'Science and magic'
Presenter : Dr. Jack Cohen
Warwick University
Director of Research : Eve Mitleton- Kelly
London School of Economics
Houghton Street
London WC2A 2A
Abstract: In attempting to understand complex systems such as biological organisms and social organisations we are caught between using methods which converge information and those in which it diverges. Natural processes and advanced technology are often driven by mechanisms and rules which are hidden and thus appear to be magic. In revealing them we need to escape old paradigms and habits which distort and restrict our view of the world and ourselves. Explanations at one level do not always have the same explanatory value at another. Dr Jack Cohen leads the session in identifying limiting aspects of our methodology and suggests ways in which we might escape our current mindset.
Compiled For The L.S.E.
by Geoffrey J.C. Higgs
Introduction
Our perception of the world is coloured by myths which prejudice our ideas and affect our science. We are likely to choose 'false' to 'fact' when it fits the picture we have in our minds and in as much as science advances by generalisation we are likely to underestimate the importance of the individual. If we are looking for patterns we may imagine them where they are not and thereby miss some of the real complexity of the system. We tend to concentrate on lines of investigation which will confirm our theories rather than those that might not and imagine that the kind of explanation at one level can always be used meaningfully at another. In this way we often fail to understand how new properties can arise in ways our theory does not cover.
Stories
We learn things at our mother's knee and we confuse an animal like the fox with its counterpart in a children's story. In England we learn that the fox is cunning, in Scotland that it is wily and Greenland that it is brave and fast. It is the hero of Inuit stories, the villain of ours and our minds hold concepts like ' sly' and 'cunning' because that is what the fox is in the story. We wouldn't trust the fox though the Eskimo might value its help. We tend to think owls are clever and wise though close attention to their habits reveals them as stupid. This is the way our minds are made by our culture. From small children we are rewarded when we think of things in the way that society approves. The collectivity conditions us and reinforces the myth. We can often see a difference in perspective in the way our languages handle the same thing: 'Objets trouvé' in French and 'lost property' in English.
At school, teachers teach us science which is simplistic and often simply inaccurate. In rainbows, for example, raindrops do not break up light rays as prisms and though this explanation might explain the colours it does not explain the shape or why it is brighter in one place than another or why there is often a second rainbow the other way round or why two people in different positions apparently see the same rainbow. The more accurate explanation is more complicated and involves several reflections in circles of raindrops which give each person an individual view. Another inaccurate explanation might be that aeroplanes fly just because air goes over the top of the wing and creates a vacuum or our picture of the solar system might be inaccurate because we have been influenced by images in books that distort the relative sizes of the planets and the distances between them. School chemistry is usually designed round reactions that work in 'two hours' or only in the grubby apparatus of the 'stinks lab'. In a book instructing teachers and pupils on how to construct a vivarium were found 103 things that would render the project a failure. It recommended, for example, that zinc and brass screws be used in the construction which would cause corrosion, that marsh plants be grown on plaster of Paris, that a sand bed be put on large stones and that the atmosphere be enclosed in such a way that the glass sides would be permanently fogged.
Our explanations of things which we see in the world can be of very different kinds. There's the old joke about how hedgehogs mate to which the answer is: 'very carefully'. It illustrates an appreciation of the fact that mating involves very close contact and hedgehog spines are very sharp. But in a more general way it is an example of the trade off between the need to reproduce and the need to make things difficult for predators. A further scientific explanation even more removed is that genes resulted in things evolving this way and that five centimetre quills for example are better than ten centimetre quills. All of these are explanations around the same phenomenon.
Dangers of Reduction
It is, (or was), thought that science proceeds by what might be called the 'one two three' method of induction. That if you see some unspecified number of white swans and have looked for a sufficient number of test cases the conclusion is reached that 'all swans are white'. You might of course use other ways of generalising, such as classifying by similarity or dissimilarity or perhaps produce algorithms of the way things behave or reactions proceed. But overall the conclusion is that science simplifies reality in a number of ways and this leads to a biased view of how the world works. We have only to look at earlier publications to see that there are in them what now appear strange and inaccurate views. For example a biology book of around 1960 describes how the egg 'solves' its problem by 'almost without fail' containing the right amount of yolk to form a new individual that in turn will make sperm for eggs that will begin another generation. Or take the model of Evolution that prevailed until about 1957 which depended on a species getting the 'right' mutation and assumed that all individuals of a species had more or less the same complement of genes except for perhaps 'one or two'. It was only if you had a couple of 'bad' genes and you were unfortunate enough to marry someone with the same bad genes then you suffered from some hereditary disease. There were a couple of papers published at the time , one called 'The Cost Of Natural Selection' and the other called 'How Many Mutations Can A Population Hold?' If you did the calculation you found that in 1000 organisms (approximately the number of breeding organisms) there were 10 genes on the way into the gene pool and 20 genes on the way out because that was as much as a population could take. The assumption that nearly all the genetics going on in a species were the same prevailed until about 1962 and still survives in such scientific goals as 'The Humane Genome Project' which attempts to identify all the genes in the human gene pool.
It was not until a way was found in 1963 to investigate the genetics of organisms without breeding that the assumption was found to be false. By spreading out the proteins in a blood sample two spots can be observed for heterozygous ones and one spot for homozygous samples. For 30 different enzymes person A might be heterozygous for 5 and person B might be heterozygous for 5 and there would be an overlap of two. It turns out that nearly all organisms are heterozygous for 10% of their genes; not ten genes on the way in and twenty genes on the way out but 10000 genes and that a third of the genes had different versions somewhere in the population. We are not all Model T Fords with just different headlights or dents in the side but all handmade cars adjusted differently to give much the same results.
This was also born out by research on the hormone profiles of three women. There were in total, six profiles for each of the three women including oestrogen, progesterone, prolactin, SSH,LH and one more. One had a level of sex hormone that was only 1/80th of the norm, another had no progesterone in the second part of the cycle but high prolactin which caused severe depression problems. The third had other hormones controlling her period cycle which were not normally involved, rather than SSH and LH. Yet all of these women produced good eggs. All worked differently but produced the same result, so it is nonsense to go to a doctor who will merely measure one hormone level and prescribe on that basis. It would be much better to make some small change in the system, say for each of the hormones and monitor the result. We mustn't assume we are all stamped from the same mold, or think only in terms of genes rather than whole organisms.
Not All In The Genes
How did something as complex as an individual fly come to be?. To say that it came from a maggot that came from an egg sounds like an explanation. Chicks and even people come from eggs. But eggs are relatively uncomplicated biological structures compared with what comes out of them, the dozens of cells on the yolk from which the chick arises are genuinely trivial compared with a tiny bit of its brain, kidney or even skin. A single growing feather is more complicated in its formative process than the cells from which the whole chick originated. What kind of organising principle or 'spirit of life' could there be?
Todays usual answer is that it is the DNA blueprint; long molecules with enormous amounts of information written along them in the language of 4 nucleotide letters in the nucleus of the cell. This code is supposed to tell the developing organism how to build itself: fly DNA makes flies, chicken DNA makes chickens, people DNA makes people. Yet in reality this is not how the DNA functions. In each human nucleus, magnified to the size of an aspirin tablet, there is about a mile of DNA wire. There is room for a lot of instructions but the DNA cannot by itself make the developed whole organism. Consider a simpler organism such as a bacterium. Bacteria are like workshops full of chemical tools. Some of the tools read along the DNA thread, others make tools according to what is read whilst further ones are structural or act as 'chemical pumps' or are concerned with food and energy. The workshop not only actively produces more of its own parts, tools or structural bricks but duplicates its DNA like copying a cassette tape in a number of ways. Particular tools then arrange a division and the proofs continue in the two daughter bacteria.
An egg is more complicated than a bacterium but more of its tools are the same. Its life processes are however completely different. Also unlike the bacterium it doesn't just grow and divide and produce the same it develops into something else. Initially as a result of what the early egg's tools do, it is turned into a bigger more complicated structure called an embryo which uses yolk as energy and building material and turns into a different thing again. The bacterial workshop makes more of the same whilst the egg makes new kinds of tools and equipment at each stage. A fly egg produces a maggot that feeds and maintains itself. A human embryo makes a placenta which obtains food and energy from its mothers blood.
When the maggot reaches a certain size it becomes a pupa, inside which the organism completely reorganises itself to become a self fuelling aeroplane, and inside half the flies are egg workshops ready to start the whole process again. DNA sequences (genes) specify biochemical tools which are like the clocks, and clamps, lathes or workbenches or worksheets and schedules, but there is no fly description in the DNA. There is no wing pattern or nose pattern. It is more useful to think of each character being contributed to by all the genes in the DNA than it is to think of each character having its own set that 'makes' it. It is because we can (almost) list all of a fruit fly's genes and work those which when mutated cause dangers, that we tend to think that these genes are the fruit fly's wing kit.
In reality, nearly all of the genes affect other things as well. For example, a vestigial wing mutation damages the molecular pump that is present in all cells with the result that the wing cannot be inflated properly when the fly comes out of the pupa. Changes in Homeotic genes which specify the geography of the workshop result in changes in the embryonic map, so that cells in the antenna rudiment positions 'think' they are in leg rudiment positions.
DNA does not of course have to specify the laws of chemistry and physics; it doesn't have to make fats unwettable or sodium chloride crystals cubical but it can change the freezing point of aqueous solutions by making antifreeze proteins. There are many biological regularities also which, like the chemical and physical mechanisms above occur without any DNA specifying them. A very important and very ancient one is the self replication of DNA. DNA tool kit copies DNA with almost perfect fidelity and there are also long established energy exchange mechanisms which are common in many kinds of living things. As much as 60% of the informational DNA consists of these 'conserved sequences' which are the same for the fly, the chicken and the human being. Indeed many of the basic 'housekeeping' genes are the same for oak trees as for bacteria. Differences between organisms, however large, need not be down to major differences in DNA. In principle, a tiny difference could switch development into a new path. Even the fly and the chicken could (in principle) have almost identical DNA except for an early switch at which the paths diverge. Moreover this development difference needn't be at the DNA level. If chickens find they like it hot and flies like it cold then the chicken program reproduces chickens with high temperature development and the fly program reproduces flies cold. They could (in principle) be using the same DNA Because of this we can see that it is not possible to tell in advance what kind of organism (in toto), a particular DNA kit
will make. To use a mathematical analogy; there is no 'mapping' from DNA sequence to structure.
DNA reading and acting tool kits are not in the DNA itself but in the rest of the egg, around the original nucleus. Development of nearly all animals begins in the ovary of the mother, as the egg cells are constructed. Even the development of the embryo doesn't need the offspring's DNA messages until the egg structure has made the basic architecture of the future animal. It is only then that genes 'know where they are' and 'what they should do'. Fertilization happens quite late in the development and the sperm acts as a trigger and supplier of more DNA which differs little from that of the egg. A good mechanical analogy is to see the non-nuclear parts of the egg as a tape player and the nuclear DNA as the tape. The tape has to go into the right slot and the volume and speed set, as well as choosing the tracks to play and in what order. Fertilization is then life pressing 'play'. Suppose we imagine the same DNA but different egg tape player mechanisms: Fly eggs read genes in a certain order and make a fly which repeats this process, chickens eggs read genes in another order and make chickens and so on. In this hypothetical case both organisms would breed true because each kind of egg 'plays' the DNA differently. Conversely if the DNA is different it is hard to imagine how a fly could develop in a chicken egg or vice versa. Thus Dinosaur DNA from dinosaur blood preserved in a tick in amber cannot make a dinosaur. There can be no 'Jurassic Park' unless perhaps you have a dinosaur egg of the same species i.e. the right tape player.
It might however be possible to 'replay' an extinct animal by taking a viable elephant egg and swapping the DNA with that of a mammoth. There are of course enormous engineering difficulties. First getting a perfect mammoth nucleus and providing a suitable environment for the elephant egg. Secondly it might take a million test tube experiments to make the elephant system work or ten years of a thousand elephants with ten experimental cycles of ten eggs per cycle to get a system which might occasionally accept a perfect mammoth nucleus providing the elephant mother doesn't react against the foreign mammoth proteins in the embryo and the baby mammoth can drink elephants milk. Of course the product of playing mammoth DNA tape in a elephant egg and then maturing it in a elephant uterus will only be a 'near mammoth' . Real mammoths are extinct. Obtaining DNA is not 'conserving' an animal or plant species. DNA does not determine what an organism is and there is no 'one to one' relationship or 'mapping' from DNA sequence to character even if it is possible to say that some particular difference may result in characteristics such as albinism or Parkinson's disease. In development, each bit of information content must be in an information context. It is the whole process of development that results in the fly, the chicken or the human being.
A Distorted view
It is not however wrong to make generalisations, classify, or produce mechanisms for processes but it tends to give us the impression that nature works more simply than it does and we tend to assume that reality really is in terms of whatever theory is current. Sometimes this is because of sheer squeamishness. We don't, for example, like thinking about death and so we often fail to appreciate how hazardous life is for individual animals in the wild. Vast numbers of lemmings die with the result that the population remains constant. An average female starling for example lays 16 eggs but for every two that achieve breeding maturity 14 die. A frog lays 10000 eggs of which 9998 will die and a female cod 40 million eggs of which an average of two will survive. Then there is what might be called the myth of efficient nature. In the making of the BBC film series 'Survival' a film sequence of a tarantula wasp killing a spider putting it in a burrow and laying its egg on it took 13 shoots. The first wasp could not find the proffered spider, then a second wasp lost it, then when the third wasp finally stung the spider a bird came down and ate them both and so it went on. Nature doesn't work half so neatly as we tend to think. Of course there may be one super wasp that accomplishes the task every time and so makes up (statistically) for those that don't, but just as we tend to believe that women always have a 30 day period so we believe tarantula wasps always get their spider. The reasons why a population remains constant however are not obvious. It is interesting to consider why in some Western countries but not others, reproduction has fallen below two parents making two parents and that the 32-42 age group has almost no children.
A Different Approach
One way of understanding things which happen in the world is to ask what could have happened instead of what did. This enables us to grasp something of the dynamics of a process just as we might investigate a system by seeing what happens when we alter things a little and see whether it restabilises or falls apart. By asking the question 'What would have happened?' we can pick out the important determining factors. But we have to ask the right questions and get the right answers. It's rather like asking an American historian about Abraham Lincoln being shot. If he or she says that the calibre of the bullet was such and the play that they were watching was such and that Mrs Lincoln didn't like it very much then you are told very little. If on the other hand the historian says that if he hadn't been shot then two days later he would have had a meeting with the Indian Chiefs which would have radically changed American history, then that is interesting. This approach is an exploration of the phase space of possibilities.
Likewise in science we might ask what evolution would have been like if a comet hadn't hit the Earth and destroyed the dinosaurs or put in more general terms, if we ran evolution again would we get human beings? The current opinion is that we wouldn't get anything familiar although it is highly probable that we would get an ecology like ours with predators with eyes on the front of their heads and herbivores with eyes at the side. Eyesight would evolve, flight would evolve because these are so called 'universals'. Alternative worlds such as Jack Cohen constructs and writes about with Ian Stewart and Terry Pratchett may seem extreme but are ways in which the phase space of possibilities is considered. The book 'Discworld' for example is about a world which is a disc on the back of four elephants on the back of a giant turtle (familiar?). In this world light travels at six hundred miles an hour and the speed of dark is not recorded but it must be faster because it gets out of the way. And the wizards who made this world had problems with the planets going round the earth because they kept falling on to it and making craters. It's a fantasy but like science fiction it explores possibilities and we can ask more general questions such as 'If different religions have been invented by people at different times would aliens do the same?' We need to escape from ways of doing science that have been honed for a very long time. We should consider the space elevator rather than the rocket because it seems to be breaking the rules. Whilst at Birmingham University Dr Cohen built a number of fish tanks the inhabitants of which all died within six months of his leaving because his successors did not know how to keep them going. Real ecosystems are complex with interdependent and co-evolving organisms and on a small scale the individual is important. This is illustrated by the anecdote of 'Dr Nordness' who when introduced by the hostess at a party as 'an expert on crocodiles' said, 'No I'm not, I'm only an expert on the crocodiles that I've got!'
Magic Technology And Hidden Nature
Arthur Clarke once said that if technology is sufficiently advanced it is indistinguishable from magic. Good technology always tries to be user friendly in that we do not have to understand the underlying mechanisms. Motor cars have become user friendly. Whereas in cold weather a 1933 Ford 8 needed to have its engine warmed and its ignition retarded now you just turn the starter and it has a little thermometer and a heater and it all works automatically. Technology seems like magic when the rules by which something works are hidden. There was a time when motorists understood how their cars worked, now most don't. They don't have to. Nature is like that and when scientists investigate it they look down a kind of funnel and find some rules at the bottom. When you've discovered the rules at the bottom you can talk about them and formulate explanations on the way up. Having looked down one funnel you find it is connected to other funnels. The physicist is especially good at looking at nature like this. Apples fall from trees, moons orbit the Earth and down here in a general sense we say it's gravity. Biology seems to come down to chemistry, chemistry seems to come down to quantum mechanics and science converges on a 'theory of everything'. Trouble is we may be missing something. If you have a skin problem you don't want to go to a doctor who sends you to a chemist who sends you to a physicist. You want your doctor to have an appreciation of you as an individual. You want him to consult the medical history of your parents and grandparents. The problem is that the skin condition is fungible. 'Fungible' is a legal word referring to replaceability. A grocer, for example, is required to sell baked beans which are all fungible in the sense that until you open a can every one can serve for any other in any ways you might think about them. A skin condition is fungible in that what creates it may be a lot of different things. And it is also 'emergent, in that it is arising in ways which we do not understand. Classical science has a way of looking at the substructure of something to see how it leads to the whole. Sometimes it is necessary to understand something as a whole and then see how it relates to the substructure. The concept of a bridge for example would not be discovered by an alien mind merely by looking at the construction without knowing the function. 'Bridginess' is an emergent property, sometimes of concrete, sometimes of steel, sometimes of rope. You could even consider that a bridge was made of nothing if it was a tunnel. An emergent property is not what something is made of. A tunnel is a sort of bridge if it's used for the same purpose. It's very easy to import the idea of function into nature and it's difficult to keep it apart from purpose in terms of intention. On a cosmic scale this gives religions. The Hindu's have a picture of the universe, the Jews and the Catholics have theirs. What does seem important is not to get the idea that something which is complex reflects something else that is complex like spilling the guts of an animal to see how you are going to do in battle. That's using one bit of 'ant country' to illuminate another.
'Ant Country'
When a human organisation such as a business starts up you can explain what's going on in terms of peoples intentions. When a business collapses you can explain why. It's the bit in the middle that's difficult. It's a bit like a chess game; in the beginning the moves are all quite easy to understand and at the end the moves are easy but in the middle when you've got a number of bits on the board even a chessmaster can't work out what you are doing without knowing the plan you are following. When the business is up and running you can't work out what's happening because the beginning and end bits aren't joined up.
The term 'ant country' refers to a model designed by Chris Langton to show how simple rules of behaviour in a simple universe can lead to a complex system. It is also known as 'Langton's Ant' because the 'ant' is an object which exists in two space on a grid of uniform squares. The rules which govern its action are:
(a) When moving onto a white square it paints it black and when moving onto a black square it paints it white.
(b) When leaving a white square the ant turns right and when leaving a black square the ant turns left.
On starting off on a single colour universe(white or black) a repeating pattern is seen for the first 120 steps, then for the next 10,000 steps the movement appears random but at step 10120 it finds something called the 'highway' when it repeats a series and moves in a particular direction. No mathematician has been able to come up with an algorithm which will give this behaviour. Conway's 'Game of Life' is similar in that it also works on a two dimensional universe. The squares are either blank or contain a single dot. From one unit of time to another only one of three things can happen:
(1) A dot is added to a blank square.
(2) A dot is erased from a square that contained a dot.
(3) A dot which was in a square remains in the square.
Each square has six neighbours and the rules for determining which of these three things will happen are:
(a) A dot is added to a blank square if exactly three of its neighbours have dots.
(b) If a square has a dot it will keep it so long as either two or three of its neighbours have one, otherwise it will be erased.
What happens is that a particular configuration of dots changes its shape through time steps until at the fifth it has the same shape it had in the first place except that it is in a different position. From slightly more complicated rules self reproduction of shapes can be made to occur. Ants and people have exactly the same thing happening in individual nerve cells but their whole nervous systems operate according to different rules. When organisations start up they may operate according to certain rules but the rules beget other rules which are invisible and that's the problem for an outsider trying to understand how an organisation works. Just as the car hides the rules by which it works so an organisation hides its rules. Trying to understand what is happening in ant country is difficult because there are no labels saying this bit is important and that is not. It may be that you can find causal connections between this bit and that bit but it's a desperately uninteresting causality.
As a Chaos mathematician Ian Stewart has suggested that causality can be understood in terms of trajectories that converge and that divergence results in tiny irresolvable differences in initial conditions leading to radically different outcomes. As a biologist Jack Cohen knows that if you cut a frog's egg in half it makes two frogs the same as the single one the egg would have made (though smaller in size). Embryology understands the ability of an egg to make the same frog, whether in an environment at 30º C. or 5º C. as convergence. The same frog is produced though perhaps in slightly different ways, just as the women who each had a different hormone makeup ended up doing the same thing in producing good eggs.
Our attempt to understand nature is a balance between making generalisations or theory formulations which converge information and capturing it in all its infinite variety which is divergent. It is a question of what is important. On the one hand we might think that the death of a man in 1865 might not mean much in the broad strokes of history on the other Chaos theory tells us that if we go out of another door instead of this one that history may be entirely different. In the ant country of developing organisations following causality would give diversity but generalisations about people in this company doing the same as people in that company would give convergence. Coherence in ant country comes with convergence. It is what you see as towards the end of the chess game when the various end games we have in our heads start to count.
Perception also paints its own picture of the world. If we stand on the seashore and look out to sea the horizon is half way up though we know its below our feet. If we put on spectacles which turn the world upside down we become so used to it that we don't notice it until we take them off. In a world in which our knowledge is limited there might be nothing to choose between two theories about where the sun is. One, that it is 92 million miles away and the light rays that come to Earth are parallel and the other that it is a little bright object above the clouds and its rays radiate out. In which case what we could say is that the rays are coming out of a hole that is sixty miles away and fall on the ground some 2 miles away and though they are actually parallel, like railway lines they appear to converge.
New discoveries in science depend on people seeing things differently from the habitual ways we have of looking at them which is why its useful to have people from different cultures doing research together. If you went to someone in 1965 and asked what it would cost to put a 100kg man into lower orbit then the scientist would have said ' Well you have to lift against the force of gravity and using a rocket it will cost around £100 million and so on. But in 1975 someone called Anderson came up with the idea of the bolas. A bolas is a weapon with three ropes and weights on the end of each. Now it's true that you would need the ropes to be 100miles long with cabins on the ends but it's the novelty of the idea that counts. You keep it spinning with solar power or putting moon rocks in at the top. When a cabin comes down you get in and you get off at your space station at the top. You have to invest a fair amount of capital initially but when working you can get a 100 kg weight into orbit for 1/15 of the original cost of using a rocket.
The Belousov Zhabotinsky Reaction
The Universe presents us with many patterns that appear random in their production. When we were at school we were convinced that chemistry was simple (at least as far as what molecules do) and that biology was complicated. It now appears that chemistry is far more complicated than we thought. Even when hydrogen and oxygen are exploded to form water the reaction goes through 24 different intermediates with formulae like H14O3 and it doesn't work if you don't have any water there to start with. Some reactions will not work if you have very very pure substances or those which give precipitates will not do so unless there are scratches on the glass.
Belousov and Zhabotinsky when working with reactions that used starch/iodine indicator found that they were not converging as they thought they would. Moreover when the experiments were repeated the results were different every time. It was not chemistry as it was known and they couldn't get the results published. Recursion cycles had been known in biology for some time but because we had all been conditioned by the ideal of school chemistry it wasn't until oddities were found in the Ozone layer and the chemistry of clays that we realised that recursive or circular chemistry was actually quite common. Teachers doing demonstrations are rather like actors on the stage, you only see the patterns they want to put there.
What happens in the Belousov Zhabotinsky reaction is rather like what happens in a forest fire. Just as fire breaks out in spots here and there in a random manner so foci of blue appear and progress as expanding rings whose centres are oscillating foci. Different foci even in the same dish may have very different periods. This kind of activity happens in the chemistry of clay, in the Ozone layer and in the catalytic converter of your car.
A simplified version of a chemical oscillator (Zaikin and Zhabotinsky) Nature 225 535 ) appeared in Science 175 634-6 by Winfree. It works reliably with a manageable number of cheap components which have a reasonably long shelf life. Care should be taken to carry out the experiment in a well ventilated room as a small amount of bromine (toxic and corrosive) is released and malonates are moderately toxic.
Ingredients:
Solution A. 25g sodium bromate dissolved in 335cu3 water and 10cu3 concentrated sulphuric acid added.
Solution B. 10g sodium bromide dissolved in 100cu3 water.
Solution C. 10g malonic acid dissolved in 100cu3 water.
Solution D. Redox indicator (1,10 phenanthroline ferrous complex) -supplied by Fisons, Loughborough.
Method:
Put 6cu3 of solution A into a petri dish, then add 0.5cu3 of B and mix in 1cu3 of C. Leave the brown solution to lose the released bromine (by open window) until a pale straw colour or colourless( should be 2-3 minutes). Add 1cu3 of the redox indicator D, mix thoroughly and place on a white (preferably illuminated) background.
Observation:
The solution will turn patchy blue , then clear to a brown-red. After a while (up to 5 minutes), foci of blue will appear at indeterminate times and places and progress as expanding rings whose centres produce oscillating foci. Different foci even in the same dish may have very different oscillation periods. At 20º C. the pattern complicates for some 25 minutes. Homogeneity can be restored by shaking the dish when the solution turns from blue to red and the process repeats. The system will run impressively on an overhead projector but will not be clear if there is vibration. About six repeats can be achieved before the system runs down('dies'). Bubbles of carbon dioxide form at the bottom of the dish and need to be removed by agitation.
Spirals can be achieved by adding a small quantity of D to a particular area of the dish and giving a single swirl(especially with a hot needle). It is also possible to produce patterns which are more stable against vibration using wet Millipore or even filter paper.
Conclusion
When science fails, magic prevails. We don't want science to fail in our understanding of complex systems so we must expand the scientific method to accommodate them.