The Bank at the End of the Universe
Why positive interest rates are incompatible with time travel
NOTE: I’m periodically posting excerpts from my not-yet-published book, “Fifty-Million-Dollar Baby: Economics, Ethics, and Health.” The goal is to edit the manuscript in plain view, and to ask for your comments, corrections, suggestions, and criticisms. This essay is a revised version of a piece I wrote around 1999 for the Federal Reserve Bank of Richmond’s long-defunct Equilibria magazine.
In 2014, science writer George Musser explained why time travel would violate the Second Law of Thermodynamics and is, thus, impossible. In 1986, finance professor Marc Reinganum explained why time travel would violate the Law of Compound Interest and is, thus, impossible. And, to connect these two conjectures, some claim that Albert Einstein once called compound interest “the most powerful force in the universe” (though this quote is likely apocryphal).
Interest rates are the penalty we pay for our inability to travel backward through time. They are the costs demanded by our impatience (or the rewards for our patience). One could say that interest rates are the crossroads between economics and science fiction.
It is late on a cold December night. A lone car passes. The wind rattles a drugstore window. Then once again, silence. Behind the counter, a pharmacist slowly rolls a vial of penicillin between his fingers. In a few minutes, he will exchange the pills for a few dollars drawn from the wallet of an elderly man. But before the customer arrives, the pharmacist has a thought—he could easily trade this vial for a ton of gold, if only he could offer the trade to a pharaoh whose gut wound is turning septic on a battlefield 4,000 years earlier. The pharaoh, he reasons, could have the gold buried and then reveal its whereabouts only to whomever heals the wound that otherwise will soon kill him. "With these pills, I could be that healer," the pharmacist thinks. "Then I’d never have to work the night shift again."
The pharmacist’s thought is broken by the tinkling of a small bell at the front door. A stooped figure dodders toward the counter to retrieve his prescription. Another thought slowly crosses the pharmacist’s mind: "Wait a minute,” he realizes, “I don’t know how to deliver penicillin to Ancient Egypt. I guess I’ll have to work the night shift for a while yet."
But if the pharmacist actually had a time machine with which to deliver the drugs, banks around the world and throughout history could not pay depositors interest on their accounts. This connection may require a bit of explanation.
Economics in Science Fiction
If a physicist wishes to perplex his friends, he can discuss relativity or black holes. If an economist wishes to perplex her friends, she can discuss the miracle of compound interest: "Your great-great-great-grandfather saved this $10 gold piece in 1840 and now it’s worth $1,500? That’s great! But had he invested the $10 in securities paying 7% annual interest, you’d have well over $2.2 million today. Even a 5% return on a nice, safe bank account would have brought you over $70,000. Great-great-great-gramps wasn’t a very savvy investor, was he? Nice, shiny coin, though."
In his science fiction spoof, The Restaurant at the End of the Universe, novelist Douglas Adams wrote of a restaurant located in the far, distant future—at the very end of time itself. Diners traveled via time machine to the restaurant and enjoyed an incredibly lavish meal. For entertainment, they viewed the final destruction of the Universe through the restaurant’s broad windows. Afterward, they returned via time machine to their own epochs, and the next night, another crop of diners took their place. (The details are really a bit more complicated, but you can ask an Adams fan to explain.) The cost of the evening was staggeringly high, yet affordable even to those of modest means. A diner simply deposited one penny in an interest-bearing bank account in his own era, let interest accrue through the eons, and used the proceeds to pay his enormous restaurant tab.
The restaurant violates not only the laws of physics, but even the far looser laws of science fiction physics. For Adams devotees, this is the humor—the narrator fails to grasp the stark logical flaws that are blatantly obvious to the reader. (The twisted physics would lead a HAL 9000 to terminate the narrator’s life functions or Mr. Spock to raise both eyebrows. Even the ghouls from Plan 9 from Outer Space might take him to task for stretching credulity.) The economics is similarly out-of-kilter; even a person with virtually no knowledge of banking senses a big problem with the restaurant’s payment plan—that time travel would wreak serious havoc with interest-bearing bank accounts.
(NOTE: The laws of science fiction physics are not to be confused with the laws of cartoon physics, which explain, for example, the relative free-fall velocities of anvils and coyotes.)
Science Fiction in Economics
Where Adams introduces economics into science fiction, Marc Reinganum did the opposite in the Journal of Portfolio Management, a typically staid technical publication. In his tongue-in-cheek article, "Is Time Travel Impossible?: A Financial Proof," he argued that the existence of positive interest rates prove that human beings will never travel backward in time—not now nor at any time in the future. Reinganum’s logic went something like this: If a time machine were invented in, say, 1000 years, a time traveler from 3022 could carry $1 in his pocket, travel to 2022, deposit the dollar in a certificate of deposit account yielding 4%, and then travel back to 3022. When he arrived back home, the balance on his account would be over $100 quadrillion. (At 2022 prices, this is enough to purchase the nearest 37 solar systems.) And if that amount were too small to satisfy his needs, he could take some of the funds back to 2022 again and repeat the process as many times as he liked. Therefore, if time travel ever became possible, interest rates throughout history would have to be 0%. Otherwise, time travelers could use banks as perpetual motion money machines— the Universe as a bottomless ATM.
This brings us back to our erstwhile pharmacist. If he could transport penicillin to the pharaoh, then banks throughout history could only pay interest rates of 0%. Otherwise, the pharmacist, on his way back to ancient Egypt, could stop off in the United States, circa 1840. He could take a $10 gold piece and, being a cautious investor, put it into a bank account yielding, on average, 5% over the next 182 years. After dropping the penicillin off at Luxor, he could head back to 2022 and withdraw the $71,854 in his account. For a man with a ton of gold, this isn’t a lot, so he’d want to increase that investment in one of several ways. First, he could withdraw his $71,854 in 2022, take it back to 1840, reinvest it, and then return to 2022, where it would have grown to over $516 million. Better still, he could bypass 2022, jump forward 200 years to the melodious-sounding year 2222 and withdraw his funds then. At a 5% annual rate, his $71,854 will have grown to nearly $9 trillion.
Either way, after a fairly tiring day of toting penicillin and money (or tangibles purchased with that money) back and forth through history, he could go out for a really nice meal. And it would only cost him a penny.
Afterthoughts
Adams’s Hitchhiker’s Guide to the Galaxy series (of which The Restaurant at the End of the Universe is a part) is studded with bizarre plays on standard economic logic. For example, one planet’s inhabitants decide to use leaves as money and then defoliate the forests in order to bring inflation under control.
Economist Joshua Gans offered a caveat to Reinganum’s contention that, “Current economic conditions rule out the possibility of past, present, or future time machines.” Gans suggested that, “It shows that current and past interest rates are inconsistent with time travel but that doesn’t mean that at some point in the future such travel will be possible. But it does suggest that that will show up in interest rates plummeting.”
Philosopher Kelley Ross and others have argued that there are limited circumstances in which time travel would not run afoul of the Second Law of Thermodynamics.
In the final episode of television’s Better Call Saul, Walter White condescendingly tells Saul Goodman that the Second Law of Thermodynamics precludes the possibility of a time machine.
Appendix: Don't Believe the Numbers?
Compound interest calculations can tax one's credulity. It's hard to believe that a 5% interest rate over 182 years will turn $10 into $71,000. It's even more amazing to think that a mere 2% more (a 7% interest rate) would turn $10 into $2.2 million over the same period. So, for skeptics, here's the formula you can use to check the numbers presented in this article:
where:
BEGIN = initial deposit
RATE = interest rate
YEARS = number of years deposited; and
END = BEGIN + compound interest accumulated
For example, $10, invested at 5% interest for 182 years yields
And $10, invested at 7% interest for 182 years yields
Happy investing.