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Name: Tyler
Location: Mountain View, California, United States

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Sunday, July 15, 2007

Questions we can't answer

What was Zeus's favorite color?

When I was a kid, learning a million new things every day from my parents and teachers, I felt as if the realm of knowledge was boundless, and that every question I could muster could be answered, if only I asked the right person, or maybe thought hard enough for long enough. As I grew up, I began to see that many questions have no known answers, and that by the end of my life I could hope to know at most a tiny fraction of what was to be known. The next step is to see that many questions will simply never be answered, no matter how long or how hard we may try.

I would like to suggest here that, essentially, these questions do not matter, so we shouldn't feel bad about this limitation.

To clarify the discussion, let's define our terms. I want to consider objective questions about the state of the world - questions that are asking if things are one way or another. One example is: What is the average airspeed velocity of a coconut-laden swallow? Non-examples: What is the best book of all time? Could you hand me the salt, please? I will not consider questions such as these last two.

What do I mean when I say a question is answerable? I mean that, given all the information available, we can determine beyond doubt which possible answer is correct. One may think about any question as having a set of possible answers. If any two of those answers both lead to the currently available information, then we cannot distinguish them and thus cannot answer the question.

So, what was Zeus's favorite color? Intuitively, you might protest that this question seems to not be about the world, so much as about an imaginary creation within it - but bear with me, and let's accept this as a real question for now. This questions is certainly unanswerable. If Zeus's favorite color were blue, the world would be exactly the same as it is now, which could also be the case if his favorite color were orange. There are no historical records about these alternatives, and no authorities on the matter who would be able to give a definitive answer. We do not know, cannot know, and never will know.

Does that make you sad? I hope not. Frankly, I really could care less about Zeus's favorite color, because it has absolutely no bearing whatsoever on my life (or yours). And the theme of this post is that it makes sense to apply this healthy apathy to all such questions.

Why should we never care about, nor feel bad about, not knowing the answer to such questions? I propose that unanswerable questions are artifacts of our creativity, and of our ignorance*. In other words, if we had complete world knowledge, we would see that asking such questions doesn't even really make sense. I think this is intuitively clear in asking about Zeus's favorite color, but less so when questions start to feel like they matter more. For example, are we in a matrix-like simulated world, run by perfect (mistake-free) computers which will never interfere with the rules set up within the system? This feels important, but again it is unanswerable, since we have no way to distinguish between an affirmative or negatory response. We could imagine a million such hypothetical different "realities" to ask about, none of which leave a clue as to their true answer, and each would be just as meaningless to ponder as Zeus's favorite color.

It's cerulean, by the way.

* The connection between creativity and ignorance is simply that the possible worlds we can imagine existing are necessarily the result of not knowing everything about the single world which does exist (metaphysicists, please forgive me for that over-simplified statement). I've mentioned this idea of ignorance being a key to human understanding in the earlier post on the subjective nature of causality.

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Blogger said...

Interesting post T. What do you say to questions that may be impossible to answer in the affirmative or the negatory. Such as one that you're yourself very familiar with, does P equal NP. Most likely, there is either a yes/no answer to this question, but there is a finite, albeit faint, chance that we cannot answer this question within our inductive/deductive reasoning systems. This question, however, does change the way we think about the world (at least as computer scienctists!), so it is important :-)

1:32 PM  
Anonymous Anonymous said...

This is enirely useless

11:22 AM  
Blogger Tyler said...

This is entirely useless.

You could say that about the majority of modern philisophical inquiries. You could say that about the majority of music, art, and entertainment. About anything you do just out of fun, interest, or curiosity.

You could say that, and even then, depending on what you consider useful, you could be entirely wrong.

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