19 replies to this topic

[arturhawkwing]

Know any good paradoxes?

My favorites are the unexpected hanging:

A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.
Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the "surprise hanging" can't be on Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.
He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn't been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.
The next week, the executioner knocks on the prisoner's door at noon on Wednesday — which, despite all the above, was an utter surprise to him. Everything the judge said came true.

and the Monte Hall one:

You are in a game show. There are three doors. Behind 2 are goats, and behind one is a shiny car. If you pick the one with a car.
after you pick a door, the host opens one of the others, revealing a goat. You are then given the option to change doors. Is it in your best interest to do so? At this point, most people would say it doesn't matter, you now have a 50/50 chance with either door. They are wrong. It is really in your best interest to switch, in which case you will have a 50% chance of winning, where as if you keep the same choice you only have a 33% chance.

Im not going to explain the mathematics behind the second one, as it is one of the most popular paradoxes, and there's a good chance that everyone here already knows why your chances would improve if you switched. If you dont, hink about it, it's really quite interesting.

[darniil]

How is the first one a paradox? It sounds to me closer to a self-fulfilling prophecy than a paradox.

[Eerongal]

I'll just leave this right here....

[Emeralis00]

I'll just leave this right here....

Mind.
Blown.

[arturhawkwing]

I'll just leave this right here....

Id heard of those paradoxes before, but no the solutions! That's fantastic!

[Silus - Shard of Flame]

I'm not sure I followed that one. Still processing.

[SOM1else]

"this statement is false."

"new mission, decline this mission."

"Does a set of all sets contain itself?"

I keep these ones handy in case of rouge AI.

[darniil]

Ah, now see, that won't work with all rogue AI. Some are too, er, clever to fall for those.

[SOM1else]

and some are just to idiotic to realize what a logical inconsistency is

[Silus - Shard of Flame]

But he's read Machievelli!

[SOM1else]

I also read it and do not know what all the fuss was about - understood it perfectly. Have you read it?

[Silus - Shard of Flame]

Yes.





(okay not really but it's for the quote, darnit!)

Edited by Silus - Shard of Flame, 29 August 2011 - 12:18 AM.

[SOM1else]

Yeah, doubt it... Wish there was more books! but there's not.









(In honesty I have read it... well I read the first half at least. Pretty intresting, at least the parts that didn't go straight over my head.)

[SOM1else]

So you know the grandfather paradox? the one where if you go back in time and kill you're grandpa you would never be born and never be able to travel back to kill him so he would never die in the first place.

Yeah that one, it's been solved

[Chaos]

So you know the grandfather paradox? the one where if you go back in time and kill you're grandpa you would never be born and never be able to travel back to kill him so he would never die in the first place.

Yeah that one, it's been solved

Nice. That's pretty awesome. Makes a lot of sense if you think about it.

However, I never got the impression in my study of quantum electrodynamics that photons actually hold more probability of going back in time. Processes, however, would be invariant under a time shift (specifically, a CPT--charge, parity, and time transformation--would be invariant). http://en.wikipedia....ki/CPT_symmetry http://en.wikipedia....wiki/T-symmetry

In the original article you linked, there was a paragraph which said "The same holds true in a less dramatic fashion for subatomic particles like quarks and photons, which hold a much higher likelihood of ever traveling into the past, based on the strange, spooky behavior they’ve demonstrated for the people who’ve studied and been alarmed by them thus far." That really seemed... incorrect to me, so I clicked the link, and it just says a bunch of stuff about the Many-worlds interpretation, which is just an interpretation of quantum mechanics. It is not the orthodox interpretation (at least, according to my wonderful quantum mechanics textbook). This does not mean that particles are actually going back in time, and I think was extremely poorly worded.

When you look through the topic on the Many-worlds interpretation, ugh... I'm in quantum mechanics right now. That article did nothing to imply that particles are going back in time. This is why you don't get your information on How Stuff Works, or pretty much any popular science article. *huff huff* You don't really start to understand quantum mechanics without a lot of math. That's just how it is.

See, you have to realize that the equations sort of allow you to do a time shift. If you give me a wave function, I can tell you its amplitude (think probability) at any time t, positive or negative. Just because I can write it down does not mean that the particle actually moved back in time. There's nothing mysterious about time travel in regular quantum mechanics. But that's not even mysterious in non-quantum systems. For example, I can write down that the distance a car moves across, I don't know, an interstate, would be d = vt. I can plug in any time that I want, positive or negative. Does that mean the car moved back in time? No. Obviously not.

Now, happyman, you know more physics than me, but I got a good taste of quantum electrodynamics. I am fairly sure "subatomic particles like quarks and photons, which hold a much higher likelihood of ever traveling into the past" is a false statement. Maybe there's some weird quantum field theory which actually states that, but I always interpreted it as that the math doesn't particularly care which direction time is moving in the process.

[Ryan]

That Skeptoid podcast reinforces my disdain of philosophy as field of study. All that time and effort spent debating the philosophical ramifications of the paradoxes, when in truth they are an easily-explained and understood math error.

[Windrunner]

There are pretty cool! I liked the hanging one alot. The whole grandfather paradox solved thing went straight over my head though. Whenever I hear quantum anything my brain shuts down.

Oh, Some1else, what page is the Dalinar quote in your sig from? I've read the Way of Kings so many times but I've managed to miss that one completely. It's one of the best lines I have ever read!

[SOM1else]

I don't have my copy nearby right now but I'll edit this post as soon as I can check it for you. I can tell you what part it is from though if that would help until I can get an exact page number though,

Spoiler

It's from Dalinar's speech right after Sadeas abandons Dalinar and his army in thier joint battle against the parshendi

EDIT*

Turns out I had the page marked in my book so I was able to find it much faster then I thought it would take me. It's on pae 908 of the US hardback edition

Edited by SOM1else, 21 October 2011 - 04:03 PM.

[SOM1else]

Sorry for the double post it's just that this one has nothing to do with the last one and it wouldn't really make sense as an edit

[Swifftalon]

"this statement is false."

"new mission, decline this mission."

"Does a set of all sets contain itself?"

I keep these ones handy in case of rouge AI.

If I'm not mistaken, all of these are a part of portal