However, there is loads of science in cooking, and this is made explicit in molecular gastronomy. It is the sort of science I know something about as it is close to my research field of ‘soft matter’.

This week one of the chefs used the technique called spherification. Basically how this works is you start with a tasty liquid, the chef on the Great British Menu flavoured it with peas. You then mix this liquid with sodium alginate. Now alginate is a polymer (derived from algae, hence the name), i.e., the molecules are very long and floppy. It is also negatively charged. That is why you need the positively charged sodium ions to make the solution electrically neutral overall.

Now each sodium ion has only a charge of +1 (in units of the elementary charge, the magnitude of the charge on the electron). This is important because if you get a sodium ion sandwiched between bits of two alginate polymers it attracts both of them and so tends to stick them together. But only weakly as it only has a charge of +1.

So, the chef then drops a droplet of  the pea-flavoured liquid containing sodium alginate into a bath of water containing calcium ions. Calcium ions have a charge of 2+. When an ion is sandwiched between two alginate polymers then doubling the charge to 2+ greatly increases the attraction. So the 2+ calcium ions stick the alginate polymers together into a mesh.

This mesh is a gel and the calcium linked alginate polymers transform the liquid into a soft solid gel. I guess that the calcium ions mostly diffuse in from the surrounding calcium solution into the initially liquid pea-flavoured droplets. This is not very fast so the chef can remove the pea droplets from the calcium solution quickly while only the surface layer is made jelly-like by the calcium ions replacing the sodium ions.

The result is a droplet with a soft jelly-like shell and liquid inside, tasting of peas or whatever the chef wants. Spherification was apparently pioneered by the restuarant elBulli. For several years this was often listed as the world’s best restaurant. It closed last year. I think it must have been a serious restaurant, the Wikipedia page claims it charged £200/meal and still managed to make a loss! McDonald’s it ain’t.

It is really impressive seeing science being applied in this way, you do not have to look up to the stars to admire science, you can look down to your dinner plate.

Over the weekend, I read the previous entry on this blog. It’s a post by my ex-PhD Student Emma, who having done a PhD in theoretical nuclear physics here at Surrey, is now working in climate change analysis at the London School of Economics. One shouldn’t really be surprised to find physicists in such places. Partly that’s because the division between disciplines is somewhat artificial. Everything, or at least all science, is connected by underlying principles, and common methods and ways of thinking. This is something to bear in mind when taking a modularised degree programme – you should definitely not assume that forgetting about the contents of one module once you’ve passed the exam is a good idea. Not, at least, if you want to have a holistic view of your subject. Emma working on climate change studies with a physics background is also not surprising since we physicists think we can turn our hand to anything. More often than not with justification.

Anyway, Emma mentioned that I was a “regular” contributor to this blog. I might argue that regular really means at fixed intervals, and that Halley’s comet visits Earth regularly, but I suppose she intended the common usage meaning often. I felt a little guilty, since I don’t post very often, at least not compared to my steadfast colleague Dr Sear. So, I resolved to post, and I thought I’d post about something I’ve learned recently. It’s nothing at all new – a method of finding the roots (zeros) of cubic equations that goes back to at least the 16th Century. I’ve known of its existence, but was prompted to learn it thanks to a Final Year Project student, who came to me with it recently.

Cubic equations are polynomial equations whose highest order is the power of 3 in the unknown quantity. In general they can be written

a·x3 + b·x2 + c·x + d = 0.

In the special case that a=0 then the equation is (at most) a quadratic, and one can use the familiar quadratic formula to find the roots. The general cubic case is a bit more tricky.  To work through an example, I’m going to pick particular values for a, b, c and d. I’ll do it by writing the equation as the product of three terms with known roots (-1, 1 and 1/2):

(x+1)·(x-1)·(2·x-1) = 0

and then expanding to give a cubic whose roots I do know, but with which I can test the general method. The expansion gives

2·x3 - x2 - 2·x + 1 = 0.

The first step is to change the variable. This is done as y = x + k where k is the coefficient of the squared term divided by three times the coefficient of the cubed term. In my case, k = -1/(3·2) = -1/6. So I have y = x - 1/6, so x = y + 1/6. This can be substituted in the original cubic equation to give

2·(y+1/6)3 - (y+1/6)2 - 2·(y+1/6) + 1 = 0.

The brackets can all be expanded to give:


2·y3 - y2 + 1/6·y + 1/108
  + y2 - 1/3·y - 1/36
        - 2·y - 1/3
                 + 1

giving
2y3 - 13/6·y + 35/54 = 0.

This is the reason for the substitution – it exactly removes the squared term. Now we divide the whole equation by 2 to get rid of the coefficient in the leading term:

y3 - 13/12·y + 35/108 = 0.

Now things get a bit strange. From out of nowhere, we make the substitution y = u + v – i.e. we write the unknown variable as the sum of two unknowns u and v. The reason for this becomes clear when we discover the trick later on. If we accept that we make this substitution, then we can work out that y³ is

y3 = (u + v)3 = u3 + v3 + 3·u2v + 3·v2u.


and substituting fully for y in the (quadratic-less) cubic equation gives

u3 + v3 + (3·uv - 13/12)·(u+v) + 35/108 = 0 .

Now the trick is to to say that u and v are not independent variables, as we have created them both from the one unknown y. We are therefore free to link them with any suitable relationship, so we choose that which makes the (u+v) term zero:

3·uv = 13/12.

We can divide by 3 and cube this equation to give

u3·v3 = 133/(3·12)3 = 2197/46656.

That we have set 3·uv - 13/12 = 0 means that

u3 + v3 = -35/108.

Now we have a pair of two simultaneous equations for two unknowns in the variables u3 and v3. Knowing both the sum and the products of our two unknowns means we can immediately say that they are the roots of a quadratic equation. This is true since if we have a quadratic with roots a and b, we can write

0 = (x-a)·(x-b) = x2 - (a+b)·x + a·b

This means that we can write down a quadratic as

t2 + 35/108·t + 2197/46656 = 0.

This can be solved with the usual quadratic formula to give values for u³ and v³:

(u3,v3) = (-35/108 ± √(352/1082 - 4·2197/64456) ) / 2 .

If we take the argument of the square root and simplify all those fractions, we find that it gives -1/12, so the argument of the square root is negative. Curious… Formally though, we could write our solution of the cubic equation, then as u+v, given by

y=3√(-35/216 + √(-1/12)/2) + 3√(-35/216 - √(-1/12)/2).

This is a very strange way of representing the number y=5/6 leading to the correct root x=1.  When evaluating the above expression the imaginary parts cancel out.  This was the first use of complex numbers in the history of mathematics – in finding the real roots of cubic equations.  In the style of annoying textbooks everywhere, I’ll leave the evaluation of the above expression to the reader (perhaps one who will give the answer in the comments?).

The other two roots can now be found by factorizing the cubic to leave a quadratic factor that is easily solved with the quadratic formula.

I am currently a Research Assistant at the London School of Economics (LSE) working in the Centre for the Analysis of Time Series (or CATS), which is a relatively small research group affiliated to the Department of Statistics. My research is mainly focused on developing mathematical and statistical approaches to analyse nonlinear dynamical systems, like the weather or climate system. I am particularly interested in thinking about ways to extract useful information about the future climate by combining knowledge from climate model forecasts, the statistics of past observations (such as temperature and rainfall records) and our understanding of the underlying science – all of which contain some uncertainty. Much of the work I do forms part of a project called EQUIP, which brings together scientists across several UK-based institutions with the aim of providing robust and useful information that could help decision-makers in planning how to adapt to future climate variability and change, which is an interesting but challenging task! You can find out more about what I do here.

I suppose the LSE – a school renowned for its social sciences – may not seem like the most natural choice of career move for someone with a background in the physical sciences. But climate science, and more specifically tackling the grand challenges involved in understanding the science behind, mitigating against and adapting to climate change is a task that benefits from a multi-disciplinary approach, including research across areas from physics, maths and statistics, to economics, philosophy and politics. I am very fortunate to work with people across all these subjects and more!

Of course, I would not have been able to do the research I do now without the skills and background that I gained from both my undergraduate degree and my postgraduate research (I did a PhD in theoretical nuclear physics under the guidance of Paul Stevenson, who is a regular contributor to this blog). I was also lucky enough to have gained invaluable experience – that relates directly to some of the work I do now – as an undergraduate student on the professional training year. Students studying for the BSc are usually offered the option of spending the third year of their degree working in industry at any number of different companies and institutions around the country. I spent my year in the Climate Change Team at the Met Office. Not only was it a fantastic opportunity to put some of the things I’d learnt in lectures to good use (and earn a decent salary at the same time), it inspired me to pursue a career in research and motivated me to work a little harder in my final year! It was also the place I met my husband )

Of course we have been calculating the orbit of the moon very accurately for a long time, so we know it will go dark exactly when and where astronomers predict it will. Our climate is more complex than the orbit of the moon, and climate science is controversial due to various climate-change deniers deciding they don’t want to believe the evidence that our planet is warming.

As our climate, and any changes in it, are so important, we need to test climate science, to distinguish good from bad, reliable from unreliable. A nice example of this is discussed in a post over at RealClimate.org. The post discusses a 1981 paper by Hansen et al. The paper is now 31 years old and made predictions for the global temperature for the 40 years from then to 2020.

So, as we now know the global temperatures from 1981 to 2011, we can test the predictions made in this paper. Over the 30 years their estimated range of temperatures is a little on the low side, i.e., they predicted global warming but underestimated its magnitude a little. To me this looks like a pretty good job by Hansen et al.

The fact that the less sophisticated (and using simple models on much slower computers) climate models of 1981 do so well is reassuring. Its give us confidence that modern predictions are very likely to be accurate.

This caught my eye, after all Harvard charges fees of (at the current exchange rate) almost £24,000/year. Even this coming year our fees, like almost all UK universities, are only going up to £9,000. If Harvard cannot afford journals, what hope do we (or Imperial, Cambridge, Sussex, etc.) have.

So I read the Harvard announcement, and they spend $3.75 million just on journals from a couple of the big commercial publishers – that’s a lot. So let’s look at some figures. The Guardian article refers to one particularly expensive journal: The Journal of Comparative Neurology. For both paper copies and online access this costs £18,500 per year (some physics journals cost similar amounts, for example Nuclear Instruments and Methods A & B costs even more).

I quickly checked the VW website, and you can get a brand new 5-door Golf for that, and they’ll throw in a fancy digital radio, offer finance, etc. So where does this money go. Well the biggest publisher is Reed Elsevier and in 2011 they reported revenue of £6 billion and profits of £1.2 billion. I make that 20% profits.

Maybe your initial reaction to reading that profit margin is to see if you can scrape together all your spare cash and buy some Elsevier shares. But the Harvard article is just one of many signs that university libraries, academics, and funders of research are all getting fed up of journal prices. So maybe Reed Elsevier and the others are heading for a fall. They can’t get keep taking ever larger amounts of taxpayers’, students’ and charitable research funders’ money.

As an academic, it is great to see our students do so well and get the recognition they deserve. Graduation ceremonies are quite formal rituals really. The students who will get the degrees and their parents are seated first in Guildford cathedral (where the ceremony is). Then we academics file in, in two lines in a procession, and then finally the bigwigs such as Vice-Chancellor, etc come in, and the ceremony begins.

Before we are led into the main part of the cathedral, we academics gather in the side chapel. We congratulate each other on how well our students have done, which is nice.

There is also some light-hearted joking. It is one of the few places you will hear one grown man complement another on how good they look in magenta. Indeed I guess it is one of the few places you will see man dressed in magenta as it is not a shade generally favoured by men.

Most academics have PhDs, and UK PhD gowns vary from University to University and are mostly a shade of red but can be any colour. Surrey’s are a relatively sensible dark red but my Sheffield gown is scarlet, and Heriot-Watt’s is magenta, Leeds’s is green, York’s is grey, etc.

This all makes the academic procession rather colourful of course, and I hope adds a bit to the spectacle. After all the effort they have put in the students deserve a bit of a spectacle.

The idea behind blue energy is simple. The scientist who presented the work is Dutch, and he pointed out that at Rotterdam in The Netherlands, the river Rhine meets the sea. Now The Netherlands is a very very flat country, so no waterfalls and no hydropower. You might think that this means that you can’t get power out of a river.

But you can. The reason is that rivers like the Rhine are made of fresh water, and they flow into the salty sea. So the salt concentration is high in the sea and very low in river water. This difference in the concentration of salt can be harnessed to generate power.

The talk at the conference looked at ways of using a difference in salt concentration to directly produce electricity. But perhaps the simplest way of seeing that a difference in salt concentration can generate power is to realise that the difference can drive water uphill. This is illustrated by the image above and is due to osmosis.

Osmosis will occur when you have a salt solution and pure water separated by a membrane which allows water molecules through but crucially not salt ions – such membranes are quite straightforward to make. Then, simply speaking, what happens is that in the salt solution as there are salt ions the concentration of water molecules is less than in pure water – the ions take up room. Because of this concentration imbalance between the salt solution and the pure water, the water molecules cross the membrane from the pure water to the salt solution.

So if you start off with equal heights of the salt solution and the pure water, a little while later the flow of water into the salt solution will cause the level of the salt solution to rise. The water is effectively flowing uphill, due to the concentration difference. And once the water has gone uphill, you can allow it to flow downhill and generate power. Simple.

Blue energy is very green of course, i.e., it is eco-friendly in that it does not generate CO2.

It may be some time before large amounts of power are generated this way, and it will never generate all the power we need, but it could still be useful. And the next time I see a river flowing into the sea, I will think about about the power of the fresh and salt water mixing.

As you might expect, we scientists are typically rather sceptical of the ability of a solution which has zero of the claimed active molecules in it, to cure diseases. Occasionally, attempts are made using scientific methods to show that homeopathy has a rational basis, for example Rao et al. used spectroscopy to study homeopathic solutions.

Spectroscopy can get very complex, but the idea is simple. Molecules interact with light and change it, and each molecule interacts with light in different ways, giving each molecule a unique spectroscopic fingerprint. So, in spectroscopy you shine light through the sample and look at the light that has gone through. This then tells you about the molecules in the sample.

Rao et al. did this, and claimed to see a difference between the alcohol solutions with the homeopathic ingredient, and without it, even at the extreme homeopathic dilutions.

However, as Kerr et al. point out in a comment on their paper, there is something fishy about Rao et al.‘s data for ‘alcohol’. The point is that it is not true that alcohol is alcohol is alcohol. It is just not possible to buy absolutely pure 100% alcohol, that is impossible to make. All you can do is buy pretty pure alcohol, very pure alcohol, which has less than 0.5% impurities, and even purer alcohol with even lower amounts of impurities. But you cannot buy alcohol without any impurities at all – it is not possible to remove all impurities.

For example, see the page on the SigmaAldrich website. The purest alcohol is guaranteed to have less than 0.2% water as an impurity, which is pretty good, but it is not totally pure. And for that you have to pay £46 a litre, which is more expensive than every very classy vodka, although of course it is lot purer and stronger (200 degrees proof) than any vodka.

So, if you dilute a plant extract in low grade, not very pure, alcohol, and compare that to a sample of a higher grade, purer, alcohol, of course you see differences. The homepathic remedy may contain zero molecules from the plant extract, but if it has even 0.5% impurities then that is 5*10¹⁹ molecules of impurities which show up in spectroscopy because it is such a sensitive technique.

I guess the moral is that a homeopathic remedy may contain zero molecules of whatever it is supposed to be made of but will contain many trillions of molecules of various impurities: maybe some salts, a few hydrocarbons, the odd protein molecule, ….

Clearly, the slice of lemon was a little less dense than water while the slice of lime was a little more dense. I suggested to my sister (also a scientist) that maybe the lemon slice floats because it had more pith on it than the lime, and that the softer white pith is the least dense part and so if a slice has a large fraction of this pith it will float.

I should say that I think that lemons and limes are very similar fruits, so it seems unlikely that there is much difference in density between say lemon pith and lime pith.

So I bought a lemon and a lime at Tescos and experimented – see the picture above. I sliced the lemon and lime in different ways to get slices with varying amounts of: rind, pith, and the bit in the middle with the actual juice (sorry, don’t know what that is called).

If you look at the picture, all the pieces are floating except two small bits at the bottom. The left hand one of these is easy to see at the bottom but the other part is smaller and harder to see – sorry. Both of these pieces are mostly rind. So I think the rind is the dense part and that slices should sink if they have a lot of rind, but should float to the top of the water if they have relatively little rind. I then tested this but taking a small piece of lemon rind – which sank.

So I am feeling quite good about myself, I have followed the scientific method. I started with an interesting observation, formulated an hypothesis, tested it with experiment, drew conclusions from this and modified my hypothesis, and then even did a final experiment to confirm my finding.

But it was only one lemon and one lime, if you come across different observations, at home or in a restaurant, comments are open below for two weeks.

Staying near the top of a competitive profession, which is what both science and light enetertainment can be, must be almost impossible without out of the ordinary levels of drive, of determination. Fortunately for people with more normal levels of determination, like me, you can do OK in science without this.

But even so, science is often hard work, and so requires dedication. At the moment I am working on modelling some experimental data. The data is hard to acquire and so noisy. This makes it hard work to draw conclusions you can be certain of.

Fortunately, there are number of us working on the problem, so we can each push each other on. Most science is done in teams and a good team spirit can really help the non-Newton/Monkhouse types among us.