Cuban Terrorist Posada Carriles and Exponential Growth

Erasmo Calzadilla

 “The most powerful force in the universe is compound interest.” -Albert Einstein

“Anyone who believes that exponential growth can go on forever in a finite world is either a madman or an economist.” -Kenneth Boulding

HAVANA TIMES — In a previous post,  I wrote that an economy that grows by a certain, steady percentage over time is experiencing exponential growth. I feel this issue deserves some additional lines, because no one seems to know exactly what this means or what its consequences are. Even the mathematicians seem a bit confused on this issue.

Exponential growth refers to a process whose rate of development is proportional to the magnitude of the process at any given point. The classic example is the spread of an epidemic, in which each new carrier becomes a new source of the infection.

The same holds for a colony of living beings that reproduce freely, unchecked by any predators. Another typical example is the snowball that rolls down a snow-covered slope: small at first, destructive avalanche shortly afterwards.

If we use a traditional system of Cartesian axises to plot the growing variable (across the vertical) against time (across the horizontal), the result will be a curve that begins as a slightly inclined slope and then suddenly shoots upward, tending more and more towards the vertical as time passes. The final result is something that resembles a hockey stick.

I won’t go into the mathematical explanation for this, which is relatively complex. I would rather devote some lines to the consequences of such processes. To do so, I will rely on the concept of the organism.

An organism is a system composed by elements that maintain relationships of synergy, of collaboration, among them. In addition, these elements also mutually sustain each other. Society, for instance, is made up of individuals who struggle among themselves and thus limit one another in certain ways. This principle applies to the biosphere, living beings, the economy and god knows how many other processes.

If, for whatever reason, this balance is broken, if this containment mechanism fails and one of the elements propagates unchecked, the entire system is gradually weakened and ultimately collapses.

Cancer is an example of such a process. Unlike healthy cells, malignant cells reproduce exponentially. In their propagation, they destroy neighboring tissues and, if nothing stops them, ultimately cause the death of the organism.

What’s most worrying about exponential growth is that it catches you by surprise: when the alarm goes off, there’s practically no time left to do anything.

I will use a fictional situation to illustrate this point.

Imagine that, thanks to Raul Castro’s reforms, you manage to check into a room at the Habana Libre hotel. You ask to be put up on the top floor, so as to be able to enjoy a panoramic view of the city and get away from its noise and foul smells for a while.

It’s not your lucky day, however, and, that day, terrorist Luis Posada Carriles arrives at the hotel dressed as a bus boy and equipped with a sinister plan. Carriles has given up on explosives. Now, he uses methods that are cleaner and more sophisticated than those the CIA taught him.

Craftily, as though mopping the floor, the veteran terrorist spills a bucket of water on the floor. His plan, see, consists in spilling 1 % of what has already been spilled every minute.

Let us assume that all of the hotel’s doors and windows are shut and the water begins to flood the building.

In your room at the top floor, you’re lying comfortably in bed, watching television as you sip on a cocktail. You hear distant screams, but no one and nothing is going to spoil your deserved vacation. So you pick up the remote control and pump up the volume.

So, from the instant the terrorist began the whole operation, how long will it take for the water to start seeping in under your door?

If, 29 hours after the first drop was spilt, you got out of bed to go to the bathroom, you would find your slippers soaked and might start to get alarmed.

From the moment in which you perceive this rather unusual situation (which does not yet pose a danger to you), how long do you have before your whole floor is under water? The answer is less than four minutes. Use them to contemplate Havana one last time, as there is really nothing you can do at that point.

Developed and developing countries have been growing exponentially for years. The consumption of fossil fuels and everything derived from them follows the same growth pattern, as does, consequently, the concentration of greenhouse gases, the melting of the polar ice-caps and the extinction of species.

It is evident Western civilization (the one responsible for this) isn’t reacting as it should in light of the circumstances. And the worst thing is that everyone – the guilty as much as the innocent – are going to pay for the consequences.

Note:

The Habana Libre hotel is 126 meters high. I assumed the building was 90 meters long and 30 wide. The total volume would thus be 340,200.00 cubic meters (not including the lobby and surrounding areas).

The hotel has 27 floors. Using the rule of three, I calculated that there would be 327,600 cubic meters between the ground and 26th floor.

To calculate the time needed by the water to reach the top floor, I used the following compound interest formula:

t = (log (Cf) – log(Co))/ log (1 + r)

Whereby:
Cf (Total quantity).
Co (Initial quantity) = 0.01 cubic meters (a 10-liter bucket)
r = 0.01  (1%)

References:

Crash Course, Chris Martenson, Chapters 3 and 4 (the images are taken from the book)