-Hilbert’s paradox of the Grand Hotel

-Birthday paradox

DanielMoore1991 - 25 July 2012 09:10 PM

-Hilbert’s paradox of the Grand Hotel

-Birthday paradox

I think they were solved in the Xenosaga trilogy.

what

DanielMoore1991 - 25 July 2012 09:10 PM

-Hilbert’s paradox of the Grand Hotel

-Birthday paradox

The hotel is no paradox at all, it just illustrates the properties of infinite sequences.  Don’t know what the birthday paradox is.

I don’t know what the paradox is. The birthday problem that I’m aware of involving probability that two or more people share one isn’t a paradox. But rather an illustration of probability.

My answers:

-How long is a piece of string?

-23

Do they really need solving? What are your thoughts on these matters Daniel?

How about the Monty Hall paradox? Perhaps more of a mathematical/probability problem than a paradox, but I still have a hard time getting my head wrapped around it.

In short: you have three doors to choose from. One has a prize, the other two do not. You choose one door, which is opened to reveal nothing. Should you stick with your original choice or switch? Intuition would say that you now have a 50/50 chance to have the right door, so most people just stick with their initial choice. In fact, you have a much higher probability of getting the prize if you switch. It’s weird.

The Monte Hall thing still bewilders me too, for mathematics is my weakest of arenas, sadly to say. This just seems illogical to me.

Not a paradox as such either. Simply the dissonance of uninformed intution colliding with demonstrable proability.

It’s fairly straightforward really. Any single door has an initial one-third chance of concealing the prize. Any two doors, therefore, have a two thirds chance. When Monty, who isn’t subject to probability since he knows where the prize is, eliminates a door he is essentially giving you the option of opening two doors rather than one. Which clearly, I think, offers twice the chance of being correct.

The birthday paradox isn’t a paradox, it’s simple a fuction of probability. It’s essentially the follwing problem.

Give everyone a 365-sided die. Given that are X number of people, what’s the probability that 2 of them will roll the same number. The counter-intuitive “problem” is that while 100% probability is reached at X = 366, 99% probability is reached at X = 57 and 50% probability is reached at X = 23.

The only paradox here is that more people don’t understand probability theory.

The Monte Hall problem is easier to understand visually. I’m attaching a picture from wikipedia. The top numbers represent your probabilities before the door is opened and the bottom is after the door is opened. EDIT: Brick beat me to it. The pic is the visual for his explanation.

I just woke up but ... hold on

Brick Bungalow - 26 July 2012 09:46 AM

Not a paradox as such either. Simply the dissonance of uninformed intution colliding with demonstrable proability.

It’s fairly straightforward really. Any single door has an initial one-third chance of concealing the prize. Any two doors, therefore, have a two thirds chance. When Monty, who isn’t subject to probability since he knows where the prize is, eliminates a door he is essentially giving you the option of opening two doors rather than one. Which clearly, I think, offers twice the chance of being correct.

The problem has another dimension to it that whoever originally formulated it didn’t seem to have in mind.  Recall that Monty Hall didn’t always give the option to the contestant to change doors—sonetimes he just revealed what they had selected and that was that.  The analysis that suggests that it is to your benefit to change doors assumes that Mony’s decision to offer the door exchange option is an unbiased one.  If Monty were to bias his decision by say giving the option to change doors 2 out of 3 times when the contestant has picked the fabulous prize and only 1 out of 3 times when a goat was selected then the benefit of changing ones selection is eliminated.  More bias than this would result in a benefit to not chnaging one’s selection.

burt - 25 July 2012 10:27 PM

DanielMoore1991 - 25 July 2012 09:10 PM

-Hilbert’s paradox of the Grand Hotel

-Birthday paradox

The hotel is no paradox at all, it just illustrates the properties of infinite sequences.

Are the properties logical given the definition of infinity? Is the presentation of the abstract so lost in the scenario that it cannot be applied to the reality of logic?

Brick Bungalow - 25 July 2012 11:33 PM

I don’t know what the paradox is. The birthday problem that I’m aware of involving probability that two or more people share one isn’t a paradox. But rather an illustration of probability.

Then my question is has someone created an understanding of why those percentages of probability follow the given statistics ? Has anyone given a reason as to the nature of scenario or the reasoning on why those given numbers are presented in the given manner ?

DanielMoore1991 - 26 July 2012 06:40 PM

Brick Bungalow - 25 July 2012 11:33 PM

I don’t know what the paradox is. The birthday problem that I’m aware of involving probability that two or more people share one isn’t a paradox. But rather an illustration of probability.

Then my question is has someone created an understanding of why those percentages of probability follow the given statistics ? Has anyone given a reason as to the nature of scenario or the reasoning on why those given numbers are presented in the given manner ?

Or in other words has anyone presented logic as to why the given birthday trend is so?

3 doors, one with a prize. One door chosen but not revealed. One door revealed with no prize and it is not the one previously chosen, thus it is removed from contention.That leaves two doors remaining including the one first chosen. Why is it advantageous to switch from the door initially chosen to the other door not chosen?

Neither door has been revealed, yet one of the two has a prize. The one other door has been removed from contention.

Why is this a 66/33 proposition by changing door choice, and not a 50/50 proposition by not changing door choice?

How is mathematics and probability theory more logical here?

The end result is two doors, one choice. Does not the probability change with previously ruled out contentions?

Mind fuck for me….and weird.

Damn I wish I could think like Brick!!!