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fun paradoxes

 
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phillip1882
Bit Part


Joined: 14 Sep 2009
Posts: 9

PostPosted: Mon Sep 14, 2009 11:38 am    Post subject: fun paradoxes Reply with quote

the liar paradox:
assume i always lie, and i make the statement, "I am a liar." is this statement true or false?

the light paradox:
if you somehow managed to travel faster than the speed of light (warp drive engine say.) and turn on headlights, what would happen?

the value of irrationality paradox:
a person who has great insight and has studied your habits for while decides to offer you a challenge. there are 2 cups, cup A has 1000 dollars, and cup B can either be empty or contain 1,000,000. you can either only pick cup B or pick both cup A and B. if he predicts that you will only pick cup B there will be 1,000,000 dollars under cup B. if however he predicts you will pick both, there will be nothing under cup B. which choice do you take?

the self referential paradox:
take all self referential statements, such as "this statement is true", and let's call them heterogeneous. any statement that does not refer to itself is homogeneous. which classification does that statement fall under?

the nothing paradox:
nothing is better than God, but bread is better than nothing, therefore bread is better than God.

the everything paradox:
does the set that contains everything contain the set that contains everything?
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TFBW
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Joined: 07 Oct 2006
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PostPosted: Mon Sep 14, 2009 2:45 pm    Post subject: Re: fun paradoxes Reply with quote

My answers aren't necessarily right. Feel free to disagree.

phillip1882 wrote:
assume i always lie, and i make the statement, "I am a liar." is this statement true or false?

I'd have to say that the statement disproves the assumption (by leading to a contradiction).

phillip1882 wrote:
if you somehow managed to travel faster than the speed of light (warp drive engine say.) and turn on headlights, what would happen?

Warp theory supposes that it's possible to move a bubble of space-time faster than the speed of light. Your headlights shine forward, the photons racing away from you at a relative velocity of C, as always. I have no idea what happens when they hit the warp envelope, however.

phillip1882 wrote:
a person who has great insight and has studied your habits for while decides to offer you a challenge...

I'm not sure I understand the question, so I'll pass on that one.

phillip1882 wrote:
take all self referential statements, such as "this statement is true", and let's call them heterogeneous. any statement that does not refer to itself is homogeneous. which classification does that statement fall under?

That sounds like a corrupt version of the Grelling–Nelson paradox. I'll leave it at that.

phillip1882 wrote:
nothing is better than God, but bread is better than nothing, therefore bread is better than God.

This is equivocation on the word "nothing". "Nothing is better than God" uses "nothing" as a denial that a hypothetical thing exists: it can be rephrased, "there exists no thing which is better than God." "Bread is better than nothing" uses "nothing" to denote the absence of all things.

The problem is clearer when described with sets. "Nothing is better than God" means, "the set of things better than God is empty", not "the empty set is better than God".

phillip1882 wrote:
does the set that contains everything contain the set that contains everything?

Yes, so long as you include abstract concepts like "sets" in your formulation of "everything". The set of all sets also contains itself. Some sets contain themselves, and some don't. You can therefore have the set of all sets that don't contain themselves. Does that set contain itself?

(That's Russell's paradox.)
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PostPosted: Mon Sep 14, 2009 5:58 pm    Post subject: Reply with quote

basically the cup question asks the following:
you have two choices, you can either get 1,000 guaranteed by taking both cups and have a low probability of getting an additional 1,000,000, or you can have a high probability of getting 1,000,000 by acting in an irrational manner, and only taking cup B.

here's another fun paradox:
there are two boxes. one box has 3 times the amount of the other. you open the box and see that there is 9 dollars. is it in your benefit to switch? I'd say yes, as the other box contains either 27 or 3 dollars, and since you gain more than you lose, it's to your benefit. now imagine i didn't open the box. that is, the two boxes are closed, I pick a box, would it still be in my benefit to switch?
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TFBW
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Location: Sydney, Australia

PostPosted: Tue Sep 15, 2009 1:44 am    Post subject: Reply with quote

Anonymous wrote:
you have two choices, you can either get 1,000 guaranteed by taking both cups and have a low probability of getting an additional 1,000,000, or you can have a high probability of getting 1,000,000 by acting in an irrational manner, and only taking cup B.

In what sense is the behaviour irrational if it corresponds with the best expected outcome?
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phillip1882
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Joined: 14 Sep 2009
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PostPosted: Thu Sep 17, 2009 8:03 am    Post subject: Reply with quote

well the key is you would have to act in an irrational manner. note that the person who desides what to put in cup B (either nothing or 1,000,000) does so based on your actions. a very logical person wouldn't have much choice other than to take the 1,000, as he knows that by only taking cup B would be "irrational" in the sence that he has a low probability of getting 1,000,000. where as an irrational person would almost guaranteed to get 1,000,000 by picking only cup B, and may even get the 1,000 as well if he picks both.
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Bezman
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PostPosted: Thu Sep 17, 2009 5:43 pm    Post subject: Reply with quote

Unless I am misreading something, the way the original statement was put, it does not matter how many cups a person picks up, as long as the studier has predicted "B only", there WILL be 1,000,000 under B, and the picker will get both cups' values.
I does not say anything that the predictions must be right.

So, the logical thing to do would be to pick up both (or just B) and hope by the All-Father (or whatever you believe in Smile ) that he has indeed predicted "B only". Worst case, you miss out on 1000 by only picking B, but that sum would hardly change your life anyway...
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Caldazar
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PostPosted: Sat Sep 19, 2009 1:01 pm    Post subject: Reply with quote

yah your choice is actually irrelevant since the value of the cups are based on observations of your previous actions. Sad thing is that everyone who comes to this conclusion most certainly won't get more than the 1000 dollars.
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Masterweaver
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Joined: 22 Feb 2010
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PostPosted: Thu Feb 25, 2010 7:06 pm    Post subject: Reply with quote

The Myst Paradox

Billy writes a book about swords and dragons and stuff. Billy is transported to a world about swords and dragons and stuff. The world is identical to the one he made up. Did Billy write the world?

The Ghen model: Yes. Yes he did. He is God in this world. Pay him tribute.

The Atrus model: No, it was just coincidence. The guy's just a guy.

The Criad model: Well actually it's a little more complicated then that, because you see there were these guys from a third world who read Billy's book and made sure there was a world that matched the events by manipulating that world in order to provide a decent multi-world travel network...

The Warp Beast model: It's all meaningless. Billy's arrival punctured a hole in reality and now Cthulu and crew are running around.

The Insanity model: Cupcakes are glorious fizzbin players when they burn lettuce.
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YawningMan
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Location: Texas, USA

PostPosted: Wed Sep 01, 2010 12:34 am    Post subject: Reply with quote

Good heavens. The human mind and the English language. Two things that just don't go together.

Who's (whose?) got the time?

Forget it. The grammar is probably wrong, anyway. At least my grammar liked to bake pies.
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Caldazar
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PostPosted: Sat Sep 25, 2010 2:18 pm    Post subject: Reply with quote

oh and again on the cups if you have a gamblers mind you could say that by taking only cup B you're betting 1 000 for a chance on 1 000 000 that is you get a 1:1000 pay off on your bet. So with that in mind Taking cup B would be the logical choice assuming you believe the odds to be reasonable (even a 1:10 odds would make it worth the bet). And if you do have a gambling mind odds are that the person will predict that you only pick cup B so you're homefree. But once again your choice on this occasion doesn't matter as much as your previous choices...since the value in cup B is dependant on your previous actions.
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kyn
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Joined: 28 Mar 2011
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PostPosted: Mon Mar 28, 2011 1:55 pm    Post subject: Reply with quote

Why would the choice be reasonable though?
If I was the one offering the choice to someone. Why would I ever think the person would pick cup b. If I always said he would pick both then I would save 1mill. Therefor, I would always say you are going to pick both. Even if I'm wrong I'll lose no money. If I'm right I'll have saved 999,000.

If we reverse the reasoning then I would always pick both as well as I wouldn't want the guy to cheat me and it is free money.
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