One more thing comes to mind regarding the heap of sand.

No matter what, when you have only one grain of sand, it’s not a heap of sand anymore. Me, I think one is the answer (and it’s the loneliest number). Maybe two is still a heap, maybe it’s above ten, or a hundred, or a thousand, or…

But one is never a heap of sand.

Newcomb’s Problem

Let us stick to how it’s originally stated and not give the scientist’s predictions any margin of error; he is ALWAYS correct. Does he determine the outcome, or does the outcome determine the prediction? Not unlike the chicken or egg question, although certainly with less flavor.

Given that he’s always right, you’re walking away with at least $1,000, provided you play by the rules and not choose to take only box A instead. You’re not going to lose. But, one million dollars is more than a thousand and so long as you trust that the scientist will keep his word, take box B and walk away with the million; don’t question the amount each box could hold. If you want a million dollars, that’s what you’re walking away with.

So long as you’re dealing with a person who knows the difference between the contents of the boxes and/or their value or importance, the million dollar box is the choice. Logic doesn’t need to be dragged through all of this. Take the million dollars and be done with it.

Take away the money and its effect on people and you have a harder choice. Box A has a cube. Box B has a sphere. Now what?

The difference between the two doesn’t have the same meaning for us that the difference between one thousand dollars and one million dollars does. There is no ‘greater than’ involved. They aren’t the same thing, but as far as we are concerned, they are on equal standing. It’s just a matter of simply choosing one, not taking what we want.

Now you get to what I think the problem is and what the situation should be (just my opinion, mind you).

By using money, you’re playing off something we’ve been taught, not things we know.

For the sake of argument, you had someone who was blank slate, never taught, never had contact with anyone else. They are completely oblivious to everything we do, everyhing we know. Forget the problems one might encounter presenting this game to them, let’s just say they understand that taking one box grants them one thing, taking both gets them something different.

While they could probably tell the difference between one million things and one thousand things, to stick to the original amounts presented here, and might also be able to understand a concept of “more” (don’t assume either way). that doesn’t mean they’d make the choice the same way we do. Take one, get one thing. Take two, get another thing instead. Here’s where the scientist’s game could get interesting. Maybe, but it could very well be the thing that proves that he can do what he can, dealing with someone who doesn’t know what the two prizes are or what they mean.

We’ve put value and importance on things. But, give a monkey two checks, each for a different value. Is the monkey going to know the difference? No. Monkeys don’t know about money and in general aren’t taught anything about math or values. It’s just a piece of paper with ink on it. While monkeys and chimps may be able to grasp some of these things like we are, it’s not something that’s of use to them. They are intelligent, but in a different way than us. To us, the check represents money, a value, something we can use. To them, the check is just apiece of paper with ink on it. The check matters to us, because we equate it to having a value. The monkey has no idea what it is or what it’s for.

With the cube or the sphere, even if you had never seen one before, had no clue what we called them, and didn’t know what it was that made a cube a cube and made a sphere a sphere, you should still be able to know there’s a difference. There’s no meaning to them and no reason to have instead of the other. It’s just something in a box.

Just like a checks given to a monkey, and I don’t mean the boss’ inept relatives.

There’s no incentive, but you have to decide.

It’s a level playing ground now. Make your choice.

Imagine the [added] chaos if you could choose between A, B or both boxes!

The Unexpected Hanging

The prisoner is hanged because he thinks that he won’t be. Forget the lawyer who gave him bad advice, send him to the gallows first.

I don’t think it matters how many days he’s survived, he’s going to be surprised when they hang him without telling him about it before hand, no matter how prepared he is.

“They’re coming to take me away, ha-ha!”

Sorry, I had to do it…

“I know it, so they can’t take me.”

We’re taking you anyway. Surprise. Wasn’t this fun?

If you want to go by days, the seventh day is the perfect day to do it, unless the day is the only thing that matters (as in only being able to do it at one point in the day, something we aren’t told). Why?

“I just survived trough six days, they can’t do it today! I’m in the clear.”

If he really believes this, he won’t expect it to happen. But we don’t really know how the prisoner is really thinking about this, other than he doesn’t seem to be worried. For all we know, armed with this last possible day logic, he could completely disregard the first day and be hanged then. Why it happened Wednesday, I don’t know. The judge could have already made up his mind and decided to not tell the prisoner, instead giving him something to occupy his mind.

Surprise, you’re dead.

The Sorites Paradox

The heap of sand isn’t a heap anymore once you’re down to the last grain. Forget how many items the average human can tell apart under normal conditions. Forget that the word heap is used. It could be pile, it could be mass. Heck, you might even be able to get away with collection. And let’s toss out a ‘what if’ that briefly came to mind. Disregarding how large or small this ‘heap’ is, the grains of sand don’t have to be touching, just within a defined area. You can have two grains of sand left and it’s still a collection of sand. Not a large collection, but it’s still more than one.

Like my take on Newcomb’s Problem, this comes down to our own, often confusing, way of thinking about things. Where’s the threshold? Are we looking to find a point where the “heap” looks different than it did before? If so, that’s not going to happen if you’re taking sand away grain by grain AND are paying constant attention to all the sand from start to finish. If you get up and leave for a while, then return, you might see a difference, more so if you’re just an observer. It’s the same with watching grass grow. You aren’t going to notice any progress as you’re watching it. You’ll only notice if you pay attention to it at different times.

Maybe when you return, you wouldn’t consider it a heap anymore. But that’s open to interpretation.

Just as grass doesn’t grow fast enough for us to see it happening, taking sand away grain by grain isn’t enough of a change to notice, so long as it remains a single grain each time. If we leave or look away long enough, then return our attention to the sand, it’s possible we’d see a difference. You could say the same about the grass. It all depends on how much time has passed and what the rate of growth ( the grass) or de-heaping (the sand, and yes, I just made that up) is during that time.

If you can rememeber with 100% accuracy how far along the grass was or how exaclty how much was left in the heap when you stopped paying attention, and knew the exact figures for the current time, then you’d notice the difference, not just know that there should be one.

One grain.

Okay, my head hurts now. I think I’m done for a while.