Science – Page 4 – Chance & Necessity

End of an era

One of the giants of twentieth century physics, Philip Anderson, died at the weekend, aged 96. He retired from Bell labs in the 1980s and from Princeton University maybe 20 years later, but a couple of years ago we were briefly at the same workshop at Princeton. Bell labs was where the solid state transistor — at the heart of all modern computers — was invented.

How accurate do you need to be?

One of the (many) things that makes middle aged academics like me grumpy, is students giving answers like speed = 4.738281 m/s, by just copying the number from the screen of their calculator/mobile-phone-app, without any thought at all. But I am actually paid to do something more constructive that be grumpy about this sort of poor practice, so this year I have done a little set of notes on accuracy for my final year class. They take the students through a couple of examples.

Self-destructing droplets

Above are droplets of balsamic vinegar (mainly water, but tastier of course) in olive oil. Water and oil phase separate, hence the droplets. The droplets above are maybe a few millimetres across, and they won’t move unless you stir the oil. This blog post is about much smaller droplets, too small to be seen with the eye, so the picture above of much larger droplets, will have to do. Smaller droplets can move. And two scientists working in Darmstadt in Germany, Hajian and Hardt, have seen small droplets move, which is not so surprising. But what is surprising is that they then dissolved.

Reacting droplets

The movie shows a system that starts to separate into two liquids (yellow and purple), just as oil and water do, but is then kept as a dynamic system of droplets that split, evaporate and form again, by a chemical reaction. This chemical reaction converts yellow molecules to purple, and then back to purple again, and this cycle drives the droplet breakup seen in the last two-thirds of the movie. This simulation is of a very bad model of liquid droplets in living cells, there is a movie here of real droplets in real living cells, from the work of Cliff Brangwynne and co-workers.

Statisticians for machine learning

I am starting to sort out my Python teaching for the coming semester; the course contains some introductory data analysis. As part of this, I have just read a relatively old (2001) but I think influential article that compares and contrasts two schools of data analysis. Roughly speaking these are:

School A): fit a simple-as-possible model function to the data, for example a straight-line or exponential fit, to try and understand what is going on.
School B): use a machine learning algorithm such as a neural net, or a support vector machine, to obtain the best possible predictions.

The author is Leo Breiman, a statistician, who was encouraging his fellow statisticians to give School B a try. He thought many statisticians were sticking too rigidly to School A, and this inspired him to write this article, which argues for School B.

Seventeen top-ten universities

The 2020 Guardian University League Tables are out, and Saturday’s print edition ran with the headline “Oxford falls to third place in university rankings”. As someone who teaches data analysis that seemed to be quite a definite statement to me — there is no obvious caveat to indicate how confident they are of this statement. This omission concerns me, but to be fair to The Guardian, they have the 2020 league table data available for download as a spreadsheet. It looks like a fair number of the data values are missing, so I turned to the 2019 league table data. This data set looks complete, and is of the same form. Each university has nine data values, and in each case the analysis assumes that it is the bigger the better, i.e., large values of each number indicate a good university, or good teaching, somehow*.

Dissolving together

I am continuing to play around with systems that start to separate into two phases (the green and the red phase in the movie above) but don’t get very far before one phase (the green one) dissolves. I have tweaked some parameters above, so that green droplets form, and the system is a bit bigger (I also changed the orientation, sorry if that is confusing). if you follow the movie carefully, it seems clear that the dissolution of the green droplets is via fronts that are pretty straight (horizontal), one front that moves upwards, dissolving droplets as it goes, while another moves downwards. When they meet in the middle, the green droplets are all gone.

A story of a Frenchman, a Baron and a paint guy

Just before Christmas I wrote a blog post about Baron Rayleigh’s work on convection, he showed how a layer of colder fluid (eg air or water) on top of warmer fluid, would lead to convection — flow of the colder fluid downwards to be replaced by warmer fluid from the bottom. Rayleigh’s work is a classic, and has been built on to help us understand, amongst many other things, Earth’s weather/climate. Rayleigh assumed that the flow was driven by gravity. The colder fluid on top falls because it is denser. Convection is everywhere in Earth’s atmosphere and oceans. It is sometimes called Rayleigh-Bénard convection, to honour Baron Rayleigh who developed the theory, and Henri Bénard, who did the experiments that inspired the theory.

Salt fingers

Above is a computer simulation of a phenomenon often called salt fingers. They occur in world’s seas and oceans, for example they are common in the Caribbean. Salt fingers form when there is a layer of warm salty water above a layer of colder but less salty water. The point is that salty water is denser than less salty water, so typically a layer of salt water on top of a layer of fresher water is unstable, the denser layer on top falls down through the less dense layer below due to gravity — this is convection. However, here the water on top is not just saltier it is also warmer. This temperature difference works in the opposite direction to the difference in the amount of salt. Warmer water is less dense that cold water and so a layer of warm water floats on a layer of colder water.

Rising hot air and a Baron

As I write the UK politics is in a bit of a mess. The referendum that kicked off this mess started in the actions of an Eton educated posh boy: David Cameron. But not all Eton educated posh boys have been a disaster for Britain. The picture above is of the partially-Eton-educated 3rd Baron Rayleigh, a brilliant late-Victorian scientist and genuine member of the aristocracy.