[geeks] Why? i.e. why do people have such poor math & engineering skills?

[Greg A. Woods]

[ On Wednesday, July 31, 2002 at 07:36:46 (-0700), Fogg, James wrote: ]
> Subject: RE: [geeks] Why?
>
> ~ > > "Fogg, James" <JFogg at vicinity.com> wrote:
> ~ > > > Of course, wait until you see a walking dragline.  500K-tons of walking
> ~ > > > earth moving beastie. I watched one for a few days in  Pennsylvania at
> ~ > > > a coal strip-mine.
> ~ > Woah, what's this?  A machine that weighs 500 tons and it walks?
> ~ 
> ~ five hundred THOUSAND tons!

No, not that much -- you're over by at least an order of magnitude, or
even two (most of the big walkers are only 5,000 tons).

Big Muskie, a (well, "the" -- only one was built) Bucyrus-Erie 4250-W,
weighed in at an estimated 15,000 tons, and was as far as I know the
heaviest moving land machine ever built.  It's recently been demolished
though....

By comparison the biggest stripping shovel ever made, the Marion 6360
weighed in at about 14,000 tons.  There are some pretty big bucket wheel
excavators too....

> OK, I was guessing. Lets just say I wouldn't want one to travel over my
> septic leach field.

Hmmmm.... that's interesting.  You were only out by three orders of magnitude. :-)

Now I don't want to pick on your particular mistake, but I do want to
use it to make a much more general and related point.

Last winter I went to a talk here at the UofT by Brian Kernighan (he's a
UofT alumnus).  He's now teaching basic math and computer skills to
non-science students at Princeton:

	http://www.cs.princeton.edu/course/archive/fall02/cs109/

In the lecture he described some simple skill testing problems he gives
his class and how most of them invariably fail at what most engineers
would consider common sense.  One great example he described that
relates almost directly to your guess about the weight of a gigantic
machine such as a walking dragline is where he asked students to guess
the weight of an old cannon barrel that's mounted on a pedestal on the
campus.  The students are allowed to go out to climb on, measure, and
otherwise examine the barrel.  IIRC he said none have ever even come
close to guessing its weight, and for demonstration in this lecture he
described how he then goes about teaching the class how they should have
done the job and how they could have come well within a reasonable
percentage of its actual weight.  Using a similar technique, but
backwards, let's sanity check your guess:

	Although water is considerably lighter than iron, let's use it
	as a starting point.

	How big a volume would 500 tons of water be?

	well 1 cubic foot of water weighs about 62 pounds (ten pounds
	per Imperial gallon, or 8.33 pounds per US gallon) [*]

	500 tons of water (i.e. 1 million pounds, or 100,000
	Imp. gallons) would be about 16,000 cubic feet, or a cube
	roughly 25 feet on a side.

	You could probably fit four or even six such cubes inside the
	main body of a really big walking dragline, and though the
	inside of the body is quite open and airy, remember that steel
	weighs a lot more than water, and there's a lot of steel and
	other heavy stuff in the walkers, boom, bucket, etc.  In fact
	the 220 cu.yd. bucket alone on Big Muskie weighed in at 550
	tons all by itself.  :-)

	(one million US gal. would be roughly a cube 51 feet on a side)

([*] kids in Canada these days might not know that 1 cubic foot of water
weighs, but if they can't figure it out in metric given the standard
definition of a litre, then they really didn't learn anything!)

-- 
								Greg A. Woods

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