Tuesday, September 25, 2007

Exponential Growth and Immortality!

Our use of meaningless words may be unsustainable
Sustainability is such a word. It was popularised in 1968 when 12 million copies of the Club of Rome's The Limits to Growth showed that exponential growth was unsustainable.

TIPS (treasury inflation protected securities) are paying roughly 2% over reported inflation. Let's say we'll pay 1% of that as taxes, just to make some nice round numbers. We're not being greedy, right? That allows our money (after taxes) to grow at 1% each year (even after reported inflation takes its bite). Since the growth is based on the amount we currently have, it is definitely exponential growth. In theory, it grows at roughly the same rate as our population does (which perhaps isn't a coincidence).

Now let's assume we buy a penny's worth of TIPS and continually reinvest. Let's also assume we live forever, or at the very least pass this savings down to our grandchildren (and so on and so on). Why not! Let's be optimistic for a change.

So how much money will we have made off of that penny in a million years?

Future Worth = $0.01 x 1.01^1000000 = $2.365 x 10^4319

That's a number with 4,320 digits in it. Mwuhahahahaha! We are going to be so filthy rich we won't know what to do with ourselves!!! That's in inflation adjusted dollars too! Just think of all the canned goods we'll be able to hoard!!

And those stupid Romans thought exponential growth was unsustainable. Hahaha! Fools! Well, we're not living in Roman times are we. This is America the Sustainable! As an added bonus, since our TIPS will be growing at roughly the same pace as our population is growing, there are going to be VAST numbers of people to admire what we did with a penny. VAST numbers!!!

Good grief. Why was I ever a pessimist? For those who can't quite comprehend a number with 4,320 digits in it, here's the number we'll be seeing on our account statement:

$236,500,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000

Actually, I somewhat joke. The number on our account statement will be VASTLY larger, since it will have one million years of inflation driving it higher (since we were invested in inflation protected securities).

I should probably mention one thing required when it comes to exponential growth before we break out into a song of sheer ecstasy.


Exponential growth
For instance, a population in a closed environment cannot continue growing if it eats up all the available food and resources; industry cannot continue pumping carbon from the underground into the atmosphere beyond the limits connected with oil reservoirs and the consequences of climate change; etc.

That is a major bummer. It seems not everyone is going to be able to make out like bandits on their pennies nor does it seem likely that the population can continue to grow exponentially forever either.

Once again, this is not investment advice. Like Greenspan, I continue to believe that nothing is truly safe when we live in a welfare state. I have somewhat heckled my own investment as you can see, which tells you a lot about how I value the relative safety of its alternatives. Hand basket, meet destination. Maybe not now, maybe not in my lifetime, but certainly within a million years (most likely much sooner).

4 comments:

Eternal said...

Technology exhibits exponential growth. Perhaps one way of looking at it would be to consider the value of the technology, in constant dollars, you'd have access to in a million years.

Stagflationary Mark said...

Hi Eternal,

Thanks for the comment.

The problem is that I'd have $2.365 x 10^4319 (in today's dollars).

Unfortunately, there are only supposed to be about 3x10^79 hydrogen atoms in the observable universe. I could lose a trillion dollars (in today's dollars) per hydrogen atom in my couch and not even know it was missing, lol.

That's a bit of a paradox, since my money was supposed to be keeping up with inflation.

http://en.wikipedia.org/wiki/Observable_universe#Matter_content

That being said, I can't even begin to imagine what technology will be like in a hundred years, much less a million. I'm still waiting for the bottom in big screen TV prices. I'm such a cheapskate.

russell120 said...

If your grandchildren are fruitful and multiply at only a 1% increase per year, you will have exactly one penny per great x 10^4319 grandchild.

The House of Saud is having this problem. As much as their pennies multiply, the junior prince output is even higher still.

Stagflationary Mark said...

Perhaps this is the way out for us. I can get each of those grandchildren a credit card right now and single handedly pull this economy out of any financial dangers.

Hey, Detroit! You want to sell cars? My future grandchildren are ready to buy!

(It wouldn't be the first time we've tried this plan.)