Thursday, October 12, 2006

How high?

While writing last night's post, a sick question occured to me: how high is Bush's pyramid of skulls? So, I tried to work it out: (Warning: sick maths follows):

  1. Assume a cubical skull (I just love the way physicists say things like this; its so they stack nicely);
  2. Assume the volume of a single skull is about 2 litres, or 0.002 cubic meters (not unreasonable, looking at the cast on my mantlepiece, and if its too large, call it packing fraction);
  3. So the volume of 655,000 cubical skulls is 13,100 cubic meters - enough to fill five standard Olympic swimming pools or bury a rugby field to a depth of 1.3 meters;
  4. If we use a 45 degree cone, with height equal to radius (to make the maths simple), we have v = 1/3 pi r3. Solving for r gives a final height of 23.2 meters, or 76 feet for those still stuck in the dark ages. So if stacked on the White House lawn, they would be taller than the White House.

Interestingly, the above website also gives the floor area of the White House: 55,000 square feet, or 5100 square meters. So Bush's pyramid of skulls would fill every floor to a depth of 2.5 meters - burying the President and his staff in the death they have caused.

Correction: As pointed out in the comments, I'm out by a factor of ten in the total volume, which means the pile is somewhat smaller (only half the height of the White House). Teach me to use a calculator in the morning...


Nice post that one (seriously I mean no sarcasm). Maybe you can start a meme with it - did you think it up yourself?
It brings home the point in a slightly comical (but at the same time morbid) way.

Posted by Genius : 10/12/2006 06:35:00 PM

Your calculation is wrong, you made a 10 fold error in calculating the volume of the skulls, they're actually 1310 cubic metres. Also I think your estimate of skull volume is way too low, the average brain volume is 1600 cc, doubling that would give a better estimate. Now assume a spherical skull, this gives a radius of just over 9 cm (seems good, the circumference of my head is about 58 cm, using 2 pi r gives a radius of 9.2 cm). Next, rather than assuming a cone, stack the skulls: 1 at the apex, sitting on 4 below it, then 9 the next layer. This will give a stable pyramid with a square base, each layer have a number of skulls equal to the square of the number of layers it is from the top. Somewhat fortuitously, such a pyramid 125 layers high will use 658,875 skulls, close to the right number. This kind of pyramid uses body centred cubic packing, with the distance from sphere to sphere in a layer and the distance between the centre of spheres two layers apart equal to 4 r / root 3. This gives a square base of 26.4 metres and a height of 13.5 metres. Interestingly, Bush's estimate of around 30,000 dead will be contained in the bottom two layers of this pyramid

Posted by Anonymous : 10/13/2006 08:58:00 AM

Bob: Your calculation is wrong, you made a 10 fold error in calculating the volume of the skulls, they're actually 1310 cubic metres.

Fuck, you're right.

Mea culpa, mea culpa, mea maxima culpa.

(And yes, I was having doubts about skull volume as well).

Posted by Idiot/Savant : 10/13/2006 02:34:00 PM

After some more thought, I realised that by pushing the skulls together in each layer, you can make the pyramid taller than using body centred cubic packing. This would give a pyramid with a base of 22.9 metres and height 16.2 metres. For even more height, build a triangular pyramid (ie one skull on the top layer, three on the next, then 6 then 10 etc.). This will need to be 157 layers high for 657,389 skulls, length at base 28.7 metres and height and 25.9 metres high. Finally definitely higher than the Whitehouse. Spheres pack with a best packing ratio of 0.74, so filling a swimming pool with 3.2 litre skulls is equivalent to filling with 4 litre cubes. So the skulls will *only* fill a single Olympic swimming pool. And will only fill the Whitehouse to half a metre. I guess that's why they haven't noticed.

Posted by Anonymous : 10/14/2006 08:28:00 AM

Good work bob.

Posted by Genius : 10/14/2006 09:20:00 AM