## 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).

## Monday, July 30, 2012

### Induction, deduction, and the Newtonian paradigm, part 1

When I was in grad school, I had a roommate who was studying philosophy. One day he decided that he would no longer accept any conclusions that came from inductive reasoning, as deductive reasoning was superior. It was not long before he was refusing to accept premises like the sun would rise on the morrow, or  that he would have to eat the next day, saying that just because these things happened in the past, we could not conclude they would continue to happen in the future.

Most of what we imagine we know about the world was arrived at through inductive reasoning. From a scientific perspective, my ex-roommate's decision was catastrophic. In reality, however, it was probably no different from the way most people live their lives. He went out looking for food when he was hungry (I never investigated how he deduced where to find food). He avoided being run over by cars or starving to death, at least as long as I knew him. In a modern society, planning for future events like becoming hungry isn't really necessary--although whether he would have been as successful in the distant past is an open question.

Mathematics is deductive--this works because mathematics has little to do with the real world. You've never seen a triangle with internal angles adding up to 180 degrees. But mathematics was one of the first tools used to study the real world, so it is no surprise that early sciences proceeded on the basis of a modified form of deduction.

Deduction works on the basis of axioms--which are irreducible, true statements (at least within some sort of formal system)--and rules of inference, which allow us to generate more true statements from our axioms. These new true statements so generated are called theorems. An example of an axiom might be "all right angles are congruent". An example of a rule of inference might be "things that are equal to the same are equal to each other".

In the early days of geology, for instance, there were constant conflicts between different "schools"--for example, the Neptunists and the Plutonists. The schools were framed by their various axioms; which in the case of the Neptunists were that all rocks formed by the lithification of sediments in water, as compared with the Plutonists who believed that all rocks formed from crystallization of magma. These axioms shaped the thinking of geologists from the respective schools so much that geologists from different schools could look at the same rocks and interpret them differently. Discussions between geologists of the two schools must have been as exciting as those between the Montagues and  the Capulets (Romeo and Juliet notwithstanding).

The first revolution in science was to change its basis of operation from deductive to inductive. Central to this was the idea of formulating testable hypotheses. Although there has been a major improvement in our understanding due to the notion of testing hypotheses, something that can be overlooked is the general framework which limits the hypotheses we choose to test (and influences our approach to developing new hypotheses). This framework has been described elsewhere as a paradigm.

A paradigm is an overarching set of preconditions generally accepted by practitioners at a particular time. In one sense, it is not that different from having a set of axioms underlying your school--the one difference is that in principle, the paradigm is falsifiable, and so may be discarded should a better one come along. In reality, too many scientists have too much at stake to allow any paradigm to fall without a major struggle.

The next big debate in geology was between Catastrophism and Uniformitarianism, the central tenet of which is that the processes acting on the earth are consistent, for the reason that the laws of chemistry and physics do not change with time. The uniformitarian concept was of an ancient earth, which changes happening gradually over unimaginably long periods of time.

We can imagine Hutton, drawing on his father's experience as a lawyer, summarizing his arguments and presenting them logically as follows:

". . .as illustration of my views of those principles, and as evidece strengthening the system necessarily arising out of the admission of such principles, which . . . are neither more nor less than that no causes whatever have from the earliest time to which we can look back, to the present, ever acted, but those now acting; and that they never acted with different degrees of energy from that which they now exert." (15 Jan 1829, letter to Murchison).

Once the idea of uniformitarianism took hold, it proved to be nearly as restrictive as either the Plutonists' or Neptunists' schools. Even though geology advanced by testable hypotheses, the prevailing paradigm placed limits on the kind of hypotheses that could or would be tested. The last portion of his quote is the problem--that the forces of nature have never acted with degrees of energy than they do at present. That means that there were no storms greater than any we have witnessed, nor volcanic eruptions, nor earthquakes. The problems with this are well understood in the present day, but were the focus of intense debate in Hutton's time.

Hutton's intellectual opponents drew on different oratorial backgrounds. We can picture Adam Sedgwick, a Minister, thundering from the pulpit as follows:

"To assume, then, that . . . forces have not only been called into action at all times in the natural history of the earth, but also that in each period they have acted with equal intensity, seems to me a merely gratuitous hypothesis, unfounded on any of the great analogies of nature. . . This theory confounds the immutable and primary laws of matter with the mutable results arising from their irregular combination. It assumes, that in the laboratory of nature, no elements have ever been brought together which we ourselves have not seen combined; that no forces have been developed by their combination, of which we have not witnessed the effects. And what is this but to limit the riches of the kingdoms of nature by the poverty of our knowledge; and to surrender ourselves to a mischievous, but not uncommon philosophical scepticism, which makes us deny the reality of what we have not seen, and doubt the truth of what we do not perfectly comprehend."  (18 Feb 1831, address to the Geological Society).

The current view in geology is rather a combination of the two views, whereby catastrophes are part of the natural process of the world, and are therefore sprinkled throughout the geological record in conformance with the general principle of uniformitarianism. The debate as to whether or not catastrophic events are important in the geological record has been resolved in the affirmative.

The work I have presented over the course of the last year or so has a lot in common with the above Sedgwick quote. With the idea of innovation in earth (and other complex) systems is my attempt to not "limit the riches of nature to the poverty of our observations".

The epsilon machine approach to characterize the dynamics of the data set in a manner consistent with Occam's Razor is intended to be repeatable in a way that geological interpretation usually is not. It will still take time to establish whether this method is successful. The interpretation of the dynamics and exposition of its implications in terms of real earth dynamics may still vary from one geologist to another.

The Newtonian paradigm suggests that complex systems can be understood by detailed study of each of their components in isolation. Hypotheses are formulated and tested about each component, trusting that their combination would lead to a full understanding of nature. Testing multitudes of hypotheses, each of which leading to a small improvement in our knowledge, has built our current understanding of the world. The Newtonian approach has had the advantage over time, primarily because it is easier to formulate testable hypotheses.

Unfortunately, the Newtonian paradigm has its limits, and these limits have been visited in geological and biological systems. An understanding of complex systems still eludes us. But Newton had a rival, Leibniz, whose approach of viewing complex systems as essentially being characterized by information, or sets of rules which could in principle be determined from observation, as being complementary approaches. I will expand on this idea in a later posting.

## Tuesday, July 24, 2012

### Price and production in selected metals

Today we present the second part of the figure presented last week--per capita value of production for nickel, zinc, molybdenum, silver, and lead (tin, cobalt and tungsten are the unlabelled lines). Results are calculated from annual production and annual average price, obtained from the USGS.

The largest control is the rise in price. Nickel saw a tremendous price spike in 2007, which saw the metal value of pre-1982 Canadian nickels reach 27 cents. Note the recent increase in importance of silver.

## Friday, July 20, 2012

### Inflationary impulses in commodities

Today's chart is an update of one we have seen before--a state space plotting the gold-copper ratio against the silver-rough rice ratio (month-end prices) over the last fifteen years.

The plot has been confined to the yellow blob for most of the past sixteen years. Generally speaking, all four of these commodities have been inflating at the same rate, with excursions in one direction or another, normally in response to inflation appearing in one or two of these commodities for a short time before the others catch up--which could be viewed as reversion to the mean.

Prior to the beginning of last year, the only two excursions outside of the yellow area were: the one at the top of the graph, reflecting the collapse of commodities in late 2008 (with gold relatively outperforming); and the one at the bottom, reflecting the rapid increase in both copper and silver in 2006.

In the last eighteen months we have seen a remarkable excursion, mainly reflecting a rapid increase in the price of silver. Going forward, there are two possibilities, each with its own implications for the resource space. One possibility is that we are seeing some kind of breakout with respect to the metals in comparison to agricultural commodities. The other possibility is that we are only seeing a burst of inflation in the metals prices, which will shortly be matched by a rise in agricultural commodities (we would need to see roughly a doubling in the price of rice to return to the yellow blob--or a halving of the silver price). The billion dollar question is which scenario will play out.

Disclosure: long gold, long silver, long rice (physical possession only).

## Tuesday, July 17, 2012

### Brazilian days

In honour of being added to the IKN blog list, I thought I would put up a posting with a little LatAm flavour. I have to go back in time to 1993 when I joined a Brazilian expedition to Antarctica.

It all started at a party. My thesis supervisor knew of this project, and had been invited to assist the Brazilians, but was unable to for some reason. So I asked if I could go. I had had experience in the Canadian Arctic, and so it seemed a reasonable fit. The Brazilian program consisted of academics and Petrobras geologists. I was on one of several teams, and our goal related to developing an understanding of glacially influenced marine sediments, which was to be applied to the Parana Basin in Brazil (a major oil producing region generally only understood from boreholes).

I had initially planned to spend a little time working on my Portugues before flying off to São Paulo--but I was working on another project which didn't finish until late in the evening before my flight. So there I was trying to rest up and study Portuguese on the flight down. I decided to focus on whatever I needed to learn in order to get through the airport, as my instructions were to phone one of the geologists from the airport for a pickup.

To try to understand my mindset at the time: in North America (in January 1993), Brazil was believed to be a dangerous place. Before the trip some friends of mine were taking bets on the likelihood that I would be killed at the first intersection I encountered. Inflation was running at about 25-30% monthly, so managing currency conversion for a long trip was key. I had been told by a colleague that when he was about to begin a stint in Brazil, he arrived planning to transfer money from Canada to a local bank in Brazil, but on the day he arrived the banks were closed by order of the President (possibly the event described here).

My Brazilian colleagues had arranged for me to stay in a room at the USP, which was closed for the holidays. I was asked to wait--there was some political turmoil with the program, and there was some doubt as to whether the trip would go ahead. After awhile I decided to wander around to locate food and amenities, which turned out to be a good idea because my handlers didn't come back for some days.

I chose a street at random and walked along it, eventually arriving at Praca Pan Americana. After narrowly escaping being run down at the traffic circle, I saw the wisdom of crossing the street in the middle of blocks like everyone else seemed to. There was a grocery store, Se. The parking lot was pure chaos. I ended up buying a lot of oranges and bananas, because my guidebook was unclear about whether or not the water was good to drink (it was).

A different street led me past what were probably the student hangouts, at least when the University was open. I had a sandwich at a hole-in-the-wall cafe with the loudest, most exciting futbol game in history blaring over the radio. Further up the street I bought a green coconut, and walked back to the residence. A soft warm rain began to fall. Sublime.

Over the next few days my confidence increased and I wandered farther away from the residence, eating at a variety of hot dog vendors and other hole-in-the-wall cafes with similarly exciting futbol games coming through their radios. I have to say that I never encountered anything but goodwill anywhere I went; not to mention great patience with my ongoing struggle with portuguese. Even the poor bank manager who had to explain to me three times why I couldn't convert foreign currency at the bank. One day, on returning to the residence, two of my Brazilian colleagues were waiting for me, and it was time to go.

We flew by commercial flight to Rio where we stayed one night in a hotel some distance from the beach. My Brazilian colleagues impressed upon me how dangerous it was for us to walk around Rio at night (as there were only seven of us). They all showed  me various methods of hiding cash. I was disappointed when the restaurant was across the street. It was well-lit, and everyone inside was well dressed. Most patrons donated some of their leftovers to children begging on the patio.

The morning featured a sunrise over a mist-shrouded Sugarloaf. We raced off to the military airport in the fastest taxi in the world. Eventually we were packed like sardines into the plane below, and headed south.

Military transport to southern Brazil, en route to Antarctica.

The first leg of the flight was to Pelotas, in the Rio Grande do Sul area. It was a nice old town, with cobblestone streets. Police were armed with batons. At night, the locals sat out on their porches facing the street, and the whole town had a happy vibe.

Street in Pelotas. In the foreground is Victor, a geologist at Petrobras.

The second leg was to Punta Arenas in southern Chile. My initial impressions of the place as we took a bus into the city from the air force base was that it was a lot like Newfoundland--both in topography and in the colour of the houses in the fishing villages.

Chile, on the whole, seemed a lot calmer than Brazil. Currency exchange was easier too.

The last leg of the flight was to the Marsh station on King George Island (the South Shetland Islands). If you talk to a Chilean, you would discover that it was part of Chile. Very few others in the world would agree. But there were families there, who told me their children were born in the local hospital, so it looks like Chile is building a colony.

We were transferred onto the Barão de Teffé, a support vessel for the mission.

Me with my bowling-ball haircut, surrounded by Brazilians. Sadly, these weren't the
ones coming out to the field with me.

Flying to camp.

Some of our impressive supplies.

Supplies, yes. Very nice. Several cases of wine. Chocolate. Lots of food. My experience in field camps up until then had been dried food, all of which was carried in by hand. I'd never been in a camp like it. I have to say, it was very civilized. After a typical day in the field, we would spend a couple of hours talking about the day, drinking wine, and eating chocolate, while the cook prepared dinner. Sometimes for a change in pace we ate canned palm hearts or sardines. They also had a few cases of cola, and a guarana drink.

I had a very important role at afternoon tea time. It appears to be rude to take the last piece of chocolate, or so I infer from the fact that none of my Brazilian colleagues would take it. No matter how small it became, they would always break it and take only a part. I would eat the last fragment, giving us the excuse to open a new package.

After five weeks, we were picked up again. On one of the first meals back on the ship we were given an apple for dessert, which I ate in about ten seconds. Everyone else at the table ate theirs with knife and fork.

Camp on King George Island.

## Sunday, July 15, 2012

### Reflections on market and commodity risks

Consider these two charts (both have appeared here before).

Per capita (dollar value) annual production of certain metals. A note here--I have some different numbers for iron suggesting it has more dominance over Cr, although there are a couple of years going back to 2001 where Cr > Fe, though not as much as it appears on the chart above.

Fraction of global mineral exploration budgets (nonfuel only) for gold and copper. Gold exploration comprises over 50% of the global exploration total, and has done so for many years. Some years, gold and copper exploration combined for over 80% of all nonfuel exploration, including iron, chromium, manganese, aluminum, diamonds, and many other minerals.

One reason for the lack of expenditure on iron--it is relatively easy to find.

See if you can spot the iron deposit in the above image. This is a Google Earth image encompassing the Tonkolili project in Sierra Leone. The red line at lower left is as close to 20 km as I could make it. The artisanal mining area is gold in a project I looked at a few years ago.

Gold is very interesting. On one hand, gold exploration accounts for over 50% of nonfuel exploration effort, yet less than 10% of the value of mined minerals on an annual basis. Why is this? I think the explanation is that gold is the least risky commodity--from a marketing perspective.

If you plan to develop a new iron mine, and demand falls below existing production, you had better stop. If world demand is a billion tonnes per year, and you will be producing the billion and first tonne that year, then you are SOL. Gold, on the other hand, (and to a certain extent copper) can always be sold at reasonably close to spot price, which reduces its risk. Yes, it can be hard to find. But you never have to worry about being able to sell it.

## Wednesday, July 11, 2012

### Poor Gordon Brown . . . (part 2)

Last year we discussed Gordon Brown's misfortune for being considered more foolish than the government of Canada in his treatment of gold sales.

Yesterday the World Gold Council came out with its latest bit of advice--Gold as a strategic asset for UK investors (accessable here, but you need to set up a free account to download it). The report highlights gold's role in preservation of capital.

Poor Gordon Brown. He must be heartbroken. If only, if only, if only this advice had been available to him when we made his fateful decision.

## Tuesday, July 10, 2012

### Gold is working its way up the ranks

Behold world metal production for the past five years, expressed in dollars per capita. For now, I am only offering minimal comment.

Data for production and values from the USGS commodity reports; population data eyeballed off a chart. I used reported annual average prices rather than closing prices.

It's ferrochrome's world--the rest of the metals just live in it.