The Law Of Large Numbers
Posted on November 30, 2006
Filed Under Evere Wonder?, Timeless Questions | Leave a Comment
Do small numbers act the same as large numbers? Do numbers act at all? (already I digress) In his book Stumbling on Happiness, Harvard psychology professor Daniel Gilbert explains the law of large numbers to address that question. As a test for the law of large numbers Gilbert proposes an experiment called “split the tab with Dan”. This involves going to a local bar and flipping a coin to see who pays the tab. If you flip the coin four times and Dan wins three of them you might consider yourself unlucky. If you were to flip the coin 4000 times and you lost 75% of those flips you might become suspicious because large numbers do not act the same as small numbers. It is rational to consider loosing three out of four coin tosses due to some imperfection in the coin or the coin tosser (or is it tossee?), but if those same statistics held true for a much larger sample your intuition and rational capacities would suggest that something was amiss and you would be correct.
So, you might ask, what does the law of large numbers have to do with Ultimate Pursuits and asking life’s most important questions? Excellent, thank you. That is precisely the question I asked myself while listening to Gilbert’s book on my iPod while riding a stationary bike and feeling like I was going nowhere. Then it struck me, for all of the important questions in life (at least all that I can think of right now) it is crucial to apply the law of large numbers when drawing conclusions and arriving at answers. For example, it would be possible to conclude, after surveying 10 clinically depressed individuals residing at a psychiatric hospital, that there is no ultimate meaning to one’s existence. A broader survey of the population at large might yield much more optimistic and statistically accurate results.
Wouldn’t the same principles come into play with questions about such vast and important topics as say the existence of God? Granted, that is a question that can seem somewhat like eating an elephant for dinner; it is difficult to know where to start. If that is the case it may not be most important where you begin, but how far you get. For example, many an undergraduate student has been discouraged by a single university science or philosophy professor who has declared that there is no God. As a result, on the basis of one academic, that freshman has concluded that all (or most) thinking university types must have arrived at the same conclusion. Who would argue against encouraging that student to explore further, read more widely, and gather more knowledge before arriving at a conclusion on such a weighty matter?
A friend of mine who is an eminent philosopher suggests that when tackling the important questions we ought to state the question in the form of a proposition and then set out to see where all the lines of evidence converge, apply some logical tests and make a decision accordingly. My guess is that this is actually the process you use subconsciously to make decisions on a regular basis. How about deciding where to go and what to do on a vacation? Aren’t you ultimately asking what will make you happy or what is worth pursuing?
The law of large numbers does not mean that you have to have weighed every apple in a barrel to determine the average weight of the apples. It does mean that weighing seven out of ten apples will give you a more accurate average than by only weighing three. Regarding Ultimate Pursuits types of questions I think it is safe to say that you are more likely to arrive at true and satisfying answers if you ask focused questions, gather as much relevant information as you are able, and test those conclusions to see how they work.
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