The penny drops

After years of debate, Canada is losing an old friend--the penny.

Excuse me, this is an emotional moment for me.

It looks like they will continue to be legal tender even after they are no longer produced, so it will likely remain illegal to melt the old copper ones down (for Canadians, those would be 1996 and earlier). But it seems we won't be able to go to the bank and get them any more after the fall. I'll need a new hobby.

This is not a story about SNC Lavalin

 . . . even though they have a $56 million mystery on their hands.

If you read John Perkin's book Confessions of an Economic Hitman, he discusses a certain company--shall we call it Blandcorp--which would carry out economic assessments about prospective projects in developing countries--say, a hydroelectric dam--exaggerate the economic benefits of said project, and assist the government of the developing country in applying for international funding for said project. When the benefits of the project prove to be less than anticipated, the government in question is unable to pay its debts. Then the hammer falls--the US pressures on the developing country to support its international agenda, typically through votes at the UN. In this way, many countries were politically neutralized, impoverished, and pushed to the edge of the world stage.

The business model really caught on in the sixties and seventies. There's a coup in Albizia, and Colonel Hardcore takes over. The Colonel could never apply for financing for a sweet hydroelectric plant from the World Bank, but if an internationally recognized engineering firm, with a listing on the New York stock exchange (other exchanges are acceptable as well, but the New York listing is particularly important)--in this case, let's say ABC Julien--opines that a new power plant would be a major boost to the economy and could be built for a mere $2 billion; then funding may flow through to the project "on behalf of the people of Albizia". ABC Julien then builds the plant for $500 million, splits the profit with Colonel Hardcore (most likely by subcontracting a related party to carry out unspecified tasks in country), and the long-suffering people of Albizia are stuck with the debt.

Indeed, this was part of the justification for the debt cancellation proposed by the G8 in 2005. It would be no different than if armed gunmen came to your house, kidnapped you, brought you to your bank, made you sign a $500,000 mortgage, then walked away with the cash leaving you to negotiate repayment terms with your banker. You would be forgiven for being angry with your banker, feeling that she should have seen the situation as it was.

As I said above, this has nothing to do with SNC Lavalin. So stop calling.

Has NATO scored an "own goal" in Mali?

France and other European countries have decried the ongoing coup in Mali.

But is there a connection between the coup and last year's NATO attack on Libya?

The soldiers involved in the coup have stated that their grievances with the sitting government are primarily related to low-level conflict between government forces and an insurgency amongst the Tuareg. The soldiers have complained of being inadequately armed.

The Tuareg are scattered across several countries, the boundaries of which were determined arbitrarily by colonial powers. In this sense, they are like the Kurds--a people rebelling against several countries, hoping to create a nation out of their ancestral lands. The Tuareg do not recognize the artificial boundaries that bind them. They have been a despised and mistreated minority in the different countries of the Sahara. Although a low-level rebellion has been brewing for many years, it was largely mitigated by Algeria and Libya.

The Tuareg had been grateful to Colonel Gaddafi, who had saved thousands of them during a famine in 1973. Many Tuareg took shelter in Libya after conflicts in Mali and Niger, and many served in Gaddafi's forces.

After Gaddafi's fall, heavily armed Tuareg returned to Mali, and the insurgency in northern Mali flared up. Which brings us to today.

Despite the geographical proximity, the only impact I can see the coup having on Ghana is that Ghana may have to send troops as part of an ECOWAS peacekeeping mission.

Constructing an epsilon machine--a worked example, part 1

Started feeling a little under the weather just as the madness of PDAC settled down. Really busy over the past few days.Fell asleep feverish and had this world-transforming idea of an entirely new kind of testable hypothesis. I was convinced that I had something about which papers--no, entire scientific volumes--would be published. Unfortunately when I awoke it was gone, and the parts that I remember (it seemed to involve measuring the girth of everyone who left a particular poster session at which I would present--that and a great deal of cotton stuffing) do not seem promising. But I'll work on it and let you know how it goes.

In the meantime I want to work in more detail on concepts that I have just glossed over--epsilon-machine (which may unfortunately be confused with machine-epsilon--I do wish these researchers would do a search before naming something) reconstruction from paleoclimatic data. I have earlier posted here and here on this topic, and have presented here at GAC a couple of years ago.

We will be working with the ocean condition probability density plots shown here, based on data presented in Raymo et al. (2004) and methodologies described in Gipp (2001) (also here).

Probability density plot. The probability density portrait was computed over the interval 1299 ka to 1029 ka. The two ellipses are preliminary interpretations based on the contours of probability density--I inferred limit cycles in addition to the single LSA labelled O4. The lower limit cycle I have called LC12, and the upper one is LC23.

Now let's add some of the reconstructed phase space portrait.

This is an enlargement of the above plot. The green curve is the reconstructed phase space over the interval 1119 ka to 1059 ka (so 60 000 years). At 1119 ka, the system is in the lower limit cycle--it then moves into the upper limit cycle where it stays until at least 1059 ka. The little yellow blobs represent direct observations (at 3 ky intervals). The green line is a curve fitted through the points, as suggested by Abarbanel (1997). We record this as a transition from LC12 to LC23. Over the entirety of the record--or over a distinct subset--we will see many transitions. These will be counted and enumerated to produce our epsilon machine.

References 

Abarbanel, H. D. I., 1996. Analysis of Observed Chaotic Data, Springer-Verlag, New York.

Crutchfield, J. P., 1994. The calculi of emergence: Computation, dynamics, and induction. Physica D, v. 75, 11-54.

Gipp, M. R., 2001. Interpretation of climate dynamics from phase space portraits: Is the climate system strange or just different? Paleoceanography, v. 16, 335-351.

Raymo, M. E., Oppo, D. W., Flower, B. P., et al., 2004. Stability of North Atlantic water masses in face of pronounced climate variability during the Pleistocene. Paleoceanography, v. 19, 13p.
doi: 10.1029/2003PA000921.

Snapshots of multistability in the climate system

Today the World Complex presents images from the recently redrafted movie of the probability density plot of the proxy record for global ice volume over the past two million years. The reason for the redrafting was to shorten the window, improving the resolution of the individual frames.

The methodology for deriving these plots from original data has been previously described here. The O-18 data used below are from Shackleton et al. (1990). Variations in O-18 in the deep ocean reflect global volumes of glacial ice.

This figure is a map of a ice-volume phase space over the interval 189 ka to 39 ka (ka = thousand years ago). There are three distinct regions of higher probability (grey areas) in phase space, which represent stable global glacial volumes. This figure suggests that over the interval in question, there were three stable global ice configurations--one corresponding roughly to the interglacial condition we have today (at lower left), and two more with considerably more (glacial) ice--and that transitions from one to another happened relatively rapidly. As the probability of any state outside of the three LSAs is low, global climate change was rapid during the interval in question. Glacial ice volumes therefore have three conditions of equilibrium, which are punctuated by brief episodes of rapid change. Using our dynamic interpretations from previous articles, we have inferred three areas of Lyapunov stability in the time delay state space of global ice volume.

The graph only tells us about global ice volume, but not where the ice is. Thus we cannot infer the global glacial configurations for each of the three LSA.

In the 699-519 ka interval (still Late Quaternary) we still see multiple areas of stability. There may be a limit cycle in the low volume section of probability density diagram.

The interval 1509-1359 ka was characterized by a large limit cycle, with a couple of particular regions of higher probability. The high probability peak at lower left represents an area of Lyapunov stability. Limit cycle behaviour in the ice volume system suggests oscillatory growth and decay of ice sheets.

This plot shows a limit cycle and two areas of Lyapunov stability. The lower one, near (3.5, 3.5) is the same as the one in the next figure above. The second area of attraction, near (3.9, 3.9) is present in the figure at representing the interval 1599-1449 ka above.

In general, limit cycle behaviour is more common in the Early Quaternary, and simple LSA multistable behaviour is more common in the Late Quaternary. This observation is reinforced in observations of reconstructed phase space portraits of smoothed C-13 measurements from cibicidoides sp. (Raymo et al., 2004).

The C-13 data is purported to represent oceanographic conditions and are reflective of overall glacial conditions, with lower values corresponding to glacial maxima (Bickert et al., 1997). The phasing of variability in the C-13 differs from that of O-18 at different frequencies and is thought to reflect changes in oceanographic flow at least partially in response to glacial cycles (Raymo et al., 2004).

In the Early Quaternary, the probability density plots of the reconstructed state space mainly suggest limit cycle behaviour. The period of the oscillations is approximately 41 ky.

In the Late Quaternary, the oceanographic state is more suggestive of multiple metastable equilibria, punctuated by brief episodes of rapid change.

Limit cycle behaviour is still observed in some windows in the Late Quaternary . . .

 . . . but multiple equilibria is the predominant state in the Late Quaternary. 

I have recently completed epsilon machine reconstructions for the 13C predictive states (at least the forward-evolving e-machines as described briefly here in the references) and will be posting these shortly.

References

Bickert, T., Curry, W. B., and Wefer, G., 1997. Late Pliocene to Holocene (2.6-0 Ma) western equatorial Atlantic deep-water circulation: Inferences from benthic stable isotopes. In Shackleton, N. J., et al. (eds.), Proceedings of the Ocean Drilling Program, Scientific Results, v. 154: 241-254.

Raymo, M. E., Oppo, D. W., Flower, B. P., et al., 2004. Stability of North Atlantic water masses in face of pronounced climate variability during the Pleistocene. Paleoceanography, v. 19: 13p. doi: 10.1029/2003PA000921.

Shackleton, N. J., A. Berger, and W. R. Peltier, 1990. An alternative astronomical calibration of the Lower Pleistocene timescale based on ODP site 677, Trans. R. Soc. Edinburgh, Earth Sci., 81: 251-261.