*‘What can be avoided*

*Whose end is purposed by the mighty gods? *

*Yet Caesar shall go forth, for these predictions *

*Are to the world in general as to Caesar.’ *

*Julius Caesar, II.2.*

*‘Ideas thus made up of several simple ones put together, I call Complex; such as are Beauty, Gratitude, a Man, an Army, the Universe.’ Locke.*

*‘I can calculate the motion of heavenly bodies but not the madness of people.’ Newton, after the South Sea Bubble ‘Ponzi scheme’. *

*‘Everything in war is very simple, but the simplest thing is difficult. The difficulties accumulate and end by producing a kind of friction that is inconceivable unless one has experienced war… **Countless minor incidents – the kind you can never really foresee – combine to lower the general level of performance, so that one always falls short of the intended goal. Iron will-power can overcome this friction … but of course it wears down the machine as well…** Friction is the only concept that … corresponds to the factors that distinguish real war from war on paper. The … army and everything else related to it is basically very simple and therefore seems easy to manage. But … each part is composed of individuals, every one of whom retains his potential of friction… This tremendous friction … is everywhere in contact with chance, and brings about effects that cannot be measured… Friction … is the force that makes the apparently easy so difficult… Finally … all action takes place … in a kind of twilight, which like fog or moonlight, often tends to make things seem grotesque and larger than they really are. Whatever is hidden from full view in this feeble light has to be guessed at by talent, or simply left to chance.’ Clausewitz.*

*‘It is a wonderful feeling to recognise the unity of complex phenomena that to direct observation appear to be quite separate things.’ Einstein to Grossman, 1901.*

*‘All stable processes we shall predict. All unstable processes we shall control.’ Von Neumann.*

*‘Imagine how much harder physics would be if electrons had feelings.’ Richard Feynman.*

At the beginning of *From Russia With Love *(the movie not the book), Kronsteen, a Russian chess master and SPECTRE strategist, is summoned to Blofeld’s lair to discuss the plot to steal the super-secret ‘Lektor Decoder’ and kill Bond. Kronsteen outlines to Blofeld his plan to trick Bond into stealing the machine for SPECTRE.

Blofeld: Kronsteen, you are sure this plan is foolproof?

Kronsteen: Yes it is, because I have anticipated every possible variation of counter-move.

Political analysis is full of chess metaphors, reflecting an old tradition of seeing games as models of physical and social reality. (‘Time is a child moving counters in a game; the royal power is a child’s’, Heraclitus.) A game which has ten different possible moves at each turn and runs for two turns has 10^{2} possible ways of being played; if it runs for fifty turns it has 10^{50} possible ways of being played, ‘a number which substantially exceeds the number of atoms in the whole of our planet earth’ (Holland); if it runs for ninety turns it has 10^{90} possible ways of being played, which is about the estimated number of atoms in the Universe. Chess is merely 32 pieces on an 8×8 grid with a few simple rules but the number of possible games is much greater than 10^{90}.

Many practical problems (e.g logistics, designing new drugs) are equivalent to the Travelling Salesman Problem (TSP). For any TSP involving travelling to n cities, the number of possible tours when starting with a specific city is: (n-1)!/2. For 33 cities, the total number of possible journeys is:

32!/2 = 131,565,418,466,846,765,083,609,006,080,000,000

The IBM Roadrunner, the fastest supercomputer in the world in 2009, could perform 1,457 trillion operations per second. If we could arrange the tours such that examining each one would take only one arithmetical operation, then it would take it ~28 trillion years to examine all possible routes between 33 cities, about twice the estimated age of the Universe. As *n* grows *linearly* (add one city, add another etc), the number of possible routes grows *exponentially*. The way in which the number of possible options scales up *exponentially* as the number of agents scales up *linearly*, and the difficulty of finding solutions quickly in vast search landscapes, connects to one of the most important questions in maths and computer science, the famous $1 million dollar ‘P=NP?’ Clay Millennium Prize.

*Kronsteen’s confidence, often seen in politics, is therefore misplaced even in chess*. It is far beyond our ability to anticipate ‘every possible variation of counter-move’ yet chess is simple compared to the systems that scientists or politicians have to try to understand and predict in order to try to control. These themes of *uncertainty, nonlinearity, complexity and prediction* have been ubiquitous motifs of art, philosophy, and politics. We see them in Homer, where the gift of an apple causes the Trojan War; in Athenian tragedy, where a chance meeting at a crossroads settles the fate of Oedipus; in *Othello’s* dropped handkerchief; and in *War and Peace *with Nikolai Rostov, playing cards with Dolohov, praying that one little card will turn out differently, save him from ruin, and allow him to go happily home to Natasha.

* ‘I know that men are persuaded to go to war in one frame of mind and act when the time comes in another, and that their resolutions change with the changes of fortune… The movement of events is often as wayward and incomprehensible as the course of human thought; and this is why we ascribe to chance whatever belies our calculation.’ Pericles to the Athenians.*

**Maths and models**

Because of the ‘unreasonable effectiveness of mathematics’ in providing the ‘language of nature’ and foundations for a scientific civilization, we understand some systems very well and can make very precise predictions based on accurate quantitative models. Sometimes a mathematical model predicts phenomena which are later found (e.g. General Relativity’s field equations); sometimes an experiment reveals a phenomenon that awaits an effective mathematical model (e.g. the delay between the discovery of superconductivity and a quantum theory). The work of mathematicians on ‘pure’ problems has often yielded ideas that have waited to be rediscovered by physicists. The work of Euclid, Apollonius and Archimedes on ellipses would be used centuries later by Kepler for his theory of planetary motion. The work of Riemann on non-Euclidean four-dimensional geometry was (thanks to Grossmann) used by Einstein for General Relativity. The work of various people since the 16^{th} Century on complex numbers would be used by Heisenberg *et al* for quantum mechanics in the 1920s.

The work of Cantor, Gödel, and Turing (c. 1860-1936) on the logical foundations of mathematics, perhaps the most abstract and esoteric subject, gave birth to computers. The work of Galois on ‘groups’ (motivated by problems with polynomial equations) would be used post-1945 to build the ‘Standard Model’ of particle physics using ‘symmetry groups’. In a serendipitous 1972 meeting in the Institute of Advanced Study cafeteria, it was discovered that the distribution of prime numbers has a still-mysterious connection with the energy levels of particles. G.H. Hardy famously wrote, in ‘*A Mathematician’s Apology*’ which influenced many future mathematicians, that the field of number theory was happily ‘useless’ and did not contribute to ‘any warlike purpose’; even as he wrote the words, it was secretly being applied to cryptography and it now forms the basis of secure electronic communications among other things. Perhaps another example will be the ‘Langlands Program’ in pure mathematics which was developed in the 1960’s and work on it is now funded by DARPA (the famous military technology developer) in the hope of practical applications.

Mathematicians invent (or discover?) concepts by abstraction and then discover connections between concepts.* Nature operates with universal laws and displays symmetry and regularity as well as irregularity and randomness.

‘What do we mean by “understanding” something? We can imagine that this complicated array of moving things which constitutes “the world” is something like a great chess game being played by the gods, and we are observers of the game. We do not know what the rules of the game are; all we are allowed to do is to watch the playing. Of course, if we watch long enough, we may eventually catch on to a few of the rules. *The rules of the game* are what we mean by *fundamental physics*. Even if we knew every rule, however, we might not be able to understand why a particular move is made in the game, merely because it is too complicated and our minds are limited. If you play chess you must know that it is easy to learn all the rules, and yet it is often very hard to select the best move or to understand why a player moves as he does. So it is in nature, only much more so; but we may be able at least to find all the rules. Actually, we do not have all the rules now. (Every once in a while something like castling is going on that we still do not understand.) Aside from not knowing all of the rules, what we really can explain in terms of those rules is very limited, because almost all situations are so enormously complicated that we cannot follow the plays of the game using the rules, much less tell what is going to happen next. We must, therefore, limit ourselves to the more basic question of the rules of the game. If we know the rules, we consider that we “understand” the world.’ Richard Feynman.

These physical laws, or rules, use mathematicians’ abstractions.**

‘It is an extraordinary feature of science that the most diverse, seemingly unrelated, phenomena can be described with the same mathematical tools. The same quadratic equation with which the ancients drew right angles to build their temples can be used today by a banker to calculate the yield to maturity of a new, two-year bond. The same techniques of calculus developed by Newton and Leibniz two centuries ago to study the orbits of Mars and Mercury can be used today by a civil engineer to calculate the maximum stress on a new bridge… But the variety of natural phenomena is boundless while, despite all appearances to the contrary, the number of really distinct mathematical concepts and tools at our disposal is surprisingly small… When we explore the vast realm of natural and human behavior, we find the most useful tools of measurement and calculation are based on surprisingly few basic ideas.’ Mandelbrot

There is an amazing connection between mathematicians’ aesthetic sense of ‘beauty’ and their success in finding solutions:

‘It is efficient to look for beautiful solutions first and settle for ugly ones only as a last resort… It is a good rule of thumb that the more beautiful the guess, the more likely it is to survive.’ Timothy Gowers.

‘[S]ciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work – that is, correctly to describe phenomena from a reasonably wide area. Furthermore, it must satisfy certain aesthetic criteria – that is, in relation to how much it describes, it must be rather simple… If only relatively little has been explained, one will absolutely insist that it should at least be done by very simple and direct means.’ Von Neumann.

Some of these models allow relatively *precise predictions* about a particular physical system: for example, Newton’s equations for classical mechanics or the equations for ‘quantum electrodynamics’. Sometimes they are *statistical predictions* that do not say how a specific event will turn out but what can be expected over a large number of trials and with what degree of confidence: ‘the epistemological value of probability theory is based on the fact that chance phenomena, considered collectively and on a grand scale, create a non-random regularity’ (Kolmogorov). The use of statistical models has touched many fields: ‘Moneyball’ in baseball (the replacement of scouts’ hunches by statistical prediction), predicting wine vintages and ticket sales, dating, procurement decisions, legal judgements, parole decisions and so on.

For example, many natural (e.g. height, IQ) and social (e.g. polling) phenomena follow the statistical theorem called the Central Limit Theorem (CLT) and produce a ‘normal distribution’, or ‘bell curve’. Fields Medallist Terry Tao describes it:

‘Roughly speaking, this theorem asserts that if one takes a statistic that is a combination of many independent and randomly fluctuating components, with no one component having a decisive influence on the whole, then that statistic will be approximately distributed according to a law called the normal distribution (or Gaussian distribution), and more popularly known as the *bell curve*…

‘The law is universal because it holds regardless of exactly how the individual components fluctuate, or how many components there are (although the accuracy of the law improves when the number of components increases); it can be seen in a staggeringly diverse range of statistics, from the incidence rate of accidents, to the variation of height, weight, or other vital statistics amongst a species, to the financial gains or losses caused by chance, to the velocities of the component particles of a physical system. The size, width, location, and even the units of measurement of the distribution varies from statistic to statistic, but the bell curve shape can be discerned in all cases.

‘This convergence arises not because of any “low-level” or “microscopic” connection between such diverse phenomena as car crashes, human height, trading profits, or stellar velocities, but because in all of these cases the “high-level” or “macroscopic” structure is the same, namely a compound statistic formed from a combination of the small influences of many independent factors. This is the essence of universality: the macroscopic behaviour of a large, complex system can be almost totally independent of its microscopic structure.

‘The universal nature of the central limit theorem is tremendously useful in many industries, allowing them to manage what would otherwise be an intractably complex and chaotic system. With this theorem, insurers can manage the risk of, say, their car insurance policies, without having to know all the complicated details of how car crashes actually occur; astronomers can measure the size and location of distant galaxies, without having to solve the complicated equations of celestial mechanics; electrical engineers can predict the effect of noise and interference on electronic communications, without having to know exactly how this noise was generated; and so forth.’

Many other phenomena (e.g. terrorist attacks, earthquakes, stock market panics) produce a ‘power law’ and trusting to a *CLT model* of a phenomenon when it actually follows a power law causes trouble, as with the recent financial crisis. When examining *phase transitions *of materials (e.g the transition from water to ice), the patterns formed by atoms are almost always *fractals* which appear everywhere from charts of our heartbeats to stock prices to Bach. (Recent work (here) has made breakthroughs in understanding the statistics of phase transitions.)

However, even our best understood mathematical models can quickly become practically overwhelming. Laplace voiced a famous expression of the post-Newton Enlightenment faith in science’s potential to predict.

‘We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all the forces that animate nature, and all positions of the beings that compose it, if this intellect were vast enough to submit the data to analysis, would condense in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes… Present events are connected with preceding ones by a tie based upon the evident principle that a thing cannot occur without a cause that produces it… All events, even those which on account of their insignificance do not seem to follow the great laws of nature, are a result of it just as necessarily as the revolutions of the sun.’ Laplace

Newton himself had warned of the potential complexity of calculating more than two interacting bodies.

‘The orbit of any one planet depends on the combined motions of all the planets, not to mention the action of all these on each other. But to consider simultaneously all these causes of motion and to define these motions by exact laws allowing of convenient calculation exceeds, unless I am mistaken, the force of the human intellect.’

It turned out that Newton’s famous gravitational equation *cannot* be extended to just three bodies without producing ‘*deterministic chaos*’, so although ‘cosmologists can use universal laws of fluid mechanics to describe the motion of entire galaxies, the motion of a single satellite under the influence of just three gravitational bodies can be far more complicated’ (Tao). *Deterministic chaos*, a system which is ‘sensitive to initial conditions’, was first articulated by Poincaré as he struggled to solve the ‘three-body problem’, and broke Laplace’s dream of perfect understanding and prediction:

‘If one seeks to visualize the pattern formed by these two [solution] curves and their infinite number of intersections, . . .[their] intersections form a kind of lattice-work, a weave, a chain-link network of infinitely fine mesh; … One will be struck by the complexity of this figure, which I am not even attempting to draw. Nothing can give us a better idea of the intricacy of the three-body problem, and of all the problems of dynamics in general…

‘A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that that effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation *approximately*. If that enabled us to predict the succeeding situation *with* *the same approximation*, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by laws. But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.’ (Poincaré, *Science and Method*, 1913)

Even with systems displaying chaos because of sensitivity to initial conditions, short-term predictions are not hopeless. The best example is weather – the study of which was actually the prompt for Lorenz’s re-discovery of ‘chaos’. Weather forecasts have improved greatly over the past fifty years. For example, 25 years ago forecasts of where a hurricane would hit land in three days time missed by an average of 350 miles; now they miss by about 100 miles. We have bought ourselves an extra 48 hours to evacuate. Is a weather forecast better than it would be by simply a) looking at historical data (climatology), or b) assuming tomorrow will be similar to today (persistence)? Our forecasts are significantly better until about day 9 when forecasts become no better than looking at historical data.

However, chaos means that beyond the short-term, forecasts rapidly break down and usually greater and greater resources are needed to extend the forecasts even just a little further; for example, there has been a huge increase in computer processing applied to weather forecasts since the 1950’s, just to squeeze an accurate forecast out to Day 9. (Cf. Nate Silver’s ‘*The signal and the noise*‘ for more details.)

‘Even when universal laws do exist, it may still be practically impossible to use them to predict what happens next. For instance, we have universal laws for the motion of fluids, such as the Navier-Stokes equations, and these are certainly used all the time in such tasks as weather prediction, but these equations are so complex and unstable that even with the most powerful computers, we are still unable to accurately predict the weather more than a week or two into the future.’ (Tao)

Between the precision of Newtonian mechanics (with a small number of interacting agents) and the statistics of multi-agent systems (such as thermodynamics and statistical mechanics) ‘there is a substantial middle ground of systems that are too complex for fundamental analysis, but too simple to be universal. Plenty of room, in short, for all the complexities of life as we know it’ (Tao).

**Conclusion**

In England, less than 10 percent per year leave school with formal training in basics such as ‘normal distributions’ and conditional probability. Less than one percent are well educated in the basics of how the ‘unreasonable effectiveness of mathematics’ provides the language of nature and a foundation for our scientific civilisation. Only a small subset of that <1% then study trans-disciplinary issues concerning complex systems. *This number has approximately zero overlap with powerful decision-makers*.

Generally, they are badly (or narrowly) educated and trained. Even elite universities offer courses such as PPE that are thought to prepare future political decision-makers but are clearly inadequate and in some ways damaging, giving people like Cameron and Balls false confidence in 1) the value of their acquired bluffing skills and 2) the scientific basis of modern economics’ forecasts. Powerful decision-makers also usually operate in institutions that have vastly more ambitious formal goals than the dysfunctional management could possibly achieve, and which generally select *for* the worst aspects of chimp politics and *against *those skills seen in rare successful organisations (e.g the ability to *simplify, focus*, and *admit errors*). Most politicians, officials, and advisers operate with fragments of philosophy, little knowledge of maths or science (few MPs can answer even simple probability questions yet most are confident in their judgement), and little experience in well-managed complex organisations. The skills, and approach to problems, of our best mathematicians, scientists, and entrepreneurs are almost totally shut out of vital decisions.

These issues are connected to the failure of political elites to get big decisions right since the 1860s, as I discussed in *The Hollow Men*. In Part II next week, I will discuss some of the issues about how Whitehall works that cause so many problems and what can be done to improve this situation. In Part II of *this* blog, I will explore some more of the science of prediction. But I’d prefer you to look at my essay, from which most of this is taken…

* This happens in social sciences too. E.g. Brouwer’s fixed-point theorem in topology was first applied to ‘equilibrium’ in economics by von Neumann (1930’s), and this approach was copied by Arrow and Debreu in their 1954 paper that laid the foundation for modern ‘general equilibrium theory’ in economics.

** Einstein asked, ‘How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?’ ‘*Is mathematics invented or discovered?*’, Tim Gowers (Polkinghorne, 2011). Hilbert, Cantor and Einstein thought it is invented (formalism). Gödel thought it is discovered (Platonism). For a non-specialist summary of many issues concerning maths and prediction, cf. a talk by Fields Medallist Terry Tao. Wigner answered Einstein in a famous paper, ‘*The Unreasonable Effectiveness of Mathematics in the Natural Sciences*’ (1960).

So much I know I didn’t understand and so much more that I think I might have understood but probably didn’t. Thank you. I think I might have learnt something.

@HuwSayer

@Business_Write

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Thanks. D

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I think an education in ethics and empathy might be of use as well.

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Pingback: On economics not being weather forecasting | Freethinking Economist

As politics, economics and human behaviour is essentially chaotic, then it doesnt matter whether politicians have any mathematical training at all. Maybe being confident and decisive is more important in leading the country than being “right”.

“Prime Minister, should we raise interest rates?”

“Interesting question. Using Bayesian logic, statistical mechanics and matrix algebra I have come to the conclusion that I havent a clue and never will”

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PM’s don’t set interest rates any more precisely because they manipulated them for political interest. Re your broader point… They have to take many decisions about risk. But most MPs cannot answer the question – what is the probability of flipping a head twice in a row. Yet they THINK they do they know. This explains many disasters. I do not think they need to study linear algebra, but some basic conditional probability would be useful. The Fields medallist Tim Gowers is doing a ‘maths for presidents’ course with MEI which will include all the main subjects that PMs should know. Best wishes, Dom.

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The best explanation I’ve seen of the assumptions behind a normal distribution: thanks.

The point about whether, and the extent to which, we can perceive and understand the rules of the game, reminded me of the recent programme by Jim Al-Khalili on information in nature: http://www.bbc.co.uk/programmes/p00zv7n6

A useful reminder (as is this) of the insufficiency of human perception and the need to embrace uncertainty and humility.

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Thx David. I hope the Tim Gowers ‘maths for presidents’ course with MEI will help spread this knowledge to wider audiences… D

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OK Dominic,

Politicians lack the analytical skills to understand what will be the consequences of their actions. Can they then rely on their more educated advisers?

But in your extended essay on education written last year, you identified and considered briefly genetic components being dominant in determining educational success.

The Gove education agenda has been largely indistinguishable from a left wing equality agenda – same exam system for all, pulling up all to the standard of the best, etc, etc, instead of accepting the population as it is and, whilst recognising that modest educational improvements are possible, one does better by tailoring expectation and training to the abilities of the different ability populations. Hence we still impose an academic education on all and import our plumbers from Poland.

DId Gove understand this point that you made?

Good wishes.

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Don’t agree. A Levels gone back to universities. National pay system gone. Blah.. Yes we lost on GCSEs cos Cameron gave in. Nobody is saying ‘pull up all to standard of the best’ – that would be fundamentally impossible/stupid! There’s good evidence for giving the vast majority a mainly academic education to 16. Poland does. There’s no evidence yet about what different level IQ people are capable of with great teachers. There should be say a £10 million DARPA-style Grand Challenge to incentivise people to find out what level of maths can be taught to 100IQ kids by brilliant teachers. Such research would provide v useful data. In meantime, it’s obv best to err on side of high expectations… Best, D

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Hi Dominic again,

There doesn’t seem to be a reply button under your response to my comment and I wonder if you might notice or respond to this follow up.

You mentioned Gove’s great successes. Let’s look at them.

A levels back to the Universities. It’s an interesting point. What good is that likely to do? I was, for fifteen years, a University of London Chief Examiner when the exam boards were controlled by the universities. What stopped this? Tory tinkering in three areas:

1. Increasing spur of the moment imposition of ‘good ideas’ as we have seen under Gove.

2. Tory directives to reduce the number of exam boards.

3. But more than anything else, by Conservative governments failing to leave the universities alone to use A levels for their primary purpose: to select the best students for university and trying to use them to judge the quality of education in schools. This is a total failure. Collectively a school’s exam results judge the quality of a school’s intake, not the quality of teaching.

You mention national pay scales abolished. Fair enough.

You say ‘There is no evidence yet of what IQ different level of IQ people are capable of with great teachers.’ That simply isn’t true. Ofsted observes that the difference between good and bad teachers can be up to half a grade on average at GCSE. That is significant but not overwhealming. Why such a small effect? Because academic achievement is largely determined by heredity and the home.

There is this constant search for the ‘mythical magical teacher’ and the whipping of the teaching body to turn them into these fantasies of education secretaries’ imagination. But in fact schools that are excellent one year are often only average or even below average a few years later because random effects in the population far outweigh the variation achievable by teachers.

You are happy to cite Poland as giving the vast majority of pupils an academic education without even a mention as to demographic effects of the tax and welfare system in this country providing differential incentives to reduce the number of children born by well educated women and encouraged the opposite.

I could make similarly detailed comments about thoughtless fiddling with maths teaching or even to the total chaos caused by purely administrative matters like safeguarding.

Dominic, I challenge you to a debate. Any time, anywhere. That for all its verbosity, the Coalition Government, by failing to understand the primary influences on educational achievement has continued the decline in education demonstrated by its predecessors over the last forty years.

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Thank you Dominic, entertaining, thought provoking and I can’t wait for HM II.

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Thanks. Tomorrow, hopefully. D

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Don’t you think it’s interesting that maths, economics and business have all moved in approximately the same direction in the past 30 years which is (summarised less elegantly than your essay) data chasing, instead of appliance of simple principles (big thinking). Lee Smolin’s book about String Theory was an entertaining exposition of this. Data chasing is a comfortable way to build a big safety net under your ideas (climate science anyone?) but the principles are lost. The Israeli Palestinian conflict is about land – pretty simple – but it can’t be solved because people try to understand it at too complex a level: religion (moving part 1), casualties (moving part 2), global allegiances (moving part 3) = chaos. What is interesting is that this data chasing probably drives the widening (in)equality gap – not because very clever people can earn more but because data chasing presents all sorts of opportunity for arbitrage (see Michael Lewis) and because ‘complexification’ obscures idiocy among people who hold power – why has executive pay risen faster than corporate growth? Why was Steve Jobs on the lowest rung of CEO pay (on a performance basis) according to the Economist? Because if a CEO talked about people, products and creativity, she would be asked to supply her quarterly growth figures or be kicked out. Actually, I think I’m saying that you’re right and wrong. Children do not need to understand Gaussian distribution, they need to understand human nature (WB: “Never invest in a business you do not understand”). You could force them to evidence reading of Daniel Kahneman in their reading books but aren’t you indulging in the error your essay implies: understanding the rules is not the same as understanding the application. (My friend’s mechanic brother always beats me at chess and he didn’t spend 4 years at Cambridge – go figure). Anyway, thanks for the diversion. The corporate world is very dull at times.

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Yes data chasing is obv growing and will keep growing for technological reasons + ££ incentives. Not all kids need to understand Gaussian distrib but it isn’t good to restrict it to <10% of population either. How do you understand financial crisis if you don't understand that many of the models that blew up did so cos the models assumed Gaussian distribution (despite Mandelbrot pointing out decades ago prices don't fit Gaussian distrib but that's another story)? Nobody knows what % of kids are capable of understanding it cos the research hasn't been done. But it's a lot more than 10%. No I don't think it's an error to force people to read DK – not all will learn but then most people who read Sun Tzu and Thucydides don't learn much from it either. That's life / human nature. But it's worth trying to expand the % who can think across subjects, from Sun Tzu to Gauss cos big decisions require 'a crude look at the whole', as Murray Gell Man, namer of the quark, put it… Cheers, D (if you come back!)

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I wouldn’t take IBM’s word for what was the fastest computer, super or otherwise, in any given year, these snippets of hype from their PR folk are always rather biased.

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I didn’t. It was from a computer scientist. D

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re “I didn’t. It was from a computer scientist” what some clown like Liam Maxwell who knows less about computer science than my little finger?

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William J. Cook, professor of combinatorics, University of Waterloo.

I’ve got no reason to think you’re more likely than him to be right but if you are explain why instead of being sarcy.

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To be honest I don’t know off the top of my head, although I could make a few calls and find out. I do however have a lot of experience of IBM claiming credit for things that were fake, or done by others, smoke and mirrors, and so on. I worked on something that they trumpeted as exceptional and a great victory for IBM, the reality was the people who did it had nothing to do with IBM other than that they funded it and we were all under NDA forcing us to keep quiet about the reality, such is the way. I have seen similar claims under the timeline for fastest computers through time, but I can spot mistakes in such articles so treat the rest of them with some cynicism, and of course by their nature the top spec machines are often classified etc, and often the building blocks are not those of the maker who plaster their name allover the cabinet. Recent history like this is full of bias from the PR departments etc. I know more computer science professors than you ever will, and I know a few who know little about the subject too so badly has the title been devalued by some uni’s.

I am not really having a pop at you, just expressing frustration at the misinformation that is common out there, and repeated endlessly lazily.

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Yes I’m sure there’s lots of PR/misinformation. I don’t think here it makes much difference as the point about the practical unsolvability of checking each option stands whether IBM is lying or not. Do you trust the numbers put out twice a year on the ‘top 500 fastest supercomputer’ list or do you assume they are often lies too?

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Re ” Do you trust…”

Not necessarily intentional lies. But these things are not written by the practioners, its regurgitating the output of the PR departments and senior spokespeople. I would no more use this as a reliable source of fact than I would use the accumulated Conservative party press releases as a balanced description of what went on in their periods in government.

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Nothing wrong with “Sarcy” either, its one of the ways ordinary people communicate all the time, rather better than the fake wishy washy communication style of most politicians 🙂

Again not really having a pop at you

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On your point about the background of politicians, there is a lot in what you say. There are other simpler perspectives on the same set of issues. Far too few of our political and journalistic bubble studied science, they are far too dominated by arts grads, PPE and the rest. They are far too much dominated by the same old small social circles, and output from the same small group of schools. These pressures make them much more susceptible to group think, and lack of empathy or understanding for those of other backgrounds.

The Americans did a lot of research into what mix of people make the best submarine crew, a lot of that stuff is relevant to what would make the best ministerial cabinet.

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I agree and discuss exactly this issue in my long essay as well as some of this research. We’re now in a vicious circle in which the people at the apex of power don’t know what they don’t know, spend all their time incompetently chasing the media, and the public plus the media assume the people in charge are far more competent than they are. Yes people are cynical and full of hate but whenever I explain how decisions are really made the same cynics can’t believe it. Ironically, despite the supposed ‘death of deference’ people remain remarkably deferential/ hopeful and find it so uncomfortable to think those in charge are clueless they prefer to think of them as crooks.

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V. interesting.

Now I’ll always be wondering what historical outcomes could’ve been if the decision-making process were governed by Occam’s Razor…

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Good day! I know this is kinda off topic nevertheless I’d

figured I’d ask. Would you be interested in exchanging links or maybe guest authoring a blog article or vice-versa?

My site covers a lot of the same topics as yours and I think we could greatly benefit from each other.

If you happen to be interested feel free to shoot me an e-mail.

I look forward to hearing from you! Fantastic blog by the way!

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