The Scrooge Swim

Matt Powers calculates how much money you would need to dive into a pile the size of Scrooge McDuck's:

Looking at some of the best pictorial evidence of the McDuck vault, it is evident that this large pile of gold on the left appears to be five feet tall. This is deduced under the assumption that the average duck 14 inches tall, which is then used comparatively to quantify the pile (5 ft = 4.3 duck heights). … The assumption will be made here that one cubic inch is roughly one ounce of gold. To convert that into a dome shape the value is simply cubed, which becomes 97,366 ounces. Given that 1 ounce of gold is roughly $5.00, it can extrapolated that each large pile of gold in the vault is worth $486,830.

However, Scrooge McDuck was first drawn in 1947, therefore inflation must be adjusted for which totals a whopping 5.2 billion dollars per pile. In the picture, there are two smaller piles which roughly equal the larger doubling the total to 10.4 billion. However, the shadows in the corner suggest that the room is a least three times as large as it is. Therefore, Scrooge was privy to a cool 31.2 billion dollars.

This means that only the six richest people in the world could afford to pull off the Scrooge swim.

Update from a reader:

Hopefully I'm not the only reader writing in protest about the Scrooge McDuck calculation. I quite enjoy it when people devote ridiculous amounts of time and energy coming up with plausible calculations, and thought since you were sharing it this would be one of those moments. Instead when I read the article I was treated to bullshit piled atop made-up numbers. Every time he has to give a number, it's wrong. And it's not just wrong by a small estimation factor. It's so far off it's clear that he made no attempt to combine his wit with any mathematical acuity. There are so many errors I'm just going to number them:

1) "The assumption will be made here that one cubic inch is roughly one ounce of gold." Wrong. It's not actually very difficult to calculate how much a cubic inch of gold weighs, and it's around 11 regular ounces (of course gold is generally measured with troy ounces).

2) "Given that 1 ounce of gold is roughly $5.00." I'm not a monetary expert, but it seems pretty easy to check this online. A (non-troy) oz of gold appears to cost around $1400.

3) The worst thing that he does is the only part that has even a veneer of math, when he calculates the volume of the big gold pile. He calculates the area under an integral and then, to get the volume, cubes it, giving an answer with units of inches to the sixth power. Perhaps the implication is that Scrooge is so wealthy he has six dimensional gold, but it seems unlikely. If he wanted to calculate the volume of a single pile, he could do so with a double-integral (but Powers didn't make it to multivariable calculus). In any event, these calculations are just flash, because the better estimate of the gold would be to treat it's volume like any other rectangular solid, since the fluctuations at the top will mostly even out.

If we were to assume that the room is 25 ft by 25 ft and that if the gold had a uniform surface, its depth would be 10 feet, then we get a total volume of 6250 ft^3. I think this is actually a bit small, but I wanted to be conservative. This is 10.8 million cubic inches. This is around 7.52 million pounds of gold (figuring .69663 lbs/cubic inch). This would be worth around 180 trillion dollars (using the avoirdupois pound value I got here). Of course, my calculations assume solid gold, which obviously isn't possible since Scrooge is swimming in it, so we would need to work in some factor to account for airspace, maybe assuming that 60% of it is gold and the rest is air, money bag material, etc, so to my reading, a conservative estimate of his wealth is 108 trillion dollars.

It's amusing that the people who comment on Powers article are either people pointing out how wrong he is or people calling those people pedants (although I do love the one who misspelled it "pendant"). One last error that I just noticed. I don't think Powers understands how inflation works. The value of McDuck's gold in 1950 (easier to find than 1947) dollars is not done with some bullshit inflation calculation, but by multiplying the weight of gold by is 1950 value, which is also easy to find on the internet: $41 per troy oz. Again, note that this is not the $5 Powers originally claimed as the value of an oz of gold. But most of this comes from his ass.