Tuesday, January 29, 2008

Is there intelligent life out there?

I was asked three questions by a friend, in the comments section a couple of posts back. These were:
1)Do you think that extra-terrestrial life is likely?
2)What is the smallest galaxy there is?
3)Can you explain what happened before time?

The second question I have to look up in the appropriate source, the third question I will have to clarify my own thoughts before imposing them on the world. The first question however I have relatively clear views on and so give the following answer:

The probability of there being extra-terrestrial life is made up of many factors, but I think that it's most useful to break it down into two main parts. Both of these are still somewhat unknown but we are learning more and more about them all the time.

The two factors are:
1) How many planets in the near vicinity/observable universe are there which are suitable for supporting life.

2) What are the chances, given the right conditions, for life to form on one of these planets?

The chance of there being extraterrestrial life out there comes from appropriately combining these two numbers.

I'll deal with each of the above factors separately.

Up until about 10 years ago we didn't have a good idea about whether we were special in terms of having a planet of our size, with water, going around a star at the right distance for water to be in liquid form. (Although the first published discovery of an extrasolar planet was in 1988, later confirmed, it is only more recently that we have had a good handle on these observations.)

The power and accuracy of our telescopes is constantly improving. Not just for the case of telescopes which view in the visible range of the electromagnetic spectrum. There are giant telescopes on earth which view radio signals and, at the other end of the spectrum, there are telescopes which we've put into orbit which look at very high energy rays in the x-ray and gamma-ray range of the spectrum. These see some of the most energetic events in the universe and we're learning a huge amount about some incredible phenomena which happen out there.

Credit: X-ray: NASA/CXC/CfA/D.Evans et al.; Optical/UV: NASA/STScI; Radio: NSF/VLA/CfA/D.Evans et al., STFC/JBO/MERLIN

What the improvements in technology have allowed is for us to study stars in much finer detail. We can look at the amount of light coming from a distant star to a very high accuracy, as well as knowing where it is to large precision. If one of these stars has a planet circling around it there can be several effects. The easiest cases are when the planet is rotating such that it comes between us and the star. The star will block out some of the light as it passes in front of the star and it will also make the star wobble as the gravitational pull of the planet will mean that the star is also circling, though round a much smaller circle than the orbit of the planet. Of course the larger the planet, the easier these effects are to see but we're getting better and better at seeing even small planets. In the last ten years we've gone from thinking that we might be unique to finding that in fact there are planets circling many many stars just in our neighbourhood of the Milky Way. Our observations are now so good that we can even look at the chemical composition of the atmosphere of the planet. As the light from the star passes through the atmosphere, certain wavelengths are absorbed by the molecules in the gases and we see this effect in the light that reaches us. We're learning more and more about these extra-solar planet and are finding planets which are more and more Earth-like all the time.

So, it seems that there are plenty of planets in the stars nearby us. There are a few hundred billion stars in the Milky Way and around the same number of galaxies in the observable universe. So the number of Earth-like planets (or even not that much like earth, but at least with an atmosphere and a solid ground) is probably huge, almost certainly it's millions of billions in the universe. That's the good news!

Digital Sky.LLC

(NB. There are actually somewhat more strict criteria for a habitable planet)

So, it seems that the first number is a really big one!

How about the chances for life forming? Well, before I come onto that, how about the chances of forming intelligent life from the first very simple life-forms through billions of years of evolution? You might say that if it happened here, it should be quite likely to happen anywhere else. One could raise a warped version of the anthropic argument to say that even even if it was only us in the whole universe who had been lucky enough to become conscious beings, it would also be us who asks the question: "what's so special about us?" (this is a slightly twisted form of the anthropic argument, but it's the same basis).

We are a long way from understanding consciousness and there are a variety of schools, from the extremes who believe in a soul and think that consciousness doesn't come from something physical in our brains, to those who believe that consciousness is simply a matter of the firing of neurons in the brain which could be modelled equally well on a sufficiently complex computer program. I'm of the latter school.

Some systems which evolve genetically (many such systems can be modelled on computer) will end up in a similar state, relatively insensitive to the environment or the starting conditions. Other systems are very sensitive to what is around them and how they start. It's my belief that given a somewhat different environment and a system which can evolve (reproduce, mutate and compete within its environment) will evolve into something which may not look like us, but will probably have a branch which develops consciousness - I don't see consciousness as anything magical, just very hard to understand! This is simply my gut feeling as a non-expert.

So, I think that once evolution is in place, as long as there are not events which halt that evolution (meteor impact, lack of resources, violent changes in environment) given enough time, conscious beings will evolve which will end up with something comparable with our society and technology.

For me the hardest question is how likely it is for all of this to start. If you look at the structure of DNA, RNA, amino acids and proteins, it seems incredible that this has come into being, but we have to remember that these things themselves have evolved from something simpler. This original structure only had to have the properties which I mentioned above: reproduction, mutation and competition for environment. It is likely that given enough complexity in an environment (perhaps a large selection of molecules to play with), once you have a simple molecule which can reproduce with some variation, the creation of a DNA-like structure isn't that unlikely. From what I understand, there are many people trying to make this (abiogenisis) work in the lab. I don't know much about the levels of success so far, starting from a very simple molecule. It seems likely that the beginnings of life probably started in the chemical-rich, hot environment in a volcanic system - deep sea vents being the usual suspect, though there are possibilities of more exotic beginnings.

Volcanic environments shouldn't be that rare on earth-like planets so it seems that the likelihood of planets with the right conditions for life to start is still a large number, even when you specialise to those with water and volcanic activity. The question of whether life will form there seems to be a tough one, but I believe (with no qualification) that the chances are pretty good.

So, my view is that the small number that you have to multiply by the very large number (the number of earth-like planets) probably isn't that small and so I believe firmly that there is life out there and what's more, intelligent life.

How about spotting them? Well, we've been sending out radio waves for around 100 years. These will now be 100 lightyears away and the very first ones which were sent will, at that distance, be very very weak. Somebody with more knowledge of astronomy than me could probably tell you the ratio of background radio noise to our most distant signals and whether A) It would be theoretically possible to detect it and B) whether we could detect it with the technology we have if we were on the receiving end. Note that there are of the order 10,000 stars within 100 light years of us (extrapolated from densities in closer regions where we can detect the fainter stars).

The signals that we are sending out now are stronger and in 100 years, there will be a large number of stars and possibly planetary systems which will be receiving these signals. The same question could be asked about these signals that one could ask about the signals which are just getting to those distances now. If we were on the other end, could we see the signal? If the answer is yes and there is intelligent life somewhere in the near vicinity then as our detection techniques improve, the likelihood of finding a signal goes up - this is really exciting!

There is already a search on (SETI - the search for extraterrestrial intelligence). Radio signals are picked up and the data is sent around the world where it is analysed on the personal computers of individuals and organisations who have agreed to put in a percentage of their processing time to looking for the mark of intelligent life out there - the sort of signal which would be unlikely to come from one of the many events which give out radio waves all the time.

There have in the past been hints that signals have been seen, but up until now we've been disappointed. My view is that it's only a matter of time, the signals are out there and I think that we are likely to see something in the not-too distant future. However, if the chances of the original formation of life, even given the right conditions, are very small, then we may remain alone for some time to come. As we find out more about what's out there and where we came from we are getting closer and closer to an answer.

That's my tuppence anyway :-) I'll try and answer your other questions when I have a bit more time!

(Edit - Strangely enough there has been a post from Isabel on a part of the above topic, talking about diversity from evolution - read it at God Plays Dice).

Sunday, January 27, 2008

Photos from CERN

As I mentioned a couple of posts back, we were lucky enough to go the 100m down into the chamber for the CMS detector. I got a few pictures while we were there.

First of all, on the surface before going into the cavern and indeed all around the CERN sites you see huge gas tanks. These tanks are for storing helium. The detectors and accelerator have to be cooled to just above absolute zero (there are superconducting magnets for the accelerator which only work at very low temperatures). If there is a problem with any of the components they may have to be taken apart, or at least looked at in detail. In order to do this, the helium will be released and the parts will warm back up. CERN has the largest supply of helium in the world and this is both expensive stuff and not easy to produce. It is still being produced now in order that they have a large enough supply. So, when you release the helium you want to store it somewhere, not just let it off into the atmosphere, and that is what these enormous tanks are for. The circumference of the tanks is, I guess, around 2 or 3 meters.
LHC helium tanks
100m down into the cavern and we were lucky enough to see the last two pieces of the CMS detector being readied to slot into place. The following panorama is from 6 shots, which don't go together perfectly, but give a pretty good impression of the complexity of the detector:
CMS detector panorama
The largest component of the CMS detector weighs in at 2000 tonnes. Your average crane cannot carry this sort of weight and so in order to lower it into the cavern they had to construct a specially designed pulley system. The two towers on top of the CMS building housed the wheels for this pulley. In the background of this picture is Mont Blanc:
CMS and Mont Blanc
Mont Blanc can be seen more clearly in this picture which I took as we were taking the bus to the site. The new polarising filter for my camera works very well at removing the reflections from the glass in the bus. the extreme blue in the sky in the picture of the helium tanks also comes from using a polarising filter which helps to remove any haze:
Mont Blanc
See here for a couple more from the detector.

RTN recap part 1 and gauged supergravities

I'm back in Santiago after a week at the RTN winter school in CERN. I have a full list of topics that I want to go over from the school, and this time I REALLY will do it (I may have said that before, but this time I really mean it). In particular Henning Samtleben gave an excellent course on gauged supergravity and flux compactifications which was extremely clearly presented for what is not an easy topic to get your head around. There's a reading list which was supposed to be read before the lectures but I feel that I will get more out of them now. I'll put up a link as soon as the videos are up online.

I'll see if I can give a basic overview of gauged supergravities, if only to get it clear in my own head.

Gauged supergravities can be understood from two points of view.

The first route is to take an ungauged supergravity which comes from a compactification of 10 dimensional supergravity on a torus of some number of dimensions. This will give you an effective theory in D=10-d dimensions where d is the dimension of the torus. The second route is to compactify on a less trivial space and to turn on n-form fluxes in your theory.

For the first route, the D-dimensional theory which you obtain from compactifying on a torus will have both gauged and global symmetries. The gauged symmetries will be abelian and there will be a gauge field for each of these U(1) symmetries. Then there will be a global symmetry, which typically will take the form of an exceptional group (one subset of the semi-simple Lie groups).

The theory you now have is an ungauged supergravity (although it does have gauge fields, the name comes from the fact that there are no non-abelian gauge symmetries). A gauged supergravity is formed by gauging some subset of the global symmetries.

There may be many ways to do this (to choose the subset of global symmetries to gauge) which will put the abelian gauge fields that you already have into the adjoint representation of the now non-abelian gauge group. The way in which you do the gauging (choose the subgroup of the global symmetries to gauge) is all defined in terms of a single tensor. This tensor has a series of constraints which must be imposed in order to form a closed algebra when you perform the gauging and also to keep supersymmetry (though you may wish to break some number of the supersymmetries in the gauging - giving you a maximally or non-maximally supersymmetric gauged supergravity).

As I said, there are two routes to gauged supergravity. The second route is to go back to the 10 dimensional supergravity that you started with, and rather than simply compactifying on a torus, you compactify on a more complex manifold - a d-sphere, a torus with torsion, or you may turn on some fluxes which wrap closed cycles in the compactified directions. This process results in the same gauged supergravity theories that you would have obtained by gauging a subgroup of the global symmetries in your 'trivially' compactified theory.

The point about these theories is that you have gone from a 10 dimensional theory to a lower dimensional theory with a non-abelian gauge group. This is clearly an interesting area to explore and has many applications, from the AdS/CFT correspondence to model building and more...

Anyway, that's the very basics (the flow chart as I have picked it up over the last week) of gauged supergravities.

As far as I can tell, the main subtleties come from 1) applying the constraints on the tensor which encodes the gauging of your global symmetries and 2) finding a realisation where the gauge transformations act in a manifestly covariant manner on your fields.

I may try and do the same thing for the other lectures if I get some time. For now I'll upload some photos from the trip.

Wednesday, January 23, 2008

Strings in CERN

I'm currently in CERN, in Geneva at the RTN winter school on Strings, Supergravity and Gauge Theories which is proving to be both extremely interesting and exhausting in equal measure. With five hours of lectures a day and several hours spent every evening working with my collaborator, it feels like we've had weeks here already although the whole thing will be over on Friday. Though I hadn't been particularly looking forward to the topics, the lecturers are all excellent and I'm learning more from these courses than I have from a school in some time. Many of the lecture notes are up online and the videos I presume will follow.

Today we were lucky enough to take a trip to one of the two main detectors for the LHC, the 27km circumference proton accelerator to be turned on later this year. The CMS detector had its final segment lowered 100m into the ground yesterday and so the bulk of the machine is now in place, getting ready to start taking data from the particle collisions some time in the summer (data is already being taken in the detectors from cosmic ray events). At 12,500 tonnes, and around 21 by 16 meters, this is in essence a huge piece of electronics which will be a general purpose detector (one of the two, the other being ATLAS) monitoring some of the 40 million collisions per second when the machine is running at full pelt.

I'll get my own photos up online when I'm back in Santiago. Having spent some time working on Babar it was impressive to see the next generation of machine which we hope to give us some of the missing pieces which we know must be out there to complete our understanding of of elementary particle physics.

In the time outside lectures I'm working as quickly as possible with my collaborator on a project which has taken far too long and we are finally trying to get it finished off. Having spent almost all of the time working on this project in different continents we're taking full advantage of our current state. Will update more when I'm back home.

Saturday, January 12, 2008

Christmas roundup

A few more pictures to get back up to date with the Christmas break back in the UK.

I mentioned in a post a week or so back that I'd been with a friend to the South Bank to see a couple of exhibitions. The usual skateboarders and bikers were falling off their respective pieces of equipment in the concrete playground by the side of the river. There was however one guy who seemed to be consistently not falling over and he gave me a chance to try some shots in the shade at high speed. With a bit of playing around I got this image:
The next day, the changing of the guards at Buckingham palace drew a huge crowd, and I'm still unsure if I missed seeing the Queen by a matter of minutes. Anyway, in one of the doorways of the palace I spotted this royal pair who were clearly interested in taking my photo:
For New Year's Eve I was back in London and we headed for the London Eye to get prime viewing position for the fireworks. Waterloo was mayhem and there were apparently 700,000 people out on the streets for the event. The fireworks were spectacular and the slight drizzle didn't put a damper on the atmosphere:
Next week I head to Madrid for a couple of days before going on to the winter string school in CERN which I'm thoroughly looking forward to. I hope to report on some physics from the school - there will be a working group on AdS/CFT with flavour.

Friday, January 11, 2008

Astrophotography first steps

My first attempt at non-lunar astrophotography. Taken in a village in Leicestershire, UK, with a 30 second exposure at f/4.5 and a focal length of 17mm (fully zoomed out on the Canon 17/85). I've never been able to see Orion's nebula with the telescope I bought when I was 13 as well as I can with this long exposure on the camera. If the rain ever leaves Santiago again I'll head out to the countryside to try some more shots.
(The highlights in the tree are simply where I attempted to brighten the highlights and caught a few spots I didn't want to) Another shot here which includes an airoplane trail streaking past the Pleides, sadly not a comet.

Thursday, January 10, 2008

Reversal Of Alzheimer's Symptoms Within Minutes In Human Study

Sorry for the lack of commentary but these days I rarely blog in any depth from work. However, this article is well worth a read!

(From TMT)

Final adventures of the Pisco Kid?

Perhaps your last chance to get a copy of The Adventures of the Pisco Kid - the book I reviewed several weeks ago with high praise.

Sadly the distributor is in difficulty and soon (perhaps today) will be the last chance to buy the book (at least in its current incarnation). I'll leave you with the words of Michael himself:

One of my New Year’s resolutions was to have no shame. No, that’s not true. The main one was to be as honest as possible. That said, I don’t enjoy self-promotion, but circumstances dictate drastic measures. My publisher informed me a couple of days ago that Biblio, the distributor, is close to dropping them from the roster. This means they’ll also try to get the publisher to fit the bill for the unsold stock of my novel, The Adventures of the Pisco Kid. And that, likely, will be the final suffocating nail to seal the lid on Arriviste Press and force it into bankruptcy. I’ve also just found out that the remaining 1,350 copies of the book are likely bound for the shredder. We’ll know by Friday.

The latest news comes just a week after Publishers Weekly put their review of Pisco back up for their highlights of the best web reviews of books that fell through the cracks in 2007. Here's that review:

Other than the PW review, we’ve had a review in GUD and another one on a weblog. No print coverage and we still managed to sell around 150 copies. Who these crazy people are, I often wonder.

So what am I asking? Basically I’m asking you to just take a look and see if Pisco is of interest to you. We also have a few review copies left over I believe, so if you’re interested in one of these, message me and I’ll see what I can do about getting one to you. One stipulation: We’re not giving out “free copies” so you have to give your gentleperson’s word that you’ll review it somewhere. This does not hold you to a good review either. It is the Year of Being Honest, you know. It is also the Year of the Rat (as of February 7) and there are plenty of rats in Pisco to satisfy all so vermin enthused.

So help us jolt Biblio into hanging onto the book for at least a little while longer. There isn’t much more time. The shredder blades are being sharpened and the gears are being greased.

The Intro …

"In the not so distant future a hero will come—some say a messiah—to save us from ourselves. To save us from the destruction, hopelessness, death, tribulation and the haywire weather; to save us from the cabal that has taken over the shining city on the hill, and from the powerful forces of evil that seek to control the world; to save us from ourselves. Could Pisco be that hero? Find out as he discovers his purpose driven life, finds love and adventure, and how eventually, he finds his albedo. At once a surrealistic love story, an adventure story, a satire The Adventures of the Pisco Kid is really just the simple story of a rodent exterminator tapped for greater things.

What others are saying about The Adventures of the Pisco Kid:

The Adventures of the Pisco Kid does something that many books featuring inexplicably expanding fat chicks don’t: it makes you think... and not in a dorky math way either. Pisco Kid will have you reexamining your life -- your goals, your relationships, your job -- and it reafirms that life is much better when it contains meat. — A.J. Daulerio, “Cultural Oddsmaker” for Deadspin.com

A delightfully damaged mash-up of toxic punk fury, inbred bluegrass madness, and a thousand other forgotten and priceless rhythms. Michael Standaert will take you on a journey of fear and loathing on the trail of rats, hypocrisy, and redemption. — Mark Swartz, author of H20

From Greatest Common Denominator: http://www.gudmagazine.com/review/archive/2007/6/18/the-adventures-of-the-pisco-kid-by-michael-standaert/

The thing about Pisco is, he can't catch a break. The kid is winless. But he keeps moving, keeps reaching despite the waves of destruction that follow him. Surfing his wake is worth the risk, though. Michael Standaert takes the reader on one hell of a trip in The Adventures of the Pisco Kid.

From Jon's Travel Adventures: http://jonstraveladventures.blogspot.com/2007/11/adventures-of-pisco-kid-review.html

If Kafka were to have gone to Las Vegas on a drugs bender, or Hunter S Thompson had tried to rework The Trial, they may have come up with something along the lines of The Adventures of the Pisco Kid. Surreal, satirical, moody, funny, chaotic and extremely eloquent, it's rather difficult to write a review about this book and not look like I'm simply writing a good review for a friend. However, I promise this isn't the case!

From Jason DeBoer at Goodreads: http://www.goodreads.com/book/show/1350968.The_Adventures_of_the_Pisco_Kid

Standaert revives a now sadly neglected genre: the picaresque novel. Full of savage humor a la Burroughs and Celine, there are few subjects that Standaert's acid does not rain upon. If you're sick of wimpy contemporary satires, you'll be delighted with the downright dangerous Adventures of the Pisco Kid.

From an Amazon.com reader: http://www.amazon.com/Adventures-Pisco-Kid-Michael-Standaert/dp/0974627038

Mr. Standaert has created a whole new writing style with his effort, The Adventures of the Pisco Kid. Clearly a disciple of Hunter S. Thompson, Charles Bukowski, with maybe a hint of Robert Hunter mixed in, Standaert's first novel is a good one. When I grow up I know for sure.....the rodent business is not for me. Long live Pisco!!!!

Join the Facebook group to add your support, or even better, buy a few copies of the book!

Monday, January 07, 2008

recipe intermission

After a virtually non-stop couple of weeks in the UK I'm back, safe and sound in Santiago, where it's already feeling like home. One of the many lessons I learnt from living in China was that I should make my house as personalised as possible as soon as I can. Two years didn't feel like long enough in China to invest in decorations for my flat and consequently it was always rather utilitarian - read bare and boring. After two years I realised that this had been a mistake and so I'm trying to make up for this in Santiago. I've now printed out some of my favourite photos from China which are up on the wall (as well as a few which are now in a cafe in the old town) and have found a second hand book shop which sells unusual movie posters (Chungking Express has a wonderful poster). I also never had a TV in China which again was perhaps a mistake as I now see it as a great tool to learn the language. So, TV and a selection of Spanish DVDs are on almost constant play while I'm pottering about.

I'm looking forward to getting back to work, too. One of the negative sides of being a physicist is that it's rather difficult to completely switch your mind off from research. I guess that just about 100% of us in this field are here because we enjoy what we do and therefore the problems in the office come home with us, not as a matter of diligence, but as a matter of it being such a large part of our lives. Somehow I put this in a different class from that of being a workaholic, though if people in non-academic fields worked the hours that most academics do I would put them firmly in the workaholic's category. Anyway, I've now been away from my papers for far too long and I'm looking forward to getting back to them tomorrow.

In the two days between getting back to Santiago and getting into the office I've spent my time equally between catching up with Spanish and Chinese and getting my kitchen into the state that I want. This consists mostly of making large batches of stocks and sauce bases which I'll be using over the next weeks. The nearby Carrefoure has also been a great sauce of jars to fill with grains, pulses and dried fruits.

I don't think it's simply because I was bought up in a Jewish household that I have a seemingly spiritual yearning for good chicken soup. The fact that one can buy a chicken carcas for less than a euro here suits me just fine and so Friday night was spent making enough stock to last a while. Boiling up the chicken with onions, leeks and carrots with a couple of bay leaves, salt, pepper and a few woody herbs for around 3 or 4 hours leaves a deep, rich stock which can be sieved, cooled and separated into the jelly (which goes in the freezer as stock for risotto amongst other things) and the fats which make a really tasty grease for future roasting and frying (also add a teaspoon of the clear fats when cooking couscous instead of using olive oil or butter - really tasty). The rest of the stock which doesn't go through the sieve is then picked apart by hand (making sure to remove all the little bones) and gives enough chicken for a few more meals.

Secondly I've found that one can buy pig's trotters in the shops here which have been salted and, when left to desalt in cold water for a few hours, can then be boiled up in a similar way to the chicken (though these need a good 5-7 hours to become really tender). The gluten in the bones and cartiledge makes an extremely thick jelly which is flavoured with a little star anise and sichuan pepper along with the vegetables. The fat is used just as the chicken fat and the meat, cartiladge and remaining fat from the feet makes another couple of meals - see good recipes here and here - My taste for fatty meats was nurtured in China. Try and mix some of the meat from the feet with some pork loin meat (reducing the percentage of very fatty meat) and a few slices of chorizo with a little Chinese chilli paste and vegetables, fried up for a few minutes together for a really simple and tasty dinner.

Finally for this weekend I prepared a base for curries which I've found is vital for making a really rich, authentic Indian meal. In contrast to Chinese food, I found that the food in Indian restaurants in England is actually pretty close to the food that I ate in India (perhaps not that surprising). The only cook book I've found which really captures these flavours is The Indian Restaurant Cookbook which gives not only the basic recipes but also a large number of techniques to use for getting the most flavour out of the spices used - The bhuna method I now used regularly. The puree recipe from this book takes sweat and tears, if not blood to make but is well worth it:

Chop up 10 onions, 20 cloves of garlic and 4 oz of ginger into thin slices. Heat half a pint of oil (Ghee is more authentic, and richer but I don't have this at the moment - ghee isn't too hard to make either) in a saucepan and then add the onions, garlic and ginger. Fry lightly for about 15 minutes (not browning, but softening the ingredients). After 15 minutes turn it off and let it cool a little. Then blend the whole lot together - it doesn't need to be perfectly smooth, try for the consistency of a well cooked porridge. Then heat another half a pint of oil in a pan and when it's hot, add the pureed mixture. It won't seem to mix very well at first but keep stirring and make sure it doesn't bubble all over the place. Keep cooking it for another 15 minutes, again, not browning but keeping it as a white, smoothish mixture. After 15 minutes let it cool. I then bag it up into sandwhich bags and put it in the freezer for future use. This should make enough curry for at least 20 servings. When you're making a curry, take this out, defrost it and fry it quickly to the point you want. The half an hour of cooking at the beginning brings out the sugars and reduces the harshness of the ingredients. The rich sauce really does add a great deal to a curry but can also be used for many other dishes.

Anyway, I hope those are actually of some use. I find they all add greatly to a kitchen store and although stock cubes are just as flavoursome, I like to be able to choose what goes into mine, for flavour, for piece of mind and simply because I enjoy the process.

Back to the Spanish vocab which has gone into deep freeze in my mind over the last couple of weeks and now needs reheating!