Reconstructed phase space portraits and charting

It's been awhile since we last checked in on Detour Gold Corp. (disclosure: long).

Over the past seven months, we have seen some nice price action, with a major rise in the early summer.

The two-d reconstructed phase portrait using the time-delay method with a lag of three days (as last time).

In our last installment on this stock the price was rising more or less monotonically. Now we see that what happened was a distinctive shift from one range (at lower left) to a higher price area, where the price has been bouncing around for awhile.

Looking at the two LSAs above, one represents a price range in the $21-25 range, and the second is $27-33. Should it fall out of this range, we would presume it could fall back into the other.

We can see a connection between the price chart and the reconstructed phase space portrait. It is clear that what we call confinement to a Lyapunov-stable area (and use as an indicator of at least temporary stability) . . .

 

 . . . may be perceived by the chartists as "trading within a range".

 

(Those diagonal lines aren't intended to be there--they magically appeared during the conversion of the above chart from excel to corel to jpg). 

If we look at the higher of the two Lyapunov-stable areas (LSA30), we see that different parts of it are occupied at different times.

 

Detail of LSA30 by month.

In particular, the regions of phase space centered at about $30 and at about $31.50 are visited at least three times, and several of those visits are characterized by small loops in the phase space portrait, suggesting quasi-stability. On the price chart above, those regions correspond with what chartists would call support and resistance. 

The phase space portraits of complex systems are often characterized by areas of high probability density, which are sometimes (if they have the correct characteristics) called attractors, but may more commonly be referred to as Lyapunov-stable areas (LSA). An LSA is an area in phase space where the state of the system tends to remain assuming there are no dramatic changes in the dynamics of the system. We would normally interpret such an area as evidence for a metastable state in that region of phase space.

If the state space of the system normally occupies an area below the range of values represented within the LSA, then the upper and outer limit of values will appear (on a one-dimensional chart) to be resistance--and chartists frequently describe such phenomena as the price "bouncing" off resistance.

If the state space of the system is occupying the region above the LSA, the chartists will term the lower boundary of the LSA to be "support".

If support is broken, it means the system has left the LSA, and is moving towards another one, presumably at a lower price. The chartist will say that support has failed, and will look back along the chart for the next region of support, which will have been the lowest value of the next lower LSA. If the price has broken down through an all-time low, then there is no telling how low the price will go.

If resistance is broken, the price may move towards the next higher LSA if one is present. If so, the highest value within the LSA will be seen by the chartist as "the next area of resistance". If the price has broken to a new all time high, then we are probably all in the dark.

A New Invention.

Everyone here at the World Complex is thrilled about our latest invention--peanut butter and banana oatmeal!

Steampunk sidescan sonar

Over the past couple of years I have been using a home sidescan sonar system to map portions of the continental shelf of Ghana.

Sidescan sonar uses sound to produce images that are analogous to aerial photographs of the seafloor. The images need to be interpreted and if you have the right technology you can stitch the images into a large mosaic which makes producing a map much easier.

Conventional systems run in the $40 thousand to $120 thousand range, but it is possible to make systems yourself for much less.

The system requires an electronics package which consists of a signal generator/receiver (typically a piezoelectric transducer) attached to a towfish, which is towed behind the vessel as it plows through the waves.

I have been using a Humminbird 1197c fishfinder, the transducer of which I have attached to a homemade towfish in order to add stability. The Humminbird is designed to run mounted on the transom, which is fine for small inland lakes and still waters, but is not suitable for marine operations.

The towfish is a 3" ABS pipe with wooden fins, held on by copper strapping. The transducer is the small black object on the bottom at the end of the coiled black cable. The fish is towed by a rope which is attached at a towpoint on the top near the front (we don't tow it by the electronics cable, although that is done on commercial systems). The rebar wired onto the front is to provide weight at the front and forces the fish down to a depth where the upward force of the rope balances the weight.

The copper strapping gives it a nice Victorian look. The screws were all hand-tapped, just like in the 19th century.

Old-time marine sonar, 1875. Image from Physics Today (don't recall the issue).

The system is being a little like a laser pointer that flashes in a series of straight lines across the seafloor, making one measurement in each instant, and later reconstructing all of the images into a coherent image. Now if your laser pointer is attached to a ship which is pitching and rolling all over, then instead of tracing out parallel lines on the seafloor, the laser pointer is going to illuminate the seafloor more or less randomly and the resulting image won't make sense.

The towed fish will tend to be more stable. At depth the wave amplitude is smaller and the data are less noisy.

Here is what the seafloor looks like illuminated by sonar.

For this image, the "colour" is related to acoustic reflectivity. Harder substances appear lighter in this image, so the dark background material is relatively soft silt. The sand bodies have dunes (the ripples). The image is about 90 m from left to right. Shoreline is to the right.

This image shows bedrock exposed at the seafloor. On the left side, the bedrock has been covered by fine sediments. The blocky structure within the bedrock reflects foliation in the bedrock (metasediments and metavolcanics). The bedrock surface is very rough with high (up to 2 m) peaks of bedrock, with acoustic shadows visible behind them.

Joining the images is very difficult with this system, but there is one advantage. The system is cheap and robust enough to use in the surf zone. I know of no commercial system with this feature.

African Economics 2: Private vs. public transit

The traffic in Accra (Ghana) is incredible. A major problem is that the road network is inefficient as all traffic moving from one neighbourhood to another must pass through a single road. I had at one time believed this to be deliberate, so that in the event of a coup, traffic can be controlled from a few chokepoints.

But locals assure me that the reason is much simpler--the original plan was to have more of a grid network of roads, but after the maps were drawn up, the local chiefs sold the land needed for the extra roads. Once sold, the lands were developed, and as Ghana has no rules for expropriation, the roads could not be built.

The result is heavy traffic.

The cure is a transit system. But what kind?

Because of my experiences growing up in Toronto, it seemed unimaginable to me that a transit system could be run by any entity outside of government.

Then I saw the trotros running in Ghana.

Anyone with a minivan is free to start a service. Simply drive anywhere where there is a line of people,  suggest a destination, and see how many try to board.

People waiting at the local trotro stop at Dansoman.

At any major intersection there are one or more large areas assigned to transfering trotros. Additionally, there are known stops along major arterials and even on narrow back streets.

No one planned the location of these transfer points. They arose from the self-interested actions of the various market participants. The one near Mallam Junction is, admittedly, a little hard on traffic.

Trotro loading on Indepedence Ave.

The most interesting thing about the trotro system is its complete lack of central planning. It has arisen "organically" simply by the actions of self-interested participants. Nevertheless, it is a superior system to the parallel state transit system which tries to do the same thing.

State transit--like most buses, nearly empty.

When I saw all the state transit buses running empty I asked whether it cost more to ride the bus than the trotro. But Ghanaians have told me that the price of the bus is competitive. So the bus is empty presumably because it is not as convenient as the trotro. My contacts tell me that the system is fairly heavily subsidized, yet still doesn't compete against the humble trotro.

The main problem with the state transit system is that it is unable to respond to sudden changes in demand. The exact routes and the number of buses on each route is determined by bureaucrats who have no stake in the actual quality of the system--worse, the system reinforces bad decisions because the bureaucracy does not want to be seen to have made an error. So if empty buses shuttle back and forth along one route all day, while elsewhere thousands stand waiting for a bus that never comes, there is no incentive to change the system.

Waiting for a bus at the main bus station, Opera Square, Accra (also used as a car park).

In the privately run system, any trotro driver who sees nobody waiting to go on his normal route can change at will. Indeed, there is an incentive to do so, as it increases immediate cash flow. 

I was involved in a debate with a couple of our local contractors about transit a few weeks ago. Our naval architect was of the opinion that the private system was superior to any public system that could be developed, whereas our Ghanaian geologist was certain that a government-run system was the modern way to go. He seemed a little ashamed of the trotros.

I found his faith in government particularly disturbing, considering he was from a tribe that was displaced from its homeland by a singular government project.

Trotros at Kaneshie.

A couple of weeks ago, as we left SCC junction on the road towards Kokrobitie, I saw a very large line of people waiting for the trotro. For just a moment I had the urge to tell the driver to pull over, shout out "Bortianor!" and open the back of the truck. The driver assured me we would fill the truck, but on reflection I decided it probably wouldn't be wise. A western company has to worry about liabilities, unlike the local trotro drivers (at least they don't have to worry about them as much).

An interesting property dispute

In north Kaneshie (a suburb of Accra) there is an ongoing property dispute which has now reached some kind of impasse.

 

One man has built a house. Another has built a wall through the house.

We are all eager to see the result of the pending court action.

Why the Canadian political landscape seems so familiar.

It's like a movie.

High in his tower, Prime Minister Stephen Harper searches endlessly for the 

source of ultimate power--the Majority Government of DOOM.

Two stories come to mind. The Senate, now stacked by Conservative appointees, quashed a piece of legislation without debate. Now it is true that the Senate is supposed to act as a brake on the House of Commons, but it should appear that there is an intellectual process involved, not simply the actions of mindless undead.

Recent Tory appointments to the Senate killing the climate bill.

And now the PM has decided to extend Canadian presence in Afghanistan a few more years. Why bother with debate over such a trivial matter? One would hope that the Opposition would have more to say.

Michael Ignatieff and his personal manager prepare for another campaign. 

"A vote for me is a vote for against for against Mordor!"

Talk about "loyal opposition".

Ignatieff consults the Magic 8-ball for yet another important policy decision.

Of course there are those that seek to return Canada to a state of democratic grace.

"Of course I pledge to help destroy the One Ring. My preciousssss!"

Voting Bloc is not an option for most of us in Canada (outside of Quebec). I would equate them with dwarves, working on their things and not bothering much with the rest of us.

The Green Party is the party of hobbits.

"Go hobbits! Longbottom, er, leaf for all!"

The trouble with hobbits is that they aren't renowned for their strength.

No problem. I hear four hobbits are on their way to help.

But in the end all politicians are the same.

The majority government is mine!!!!

Next election--whenever it is--destroy the Ring. Destroy power. Don't vote.

Some thoughts on NI 43-101

In mining work, dishonesty can have obvious rewards. Some of the scandals that occurred in the fairly recent past—Bre-X, Golden Rule, have led to an increasingly onerous set of regulations on reporting.

Some standardization in the rules of reporting mineral exploration results is a welcome step and the agencies which initiated these steps should be congratulated for their attempt to bring clarity to the market.

Nevertheless, it is important that while bringing clarity we don't make the entire system opaque. One problem with the NI 43-101 setup is in the review of reports. Many of the reviewers do not have expertise in geology--in fact, they are lawyers and accountants, and they expect the document to read like a legal acounting document. This places a burden on the poor geologist writing the report, and favours instead larger geological consulting companies who have legal and accounting staff to vet reports prior to submission.

It is a truism that when the major players in an industry feel threatened by smaller upstarts, the most certain way to overcome such competition is through enacting industry standards.

Additionally, geology is not like most of the other "hard" sciences. There is, of necessity, a great deal of interpretation of observations. Simply reporting observations is only part of the science--the interpretation is the key area. Much of this interpretation follows from previous experience. Consequently, it is common for geologists to make a key interpretation about a project on the basis of previous experience. But this is not something that translates easily into an accounting or legal document.

Two geologists may make the same observations about a project and arrive at different conclusions. This is a reflection of the nature of geology, and is not something that is helped by needless quantification. 

The rules of reporting on mineral properties make it very difficult for a geologist to express certain reasoned opinions which have arisen from interpretations of observations in light of past experiences. This means that a great deal of the value that a geologist can bring to a property is no longer reportable, and the exploration progress on a property must be reduced to the reporting of a series of dry numbers. The flavour is lost.

Consider this--in 1897, the Ashanti Mine began production. It was financed by the issuance of shares, at 100 pounds apiece, on the London Stock Market. How was it promoted? The founders of the company simply reported that they had visited the site in Ghana, and that the valley was full of artisanal miners recovering gold from rich seams within the bedrock.

Early this year I wrote an NI 43-101 report on a property in Sierra Leone--a report which is still bouncing back and forth between myself, the company in question, and Canadian securities regulators. One of the earlier issues, since resolved, was my contention that the number and extent of artisanal mining operations on the property meant that it would be reasonable to assume some chance of successfully exploring the property for gold.

The securities regulators took exception to that conclusion. I had no specific numerical measurements of the gold recovered by the miners. There were no numbers to report. So the observation had to be withdrawn, or at least, very heavily discounted.

Were the Ashanti Mine property being explored for the first time today, it is highly doubtful that it could be brought into production. The actual structure of the gold shoots are like long, thing, curving cylinders that plunge steeply near the surface, and gradually level out at depth. The gold-bearing zones of the shoots are only a few m in diameter, but they are perhaps 3 km in length, and each one carries 2-4 million ounces of gold.

A cylinder is very difficult to find, let alone completely define, by drilling. The only way they could have been found and mined was the way it was done. Artisanal mining was observed at the surface, and so a proposal is made to start at the surface and mine down. No drilling, just start mining. But in today's environment, it would be impossible to raise the financing for such a venture (what are the numbers?), and it would be practically impossible to define a resource using the normally accepted methods (which are more suitable for bodies with a tabular geometry).

Dynamic stability in probability density plots

Probability density diagrams of the two dimensional phase space portraits of climate proxies show two forms of stability. The first is the obvious form--stable (in this case, ice volumes) over comparatively long periods of time, broken up by brief periods of rapid change where the ice volume changes to another metastable state.

Using a stacked time series (from Huybers, 2004), we observe a different form of stability--one in which repeated cycles of growth and decay generate ring structures in the probability density plot.

Just as a car driving around a track at a constant speed is a form of stability, so are the two "limit cycles" inferred in the frame above. The system is stable, even though it is in a constant state of motion.

In the animation below (click and with luck it will run), the probability density space is characterized in the early Quaternary (about the first half of the animation) by stable cycles, which give the ring forms as in the still image shown above, but in the late Quaternary, the rings disappear and are replaced by probability peaks.

Both segments of the record show multi-stability, but the forms of individual metastable states in the early Quaternary differ from those of the late Quaternary.

Close-up with copper

In the back alleyways of SCC, about 50 m north of the main highway out of Accra (to the west) is an unnamed transformer workshop. There, old burnt-out transformers are unwound by hand, and new transformers are built.

 

Shop owner in foreground. The fellow behind him is unwinding a voltage regulator.

All right--the place doesn't look like much. Maybe you wouldn't feel comfortable buying a transformer from such an establishment in Toronto or wherever.

Isn't that beautiful?

The old copper wire is sent off to be melted down and is drawn out again. I didn't ask if they ever used pennies. They check gauge with a micrometer and their work standard is really good. It just takes awhile to receive a product.

We went to see them about building a three-phase step down transformer. We have this submersible slurry pump which we brought over in 1997 and used from an American vessel--it ran on 208 V 3-phase power. We have a newer pump arriving shortly by sea, and the local generator we picked up for it provides 380 V three-phase power. While waiting, we would like to use the old pump.

Apprentice unwinding the voltage regulator.

We went over the circuit diagrams for the transformer we wanted. He was willing to price and acquire the materials and dielectric oil and seal the whole thing up at a reasonable price. But that hand winding--it would take a week. He was willing to guarantee the work.

Reluctantly we decided to assemble one ourselves using store-bought transformers, stepping down the phases separately and recombining them. We successfully tested the contraption yesterday and are spending the next couple of days getting it field ready for deployment next week.

Three phase transformer. Inelegant, but it worked once we replaced the fuses that came with the transformers with the ones which should have been supplied.

Gold needs a correction

Bull markets need to rise the farthest with the rewest people on them. So if the gold market is to remain in a bull market, something has to be done to cool off the market.

These short sharp drops of $50 or so just aren't doing it anymore. The price and enthusiasm comes roaring back each time.

In the 1970s, during gold's run from $35 to $800, there was an 18-month interlude where the price was cut in half (from about $200 to $100). I've thought for a few years now that a similar correction has to occur sometime during this bull market in gold. Now, however, I think that the level of patience in the market in general is such that only half of such a correction is necessary--say 25% over nine months.

This could be achieved by a slow grind downward at a rate of $50 per month for nine months.

Can you imagine the mindset if the price of gold were $900 in nine months time? The gloating on financial TV. That would definitely look like the end of the bull market. And that is the perception that has to come.

Of course, it wouldn't be a straight grind downward. It would be punctuated by brief $50 to $100 rallies to suck speculators in repeatedly and destroy them. That's how you destroy speculators.

So if such a correction is coming (it may or may not be starting now) what is the plan?

First of all I never sell any physical metal. In previous selloffs I find you can never get it back at the lower price.

I am building cash in stock trading acccounts, but holding core positions. Just selling a little in to strength, and occasionally buy on weakness.

Ghanaians: The Beautiful People

Ghanaians are among the most beautiful people in the world. This is based on careful observation over several years.

 

Kwame visits a herbalist, Makola Market, Accra 2010.

Coffin-makers in Axim, 2002.

Bartender, Shama, 2008 (left). Electrician near Bortianor, 2010 (right).

Father and son, Central Region, 2007 (left). Egg-seller and children, Adabraka, 2010 (right).

Artisanal miner, Western Region, 1997 (left). Hotel staff, Axim, 2008 (right).

Market seller and daughter, Agbogbloshie, 1997 (left). Grasscutter vendor, Mankessim, 2007 (right).

Village elder, Kakum, 2007 (left). Women and child at block plant, Central Region, 2005 (right).

Visiting dignitaries at the funeral of the Asanta Chief, 2008.

Corn vendor, Awuna Beach Village, 2002.

Children returning from school in SCC-Mandela, 2007.

Workmen near Oshiye, 2010. They said I could take their picture but had to help them find wives.

Communal labour day in Axim, 1997.

Parade in Axim, 2002.

Looking at these pictures I see the majority of the people are Nzema (from the Western Region). Not to say these are the most beautiful in Ghana, just I spend most of my time there.

What has made you rich has made you poor

Electricity has been at a premium since a fantastic lightning storm here in Accra ten nights ago damaged the local power grid. We have had electricity over only about 24 hours in the first five days. It's been better since.

 Blogging by battery. Unfortunately I blew up the inverter last night.

Such things get me thinking about scarcity in general. The prices of many commodities have soared over the past two decades, particularly in the last ten years. What’s behind it?

Some have argued for “peak everything”.

Much has been written on the concept of peak oil. The idea here is that once we reach the point where we have produced about one-half of all oil in existence, oil production will decline. Some might argue we can keep production up awhile longer, but the idea is that as the amount remaining declines, eventually production must decline.

Hubbert said “We cannot produce what we have not discovered.”

The Earth is large, and for the most part we have barely scratched the surface. If the world were the size of a billiard ball, the depth to which we have plunged in search of resources would not even be visible. From my perspective as a geologist whose prime interest is in metals, we are nowhere near the peak ability to produce metals.

A paper published some years ago proposed the existence of a sphere of uranium (and other heavy metals) at the centre of the Earth, and some preliminary evidence that this sphere would have a radius of up to 6 km. Quite a lot of uranium, but I don’t care to hazard a guess as to the cost of its extraction*. 

Oil, however, is a different matter. Given what we know of its formation, there cannot be substantial and increasing pools of accessible hydrocarbon at successively greater depths within the Earth beyond some level fairly close to the surface. Alternative theories of deep hot biospheres or primary hydrocarbon have extremely limited evidence in their favour, and in any case, the few molecules of hydrocarbon which may have been demonstrated to have drifted up through the basement geology from the deep Earth are but a small drop in the ocean of world demand. Oil is definitely a commodity which could be at or near its peak of production.

Having said that, I think we would find that at a price of about $1000/bbl (in constant 2010 dollars—no fair printing your way to this price!) we would still find a lot of oil at depth. But for geological reasons, this oil will be extremely expensive to discover and produce (hence the need for $1000/bbl).

The deeper the rocks are, the more tectonic episodes they have experienced. An oil reservoir is very simply the volume contained within a fold in the rocks. The deeper you go, the more complex the folding, and the smaller the individual volumes. You have two technical challenges, leading to greatly increased costs—first, the targets are small, so they are difficult to “image” using geophysical techniques, and difficult to hit with a drill; and second, the reservoir is small, so there is not much economic benefit to offset the much higher costs (except by a much higher price).

Beyond this depth, you don’t have much chance of finding anything at all, as the temperature is too high to preserve the most valuable hydrocarbons.

Most of the data we have collected to date in the search for oil (and there are reams of it—I once heard that a major oil company was prepared to donate its entire collection of eastern Canada seismic data to the Geological Survey—just the tapes alone would fill a small building) are useless for looking for these deeper, smaller structures. It hurts to admit it, but there it is.

There is a small problem called spatial aliasing. You have a complex curve as in the figure. But your sampling is limited. How you sample is called CDP stacking. A series of shots are set off and the results recorded on geophones, and simply, all the reflections occur off one common point at depth, which is the sampled point. Then the entire array is dragged along some distance and repeated. But the smallest target that can be resolved is a function of your sampling interval. In particular, you need two samples to define a bend in the rocks (defining it accurately requires more).

If exploration geophysicists had unlimited budgets and placed no value on time, I have no doubt they would sample more frequently. But budgets are limited, and so geophysicists collect the minimum amount of data necessary to define their targets of interest, which over the past couple of decades have been that second layer of hydrocarbons in my cartoon of oil distribution. This data is not nearly dense enough to resolve the smaller targets on the third layer above.

What happens when you try to interpret geology without adequate data?

Oh yeah--you have to click on this figure for it to do anything.

Holy crap! Those hundred-million dollar holes that were supposed to be into a fat juicy anticline went into nothing! Not only are you fired and blacklisted from the industry, but you and your extended family are hereby sold into slavery.

So let’s leave aside oil for a moment.

What about metals? If we are nowhere near their peak production, why have their prices risen so sharply?

One reason may be inflation. More dollars chasing the metals.

There could be another—and that has to do with the fall of the price of metals (and most commodities) that began in the early 1970s. This fall had more to do with the rise of commodity futures trading than it did a sudden per capita increase in metals production. Many charts showed a drop in per capita production of basic commodities.

 Global copper production in tonnes per thousand population. Data compiled from

USGS and UN 2004 projections, digitized at five year intervals.

The per capita production of copper has risen through the 20th century, but four declines are apparent--WWI, the Depression, WWII, and the period from 1975 to 1985 or 90. Other commodity graphs appear similar. Was there an economic implosion equal to a Great Depression or a World War in that period?

When I was teaching early in the last decade, it was fashionable to look at such graphs and wonder if production for many of these metals was peaking.

The real reason for the drop in per capita production has to do with the fall in price. For producers, price is a signal. A rising price tells you to increase production. A falling price tells you to reduce production.

The problem comes from the paper pushers. If you have a certain amount of wealth, it seems intuitively obvious that if the price of what you have to buy falls, then you become wealthier. But this is only true if price falls due to an increase in supply.

If the price has fallen because of the ability of large corporate and banking interests to control the price downwards through the issuance of paper, then your wealth is not actually increasing.

After all, what is wealth? Isn’t wealth actually stuff—gold, oil, copper, grain, meat? If you drive the price down, but at the same time you have less stuff, then you have become poorer—for wealth is an abundance of oil, of gold, of food; but not of paper (or its electronic equivalents).

Creating all this paper has not made us richer! It has made us poorer!

Notice how per capita production of copper has increased over the past fifteen years. Do you feel richer? You should . . . except that much of that extra copper has gone to China, so unless you have been Chinese over that interval, you are not much wealthier (much like how the rapid growth from 1950 to 1975 was mainly experienced in North America).

We are a long way from the peak of everything (oil being the probable exception). We are currently in the process of revaluing real commodities in terms of paper. This revaluation is the equivalent of a complex system leaping from one metastable state to another. Huge volatility lies in our future, as corporate and banking interests, backed by huge government bailouts, double and redouble their efforts to regain control of commodity prices.



*The cheapest way to extract it may be to blow up the Earth. But there is an easy way to protect yourself. You simply buy land futures and take delivery after the Earth is destroyed!