Law School Discussion

Chicago Countdown Thread

stjobs

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Re: Chicago Countdown Thread
« Reply #10 on: January 13, 2007, 10:08:10 PM »
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That is so weird.

Why? Most people can't intuit whether it's actually 8 PM or 7:58 PM without consulting a clock, which may be off to start with.

EEtoJD

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Re: Chicago Countdown Thread
« Reply #11 on: January 13, 2007, 10:11:31 PM »

Darn you stole my answer, I was going to answer and sound all smart.  BUT, if however, it's an iterated PD, then the best course of action would probably be to cooperate. So there.

There's no iteration in real life. Only dumb people who can't get it right the first time. ;)

EDIT: Data Structures was one of my favorite courses. I like writing different quicksorts and binary search trees. A BST was one of the only things I ever wrote that compiled and ran correctly the very first time.

Oh, I don't know, we have history, don't we?  :D

Indeed. The iterated PD actually raises another paradox. If both people act rationally, neither can cooperate in the hope of getting the other to cooperate because backward induction shows that they will rat each other out every time. When the final iteration occurs, there's no "tit-for-tat" pattern, so the most selfish choice will be made. But then, the same choice has to happen before that, and before that, and so on back to the first choice.

However, for the backward induction to begin, both people have to realize they've made the final choice when they get to it. In CS, this is obvious. For real people, not so much. Plus, like I said before, we're never really confident that other people will act rationally, so the first choice wouldn't be one of cooperation.

mL4300ic

Re: Chicago Countdown Thread
« Reply #12 on: January 13, 2007, 10:12:19 PM »
EDIT: Data Structures was one of my favorite courses. I like writing different quicksorts and binary search trees. A BST was one of the only things I ever wrote that compiled and ran correctly the very first time.

DS is cool. Algorithms/Algorithmics is not so cool. And a lot harder. And painful. Ugh.

Re: Chicago Countdown Thread
« Reply #13 on: January 13, 2007, 10:12:32 PM »
Ah the prisoners dilemma.

Brito

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Re: Chicago Countdown Thread
« Reply #14 on: January 13, 2007, 10:13:14 PM »

Darn you stole my answer, I was going to answer and sound all smart.  BUT, if however, it's an iterated PD, then the best course of action would probably be to cooperate. So there.

There's no iteration in real life. Only dumb people who can't get it right the first time. ;)

EDIT: Data Structures was one of my favorite courses. I like writing different quicksorts and binary search trees. A BST was one of the only things I ever wrote that compiled and ran correctly the very first time.

Oh, I don't know, we have history, don't we?  :D

Indeed. The iterated PD actually raises another paradox. If both people act rationally, neither can cooperate in the hope of getting the other to cooperate because backward induction shows that they will rat each other out every time. When the final iteration occurs, there's no "tit-for-tat" pattern, so the most selfish choice will be made. But then, the same choice has to happen before that, and before that, and so on back to the first choice.

However, for the backward induction to begin, both people have to realize they've made the final choice when they get to it. In CS, this is obvious. For real people, not so much. Plus, like I said before, we're never really confident that other people will act rationally, so the first choice wouldn't be one of cooperation.

See, this thread is cool, because if the Chicago adcomm members see it, they will realize how awesome we are and admit us all.  Please.

EEtoJD

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Re: Chicago Countdown Thread
« Reply #15 on: January 13, 2007, 10:14:18 PM »
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That is so weird.

Why? Most people can't intuit whether it's actually 8 PM or 7:58 PM without consulting a clock, which may be off to start with.

Because that person purposely set the watch that they are looking at to be fast. For someone to forget a conscious decision like that, something must happen in the person's mind. Either the mind knows that the person wants to forget, the people somehow force themselves to forget (maybe by letting a good amount to pass between the time they set the watch and the time they next use it, although this never seems to be the case in real life), or... something else.

Brito

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Re: Chicago Countdown Thread
« Reply #16 on: January 13, 2007, 10:14:50 PM »
Quote
That is so weird.

Why? Most people can't intuit whether it's actually 8 PM or 7:58 PM without consulting a clock, which may be off to start with.

Because that person purposely set the watch that they are looking at to be fast. For someone to forget a conscious decision like that, something must happen in the person's mind. Either the mind knows that the person wants to forget, the people somehow force themselves to forget (maybe by letting a good amount to pass between the time they set the watch and the time they next use it, although this never seems to be the case in real life), or... something else.

My problem is that I know the watch is fast, so I subtract time, usually more time than has actually been added.

stjobs

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Re: Chicago Countdown Thread
« Reply #17 on: January 13, 2007, 10:17:05 PM »
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For someone to forget a conscious decision like that, something must happen in the person's mind.

'Happen' may be one way to describe it... I have many other things on my mind, so I really do forget that I set the watch ahead after 12 hours...

Brito

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Re: Chicago Countdown Thread
« Reply #18 on: January 13, 2007, 10:26:24 PM »

I like this thread very much, kudos Brito!

Thank you!

I set it up so that hijacking would, paradoxically, keep it on topic.  It's what we need right now in this difficult time.   :D

EEtoJD

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Re: Chicago Countdown Thread
« Reply #19 on: January 13, 2007, 10:28:14 PM »

See, this thread is cool, because if the Chicago adcomms see it, they will realize how awesome we are and admit us all.  Please.

I have two books just about paradoxes. My favorite paradox of all time is called "The Heap". It goes like this (taken from Paradoxes from A to Z by Michael Clark):

A pile of 10,000 grains is a heap.
For any number n>1, if a pile of n grains is a heap, then so is a pile of n - 1 grains.
So one grain is a heap.

This form of argument (p->q; p; therefore, q) is known as modus ponens. It works fine with pure logic, but not with how we define a heap. The paradox lies in the definition of words. A "heap" is not a sharply defined word, so we don't have a specific point that we'd call the pile of grains a heap, or stop calling it a heap.

My favorite resolution of this argument comes about by using "degrees of truth". Let's say that we're at the borderline of a heap when we reach 70 grains, and consider the following:

If 71 grains makes a heap, then so do 70.

The "if" part of the statement (71 grains) is more true than the "then" part (70 grains). So, if one part of the if-then statement is more true than the other, then it's reasonable to say that the statement isn't strictly true. It may be only by a small degree, but if we keep making these inferences down the chain, the small errors propagate and make it impossible to say that only one grain is a heap.

There are other approaches (fuzzy logic, supervaluations), but they're not as interesting, I think.