Keeping up with the well-established tradition of year-end lists, here is one from Nature’s blog:
Born on December 3rd 180 years ago, Carlos Juan Finlay is the man who came up with the theory that yellow fever was spread by mosquitoes. Glad to see that a Google Doodle can help with letting people know about this important Cuban scientist.
Finlay’s research on cholera and yellow fever didn’t initially get much support. He suggested that yellow fever was carried by mosquitos and he suggested that cholera was waterborne. His work was proven later by the Walter Reed Commission and in 1902 Finlay became the chief health officer in Cuba. This confirmation paved the way for the eradication of yellow fever, creating the chance to save thousands of lives.
The Way of All Flesh by Adam Curtis: a one-hour BBC documentary on Henrietta Lacks and HeLa directed by Adam Curtis. It won the Best Science and Nature Documentary at the San Francisco International Film Festival. Immediately following the film’s airing in 1997, an article on HeLa cells, Lacks, and her family was published by reporter Jacques Kelly in The Baltimore Sun.
I was listening last week to the “More or Less” podcast with Tim Harford, which by the way is one of my favourite Radio 4 programmes and I highly recommend it. In the programme they were discussing the proposal of Mr Nick Clegg, the UK’s Deputy Prime Minister, to offer free school lunches to all pupils at infant schools. The proposal follows from a pilot study that seemed to suggest that giving free meals to school children was good for their academic performance.
As usual, not all is what it seems and the programme goes on to discuss this. I’m afraid is the old adage of correlation and causation… In any case, the commentators in the programme made a reference to the Hawthorne effect, and although Tim Harford mentioned something about this I ended up with the curiosity to find out more about it. It turns out that the Hawthorne effect is at work when subjects modify and change their behaviour in response to the fact that they know they are being studied. You might think that this is similar to the quantum mechanical observer affecting the system they observe, except that in this case the system is patently aware of the influence of the observation. I would leave it at that…
The effect is named after Western Electric’s Hawthorne Works in Cicero, Il somewhere close to Chicago. Between 1924 and 1932 Elton Mayo carried out some productivity trials that have become some of the most well-know in social science, as the study is often held as a demonstration that people respond to change when they know you they are being observed or studied. So, who knows, perhaps the pupils, parents and teachers did indeed change their behaviour while the study was taking place… Oh well…
If you encountered a pendulum going round in the Google page this morning it is because the Google Doodle is celebrating the birthday of Jean Bernard Léon Foucault, a French physicist and inventor of a pendulum that demonstrated the rotation of the earth.
Among other things he is credited with making an early measurement of the speed of light. Foucault was born in Paris in 1819, where he initially studied medicine but soon switched to physics (hurray!). He demonstrated his 67-metre, 28kg pendulum at the Panthéon in Paris in 1851. The plane of motion of the pendulum with respect to the earth, rotated slowly clockwise.
I was talking to some students the other day (actually… a couple of months ago… ahem…), they had some questions about some problems on linear algebra and after a short while it became clear that they had mastered some of the techniques to deal with matrices and transformations, but sadly they had no idea about some of important concepts. The discussion moved into what the importance was for Eigenvectors and thus Eigenvalues. They could not answer, other than… “the way to calculate the Eigenvalue is…”. So I decided to do an entry here about why we are interested in these things (other than to pass the exam…).
Let me start by the origin and meaning of the word Eigen: it comes from German and it is a prefix that can be translated as “proper”, “own”, “particular”. That perhaps hints at the mathematical meaning, which could be even translated as “characteristic”, which was first used by David Hilbert (I believe…). Some times Eigenvectors are thus called “Proper Vectors” although that is not my personal preference.
If we consider a collection of numbers arranged in rows and columns, i.e. a square matrix that we will call . Let us also consider a column vector with non-zero elements. We can therefore carry out the matrix multiplication . Now we raise the following question: Is there a number such that the multiplication gives us the same result as . In other words: , if so, then we say that is an Eigenvalue of and is the Eigenvector. Great! That part is fine and we can compute these quantities, but why are we interested in this? Well, it turns out that many applications in science and engineering rely on linear transformations, which in turn use Eigenvectors and Eigenvalues. A linear transformation is a function between two vector spaces that preserves the operations of addition and scalar multiplication. In simpler terms, a linear transformation takes, for example, straight lines into straight lines or to a single point, and they can be used to elucidate how to stretch or rotate an object, and that is indeed useful.
So, where do Eigenvectors and Eigenvalues come into place? Well, they make linear transformations easier to understand. Eigenvectors can be seen as the “directions” along which a linear transformation stretches (or compresses), or flips an object, whereas Eigenvalues are effectively the factors by which such changes occur. In that way, Eigenvalues characterise important properties of linear transformations, for example whether a system of linear equations has a unique solution, and as described above, it can also describe the physical properties of a mathematical model.
Do you want a concrete example in which this is used on daily life? Well, have a look at PageRank used by Google…
Time flies, time is money, time is a wise counsellor, time is relative, time is… very hard to define. Paraphrasing St Augustine I can say that I know what time is if no one asks me, but if I try to explain it I simply do not know. It seems to be very natural to acknowledge the passing of time, however when we take a moment to think about its meaning, we quickly find ourselves with a few problems.
We start by arguing that time can be defined by the interval between two successive events and thus we need a ruler to measure that interval. This is indeed a quest that us humans have pursued since the dawn of civilisation; it is very easy to see how the definition of day comes about: it is the interval between two successive sunrises. Once we have this in place a lot follows effortlessly: on the one hand we can start taking smaller intervals and define hours, minutes, seconds, and on the other, it is now possible to refer to events taking place in the past, the present and even the future. The ordering of these three concepts is intuitive as time flows from the past to the future, and we even see it manifested in the objects around us. We can imagine that we go to a museum where a film installation is being shown. The film starts with a large red stain in an otherwise immaculately white carpet. The camera spans and we see some pieces of glass strangely being attracted to each other while the red stain starts to shrink. The next thing we see is a wine glass appear before our eyes and wine droplets jump into it as if by magic. It is immediately obvious that the film was played in reverse as there seems to be a natural “forward direction”. This directionality is often referred to as the arrow of time and whenever it is discussed the subject of causality arises, and even time travel.
When I mention causality I am referring to the relationship between causes and effects; in the case of the film I used as an example, the cause of the spill is shown to us as artist hits the wine glass. When the film is shown in reverse, we tangibly notice that there is something missing: the glass cannot “unbreak” out of its own accord. What does physics have to say about this? If we were to analyse the film using the laws of motion described by Newton, we would find that there is no difference between the forward and backward directions. In other words, time reversal is not prohibited anywhere in Newtonian mechanics. This means that, given a present state under specific conditions, we are therefore able to predict the future, but also retrodict the past, as there is no distinction between the two. This sounds surprising as this sort of thing does not happen in our daily lives.
Scientists have come up with their own versions of the wine glass film described above. In one case, they have taken two particles of light, known as photons, with certain energies and mashed them together; after the collision they observed a pion and a deuteron as a result of the collision. Do not be too concerned about what these two new particles are, this will not affect the discussion. When the film is reversed, it shows a pion and a deuteron colliding and producing as a result two photons. This new experiment has been realised and lo and behold the physicists observed the generation of the two photons as predicted, giving them a confirmation that the laws that govern these phenomena do not change when time is reversed. As you may have noticed, we have blatantly ignored the present, and this is because we think of it as a transitory state between the past and the future. In other words, the past is gone while the future has not arrived, and the ephemeral present expires as soon as we try thinking of it.
From this point of view, the result of these experiments seems to indicate that the arrow of time is embedded in our perception. It has been argued that the arrow of time is a psychological effect, and that this feeling that time flows mercilessly from the past to the future is all subjective. Let us take these arguments a step further, if indeed there is no difference between past and future, then there is nothing stopping us from travelling to the future (as we imminently do) or to the past (as we clearly are not). Believe it or not, but physics has something to tell us about this. I mentioned above that time reversal is allowed by Newtonian mechanics, so why can we not put together again the wine glass by time reversing the process, rather than supergluing the broken pieces? The answer is not in the realm of mechanics, but in that of thermodynamics, in other words the study of how energy converts between heat and other forms of energy. In that manner, physicists also talk about a thermodynamic arrow of time, in the sense that a given physical system invariably becomes ever more disordered, and since disorder is therefore important we quantify it with a quantity called entropy. This rule that tells us that entropy increases with time is known as the second law of thermodynamics. Following this line of thought, we are not allowed to fix our broken wine glass by running time backwards because it would imply going from a more disordered state to a more ordered one without using any extra energy, and so travelling to the past is not an easy task to achieve.
What about travelling to the future, or in the direction pointed by entropy? Well, in that case there is certainly nothing that stops us in our tracks. In fact, as I pointed out earlier on, we are already travelling to the future, and we do that at a pace of sixty minutes an hour. However, if we wanted to travel to the future at a different rate, Einstein’s theory of relativity gives us a recipe to achieve this. In the so-called special theory of relativity the world has four dimensions: the usual three space dimensions that we know and love, i.e.. length, width and height; and one dimension that is related to time. In other words, when you walk from one place to another in the gallery where the wine glass video is being shown, you automatically change your position on the time coordinate, even if you don’t notice. Einstein tells us that if we were to travel at the speed of light, time expands from the perspective of a stationary observer, whereas space contracts from the point of view of the moving person. This brings into question the notion of simultaneity, as two events that seem to happen at the same time for the stationary person, could in principle happen at different times from the point of view of the moving person. It is fascinating to compare Einstein’s efforts to unravel the secrets of simultaneity in time, with Picasso’s cubism to depict simultaneity in space. The effect of time dilation has been experimentally confirmed with very precise caesium clocks. Unfortunately, it is completely outside of human experience, because we have not yet devised a way of travelling at speeds where relativistic effects become noticeable. Even if we were to spend our entire lives in a plane that moves at supersonic speed, we would barely win a second over our contemporaries on the ground.
So, time travel as presented to us in sci-fi films is not yet possible but that has not stopped us from imagining its consequences. As for the definition of time, I am sure that there are many other things that can be said on the subject. Unfortunately, time is a merciless master, and that is all the time and space I have for now.
Dr Jesús Rogel-Salazar
(originally appeared in Artesian : Issue Three : Time : 2011)
I twitted earlier this week an Open Letter to the Royal Institution by Ian Gent in response to the bizarre and quite frankly ludicrous decision by the RI to trademark the term “Christmas Lectures”. I agree with the points made by Ian as well as others (see here and here). I find it quite offensive to the scientific and science communication communities to make it illegal to use the term Christmas Lecture if you happen to organise an event where a lecture will be given during the Christmas period… I suppose people will have to start organising Yuletide Disquisitions…
Have you ever wondered how Albert Einstein sounded? Well here you have an opportunity to find out. In the link above there is a recording of Einstein reading an essay (in English) called .