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Innumeracy in print

An article in today’s Fox News contains an interesting numerical statement, one of those ‘gee whiz’ comparisons we so often see:

Compounding Aziz’s information, U.S. intelligence agencies have been going over millions of documents — 9 1/2 miles’ worth if laid end to end — left behind by Saddam’s government after its sudden collapse around April 10.

There is just one problem: their math is wrong. There are 5,280 feet in a mile; and 12 inches in a foot. Since Fox is an American news outlet, the paper size can be assumed as 8.5×11 inches. So we have, using the archaic system of measurements based on lengths of a long dead English Monarch’s appendages:

9.5 miles x 5,280 feet/mile x 12 inches/foot = 601,920 inches.

If we take ‘end to end’ literally, we get:

601,920 inches / 11 inches/sheet = 54,720 sheets.

This falls a few short of millions. Oh well… let’s try again. We’ll give them the benefit of the doubt and line the pages up side by side instead of end to end:

601,920 inches / 8.5 inches/sheet = 70,814 sheets.

Either there are only .07 million pages or someone can’t handle simple math.

Any engineer who grew up using a Pickett (sliderule) would have immediately seen the unreasonableness of the statement.

18 comments to Innumeracy in print

  • …or maybe Fox meant laying the papers side by side, so that only their sides would be facing you…in which case millions of sheets would measure miles from ‘end to end’…

  • Dale Amon

    That’s a possible mis-statement on their part. If they were talking about a 9.5 mile high stack of paper, they would almost certainly be up into the millions. But they didn’t say stack, they said ‘laid out end to end’.

  • Theodopoulos Pherecydes

    I’d as soon base my measurements on a long dead monarch’s appendage as an arbitrary division of an incorrect estimate of the circumference of what is in fact an irregular sphere.

  • David Hall

    Maybe they’ve got multiple lines of paper?

  • Shaun Bourke

    TV journalists can count ??

  • Mark Hulme-Jones

    Why assume that the paper size is US Legal? Surely, if these are Iraqi papers, they’d be whatever size the Iraqi’s use?

  • John Swartz

    It’s a dangerous game (for me) to criticize anyone’s math, but are you suggesting that standard Iraqi paper size might be about two thirds of an inch? (601,920/1,000,000= .601… and that doesn’t account for the plural “millions”.

  • zack mollusc

    Maybe it is 9.5 miles of binders, each binder containing more than 1 document?

    Or am I being ignorant again?

  • Sigivald

    In American English, we’d say “edge to edge” as likely as not for what you describe.

    “End to end”, while a clumsy construction, works as well for flat-to-flat as edge-to-edge, and I’m sure they meant the former, given the rest of the indications.

    Documents are, after all, often in binders or files, and their front and back are “ends” as much as the tops and sides.

  • Maybe they’re all on microfilm…? 😉

  • Dale Amon

    Sigivald: Nah, they don’t get off that easily. Do a bit of searching and you will find endless examples of constructs like: “If you put all the X’s end to end, they would reach to the Moon!” It’s more American NASA than anything else.

  • The cool thing about a long-dead monarch’s appendage, is that the units derived from its measure (or, in the case of a mile, the stride of a Roman legionnaire) are more likely to fit the human scale and be relevant to everyday human life.

    The metric system works on the scale of machines: very large numbers, very small numbers, base-10 math, often involving fractional exponents. The common law weights and measures system lends itself more to everyday concerns, and their corresponding arithmetic: tiny to moderate quantities and numbers, split or multiplied, as necessary, by factors of 2, 3, and their multiples.

    There is good sense in both approaches, within their respective spheres, so to characterize either system according to its anomalous or problematic aspects is to deny its inherent value. This is similar to the conceptual mistake that some critics of political parties make, when fixating on the party wackos (which all parties have) as being “representative.”

  • James

    It is actually 91.5 miles as opposed to 9.5 mi.

  • Reminds me of a joke:

    If you took everyone who was asleep in Church on Sunday and laid them out end to end…..

    ….they would all be much more comfortable than they were sleeping in those awful pews!

  • David Gillies

    Lets look at the ‘stacked on top of each other’ idea. I measured a stack of paper. 50 sheets was 3mm thick. 9.5 mi = 601920″ = 15288768 mm. Multiply by 50/3 = 254812800. If this was the number of documents that the US was analyzing the story would have said ‘hundreds of millions’. Of course that’s assuming that each ‘document’ was a page, but without the information on how many pages there are in the average document, the 9.5 miles figure is meaningless. If the US analysts really have to read a quarter of a billion pages of info, they’re going to be there for a long time.

  • John

    I wish I could remember the source, but I recall that the 9 1/2 miles refers to the amount of film only that had beend discovered. Not the amount of documents.

  • Old Patriot

    I was a database manager for an Intelligence Data Handling System for awhile, so this whole thing has me a bit puzzled. I had about 275,000 DOCUMENTS on file: some of those were fewer than 350 bytes, while others soared to megabyte size. Each was a single DOCUMENT. Those documents were organized into approximately 17,800 “FILES”, or reports on single installations or areas. The entire thing filled up a huge number of 11-inch magnetic disks in 24 disk-packs. Today, you could probably do the same thing with a single PC and two internal, 80gb hard drives, but this was in the early 1980’s – several ‘generations’ before PCs became practical for the average home-body.

    “Millions” of “documents” may have been collated into several thousands of “files” – which could easily be laid end-to-end to measure 9.5 miles. That figure tells us nothing about the files themselves, or the documents, or anything else to make sense of. I’d be willing to bet that the entire “9.5 miles” nonsense was inserted by some editor that never got closer than the city boundary to Iraq, and who has no more knowledge about the files than we do.

    The important thing is not how many files, or how long they stretch end-to-end, but how many people are sweating bullets this minute, worrying that their name will come to light in all those files, and they’ll be exposed for the bloody criminal accessories they truly are.

  • CS

    ‘I arst you civil enough, didn’t I?’ said the old man, straightening his shoulders pugnaciously. ‘You telling me you ain’t got a pint mug in the ‘ole bleeding boozer?’
    ‘And what in hell’s name is a pint?’ said the barman, leaning forward with the tips of his fingers on the counter.
    ‘Ark at ‘im ! Calls ‘isself a barman and don’t know what a pint is! Why, a pint’s the ‘alf of a quart, and there’s four quarts to the gallon. ‘Ave to teach you the A, B, C next.’
    ‘Never heard of ’em,’ said the barman shortly. ‘Litre and half litre — that’s all we serve. There’s the glasses on the shelf in front of you.
    ‘I likes a pint,’ persisted the old man. ‘You could ‘a drawed me off a pint easy enough. We didn’t ‘ave these bleeding litres when I was a young man.’
    –Orwell, 1984

    Phasing out of the metric system, decimalisation of the pound, evisceration of the House of Lords–these and many other actions taken over the past several decades are all part of the gradual ‘abolition of Britain’, and ought to be repudiated at every turn.