Yes, exactly—thank you. It depends on the interpretation of the phrase “given that all rolls were even”. Most ordinary people will assume it means that all the rolls were even, but as you have succinctly explained, that is not what it means in the specialist language of mathematics. It is only when you apply the latter interpretation, that some of the rolls are odd but we throw those out afterwards, that the result becomes at first surprising.
I do find LessWrong a curious place and am not a regular here. You can post something and it will get downvoted as wrong, then someone else comes along and says exactly the same thing and it’s marked as correct. Heh.
darrenreynolds
Karma: −4
Nah.
The problem with the explanation is this line of code:
x=random.randint(1,6)
That will generate odd numbers. The introduction to the problem states, “given that all rolls were even.”
That’s why you’re getting a surprising result. It’s the differing interpretation of what ‘all’ means. If you think it means what it says—all rolls—then there is no surprise. But if, as the explanation implies, you think it means that some of the rolls were odd, but not those involved into the success condition, that’s when you get a different outcome. It’s not a paradox. It’s just how the question is interpreted.
Thanks for engaging on this—I’m finding it educating. I’ll try your suggestion but admit to finding it hard.
So, there’s a Chinese rocket-maker in town and Sir Isaac Newton has been offered the ride of his life atop the rocket. This is no ordinary rocket, and it’s going to go really, really fast. A little boy from down the road excitedly asks to join him, and being a jolly fellow, Newton agrees.
Now, Newton’s wife is pulling that funny face that only a married man will recognise, because she’s got dinner in the oven and she knows Newton is going to be late home again. But Newton is confident that THIS time, he’s going to be home at precisely 6pm. Newton has recently become the proud owner of the world’s most reliable and accurate watch.
As the rocket ignites, the little boy says to Newton, “The vicar told me that when we get back, dinner is going to be cold and your wife is going to insist that your watch is wrong.”
Now, we all now how that story plays out. Newton had been pretty confident about his timepiece. 99.9999%, in fact. And when they land, lo and behold his watch and the church clock agree precisely and dinner is very nice.
Er, huh?
Because in fact, the child is a brain in a vat, and the entire experience was a computer simulation, an advanced virtual reality indistinguishable from the real thing until someone disconnects him.
That’s the best I can do without breaking the taboo.
“Throughout this process, what I’m doing is using my observations as evidence for various propositions. “Reality” is my label for the framework that allows for those observations to occur, so what we call this process is “observing reality.”
“What’s confusing?”
It seems to me that given this explanation, we can never know reality. We can only ever have a transient belief in what it is, and that belief might turn out to be wrong. However many 9′s one adds onto 99.999% confident, it’s never 100%.
From the article: “Isn’t all this talk of ‘truth’ just an attempt to assert the privilege of your own beliefs over others, when there’s nothing that can actually compare a belief to reality itself, outside of anyone’s head?”
I think the article was, in part, setting out to debunk the above idea, but surely the explanation you have provided proves it to be the case? That’s why I’m confused.
“It’s not, we know it’s not, and I bet that you yourself treat reality differently than you treat fiction, thus disproving your claim.”
How do we know it’s not? You might say that I know that the table in front of me is solid. I can see it, I can feel it, I can rest things on it and I can try but fail to walk through it. But nowadays, I think a physicist with the right tools would be able to show us that, in fact, it is almost completely empty space.
So, do I treat reality different from how I treat fiction? I think the post we are commenting on has finally convinced me that there is no reality, only belief, and therefore the question is untestable. I think that is the opposite of what the post author intended?
History does tend to suggest that anyone who thinks they know anything is probably wrong. Perhaps those here are less wrong, but they—we—are still wrong.
“And one of the beliefs they’ve confirmed is “reality is really real, it isn’t just a belief.” :-)”
Hah! Exactly! The experiments confirm a belief. A confirmed belief is, of course, still a belief. If your belief that reality is really real is confirmed, you now have a confirmed belief that reality is really real. That’s not the same thing as reality being really real, though, is it?
;-)
Why is it accepted that experiments with reality prove or disprove beliefs?
It seems to me that they merely confirm or alter beliefs. The answer given to the first koan and the explanation of the shoelaces seem to me to lead to that conclusion.
″...only reality gets to determine my experimental results.”
Does it? How does it do that? Isn’t it the case that all reality can “do” is passively be believed? Surely one has to observe results, and thus, one has belief about the results. When I jump off the cliff I might go splat, but if the cliff is high enough and involves passing through a large empty space during the fall, there are various historical physical theories that might be ‘proved’ at first, but later disproved as my speed increases.
I’m very confused. Please forgive my naivety.
Similarly:
“If we thought the colonization ship would just blink out of existence before it arrived, we wouldn’t bother sending it.”
What if it blinks out of our existence, but not out of the existence of the people on the ship?
I’m not sure about the off-topic rules here, but how about this:
Why are some of the drinks so expensive, given that all of them are mostly water?
Sometimes we use the phrase “given that” to mean, “considering that”. Here, we do not mean, some of the drinks are not mostly water but we are not talking about them. We mean that literally all the drinks are mostly water.