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A Puff of Logic

The following is mostly written in order to put my thoughts about this matter into words. A lot of people think about this stuff quite a bit though, so I thought I’d share it just in case anyone found it interesting.

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I tried. I really did.

I grew up in a christian home and had christian friends all my life. I went to church on Sundays and camps in the summers. I went to Bible groups, and eventually even to Bible college and got an under graduate degree in Christianity. I tried hard to believe it all, but I mostly just blindly trusted what the various religious leaders told me and tried to make sense of it and apply it to my life. However, I never really bought it. Not really. There were always way too many questions in the back of my mind that kept nagging at me. For the longest time I just dismissed it as Evil trying to tempt me or something.

Don’t get me wrong, I had a magnificent youth (and hey, I’m still young). I honestly believe I’ve had the privilege of growing up in one of the very best families this world had to offer. I have truly amazing friends. Most of whom are Christian. A few are muslim, and quite a few are atheist. I know one or two New Age buffs too.

However, I’m pretty sure none of the great people in my life are great people because of their religious beliefs. I’ve come to the conclusion that religious beliefs have very little impact on what kind of person you are. It’s what kind of person you are that decides how you use your religious beliefs. If you’re a narcissistic megalomaniac you’ll find some way to exert excessive power over other people to serve your own selfish desires whether you’re a priest, an imam, a scientist, or the guy behind the counter at your local 7-Eleven. If you’re an unselfish person always eager and willing to help others, you’ll do so no matter what your religious beliefs or vocation. It can’t be denied though, that the characteristics of large congregations of religious people present a very potent channel for maximizing a person’s megalomaniacal tendencies. It’s so potent that it naturally attracts the kind of people who wish to exploit it. Certain religions are quite simply incompatible, and that combined with the fact that they require their followers to try to convert everyone else to their religion has caused much of the grand-scale suffering throughout history. That, and the various interpretations of how far one can/should go to achieve this goal of course.

A few years ago I decided to stop going to church to get some distance in order to think this religion thing through more clearly. I’ve concluded that my thoughts on the matter can actually be summed up relatively succinctly:

Religion is used to explain how and why we exist and things happen. However, we now find ourselves at a point in history in which science has much better explanations for all the hows religion has ever attempted to answer, and then some. Science still can’t answer the why, but I actually don’t think religion can either.

To elaborate:

Science’s explanations make a whole lot more sense than the ones found in various religions, in no small part due to the fact that they’re backed by empirical evidence. The latter aren’t backed by any evidence other than simple observations followed by the use of a vivid imagination by a person or group either not capable of, or unwilling to, think the problem through to the end, and/or with a significant lack of logical reasoning abilities. The only thing science can’t explain, at least not yet (and maybe never - but never say never (oops)), are the whys. At least for the really big questions. However, like I said, I don’t really think religion can either. Religion explains why we exist in the same way a Calvin and Hobbes comic explains what tigers are like. Evidence, combined with reason, strongly suggest that God, the gods, Heaven, Hell, Nirvana - whatever - are simply human created concepts designed to explain certain phenomena and control certain groups of people (admittedly, sometimes for their benefit). At the very least, there’s no way to separate the belief that Jesus Christ is God from the belief that thunder is a sign that Zeus is angry by the way of evidence of any kind. Given the large number of religions, many of which have a long and rich history, and the fact that none of them are based on any evidence, the likelihood that any particular belief is the correct one isn’t very high. That, and the large amounts of contradictions found in the various holy texts, don’t make for a particularly strong case.

I think the main reason religion is still so prevalent is that our universe is so amazingly complex that most people don’t understand science’s explanations - and thus religion assumes its historical role of providing simple, albeit erroneous and illogical, explanations that these people accept in order not to have to think about them and simply go on with the business of living. Also, people are constantly looking for “some kind of meaning of it all”. That’s only natural, since we are beings who act with purpose, and therefore instinctively assume the universe we inhabit also acts with purpose. I think meaning is something each and every one of us need to find for ourselves - there’s no evidence of any universal purpose.

As you no doubt have guessed by now, I could ramble on and on and on about all this, and I’ve deliberately avoided talking about what made me jump off the Christianity band-wagon because I could probably go on for pages and pages. It starts with this: For religious people, their faith is so extremely important to them considering its consequences both in this life and beyond - so why in the world would they blindly agree to throw out the need for any evidence what so ever for religious matters when they require it for everything else in this world about which they want to know the truth? I’ll stop there and sum it all up with my answer to The Big Question:

Why are we here? Because it was inevitable.

Go Crazy

If everyone hallucinated on average, say, two random people per week, mostly passers-by - would anyone ever notice? What if those we institutionalize simply have an above average amount of, or more consistent, delusions?

Have a great day!

The Monty Hall Problem - Am I stupid?

UPDATE: I get it now. Thanks to MHW, Jan-Helge and Wikipedia :O) I got way too hung up on isolating each choice. If the number of choices is expanded to, say, 1 million doors, then it’s easier to not overlook the probability of the first choice. If you have 1 million doors, there’s only a 1/1,000,000 chance of getting the right door the first time, and then the game show host removes all but 2 doors, so that makes it quite intuitive that changing doors gives you a good chance of choosing the right one. For some reason this is quite easy to overlook when there are only 3 doors in the first place. Some kind of mental misdirection going on there.

ORIGINAL POST:

The Monty Hall Problem is fascinating, and frustrating. I get the math, I just don’t agree that it solves the particular problem at hand. But I see that it actually does solve it. But it really doesn’t. Confused? Read on…

When presented with the option to switch doors, you have in practice re-started the game with two doors - one of which hides a car and one which hides a goat. This gives a 50/50 percent chance of choosing the door hiding the car.

I fail to see the practical relevance of whether the host (of the game show) knows which door the car is behind. No matter what happens, you end up with a choice between two doors, one of which hides a goat and one which hides a car. There is no other possible final choice in this “game”.

So, in practice, this is a simple probability without replacement problem. You have a jar with 2 white marbles and 1 black marble. The probability of choosing a white marble is 2/3 and 1/3 for a black marble. The host removes a white marble for you. You’re left with a 1/2 chance of a white marble and 1/2 chance of a black marble.

The Wikipedia article points out that it’s never disadvantageous for the player to switch, because the probability of getting the car is always at least 1/2. I simply mean to say that, as far as I can tell, the probability is always, in practice,  exactly 1/2.

This whole thing comes down to how you define the problem. Yes, if you choose one door, then the host chooses another door, then you switch, there is a 2/3 chance that switching will get you the car - theoretically speaking, because you can’t (and wouldn’t want to) choose the door the host chose, and that door is still defined as being in the game. However, keeping the door the host chose in the game makes no sense precisely because it’s already opened to reveal a goat at the time you are to make your final choice and thus gives you 2/3 chance of getting the car if you don’t switch and a 2/3 chance if you do switch. That obviously doesn’t add up. So the game is, effectively, like I noted above, reset and becomes a new game with only two doors.

This is starting to look like one of those “magic” quantum theory things, where the right answer is that there is a 2/3 AND a 1/2 chance of getting the car (NOTE: I do realize this doesn’t actually have anything what-so-ever to do with quantum theory).

For fun I whipped together a little Java app to simulate 1 million rounds of this game, using the theoretical version, and sure enough, switching doors results in winning 2/3 of the time. So even though both definitions of the game, and their corresponding answers, can be said to be correct, it seems only the theoretical and least intuitive one is available to us in practice - which makes no sense to me.

Hey, I never promised you’d be less confused when done reading…

If you happen to know why my assertion that this problem can also correctly be defined as a simple probability without replacement problem is false, please feel free to explain it in the comment section below. Because that’s either the case, or this problem does indeed have two mutually exclusive correct answers - which, well, my rationality-loving mind would have a hard time accepting.