Orlov: The wrong math

This is an excerpt from The Five Stages of Collapse: Survivors’ Toolkit. Please order your copy for shipment in May.

An argument can be made that lending at any rate of interest above 0 percent eventually leads to a deflationary collapse followed by a quick but painful bout of hyperinflation thrown in at the very end. A positive interest rate requires exponential growth, and exponential growth, of anything, anywhere, can only produce one outcome: collapse. This is because it quickly outpaces any sustainable physical process in the universe, outside of a few freak cases such as a sustained nuclear explosion, where the entire universe blows up, taking all of us with it, along with all of our debts.

Here is a thought experiment that illustrates this point. Suppose we solve every technical problem on Earth and go on and colonize space, found space colonies and take over the solar system, and the galaxy, and other galaxies, and the entire universe (which may not be infinite, which would give us another cause for eventual collapse, but let’s ignore that for the moment). As everyone knows, space empires aren’t cheap, and to get our space empire started we borrow some money, at an introductory low rate of interest (after somehow convincing the lenders that building a space empire is a low-risk proposition). Suppose we expand this empire at close to the speed of light (since it requires infinite energy to accelerate a finite mass to the speed of light). A space empire expanding even at the speed of light in all three dimensions will only grow as t³ (time cubed). (Let’s ignore the fact that initially, while taking over the solar system and the Milky Way galaxy, which are both flat, our empire will only be able to expand in two dimensions.) Meanwhile, our empire’s debt will grow as D^t (debt raised to the power of time). And here is the problem: it is a mathematical certainty that as time passes (t increases), debt grows faster than empire for any initial amount of debt. Exponential growth outpaces any physical process.

Suppose the empire’s engineers struggle mightily with this problem and, after taking on even more debt to finance research and development, eventually invent “warp speed,” which flouts the laws of physics and allows our space empire to expand faster than the speed of light. But to their surprise, debt just keeps increasing. Eventually they discover the answer: even at “warp-10,” which is ten times the speed of light, debt is still increasing faster than the empire:

One brilliant engineer (who happens to be a fan of the band Spinal Tap) hits on a brilliant idea and invents “warp-11.” Everyone is hopeful that this invention will give the imperial growth rate “that extra push over the cliff” and allow it to catch up with its ballooning debt. But this too is to no avail, because…

Perplexed, the engineers wander back to their drawing boards. Then one remembers a film he saw once — The Adventures of Buckaroo Banzai Across the 8th Dimension — and is struck by a brilliant thought: what if they were to actually invent the circuitry that allowed Buckaroo to penetrate solid matter and travel across eight dimensions instead of just three? Then their space empire could expand across eight dimensions at the same time! They get to work, and quickly cobble together the Oscillation Overthruster (Buckaroo’s fully automatic 12-volt cigarette lighter socket plug-in unit, not Dr. Lizardo’s bulky foot-operated floor-mounted kludge). A bit more effort is required to compensate for strange hyper-relativistic effects when using the Overthruster at “warp-11” (Buckaroo’s was only tested at just over Mach-1) but once they got the hang of it their space empire starts expanding across eight dimensions at eleven times the speed of light, quickly conquering and enslaving the Lectroids of Planet 10, along with billions and billions of others. Alas, it soon turns out that even this rate of growth is nowhere near fast enough to keep up with their debts, because…

After some more fruitless exploration, the engineers decide to overcome their innate distrust of mathematicians and invite one to join the team, hoping he might be able to explain why this keeps happening to them. The mathematician asks for cocktails to be brought in and, once he sees that the engineers are sufficiently inebriated to take the edge off the bad news, he grabs a cocktail napkin and furiously scribbles out a proof (here omitted for clarity). His proof attempts to demonstrate that exponentially expanding debt will eventually outpace the rate of growth of anything finite that grows at any finite speed across any finite number of dimensions. He then goes on to say that “things get much more interesting once we move into the infinite domain,” and, even more enigmatically, “we can always renormalize it later.”

Shocked, they dismiss the mathematician and, grasping at straws, hire a shaman. The shaman listens to their problem and tells them to wait until sundown for an explanation. Then he asks them to shut off electricity everywhere and to join him outside in the middle of the parking lot and form a circle around him. Once their eyes adjust to the darkness, he points to the sky and says: “Look at the darkness between the stars. See it? There is nothing there. Now look at the stars. That is all there is.”

Since the engineers all happen to know that what they can see is limited by the age of the universe and the speed of light, not the size of the universe, which, for all they know, could very well be infinite, they dismiss the shaman, turn the lights back on, drink some more, then nurse their hangovers. One of them (a bit of a class clown) writes “It’s The Exponential, Stupid!” on a placard and pins it up on a wall next to their cubicle farm. But then another one, a fan of The Time Machine, the 1895 novella by H. G. Wells, hits on yet another brilliant idea. What if they invent a time machine, and go back in time to settle the empire’s debts? With that, the math would finally work in their favor, because they could go back in time and pay each loan off with just the principal. Being short of cash, they try taking out another large loan to finance the development of the time machine, but their creditors balk, declaring the project “too risky.” And so the empire defaulted on its debts. Shortly thereafter, it turned out that it was no longer able to secure the financing it needed to continue interplanetary oxygen shipments, and they all died of asphyxiation.

Conclusion: borrowing at interest is fine provided you have plans for a time machine and enough cash on hand to actually build one, go back in time and pay off the loan with just the principal; it is not recommended otherwise.

Club Orlov