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Author Topic:   Counter-Intuitive Science
Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 106 of 182 (600459)
01-14-2011 2:46 PM
Reply to: Message 103 by Iblis
01-14-2011 1:16 PM


This one tells us more about morbid psychology than it does about physics.
Asking you questions that you can't answer is not, I think, listed in the latest edition of the DSM; but if you write to them and ask nicely perhaps they'll put it in the next one.

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onifre
Member (Idle past 2950 days)
Posts: 4854
From: Dark Side of the Moon
Joined: 02-20-2008


Message 107 of 182 (600474)
01-14-2011 3:47 PM
Reply to: Message 105 by DrJones*
01-14-2011 2:28 PM


Air resistance is dependant on the shape of the object not the mass.
True that; I should have been specific.
acceleration due to gravity is not related to the masses of the objects.
Isn't it directly proportional to the mass of the object under the effects of only gravity?
And when you include inertia it would be, because the gravitational and inertial masses are equal for all objects thus irrelevant.
Is that right?
- Oni
Edited by onifre, : No reason given.

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slevesque
Member (Idle past 4640 days)
Posts: 1456
Joined: 05-14-2009


Message 108 of 182 (600481)
01-14-2011 4:59 PM
Reply to: Message 105 by DrJones*
01-14-2011 2:28 PM


Air resistance is dependant on the shape of the object not the mass. So a properly configured heavy object could fall slower than a lighter one.
But you're right about it needing to be a vaccum (or two identically shaped objects) to show that acceleration due to gravity is not related to the masses of the objects.
Two identically shaped objects will have the same air resistance, but won't fall at the same speed if they don't have the same mass ...
This is why when skiing, a bigger person will still go faster even though he has more air resistance.
Edited by slevesque, : No reason given.

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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 109 of 182 (600493)
01-14-2011 6:55 PM
Reply to: Message 108 by slevesque
01-14-2011 4:59 PM


Counter-Intuitive Math
I could tell you many strange stories of counter-intuitive math (my favorite of all my own theorems is the one that makes everyone cry: "That can't be true") but this one has the merit of being comprehensible to everyone who can do division.
The story goes (it doesn't matter if it's true) that at a certain university it was noted that in every single subject a higher proportion of the male applicants were admitted than the proportion of female applicants who were admitted.
Everyone was all set for a big lawsuit when some smart alec observed that for the university as a whole a higher proportion of female applicants were admitted than male applicants.
This sounds impossible.
---
Now watch this.
Suppose there are only two subjects taught, subject A and subject B.
10 male students apply to study subject A, and 5 get in.
10 female students apply to study subject A, and 4 get in.
10 male students apply to study subject B, and 10 get in.
20 female students apply to study subject B, and 19 get in.
23/30 > 15/20.
So much for the Fallacy Of Composition.

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Replies to this message:
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 Message 129 by NoNukes, posted 01-16-2011 7:33 AM Dr Adequate has not replied

  
sfs
Member (Idle past 2533 days)
Posts: 464
From: Cambridge, MA USA
Joined: 08-27-2003


Message 110 of 182 (600494)
01-14-2011 7:05 PM
Reply to: Message 100 by Dr Adequate
01-14-2011 11:09 AM


quote:
But if the force with which I came down was sufficient to open the door, then so would be the equal force with which I went up, and the door would (as in fact it did) open when I left the ground, not when I struck it.
Equal impulse, not equal force (or at least there's no reason to expect the forces to be equal).
quote:
This all goes to show, I think, that the simplest aspects of physics can elude the intuition of the cleverest people.
Uh huh.

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Panda
Member (Idle past 3712 days)
Posts: 2688
From: UK
Joined: 10-04-2010


Message 111 of 182 (600510)
01-14-2011 9:32 PM
Reply to: Message 109 by Dr Adequate
01-14-2011 6:55 PM


Re: Counter-Intuitive Math
The Monty Hall Problem seems to cause people a lot of grief.
quote:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Luckily, when I first heard of it, it was from a very clever friend who successfully explained it to me in 30 seconds.
I did once see a forum thread that dragged on for over a year with people constantly arguing back and forth about what the correct answer was.

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Replies to this message:
 Message 112 by Dr Adequate, posted 01-14-2011 9:46 PM Panda has replied

  
Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 112 of 182 (600512)
01-14-2011 9:46 PM
Reply to: Message 111 by Panda
01-14-2011 9:32 PM


Re: Counter-Intuitive Math
The most intuitive explanation I can think of is this.
Suppose there were a thousand doors, you pick one, and then the host opens 998 out of the 999 that you didn't pick.
Is there really a 1 in 1000 chance that the door he didn't open is the one with the car behind it?

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 Message 111 by Panda, posted 01-14-2011 9:32 PM Panda has replied

Replies to this message:
 Message 113 by Panda, posted 01-14-2011 10:14 PM Dr Adequate has not replied

  
Panda
Member (Idle past 3712 days)
Posts: 2688
From: UK
Joined: 10-04-2010


Message 113 of 182 (600517)
01-14-2011 10:14 PM
Reply to: Message 112 by Dr Adequate
01-14-2011 9:46 PM


Re: Counter-Intuitive Math
Dr A writes:
The most intuitive explanation I can think of is this.
In the thread (mentioned previously) they went to far more effort than that (after trying your explanation and getting nowhere).
They posted code (in various languages) so that people could see the actual results.
They had graphs and Venn diagrams and...well, everything you could think of and more.
But it is so counter-intuitive that some people never understand.
It is annoying that I can't find that thread again.
It was epic and epic fail simultaneously.
Edited by Panda, : No reason given.

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RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 114 of 182 (600521)
01-14-2011 10:34 PM
Reply to: Message 113 by Panda
01-14-2011 10:14 PM


Re: Counter-Intuitive Math
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.
Enjoy.

we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
... to learn ... to think ... to live ... to laugh ...
to share.


Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click)

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Replies to this message:
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Panda
Member (Idle past 3712 days)
Posts: 2688
From: UK
Joined: 10-04-2010


Message 115 of 182 (600522)
01-14-2011 10:43 PM
Reply to: Message 114 by RAZD
01-14-2011 10:34 PM


Re: Counter-Intuitive Math
RADZ writes:
Simply put, the contestant will be wrong 2/3rds of the time, and the host will obligingly eliminate the other wrong choice.
Succinctly put? Maybe.
Simply put? Not so much.
My favourite comment is:
If you switch, you halve your chance of winning a goat! *sadface*
Edited by Panda, : No reason given.

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RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 116 of 182 (600523)
01-14-2011 10:53 PM
Reply to: Message 115 by Panda
01-14-2011 10:43 PM


Re: Counter-Intuitive Math
add this picture then (worth a thousand goats)
Enjoy

we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
... to learn ... to think ... to live ... to laugh ...
to share.


Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click)

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xongsmith
Member
Posts: 2578
From: massachusetts US
Joined: 01-01-2009
Member Rating: 6.8


Message 117 of 182 (600607)
01-15-2011 3:01 PM
Reply to: Message 86 by jar
01-13-2011 5:44 PM


Re: Dr. A's doors
jar admonishes:
Doubt it, that was tried back in Message 67.
...but Dr. A did not reply saying "...wrong, not the answer."
He might have missed it.
That was my first thought as well.
Here's my second thought:
Just as the people in front of Dr. A were walking through the entrance door, the store manager, having given his warning to the shoppers inside that it was time to close, noted that it was in fact now time to close and hit the switch that locked the entrance doors just fractions of a second before Dr. A stepped on them.

- xongsmith, 5.7d

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ringo
Member (Idle past 411 days)
Posts: 20940
From: frozen wasteland
Joined: 03-23-2005


Message 118 of 182 (600610)
01-15-2011 3:17 PM
Reply to: Message 117 by xongsmith
01-15-2011 3:01 PM


Re: Dr. A's doors
xongsmith writes:
Just as the people in front of Dr. A were walking through the entrance door, the store manager, having given his warning to the shoppers inside that it was time to close, noted that it was in fact now time to close and hit the switch that locked the entrance doors just fractions of a second before Dr. A stepped on them.
In my experience, the doors are turned off by a switch at the top of the door by a manager who is standing right there and who then locks the doors manually. It seems unlikely that they would be closed in somebody's face with no explanation.

"I'm Rory Bellows, I tell you! And I got a lot of corroborating evidence... over here... by the throttle!"

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xongsmith
Member
Posts: 2578
From: massachusetts US
Joined: 01-01-2009
Member Rating: 6.8


Message 119 of 182 (600612)
01-15-2011 3:27 PM
Reply to: Message 118 by ringo
01-15-2011 3:17 PM


Re: Dr. A's doors
It would be helpful if Dr. A could wag his finger at jar & myself, saying something like "Nice try, but Wrong."
Another possibility that would get a round of boos is that the door-opening mechanism broke just after the people in front got in.
"Boo" if that's case, although, if this was a real-life event, then it's okay. But I do see it as a riddle. Perhaps that assumption is False.

- xongsmith, 5.7d

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Panda
Member (Idle past 3712 days)
Posts: 2688
From: UK
Joined: 10-04-2010


Message 120 of 182 (600613)
01-15-2011 3:54 PM
Reply to: Message 119 by xongsmith
01-15-2011 3:27 PM


Re: Dr. A's doors
xongsmith writes:
It would be helpful if Dr. A could wag his finger at jar & myself, saying something like "Nice try, but Wrong."
The answer is here: Message 69.

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