Pie Are Square; Oil Spills Are Round

By Sean Carroll | June 8, 2010 4:43 pm

Ah, not this one again. The folks at Iglu Cruises have put together a helpful infographic to explain various features of the Gulf of Mexico oil spill (via Deep Sea News). Here’s the bit where they compare the recent spill (which, by the way, is still ongoing at a fantastic rate) to previous oil spills. Click for full resolution.

Oil spills: diameter vs. area

Doesn’t make the current fiasco seem so bad, does it? That little blob on the left looks a lot smaller than the blob right next to it, representing Saddam Hussein’s dump of oil into the Persian Gulf during the first Gulf War. In fact, when you think about it, it looks a lot smaller. Which is weird, when you look at the numbers and see that the current spill is 38 million gallons (as of May 27), while the Iraqi spill was 520 million gallons, a factor of about 14 times bigger. The blob representing Iraq’s spill seems a lot more than 14 times the size of the blob for the current spill. You don’t think — no, they couldn’t have done that. Could they?

Yes, they did. When measure the diameter of the circle representing the Iraqi spill, I get about 360 pixels (in the high-res version), while the smaller spill is about 26 pixels — a factor of about 14 larger. But that’s the diameter, not the area. The area of a circle, as many of us learned when we were little, is proportional to the square of its radius: A = π r2. The radius is just half the diameter, so the area is proportional to the diameter squared, not to the diameter. In other words, that big blob is about (14)2 = 196 times the area of the little one, when it should be only 14 times bigger.

I remember reading on some other blog about this same mistake being made in a completely different context, but I have no recollection of where. (Update: it was at Good Math, Bad Math, sensibly enough.) Probably won’t be the last time.

CATEGORIZED UNDER: Mathematics
  • Fiziker

    This is the post that I thought of immediately when I saw it: http://scienceblogs.com/goodmath/2009/02/financial_morons_and_quadratic.php
    Maybe it’s the one you’re thinking of.

    • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

      You’re right, thanks — I’ll update the post.

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  • http://deepseanews.com Kevin Z

    Ha! I just assumed they were making up the sizes and not even putting math into it all. Have I become that cynical??

  • http://eberkowitz.com Evan Berkowitz

    Also, this oil spill isn’t round, as is being discovered; there are giant plumes underwater so that the spill has a significant third dimension. Comparing the actual volumes leads you to compare radii cubed. That said, the actual geometric shape of surface spills is accurately given by ~radius^2 * comparatively small thickness. A graphical comparison like this is not straightforward if you strive for honesty. Don’t get me wrong, what they did is definitely wrong, but I don’t think comparing areas is necessarily the right thing either (though it is certainly better than what they did!).

    As an additional level of complication, the oxygen levels are being depleted (not dangerously, yet) by bacteria living not just on the surface but also deeper, feeding on the plumes. So perhaps none of these comparisons give a good idea of environmental impact…

  • Jason A.

    Worse, if they’re representing them by ‘blobs’, you’d think they’d compare volume, not cross-sectional area. The drips at the bottom make you think of a three dimensional thing.

  • http://blog.itsathought.net/ Non-Believer

    Has anyone told the folks who created the graphic, so they can fix their mistake.
    This is going to get used by lots of folks. Of course even if the graphic were right, it would be wrong the day after and more wrong every day following until the leak is fixed. But still, starting with the wrong impression makes it worse.

  • Andy H

    I’m a lawyer. This reminds me of a recent court decision in Virginia where the Court struck down a non-compete agreement in part because the former employee was prohibited from working for a competitor anywhere within a “100 square mile radius” of his former employer, which, as the Court pointed, out didn’t make any sense.

  • http://poetryoutwest.wordpress.com Jodine Butler

    What gets me is that some commentators seem to think that it will all be cleaned up in 8-9 months. It to sounds to me like they are putting a time frame on washing their hands clean! They have no idea of the sheer scale of the spill and the impact is yet to be felt. This diagram is great for putting it into persepctive. I wrote a poem called Oil Birds on my poetry website http://poetryoutwest.wordpress.com because I was so moved by those photo’s. I couldn’t really add much more than what was already written… Jx

  • improbable

    The word “infographic” is apparently pronounced with the stress on “graphic”.

    There has been a fad of these things, most of them pretty, many of them (like this one) criminally misleading, and very very few of them with anything useful to say. It seems like the tribe of graphic designers all woke up to realise that better packaging for milk isn’t really all that important, and then they stumbled across E Tufte’s books and decided this could make them relevant to big questions in the world, like oil. Except that they only saw his pretty pictures and clearly didn’t read the text…

  • improbable

    Elsewhere on the oil “infographic” they also compare the area of the spill to:

    280000 football fields (with picture of a football)
    8 new york cities (with picture of madame libety)
    3 hawaiis (with a garlanded dancer)

    How the hell is this useful for understanding its growth? It would be a fair puzzle to put these things in order, never mind to understand that they are each about 10 times the area of the last one.

    The only graph in the thing is also labelled “variance in reported flow rate”, confirming (if there was any doubt) that the author does not know what the word variance means.

  • Jessica

    You are all cynics who seem to have nothing better to do than to criticise the minor detail – the fact is that the figures ARE CORRECT having looked into this. They seem to have succeeded in creating an informative piece to people who quickly want to scan the info without criticising every detail. You should be ashamed of yourselves, I personally like it.

  • http://drip.de davidmaas

    Another example: http://www.cringely.com/2009/02/wall-street-cant-count/

    @Jessica, I don’t see this as cynicism at all. Its scarier to see the true relation of the current catastrophe to the Iraqi oil spill. I think this is a valid correction.

  • JollyJoker

    http://en.wikipedia.org/wiki/List_of_oil_spills

    Has numbers for historical oil spills. It seems they took a high estimate for the Iraqi spill and and a fairly low for Deepwater Horizon (although min / max figures of the latter differ so much its hard to pick a decent estimate). I’m not sure if there’s any substance to this; I just usually check the figures elsewhere when I see a graph that’s this misleading.

    It would be nice to see a corrected pic.

  • Gordon Pasha
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  • http://www.sciencebase.com David Bradley

    I’ve re-done their graphic based on area to show approximate relative scale of the oilspills (red blobs within oily black circles). It’s not nearly so shocking as the original but mathematically a more accurate visualisation.

    http://bit.ly/bFp1eu

  • Pieter Kok

    Here is my corrected graphical representation, where the area shown corresponds to the volume of the spill:

  • Benji

    Worst thing:

    most people will never figure out they´re being lied to.

  • Alex

    You should share this with FlowingData or Information is Beautiful; they’re always looking out for things like this.

  • Mark B.

    Edward Tufte talks about this kind of thing in his books. Even when done with correct dimensions, this kind of graphic is misleading because most people don’t tend to estimate areas (or volumes) correctly — we have a much better sense for estimating lengths, so, Tufte argues, graphics with integrity should stick to linear comparisons.

  • Eugene

    @Benji : some just wanted to be lied to (see Jessica post #12)

  • lylebot

    They also seem to have confused American and British English. The thing about “football pitches” is illustrated with an American football. As far as I know, a “football pitch” is what an American would call a “soccer field”. And even if it’s not, an American would say “football field”, not “pitch”. And worst of all, soccer fields and football fields are not the same size.

    This is probably one of the worst of a lot of really bad infographics I’ve seen recently.

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  • Oliver

    Does that mean that every time I make a pie chart I have to use the sqrt(data) values instead of the abs(data) values to display it?
    Do those spreadsheet programs like ‘Origin’ or ‘Igor Pro’ do that already when using pie charts or do i also have to take care of this myself?

    Just wondering, since I never actually use pie charts like these to display data :-)

  • Jessica
  • Chase

    Looks like it’s been updated.

  • Nowhere Man

    @Oliver: The values displayed within a pie chart *should* all have the same radius. That takes the area formula out of the picture, so to speak. As long as each slice is allocated a percentage of the pie’s circumference that’s equal to that value’s percentage of the sum, the pie chart will be accurate.

    (I say *should* because I’ve seen pie charts where, oddly enough, some slices of the pie do have a larger radius than other slices. Fortunately, I haven’t seen this recently.)

  • http://washparkprophet.blogspot.com ohwilleke

    Current estimates of the Deepwater Horizon oil spill magnitude are more like 630 m barrels, making it the worst U.S. oil spill of all time and the second worst in world history.

    Moreover, unlike the 1991 Gulf War spill, this one isn’t over yet.

  • RJ

    @ohwilleke – Ok, I just took a quick glance at the link you posted and the number I am seeing is 630,000 barrels not millions.

  • Cary

    The graphic at the site has been corrected and updated.

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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .

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