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.

Costa Concordia: catataxic catastrophe

Costa Concordia catataxic catastrophe

On the centenary of the Titanic disaster of 1912 another huge cruse ship sank. The Costa Concordia ran aground in January 2012 hitting a rock in the Tyrrhenian Sea. Although most of the passengers and crew were evacuated safely over a 6 hour period, 32 people died. There is a catataxic side to this tragedy. As cruse liners have ballooned in size, the safety systems have not scaled up appropriately. In this case, more of the same is not just different but also deadly.

Big cruise ships are top heavy

Cruise ships have been a boom industry and as a result the ships have got bigger and bigger in order to achieve economies of scale. Today’s ships are twice the size of a decade ago and can carry 6,000 passengers and 1,800 crew. That’s the size of a small town and four times bigger than the Titanic. Since most passengers want a nice view from their cabin, there are more and more decks stacked above the waterline. At the same time, the ships need to be able to get into traditional old ports (where tourists like to go) rather than to anchor offshore and be ferried in on small boats. That means they need a shallow draught. Both factors mean that ships are becoming increasingly top heavy: there is a lot more above the waterline and too little underneath.

Lifeboats and logistics

A second factor is the lifeboat problem. This technology has not really changed since the time of the Titanic. When the top heavy Costa Concordia heeled over, that put half the life boats out of action because they could no longer be lowered into the water. Every passenger is (in theory) allocated a berth in a lifeboat matching their cabin allocation. It is a logistical nightmare to try and shepherd 7,800 people to their allocated lifeboat seat. Just picture this. A typical movie theatre has say 250 seats. Now imagine 30 cinemas stacked on top of each other in a sky scraper with every seat full. You randomly distribute tickets with seat numbers in a different cinema to all the members of all the audiences. Then you blow a whistle and tell them to find their new seats in the new auditoriums. Result: utter chaos. Now imagine doing it in the dark, at sea with the rooms gradually tilting over to one side…..

This lifeboat issue is such a logistical problem that the International Maritime Organisation advises Captains to try and use the ship itself as a “big lifeboat” and return as fast as possible to port for evacuation. In other words, the best advice available about lifeboats is to try to avoid using them at all.
Both the ship design and the lifeboat problem are problems of scale. Andrew Linington of Nautilus International, a maritime union, says “The alarm bells have been ringing with many of us for well over a decade now. These ships are floating hotels – skyscrapers, really. The design has been extrapolated from that of smaller ships. We believe a lot of basic safety principles are being compromised to maximise the revenue”

Surface area to volume problem

A big ship is different from a scaled up small ship which is the essence of catataxis. If you just inflate the ship design like a balloon it becomes top heavy. This is a version of the surface area to volume problem.  The outside surface of the ship – which passengers have to get to in order to escape  – increases with the square but the internal volume increases with the cube. So logistical problems with ever larger cruise ships grow exponentially. More of the same is different.

If you build it they won’t come

I was working on a local history project in Kent (where I live) when a friend gave me some old photos. They showed men in frock coats handling hops on long trestle tables. These are city workers handling an agricultural product. It took me some time to track down where the photos were taken.  It turns out they were hop factors in the 1920s, working in 15 Southwark Street opposite the Hop Exchange in London.

The vanished hop trade

The hop trade was once a major industry in Southwark. Back when there was only one bridge over the Thames (London Bridge) everyone passed through  Southwark . Its coaching inns and breweries have been famous since Chaucer’s time; this is where the pilgrims gathered before setting off for Canterbury. There was plenty of traffic up the other way too. Kentish hops, grown in the Garden of England, came up the A2 and the Old Kent Road to the market traders in Southwark Street, around the corner from Borough Market.
The hops were dried in oast houses and then tightly compressed into 6 foot sacks called ‘pockets’ and sent up to the middlemen, known as hop factors, in Southwark Street. Each load was sampled by cutting a foot square brick of pressed hops out of one of the pockets. This cube was wrapped in brown paper and secured with brass chair nails. Samples from a particular grower were all strung together with waxed hemp.

Another set of middlemen, the hop merchants who acted for the brewers, came to inspect the samples. These photos show the merchants (e.g. man in top hat on left) examining the hop samples displayed by the hop factors. The room is starkly functional. A big glazed roof lets in plenty of natural light to help the inspection and a big clock to measure opening and closing times. Nothing else. No decorations at all. After all, this is a serious place of business.

Three factors kill the trade

Hop production peaked in Kent in 1878 and has been declining ever since. Kentish hop varieties, such as Fuggles and Goldings, add bitterness to beer and ales, whereas German hops have low bitterness and strong aroma and are used for lager. So a number of trends conspired in the decline of the Kentish Hop industry. First was the trend towards lager over bitter. Second was the decline in exports as Australia and South Africa began growing their own hops. The third blow came in 1973 when Britain joined the Common Market and cheaper continental hops wiped out most of the growers in Kent.

Bomb damage in WW2 meant that many warehouses were rebuilt in Paddock Wood in Kent and the hop merchants moved what was left of the industry down there in the 1970s.The last hop merchant, Wolton Biddell in Borough High Street, closed its doors in 1991. All the buildings have been redeveloped. The area around London Bridge and Borough has become one of the hottest development areas in London as evidenced by the Shard, Europe’s tallest building. The old Hop Exchange has become a general purpose office building.

A magnificent open outcry design

But what a beautiful building. Opened in 1867 and designed by R.H.Moore it is now Grade II listed. When you step inside you can see the vast open atrium and the three tiers of balconies overlooking it. It is designed to allow ‘open outcry’ ; traders on the floor, merchants on the balconies shouting their orders back and forth to each other. Its just like the old stock exchange before it became computerised, or the Royal Exchange where futures were once traded but which is now an upmarket shopping mall. The Lloyds Insurance building has the same “atrium and balcony” design, letting all the brokers hear the stroke of the Lutine bell to inform them of bad news. In the hop exchange, all the balconies bear the crest of Kent – a white horse on a red shield – to remind occupants that this is the trading place for Kentish hops.

I live opposite a oast house and travel to London Bridge every day. The oast house across the road from me has been converted to a spectacular county home. My daily journey encompasses the agricultural history of Kent both at the beginning and end; from an oast with no hops to a hop exchange with no brokers. A palace for a product that no longer exists. There are plenty of brokers getting off the train at London Bridge these days, but they are not broking hops any more but financial products instead.

If you build it, they won’t come

You may be wondering where the catataxis comes in all of this. This tale is not just a personal trip of nostalgia, because there is one more twist to the story: the hop exchange was never full of brokers. The Victorian developers built it in a burst of progressive optimism hoping to capture and consolidate the hop trade inside its walls. But the hop factors and merchants already had their own various premises and saw no reason why they should move. So the hop exchange has only ever been a general office building and not a commodity exchange at all.

The Victorians were keen on making the abstract concrete. Think of the statues of “Trade” or “Progress” that adorn Victorian metropolitan buildings. These are industrial versions of the ancient Greek muses; abstract concepts in female form. The Hop Exchange was an attempt to cast economic activity in architectural form. Sadly, it did not work. This building designed to house speculators was itself a speculative failure. This was a catataxic blunder. Just because a building exists at level 1 does not mean that the trade at level 2 will be captured by it. In this case, the motto is: if you build it, they will not come.

Markets are a bottom up phenomenon; a spontaneous eruption of emergent behaviours. They can not be created top down. Building a building to try capture that magic is a s fruitless as running around trying to capture lightning    in a bottle. That does not stop people from trying. The latest disaster in the making of this type is the King Abdullah Financial District in Riyadh, Saudi Arabia. Some $10bn has been spent building 59 skyscrapers in an attempt too lure international banks into the desert.  These hopes are built on sand.

General McChrystal’s catataxic blunder

General McCrystal's catataxic blunder

General Stanley McChrystal, the most senior military commander in Afghanistan, was summoned to the White House in 2010 and sacked by President Obama following a candid interview in Rolling Stone magazine. What does this demonstrate? Well, one conclusion is all is well. Here is proof that the military is subordinate to politics, just what a healthy democracy needs. Another conclusion is they are both subordinate to the media. This is also probably healthy also.   Journalists got the President sacked in the Watergate scandal. Rolling Stone Magazine are probably very happy though. It’s a triumphal moment for the leading counter cultural monthly to take a general’s scalp.

What did General McChrystal do wrong? Is it really news that a bunch of soldiers when relaxing in a bar bitch about politicians? Is the public really shocked? There has been a scene like that in almost every war movie. It’s so commonplace that it can’t be news. A soldier fighting a war thinks the politicians on the other side of the world are out of touch. That’s such a cliche…

So what did he do wrong? This was a catatactic blunder. It was a level confusion, a breaching of the barrier between the private man and the public role. In this case, the individual is on level one and the public office is the meta-level above it. There is no problem with an individual having those thoughts. There is a problem with the leader of the armed forces disagreeing with the President in public. Rolling Stone is also guilty here. General McChrystal did not call a press conference and announce to the world his misgivings. His aides were making in appropriate jokes getting drunk in a bar in Paris. We have all done that. It was Rolling Stone who took it across the barrier from the private to the public.

You may say it is foolish to air your true feelings when there is a journalist lurking around. Its only a small step from there to believing that public officials should routinely lie to the press. That is not a good result. The real fault lies with us – the reading public – and the need to view the category of ‘public role’ as more important than the human one. Surely this was a case where the context of the comments  was a vitally import qualifying factor. They got ignored as the categorisation process crossed the catataxic boundary between the human level and the public level. 


The Catataxic baguette

Catataxis baguette

One of the great joys of a holiday in France is the early morning trip to the boulangerie, in my case the Ti Ar Bara in Audierne. The baker has been up since 3.00am, working hard for your sybaritic pleasure. And what a true pleasure it is. As that gorgeous smell of freshly baked bread steals into the still morning air, you feel a rushing lift of the spirits. Yes, any day with such a blest beginning will surely bring all manner of  wondrous things later.

Not just ‘your daily bread’

It’s not just the smell of the bread, it’s the glorious range of different things on offer. It is a mark of true civilisation to take a so pedestrian a concept as ‘daily bread’ and turn it into this  transcendent cornucopia of golden joy. There are croissants and pan chocolat, flaky and light as a cherubim’s kiss, the eggy richness of the many different styles of brioche and, here in Brittany, the dense layers of caramelised butter in the kouign amann  and the far breton. But even in the simplest things there is still a riotous diversity.  ‘White bread’ in the Anglosphere is a simile for bland and unimaginative mediocrity. In France, white bread comes in dizzying array of forms; boules, epis, plats and rondes. Even the quintessentially French baguette comes in many different formats. There is the Ficelle, thin as the string it is named after, the shorter Batard, the pointy ended Festive, the double sized Parisienne and the giant Pan Ordinaire, which is not ordinary at all but a massive truncheon of crusty extravagance.

Surface area to volume ratio

Where does the catataxis come in? Well, it’s to do with this variety of forms. Why so many different types of baguette? If you want more bread why not just buy two normal sized ones rather than one big one? Two Ficelles weigh the same as one Batard so in ‘volume of bread’ terms they are identical. But mathematicians know that they are not the same thing at all. This because surface area and volume don’t scale up in the same way. Surface area scales in proportion to the radius but volume scales with the square of the radius. Gourmands know this difference too, but they put it a different way: you get a lot more crust with two Ficelles. A Ficelle is all crust; it’s so thin that there is very little doughy interior. So if you like the crust then get two Ficelles. By the time you get up to the monster Pan Ordinaire there is relatively little crust and a huge expanse of doughy interior. You can easily slice it and put it in a toaster.

This surface area to volume issue is a key factor in catataxis, and one of the main ways that ‘more of the same is different’ when you try to change the scale of something. For another example, consider the reason why no insect is ever bigger than a foot long: its exoskeleton design cannot support the interior  mass at bigger scales.


How Microsoft’s management killed innovation

microsoft logo

Vanity Fair in July 2012 had a great article titled “Microsoft’s lost decade”. It described how the corporate giant lost its way and changed from being an indomitable technology Titan to a has-been. Just as IBM did a decade earlier. The reason? A management technique known as “stack ranking”. Every business unit had to rank a certain percentage of its employees as “top performers”, “average” or “poor” and this effectively crippled the company’s ability to innovate. In contrast, Apple (for decades underdog to Microsoft) generates more revenue with a single product  – the iPhone – than the whole of Microsoft Corp.

“Every current and former Microsoft employee I interviewed—every one—cited stack ranking as the most destructive process inside of Microsoft, something that drove out untold numbers of employees,” Kurt Eichenwald writes in Vanity Fair. “If you were on a team of 10 people, you walked in the first day knowing that, no matter how good everyone was, 2 people were going to get a great review, 7 were going to get mediocre reviews, and 1 was going to get a terrible review,” says a former software developer. “It leads to employees focusing on competing with each other rather than competing with other companies.”

This internal competition vs external competition is a catataxic debate and it lies at the heart of the resurgent interest in group selection theories of evolution. The question is whether the natural selection that drives evolution acts at the level of the group or at a genetic level. If evolution is the “survival of the fittest”, then the question becomes the fittest what? Is it the fittest group? The fittest species ? The fittest individual? The fittest set of genes ? This question about “which level rules” is the essence of catataxis.

In social animals such as ants and termites you can clearly see a form of individual altruism: insects that sacrifice themselves for the good of the colony as a whole. This seems to imply that natural selection is operating at the level of the group. However, Richard Dawkins in his book “The Selfish Gene” pins natural selection definitively to the genetic level. He explains the “self sacrificing ants” in a bottom-up genetic way. The ants in the colony are all related to each other; they share the same genetic material. So in sacrificing yourself for the sake of the group you are still indirectly propagating your genes. This genetic cause of altruism is summed up in Hamilton’s Rule which states that the degree of altruism depends on the degree of genetic relatedness. It can be summed up in this grim biologists joke :

I will lay down my life for two brothers, four nephews or eight cousins

Other biologists such as David Sloane Wilson see a group selection argument for altrusim which goes like this: If you mix a group of selfish people and altruistic people together, then the selfish people will always win. They act in their own self interest and exploit the generous altruists. But if you move up a level and observe the competition between groups then you see a different effect. Groups that are full of altruists working cooperatively together outcompete groups full of selfish people fighting each other. So at a group level teams of altruists win, but at an individual level selfish people win. So, turning this around, you can say that wherever you see altrusitic behaviour then it is a sign that competition between groups is a stronger force than competition inside groups. Or, as Microsoft has found out, when management emphasises internal competition the group as a whole will fail.

This “level of selection” controversy is still a hot topic of debate amongst biologists. In the  June 2012 issue of Prospect Magazine,  Richard Dawkins wrote an excoriating review of a book by fellow biologist Edward Wilson titled “The Social Conquest of Earth”. Wilson was arguing for the theory of group selection outlined above. Dawkins violently disagreed. His review concludes “…this is not a book to be tossed lightly aside. It should be thrown with great force…”. This vigorous denunciation provoked a huge backlash. The Dawkins article received more responses than any other in Prospect Magazine’s history. In effect, it was the atheist equivalent of watching the Pope beat up the Archbishop of Canterbury on the steps of St Paul’s Cathedral.

The debate also provides a controversial conclusion for management consultants. If you want your company (group) to win then you should embrace the cult of mediocrity. Suppress internal competition and focus on external competition.

In fox hunting circles, when the Master of the Hounds is training a new pack, he takes the dogs for their first outing in spring to see how they perform. He then shoots both the first few pack leaders and the last few stragglers, keeping the mediocre middle performers because he knows they will form the most effective team.

Could this translate across to corporate management. Is the secret to commercial success to sack not just your worst salesmen but also your best? Let me know what you think….