conscious observers must appear. The "must" is what makes the version strong. I have very little to say beyond the fact that this is a highly non-falsifiable argument. It claims that conscious beings are somehow an objective to be reached by an universe and that the laws of the universe should be such that they allow them to appear. Or that without these beings the universe cannot exist somehow. It's actually quite easy to smell a bit of deism in this kind of argument. You may argue that this has something to do with some kind of natural selection principle where universes with conscious beings are fitter, but in fact I do not know any convincing argument apart from shear speculation. The fact that it is not falsifiable should be clear. How would we falsify it? Well, we could if the universe did not have conscious observers from the beginning to the end. Too bad it does. We could construct this kind of universe... oh, but wait... if we are constructing them, then the universe that include ours and that one also contains conscious observer. This is the version I call wrong. I know it's too strong to call it wrong, specially for a philosopher, but it's basically true. 

The fact is that, in principle, there is nothing that prevents a version of our universe that is too fast to be able to sustain any kind of life, be it conscious or not, to exist. Mathematically, for instance, I see no problem. The issue is even deeper, because we don't really have a detailed understanding of the phenomenon of conscience or even of life itself. The only example we have of life is the one we can observe on Earth, which is hardly a fair sample of the whole universe. It's true that according to some calculations, a slight deviation from the known versions of the physical constants would have a huge impact on life as we know it to the point it would not be able to exist, but we are not really sure that some other kind of life would not. That brings me to the second group of definitions.  

The second group are collectively known as weak versions. These are the ones I am calling trivial. Again, I am exaggerating on purpose. They all say that the constants of physics must be such that they allow (conscious) life to develop. For example, based on the fact that humans exist, you can get a good estimative of some physical constants and the allowed range of the estimative falls very close to the real value. I hardly see the point of calling such and observation by the term "Principle". I tend to think that every person in the world which works with some kind of inference procedure, which obviously include science as well, should see that if you assume life and try to estimate a physical constant, it just shows that your model is correct, not much else. The fact that humans exist is data. It's given evidence. If you do your estimate and reach a wrong value, it would mean that you should work on a better model for your physics. Now, you can take every piece of evidence in the world and associate some kind of principle to it. For instance, let's talk about the 'Bread Principle'. It says that the physical constants must be such that bread can exists. Now, bread requires yeast among other things. So the 'Bread Principle' says that microscopic life must exist. And it must be such that the chemical reactions that take place in the yeast must occur in such a way that allows bread to grow (!). You probably see where do I want to get.

At the end, my point is in fact very simple. Any idea trying to justify the laws of the universe by requiring consciousness are relying on a phenomenon that we are not even close to understand at the moment and, to be honest, are nothing more that some sort of religious argument disguised in science cloths. On the other hand, the fact that the laws of the universe are compatible with our existence and that given the correct model we can calculate things backwards is just a statement of the obvious: the model must agree with the experimental evidence. I am not aware of any breakthrough provided by the so called Anthropic Principle idea, and I am willing to bet that none will ever come from it, besides of course the usual ones provided by probabilistic inference. 

xkcd: 3D

xkcd: 3D

Critical Care

For those who are not Star Trek fans, it is probably not very clear what a geek sci-fi show that is not even being broadcast anymore has to do with anything barely real. Fans, otherwise, know better. When Gene Rodenberry created Star Trek, his idea was to to discuss the problems of society in a disguised language. By placing them into the distant future and on distant planets, he could be excused from criticizing his own country. Just to give an example, it was on Star Trek (the Original Series) that the first interracial kiss in the US television took place, with William Shatner being highly responsible for it not being cut from the original text. But that's another episode. The episode I really want to talk about was the one I watched last weekend.

By showing the social side of Star Trek to my wife, I was able to convince her, who's a lawyer, to watch the whole five Star Trek series with me. She's actually enjoying it so much that she's also a fan now. Okay, from now on I will spoil the episode. So if you like surprises, stop reading now. The episode is from the last season of Voyager and it is called Critical Care. The ship's doctor, which is a hologram, is stolen and sold in a planet where the health system has some similarities with the real (not the idealised) terrestrial one. The story goes like this. The planet's economy was crashing (any similarity here?) and then an alien race appeared to help. They ended up leaving them with a health system where people would be treated accordingly to an index named the treatment coefficient, TC for short. The TC of a person would be calculated by an advanced computer, left by the nice aliens, that would carefully take into consideration the impact of the corresponding person upon society, i.e., how much the person in question contributes to the well being of all.

As in all societies, it turns out that the ones with the highest TC receive the best treatments, while the others, which are less relevant, receive just an annual quote of treatment. You can read other synopses on Wikipedia and IMDB. Alternatively you can watch the whole episode, although I am not sure for how long, on YouTube by following the links starting with this:

• Critical Care - Part 1

There are very interesting dialogues and scenes. For example, the higher TC patients are treated in a Blue Zone (or something like that) where everything is nice and clean. Then, the computer allows the doctors to treat the patients with a certain quote of medicines but if the doctors do not use everything, the computer decreases it in the next month. At first sight, it seems okay, but if you think deeply, that is just absurd. Try. Of course the episode was meant to be a direct critic of the US health system, but if you change the time to today, the country to UK and the terms Treatment Coefficient by Research Impact and patient by scientific project, you have an isomorphism.

As a friend of mine said, the messenger changes, but the message is always the same. In fact, what is happens with people in that episode is presently happening with science and education in the UK. And it's not just metaphorically. The methods are literally, and I really mean LITERALLY, the same as in the Star Trek show! Is it possible that there are profound and important things that science fiction writers can see about how to make a better society while politicians cannot? If so, aren't we giving the wrong job to each of them?

I am not a person who thinks that politicians do not know what they are doing (well, maybe some...). They are clever people. They know exactly what they are doing. Our duty is not to call them stupid. That's actually just helping them. What we need to think is 'They are not stupid, so they are doing this for some reason. What is the reason?'. The answer to this question is the most important.

The Holographic Way

Those of you who have been following me on Twitter (and had the patience to read what I am posting there) probably noticed the huge amount of twits with the tag #holography attached. The reason is, naturally, that I am trying to learn it. But before I enter in details, I need to explain what it is all about. If you already know what it is, I will hardly say anything new. 

The term "holography" has two meanings in modern physics, and they are obviously related. The first and most popular one is the technique used to create holograms, those three dimensional images embedded in a two dimensional sheet of paper or plastic. The second one is derived from an analogy with this property of storing the information for a three dimensional environment into a two dimensional one. The story starts with Jacob Bekenstein, a theoretical physicist that was thinking about thermodynamics and black holes. Although I will cut the story a lot, the main point is that he discovered that the entropy of black holes should be proportional to the area of their even horizon, the surface after which nothing can come back. That's what we call, in statistical mechanics language, non-extensive. We call a property extensive when it's proportional to the volume of the object.

The story actually mixes a lot of things. But I will try not to rush in. Back to the black holes, they are in fact the most entropic "objects" in the universe. The argument is simple enough and works by, as in many situations, invoking the Second Law of Thermodynamics. Suppose that in a region of space of radius R there is more entropy than a black hole the size of that region. Then, by adding matter to the region you can increase its mass. If you do that with no care at all, you can always increase the entropy by creating disorder, which is actually very easy as anyone know. It's easy to see where it ends. With enough matter, you can create a black hole the size of the original region. If the black hole has less entropy, than you decreased the TOTAL entropy of the universe and broke the Second Law.

Enters statistical mechanics. In the late 19th century, Boltzmann discovered that the entropy can be understood microscopically as the number of states accessible to some system. And it was by using this concept, that two other physicists, 't Hooft and Susskind, suggested which became known as the Holographic Principle. Consider a region in space. The entropy of that region is bounded by the area of the event horizon of a black hole the size of that region, which means, that the maximum entropy of that region is given by this area. Therefore, the number of possible states in which the entire region can be is proportional not to the volume of the region, but to its area!

Now it's easy to see why it is called the Holographic Principle. The possible configurations of the whole three dimensional region are in fact limited by the two dimensional area of its boundary. Like a hologram. Well, the Holographic Principle actually go one step further by suggesting that the boundary actually ENCODES the degrees of freedom (the equivalent of the possible configurations in some sense) inside the region. That's a bit more difficult to accept, but around 1997, a string theory guy named Juan Maldacena, based on his work on strings proposed something called the AdS/CFT conjecture. In a few words, the conjecture says that the degrees of freedom of a quantum gravity theory in Anti-de Sitter space are encoded in a strongly coupled conformal field theory that leaves on its boundary.

The importance of this is that in some limit, the quantum gravity theory becomes classical gravity, which means general relativity. In fact, it means a classical field theory with a dynamical metric, where metric is the mathematical way of encoding the distance between two points in any kind of space. I am not sure if I understood this point precisely, but I guess that this classical limit is the limit where the conformal field theory becomes strongly coupled. A conformal field theory is a special kind of field theory with an additional scaling symmetry. The good thing is that although we don't know how to deal with strong coupled field theories, we more or less can calculate things in the gravity sector of the AdS/CFT duality.

To finish, let me explain finally why I am interested in it. Recently, there has been some work where the CFT part of the duality display a phenomenology very similar to some strong coupled systems in condensed matter. Now, these systems are quite important and very difficult to deal with with traditional methods like statistical physics or perturbation theory. One of the most famous example is the high temperature superconductor. These superconductors were discovered in 1986 and we still do not have a good understanding of them. It seems that AdS/CFT can shed some light on this. Another problem is called non-Fermi liquids, which are also  strong coupled systems of fermions in condensed matter.

Well, this was just an introduction to the topic. I will try to write more about it as I read. It's a selfish endeavour as it's meant to help myself to think more clearly and understand better this subject. If anyone have comments, suggestions or want to correct the probably lots of mistakes I wrote, or the ones I will write, feel free. That's the aim after all. :) Oh, and by the way, the video has really nothing to do with the text. I just thought of it as a nice example of a hologram. :)

Intuition and Neural Networks

I had an interesting discussion with a friend during Christmas. It started because one of my presents, which I chose, was Richard Dawkin's The God Delusion. The discussion at some point became one about spirituality. He was arguing in favor of the existence of it and I was trying to understand what he exactly meant by the word spirituality. The details of the conversation are really not important, but at some point he argued that spirituality was related to intuition, and intuition is something that cannot be logically understood. Of course I disagreed for to me that sounds like a very fun remark as, among all cognitive phenomena, intuition is the one which I would say that was most illuminated by the study of artificial neural networks and machine learning in general.

For many the above statement may seem not only surprising, but highly unbelievable and extremely exaggerated. It's not. In order to prove it, let me start by explaining what I understand by intuition. This is also probably the concept that everyone shares. Most people have already been in a situation where you have to take a decision and, although you cannot explain why and it may even sound counterintuitive, something inside you tells what is the correct answer. I will not use intuition in the sense of premonition or anything like this. I will concentrate on this sort of "I know this is the correct answer but I can't explain it." thing.

You may think that the fact that you cannot explain the decision makes it something beyond logic and therefore impossible to understand. Actually, it is the complete opposite. The explanation is in fact the simplest one: the feeling of what is the correct decision comes from our brain's experience with similar situations. Too simplistic, you would say. Okay, but why should this not be so? But this is not just a guess, we can actually reproduce this in a computer. That is exactly how machine learning algorithms work. 

Let me start by describing the simplest machine learning model, the perceptron. The perceptron is a mathematical model inspired by a real neuron. It has N entries, which usually are taken as N binary numbers, and computes what is called a boolean function using them, giving as a result another binary number. The simplest rule is this

\[\sigma(\mathbf{x})=\mbox{sign}{\sum_i x_i w_i},\] 

where the $\mathbf{x}=(x_i)_{i=1,...,N}$ are the N boolean entries and the real numbers $w_i$ are what enables this simple model to do some kind of very basic learning. The trick is that, if we change these numbers, we can change (to some extent, which is already a technical issue) the boolean function that is implemented by $\sigma$. The idea is that we have what is called a dataset of pairs $(\sigma_\mu,\mathbf{x}_\mu)$, with the indices $\mu$ labeling the datapoints. We usually call these datapoints by the suggestive name of examples, as they indicate to the perceptron what is the pattern it must follow. We then use a computer algorithm to modify the $w_i$ such that it tries to match the correct answers $\sigma_\mu$ for every corresponding $\mathbf{x}_\mu$. The simplest algorithm that works is the so called Hebb algorithm, which is based on the work of the psychologist Donald Hebb, and amounts to reinforcing connections (by which I mean the numbers $w_i$) when the answer is correct and weakening them when it's wrong. 

As I said, in simple situations this algorithm really works. Of course, there are more complex situations where the perceptron does not work, but then there are more sophisticated machine learning models as well as algorithms. I will not discuss these details now, as this is not important to our discussion. The important thing is  that, after learning, the perceptron can infer the correct answer to a question based simply on the adjusted numbers $w_i$. Now, notice that the perceptron does not really know the pattern it's learning. It is too simple a model to have any kind of awareness. The perceptron also does not perform any kind of logical thinking to answer the questions, it just knows the correct answer as soon as the question is presented. It never really knows the pattern it's following after learning. Basically, it gives an intuitive answer. But what is really more incredible is that, even if we look at the numbers $w_i$, we also cannot explain what is the pattern the perceptron learned. It's just a bunch of numbers and if the number N is too large it becomes even more difficult for us to "understand" it.

Looks too simplistic but this is exactly what we called intuition above. In the end, taking a decision based on intuition happens when your brain tells you that the question you are faced with follows some kind of pattern that you cannot really explain, but just seem right. You learned it somehow, although you cannot explain what you've learned. As you can see, intuition is in fact the first thing we were able to understand with machine learning and the myth that this cannot be understood is just that: a myth.

Graphene

Via physicsworld.com

About Testing String Theory by Analogy

I like string theory, but as sad as it may seem we have to face that there is still no experimental test of it. And again, as desperate some people may be not to have wasted their lives (which actually is an unjustifiable fear), if string theory turns out to be not falsifiable, it is not science, but just a book keeping device. That's true. Without any falsifiable prediction, string theory becomes an extremely elegant and compact way to express our nature's knowledge up to date. If you are fine with that, no problem, but sincerely I prefer not to be sure that there will be no more experiments with explanations requiring new physics to be done even in principle. But I can be wrong.

But what this post is really about is alleged tests of string theory based on mathematical analogies. I can't deny that supersymmetry is a non-trivial prediction. If it is true, point to string theory. But other theories can be supersymmetric too. Another day, I heard about a paper using string theory to quantum computing, and these days I have heard a lot about holographic superconductors and AdS/CFT applied to condensed matter.

However, people must remember that applying the methods developed in one theory to other does not provide a proof of the former. The fact that you can use Feynman graphs in condensed matter and it works for explaining superconductivity does not mean that QFT is proved by it, experiments do. There is a difference between the mathematical methods developed to deal with a theory and the theory itself. Some people will say that there isn't, but that is dead wrong! The power of mathematics comes from abstraction and this allows for the use of the same tools to different problems. But physics is not only mathematics and depend on principles that are derived from and tested by experiments.

I am not saying that string theory is not science. On the contrary. It is a possible hypothesis which is being explored. However, it is not a proved theory no matter what the most intelligent people in the world say. Nature usually cares very little about what intelligent people think. There are many examples of it in human history. And the bottom line is that, even if the mathematics of string theory helps other theories, that does not count as a verification of string theory.

Nobel Prize of Physics for Graphene

I know news run fast through the web and everyone knows by now that the Nobel of physics this year went to Andre Geim and Konstantin Novoselov, from the University of Manchester here in the UK, for the discovery/invention of graphene. As usual, it was a busy week and the only thing I had time to do about it was to put together a gallery of graphene pictures on my other blog Sciencescapes. And probably everyone also knows by now that Andre Geim won the IgNobel prize of physics in 2000 for levitating a frog over a superconducting magnet. The frog paper is free to read: Of Flying Frogs and Levitrons,  by M.V. Berry and A.K. Geim, European Journal of Physics 18, 307 (1997) .

Graphene is a very interesting material. It is the closest you can get to a two-dimensional sheet  for it is a carbon sheet just one atom thick. The picture above is an artistic rendering you can find on Wikipedia. It shows that graphene forms what we call a regular hexagonal lattice. I should have written in this blog about that before, because I always thought these guys would win a Nobel soon, but now I cannot prove it. It was somewhat logical to assume it as if you check the condensed matter part of arXiv daily, you will see that it is hard to find a day without a paper about graphene. 

Due to the fact that it is practically two-dimensional, graphene has many interesting physical properties. In particular, at least for physicists, you can find an anomalous quantum Hall effect. Also, being 2D, graphene can support anyonic quasi-particles, elementary excitations that have statistics which are neither bosonic nor fermionic (see the previous post Anyons). As an extra bonus, graphene appears to be one of the strongest materials that exists, with a breaking strength 200 times greater than steel.

Geim, Novoselov and others wrote a nice review on graphene: The electronic properties of graphene, Neto et al., Reviews of Modern Physics 81, 109 (2009).  There is also this other paper by Peres: The transport properties of graphene: An introduction, Peres, Reviews of Modern Physics 82, 2673 (2010). Unfortunately, you need a subscription to access them. 

As I lost the opportunity to predict the graphene Nobel, this time I will take the risk of making the prediction (which is again fairly obvious) that soon the Nobel will be given to the guys who discovered that the universe expansion is accelerating. They were called the High-z Supernova Search Team, and the discovery came on 1998. Adam Riess was the leader of the team, so he is probably one of the guys who will win the prize. That discovery was completely a surprise at the time as everyone were expecting a decelerating universe. This also led to many famous hypothesis to try to explain it, like dark energy and quintessence.

Viscosity

I have just started reading Chapter 5 of the book Biological Physics by Philip Nelson, which is called Life in the Slow Lane: The Low Reynolds-Number World. The book is an undergraduate introduction to biophysics which is extremely well written and very pedagogic. The undergraduate word however just means that the mathematics of the book is not very advanced, for there are a lot of physical insights that are extremely interesting and valuable for any physicist.

In this chapter, Nelson is writing about the difference in the relative viscosity for macroscopic and microscopic objects and the effect of it to the world of cells. In the very beginning, he explains the experiment in the video above, the only difference being that in the book you only have one coloured drop.

In the experiment, the container is composed by two concentric cylinders with corn syrup, a very viscous fluid, filling the space between them. As you then can see, drops of coloured syrup are put in this space. Note how the fluid is viscous by the fact that the drops don't even move once they are there. Then, the handle is turned and the internal cylinder is rotated a number of times. The fluid is dragged by the rotation and the drops apparently mix. The magic happens when the cylinder is rotated in the opposite direction and, miraculously, the drops unmix and reappears almost intact.

The explanation of how this can happen is quite interesting and is given in Nelson's book. What happens is that the drops never really get mixed, because the fluid is so viscous that there is no turbulence. Without turbulence, there is only a very organised laminar movement of the fluids and not the disordered wandering of molecules that causes mixing. The molecules actually stop moving (at least almost) when the rotation stops. When the rotation is realised in the opposite direction, the molecules simply retrace their previous steps and come back to the place where they were in the beginning. Of course, that's not perfect and you can see the drops had fuzzy boundaries where some diffusion and mixing did happen, but that is negligible.

The most interesting part of the discussion in Nelson's book comes afterwards where he explains that water is very viscous from the point of view of bacteria and this kind of effect happen in the microworld. This brings problem for them to move as, if they just swing upwards and backwards some kind of structure, they will never move because the fluid will just trace back the previous movement. I stopped somewhere around there.  If you are interested, I highly recommend Nelson's book.

 

Values

"An investment in knowledge always pays the best interest"

Benjamin Franklin

It was a beautiful morning and the singer, who was one of the most popular in his planet, sat in his living room to read a magazine. He was feeling well and happy. He suddenly felt like doing something good something honourable. Then he passed his eyes over a small note in one of the magazine's page. Archaeologists were trying to raise 500 000 pieces to complete a project not far from where he lived. They had found two truly beautiful floor glass and metal mosaics, almost complete. Both dated from around two thousand years before, said the magazine. It was one of the brightest periods in the Jau history. The amount would be spent in the construction of a museum over the art crafts, mimicking the structure that should have been there before. The mosaics were not the only things they found. Many other pieces were there. Parts of the original construction, daily utensils, artwork. The project would allow people to walk around the whole reconstructed structure in suspended glass platforms.

The singer smiled. 500 000 was not too much. Actually, he himself had spent more than that in a flying vehicle three months ago. And last week holiday in the south continent with his friends has costed as much as ten times that. He felt sorry for those archaeologists. So little and still they could not raise it. At some point, the article said that the government was going to give them funding, but then decided to cut it because the project would not have a big impact on society. Then, he decided that he would give them the amount.

But he was the most popular singer in his planet and it was too difficult for him to do something in secret. Besides, his public relations team decided that would be good for his image to transform the occasion into a big event. However, when the people of the city discovered his plans, they wondered if that was the best use to that money. Soon, a campaign led by the citizens was urging him to give the money to a more useful cause. What a waste of money was to donate 500 000 pieces to restore some old bricks while people was suffering every day with more immediate problems. Little time passed before they agreed on the cause. Scientists have been searching for a cure to Jora's disease for more than sixty years and that amount could help them. Obviously, those scientists agreed.

The singer was puzzled. All he wanted was to do a good action. There was no campaign against his new car or his previous week holiday, so he could not understand why people were making a big deal of that. Lots of people were holding huge signs in front of his house. His advisers suggested him to give up the idea and give the money to the disease's research instead. It would be better for his image. He was tired but he was decided to do a good action. Then, he went to the bank, collected the amount and finished what he begun and do what he thought was right. 

One kid stopped on the highest platform and stared at the mosaic in awe, her tentacles holding firmly to the coloured plastic bars. She had never seen something like that before. The fantastic bipedal creatures depicted in the artwork made her chill. She never forgot that. The whole structured filled her dreams. Inspired her like nothing else before. She looked for the creatures on the network and read all the stories. When there were no more stories about the creatures, she started to read about the people who created them. And then she read about why they created those creatures. What inspired them? And she learned that those people, who lived much before She was born, asked the same questions about the world that she used to ask herself and her parents. She wanted to know the answers and she studied hard for that. She became a biologist and she ended up knowing many of the answers, but in the process, she also find out many other questions. She was seeking the answer for one of them, the cure for Jora's disease? Late that night, she remembered the mosaic. And when she looked at the pattern of the molecules in her computer screen, she saw something wonderful. The answer had always been in the mosaic. Jora's disease was eradicated form her planet in fourteen years.

But, in fact, the child never saw the mosaics, for the singer was convinced by the citizens that giving the money to the disease's research was much more important than to give the money to maintain some old stones. The archaeologists could never raise the money and the mosaics were lost to the action of the planet's harsh weather. The kid was inspired by that, so she became a singer. A famous one. The best of her planet. She always had enough money, but she also remembered about what happens with the old singer in her childhood time and always kept secret about her own possessions. She died of Jora's disease, as many other people. Eventually, they found the cure some centuries after that. But that was okay, for the people was happy. They never stopped singing. 

• Chedworth Roman Villa
• National Trust 
• Fundraising
• Mosaics unearthed for display at Chedworth Roman Villa