Incomprehensibly huge disasters

There is a tribe in the Amazon whose members can only count to five. Any amount greater than five is simply "many." We're surrounded by numbers in the millions (executive salaries), billions (Canadian government debt), and trillions (US government debt). But how much better are we than Amazon tribespeople in understanding what these amounts mean?

A few years back Jack Knetsch and Danny Kahneman published an article describing an apparent inconsistency in how people value the environment. If you ask people how much they're willing to pay to save fish, they'll give more or less the same answer if you ask about the willingness to save the fish in just one lake, all the fish in Ontario, or all the fish in Canada.  Our brains just don't process the differences between these options. They all involve saving many fish.

It's not just fish lives, it's human lives, too. In his article Math Murders, Jim Holt writes:

Where mass death is concerned, the moral significance of scale seems to be one of those things that our brains aren't equipped to handle. A single life may have infinite value, but the difference between a million deaths and a million and one strikes us as negligible.

Adam Smith's take on the matter in The Theory of Moral Sentiments is brutally cynical:

Let us suppose that the great empire of China, with all its myriads of inhabitants, was suddenly swallowed up by an earthquake, and let us consider how a man of humanity in Europe, who had no sort of connection with that part of the world, would be affected upon receiving intelligence of this dreadful calamity. He would, I imagine, first of all, express very strongly his sorrow for the misfortune of that unhappy people, he would make many melancholy reflections upon the precariousness of human life, and the vanity of all the labours of man, which could thus be annihilated in a moment. He would too, perhaps, if he was a man of speculation, enter into many reasonings concerning the effects which this disaster might produce upon the commerce of Europe, and the trade and business of the world in general. And when all this fine philosophy was over, when all these humane sentiments had been once fairly expressed, he would pursue his business or his pleasure, take his repose or his diversion, with the same ease and tranquillity, as if no such accident had happened. The most frivolous disaster which could befall himself would occasion a more real disturbance. If he was to lose his little finger to-morrow, he would not sleep to-night; but, provided he never saw them, he will snore with the most profound security over the ruin of a hundred millions of his brethren, and the destruction of that immense multitude seems plainly an object less interesting to him, than this paltry misfortune of his own.

Smith's point, perhaps, was that people don't care as much about things that don't affect them directly. But I think he also understood that the loss of a hundred millions of lives is simply incomprehensible.

The latest estimates of the size of the oil spill in the Gulf of Mexico are between 23 and 89 million gallons. The difference between the high and low estimates is six times the size of the Exxon Valdez oil spill. But none of the numbers have any meaning to me.

Perhaps this is the reason why the news networks cover the spill by showing oil-covered birds - I can comprehend and grieve over the death of a pelican. 

Comments

[Brian Finch]

I like to do a little mental arithmetic in cases like this: 50 million gallons is volume of about 10 million cubic meters. The cube root of 10 million is about 215, so we're talking about a volume of oil 215 meters (two football fields) x 215 meters x 215 meters - roughly enough oil to fill a typical football stadium or two. OK, we can picture that now. The next problem is to compare that to the volume of water in the Gulf of Mexico, which I admit to having a harder time with.

[Just visiting from Macleans]

This site is helpful to comprehend the full extent. Just type in your location in the upper lefthand form (google recognized my location automatically) and it shows how far and wide the oil slick will cover.

The Report on Business section of the G&M I thought has been using graphics very effectively in its print editions (don't know if they are online) when reporting on this story. For example - on the risks of offshore NL deepwater drilling by Chevron - comparing it with a well drilled in Hibernia , then the Gulf of Mexico spill- with bar graphs starting at sea level downward. The difference in depth(risk) was quite striking visually.

USA Today (onetime largest US daily paper by circ. - looks like Rupert Murdoch's revamped WSJ has overtaken according to wiki) came out of nowhere in the early 80's to gain national prominence and financial success in no time (quite a feat for a startup newspaper) partly though the use of graphics and colour. Whenever I had occasion to read it (some time ago) I was always amazed at how creative they at conveying info graphically (some may argue it dumbs down the news, but I thought of USA Today when I saw the G&M's latest efforts mentioned above).

[Frances Woolley]

jvfm - very cool site. Brian, let's say a football field is roughly 107.5m x 53.75m. Then 215x215 is roughly 8 football fields. One story of a building is usually, say, 15 feet. So a stadium 10 stories high is 150 feet tall, or about 50 m. So 215 m would cover each of the eight football fields the depth of an average stadium 4 times, so that's 32 stadiums. Stadiums actually fan out from the field, though, so let's call it 16 stadiums. Have to say your estimate was much more comforting! Frances

[Brian Finch]

Frances, you're right, I was a little sloppy with my numbers - I was thinking a stadium would be roughly double the length and width of the pitch, 200m x 200m. The width is off by a factor of two at least. Then I assumed a stadium would be about 100m deep, but that's probably way off.

[Mike Moffatt]

50 million gallons is also 535 million tall (12 oz) cups of coffee at Starbucks, a unit of measurement I can identify with. It would take me several *weeks* to drink that much Starbucks. :)

[Frances Woolley]

Mike, only about 1000 years, drinking a cup a minute 24/7!

Brian, I was being way too pedantic, I have absolutely no idea how big an average football stadium is.

[J. Powers]

Five is also the maximum number that people can intuit directly. Most people see five oranges on a plate, and they just see that there are five. If there are eight, most people have to count to make sure. (Apparently a handful of people can intuit up to seven, but almost never more than that.) I bet there's a correlation.

The reaction to an earthquake in China that Smith describes strikes me as eminently sane. What should we do in the the face of mass calamity? Quit our jobs and volunteer to help save more pelicans (I doubt we would be much help unless we were willing to commit months or years to becoming expert in how to handle them)? Fall into profound despair and depression because humanity is so awful (seems like adolescent histrionics to me)? Complain cynically about BP's greed (as opposed to pushing our own lawmakers to regulate Canadian oil companies more stringently)? Would any of these be helping--or would they be simply emotionally self-indulgent?

It is a great strength of the human spirit that we can go on in the face a calamity--I mean "go on" in the sense of love our friends and family, enjoy the small pleasures of life, contribute constructively and directly to the communities we live in. We must help where (and I mean this geographically) we can. This is one of the main reasons that men and women of a philosophical bent have scoffed at the daily news. It is a fatuous and silly kind of knowing, for the most part, that leads us to feel sorry or frustrated about things over which we have little to no control. Better to stay informed about things about which we can do something here and now. Psychologically, we're just built to perform better this way; I suspect for good reason.

[Brett]

Your comment about the tribe in the Amazon brought to mind a post by Mark Liberman entitled THE PIRAHÃ AND US. It's also about our poor ability to grasp numbers, in particular when comparing groups.

[Andrew F]

Sorry for more pedantry, but the conversion of gallons to cubic meters was off, I believe.

50 million gallons ~= 13 million L ~= 13,000 m^3 = ~23.5 m per side of a cube. I think you missed the conversion from L to m^3.

In scale, this is 5 Olympic swimming pools.

[Frances Woolley]

Andrew, sorry, I don't understand, 1 gallon is about 4 to 5 litres, depending on whether it's US or imperial gallons. So probably closer to 50 pools than 5.

[Andrew F]

Oh you're right. Embarrassing to make your own mistake when correcting someone else. 50 million gallons is indeed ~190 million litres, or 190,000 cubic m. Regardless, it'd be a cube 57.5m to a side, or 76 swimming pools. I have to admit, I thought 5 sounded low (I was off by a factor of 3.78^2).

[Phil Koop]

This territory has been covered quite well by the cognitive psychologists. See Dan Gardner's excellent book "Risk" for an accessible survey that includes many examples of practical importance for public policy.

[Brian Finch]

Sorry for opening up the debate on volume and measure - at this point I'm pretty sure that any flaws in my assumptions and calculations will be subsumed by the error in the original estimates of the amount of oil leaked!

[Simon van Norden]

Another common approach to improve our ability to grasp large numbers is to scale them by person or by household. So if I assume a US population of 'round about 300 million, an oil spill of 23-89 million gallons is "only" 0.08 - 0.3 gallons per capita. In terms of environmental impact, I'm guessing that's less than the *daily* amount of urine produced by the same population (although I'm also guessing that the latter biodegrades more quickly.)

[Mike Moffatt]

"I'm guessing that's less than the *daily* amount of urine produced by the same population"

Particularly if they're drinking a tall cup of coffee a minute, 24/7, for 1000 years.

[Frances Woolley]

Simon, interesting approach (makes me feel much better about the spill), but could be potentially misleading if the cost of exposure to environmental harm is non-linear in the amount of exposure received. E.g. evaluating Chernobyl in terms of total radiation emitted divided by the number of people on earth would probably not give a good estimate of the potential impacts of that disaster (though it's been great for the local bird populations, apparently, and some other species of wildlife).

Actually, what would be the health impacts of drinking 0.3 gallons of oil? Just how toxic is it?

As an aside, that may or may not be relevant to anything, lots of rent-seeking activity, e.g. milk quotas, relies on the fact that a large benefit to a small group of people is a small benefit to a large group of people.

[Andrew F]

Oil is full of nasty things like benzene. I'm sure it's pretty toxic.

[Patrick]

Simon: Great example of how to mislead with numbers. Read this: http://en.wikipedia.org/wiki/Toxicity.

[Simon van Norden]

Frances, Andrew and Patrick: I agree with you; distribution matters, toxicity matters, as do many other things (such as the fact that most urine is very carefully channeled into specially built and maintained treatment plants.)

But it puts the numbers on a scale that we can relate to (which was the topic of the post.) It also lets you start to imagine how this compares to our daily oil consumption, potential conservation measures, how much oil we personally spill into the environment....

[Just visiting from Macleans]

More fun with numbers:

World oil consumption: One thousand barrels a second

Latest worst case production rate: 60,000 barrels/day (1 minute of daily world consumption).

Fine for spilling oil ONLY (not including cleanup and legit opportunity costs): $1000/barrel.

Daily ticket for BP shareholders (notwithstanding SG, NR and Bob Smith longstanding arguments on "who ultimately pays"): $60 million

Monthly fine - ticket only - approaching $2 billion

[Bob Smith]

Of course, since BP was probably operating its drilling operation through a subsidiary, technically BP's liability is limited to whatever the value of that subsidiary is (since they have no obligation to satisfy its claims). Also, I gather US law limits liability for these sorts of oil spills, in certain circumstances, to $75 million - though Congress is hurriedly trying to amend that law retroactively. As a practical business matter, BP ios probably going to have to pony up more money that it's legally obliged to to cover the costs of cleanup if it wants to be able to continue carrying on business in the US, but I doubt they'll end up paying everything that Obama (and others) want them to.

Of course, if the US government gets too demanding, BP might just say "screw it" , shut down their US subsidiary, and leave the government (and others) to pursue their claims against that subsidiary in a bankruptcy court (for which they'll probably get pennies on the dollar, since I have to imagine that BP's US operations are worth a lot more as a going concern).

And Just, in this case, to the extent that BP gets hit with the bill, it will be borne largely by its shareholders, since they probably won't be able to pass on higher costs to their consumers or their employees (both of whom can buy oil or work for, other oil companies).

[Frances Woolley]

JVFM and Simon's (thoughtful, as always) comments make me wonder - how does the toxicity of
- spilling a barrel of oil into the gulf of mexico
compare with the toxicity of
- converting a barrel of oil into gasoline and using it to fuel your car?
Why would spilling oil be so much worse than refining and burning it?

[Just visiting from Macleans]

Also, I gather US law limits liability for these sorts of oil spills, in certain circumstances, to $75 million - though Congress is hurriedly trying to amend that law retroactively.

Limit is voided, I believe, if there is negligence (criminal or otherwise). Read background - Eric Reguly column yesterday:

BP PLC took another political and stock market pounding as allegations surfaced that the British oil giant took shortcuts that created a “nightmare well” in the Gulf of Mexico, according to internal documents released by U.S. lawmakers investigating the explosion that triggered the U.S.’s worst oil spill.

The comment was made by BP drilling engineer Brian Morel in an e-mail on April 14, six days before an explosion destroyed the Deepwater Horizon offshore drilling rig, killing 11 crew. The e-mail and other documents were released by the U.S. House of Representatives Energy and Commerce Committee, which is investigating the explosion and the spill.

The committee accused BP of making decisions that “posed a trade-off between cost and well safety,” outlining its findings in a 25-page letter to BP CEO Tony Hayward.
http://www.theglobeandmail.com/globe-investor/congress-accuses-bp-of-cutting-corners-to-create-nightmare-well/article1604215/

Also, it seems to me wild guesstimates of cleanup to date $20-$45b, BP's US assets $100-$150b? Easily transferred to another operator- don't see why there would be a discount.

[Just visiting from Macleans]

Why would spilling oil be so much worse than refining and burning it?

Allow me to access the recesses of my early work experience (reservoir engineering).

Hydrocarbons in a reservoir primarily come in the form of C(n)H(2n+2):

CH4 (methane)
C2H6 (ethane)
C3H8 (propane)
C4H10 (butane)
===
C5H12 (pentanes +)
etc

The first 4 are gases at STP (standard temp and pressure) - so they would flare off, or vent. The lighter stuff would eventually also evaporate with heat. The really heavy stuff (asphaltenes) would probably sink.

In the raw, you can also have impurities (sulphur) which defines the oil or gas as sour. SO2 is poisonous, and can kill (remember when Weibo Ludwig was blowing up things in Alberta - and terrorizing neighbours - it was due to the proximity to sour gas wells he claims caused nausea and miscarriages). Impurities are separated at the refineries, and the hydrocarbons are separated , cracked, etc - to make various feedstocks depending upon the "recipe".

In complete combustion - you have two products - CO2 and H2O.
ie - CH4 + 2O2 => CO2 + 2H2O
incomplete - you get carbon monoxide,CO (a poison) and depending upon the impurities - SOx (sulphur) and NOx (brown haze). No matter whether complete/incomplete combustion - mainly gases that mix in the atmosphere and are diluted. Not same with raw crude, immersed/emulsed in water.

We also know CO2 causes climate change - but vented gas (methane - the prime component of your home heating gas) is many times stronger as a greenhouse gas. Same with gasoline venting at fillup stations.

[Just visiting from Macleans]

SO2 is poisonous, and can kill (remember when Weibo Ludwig was blowing up things in Alberta - and terrorizing neighbours - it was due to the proximity to sour gas wells he claims caused nausea and miscarriages)

Oops - bad memory. H2S is the poisonous sour gas - "rotten eggs" smell. SO2 is a by product of combustion with fuel containing sulphur - precipitates out in acid rain.

[Bob Smith]

Just,

You're right that liability is only limited to $75 million if the government can establish that there was gross negligence on the part of BP or its constractors (which is hard, though, since it involves more than simple negligence) or that they violated a regulation.

But the limitation of liability issue is a real concern for the government. First, I doubt the fair market value of BP's US assets are in the $100-150B range. Even before the spill, the market capitalization of BP was only 200B, and BP's annual report suggests(though not definitively) that most of BP's assets are non-US assets. I'd think your $100B figure might be, charitably, the maximum value of US assets (some of which are not readily convertible into cash, goodwill, for instance), not the minimum (others have suggested $50B might be a more accurate estimate of the value of BP's tangible North American assets, but I have no idea where they got that from).

But that's based on the pre-spill valuation. Some of those assets have probably seen real declines in value since the spill (what are BP's offshore drilling properties worth now?) and other assets would be hard pressed to convert to cash? A few years ago, when people were lending money like crazy that would be no problem, but I'm not sure the same is true now. Certainly, they'd probably only do so at a hefty discount.

But there's a final problem. I simplified it earlier, but BP doesn't carry on business in the US through one subsidiary. Their annual report lists 11 "important" subsidiaries in the US, and there are probably dozens (if not hundreds) of others whcih hold individual projects or assets. Legally, the government can go after BP Gulf Oil Spill Inc. (or whatever the company which operated the Deepwater Horizon is called - I'm making up all the BP subsidiary names), but it doesn't have any legal claim against BP Texas Refinery Inc., or BP Alaska drilling inc, or BP's variousother subsdiaries).

Although it is possible, in very rare circumstances, to pierce the corporate veil, court are exceedingly reluctant to do so and, if I recall correctly, will do so only where the operations of the BP subsidiary was really run as part of BP's operations (which is unlikely in a company as, presumably, sophisticated as BP). If push came to shove, BP could say, "fine, please take whatever you want from BP Gulf Oil Spill Inc. Oh, by the way, that company's only asset was a bunch of contracts with Haliburton and Deepwater to operate an oil rig, which rig is now sitting on the bottom of the Gulf of Mexico. Have fun."

From a practical business perspective that would be a risky strategy (I'd imagine the American public would be enraged), but that gives them considerable leverage in dealing with the US government since, if pushed too hard, they can probably just walk away and stick the government with the clean-up bill.

[Just visiting from Macleans]

Interesting analysis Bob.

O/T but related - I once met a guy at BP in Anchorage (pre Amoco takeover) who was managing some aspect of their ops. He was an instumentation guy promoted from the North Sea, and was quite proud of the fact that he does the thinking, and the contractors do the "real work". (A canary in the coal mine , perhaps - btw the phrase originating as they were used to detect low levels of explosive methane as they are sensitive and succumb to it at low concentrations).

Veco Engineering (an Alaska based firm) had its beginnings directly as a result of the Exxon Valdez cleanup - at the right place at the right time. They eventually were taken over by a Canadian firm (well, the Canadian assets anyway) a few years ago some time after a Veco executive was secretly filmed in a hotel room bribing some Alaska gov't officials.

[Bob Smith]

Mind you, it seems like practical business considerations have won out over legal technicalities, as BP has announced that it will set up a $20 billion compensation fund (http://www.theglobeandmail.com/news/world/americas/bp-agrees-to-20-billion-fund-for-spill-victims/article1606173/). I guess investors were betting that they'd cave, as the announcement hasn't really affected BPs share price.

[Andrew F]

Bob, how could BP have all the assets isolated from liability and claim that they were self-insuring at the same time? How could they be allowed to self-insure if their assets were isolated?

If this is the case, then BP wasn't insuring the well, but rather the US government was, which is effectively a subsidy. One way to shut down future offshore oil drilling to require liability insurance upwards of $100 billion per well (or perhaps scaled to the potential worst-case damage a disaster might cause).

[Bob Smith]

Andrew.

Well, they can do that if the ultimate subsidiary if BP (i.e., the ultimate parent company) doesn't have a LEGAL obligation to insure losses incurred by BP Oil Spill Co. Self-insurance can mean a number of things. It could mean that BP has a contractual obligation (or some other form of legal obligation) to pay for losses caused by BP Oil Spill Co (and maybe it does, I wouldn't know). In that case, BP is legally on the hook for the liabilities of its subsidiaries.

It could also mean that BP just has an internal policy to pay for any losses incured by it (or its subsidiaries) rather than paying premiums to insure against those losses. This is a common enough practice in most businesses for risks which occur with some regularity but which are generally small (fires, vehicle accidents, workplace injuries, etc.), and it generally makes sense (since its cheaper to insure yourself than to pay someone else to do it for you). Of course, in the latter scenario, BP could just as readily make the business decision to say, "we'd rather not pay for those losses, sorry" (though, as I noted above, from a business perspective that probably isn't a good idea). In this scenario BP is literally "self" insuring (i.e., it'll make itself whole in the event of losses, but not neccesarily others), but only if it wants to.

I also understand that BP has a captive insurance company (based in Guernsey) which it uses to insure the operation of its subsidiaries, where they are required to have a formal insurance policies (for example, pursuant to government regulations). So, it "self-insures" through a special purpose insurance subsidiary. Now, that subsidiary has a legal obligation to pay out any claims under its policy, but that obligation is limited to the policy limit, which I gather is about $700 million. I think they blew through that months ago.

But you may have hit on why BP is agreeing to pay all "legitimate claims" (their words). Even if it didn't have a legal obligation to pay those claims, if it didn't, the first response of governments world-wide would be to demand external insurance policies rather than letting large companies self-insure. BP may figure that it's far better for them to pay up, in this instance, rather than "get away" with one this time (at the expense of significant cost to their business and of making itself a pariah in the oil industry) only to get hit with additional insurance obligations down the road. From a purely business perspective, it makes sense.

[Andrew F]

I don't know if it makes sense to leave that loophole. Eventually some company somewhere will face a liability so huge that they will balk rather the voluntarily cover these liabilities. So, if we're allowing companies to self-insure for damages to the property of others, then it needs to be proper insurance and not something they can shirk if the burden is too large (or is too large for their balance sheet).

[Simon van Norden]

I think Dot Earth over the NYT has suddenly had an idea similar to yours, Frances.
http://dotearth.blogs.nytimes.com/2010/06/18/25000-barrels-of-oil-seen-a-new-way/

[Patrick]

BP is quite the cash generating machine. So long as they are a going concern, they can afford rather a large hit - many tens of billions I would guess.

By way of comparison, in 1979 it took Pemex 30 months to cap Ixtoc in 150 ft of water. The well was about the same volume - 30K bbl. The first relief well failed. This well is in 1 mile of water. And I've read some credible accounts (see the theoildrum.com) that suggest the blow-out damaged the casing and the flow is eroding the well bore - essentially their is a open bore hole 18K ft into the earth. If that's the case, we'll get a whole new lesson on incomprehensibly huge disasters.