Thoughts on Infinity

Numbers are a funny thing.  Or, to be more accurate, humans tend to deal with numbers in strange ways.  Most of the time, we don’t have too much trouble with them.  We can generally make change for a twenty dollar bill, or keep score at a basketball game.  These are the sorts of numbers we can handle, and we encounter them every day.  They mean something to us, and we understand what they represent.  Things get tricky, though, when we get into very large numbers, numbers that usually aren’t relevant to our day to day lives.  At some point, it all just sort of blurs together in our minds.  The difference, for many people, between 100 million and 100 billion is relatively small.  Both are larger than anything we can really visualize, far larger than anything we need to understand when buying groceries, for example.  We understand, of course, that one is larger than the other, and we could subtract one from the other if need be, but we still don’t have a good grasp for just how much bigger a billion is than a million.  And most of the time it doesn’t matter, either.  It doesn’t matter if something weighs a million pounds or a billion, we’re still not going to be able to lift it or carry it in the back seat of the car.  We’d be just as happy with winning a billion dollars as we would 100 billion.  At that point, what difference does it make?  Either way, it’s an obscenely large amount of money, more than any individual has any real use for.  In fact, our brains seem to have such a struggle with large numbers that, at some point, we start to get them confused with infinity.  Once something becomes too big for us to really understand, there doesn’t seem to be much difference between extremely large and infinitely large.

This seems to be something inherent in the human brain, at least as far as I can tell, and it’s certainly something we’ve struggled with for a long time.  The first colonists from Europe in North America saw a huge land, covered with seemingly endless forests, and I imagine that many of them considered the land and its resources to be infinite, or so large that it might as well be.  They didn’t even have a good idea of how large the New World really was, so it may have seemed quite reasonable to act as though they could never use it all up.  After all, they were so few, and so small, being but tiny men faced against the vastness of nature.  Why bother with conserving resources when you could never possibly run out of them?  Fast forward just a couple of hundred years, and here we are, constantly arguing amongst ourselves over what to do with the little bit of wild terrain left in the nation.  There are certainly many reasons behind the deforestation of America, but surely a contributing factor was our inability to understand the difference between a very large amount of land and an infinite amount.

While that’s all fine and good, it’s still just idle speculation about a topic that many Americans still aren’t very concerned about.  Let’s consider something that almost everyone can relate to:  oil.  Here we have a finite, non-renewable resource that every single American consumes, often every day, and yet, despite periodic shortages, we still behave as though it’s never going to run out.  When oil is cheap, we go through petroleum products like it really is an endless supply, and when it’s expensive, we consume it more efficiently, but we still consume it.  We never consider, at least not as a society, finding alternatives.  Even though there has been strong evidence for years now that the end of the worlds oil supply could occur within our generation, we still act as though it will never ever run out.  All we ever really consider is the price.  Even then, we’ve never considered other ways we consume petroleum, such as plastics and other synthetic materials.  We’ll bitch about the price of gasoline, then go to the grocery store and buy our food in plastic containers, wrapped in other plastic containers, and take it home in plastic bags, and never consider the irony.

Mind you, when I say we behave as though oil supplies are infinite, I mean that literally.  There are people out there who really, seriously, argue that we will never and can never run out of petroleum.  The arguments run from the plausible but unlikely (petroleum is a renewable resource that is constantly replenished via either biological or geological processes) to the illogical (as we run out of easy sources of oil, we will simply learn to extract it from more and more difficult sources, without ever running out) to the WTF (God will provide us with all the oil we need).  The belief in literally infinite oil blew my mind when I first heard about it, but it’s not that uncommon of a viewpoint.  Many people honestly think we will never run out, or that if we do it will be centuries, perhaps millennia, in the future, and therefore nothing to worry about.

There is some reason to think that a small amount of petroleum production is actually going on underground, but for this particular case, let’s just assume that petroleum is not regenerating, or at least not at any rate that is meaningful to us for the next few centuries.  I say “assume”, mind you, but this is actually the prevailing view.  Given that, even if the entire planet were just a thin shell of rock floating on an enormous sea of light, sweet crude oil, there would still be a finite amount of it.  It’d be a hell of a lot of oil, but the amount would be discrete and limited.  Given enough time, even an entire planet made of nothing but petroleum could eventually be consumed entirely.  It’s a preposterous notion, of course, but the point is that, even if we get that crazy with it, it’s still not an infinite supply and we’d still, at some point, need to take measures to conserve it.  We obviously don’t have that much oil available, and far from it.  Even if it’s regenerating, there’s absolutely no reason to believe that the rate of regeneration is outpacing the rate of consumption, so we’re still running out.  We probably won’t run out of it entirely, but it will eventually become so scarce as to make it unfeasible for general use.  It’s just simple math, folks.  So why can’t we behave accordingly?  Why do we still burn it at the drop of a hat?  Why do we use it to make packaging that’s just going to be discarded?  Why do we not only fail to conserve it, but actively and willfully WASTE it?

Our problem with confusing large numbers with the infinite is not limited to current situations, but also the way we think about the future.  We often think that things can eventually become infinite, not realizing that in actuality there is eventually a limit, no matter how large that number actually is.  Consider another topic you hear about all the time in the news: economic growth.  It’s a positive thing, right?  The more our economy grows, the better off we all are.  That’s how it’s always portrayed.  A growing economy means more jobs, more money, just more, more, and more for everyone.  Nobody ever stops to think this through to its logical conclusion, however.  Economic growth can not be infinite.  The resources, energy, and manpower of any nation, even the entire planet, is limited.  At some point, no matter what you do, you won’t be able to squeeze another drop of productivity out of the economy, and further growth will become literally impossible.  Economic growth isn’t inherently a good thing (or a bad thing either), and beyond a certain point, it’s unsustainable.  Eventually growing more just isn’t worth it.  What we’d really strive for, if we stopped to think about it, is economic STABILITY, preferably at some comfortable level that everyone can live with.  Growth, by definition, is unstable, and the series of booms and crashes that we’ve seen in the last century in the United States is evidence of that.  We’d probably all be better off having a nice, steady economy, without all these spikes and falls, always either wondering when the bubble will burst, or else when things will get back to “normal” again.  But, instead, we think we can just keep growing forever, with no problems, and we make no attempts to reel in the economy when it starts to grow beyond our needs.

Finally, I’m going to point out something that should be blindingly obvious, but which, for some reason, is not.  Human population can not reach infinite size.  We are limited, like every other living thing, by our environment.  We need space, air, food, and water.  Each of those resources is in limited supply.  The world may be a big place, but it’s not THAT big.  How many people can the Earth possibly support?  No matter what your answer is for that, the point is, there IS a number that represents a cap to human population.  At some point there’s a bottleneck in our resources, and growth will not be able to go beyond that point.  No matter how big that population is, even if it’s an obscenely huge number that we’d have to invent a name for, if every day our population grows by a certain percentage, any amount at all really, eventually we’ll reach that maximum size.  At that point, every available speck of land and water on the planet would be devoted to the survival of the human race, and nothing else.  We’d be teetering on the edge, with just barely enough food and water to go around.  Beyond that level, our population could not expand any further.  Not for long, at any rate, without adequate resources.

So, we can’t continue to make as many babies as we want forever.  Eventually, we’re going to have to either control our own population levels, or starvation, thirst, and disease will do it for us.  The hard way.  And yet, despite what, to me, is an obvious conclusion, we continue to not only tolerate unlimited population growth, but actually encourage it.  Every institution we have, from the federal government to the local place of worship, gives reasons and incentives to have babies, and we as a society judge it to be the highest goal for any person.  Even the countries that do impose some form of population control, namely China, aren’t actually halting growth, they’re just slowing down the rate of growth.  I’m not saying that we’ve reached the point where we can’t support any larger population (although some models predict that we’re pretty close).  I’m just pointing out that we are at a pretty large size as it is, and since we don’t know what the limit is, only that there certainly must be a limit, it might be wise to throttle back the baby production, lest we realize suddenly that we’ve already gone too far.  We clearly have limits to our potential population, but our behaviour suggests that we don’t believe that we do.  We keep on expanding at a time when we need to be considering what the costs of expansion really are.

Each of these issues I’ve touched on are complex and would take volumes, literally, to fully explore, but I see a common thread underlying the cause of each one.  We just can’t wrap our minds around hugeness.  In the case of resources, we often have a finite, but very large, supply, and the figures are so large that in our minds they become nearly infinite, unlimited.  In the case of growth, the lack of a clearly defined limit causes us to behave as though there were no limit at all.  It’s the same mentality that makes “all-you-can-eat” promotions popular at restaurants.  All we can eat?  That means an infinite amount of food for a finite price, which surely is a great deal.  Of course, there actually is a limit to how much any person can possibly eat at one sitting, and depending on what that limit is, the price may actually not be worth it.  It’s the same for environmental issues.  There’s a limit to how much oil we can consume, how much land (or water) we can use for food production and living space, and how many people we can squeeze onto this planet.  But without an easy way to know what those limits are, we behave as though there are no limits, as though the potential was infinite.  When you’re handed a large sum of money and you know exactly how much there is, you can form a budget.  You can make informed decisions on how to spend it, and on what.  But if someone gives you a huge amount of money, and you’re not allowed to know how much there is, only that it’s a “large” number, you’ve got a problem.  You can spend it like mad, but you won’t know when you’re out until it’s too late.  A wise person would conserve it, spend it carefully, and never assume that they could never possibly run out.  Fortunately, it’s not a perfect metaphor, because in reality we will have signs that we’re approaching the limits.  There’s two problems, though.  Will we be able to recognize those signs in time to change our behaviour?  And will those signs, in themselves, be events we’d rather avoid?

We live in a finite world, folks.  Even the universe itself has boundaries and limits.  Nothing is infinite.  In the long term, everything is in short supply.  Just because you’re wealthy doesn’t mean you should spend your money like you’ll never run out of it.  If you do, then eventually you’ll be broke.  Just because we live on a rich planet with abundant resources doesn’t mean we can use it thoughtlessly forever.  Eventually, there will be nothing useful left.