ACCUMULATING PERIPHERALS


Google minus one, or Ponzi vs. Ponzi by mattsteinglass
February 17, 2009, 2:41 pm
Filed under: Uncategorized

John Allen Paulos brings up Robert Louis Stevenson’s clever “imp in a bottle” problem:

The story tells of a genie in a bottle able and willing to satisfy your every romantic whim and financial desire. You’re offered the opportunity to buy this bottle and its amazing denizen at a price of your choice. There is a serious limitation, however.

When you’ve finished with the bottle, you have to sell it to someone else at a price strictly less than what you paid for it. If you don’t sell it to someone for a lower price, you will lose everything and will suffer excruciating and unrelenting torment. What would you pay for such a bottle?

Certainly you wouldn’t pay 1 cent because then you wouldn’t be able to sell it for a lower price. You wouldn’t pay 2 cents for it either since no one would buy it from you for 1 cent since everyone knows that it must be sold for a price less than the price at which it is bought. The same reasoning shows that you wouldn’t pay 3 cents for it since the person to whom you would have to sell it for 2 cents would object to buying it at that price since he wouldn’t be able to sell it for 1 cent. Likewise for prices of 4 cents, 5 cents, 6 cents, and so on.

We can use mathematical induction to formalize this argument, which proves conclusively that you wouldn’t buy the genie in the bottle for any amount of money.

The solution is simple. You buy it for $1, plus a one-week IOU for Google dollars in a giant steel safe at the bottom of the Atlantic. You then ask the genie to create a giant steel safe containing Google dollars at the bottom of the Atlantic. Done with your genie, you sell him to the next guy for $1, plus a one-week IOU for (Google-1) dollars in that giant steel safe at the bottom of the Atlantic, which you in the meantime have given away to the guy you’re selling the genie to. He then sells the genie to the next guy for $1 plus (Google-2) dollars in the… This process continues through ((Google iterations) – (time until Earth’s Sun burns out)).

You could actually probably turn the Google dollars in the safe into a forward contract and obviate the whole need for them to have any physical reality. This has been an exercise in Derivative Magical Thinking 101, also known as Dueling Ponzis.

Add. It occurs to me that you can avoid the whole issue by buying the genie for 1 cent and selling him to the next guy for -1 cents — i.e. giving someone the genie, plus one cent. Alternatively, if the genie-sales-terms gods won’t allow negative numbers. you could get the genie, while you have him, to suck 99% of the currency in the economy out of circulation, creating a vicious deflationary cycle that would force the government to issue a 1/2 cent coin, and sell him to the next guy for 1/2 cent; he in turn does same and sells for 1/4 cent; and so on ad infinitum.

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3 Comments so far
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You could also buy the bottle for penny, and have him take you to Zimbabwe or some other high-inflation country. If a million Zimbabwe dollars are the equivalent to a penny, you sell it for a million-1 Zs. Heck, assuming the rate is high enough and if you wait long enough, when you sell the bottle to the next person, you could probably sell it for 10 million Zs, and still have less money to show for it than the million you spent previously.

Lastly, I would have no qualms of buying in the $1000 dollar realm – I’m quite confident I could find someone who would buy it for $999.

Even if I couldn’t find it at that price, I would still suspect that I could sell it to someone who was already terminally ill, or, perhaps, to someone who was in love with someone terminally ill.

Comment by jb

[…] there’s some further discussion of the problem, plus some interesting possible solutions, here. Possibly related posts: (automatically generated)Google minus one, or Ponzi vs. […]

Pingback by The puzzle of the imp in the bottle « remnants of remnants

[…] Edit 1: there’s some further discussion of the problem, plus some interesting possible solutions, here. […]

Pingback by Toby Wardman — The puzzle of the imp in the bottle




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