Time and Again the Pattern of Spider Webs Come Out the Same Bob Hicok

If you are worried about oil shocks, information technology is natural to ask the questions "what are the hot spots we demand to worry about" and "what is the overall tolerance of the GFFSC" to ruptures in production or consumption of fossil fuels in those places. A related question involves the degree of disruption in a given identify (if we can define that).

The standard theory of scale-free networks is that they follow a power police force distribution. But before we get into that, let'southward make the bones analogy between the GFFSC and the internet. Our naive model runs equally follows.

1. A node in the network is a country.
2. A link (or connection) in the network is the exchange of some fossil fuel between ii nodes.
3. Nodes have links to themselves. This is but the instance where fossil fuel production is used to run across domestic consumption. On the internet, this is a analogous to internal links within a website.
4. Links come in 2 flavors, outgoing (exports) and incoming (imports) with respect to some fossil fuel. Links are always reflexive ie. bidirectional (my exports are your imports). On the net, site 10 may link-in site Y merely not vice-versa. In other words, X exports traffic to Y and Y recieves imported traffic from 10. In this sense, the analogy holds and the lack of across the board cantankerous-linking makes no deviation to this analysis.
5. Links are not all created equal. They must exist weighted (as is done in neural networks). The weight for a given fuel (eg. natural gas) could be simply the amount moved along the link in 1 management or some other, in this case as measured in billion cubic feet per 24-hour interval. Generalizing, 1 could utilise British Thermal Units (btu) to measure out the weight, thus roofing all fossil fuels. Chiefly, weights employ to intrasite (domestic consumption) connections.

And that'south it. Pretty simple, hey? Only similar the internet except for the weight (#5 -- although we could make an analogy in that location, too). Looked at this way, a number of the stories nosotros write or the comments that are posted are well-nigh changes in the network including

• new (or recent) connections (Angola/Communist china for oil )
• stronger/weaker connections (US/Qatar for natural gas)
• lost, or dropped connections (Indonesian exports for oil)

Finally, I must mention two aspects of the GFFSC non covered hither. First, inventories are discounted. I consider those to be fossil fuels that take already been delivered (if imported) and equally hedges against lost connections. Second, spot cargoes are "free floating" links looking for an zipper. They are not direct considered here but practice highlight the dynamic nature of the GFFSC.

Now, from Wikipedia (run into the scale-costless link above):

A scale-free network is a specific kind of complex network that has attracted attention since many real-world networks fall into this category. In calibration-free networks, some nodes deed as "highly connected hubs" (high degree [of connectivity]), although most nodes are of low degree....

In physics, such correct-skewed or heavy-tailed distributions often have the form of a ability constabulary, i.east., the probability P(k) that a node in the network connects with one thousand other nodes was roughly proportional to k−γ, and this function gave a roughly proficient fit to their observed data.

Pursuing our illustration, Russia or the U.s. are both hubs -- they are highly connected. Outer Mongolia and even Chad are not -- they have a low degree of connectivity.

But here nosotros need a conjecture and an assumption. The conjecture is that if we assessed and counted all the import/export links in every country of the earth, we would get a power law distribution. The assumption is that the conjecture is truthful. In any case that is my intuition virtually the GFFSC ie. that it is like the internet, information technology is scale-free to some large extent. Just to strengthen our conjecture and assumption, we must add in the weight Westward of the connections to the degree of connectivity. So, I am really assuming that the mensurate of a country's importance in the network comes from some function f(D,W) where D is the degree of connectivity. A hub has a high value for f, a singly connected node (eg. the Falkland Islands) has a low value. Once we've fabricated this move, I believe that the conjecture becomes much more than plausible. I large deviation between the net and the GFFSC, all the same, is the overall size.

There are only so many countries in the world but the cyberspace is made of literally billions of nodes. We could consider individual oil fields or producing basins every bit nodes in our GFFSC graph. This would make the network bigger merely still considerably smaller than the cyberspace. However, the power law distribution can apply to a smaller network. The standard employ of the power law in the analysis of the meridian oil situation applies to oil field reserves as Khebab did recently in What tin can we learn from the oil field size distribution? originally from his Graphoilogy blog. Highly recommended. His analysis considers the top 2092 earth oil fields (excluding the US and Canada) with sizes greater than fifty Mb (1000000 barrels). Specifically, I am making the claim that S(yard) is close to ane as shown below.

Although the scientific community is nevertheless debating the usefulness of the scale-free term in reference to networks, Li et al (2005) recently offered a potentially more precise "scale-free metric". Briefly, permit g be a graph with edge-set ε, and let the degree (number of edges) at a vertex i exist di. Ascertain

This is maximised when high-degree nodes are connected to other high-degree nodes. Now define

where smax is the maximum value of southward(h) for h in the set of all graphs with an identical degree distribution to thou. This gives a metric between 0 and 1, such that graphs with low S(g) are "calibration-rich", and graphs with Southward(g) close to 1 are "scale-free". This definition captures the notion of self-similarity implied in the proper noun "scale-free".

Visually, a power police distribution often looks like this.

Highly connected nodes and a power
law (not-gradual) relaxation

Looked at another manner, hither's Wikipedia'south illustration of a calibration-gratuitous network.

The dark nodes are hubs -- Click to Enlarge

My strong intuition is that the GFFSC is not a random network. And if y'all think virtually it, that is just obvious. There are 2 standard results as regards scale-free networks. The outset is that strongly connected nodes (using our function f above) garner more connections over fourth dimension. This is known as the rich get richer or winners take all. The second result is that a disruption (oil daze) in a highly connected hub can have a cascading result in the network, thus bringing information technology down. Permit'due south take our illustration further for both results.

Regarding the rich getting richer, as oil declines keep in diverse countries (eg. the U.k., Indonesia, Mexico), export connections in the network are dropped though they may exist replaced by incoming links -- imports. On the other paw, for the rich, similar Saudi Arabia or Russia, the number of connections increases. For case, China has recently renewed efforts to constitute connections with Saudi arabia and other Middle Due east suppliers. This results in a college degree of weighted connectivity for both countries. The rich get richer. In detail, every bit Wikipedia notes, "these scale-costless networks do not arise from hazard lonely". What is required to model a network this style is to define a growth procedure. In the usual case, this is referred to as preferential attachment (run across the calibration-free networks link cited above). In the case of the GFFSC network, this can exist described by this adequately simple formulation which quotes Billie Holliday:

Them that's got shall get
Them that's non shall lose

Those who take the fossil fuels and export chapters and tin can easily support their ain needs or tin can pay for their required imports will thrive -- the value of f(D,W) increases. Those who tin can not do either will suffer -- the value of f(D,Due west) decreases.

For our original topic, oil shocks, the analogy is even stronger. If a strongly connected fossil fuel consuming or producing nation (hub) is "taken out" to a some (undefined for at present) extent, the results for the network as a whole could be disastrous. Nosotros need to look more closely at this question. Would the furnishings cascade thoughout the entire network causing harm everywhere? Or is the network resilient enough to absorb the loss of a hub and continue the damage in the firsthand network neighborhood?

As described in the start New Scientist article "The Net Reloaded", John Doyle of MIT casts some doubt on the internet every bit a scale-gratuitous network following a ability law distribution. Speaking of the cyberspace, nosotros read

After finding that this ability law described the statistics of cyberspace routers, Barabisi and colleagues [who discovered the scale-costless network/power law result for the cyberspace] used a theoretical network with the same proportion of highly connected routers to model the net, and from this idea came the idea that eliminating highly connected routers [hubs] could close the net down. Doyle argues that this approach, which superficially attractive, ignores a simple fact: the highly connected routers are ISPs [internet service providers] on the edges of the network, close to stop users.... Take down highly connected routers around the US and you lot'll knock out Internet access provider'southward that serve users in certain neighborhoods.... [But] the bulk of cyberspace information ... will menses unimpeded....

The router example reveals the weakness of scale-free models as a predictor of how a system will behave .... A useful model would specify what the nodes do, where they are in the network and how their connections piece of work.

Toward making a more accurate model of how the internet behaves, Doyle and others have developed the highly optimised tolerance (HOT) model as briefly described in the link to a higher place. "With HOT", Doyle explains, "we're trying to explain [in simple models] that are more faithful to the specifics of the domain, what is general about circuitous networks". Look here to notice out more about HOT modelling of circuitous networks.

Following Doyle, we must pay attending to the specifics of the network domain which I've divers as the Global Fossil Fuels Supply Chain [GFFSC]. I do not know how HOT would model this domain but in terms of fault tolerance concerning the vulnerability of hubs to disruptions in that domain, we tin observe the following:

1. In that location is no trivial or no spare chapters in the network. This is a bit like saying that there is an internet routing system without extra bandwidth. If a major hub like Saudi arabia (eg. Ras Tanura or Abaqaiq) goes down, the withdrawal of oil supplies on the world market guarantees a cascading ripple effect over the entire network due to the supply & demand pricing mechanism. In this sense, the GFFSC network is more of a scale-free network than the cyberspace is. Unlike Doyle'due south formulation, the ISP router hubs do non lie on the periphery of the network. Think of it this manner. If the Saudi hub is crippled, does that impact Angolan imports to People's republic of china? Can China lose its Saudi Arabian exports network connection but strengthen it's Republic of angola import link to compensate? If at that place were spare capacity (bandwidth) in the system, fungible oil tin be re-routed to recoup for disruptions in the organisation. But that is not the case at present and I speculate that it will never be the case.
2. On the other hand, if a general war between Chad and Sudan occurs and the export link from Sudan to Cathay is dropped, describing a case where the degree and strength of connectivity is so much lower, can Mainland china found new import links with other suppliers or strengthen it's import links with information technology'due south of import current suppliers (Kingdom of saudi arabia, Angola and Iran)? Probably. Chad and Sudan prevarication on the periphery of the network.

Then we come across that viewing the GFFSC as a calibration-free network described by a power police force distribution reveals the extent of the security problem. The GFFSC as I have called information technology is taut as a bowstring. This is why I worry about oil shocks.

A Note on Intrinsic and Extrinsic Affects on the GFFSC

Here we render to the work of Sornette linked in at the top. In his paper Endogenous versus Exogenous Origins of Crises summarized at the cited link we observe

Assay of precursory and aftershock properties of shocks and ruptures in finance, material rupture, earthquakes, amazon.com sales, etc: we find ubiquitous power laws similar to the Omori police force in seismology that allow u.s. to distinguish between external shocks and endogenous self-organization.

This question, whether distinguishing properties characterize endogenous versus exogenous shocks, permeates many systems, for case, biological extinctions such as the Cretaceous/3rd KT boundary (meteorite versus extreme volcanic action versus self-organized disquisitional extinction cascades), commercial successes....

We study the precursory and recovery signatures accompanying shocks in complex networks, that we have tested on a unique database of the Amazon sales ranking of books and on time series of financial volatility. We find articulate distinguishing signatures classifying two types of sales peaks. Exogenous peaks occur abruptly and are followed past a power law relaxation, while endogenous sales peaks occur after a progressively accelerating power constabulary growth followed by an approximately symmetrical power law relaxation which is slower than for exogenous peaks....

Please read the whole text. Sornette is talking about existence able to distinguish endogenous versus exogenous influences on network behaviour after the fact. For peak oil, we are right in the middle of things. But I think it is possible to make a few observations. Amidst endogenous (intrinsic) causes, we annotation the following.

1. As more weight is added to intra-node links (domestic consumption), other import/consign connections in the network are weakened or lost. This is not coordinating to the cyberspace merely rather is a specific property of the network domain we are describing.
2. As oil field production in a country declines (eg. Mexico, Cantarell), nosotros observe the same effect equally in #1 above.
3. Extrapolation of the discoveries curve trend is right. The big fields are found first and are mostly all deemed for. Whatever big field discovered now would exist a statistical outlier. This in turn suppresses the creation of new, potent connections in the GFFSC. New EOR techniques for increasing URR in oil fields volition accept a negligible or even damaging effect going forward regarding #two to a higher place.

The basic ascertainment is that Sornette's Amazon sales ranking of books is analogous to fossil fuels sales ranking of exports.

Every bit for exogenous (extrinsic) causation (aka oil shocks) we note the following types that could affect hub nodes in our scale-free GFFSC network.

• Wars
• Labor Disputes
• Terrorism
• Natural Disasters
• Economical Recessions
• Political Upheavals (Coups)

This brings us to the work of Nassim Nicolas Taleb, an applied statistian who wrote the 2nd article in New Scientist Life Is Unpredictable. In particular, he is referring to Black Swans in which he distinguishes between what he terms "type one" randomness (eg. throwing a dice) and "type two" randomness (eg. a x kilometer bolide hitting the Earth). This latter is a Black Swan. His analysis claims that events of the latter type are effectively unpredictable and but a affair of luck. Why do Harry Potter or The DaVinci Code win while many other worthy efforts lose? While I agree that life is unpredictable, particularly for type two randomness, I dispute any claim that the exogenous factors that could cause oil shocks (excepting perhaps Natural Disasters) fall into this category. For instance, here is a listing of contempo conflicts in the Heart East. Not only are there current conflicts, just it would seem that new conflicts, arising from Iran and Israel for example, are adequately predictable in the future.

Notwithstanding, we must admit that luck regarding exogenous events is unavoidable as it affects the GFFSC in the time to come. However, in line with our modeling of the supply chains as a scale-costless network, I practise theorize that the rich will become richer and the poor will remain that fashion or become even more impoverished. For instance, S American countries like Argentina are already feeling the pinch. I hope this mail will stimulate some discussion of the ideas contained herein. Plain, there is lot of stuff I didn't go to talk over. Personally, I'g not feeling particularly lucky virtually the futurity of the GFFSC. In my view information technology appears to exist a real-globe calibration-free network subject to a power law distribution and the endogenous and exogenous factors affecting it as described above. To end upwardly on a lighter notation and acknowledging the part of luck in our future, we finish with a famous quote from the movies.

I know what you're thinking. Did he fire six
shots or only five? Well, to tell you the truth,
in all this excitement, I've kinda lost runway
myself. Simply being as this is a .44 Magnum
[top oil], the most powerful handgun in the
world, and would accident your head clean off,
you've got to enquire yourself i question:
Do I feel lucky? Well, practise ya punk?

Dirty Harry fired five shots, not six.

whittleseliestionce.blogspot.com

Source: http://theoildrum.com/story/2006/7/5/151350/4215

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