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Markonis and Koutsoyiannis

Demetris Koutsoyiannis emails to point me to his new paper. Markonis and Koutsoyiannis (Surveys of Geophysics) takes a look at climate variability over periods spanning nine orders of magnitude.

We overview studies of the natural variability of past climate, as seen from available proxy information, and its attribution to deterministic or stochastic controls. Furthermore, we characterize this variability over the widest possible range of scales that the available information allows, and we try to connect the deterministic Milankovitch cycles with the Hurst–Kolmogorov (HK) stochastic dynamics. To this aim, we analyse two instrumental series of global temperature and eight proxy series with varying lengths from 2 thousand to 500 million years. In our analysis, we use a simple tool, the climacogram, which is the logarithmic plot of standard deviation versus time scale, and its slope can be used to identify the presence of HK dynamics. By superimposing the climacograms of the different series, we obtain an impressive overview of the variability for time scales spanning almost nine orders of magnitude—from 1 month to 50 million years. An overall climacogram slope of −0.08 supports the presence of HK dynamics with Hurst coefficient of at least 0.92. The orbital forcing (Milankovitch cycles) is also evident in the combined climacogram at time scales between 10 and 100 thousand years. While orbital forcing favours predictability at the scales it acts, the overview of climate variability at all scales suggests a big picture of irregular change and uncertainty of Earth’s climate.

There is an interesting link to a discussion at BH here. That conversation ended when Prof Koutsoyiannis told commenters that he was unable to respond to further questions since the answers were contained in a draft paper that he had going through the peer review process at the time:

As per the “opportunity” to discuss the scientific part, I am afraid it must wait some time. We have produced some results related to your questions, but I do not wish to discuss them before we have them officially published. In this case the peer review may take some months or years, considering the necessary rejections.

This paper is the result. The discussion thread dates back a year, so you can see that the peer review process has been at least that long. The paper was rejected by Geophysical Research Letters and Nature Geoscience (the peer review comments are available here) although as DK notes in the discussion thread, those of his papers rejected by mainstream climate journals tend to be the ones most cited after finding a home in some less "plugged" publication.

(Hurst Kolmogorov dynamics are explained here)

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Reader Comments (33)

Haven't really digested this yet, but note that at last the dramatic climate variability well known from the full Phanerozoic geological record is taken into account at last. More detail and diagrams are up on a new WUWT thread here:-

Nov 5, 2012 at 11:10 PM | Registered CommenterPharos


The paper was rejected by Geophysical Research Letters and Nature Geoscience (the peer review comments are available here) although as DK notes in the discussion thread, those of his papers rejected by mainstream climate journals tend to be the ones most cited after finding a home in some less "plugged" publication.

And it's notable that comment was made in reply to BBD, who had been extremely active and voluble on that Discussion thread, on which Demetris Koutsoyiannis used his real name (as I take it he usually does) - without which such testimony would have been far less convincing. This shows that very important and insightful things can emerge in response to nyms behaving badly but depend on one or more people not using a nym. And that in itself doesn't tell the moderators of a blog like this how to deal with all ills. But I thought it worth mentioning, to provoke thought.

Nov 5, 2012 at 11:22 PM | Unregistered CommenterRichard Drake

Of all the people on BH I am the least qualified to comment on this plus I am a big fan of Doug Keenan who wrote the piece on HK dynamics. Doug writes that the HK idea is that the temperature of the last century has an effect on the temperature this century; I can not accept that logic at all.
I might to some extent be able to accept that the temperature of the last century was evidence of the impact of 'an external or internal forcing' but not that the temperature itself could in any way BE the forcing.
The temperature of the last century has no impact on solar irradiance, solar wind, ambient cosmic ray strength, volcanic activity, meteor/asteroid strikes, magnetic reversal of the poles (both of the earth and the Sun). All of these things affect the temperature of this century.
Perhaps some hyper intelligent person can let me down gently?

Nov 5, 2012 at 11:36 PM | Unregistered CommenterDung

Dung - my simple understanding is, if, at any instant, you've got a mug of tea in your hands out in the garden and there is a chill wind blowing, the wind is a variable forcing and yet the temperature of the tea in the next instant will still depend on the temperature it was in the previous instant. So an 85degC cuppa can cool to 84degC but a 65degC cuppa cannot.

Nov 6, 2012 at 12:37 AM | Unregistered Commenternot banned yet

How bizarre - I read Dung's comment and immediately thought of a cup-of-tea analogy, then someone got there before me!

Nov 6, 2012 at 12:49 AM | Unregistered Commentersteveta

From the pre-history reviewer comments file; it sure looks like the climate insider-pal anti-outsider abuse network is still in full swing. The responses to the reviewers questions by the authors were very measured, brief and comprehensive.

Forward the paper!

Nov 6, 2012 at 2:09 AM | Unregistered CommenterATheoK

I don't know if Koutsoyiannis has speculated on mechanisms, but for the sake of plausibility one possible mechanism is deep ocean mixing.

Transfer of heat downwards is slow, and gets slower the deeper you go. So if you step up the temperature for a year, it can only penetrate to a limited depth before things change. But if you hold the temperature there for a century, the effect can go a bit deeper, and if you hold it high for a millenium, deeper still. Then the temperature of the lower layers affects the rates at which net heat can transfer to or from the levels above.

Fast changes like day/night and summer/winter can only affect the surface layers - there's no time for it to penetrate far before it's winter/summer again. And so there's not much heat going into or coming out of the deep reservoir to affect things, and you don't notice it. But longer-term changes like the PDO, sustained for 30 years or longer, can build up. The process is slow, but cumulative. And like a random walk, arbitrarily large excursions can occur if you wait long enough.

That's pure speculation on my part. It might instead be changes in currents and convective circulation in the deep oceans, it might be the same sort of thing only with the deep ocean reservoir of dissolved gases, it might be biological, with warmth encouraging the rise of climate-affecting species that then take a long time to disappear (like in the CLAW hypothesis), or, for all we know, the same sort of deep hydrological processes only occuring on the sun. Dunno.

Nov 6, 2012 at 5:27 AM | Unregistered CommenterNullius in Verba

"There is an interesting link to a discussion at BH here"

Those were the days! I remember Spence pointing out round about that time that he'd spent 5 years or so trying and failing to persuade mainstream climate scientists to respond to the arguments of DK and the many other scientists investigating this area. The reason for this failure appears to be that the mainstream doesn't have a convincing response. Or at least ignoring is bliss, if AR4 is anything to go by - no references at all to the important 21st century papers in this area by DK and co-workers, Huybers and Curry, Wunsch, Ashkenazy, Lovejoy, Schertzer and presumably etc. Good to see this paper at last anyway.

Nov 6, 2012 at 6:27 AM | Registered CommenterPhilip Richens

Nullius in Verba: the CLAW hypothesis was only partially right because Sagan's aerosol optical physics is wrong. The real effect of aerosols is to reduce cloud droplet coarsening kinetics, reducing cloud albedo. In other words, more phytoplankton means warming and vice versa. Also this accounts for the real AGW via Asian industrialisation, self-limiting so switched off when the 'Asian Brown Cloud' appeared in 1999. There may be a CO2 effect but limited to dry desert regions!

Nov 6, 2012 at 8:02 AM | Unregistered CommenterAlecM

How does temperature of a previous century govern the temperature of the next, explain the Bronze Age Warm Period, the Roman Warm Period, the Medieval Warm Period, the Little Ice Age, the Modern Warm Period? In what way does this have an effect especially from warm to cool phases? No, it is far more likely that Solar output variations, whether in TSI, UV & Extreme UV, GCR, or any combination of these, coupled with internal response variations of the climate system, the amplitude of which is still completely unknown by modern science, despite £M puter models funded by huge wads of taxpayers dosh! Natural variation can only be ruled out by invoking the "Precautionary Principle", the bane of much modern day life. Milankovitch Cycles can largely (but not fully) explain the Ice Ages over the last 1.2M years or so, but not for short term changes! If one looks at the temperature plots for Inter-Glacials they all seem to look rather similar by peaking at the start, then gradually cooling with warming blips here & there, just as ths current Inter-Glacial appear to be doing! Upshot? We're probably screwed but at least the Malthusian Neo Fuedalists/Socialists will be delighted!

Nov 6, 2012 at 11:08 AM | Unregistered CommenterAlan the Brit

Nov 5, 2012 at 11:36 PM | Dung

Hi Dung,

I think you're right to criticise the statement that earlier temperature directly effects current temperature. It is possibly better to say that there is long-term variability that is unforced by any external effect (meaning everything on your list plus any human impacts). NiV @ 5:27 AM gave a beautifully clear explanation of a plausible physical mechanism by which such variability might occur. In general, it would occur due to small wandering changes in the way energy is distributed and/or albedo or emissivity.

However, the mainstream view has it that such unforced variability does not occur to any appreciable extent, at least not over time scales longer than a few decades. If they are right, then there must be a definite true preferred state of the modern climate (the "natural balance"), which is disrupted by external forcing. However, I've not seen any good physical arguments to support the existence of such a state and I don’t think it is very likely (in other words I agree with DK's conclusions).

Nov 6, 2012 at 11:09 AM | Registered CommenterPhilip Richens

That was a fun thread back there. It is good to see that the paper has gone through the "necessary rejections" and come out on the other side. It is also enlightening to see the non-substantive reasons given by reviewers for *rejection* of a paper. Since lots of climate change science merely depends on 'interpretative framework' jostling and haggling, looking at DK's reviewer comments makes it amply clear how reviewers can use the fact they don't agree with a paper as grounds for its non-appearance into the public domain.

Nov 6, 2012 at 12:13 PM | Registered Commentershub

The question about what physical mechanisms could induce century-to-century correlation was raised on the other thread. I posted a brief comment addressing this question there.

Nov 6, 2012 at 2:03 PM | Unregistered CommenterDouglas J. Keenan

You wrote:
"as DK notes in the discussion thread, those of his [DK's] papers rejected by mainstream climate journals tend to be the ones most cited after finding a home in some less "plugged" publication."

That seems to be a common finding:

Nov 6, 2012 at 3:05 PM | Unregistered CommenterBrent Buckner

not banned yet

you wrote:

Dung - my simple understanding is, if, at any instant, you've got a mug of tea in your hands out in the garden and there is a chill wind blowing, the wind is a variable forcing and yet the temperature of the tea in the next instant will still depend on the temperature it was in the previous instant. So an 85degC cuppa can cool to 84degC but a 65degC cuppa cannot.

I think this is a poor analogy ^.^
Being British I am allowed to invoke British weather: you've got a mug of tea in your hands out in the garden, there is a sudden and violent hailstorm and your mug of tea (which is left in the garden as you rush for cover) suddenly has a temperature approachng zero.

Because the external forcing is so strong, the original state of the mug of tea very quickly ceases to have any relevance.

Nov 6, 2012 at 4:25 PM | Registered CommenterDung

The only thing that this idea says to me is that in general, the forcings acting on the climate are small and not large. However the end result is still dependent on the forcings and not the original state

Nov 6, 2012 at 4:28 PM | Registered CommenterDung


In your last post Nov 6, 2012 at 2:03 PM | Unregistered CommenterDouglas J. Keenan; you talk about correlation which is absolutely fine with me but in your original post in 2011 you quote Koutsoyiannis as follows:

“The temperature of Earth this year affects the temperature of Earth the next year; for example, if this year is cold, then the next year will probably be colder than average”.

This is not correlation.

Nov 6, 2012 at 6:41 PM | Registered CommenterDung

dung - whatever.

Nov 6, 2012 at 9:07 PM | Unregistered Commenternot banned yet

I would like to thank Andrew Montford for the post and you all for the comments. This is very encouraging, especially after the two rejections from Nature Geosciences and GRL.

I see that the discussion is focused on the possible physical mechanisms that could induce short or long memory correlations, just like in Koutsoyiannis 2011. This thread is very enlightening, and I would like only to add something about the role of external forcing.

A quick literature review [both in CGM- or stochastic-oriented works] shows that we are far from clarifying the actual impact of external forcing to the climate system at different time scales. For example, an enormous volcanic eruption, which could be the analogue for the hailstorm and the cup of tea in Dung’s comment, could be amplified or dulled by what we “vaguely” call internal system variability.

In my humble opinion, we do not know that not only because we do not know the exact initial conditions of our system and their links to the forcing components, but also because we are in the dark about the actual “momentum” of our system. This “momentum” is the outcome of the fluctuations [both due to external forcing and internal physical mechanisms] at different time scales, and deep ocean mixing or solar forcing could are indeed two of its components. Therefore, Earth's climate may change in a progressive way when you may expect an abrupt transition and vice-versa.

Nov 7, 2012 at 9:31 AM | Unregistered CommenterYannis Markonis

@ dung Nov 6, 2012 at 6:41 PM

If X is a time series, then {X(i)} can be correlated with {X(i+1)}. Such a correlation (called an “autocorrelation”) is fundamental in time series, and is treated in all introductory texts.

Nov 7, 2012 at 4:31 PM | Unregistered CommenterDouglas J. Keenan

Statistics is a "language" used to analyse and describe data but it is not capable of describing why data changes. A normal distribution curve of human intelligence tells you what the highs and lows are and how many people are at each level but it does not tell you why one person is far more intelligent than another. Relying on statistics alone to describe a range of data is not enough.
The statement was made that the temperature in one century "affects" the temperature in the next century. I have said that I can not accept this which matters not one jot. The statement that the temperature in one century is likely to be similar to the temperature in the next century is fine.
The temperature in both centuries though is purely a function of forcings:the sun, ocean currents, ocean heat, cosmic rays and a number of other forcings, take away the sun and the temp heads smartly in the direction of -273.16 deg C regardless of the last century.

Nov 7, 2012 at 9:08 PM | Registered CommenterDung

Dung: who is relying on statistics alone?

The Itia group have published a number of articles providing a physical basis for Hurst-Kolmogorov dynamics (indeed, naming it after Kolmogorov underpins the physical basis of this behaviour)

You refer to temperature being a function of the forcings - but what is the function, and what are the limits of predictability of that function? That is the purpose of researching HK dynamics.

Nov 7, 2012 at 10:21 PM | Unregistered CommenterSpence_UK

Dunf...and if your mug of tea is the size of the Pacific Ocean, would that give you pause to thought? How long would that mug tke to cool?

Nov 7, 2012 at 10:35 PM | Unregistered Commenterdiogenes


My objection is to the word "affects"
Studying how temperature varies from minute to minute or century to century is fine but dont tell me that the actual temperature on one day or in one century "affects" future temperature. If you study how temperature changes you are studying the effect of the forcings (even though you do not know what all the forcings are). You can not predict what you do not understand, that is one of the reasons that CAGW is junk. Trying to find a statistical relationship based on how temperature changed in the past and then use that to bypass the fact that you dont understand all the forcings and thus predict the future is not credible.

Dunf to Diofenes

If my mug of tea had been the size of the pacific ocean I would never have got it into the garden ^.^

Nov 7, 2012 at 10:54 PM | Registered CommenterDung

Dung, I agree that the word "affects" is not really ideal, but then your characterisation is also not really correct either, since the climate is (most likely) not a Markov process and cannot be represented as a system that is independent of prior states.

Although in this I am assuming the sun will continue to generate energy at largely the same rate it has done for the last many millions of years, at least for the next century or so. :)

Nov 7, 2012 at 11:41 PM | Unregistered CommenterSpence_UK


You have effectively just stated that our climate depends upon the sun, therefore it does not depend upon the climate 100 years ago since that climate also depended upon the sun. The climate tomorrow is totally independent of the climate today, the fact that it will probably be the same or similar does not prove dependence. There are known possible catastrophic events which could dramatically change the climate, therefore for the climate to be the same tomorrow as it is today depends on those forcings NOT interfering.

Nov 8, 2012 at 12:54 AM | Registered CommenterDung

The natural ongoing temperature at any location in the universe is -273.16 deg C. For any location in the universe to have any other temperature has to be the result of external forcing. The new temperature of such a location has no connection to -273.16 deg C and is purely a function of whatever external forcing changed its temperature. Should the external forcing remain unchanged for long periods of time then the new temperature will remain unchanged but at any point in time the temperature is not "affected" or "caused" by the temperature at a point in time immediately preceding the current point in time, but totally on the continued existence of the external forcing.

Nov 8, 2012 at 1:16 AM | Registered CommenterDung

You have effectively just stated that our climate depends upon the sun, therefore it does not depend upon the climate 100 years ago since that climate also depended upon the sun.

I most certainly did not "effectively" say that. You are very confused here.

Why do you think these things are mutually exclusive? Why do you think it must depend on one thing or the other, rather than some (complex) combination of both?

The natural ongoing temperature at any location in the universe is -273.16 deg C.

No; the background temperature at any location in the universe is circa -270 deg C, about 3 deg C above absolute zero, due to residual radiation from the big bang. However, the earth would remain warmer than that, due to heating by radioactive decay internally to the planet.

Nov 8, 2012 at 8:28 AM | Unregistered CommenterSpence_UK

Dung, on re-reading your posts I think I am starting to understand what you are saying. I may now go on a long, rambling explanation of where I am coming from and why we are talking about different things. Please feel free to fall asleep at any point during this post :)

Your view is that the equilibrium temperature of a body can be determined from (effectively) the radiating sources illuminating it. Or, another way of putting it, the future temperature can be determined by knowing its current temperature and the steady state radiation impinging on it, which you refer to as "forcings". This is indeed true. But not entirely useful for predictions.

Let me consider the temperature of my local area today. This is a function of a number of factors, including the current local temperature, the insolation, etc. etc. One of my favourite examples to give in this calculation is the level of cloud cover. Clouds have a very large effect on local temperature; they block incoming solar radiation during the day, making the day cooler, and reflect outgoing temperature at night, making the night warmer. I need to know the extent of cloud cover to calculate the "forcings" and calculate my temperature.

But what about tomorrow's temperature? Well, from your perspective, I need to know what my forcings are tomorrow to calculate tomorrow's temperature. So I need information such as: will the sun be shining, will it be cloudy. Unfortunately, by your analysis, I won't know this information until tomorrow, so my prediction will be available after the event has happened. That isn't a terribly useful prediction, and it is certainly not the most useful prediction we can make - even if we don't have supercomputers and a perfect knowledge of deterministic physics (and I am sure we don't have the latter).

OK, so let us put ourselves in the shoes of a 19th century farmer. He wants to know what the temperature might be tomorrow, but he has no computer. But he can still make useful predictions of the future.

The probability that the sun is still generating energy in the same place tomorrow I would say is arbitrarily close to 1. I would confirm this prediction on this blog tomorrow, but I suspect if the sun goes out this blog may not be up tomorrow, so it would be a self-fulfilling prophecy. Our farmer doesn't understand the physics of the sun as well as I do, but he can draw from experience. He knows every day the sun has been present, and he estimates the probability that the sun will not have disappeared as being 100% based on his own historical experience.

As discussed, to improve his estimate, he needs to know cloud cover, since this is probably the second most important factor in predicting temperature after the position of the sun. This is more difficult as it is far more variable. Let us assume the underlying probability of it being cloudy where our farmer lives is 30%. This is the population probability. Our farmer cannot know this, but he has kept a tally of cloudy/non cloudy days in a journal, and uses this to estimate the probability of cloudy days. His journal says that 32 days out of 100 are cloudy, so he uses this as his estimate. He then makes a prediction, that there is a 32% chance it will be cloudy tomorrow with some resultant temperature, but a 68% chance it will be clear, with some different temperature. This is his naive baseline prediction; and it has some merit, without having to wait until tomorrow to know what the "forcings" are.

But this naive prediction assumes that the cloud cover tomorrow is independent of the cloud cover today. It is correct, but naive, because if he looks in his log, he will note that the probability of cloud cover is dependent on the cloud cover the previous day. Let us assume that the population probability of a cloudy day following another cloudy day is 42%. The farmer can estimate this by looking at the cloudy day log in his journal. He cannot know the population probability, but the journal gives him a sample probability, an imperfect estimate of the population probability, which is, lets say, 41%. If it has been cloudy today, he can revise his estimate of the temperature tomorrow - which is still a probabilistic estimate, but a more accurate one. His probabilistic estimate is more useful to him in planning tomorrow than either his naive estimate, and far more useful than no estimate at all by simply saying we have to wait until tomorrow to know what tomorrow's temperature will be.

If we fast forward to the 21st century, we now know that the farmer's insight had merit. We understand that cloudiness is a function of atmospheric dynamics, and we can use satellite observations of the atmospheric state, supercomputers and numerical models to deterministically predict cloudiness, and this tells us that a cloudy day is more likely to follow another cloudy day, than a clear day. We can predict this forward reliably perhaps to 3-4 days; at 2-3 weeks out, our deterministic predictions are once again no better than the farmer's predictions.

The farmer could have chosen to say, we cannot know what the weather will be tomorrow until tomorrow comes. But, in fact, his observations are correct, and we can get a useful prediction of tomorrow's temperature without knowing all of the "forcings" upfront. And the reason for this correlation between cloudy days is itself a function of the dynamics of the earth weather/climate system. This is also an important insight. Atmospheric dynamics results in correlations between the cloudiness from day to day, something the farmer was able to observe even with a simple journal.

Now the Itia group have taken the farmers analysis a stage further. The climacogram shows us that not only is cloudiness (as one example) correlated from one day to the next (that is, todays cloudiness is a better predictor of tomorrow's cloudiness than a naive baseline), but also that this weeks cloudiness is a better predictor of next week's cloudiness than a naive baseline; that last month's cloudiness is a better predictor of next month's cloudiness than a naive baseline; that last year's cloudiness is a better predictor of next year's cloudiness than a naive baseline, that last decade's cloudiness is a better predictor than next decade's cloudiness than a naive baseline, that last century's cloudiness is a better predictor of next century's cloudiness than a naive basline, and so on, and so on.

The farmer's neighbours may have mocked him for using the statistics in his journal to predict the following days cloudiness, as he did not know the underlying physics. But in fact the farmer was correct in his insights, and the reason the insights are correct are imprinted on the dynamics of the system, which we now know.

Likewise, we may dismiss the analysis conducted by Yannis and Demetris as being just statistical arm-waving and not providing deep insights into climate. But in fact, I would argue they are unravelling invariant properties in the dynamics of the climate system, which not only offer useful and valuable insights into the earth's climate, but is most likely the only game in town when it comes to the limits and utility of climate prediction.

Nov 8, 2012 at 10:25 AM | Unregistered CommenterSpence_UK


I too believe I begin to see some communication problems here but I am not sure it changes my opinion yet.
Would it have been a more accurate description of the proposal by HG to say "Knowledge of the climate in the last century will "affect" "any attempt to predict" the climate (instead of "affect" the climate) in the next century? I would accept that statement but I would then say that it is pointless trying to predict how climate will change in the future because we do not understand enough about the factors which affect it.
To me it does not matter how you dress it up or what you call a new system for modelling climate; its accuracy will be no better than the worlds most complete climate models running on the world's most powerful computers which can not predict tomorrow's weather.

Nov 8, 2012 at 3:08 PM | Registered CommenterDung

Dung - you've lost me there - proposal by HG - who is HG? Have I missed something?

I agree that affect gives the impression of direct causation which might be confusing. I would prefer to say that the temperature for two periods have a common related cause through the dynamics of the system - but that is wordy. The conventional name for HK dynamics - "long term persistence" or "long term memory" - comes from viewing the dynamics in the context of autoregressive time series, which is slightly misleading as well. Demetris uses a nice turn of phrase where he says that HK dynamics is much more a result of amnesia than of memory. (Essentially, the time series "forgets" where it is supposed to be). This is really caused by an interaction between the population mean and the (local) sample mean, which do not converge at increasing scale as is expected for systems with "short term memory". The sample mean spends extended time away from the population mean, at all scales.

The consequences are often quite counter-intuitive, difficult to describe, and it takes a bit of work to get up to speed with what it all means.

Nov 8, 2012 at 10:29 PM | Unregistered CommenterSpence_UK

Dung, our education is largely based on scientific and philosophical views of the 19th century (dominated by determinism) and it took me a long time to escape that. In my current view, probability (including statistics) is the only effective “language” to describe this world. In addition to Spence’s excellent explanations, and in addition to Doug’s post linked above, I wish to suggest a few relevant readings:

A random walk on water ( ): It tries to discuss why “the true logic for this world is the calculus of probabilities” (quoting Maxwell—amazingly the quotation is from 1850).

Causality in climate and hydrology ( ): Related to the previous one—also discussed in

Two-dimensional Hurst-Kolmogorov process and its application to rainfall fields ( ): If we mentally substitute space for time and view a time series like a cross section on a landscape, we may become less reluctant to accept the HK concept. Everybody accepts mountains and valleys as real and natural (see Fig. 1).

Nov 9, 2012 at 7:53 AM | Unregistered CommenterDemetris Koutsoyiannis


I've read some of the articles you link to before, but perhaps without fully taking in the bigger picture.

From time to time I have wondered about the inadequacies of education in the UK. One of the conclusions I reached was that are certain styles of thinking that people should be able to adopt (and that children should be taught). "Think like a scientist", "think like an economist" and "think like a statistician" were particular examples of styles of thinking that I think are rather distinct.

Perhaps our ideas are along the same lines.

Nov 9, 2012 at 10:48 AM | Registered CommenterBishop Hill

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