Expensive Shoebox
What would be the most expensive way to fill a size 11 shoebox (e.g. with 64 GB MicroSD cards all full of legally purchased music)?
Rick Lewis
A shoebox full of valuable stuff seems to top out at about $2 billion. Surprisingly, this turns out to be true for a wide range of possible fillings.
![Plus the value of the box.](http://what-if.xkcd.com/imgs/a/108/billion.png)
The MicroSD cards are a good idea. iTunes songs cost about $1 each, and MicroSD cards have a capacity of about 1.6 petabytes per gallon. A men's size 11 shoebox is about 10-15 liters, depending on the brand and type of shoe, which means it can hold up to 1.5 billion 4 MB songs (at about a dollar each). (That's about 20 times as many songs as the iTunes store offers, so you'll have to buy some of the songs more than once.)
Expensive software like Adobe®©™ Photoshop®©™ CS®™ 5™ has a slightly higher cost-to-megabyte ratio, since it retails for several hundred dollars and takes up several hundred megabytes of space. Or, at least, it used to, until Adobe moved to a cloud model.
Once you start considering software prices, you can probably crank the "cost" of things in a shoebox as high as you want by making unlimited in-app purchases. And while the resulting RPG character may technically represent the result of your spending that much money, it's hard to argue with a straight face that your character is in any sense worth a trillion dollars.
![It actually maxed out at 2,147,483,648 swords, but I spent the second trillion because I kept hoping they'd fix it.](http://what-if.xkcd.com/imgs/a/108/president.png)
So let's think about actual objects.
There's gold, of course. 13 liters of gold is worth about $10 million as of this writing. Platinum is a little more expensive at $13 million/shoebox.[1]Not yet an SI unit, sadly. That's about 10 times the value of a shoebox full of $100 bills. On the other hand, a shoebox full of gold would weigh as much as a small horse.
There are more expensive metals. A gram of pure plutonium, for example, would cost about $5k. As a bonus, plutonium is even denser than gold, which means you could fit almost 300 kilograms of it in a shoebox.
Before you spend $3 billion on plutonium, take note: Plutonium's critical mass is about 10 kilograms. So while you could fit 300 kilograms of it in a shoebox, you could only do so briefly.
![This means you're unlikely to find a buyer, or—if you can offer to assemble the shoebox at a specific time and place, maybe MORE likely.](http://what-if.xkcd.com/imgs/a/108/nuke.png)
High-quality diamonds are expensive, but it's hard to get a handle on their exact price because the entire industry was built on a scam the gemstone market is complicated. One site quotes a price of over \$300,000 for a flawless 600 mg (3 carat) diamond—which means that a shoebox full of perfect-quality gem diamonds could be worth as much as \$20 billion—but \$1 or \$2 billion is more reasonable.
![A Google search for unsolved+packing+problems very nearly got me just now.](http://what-if.xkcd.com/imgs/a/108/packing.png)
Many illegal drugs are, by weight, more valuable than gold. Cocaine's price varies a lot, but in many areas is in the neighborhood of $100/gram.[2]My search history after researching drug street prices would probably get me on all kinds of government watch lists, if I weren't on them all already for all the other things I've researched for this blog. Gold is currently less than half that. However, cocaine is much less dense than gold,[3]But wait—what is the density of cocaine? As usual, the Straight Dope Message Board folks are on the case; in this discussion, they consult the CRC Handbook and Merck Index, before giving up and deciding that it's probably about 1 kg/L, like most organic substances. They do, however, learn its boiling point and solubility in olive oil. so a shoebox full of cocaine would be less valuable than one of gold.
Cocaine is not the most expensive drug by weight. LSD—probably the most widely-consumed substance sold to consumers by the microgram—costs about a thousand times more than cocaine by weight. A shoebox full of pure LSD would be worth about $2.5 billion.
Some prescription drugs can be just as expensive as LSD. A single dose of brentuximab vedotin (Adcetris) can cost \$13,500, which—for the average patient—puts its shoebox value in the same \$2 billion range as LSD, plutonium, and MicroSD cards. Other drugs are even more expensive.
Of course, you could always put shoes in the shoebox.
![Oh, I guess if you don't wear them while they're in the box it's ok.](http://what-if.xkcd.com/imgs/a/108/weird.png)
Judy Garland's shoes from The Wizard of Oz sold at auction for $666,000, and—unlike the other things we've considered—may have, at one point, actually been placed in a shoebox.
If you really want to fill a shoebox with an arbitrarily large amount of money, you could get the US Treasury to mint you a trillion-dollar platinum coin.
But if you're open to leveraging our monetary system's legal authority to impart value into an arbitrary inanimate object ...
![People disagree about spelling it 'check' vs. 'cheque', but at least we can all agree that it will be nice when we can stop using the word entirely.](http://what-if.xkcd.com/imgs/a/108/check.png)
... you could just write a check.