I think the Monty Haul problem can be expressed very intuitively in such a way that can even defy the intuitive (but wrong) answers.

1) The probability of being right before removing a door is 1/3;
2) If you don’t switch, the probability of being right remains unchanged;
3a) (the correct answer) If you switch, the probability of being right is the complement of staying (ie 2/3), so you should switch;
3b) (bad reasoning/right answer) If you switch, the probability of being right is 1/2, which is greater than the probability of being right if you stay (1/3), so you should switch.

The key is establishing #2. Of course, if you’ve successfully established #2, then the intuitive (but wrong) reasoning in #3b (if you switch, the probability of being right is 1/2) should be very suspect. But even if you can’t convince somebody of that, as long as you can establish #2 and you can establish 1/2 > 1/3, then you’re home free, although you feel dirty for having used faulty logic.

Anne is looking at George, who is unmarried.

Jack, who is married, is looking at Anne.

It doesn’t matter whether Anne is married or not, because if she is then it would be a married person, Anne, looking at an unmarried person, George. Whereas if she is unmarried then it would be a case of a married person, Jack, looking at an unmarried person, Anne. To say Anne has to be married because she’s looking at the unmarried George is a mistake, because we are dealing with three people not just two.

Anne’s marital status has nothing to do with the case, it’s an irrelevancy. What matters is the marital status of George and Jack. So long as we know that they are, respectively, unmarried and married, Anne can be either without substantially affecting the answer to our question.

So, to make this succinct, is a married person looking at an unmarried person? Answer, yes.

At greater length, because we have a married person—Jack—and an unmarried person—George—-involved Anne’s marital status has nothing to do with the case. So if she’s married the fact she’s looking at George means a married person is looking at an unmarried person. While if she is unmarried means that Jack—who is married—is looking at the unmarried Anne.

He still leaves it a bit unclear why exactly making models of universes should be placed higher on the scale of worthy endeavors than other things, like eating a chocolate, or building an empire. Yes, ideas trump events in the grand scheme of things (agreed on in principle since the Greeks), but what ideas? People have different interests, and I can see this turning into a needless (and provocative) essay on a profound topic, but it is a very important topic.

Generally speaking, the more basic and fundamental an idea, the more important it is. Meta-information is more valuable than information, when it encapsulates that information, because it renders it redundant. And physics is supposed to describe fundamental reality, so it goes without saying that we honor its principal achievements like so.

But it’s not the models people write down that are ultimately important. It is the *realization* of the phenomena that is really fundamental. Who cares if you write down an equation that works in various scenarios for a hundred years? The equation itself is only as important as any other stepping stone or temporary figure or human event that perishes with the passage of time. It’s not about sentimental regards to immortality; the problem is that no model is intrinsically true to begin with. Nobody has ever built a universe. I think the grander part of science is knowing what needed to be explained and why it was explained thus, rather than the actual form you end up with.

Solutions can take equivalent forms; it’s the underlying observed phenomenon that is fascinating.

I spoke to an accomplished mathematician not too long ago at my institution, a man with fairly important discoveries in number theory, who told me he avoided physics since high school. He spent his entire life studying the realm of logic and away from “reality”, because modeling reality didn’t seem to make sense to him.

“Physics.. describing things.. How do you even go about doing that?”

And maybe he’s right. Maybe we are not in a position to truly understand anything, despite all we’ve achieved. We can have faith that reality presents itself to us in a form that is sensible and true, and it is a very noble pursuit to try to come up with formal systems describing it, but the things we scribble down are only the limitations of our imagination. Only the observable effects they try to model can ascribe to reality, so that in being aware of them we can be said to have understood something true.

All I’m trying to say is that ideas, even ingenious ideas, can rise and fall like the rest of the meaningless (and necessary) markings of human history.

…If Anne is married, she’s looking at George, so the answer is “yes”; if she’s unmarried, Jack is looking at her, so the answer is still “yes.”…

Say what? I think we’ve got a case of assumptionitis here. Let’s go over what facts we have.

Jack is married.

George is not.

Jack is looking at Anne.

Anne is looking at George.

Question: Is a married person looking at an unmarried person?

Going by the facts available, without over analyzing the problem, we don’t know. Anne’s marital status is not specified, much less hinted at. To say she is married or not requires guessing, and that is prone to error. To conclude she has to be married because she’s looking at an unmarried person is to assume something that may not be so.

Call me a strict constructionist, but I go by the information available; and if the available information says nothing about a subject or a subject’s state, then I don’t consider what isn’t there. And in this case the question says nothing at all about Anne’s marital status. In short, people are making assumptions because the authoritative answer says she is married while using some faulty reasoning of its own.

In short, this thread is an example of Appeal to Authority as Dysrationalia. Remember, the author of a piece isn’t always right.

Actually, it was the other way round. They cleaned out the pigeon droppings because they had no clue where the noise was coming from, so they had to check.

Now, if Uranium suddenly stops fissioning in the reactors powering the works, Nielsen and Ninomiya may be on to something.

The problem with the SCSC was that noöne pointed out to the Texans that the thing could double as an aid in executions. It’d almost pay itself back, too, at the rate they’re going.

(YAY! Stereotypes!)