Brexit and Arrow’s impossibility theorem

Politics in the UK has been on a rollercoaster ride in the last few weeks over Brexit. There have been many high profile cabinet resignations by ministers who are unhappy with the proposed Chequers plan.  Brexiteers and  Remainers, who are bitterly opposed each other, have managed to find one thing that they do actually agree on. They both vehemently reject the proposed compromise in Theresa May’s Chequers plan for the transition period. Note that this is just the transitional agreement, not the final agreement that will govern the ongoing relationship between the UK and Europe in the future.  For that, we can look forward to another two years of negotiation, political fighting and uncertainty. 

Arrow’s Impossibility Theorem

This turmoil supports the truth of Arrow’s Impossibility Theorem. This states that it is actually not possible to fairly combine peoples wishes into the right outcome. The view of the people can not be forged into a single coherent view. In other words, what the British people want will always be different from what Britain wants.

Kenneth Arrow, a Nobel Laureate, set up three criteria for ‘fairness’ in an electoral system and then demonstrated that no system can be designed that will satisfy all three of these. His criteria were :

  •             If every voter prefers X over Y, then the group prefers X over Y. 
  •             If every voter’s preference between X and Y remains unchanged, then the group’s preference remains unchanged 
  •           There is no ‘dictator’: no single voter possesses the power to set the group’s choice. 

I won’t go into the maths – you can look it up for yourself here on Wikipedia. It all hinges on the fact that there is a pivotal voter who tips the balance and therefore determines the outcome. So that pivotal voter is, in effect, a dictator: what he says goes.  

This mismatch between the voting public’s wishes and the higher level group outcome is a good example of catataxis. We can sum it up in the catataxic maxim :

“As above, not so below”

What happens at the group level is often the opposite of what is happening at the individual level. 

Plus ça change, plus c’est la même chose

We can draw another example by considering the differences between the American Revolution (1775) and the French Revolution (1789). Both happened within 15 year of each other but they had very different outcomes. The Founding Fathers in America made sure they built in checks and balances to the constitution to prevent any dictator emerging. In other words, conflict and argument were baked in at a lower level to guarantee stability at a higher level. 

In contrast, the French Revolution decapitated the state but did not redistribute its powers to other lower entities. So, in effect, the state was still a monolithic structure. This then led to the rise of Napoleon as a dictator followed by the Bourbon restoration which took them back to where they started. 

So maybe the optimistic conclusion to all the Brexit furore is that this vehement disagreement is  necessary. It is the messy process of democracy that guarantees a stable, unified state at the end.    At a higher level, it certainly seems to have pulled the EU together into a more coherent whole, judging by the unanimity from their side of the negotiating table. 

The law of large numbers and the meaning of life

Entropy and life

The Law of Large Numbers is a cornerstone of statistical science. It says that, while it is very hard to predict things on an individual basis, it is much easier to predict things on an aggregate basis once you have enough individuals in the group. The whole statistical toolbox of bell curves, averages and standard deviations exists to offer accurate predictions of random events using the law of large numbers.

For example. I can’t tell you the exact height of the next person to walk through the door but I can confidently say it will be between two standard deviations of 1.78 meters if it is a man and we are in the UK. So, in effect, a random event at the micro level yields a predictable outcome at the macro level.

As above, NOT so below

Consider gamblers in a casino. While it is possible for an individual gambler to get lucky and win big, in the long run the casino will always win because the odds are in its favour. This is the essence of the law of large numbers. A huge number of unpredictable micro events produce an overall system is very predictable. What is more, the larger the system the more predictable it becomes. The key criterion is that the individual events are truly random; that they are not correlated at all. In the casino example, this means that the gamblers are not colluding with each other (or with the dealers) and that the cards or roulette wheels have not been rigged. In mathematical terms, this is expressed as “the system must have independent variables”. So the ‘order’ at the macro level depends on randomness or ‘chaos’ at the micro level which is summed up in the catataxic maxim :

       “Order requires Chaos”

The macrostate and the microstate

This ‘order above, chaos below’ concept was central to the development of Statistical Thermodynamics, one of the crowning achievements of 19th Century Physics. Ludwig Boltzmann managed to forge a link between Newton’s laws of motion and the evolving field of thermodymnamics which examined pressure and temperature phenomena in steam engines. With his kinetic theory of gases, Boltzmann took a dualistic approach defining a ‘macrostate’ and a ‘microstate’ in a catataxic separation of reality.

The macrostate was the description of the whole system, observable by measuring the pressure and temperature of the gas. The microstate was was a description of the gas as a large collection of molecules all in constant, rapid, random motion. By viewing these particles as Newtonian ‘billiard balls’ banging against each other, he was able to derive the macrostate laws of temperature and pressure from the microstate motions of these particles. The pressure of the gas derived from the sum effect of these particles banging against the side of the gas container. But he could only do this by assuming that the particles were random: that interactions between them were negligible except during collisions.

You are just an eddy of entropy

This macrostate/microstate approach led to one of the most important theories in Physics : the Second Law of Thermodynamics. This states that the entropy of the universe must aways increase. Things naturally tend towards a state of disorder. At first glance, this seems to be inconsistent with our experience. How do you explain the evolutionary development of complex creatures such as animals from the primordial soup if the natural tendency of the universe is towards disorder ? The answer to this paradox also lies in changing the frame of reference. Take a catataxic step upwards and look at the bigger macro picture.

Imagine two metal plates, one hot and one cold in a bath of water. As they are different temperatures, the second law of thermodynamics states that heat will flow from the hot one to the cold one until they are the same temperature. This represents the highest state of disorder (maximum entropy) because there are no local ‘pockets’ of difference which would represent some sort of structure. Everything has become uniform and the system as a whole has achieved equilibrium.

Entropy and life

If the temperature difference between the two plates is very extreme, then you might the heat flow by convection rather than simple conduction. In other words, convection cells as in Fig.3 above could spontaneously arise in order to make the transfer of heat more efficient and drive the system towards equilibrium faster. This is an example of structure naturally emerging at a local level to speed the progress towards maximum entropy. An increase in order in the microstate facilitates a decrease in order in the macrostate. As above, not so below again.

So here, at least, is one answer to the meaning of life. Life on earth exists to drive the solar system towards maximum entropy. In the metaphore above, life is the ‘convection cell’ that has spontaneously arisen in order to dissipate the heat of the sun (the hot plate). This is why  the greatest diversity of species occurs where most of the heat of the sun falls – near the equator. If you have ever wondered why you are here, now you know. You are just a little eddy of entropy that exists to dissipate sunshine. Now get out there and start tanning….

Intangible assets and the catataxic gap

jelly babies

The problem of intangible assets

In 1988 Nestle bought Rowntree, the UK confectionary company famous for its fruit gums and jelly babies. It paid £2.5 bn which was three times more than the market thought it was worth. Nestle then had a big problem with its accounts.

Traditionally, accountants would only look at the value of tangible assets; physical things like equipment and buildings. The difference between what you paid for a company and its tangible assets was called goodwill and had to be written off. Rowntree at the time had tangible assets of £0.5 bn. So according to the accounting principles of the day, Nestle had just blown £2 bn on intangible assets that had no true recognised value. It faced having to declare a huge loss.

Nestle argued this was nonsense. The intangible assets were not worthless, in fact they were very valuable. They were consumer brand names that had cost many millions in advertising investment to build up. Moreover, they were more valuable than physical equipment. Machinery wears out and breaks down in the end; it depreciates in value. Brand names don’t. They last for ever.
This debate about accounting policies ran on for over a decade. The proper accounting treatment of brands was not settled until 1999 in the UK and 2002 in the US. Nestle’s view won out. Brands do have financial value and don’t depreciate.

Brand value is the catataxic gap

What is a Brand? It is essentially a collection of feelings and emotions in the minds of the populace. Brand valuation is an example of catataxis. It is the difference between the value of all the physical assets and the value of the company as a whole: the catataxic gap. A brand is a great example of the whole being worth more than the sum of its parts. Beauty is in the eye if the beholder. Brand is in the mind of the consumer. So accountants are now valuing things one level higher than the physical. They are pricing emotions in your head. How you as a consumer feel now has a recognised monetary value.

The ultimate expression of a brand is a pop group. Rowntree’s jelly babies is a physical product with some warm consumer associations. But a pop group is not a physical product at all. Its pure concept. So a band is the ultimate brand. It can exist without its physical parts. Forget jelly babies, look at the Sugarbabes.

Sugarbabes and the Ship of Theseus

The Sugarbabes formed in 1998 with three members: Siobhan Donaghy, Mutya Buena and Keisha Buchanan. One by one, all three of the original members  left the group. The line up in 2010 was Heidi Range, Amelle Berrabah and Jane Ewen. The constituent parts were completely different from ten years previously, but the band was still the same. It  still sold out big arenas so clearly the fans didn’t mind. The band is not its members. It exists at a higher level.

This is sometimes called the ‘Ship of Theseus‘ problem, first presented  by the Greek philosopher Heraclitus. Theseus’ ship is so old that gradually every plank of it is replaced by a new plank. Once the last piece of the old ship has been replaced, is it still correct to call it the Ship of Theseus? The example of the Sugarbabes  and Nestle’s intangible assets would prompt a yes.

Better together…

Better known bands that the Sugarbabes also demonstrate that the whole is more than the sum of the parts. The Rolling Stones as a band (and brand) is still as strong as ever. But the solo albums by the members are embarrassing flops. Mick Jagger released a solo album in 2001 which sold only 954 copies on its first day. A few years later the Stones “Bigger Bang” tour played to 3.8 million people and grossed $500m. So when Mick writes songs and releases them under the Stones banner it is completely different from releasing them on his own.

Consider Pink Floyd. This band lost its creative mainspring not one but twice. Syd Barrett left in 1968 and Roger Waters left in a very acrimonious breakup in 1985. Roger Waters wrote almost all of the The Wall which has sold 20m copies worldwide. His first solo album was “The Pros and Cons of Hitchhiking”. This is very similar to The Wall, even down to the artwork by Gerald Scarfe. It was written at the same time as The Wall and at one time could have been recorded by the band. It was an embarrassing flop.

A big dispute followed about the ownership of the Pink Floyd name. Roger Waters lost out and the remaining three band members kept ownership of it. They went on to  release two successful albums and had three sellout tours under the Pink Floyd name. Roger Waters had the humiliation of playing the same songs – songs that he wrote – in tiny auditoriums right next door to Pink Floyd rocking stadium arenas.

Catataxis : sum of the parts

This is one aspect of catataxis. In the above examples,  the whole is different from the sum of the parts. This can be summarised under the phrase  ‘more of the same is different’ which is one of the four axioms of catataxis

Lynn Margulis and the eukaryotic cell

Lynn Margulis

Fossils are not the whole story

When you think of evolution what image first springs to mind? It’s probably a hall in the Natural History Museum filled with fossils. All the dinosaurs, trilobites, coelacanths and ammonites together make an awesome menagerie of extinct creatures. The stepping stones of evolution are laid out before you in rock and bone. But there is something wrong with this picture – it’s just depicting animal evolution which means it is only telling part of the story. There are five other kingdoms of life (plants, fungi, protozoa, bacteria and archaea) and animals showed up relatively recently. Life on Earth started 4 billion years ago but the first animals evolved 0.5 billion years ago, half-way through the last quarter of the game. So that fossil hall in the museum is like a history of the world that only covers one continent in recent time. A history of the world that starts with American Independence and never strays beyond its borders. (Yes. I know. For many Americans that really is the history of the world but bear with me)

Lynn Margulis challenged orthodoxy

Most famous evolutionary biologists (Dawkins, Gould, Haldane, Maynard Smith, etc) come from a background in zoology. Their expertise is in the comparative study of animals. Lynn Margulis, who died aged 73 in November 2012, was different. She was a microbiologist who focused on the evolution of eukaryotic cells (cells with a nucleus) and became convinced that the scientific consensus was wrong. The mainstream thinking was that the engine driving the evolution of species was random genetic mutation in which only the fittest survived. Margulis agreed that natural selection picked winners but disagreed about how the competing variants were created. She believed that evolution was driven by the symbiotic cooperation of organisms: the competitors in the race worked together rather than competed with each other. The mainstream saw the creation of new species as a divergent process; just as twigs and branches diverge from the trunk of a tree. Margulis believed that new species were created by a process of fusion and merger. She wrote a paper about it in 1966 called “ Symbiogenesis: the origin of eukaryotic cells”.

And then nothing happened. In fact, worse than nothing. Fifteen academic journals rejected her paper. One actually said “Your research is crap. Don’t ever bother to apply again”. Maybe it was because she was a woman. Maybe it was her difficult personality and bad temper. After extensive reworking, she finally managed to get her paper published in the Journal of Theoretical Biology. It was a groundbreaking piece of work. For the first time, the evolution of cells had been properly examined: a history of a continent that was not America had been published. The response from the mainstream was…..complete silence. No one bothered to respond because no one really cared.

The theory of symbiogenesis

And then, very gradually, the years passed and data began to trickle in to support her theory. A single cell is more complex than you might imagine; it’s more than a nucleus in a little sack of protoplasm. The diagram below shows that there are 13 different entities inside it. The crucial evidence to support her theory came when scientists discovered that some of these entities had DNA that was different from the nucleus. The DNA of mitochondria, chloroplasts, basal granules and plastids is not the same as the DNA in the nucleus. This implies that a cell, the fundamental building block of all animals, is a fusion of different bacteria-like creatures. At some time in the past, a group of different bacteria clumped together to form a eukaryotic cell. This cell was dramatically more successful that the individuals composing it and became the basis of all higher lifeforms. The living creatures that we see around us all stem from that initial cooperative merger. Nature is not wholly “red in tooth and claw”.

Eukaryotic Cell

1. Nucleolus
2. Nucleus
3. Ribosome
4. Vesicle
5. Rough endoplasmic reticulum
6. Golgi apparatus (or “Golgi body”)
7. Cytoskeleton
8. Smooth endoplasmic reticulum
9. Mitochondrion
10. Vacuole
11. Cytosol
12. Lysosome
13. Centriole

Lynn Margulis’s theory has now become scientific orthodoxy and her book “Symbiosis in Cell Evolution” is seen as a classic of 20th century biology. Her concept of symbiogenesis could be summarised as

“Today’s groups are tomorrow’s individuals”.

Time acts to drive individuals up the catataxic ladder. In a social history of the world, families become tribes, tribes become nations, nations become empires. So too in biology. Bacteria merge to become eukaryotic cells, single cell creatures merge to become multicellular plants and animals, and the resulting flora and fauna knit together to form complex ecosystems. What you view today as a group of separate but similar things in the fullness of time will be viewed as a single entity.