Salvador Dalí’s The Persistence of Memory

Marelisa Fabrega wrote about lateral thinking and gave us some interesting logic puzzles to play with. In the spirit of promoting lateral thinking, I’ve come up with a puzzle of my own. Be the first to solve it, and win a prize.

A guy wakes up early in the morning, happy because it’s his birthday. Because he’s very precise about time, he wants to jump up and shout “Woo hoo!” at the exact time of his birth.

He looks at the clock and sees that it’s not time yet, so he waits and twiddles his thumbs. But after a while, he suddenly realizes that it will never be the right time. Why?

If you think you know the answer, leave a comment and tell us. If you’re the first one to get it, I’ll leave a comment on your blog and give you a stumble. Hey, I didn’t say it was a big prize!

Image from The Matrix Reloaded (2003)

In one scene of Enter the Matrix, Trinity asks Ghost if he really believes that Neo will fulfill the prophesy of him ending between the war between the humans and the machines.

“Do you believe that Neo is going to end the war?”

“Yes. I do.”

“So do I. But I can’t explain how or why.”

“Kierkegaard reminds us that belief has nothing to do with how or why. Belief is beyond reason. I believe because it is absurd.”

“You think it’s crazy to believe it?”

“To believe what? That a single man can defeat an entire race of machines, and end a war that has endured for over a hundred years? Of course! It’s complete lunacy. And that’s why we must believe it will happen. Faith by its very nature must transcend logic.”

I believe in global warming. I believe that it exists, that it’s caused by humans, and that it’s a big problem. You might think that I’m crazy to believe something like that with absolutely no evidence. It’s not like I’ve been measuring air and ocean temperatures, or analyzing greenhouse gas concentrations in the atmosphere.

Oh sure, there are supposedly some scientists who say the evidence is out there, but I’ve never seen it personally. I haven’t even met anyone who’s seen it. And in spite of that, I still choose to believe it.

Maybe global warming is too much of a stretch for you. Maybe you’d like to believe in something a little more certain, like gravity. But that’s a coward’s belief. You don’t believe in gravity, you know in gravity. If there’s no chance of being wrong, it’s not a belief, it’s a certainty.

A belief has to require a leap of faith in order to mean anything. And yes, that means you might be wrong. So put yourself out there and take a chance of being wrong. Don’t just sit on the sidelines playing it safe.

Image from The Matrix (1999)

In general, which is the greater mistake: believing something that turns out to be false, or not believing something that turns out to be true? People like to think that nothing is wrong with the second one, but aren’t they equally bad?

You can’t refrain from having an opinion, wait until incontrovertible proof arrives one day, and then decide to believe it and think you’re so smart for being sure not to be wrong. If you weren’t willing to go out on a limb one way or the other, you were wrong by default. We’re all going to be wrong a lot of the time no matter what, so you might as well hold beliefs that work for you.

I believe that I’ll ultimately make more money from this blog if I only promote products I like and present them fairly. Is that a sure thing? No, not at all. In fact, you kind of have to ignore logic a bit to believe it. But I think this belief serves me.

You can believe that people are fundamentally good, or that they’re fundamentally bad. You can believe in God, or believe in no God. You can believe that this is the worst time in human history, or that this is the best time in human history. Any reasonable belief will be true enough to defend, but you have to always ask if your beliefs serve you, because some can be detrimental.

Don’t be afraid to have beliefs beyond reason. Most of us believe a few things that we’ll admit don’t even make sense. And when you’re laughing at someone who won’t buy a house because the street number is 13, they’re laughing at you for not opening umbrellas indoors.

But it’s all about what works for you. If a belief feels right to you and leads you in the right direction, go for it, even though you might be wrong. That’s OK, and that’s why they’re called beliefs and not certainties.

But you know what? Even so-called certainties can be wrong. I’ve met lots of people who believed there was no such thing as a one-sided piece of paper, until I made them a Möbius strip.

Photo by David Benbennick

“Why not go out on a limb? Isn’t that where the fruit is?”

- Frank Scully

In a comment on my post Top Secret Tips For Winning Game Shows, Marelisa the abundance queen reminded me of the Monty Hall paradox, which deserves a post of its own.

This problem became famous in 1990 when Marilyn vos Savant wrote about it in Parade magazine. This is how she stated it:

“Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, ‘Do you want to pick door No. 2?’ Is it to your advantage to switch your choice?”

She said that you should switch, because switching will give you a 2/3 chance of winning the car, compared to 1/3 if you stick with door #1.

Not exactly intuitive, is it?

She received more than 10,000 letters from people (including 1,000 Ph.D.s) saying that she was wrong (and presumably saying the odds were 50/50 either way). She also got a letter from me, saying something different (we’ll come back to this).

Russian roulette

Here’s another way of looking at it. Let’s say you’re playing Russian roulette with one other person, using a gun with 6 chambers and 1 bullet. You spin the cylinder and you’re about to pull the trigger to fire chamber #1, which has a 1/6 chance of having a bullet.

But before you do, the other guy asks for the gun, saying he’ll fire four of the other chambers first. So he takes the gun and pulls the trigger 4 times, firing cylinders #2, #3, #4, and #5. Luckily for him, they were all blanks. He gives the gun back to you, and asks if you want to stick with your original cylinder #1, or switch to cylinder #6.

Because he didn’t know where the bullet was, it doesn’t matter if you switch. It’s a 50/50 chance either way.

But let’s back up and try something else. You’re about to fire chamber #1 when the other guy asks for the gun, saying he’ll fire four of the other chambers first. He takes the gun, but this time, he swings out the cylinder to see where the bullet is. Then he fires chambers #2 and #3, skips chamber #4, and fires chambers #5 and #6, all of which are blanks. He then asks if you want to stick with cylinder #1, or switch to cylinder #4.

Does it matter if you switch now? You bet! He skipped chamber #4 for a reason. And if the bullet was in any of the other chambers, you can bet that he would have skipped those instead. There’s a 1/6 chance that the bullet was in chamber #1 and he just skipped a random chamber to mess with you. But there’s a 5/6 chance that the bullet was not in chamber #1, and he specifically fired all the remaining blank chambers, leaving just the bullet.

Just like you should stick with chamber #1 to avoid the bullet, you should switch to another door to win the car.

The real answer

However, one of the reasons there was so much debate about this problem is that it’s ambiguous, and that’s what I said when I wrote to her. We just don’t know enough about the host’s reasoning for picking the door to open. For example:

• If the host had decided that he was going to open door #3 no matter what, and it just happened to be a goat, your odds are 50/50 with either door.
• If the host wanted to be nice and only offer you the chance to switch if your original choice was wrong, and only open a door containing a goat, you’d have a 100% chance of winning by switching.
• If the host wanted to be a jerk and only offer you the chance to switch if your original choice was right, you’d have a 100% chance of losing by switching.

To spell out Marilyn’s assumptions, the problem would read like this:

“Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. The host, who knows what’s behind the doors, has decided in advance that after you pick a door, he’ll open another door and give you the choice of switching to the remaining door. He’ll decide which door to open using this logic: if you pick the door with the car, he’ll open another door at random; if you pick a door with a goat, he’ll open the other door with a goat.

You pick door No. 1, and the host opens door No. 3, revealing a goat. He then says to you, ‘Do you want to pick door No. 2?’ Furthermore, he explains his logic in choosing to open door No. 3, and you know he’s telling the truth. Is it to your advantage to switch your choice?”

It kind of ruins the fun to spell out everything like that, but you can’t talk about who’s right and who’s wrong if the problem is ambiguous! When the problem is stated this way, the answer is that you should switch, because door #2 has a 2/3 chance of having the car. The way Marilyn stated it, it’s too ambiguous to answer unless you make some assumptions.

BTW, did you assume that the car is better than a goat? In a 1999 auction, someone paid $80,000 for a full-blood adult South African Boer goat. So maybe you shouldn’t switch after all!

Photo by HomeParking

So it turns out that blogless wonder Scott McIntyre has appeared on 5 game shows in the UK, including “The Weakest Link,” which he won. It reminded me that I hadn’t revealed my top secret game show tips yet. Of course, “top secret” really just means “logical,” but logic seems to be quite rare among many game show contestants (though I haven’t watched any in years, so I never saw ones like “The Weakest Link”).

Without further ado, here are three tips you can’t miss.

1. Don’t try to make the best guess, just make the right guess.

There was one show where two people had to guess how many hours of TV someone watched; whoever came closest won. The first person guessed 10. The second person, knowing the first person’s answer, guessed 5.

The second person was closest because the answer was 1, but guessing 5 was a bad idea. After the first person guessed 10, the only reasonable guesses for the second person were 9 or 11. That’s because the goal isn’t to get as close as possible to the right answer, but just to get closer than the other person. If you leave any room between your guesses, there’s a chance that the answer will be in between them, and the other person might be closer.

This doesn’t apply to The Price Is Right, where you lose if you go over. In that situation, it makes perfect sense to guess far below someone else, even $1.

2. When only one basket can win, put all your eggs in it.

There was another show where two people are asked a question, and they each answer true or false (they can both give the same answer). If someone’s right, they take a step forward. Three steps forward and they win.

In this case, the first person just needed to get one more question right to win, and the second person was further behind. On the next question, the first person makes a guess. What should the second person do?

Well, there’s only one thing they can do: guess the opposite of whatever the first person says. The only way they can win is if the first person gets all the remaining questions wrong, so they have to run with that.

Guessing the same answer as the first person doesn’t help when they’re ahead and just need one more to win. Either both people are wrong and nothing happens, or they’re both right and the first person wins. So the second person should just guess the opposite and hope the first person is wrong. It’s their only chance.

3. Don’t share lottery jackpots.

OK, the lottery isn’t a game show, but it’s like a game show in that you can influence the results. No, you can’t control your chances of winning–that’s completely random, and no “system” will change that. However, you can control the chances of having to split the jackpot with someone else in the event that you do win.

You do this by picking some numbers that other people don’t pick. This means numbers above 31, because people use birthdays and anniversaries to pick numbers. Then if your ticket is the one in 175 million that wins, you’re less likely to find that someone else has chosen those same numbers.

Better yet, don’t play the lottery.