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What Do Star Trek, The Roman Age, and Lending Have in Common?

Photo by Nathan Rupert via Flickr

Somewhere around the year 2268, the USS Enterprise found a planet with a human civilization, which had apparently followed a parallel sociological and historical path to that of the Earth. On this planet – called Magna Roma – the Roman Empire had never fallen and existed in a state of technology similar to late 20th century Earth (Magna Roma being 300 years behind Earth in technological development.)

Here, in our blog on lending and lending software systems, I find myself wondering what a loan system would look like in this world where we have late 20th century technology but Roman institutions remain. We must start by looking at the Roman mathematical system.

Roman numbers do not have a concept of place value. Instead, letters have value, and when that value is to be added more than once, it is shown multiple times. The system is additive, except in the event that a smaller number proceeds a larger number, in which case the smaller is subtracted. So, given that I = 1, V = 5 and X = 10, the count from 1 to 10 is: I, II, III, IV, V, VI, VII, VIII, IX, X. So far so good. How do we do higher numbers?

  • I = 1
  • V = 5
  • X = 10
  • L = 50
  • C = 100
  • D = 500
  • M = 1,000

For large numbers, the Romans used a system called “Apostriphus.” Enclosing a number into a forward and backward C (we will use parenthesis, which in our modern language and writing system serves the same purpose) allows us to multiply the number by 1,000. And so…

  • M = 1,000 = (I)
  • (V) = 5,000
  • (X) = 10,000
  • (L) = 50,000
  • (C) = 100,000
  • (D) = 500,000
  • (M) = 1,000,000 = ((I))

As you can see from this last one, the system can be extended indefinitely, and we now have a viable numeric system.

A competing large number system called Vinculum was sometimes used. In this system, a horizontal bar over the letter designated that the letter should be multiplied by 1000, since multiple stacked horizontal bars were not viable, then bars in front of and behind the letter (essentially enclosing it in a box) would serve to multiply it by 100,000 or a million. The nova-Romans of Captain Kirk’s time found this difficult to render on a computer screen and so they chose to discard Vinculum and go with the Aprostriphus.

But, what do we do about numbers smaller than 1? The Romans had no concept of a decimal point. They also had no zero. You don’t need it in a system with no place value. They did understand fractions, and because they liked the fractions 1/2, 1/3, and 1/4, they decided that their numeric system for fractions would be base 12 even though their system for whole numbers (as seen above) was base 10. So they adopted the symbol “s” as 1/2 (from the Latin word semi) and a dot designated 1/12. So the fractions from 1/12 to 1 would be written as:

  • * = 1/12
  • ** = 1/6
  • *** = 1/4
  • **** = 1/3
  • ***** = 5/12
  • s = 1/2
  • s* = 7/12
  • s** = 2/3
  • s*** = 3/4
  • s**** = 5/6
  • s***** = 11/12
  • I = 1

So, we have a numeric system with a lesser degree of precision than our decimal system, where the degree of precision can be fine tuned by just going further to the right of our decimal point. For the purpose of money, this is adequate. We round money to the nearest 1/100th of a dollar; the Magna Romans would round to the nearest 1/12th of a denarius.

Romans generally charged 12% interest (in Ancient Rome), allowing for easy calculation of 1 denarius interest for every 100 owed on a monthly basis. However, there is no reason to assume that any interest rate couldn’t be charged in a modern Rome with computers. Still, we will assume 12%.

So, let’s say that I want to buy a villa in Capri (not the one on Earth, this is light years away) for 100,000 denarii. Sorry, that is (C) denarii.

I’m going to put X% down so I will shell out (X) denarii and have a loan of (XC) denarii at XII% interest. I’ll take a XXX-year mortgage with standard terms.

According to the standard amortizing equation, the monthly payment is CMXXVs***, (and I didn’t even need to round.)

Now, let’s run out the amortization schedule for the first 12 months and see what it looks like.

Payment # Payment Principal Interest Balance

Total paid the first year: (XI)CIX

Total Principal paid: CCCXXVIs*

Total Interest paid: (X)DCCLXXXII*****

What conclusions can we draw from this? First, just looking at these numbers and deciphering what they mean is a damn lot of work. It worked okay for the Romans on Earth, but they never had to advance scientifically to the point where they needed to calculate the trajectory of rockets. Their empire on Earth fell about a thousand years before the invention of calculus.

Captain Kirk, just by taking a look at the financial page in the local newspaper of Magna Roma, can quickly come to the conclusion that this civilization will never be able to compete with the Federation on a Galactic scale because any scientific calculations that they attempted would just be too damn cumbersome. Bottom line: Magna Roma is no threat to the United Federation of Planets.

Amazing what you can find out by looking at an amortization schedule, isn’t it?

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