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Author Topic:   Counter-Intuitive Science
Dr Jack
Member (Idle past 209 days)
Posts: 3507
From: Leicester, England
Joined: 07-14-2003


(1)
Message 121 of 182 (600615)
01-15-2011 4:16 PM
Reply to: Message 106 by Dr Adequate
01-14-2011 2:46 PM


Yeah, but asking badly phrased trick questions and then pretending like everyone didn't grasp the science is still bullshit.
This message is a reply to:
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Adminnemooseus
Director
Posts: 3879
Joined: 09-26-2002


Message 122 of 182 (600624)
01-15-2011 5:58 PM
Reply to: Message 114 by RAZD
01-14-2011 10:34 PM


Monty Hall topics
RAZD writes:

Yes, I remember it, because I was among those who were wrong at the beginning.

Simply put, the contestant will be wrong 2/3rds of the time, and the host will obligingly eliminate the other wrong choice.

The Monty Hall shows up in quite a few topics. The main one seems to be Statistics 101, with there also being the short (13 messages) A Deep Thought, Monty Hall, and Trisecting Angles.

RAZD does not take part in either of those topics.

The forum search process didn't find anything. I did an advanced Google search for "monty hall", specific to evcforum.net. To do such, enter >"monty hall" site:evcforum.net < into the Google search box (without the ><).

Please, no replies to this message.

Adminnemooseus


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xongsmith
Member
Posts: 1873
From: massachusetts US
Joined: 01-01-2009


Message 123 of 182 (600654)
01-16-2011 12:53 AM
Reply to: Message 120 by Panda
01-15-2011 3:54 PM


Re: Dr. A's doors
Ah - thanks, Panda!

Again I did not read the exact words in front of my eyes. I glossed over that & thought all the jumping in the world wasn't opening that door. (He even put it in a little parenthesized clause which should have drawn my attention.)


- xongsmith, 5.7d
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slevesque
Member (Idle past 2745 days)
Posts: 1456
Joined: 05-14-2009


Message 124 of 182 (600661)
01-16-2011 3:18 AM
Reply to: Message 109 by Dr Adequate
01-14-2011 6:55 PM


Re: Counter-Intuitive Math
Quite funny you mention this since I stumbled upon the it's wiki page this week (apparently it's a well known phenomenon in statistics)
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Replies to this message:
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slevesque
Member (Idle past 2745 days)
Posts: 1456
Joined: 05-14-2009


Message 125 of 182 (600663)
01-16-2011 3:22 AM
Reply to: Message 113 by Panda
01-14-2011 10:14 PM


Re: Counter-Intuitive Math
But the Mounty Hall problem gets even harder to explain when you get into the the fact that if the presentator knows where the car is or not has a direct impact on your chances of winning.

Because imagine two almost identical scenario where you have a choice between door A,B,C. You choose A, the presentator opens door C and chose a goat in both scenarios.

Now, if in the first scenario he knows where the prize is, then you should change your choice when asked to. While in the second (seemingly identical) scenario he does not know where the prize is, then it doesn't matter if you change or not, you'll have the same odds of winning.


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Seizmik
Junior Member (Idle past 2914 days)
Posts: 2
From: Edinburgh, UK
Joined: 01-10-2011


Message 126 of 182 (600666)
01-16-2011 6:25 AM


Counter-Intuitive Physics
Sorry for c-c-c-combo breaking right here, but I have to interject with another statement.

Does anybody find the idea that the universe need not be governed by it's 'own' laws difficult to comprehend? An example I was thinking of was told to me by Dr. L Kormos of Lancaster University; saying that the general understanding among current-day phyicsits was that the universe was expanding at superluminal speeds. Imagine something is 'pulling' the universe in order for it to expand, then these pullers would not be inside the universe, hence not limited to the speed of light.


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NoNukes
Inactive Member


Message 127 of 182 (600669)
01-16-2011 7:20 AM
Reply to: Message 126 by Seizmik
01-16-2011 6:25 AM


Re: Counter-Intuitive Physics
Seizmik writes:

Imagine something is 'pulling' the universe in order for it to expand, then these pullers would not be inside the universe, hence not limited to the speed of light.

Why couldn't these imagined pullers be moving at subluminal speeds?

Also, as has been discussed already, the universe's expansion does not involve mass and energy moving at superluminal speeds. That shouldn't be counter intuitive to most people that have "intuited" on the subject to some depth.


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NoNukes
Inactive Member


Message 128 of 182 (600670)
01-16-2011 7:26 AM
Reply to: Message 107 by onifre
01-14-2011 3:47 PM


Isn't it directly proportional to the mass of the object under the effects of only gravity?

Nope The force is directly proportional to the inertial mass which results in the accelerations of dissimilarly masses objects due to gravity being the same.


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NoNukes
Inactive Member


Message 129 of 182 (600671)
01-16-2011 7:33 AM
Reply to: Message 109 by Dr Adequate
01-14-2011 6:55 PM


Re: Counter-Intuitive Math
Perhaps the students were simply contemplating the wrong bad law suit to file. Maybe subject A is mathematics while subject B is nursing.
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cavediver
Member (Idle past 1748 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 130 of 182 (600672)
01-16-2011 8:06 AM
Reply to: Message 124 by slevesque
01-16-2011 3:18 AM


Re: Counter-Intuitive Math
Quite funny you mention this since I stumbled upon the it's wiki page this week (apparently it's a well known phenomenon in statistics)

It is an extremely important effect in sampling bias and has resulted in some very dubious statistical results as you can probably imagine by extrapolating on Dr A's example.

Which was the Wiki page?


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Panda
Member (Idle past 1817 days)
Posts: 2688
From: UK
Joined: 10-04-2010


Message 131 of 182 (600676)
01-16-2011 9:05 AM
Reply to: Message 125 by slevesque
01-16-2011 3:22 AM


Re: Counter-Intuitive Math
slevesque writes:

Now, if in the first scenario he knows where the prize is, then you should change your choice when asked to. While in the second (seemingly identical) scenario he does not know where the prize is, then it doesn't matter if you change or not, you'll have the same odds of winning.


I am not sure I agree with this (I've not given it too much thought), but I think I have accidentally swamped Dr. A's thread with messages about Monty Hall.

If it's ok with you, I'd rather leave this as an unfinished discussion than continue to usurp this interesting thread.


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cavediver
Member (Idle past 1748 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 132 of 182 (600677)
01-16-2011 9:31 AM
Reply to: Message 125 by slevesque
01-16-2011 3:22 AM


Re: Counter-Intuitive Math
While in the second (seemingly identical) scenario he does not know where the prize is, then it doesn't matter if you change or not, you'll have the same odds of winning.

This is ill-defined - what happens when the presenter picks the car? Does the contestant win? Is the game replayed? Is the contestant unaware of what the presenter randomly picks (trivial case)?


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Replies to this message:
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slevesque
Member (Idle past 2745 days)
Posts: 1456
Joined: 05-14-2009


Message 133 of 182 (600695)
01-16-2011 3:22 PM
Reply to: Message 130 by cavediver
01-16-2011 8:06 AM


Re: Counter-Intuitive Math
After some deep memory thinking, I found it:

http://en.wikipedia.org/wiki/Simpson%27s_paradox

The school Dr.A was talking about seems to be Berkeley (see second example on the page)


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slevesque
Member (Idle past 2745 days)
Posts: 1456
Joined: 05-14-2009


Message 134 of 182 (600697)
01-16-2011 3:46 PM
Reply to: Message 132 by cavediver
01-16-2011 9:31 AM


Re: Counter-Intuitive Math
If the presentator, not knowing where the car is, opens the door with the car. The probability your door has the car immediatly goes down to zero. But if, again not knowing, he opens the goat, then your door's probability does go up to 1/2.

Now as I said, as much as some find the original version of the Mounty Hall problem counter-intuitive, those who will understand it will find this next situation equally hard to understand. (And inversely, those who think the initial case gives you a 50/50 chnce won't have any problem coming to the, correct this time, conclusion that it is 50/50 in the seond case)

Marilyn Vos Savante explained this in here 06 column of ''Ask Marilyn ?'' (She was the one who made the Mounty hall problem 'famous' to the public when writing about it in here column in 1990)


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Replies to this message:
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cavediver
Member (Idle past 1748 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 135 of 182 (600700)
01-16-2011 4:05 PM
Reply to: Message 134 by slevesque
01-16-2011 3:46 PM


Re: Counter-Intuitive Math
If the presentator, not knowing where the car is, opens the door with the car. The probability your door has the car immediatly goes down to zero. But if, again not knowing, he opens the goat, then your door's probability does go up to 1/2.

I agree. But you still haven't given guidance on how these two results are to be combined.

those who think the initial case gives you a 50/50 chnce won't have any problem coming to the, correct this time, conclusion that it is 50/50 in the seond case

And this is not correct, unless you fully define the situation. How are you dealing with the case where the unknowing presenter opens the door to the car, and how does it affect your answer? You cannot just ignore it.

Why am I so reminded of our exchanges where I claim not to understand what you mean, and you reply that I'm just being argumentative


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