The most baffling of the ancient paradoxes is probably the Sorites Paradox, attributed to Eubulides in the 4th century BC. The word "Sorites" comes from Greek sōros, "heap", and the riddle is sometimes also called "the paradox of the heap". The conundrum lies in two assumptions which, by themselves, seem totally reasonable, but combined together, quickly lead to a bizarre conclusion.
Assumption 1. A single grain of sand is not a "heap";
Assumption 2. If some sand is not a "heap" initially, one more grain won't make it a heap.
Conclusion: No finite amount of sand qualifies as a heap.
The proof is simple. Let N be any finite number, as big as you like. We claim N grains of sand don't make a heap. By the first assumption, one grain isn't a heap. Now apply the second assumption over and over: 2 grains aren't a heap; nor 3; nor 4... after N-1 steps, we're forced to agree, N grains of sand do not a heap make. Since we proved this for an arbitrarily large N, that means no finite graincount is high enough!
What can we learn from Eubulides' puzzle? The most important lesson is that language is inherently vague. We can apply this to real life in a number of ways. Here are three applications of the anomoly of the heap.
ENOUGH WORK!
Every good citizen knows that everyone should work. Labor is the cornerstone of capitalism, and if people didn't do enough work, all of civilization would collapse... right? But just how much work is "enough"? After how many hours of sweat does a man achieve that noble work ethic which drives us all?
Most people would agree that a lifetime workload of one miserable hour, isn't "enough". It's not even close. If someone out there has figured out a way to make a permanent living off one hour's service, that's disgusting!
Again, if you currently haven't done enough work for your lifetime, then toiling away one more hour isn't gonna make any difference.
Thus, the assumptions behind the Sorites Paradox are satisfied. Instead of granules of earth, we're discussing hours of work, and the word "heap" has been replaced with "enough". The argument still goes through, and we reach the conclusion: no finite amount of work is enough!
This is a rather discouraging conclusion, until you remember that Eubulides wasn't a real economist, thank God. He was just a jokester. But sometimes there's a grain of truth lurking in the jester's tricks. The real wisdom to take away from this thought experiment is that we should take the work ethic less seriously. No matter how much work I do, civilization is never going to turn to me and say, "Great show! You've done enough work now, forever!" When I realized this fact, it set me free, in a way. It liberates you from the ratrace and lets you take life a little less seriously, and enjoy it a little before you die.
READY FOR TAKEOFF
Another vague predicate is the term, "ready". This is a big one, which can hold you back a long time. It's common sense that you need to prepare before making the leap. Who would take a spontaneous trip halfway around the world with just a light backpack? It seems that the bigger the event, the more preparation and analysis are necessary.
But where is the exact threshold when the whole project finally gets the green light? It's harder to quantify in such a broad application as this, so let's focus on a concrete example: you decide to start a blog. This is easy to quantify because most of the preparation for starting a blog involves reading things. The question is, how much do you need to read before you're "ready" to launch the world's next great weblog?
Well, one solitary word is definitely not enough. You can't just dive in blind, you should at least make sure you're picking good publication software. Again, if you're not ready yet, you won't suddenly be ready after reading just one more word, I mean how much good can one lousy word do?
We've given Eubulides all the foothold he needs. Standard argument now applies, and by the Sorites Paradox, you will never have read enough to start your blog. Cue the laughtrack: those crazy Greeks and their wacky comedies!
Seriously though, the moral is, stop analyzing and planning and drawing flowcharts, and just go! No amount of dissecting the details will make you completely ready; absolute readiness is a myth, because there's risk in everything we do. That's just part of life. Take me, for instance. I took a spontaneous monthlong trip from the U.S. to Japan, with nothing but a backpack and a couple days' youth hostel reservations. It was totally awesome. I almost missed ever taking the trip, just because I never felt "ready", there was always a better time skulking somewhere in the vague future.
OVERPOPULATION
As you've no doubt heard, the world is vastly overpopulated, and it's only getting worse. You probably had to fight off a starving mob just to buy groceries recently. When I look at the writhing mass of humanity crawling all over each other outside my window, I wonder: when exactly did we get this way? Sure, I'll starve soon, but maybe I can hunt down that one baby who "broke the limit" and take him down with me!
But seriously, by now you can see how Eubulides applies without me even spelling it out. One human isn't overpopulation, and a non-overpopulated world surely has room for one more person. Conclusion: no finite population qualifies as overpopulation. Another exciting breakthrough courtesy of The Riddler!
When I applied "heap logic" to overpopulation, it made me recognize that I'd long been blindly accepting the threat as dogma. There's so much doomsaying on this issue that it's almost become a conditioned pattern: "Interesting weather today, huh. Seems kind of overpopulated." I realized that there's a lot more to it than just "Babies bad!" My girlfriend's home country is actually suffering from serious underpopulation problems. When I started thinking it over logically, I saw that a lot of the threats of population explosion, don't really stand up to scrutiny. Anyway, the point (until a later article) is just that the old adage "question everything" doesn't have a special exception clause for this case.
FURTHER READING
How to Contribute to Civilization
Short- and Long-term Assets
What is an Official Language
Assumption 1. A single grain of sand is not a "heap";
Assumption 2. If some sand is not a "heap" initially, one more grain won't make it a heap.
Conclusion: No finite amount of sand qualifies as a heap.
The proof is simple. Let N be any finite number, as big as you like. We claim N grains of sand don't make a heap. By the first assumption, one grain isn't a heap. Now apply the second assumption over and over: 2 grains aren't a heap; nor 3; nor 4... after N-1 steps, we're forced to agree, N grains of sand do not a heap make. Since we proved this for an arbitrarily large N, that means no finite graincount is high enough!
What can we learn from Eubulides' puzzle? The most important lesson is that language is inherently vague. We can apply this to real life in a number of ways. Here are three applications of the anomoly of the heap.
ENOUGH WORK!
Every good citizen knows that everyone should work. Labor is the cornerstone of capitalism, and if people didn't do enough work, all of civilization would collapse... right? But just how much work is "enough"? After how many hours of sweat does a man achieve that noble work ethic which drives us all?
Most people would agree that a lifetime workload of one miserable hour, isn't "enough". It's not even close. If someone out there has figured out a way to make a permanent living off one hour's service, that's disgusting!
Again, if you currently haven't done enough work for your lifetime, then toiling away one more hour isn't gonna make any difference.
Thus, the assumptions behind the Sorites Paradox are satisfied. Instead of granules of earth, we're discussing hours of work, and the word "heap" has been replaced with "enough". The argument still goes through, and we reach the conclusion: no finite amount of work is enough!
This is a rather discouraging conclusion, until you remember that Eubulides wasn't a real economist, thank God. He was just a jokester. But sometimes there's a grain of truth lurking in the jester's tricks. The real wisdom to take away from this thought experiment is that we should take the work ethic less seriously. No matter how much work I do, civilization is never going to turn to me and say, "Great show! You've done enough work now, forever!" When I realized this fact, it set me free, in a way. It liberates you from the ratrace and lets you take life a little less seriously, and enjoy it a little before you die.
READY FOR TAKEOFF
Another vague predicate is the term, "ready". This is a big one, which can hold you back a long time. It's common sense that you need to prepare before making the leap. Who would take a spontaneous trip halfway around the world with just a light backpack? It seems that the bigger the event, the more preparation and analysis are necessary.
But where is the exact threshold when the whole project finally gets the green light? It's harder to quantify in such a broad application as this, so let's focus on a concrete example: you decide to start a blog. This is easy to quantify because most of the preparation for starting a blog involves reading things. The question is, how much do you need to read before you're "ready" to launch the world's next great weblog?
Well, one solitary word is definitely not enough. You can't just dive in blind, you should at least make sure you're picking good publication software. Again, if you're not ready yet, you won't suddenly be ready after reading just one more word, I mean how much good can one lousy word do?
We've given Eubulides all the foothold he needs. Standard argument now applies, and by the Sorites Paradox, you will never have read enough to start your blog. Cue the laughtrack: those crazy Greeks and their wacky comedies!
Seriously though, the moral is, stop analyzing and planning and drawing flowcharts, and just go! No amount of dissecting the details will make you completely ready; absolute readiness is a myth, because there's risk in everything we do. That's just part of life. Take me, for instance. I took a spontaneous monthlong trip from the U.S. to Japan, with nothing but a backpack and a couple days' youth hostel reservations. It was totally awesome. I almost missed ever taking the trip, just because I never felt "ready", there was always a better time skulking somewhere in the vague future.
OVERPOPULATION
As you've no doubt heard, the world is vastly overpopulated, and it's only getting worse. You probably had to fight off a starving mob just to buy groceries recently. When I look at the writhing mass of humanity crawling all over each other outside my window, I wonder: when exactly did we get this way? Sure, I'll starve soon, but maybe I can hunt down that one baby who "broke the limit" and take him down with me!
But seriously, by now you can see how Eubulides applies without me even spelling it out. One human isn't overpopulation, and a non-overpopulated world surely has room for one more person. Conclusion: no finite population qualifies as overpopulation. Another exciting breakthrough courtesy of The Riddler!
When I applied "heap logic" to overpopulation, it made me recognize that I'd long been blindly accepting the threat as dogma. There's so much doomsaying on this issue that it's almost become a conditioned pattern: "Interesting weather today, huh. Seems kind of overpopulated." I realized that there's a lot more to it than just "Babies bad!" My girlfriend's home country is actually suffering from serious underpopulation problems. When I started thinking it over logically, I saw that a lot of the threats of population explosion, don't really stand up to scrutiny. Anyway, the point (until a later article) is just that the old adage "question everything" doesn't have a special exception clause for this case.
FURTHER READING
How to Contribute to Civilization
Short- and Long-term Assets
What is an Official Language
Posts
2 comments:
Thanks for this interesting post! I just wanted to say two things about the threat of overpopulation.
1. While it's physically possible to cram more spectators into an already full theater (by having them sit in the aisles, or on each other's laps), if there's ever a fire, this kind of practice increases the chances of people getting stampeded or burned to death. In other words, we also have to look at extreme situations.
2. Human overpopulation must also be considered in terms of our environment impact-- the extinction of plant and animal species, the destruction and pollution of the ecosystem, caused by human activity.
Yes, language is vague, causality entangled and systems fuzzy, but I don't think "overpopulation" is a purely dogmatic concept. It is, rather, a shorthand term for much more complex problem.
Hi Ulysses,
I don't know about theaters. Maybe if that becomes an issue, we'll see a revival of drive-in theatres (or better yet, "walk-in theatres"). Here in Columbus, there's a little shop on High Street, almost more of a booth than a shop its so small, and they regularly project movies onto the wall of the next building over, to attract customers. There's always a group of people there watching, it's a great community thing. Looking far enough in the future, who knows whether the theater will survive forever..
You're right about environment, hopefully when the population expands, technological breakthroughs will help. Thing about this point is, pollution isn't a necessary result of high population; it's a result of the waste which is so rampant in the world.
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