Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Sunday, February 27, 2011

Image of Musson and Passat off Newfoundland

As related here, the ships Passat and Musson were research vessels used by the Soviet Union to find suitable locations for hiding nuclear submarines on the Atlantic margin of North America.


Musson about to enter St. John's harbour in late June, 1986. The main thing
I remember is that they refused to allow the harbour pilot aboard.


Stern view of the Passat in St. John's harbour in early June 1986.

Tuesday, February 22, 2011

The World Complex gets mail

We recently received the following:


From :Dr.Kola Martins
Abidjan, Cote  d' Ivoire.
West Africa
 
Dear Sir,

Permit me to intruduce my good self,my name is Dr.Kola Martins . I work
with the Bank of Africa Abidjan, Cote D'IVoire as an accountant Foreign operation department. In the discharge of my duty on this domiciliary  account that has remained dormant for three years now with Four Million  Eight Hundred Thousand US Dollars ($4.8M) in it.

I  have made all the enquiries and discovered that the account holder  died in Auto-crash without leaving no next of kin to the fund deposit.  I am writing you so that I can work with you to remit the fund  into  your account as the next of kin / beneficiary to the fund.

It is simple process which will take a short while to process. outside  this, the bank management will confiscate the money if there is no one  that comes for the fund as you will be acting as the appointed  beneficiary to the fund of which the depositor deposited the fund in  the suspence account and a Foreign Partner is his next of kin which he  did not indicated.

If I hear from you, I will tell you all you need to Know about the fund  deposit for us to procced with the transaction.

Also provide me your direct telephone to reach you.

Thanks and God bless you.
Dr.Kola Martins

Always wanting to be of help, we replied with the following:

I am sorry. I cannot help you. But I recently received this entreaty in the mail. Perhaps the two of you can work together.

DEAR SIR,

CONFIDENTIAL BUSINESS PROPOSAL

I AM PRESIDENT OF A FORMERLY WEALTHY NATION.

HAVING CONSULTED WITH MY COLLEAGUES AND BASED ON THE INFORMATION GATHERED FROM THE US CHAMBERS OF COMMERCE AND INDUSTRY, I HAVE THE PRIVILEGE TO REQUEST FOR YOUR ASSISTANCE TO TRANSFER THE SUM OF $47,500,000.00 (FORTY SEVEN MILLION, FIVE HUNDRED THOUSAND UNITED STATES DOLLARS) INTO YOUR ACCOUNTS. THE ABOVE SUM RESULTED FROM AN OVER-INVOICED BAILOUT, EXECUTED COMMISSIONED AND PAID FOR BY THE US TAXPAYERS. THIS ACTION WAS HOWEVER INTENTIONAL AND SINCE THEN THE FUND HAS BEEN IN A SUSPENSE ACCOUNT AT THE FEDERAL RESERVE BANK OF NEW YORK.

WE ARE NOW READY TO TRANSFER THE FUND OVERSEAS AND THAT IS WHERE YOU COME IN. IT IS IMPORTANT TO INFORM YOU THAT AS CIVIL SERVANTS, WE ARE FORBIDDEN TO OPERATE A FOREIGN ACCOUNT; THAT IS WHY WE REQUIRE YOUR ASSISTANCE. THE TOTAL SUM WILL BE SHARED AS FOLLOWS: 70% FOR US, 25% FOR YOU AND 5% FOR LOCAL AND INTERNATIONAL EXPENSES INCIDENT TO THE TRANSFER.

THE TRANSFER IS RISK FREE ON BOTH SIDES. I AM THE PRESIDENT OF THE UNITED STATES OF AMERICA. IF YOU FIND THIS PROPOSAL ACCEPTABLE, WE SHALL REQUIRE THE FOLLOWING DOCUMENTS:

(A) YOUR BANK'S NAME, TELEPHONE, ACCOUNT AND FAX NUMBERS.

(B) YOUR PRIVATE TELEPHONE AND FAX NUMBERS -- FOR CONFIDENTIALITY AND EASY COMMUNICATION.

(C) YOUR LETTER-HEADED PAPER STAMPED AND SIGNED.

ALTERNATIVELY WE WILL FURNISH YOU WITH THE TEXT OF WHAT TO TYPE INTO YOUR LETTER-HEADED PAPER, ALONG WITH A BREAKDOWN EXPLAINING, COMPREHENSIVELY WHAT WE REQUIRE OF YOU. THE BUSINESS WILL TAKE US THIRTY (30) WORKING DAYS TO ACCOMPLISH.

PLEASE REPLY URGENTLY.

BEST REGARDS

BARACK OBAMA 
president@whitehouse.gov

Saturday, February 19, 2011

Recent price action in Detour Gold

An update on the state space for the price of Detour Gold Corp. When we last checked, the price was confined to a Lyapunov-stable area centred around $30.

Over the past two months we have seen a price correction in Detour Gold (disclosure--long position), followed by a return to the $32 level.

The two-dimensional state space shows the correction as a minor excursion towards LSA23.


The system has returned to LSA30.

Manipulation is failing all around the world

It is human nature to seek the truth, provided that there is an incentive for doing so.

The essence of manipulation, therefore, is to provide the incentive for not seeking the truth--more, for actually believing the lie.

The manipulation all around us is in this form. It is commonly viewed that CPI and unemployment numbers are manipulated, but they are generally accepted so long as people can afford to eat. It is only when a sufficient number of North Americans cannot afford to live as they have that these methodologies will be called into question.

There are many who feel the prices of gold, silver, oil, and other commodities are or have been manipulated.

Manipulation is overcome when the extra costs of the distortions caused by the manipulation exceed the perceived costs of righting them. Righting manipulation begins with communication and information. And in the days of the internet, the costs of communication--as well as the costs of research--have fallen sharply--so much so that the costs of righting manipulation are being seen to have fallen.

That is why manipulation--of the economy, politics--is beginning to fail around the world.

Foisting a dictatorship on people is a form of manipulation. It works until the people realize the cost of overthrowing the dictatorship is lower than enduring it. In the days when one would have to print and hand out leaflets or put up posters, the costs of information distribution (the actual printing, the time taken to distribute them, and the risks of arrest from either posting information or from government moles in the required distribution network) were prohibitively high. In the age of cellphones, email, facebook, and twitter, the physical costs, the time, and the risks are all greatly reduced. Furthermore, interested individuals now have the ability to cheaply search for information about previously arcane topics. In the past you might have had to go to the library (which might have been monitored) or gone off in search of books to buy.

Now, if the message is compelling, the information is free.

In any society, there are a huge number of interconnections between people. The cohesive web has so much redundancy that even if the majority of the links are cut, the information still propogates.

When communication is free, the network of connected individuals can plan and act. Whether that planning involves filling public squares with protesters, or buying futures contracts in silver and pledging to take delivery, the ability to find like-minded individuals is cheaper than it has ever been.


Individuals can learn about silver contracts much more easily now than in the past. They can find a broker much more easily than they could in the past. Thirty years ago the Hunt brothers had to fly to Iran and Saudi Arabia to find partners for their silver purchases. Today all they would need is a facebook page.

A second factor is the complexity of the world. When you are manipulating one system, you only have to concentrate on that alone. But if you are manipulating multiple systems, the distortions created by one system have the potential to undo another. For instance, the collapsing dictatorships in Tunisia and Egypt, both US clients,have been driven by the rise in food prices, which has been caused in part by the diversion of corn to make the ethanol required in US gasoline.

Rising food prices is also influenced by US inflationary policies.

Rising food prices increases the costs of enduring the manipulation. That, combined with the fall in the price of communication, has sparked the riots (last week, in 88 places!).

Wednesday, February 16, 2011

More Hands in the Till

Whenever an industry becomes more profitable, it sends a signal to governments to start looting.

Now comes word that Obama's new budget proposes a 5% royalty on gross proceeds of mining (which sounds to me like the equivalent of a net smelter return, or NSR).

True, 5% doesn't sound like much. When you develop a project which is later taken over by a larger outfit, you normally keep your share of the project in the form of an NSR--the reason being that if you maintain a percentage of the profit, the operator would never actually make one (for the same sorts of reasons that movies never make profits).

As a quick rule of thumb, every 10% interest you have in a project is converted into a 1% NSR.

A 5% NSR is what you would give to a partner who owned half of the project. So this proposed royalty is the equivalent of the government siezing 50% ownership of all qualifying hard rock mines in the US.

If this goes forward, it just may have an impact on the share prices of certain American exploration and mining companies.

Monday, February 14, 2011

Atlantis found and lost again

The internet is abuzz over what some claim to be the discovery of Atlantis, just off the west coast of Africa. This happens to be practically in my backyard.

Let's examine the evidence.



The overview map above comes from Google Earth, showing a region of the Atlantic Ocean west of Northwest Africa. The red boxes are my construction and show the location of the three images shown below. Image A is alleged to be Atlantis. The other two images show features which have not been commented upon by the discoverers of Atlantis.


Image A. The area shows the transition from the area dominated by ridge/shear structures associated with the mid-Atlantic ridge (to the west of this image) to the area where such features have been blanketed by sediments. Apart from a few seamounts, the eastern half of this area is relatively featureless--except for that impressive looking series of orthogonal "roads" near the middle of the image.

The simple story is that these "roads" are an artifact of the process by which Google compiled (and then presented) existing data to create their interactive map of the earth. Google doesn't (yet) have marine vessels surveying the oceans, so it must rely on existing data. There are two principal data types--blanket satellite coverage of the oceans, where gravitational anomalies measured over long intervals are used to infer seafloor topography, and depth soundings by marine survey ships.

The satellite altimetry, produces very low resolution images. Features normally have to be spectacular in order to have enough of a gravitational effect to be teased out from ocean surface data (subtracting out the effects of waves and tides). The resolution obtained by a ship survey is easily an order of magnitude more detailed.

Now suppose you have an area of seafloor which is covered by relatively small hills and valleys--features which are too small to be resolved by the satellite image. These small features are easily detected by a surveying ship.


Here is part of a seismic profile collected many years ago using NSRFC's V-fin (neither of which exist anymore). This shows the seafloor as well as layers of sediment below the seafloor. The v-shaped notches in the seafloor are pockmarks, which are formed by methane gas escaping from beneath the seafloor, and the two largest pockmarks in this image are no more than 10 m deep. They are considerably wider, as this image has a vertical exaggeration of about 20x. (I would have used this image in my MSc thesis, but it is not close to hand at this writing, so I don't have the exact numbers).

The point is that a surveying vessel is capable of resolving an object that may be 10 m high and a few hundred metres across, whereas the satellite gravimeter needs an object to have kilometre scale.

Google does not present contoured data. What they do is create a model, which is then illuminated, and the sense of topography is created by the resulting shadows.

If a large area that is only covered by low-resolution satellite data, and which appears to be featureless is traversed by a survey line which resolves many small features--and then that data is all illuminated by some computer program, then what you will see is a featureless plain traversed by a single dark line. That line is too thin for you to resolve any of the features it shows you, but the artificially generated shadows will trace out the track of the ship.

Now let's look at some other areas of the seafloor.


Here is area B. Notice the "road" emanating from the seamount just east of centre to another seamount just beyond the northern limit of the image. Another set of "roadways" cover the western portion of the image. Those ancients sure were busy.


Area C shows a major highway stretching from Portugal towards Atlantis. Another "road" swings to the north.

The northern Atlantic Ocean isn't the only place covered by roads. Let's take a look at southern Africa.



There are a lot of roads leading to Cape Town. I don't know what was there, but it seems to have been of some importance.


Here is a patch of the Indian Ocean, covering a mid-ocean ridge between India and Sudan. Note the high relief, but there are lines of higher-resolution surveys which show up against the lower-resolution background satellite data.

Marine surveys have two common forms. The accidental surveys, like in the image immediately above, occur when ships leave their equipment running as they leave port. You end up with a lot of lines emanating from a major port. The other common form is an orthogonal grid.


Sad to say, the above looks like a survey. If I had to guess, I would suggest an ODP site survey.


Here is a different survey. If memory serves, this is John Hughes Clarke's SEAMARC survey.


More "roads" on the Nova Scotia continental slope. I actually helped make some of these, and there were no Atlanteans on the boat with me.


Besides, I thought Atlantis looked like this.

More on the Japanese discovery here.

Sunday, February 13, 2011

Crying over spilled milk and other stories

Partially in response to the BP oil spill of last year, the EPA is apparently instituting rules to treat milk spills, as milk also contains oils.

The mission to make everyone safe no matter what the cost is back on track.

Here at the World Complex we believe in being prepared. Although the current rules are proposed for American farmers only, it is only a matter of time before the rules are extended to other countries and to households, where most milk spills actually occur.

Therefore we have acquired a Dedicated Omnivorous Guardian (DOG) to clean up household milk spills. The DOG practically begs to carry out his duties.


- - - - - - - - - - - - - - - - - - - - - - -

Elsewhere, the EPA has recently decided that perhaps there is too much fluoride in drinking water.

I smell a government admission of guilt coming on. Maybe the US government will have to pay a settlement to Americans.

The World Complex humbly  proposes a democratic, across-the-board settlement of $10,000 per person for all US citizens.

In order to pay for this (the US deficit being too large as it is), we humbly propose a $11,000 head tax on all US citizens (the extra being used to cover the costs of administering the program). It will be painful, but imagine how delightful it will be to receive the above settlement!

Saturday, February 12, 2011

Scale invariance in geological phenomena: Size frequency distributions and self-organization

Size-frequency distribution of geologic features

The size-frequency distribution of geologic phenomena is closely related to scale invariance. In particular, we recognize that small objects are more common than large objects. What is less intuitively obvious is that there is frequently a very specific relationship between the number of small objects and the number of large objects.

The number of objects of a certain size tends to fall within a log-normal distribution. If you were to graph the count of, say, faults greater than a certain size on one axis against size on the other, and if this graph were a log-log graph, the plot would be a straight line.

Furthermore, the slope of that line could be used to characterize the population of the phenomena in question, being described sometimes as a measure of the fractal dimension of the system.

It is easy to imagine applying this to a real scenario.

The above is a photo of a channelized debris flow in the Yakataga Formation exposed on Middleton Island, in the Gulf of Alaska. A close look at the make up of the debris flow would reveal sediments in a continous gradation from cobble-sized fragments down to clay. If you counted the particles, you would expect to find a great many more clay-sized fragments than cobble-sized fragments.


Idealized 1/f distribution expected for grain sizes.

Flicker noise (also known as 1/f distribution) is held to be the dominant scaling law for geologic phenomena and is a marker of scale invariance. It is observed in borehole logs (Bean, 1999), fractures (Walsh et al., 1991), ocean temperature distributions through time (Fraedrich et al., 2004), avalanches,  forest fires, earthquakes, extinctions, and many other phenomena (Turcotte, 1999).

Sediment grain-size distributions

For several decades there has been an argument about the nature of sediment grain-size distributions in real deposits. One school of thought (let's call them the statistical school) held that sediment grain sizes should be log-normally distributed, and could therefore be expressed in terms of a mean and a standard deviation agains a logarithmic size scale (below right).

Log-normal data distribution.

As outlined in Limpert et al. (2001), there are many natural processes which are believed to yield log-normal size distributions. My opinion is that the normal (or log-normal) concept is overdone because of the nature of introductory statistical education. For many who have had a rudimentary introduction to statistics, all distributions are normal (or log normal), possibly with some modification to the tails.

The alternative approach (following Bagnold, 1941) held that there are two competing processes responsible for sediment deposition--the transport to the area of interest and the transport of material away from the area of interest. Each of these processes could have its own relationship between probability and grain-size, so the size-distribution of the particles actually deposited could be asymmetric.

The log-hyperbolic distribution is named because the distribution 
has the form of an hyperbola when plotted on a log-log graph. 
The distribution is described by four parameters. Phi and gamma
describe the slopes of the two asymptotes, which reflect the likelihood
that any particle will be carried to the area of interest (gamma) and the 
likelihood that any particle will be removed from the area of interest (phi).
The other two parameters (delta and pi) are reflections of how closely 
each limb of the hyperbola follows its asymptote.

As an aside, returns on investment portfolios are usually described by normal distributions. However, it is frequently recognized that the tails of the distribution are "fatter" than should be the case (meaning that extremely large annual gains and losses are more common than expected). Possibly these distributions should be hyperbolic instead of normal. Indeed, Nassim Taleb's (2007) black swan events may fall into this category.


The log-normal distribution traces a parabola in a log-log plot. It is described by 
two parameters: mu (the mean) and sigma (the standard deviation). The weights of
the tails in the log-hyperbolic distribution will be greater than those of the log-normal
distribution, to a typical investor's regret.

At the present time it would appear that those that believe grain-size distributions are log-hyperbolic hold the upper hand. The support that exists for log-normal descriptions stems from the fact that they are more easily described.

Time distribution and self-organized criticality

Bak et al. (1987) studied a model for the growth of a sandpile by dropping individual grains of sand over a two-dimensional grid. Under a prescribed circumstance, the addition of a grain of sand would cause an avalanche, whereby one grain would cascade one gridpoint to the west (say) and another to the north (say).

This was an improvement over the typical 2-dimensional model where the grains of sand were dropped along a line. In the 2-d model, the result is very simple--the pile of sand grows until the slope everywhere reaches the angle of repose, after which every subsequent grain of sand cascades down the side and off the pile. Not very interesting.

Bak et al. (1987) considered that the 3-d sandpile might behave in an analogous fashion to the 2-d model. The sandpile would grow until the slopes reached a critical threshold, after which a single grain of sand would cause a massive avalanche. The trouble with this notion is that it did not seem logical--that a system would spontaneously evolve to a point of maximum instability.

In carrying out the experiment, they discovered that instead of having a long period of no avalanches followed by a massive avalanche; there was a actually a continuous stream of avalanches of varying sizes. The size distribution of the avalanches had a 1/f distribution in time as well as in space.


The 1/f distribution of events through time had been noted previously, but not as a general phenomenon. The Gutenberg-Richter law describing the size distribution of earthquakes is an example of 1/f noise, but this law was never treated as anything but an empirical law applicable only to earthquakes.

One significant application for flicker noise in geological phenomena is in the field of risk management. Written history over much of North America is only a few hundred years, which is not nearly enough to establish the pattern for earthquakes with a recurrence interval of, say, a thousand years. And yet knowing the size of the thousand-year earthquake may be significant.

If you are building a nuclear power plant with an expected lifespan of fifty years, then there is a 1 in 20 chance that a thousand-year earthquake will strike during its operational life. It seems prudent to design the reactor to withstand this earthquake. We establish the size of this earthquake by charting the size-frequency distribution of the earthquakes we do observe, which will have mostly been small. We can extrapolate our line of best-fit to the thousand-year recurrence-interval point on the graph and calculate with reasonable confidence the moment magnitude of the earthquake with a thousand-year recurrence interval, which will be somewhat larger than any of the earthquakes we have observed to date.

The concept of self-organized criticality has been applied to economic systems (notably stock market crashes by Sornette, 2003).

References

Bagnold, R. A., 1941. The physics of blown sand. Methuen, London.

Bak, P., Tang, C., and Wiesenfield, K., 1987. Self-organized criticality: An explanation of 1/f noise. Physical Review Letters, 59: 381-384.

Bean, C. J., 1996. On the cause of 1/f-power spectral scaling in borehole sonic logs. Geophysical Research Letters, 23: 3119-3122.

Limpert, E., Stahel, W. A., and Abbt, M., 2001. Log-normal distributions across the sciences: keys and cues. Bioscience, 5: 341-352.

Sornette, D., 2003. Why stock markets crash: critical events in complex financial systems. Princeton University Press, Princeton.

Taleb, N. N., 2007. The Black Swan: The impact of the highly improbable. Random House, New York.

Turcotte, D. L., 1999. Self-organized criticality.Reports on Progress in Physics, 62: 1377-1429.

Walsh, J., Watterson, J., and Yielding, G., 1991. The importance of small-scale faulting in regional extension. Nature, 351: 391-393.

Thursday, February 10, 2011

Fear of Democracy

Israel has long boasted of being the only democracy in the Middle East. Now they have come out and spoken about their opposition to democracy in other Middle Eastern countries.

From the referenced article:

'Deputy Premier Silvan Shalom said attempts at promotion of democracy in Egypt could strengthen what he called radical elements in the country, said Israeli website The Marker, a subdivision of the Ha'aretz newspaper.

'He asserted, “We know that, recently in the Middle East, democratic elections have caused the accession to power of radicals like Hamas in the Gaza Strip and Hezbollah in Lebanon.”

'The resistance movements, who owe their presence in the defense and political arenas to popular consensus, have invariably defended the Palestinians and Lebanese against deadly Israeli invasions.

'“Think of what would happen if the radicals become dominant over Egypt and decide to close the Suez Canal,” he said.'


That's the problem with democracy.

Think of what would happen if radicals became dominant over Israel. They might invade Lebanon or Gaza.

Wait--that already happened.

- - - - - - - - - - - - - - - -

Meanwhile in Canada, Stephen Harper seems a little reluctant to push for Mubarak's retirement.

But then he knows a thing or two about clinging to power.


Harper keeps a close eye on events in Egypt. He doesn't like seeing the hobbits in revolt.

Gold-silver ratio--breakout or the same old thing?

In another article about the gold-silver ratio, Adrian Douglas states that he believes silver has broken free of its long-term relationship with gold. The crux of the argument appears in the diagram below.


The above is a 2-dimensional phase space for the gold-silver price system. The upper trend line shows the relationship between gold and silver prior to the 2008 commodity price collapse. The lower trend line shows the relationship between gold and silver since the commodity price collapse.

In the past few months, the silver price has rallied impressively (red ellipse), but is too soon to tell whether silver is breaking out or returning to the pre-price-collapse trend.

Sunday, February 6, 2011

Contrasts in the dynamics of climate subsystems across the Mid-Pleistocene boundary

I have completed the last of the five annexes for the revised Paleoceanography paper. Of course I am having some difficulty with the most telling comment from the editors, that is the significance, if any, of the conclusions drawn from the analysis. As a result, I may submit it to a more methods-based journal.

The most significant conclusion is the nature of dynamic change in all climate subsystems from the Early Quaternary to the Late Quaternary. All of the early Quaternary systems studied in this article show both limit cycles and Lyapunov-stable areas in their reconstructed phase space plots; whereas in the Late Quaternary we only observe Lyapunov-stable areas in the same plots.

It is possible to argue a topological similarity between the limit cycles and the LSAs, but their relation in phase space strongly implies different dynamics. Furthermore, the limit cycles are observed only in the Early Quaternary, where all records show a dominance by the 41 thousand year periodicity, whereas only LSAs are observed in the sections of the records dominated by 100-ky periodicity. The boundary between these two time periods is referred to as the Mid-Pleistocene transition (or by some authors, "revolution") and in the figures below is represented by the red box from about 1150 ka to 550 ka (by "ka" we mean thousands of years ago).

Ocean circulation (d13C data)




Probability density plots of the 2-D phase space of d13C data from 
Raymo et al. (2004) for the Early Quaternary (above), 
Mid Quaternary (middle) and Late Quaternary (bottom).

The d13C data refers to changes in the isotopic composition of 13C in the shells of microorganisms, which reflects variations in bottom water carbon chemistry; itself a reflection of global oceanic circulation. The record used in the figures above is from ODP sites 980 and 981, at a depth of about 2100 m. In the Raymo et al. (2004) paper, the differences in 13C between the Early and Late Quaternary were described in terms of cycle lengths (41 thousand-year cycles in the Early Quaternary vs. 100 thousand-year cycles in the Late Quaternary) and the apparent lack of variability between glacial and interglacial times in the Early Quaternary.

The PDP plots above show one other significant change--that of ocean dynamics. The change in dynamics between the Early and Late Quaternary is reflected in the change in geometry of the greatest probability density. The toroids we see in the Early and Mid Quaternary are reflective of stable cyclical behaviour. Those disappear in the Late Quaternary.

The regions of high probability in the Late Quaternary represent LSAs, and the presence of three distinct LSAs points to the existence of three separate metastable states. Distinctive metastable states in the context of oceanic circulation points to sudden changes in the organization of global circulation patterns, and this is an interpretation that has been proposed previously for the Late Quaternary (e.g., Broecker, 2000). Cyclicity in the 13C data is more difficult to interpret--it may be due to a series of gradual changes in the relative strengths of different currents over a period of time. Such gradual changes in oceanic circulation may be difficult to infer on the basis of one-dimensional data set projections.

Global ice volume


Probability density plots of the 2-D phase space of d18O data from 
Huybers (2007) for the Early Quaternary (above), 
Mid Quaternary (middle) and Late Quaternary (bottom).

The deep-sea d18O data measure variations in deep water chemistry, specifically the variation in isotopic composition of seawater caused by the growth and decay of large (isotopically light) continental ice sheets. They are thus a proxy for global ice volume.

As noted for the oceanic circulation proxy, probability density plots of the 2-d phase space for the ice volume proxy show toroidal forms suggestive of limit cycle behaviour. There are no apparent toroids in either the Mid- or Late Quaternary. In the Late Pleistocene, we see four distinct probability peaks, each of which represents a stable ice volume.

In the early Quaternary, ice volume changed slowly, gradually, and in a repetitive fashion. By the mid- to Late Quaternary, ice volume changes occurred in the form of rapid, non-repetitive "jumps" from one volume to another as noted previously.

References:

Broecker, W., 2000. Was a change in thermohaline circulation responsible for the Little Ice Age? Proceedings of the National Academy of Sciences 97(4): 1339–1342.

Huybers, P., 2007. Glacial variability over the last two million years: an extended depth-derived agemodel, continuous obliquity pacing, and the Pleistocene progression. Quaternary Science Reviews, 26: 37-55. 

Raymo, M. E., Oppo, D. W., Flower, B. P., Hodell, D. A., McManus, J. F., Venz, K. A., Kleiven, K. F., and McIntyre, K., 2004. Stability of North Atlantic water masses in face of pronounced climate variability during the Pleistocene. Paleoceanography, 19, PA2008, doi:10.1029/2003PA000921.

How Revolution Starts

Below is the subtitled appeal for Egyptians to go to Tahrir Square on January 25.




That such a large change can be initiated from such a small trigger suggests the system was perched on the edge of chaos.

Complex systems frequently exist in such a state. Any arbitrarily large change can avalanche through the system from an arbitrarily small trigger, although the probability of any event is inversely related to its size.

But the modern situation is different--because unlike an avalanche, all of the "grains of sand" are connected via social networks and have grown increasingly unhappy with their economic/political situations--all of which increases the likelihood of further such political avalanches throughout the world.

Friday, February 4, 2011