Tuesday, February 12, 2013

Book Excerpt: 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 Dt (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.

Dt t3

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:

Dt (10t)3

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…

Dt (11t)3

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…

Dt (11t)8

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.

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


John D. Wheeler said...

Hence the ancient prohibition against usury....

Of course, there is another solution, which to my understanding has never been tried: set a date, say, 50 years in the future, when all debts will be forgiven.

Stanislav Datskovskiy said...

The story - like life itself - isn't complete without... Father War!

The Galactic Empire quickly runs into a mass shortage of the Unobtainium needed to power everybody's Overthrusters. There follows a cataclysmic Galactic Great War, where Translation Rays are fired left and right, rotating hundreds of populated planets into the 9th dimension - separating them from the light of their stars and all shipping traffic to die a most cruel death. The Empire's population thus remains stable, until the carnage repeats. The cycle is revisited again and again, until all of the Unobtainium-bearing planets end up in the 9th dimension, and everybody moves themselves and their stellar bodies there. Or until the heat death of the Universe.

Wolfgang Brinck said...

I was checking out some steady state economy website and it struck me that steady state is an unnatural state of affairs. What happens with animal populations and apparently also with economies is exponential growth corrected by periodic collapse to create a kind of sawtooth shaped wave. Zoom in close enough and you're just looking at the exponential growth portion of the curve. Zoom out and you get a saw tooth.
If we look at the evolution of life on earth we also get exponential growth up to the point where the resources are maxed out. After that we're back to the old expand and collapse theme. Evolution is nature's way of trying to get around the limits of a maxed out ecosystem where every niche is occupied and everyone's growth is maxed out. Evolve and figure out how to eat something that currently isn't being eaten or figure out how to eat it more efficiently than is currently being done.
To Mr. Wheeler I would say that debt forgiveness or bankruptcy or outright collapse are all perfectly acceptable responses to exponential growth.
I personally endorse Mr. Orlov's prescription to collapse early and beat the rush.

Robertlowrey.blogspot.com said...

All they'd have to do is get the Government to mix a Vodka Gimli: guarantee the loan, ie load all the risk onto the back of the public, funnel all the profits into the pockets of the Oligarchs and Voila!: "Certainty of death, small chance of success ... What are we waiting for?"

harry said...

John D. Wheeler

Funny guy. Of course that solution was tried. Its in the torah and you know it. The Jubilee is held every 7x7 years.

Anonymous said...

Dmitry, good show. You've even managed to capture one of the most neglected, most rarely addressed major articles of modern Ferengi faith: that the market is the sole determinant of value; that everything is, can and ought to be a market good; that nothing not worth selling is worth having.

vera said...

Mmm... it seems to me, and it can be tried with pennies on the table, that interest by itself is not necessarily the undoing, provided it is directly returned to the economy.

Compound interest, however, is a Ponzi scheme.

Ruben said...


Georgescu-Rogen called the steady state a mirage:

"The crucial error consists in not seeing that not only growth, but also a zerogrowth state, nay, even a declining state which does not converge toward annihilation, cannot exist forever in a finite environment."


k-dog said...

Exponential growth leads to collapse when growth can no longer can be fueled by available resources. This law of the universe has mathematical certainty and consequently collapse is also mathematically certain.

A steady state economy is possible but transitioning society to a sustainable mathematical framework would require the cooperation of people who hold power. Unfortunately people who hold power are also the same people who profit most from exponential growth.

Only convincing power holders that it is in their best interest to facilitate social change to a sustainable economy offers any hope for the future. The question is how to do that considering that average thoughts cannot fathom anything beyond immediate self interest.

It's a tough nut to crack and the disgusting thing is that it really shouldn't be because collapse means that everyone looses, even those who profit most from exponential growth.

William said...

152Had I not already preordered your book, Dmitry, I would do so now based solely on that Buckaroo Bonzai reference.

Glenn said...

@ John D. Wheeler
I have read that a certain Rabbi was crucified 2000 years ago for having the temerity to suggest bringing back the jubilee after a few centuries during which it had been ignored. There certainly are a lot of sermons and parables attributed to him that emphasize helping the poor.

I'm an atheist myself, but it seems the two major religions in the U.S. are unlimited growth, and greed.

Tylda said...

So doesn't it mean that money is the source of the problem? Do You think it is or ever will be possible to stop using it. I think for all of humanity it would be like growing up, just like a teenager matures and becomes an adult.

Jeff said...

I wouldn't worry. The system will be successfully delevered by depreciating currencies against gold. It's what always happens.

ChewyBees said...

Mankind has been living under this roman extortion scheme for so long now, it is nearly impossible for men to wrap their mind around anything else. There has to be class division, there has to be extortion, fraud and hoarding of wealth, there has to be war, and there has to be billions living in squalor so that self deluded psychopaths can have their opulence.

The only reason money exists, in any form or type of currency, is so the owners of money can speculate upon and devalue the labor of working men. It is cleverly disguised as a means of exchange between men for goods and services. In reality it is a scheme of debt enslavement no different than the mining community company script, paid in just small enough increments that the worker can almost buy enough food from the company store to feed himself and his family.

The value of everything is speculated on by mystery men in high places, using money as the basis of their speculation. In reality, nothing material, or the cash to buy it with, is worth anything. Even the value of the almighty gold is completely speculative. Some scheister somewhere decides that X amount of gold is equal to Y amount of labor using their debt notes as the medium of exchange. By gradually and continually raising the speculative price, while at the same time paying fewer debt notes for the hours of labor. Using this method, you can essentially squeeze the people that actually work into utter desperation.

The money supply, the speculation, and all of the paper can disappear in an instant, but the value of the labor remains constant. Just because labor has been devalued and crapped upon by those that never worked a day in their life doesn't mean that the intellectual and physical value of working men isn't necessary and highly valuable.

When it all tanks, will you, the reader, have a skillset above drinking Starbucks Lattes and pushing buttons on a keyboard? Will you be unable to waddle your way into securing yourself and your family? Or will you have the necessary ability to think critically, manage full liability and lead to rebuild.

It is the downer cattle that will fight for the system as it exists with murderous intent, even if they don't pull the trigger.

Jean-Paul Printemps said...

Here is a book that lends an interesting angle to this discussion: DeAngelis, D. L., W. M. Post, and C. C. Travis. 1986. Positive Feedback in Natural Systems. Berlin: Springer Verlag. The idea being that, similar to what you see in electronics, exponential rise due to positive feedback leads to resonance or multi-stable conditions. Curious about the architects of such an economic system, and there may be some who are smart enough to decouple themselves from the sudden end of growth.