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bill
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Joined: 22 Apr 2006
Posts: 1204
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 Posted: Tue Dec 29, 2009 11:17 pm Post subject: |
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I have proven it correct true and valid to those who are necessary and sufficient to have you proven to be a heretic. nOW ican have you arrested beaten tortured as i see fit and there is nota fng thing you can do about it how do you like them apples asshole
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JeffJo
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Joined: 10 Mar 2009
Posts: 1015
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| Posted: Wed Dec 30, 2009 8:42 am Post subject: |
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| bill wrote: | | I have proven it correct true and valid to those who are necessary and sufficient to have you proven to be a heretic. nOW ican have you arrested beaten tortured as i see fit and there is nota fng thing you can do about it how do you like them apples asshole |
Well, I guess I don't have to add anything to that to prove all of my points.
But bill, if your proof really were correct, you could easily show I'm wrong. Why haven't you even tried? Instead of invective and profanity, just:- Instead of saying "we obtain following the same procedure" when you present the equation "a^3 + 3ab^2 = ( d^3 + f^3 )/2 = c^3," show what the procedure is for the new case. Lay out the steps in a fashion you would use for a class of beginning algebra students. That shouldn't be hard, for someone who teaches graduate courses in such diverse subjects as math, physics, medicine, and religious studies.
- Explain how deriving "d^2 + f^2 = 2c^2" from the hypothesis "a^2+b^2=c^2" proves anything about the existence of integers a, b, and c, that satisfy your hypothesis.
- Explain how b^3 canceling out in the first equation I listed (assuming you can show it is correct) "proves" that there are no other integers, unrelated to your d and f, that might satisfy n^3+m^3=c^3
These are just a few of the points where I claim you are wrong, and where you seem to think my disagreement is a crime punisahble by torture in an enlightened society.
Along the way, you just might discover that you can't, and that what I've been saying is correct. As always. |
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emilynghiem
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Joined: 21 Aug 2007
Posts: 542
Location: Houston
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| Posted: Mon Feb 22, 2010 5:12 pm Post subject: |
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| bill wrote: | | I have proven it correct true and valid to those who are necessary and sufficient to have you proven to be a heretic. nOW ican have you arrested beaten tortured as i see fit and there is nota fng thing you can do about it how do you like them apples asshole |
Dear Bill: I just saw your msg which looks like you are feeling and expressing the same outrage and indignance that caused Nirmaldasan/Watson Solomon to give up, storm out and leave.
Unlike him, I do think you are mathematically minded enough to see BOTH the 2/3 answer AND the 1/2 answer. Nirmaldasan could only see the 1/2 answer and came close a time or two to entertaining the idea there was a way to have both, but got caught up in personal politics.
I hope you can overcome this and see what Nirmaldasan missed.
A. If you "pick randomly" and treat the last two doors as interchangeable then YES you DO get 1/2 results from treating the doors this way.
B. If you "keep track" of which was the first door and which was the last, then you WILL get uneven chances of 2/3 and 1/3 instead of 50/50.
C. And last, what JeffJo and other formal mathematicians were scolding if not yelling at Nirmaldasan and at me for trying to give him a break:
EVEN THOUGH you WOULD get 1/2 results by treating the two doors as 50/50, the PROBABILITY is NOT 50/50. The probability is still 2/3 and 1/3, but the way you chose you only got 1/2 instead of the higher chances.
So I hope you can see this since you have the mathematical acumen.
Nirmaldasan even limited the game to just one shot, so that when he won he attributed it to 1/2 even though it was technically 2/3 1/3 which didn't show either. You cannot tell just from one trial.
I hope you are still around and have not given up.
Technically the 2/3 answer is correct; but yes, you do get 1/2 results instead if you treat the two doors as equal and randomly pick from them.
You could have two unequal tickets, one with 99% chance of winning
and the other with 1% chance, pick randomly between the two,
and still come out 50/50 but that doesn't mean the chances are 50/50.
I hope you can understand this Bill, so maybe you can help Nirmaldasan where all the rest of us failed to explain to him what he was looking past.
Yours truly,
Emily |
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JeffJo
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Joined: 10 Mar 2009
Posts: 1015
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| Posted: Mon Feb 22, 2010 5:55 pm Post subject: |
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| emilynghiem wrote: | | Dear Bill: I just saw your msg which looks like you are feeling and expressing the same outrage and indignance that caused Nirmaldasan/Watson Solomon to give up, storm out and leave. |
Emily: What Bill is outraged about has nothing to do with you, Nirmaldasan, or the Game Show problem. As "proof" of his mathematical acumen, he posted here (yes, he could easliy have started a thread, but suggesting he could do things differently is the best way to make him not take your advice) of Fermat's Last Theorem. It was superficial at best, and blatantly wrong in several places. But Bill refuses to accept that he just isn't that smart, and usually makes mistakes. He covers them up by calling them "progress."
| Quote: | | I do think you are mathematically minded enough to see BOTH the 2/3 answer AND the 1/2 answer. Nirmaldasan could only see the 1/2 answer |
"1/2" requires changing the propblem into something else, as you point out, so it is not an answer. |
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emilynghiem
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Joined: 21 Aug 2007
Posts: 542
Location: Houston
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| Posted: Tue Feb 23, 2010 1:20 pm Post subject: |
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| JeffJo wrote: | | emilynghiem wrote: | | Dear Bill: I just saw your msg which looks like you are feeling and expressing the same outrage and indignance that caused Nirmaldasan/Watson Solomon to give up, storm out and leave. |
Emily: What Bill is outraged about has nothing to do with you, Nirmaldasan, or the Game Show problem. As "proof" of his mathematical acumen, he posted here (yes, he could easliy have started a thread, but suggesting he could do things differently is the best way to make him not take your advice) of Fermat's Last Theorem. It was superficial at best, and blatantly wrong in several places. But Bill refuses to accept that he just isn't that smart, and usually makes mistakes. He covers them up by calling them "progress."
| Quote: | | I do think you are mathematically minded enough to see BOTH the 2/3 answer AND the 1/2 answer. Nirmaldasan could only see the 1/2 answer |
"1/2" requires changing the propblem into something else, as you point out, so it is not an answer. |
Hi Jeff Jo:
Did you ever resolve the 1/2 2/3 issue with Bill on the original game topic?
Where did you and he leave off on that one?
(regarding Fermat, Einstein and other accepted proofs or theories, I understand Bill continues to contest these after the fact; even if he is incorrect or unsuccessful, I still believe by applying that mindset to other things, one day he is going to hit the jackpot and "undo" some proven assumption that turns out does indeed have flaws. While it is a waste to apply his mental energy to places that are well settled, I look forward to seeing what he does debunk in the future that could be revolutionary! He seems to be an intellectual rebel shopping for a cause, sharpening his wits on anything he finds, so why not find him a real challenge to take on) |
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JeffJo
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Joined: 10 Mar 2009
Posts: 1015
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| Posted: Tue Feb 23, 2010 4:17 pm Post subject: |
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| emilynghiem wrote: | Did you ever resolve the 1/2 2/3 issue with Bill on the original game topic?
Where did you and he leave off on that one? |
Last I recall, he misquoted an article that changed the problem. They started with N doors, and had you and the host alternate (You: choose an unopened door, HOST: open an unchosen door with a goat) until you were satisfied. The best strategy led to a probability that approached 2/pi, not 2/3 (remember, more doors). Bill claimed that was the answer for the original problem as well. Then he went off on some made-up arguments about "probability in short run" vs. "long run," as if they weren't the same thing. So no, he isn't "resolved." (But on a positive note, he finally did agree that the probability is 1/2, after you meet a boy at random from a two-child family, that his sibling is also a boy. He spewed just as much venom before doing that, then gave a "mea culpa.")
| Quote: | | (regarding Fermat, Einstein and other accepted proofs or theories, I understand Bill continues to contest these after the fact; |
No, here he claimed he had proven FLT as a child, but didn't think it was important because it was so trivial. And then his mother threw the notes (all ten lines, or so, of them) away. All his "proof" was, was a collection of unrelated and usually incorrect algebra. It looked like what he could have once seen in the actual proof for specific some N cases, but didn't understand what they did there or why it was a proof.
| Quote: | | even if he is incorrect or unsuccessful, I still believe by applying that mindset to other things, one day he is going to hit the jackpot and "undo" some proven assumption that turns out does indeed have flaws. |
"Rebel without a clue" is a better description. He recognizes that his thoughts appear related to what he wants to talk about, but really has no idea what they mean, or how to assemble a proof.
| Quote: | | so why not find him a real challenge to take on |
Because he refuses to recognize when he is wrong. Anything that you can show is wrong, he dismisses as "fighting progress." |
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emilynghiem
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Joined: 21 Aug 2007
Posts: 542
Location: Houston
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| Posted: Thu Feb 25, 2010 5:03 pm Post subject: |
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Dear JeffJo:
Thanks for the update and clear summary.
If you got Bill to agree to any change at all on any problem, consider that an achievement given his distrust of any academic types who oppose him.
(As for the shortrun/longrun probability, maybe he has the same problem as Nirmaldasan, taking exception to "either" a winning or losing outcome out of 1 or 2 runs being called "2/3 chance" since there are not 3 runs.)
I am reading a book published by a local professor in psychology on "Benign Bigotry" and stereotypical perceptions projected on an "outgroup" by people within an ingroup who make distinctions with others they identify with while generalizing for those they don't relate to.
I thought science and math would break through these barriers, but with people not trusting media or the agenda of other people, it's clear those biases can obstruct perceptions and changes even in "objective" fields.
I should recommend this example with Nirmaldasan and Bill to the professor, and see if their class is willing to observe perceptional changes if people actually go through the experiments instead of assuming ulterior motives of people telling them otherwise. Would fit right in with her studies, and maybe help our two friends out, if they are willing to contribute to a study to help other students.
Very interesting, how people's perceptions get stuck because of distrust and unforgiveness of past conflicts that get projected forward on others.
Again, if you and Bill made any progress at all in correcting even one point, that's better than anyone else accomplished.
There is hope but the environment has to be right, or people think they are being set up to fail and will weedle out to save face. So if you find a way to save face and make it safe to study this phenomena, maybe that might be good enough reason to give it a try, to study why there is resistance and how can it be overcome.
Yours truly,
Emily
The author is Kristin Anderson "Benign Bigotry"
I am only in the first chapter, and plan to offer some proposed follow up studies or tests for students willing to assess their own biases and perceptions, and what it takes to overcome them either partially or fully.
Very critical in religion and politics. But if we can start with issues in math or science that CAN be proven, and then study why the perceptions were resistant to change, then that can be applied to diffusing more volatile or arbitrary situations where it's not so clear what solutions will satisfy all.
| JeffJo wrote: | | emilynghiem wrote: | Did you ever resolve the 1/2 2/3 issue with Bill on the original game topic?
Where did you and he leave off on that one? |
Last I recall, he misquoted an article that changed the problem. They started with N doors, and had you and the host alternate (You: choose an unopened door, HOST: open an unchosen door with a goat) until you were satisfied. The best strategy led to a probability that approached 2/pi, not 2/3 (remember, more doors). Bill claimed that was the answer for the original problem as well. Then he went off on some made-up arguments about "probability in short run" vs. "long run," as if they weren't the same thing. So no, he isn't "resolved." (But on a positive note, he finally did agree that the probability is 1/2, after you meet a boy at random from a two-child family, that his sibling is also a boy. He spewed just as much venom before doing that, then gave a "mea culpa.")
| Quote: | | (regarding Fermat, Einstein and other accepted proofs or theories, I understand Bill continues to contest these after the fact; |
No, here he claimed he had proven FLT as a child, but didn't think it was important because it was so trivial. And then his mother threw the notes (all ten lines, or so, of them) away. All his "proof" was, was a collection of unrelated and usually incorrect algebra. It looked like what he could have once seen in the actual proof for specific some N cases, but didn't understand what they did there or why it was a proof.
| Quote: | | even if he is incorrect or unsuccessful, I still believe by applying that mindset to other things, one day he is going to hit the jackpot and "undo" some proven assumption that turns out does indeed have flaws. |
"Rebel without a clue" is a better description. He recognizes that his thoughts appear related to what he wants to talk about, but really has no idea what they mean, or how to assemble a proof.
| Quote: | | so why not find him a real challenge to take on |
Because he refuses to recognize when he is wrong. Anything that you can show is wrong, he dismisses as "fighting progress." |
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mmiller
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Joined: 13 Jul 2008
Posts: 144
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| Posted: Fri Mar 05, 2010 2:03 pm Post subject: She blew it: I wanted a goat! Stay w/ door #1 |
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There is nothing in the original problem from Parade Magazine that states that you must choose for the car. Some people might just want the goat, like say you live in the Kalahari Desert, in areas where there is no gas, a car is worthless, yet a goat is invaluable.
So, I want to avoid getting the car and hope for a goat. By switching to door number three, I have increased my odds of getting a car to 2/3's. But, that's not what I want! I'd prefer a goat, and since door number 2 is eliminated (there's no offer to switch to it for a guaranteed 100% correct choice to get a goat), I'd only get a 1/3 chance of getting a goat by switching, and a 2/3's by staying with door number one. So, if you want a goat, then stay put for better odds!
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JeffJo
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Joined: 10 Mar 2009
Posts: 1015
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| Posted: Fri Mar 05, 2010 3:11 pm Post subject: Re: She blew it: I wanted a goat! Stay w/ door #1 |
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| mmiller wrote: | | There is nothing in the original problem from Parade Magazine that states that you must choose for the car. |
Lots of things are implied without being stated:- The car and goats are placed randomly before your initial pick.
- Your choice was based on having no knowledge of how the car and goats were placed, either today or any trends from previous shows.
- The host always opens a door.
- The host always reveals a goat when he opens a door.
- The host always picks randomly when he has the choice of two doors with goats.
- "Advantage" means "based on the nominal value of the prizes."
If you want to be argumentative and disregard any one of these standard assumptions for such problems, then you can equally well disregard any of the others. And then no answer is possible at all.
But doing so is hardly constructive. The answer was right. |
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mmiller
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Joined: 13 Jul 2008
Posts: 144
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| Posted: Fri Mar 05, 2010 3:51 pm Post subject: |
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Talking about being dead serious! Geez! Your locked mindset is purely mathematical, sans inspiration. When is the last time you laughed?
I would think that imagination is the key to this website, that an open and creative mind that operates independently of conventional wisdom is the absolute essence of Marilyn and what she is all about. On the other hand, if you really want to be strictly 'scientfific', then the original question is ambiguous. And perhaps with my own twist I am indeed poking fun at those with a locked mindset. Grade me if you want (and others), but I thought my response followed that vein very well, imho.  Think creatively!
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ZombiePriest
Scholar
Joined: 21 Feb 2010
Posts: 40
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| Posted: Sun Mar 07, 2010 6:51 am Post subject: |
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| So who won the car? |
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mmiller
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Joined: 13 Jul 2008
Posts: 144
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| Posted: Wed Mar 10, 2010 1:54 am Post subject: |
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I won the car, unfortunately. I stayed put with my first choice, hoping my two third's chance would win me the much desired goat, but I got stuck with the car instead. Oh well...
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Zanshiro
Thinker
Joined: 17 Jan 2008
Posts: 4
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| Posted: Sun Mar 14, 2010 7:11 am Post subject: Ha! |
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Well, I thought it was pretty hilarious, mmiller, for what that's worth. Also, Emily, thank you for being you. Always a positive mindset for one such as myself who lurks on occasion, but rarely logs in to type things. Quite refreshing to read your takes on many of the questions and situations brought forth in this forth.
I only log on to the web for about 30 minutes a day now at best, to explain my long absence. However, I do stop in time to time and try to keep up with some topics, though I'm falling FAR behind. I've been working two jobs while I'm able to do so and hopefully will have enough saved to take a vacation soon. On the bright side, I do have a Hammerfall concert to attend coming up in a few weeks. Relaxation much needed! |
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nicobottoms
Thinker
Joined: 29 Apr 2010
Posts: 3
Location: Netherlands
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| Posted: Thu Apr 29, 2010 10:18 am Post subject: |
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Having worked out the example in code as obvious as possible:
| Code: |
Private Sub Form_Load()
Randomize Timer
Dim wins As Integer
Dim prize As Integer
Dim choice As Integer
Dim montysemptydoor As Integer
Dim report As Integer
Dim i As Integer
Dim j As Integer
Const samplesPerGo As Integer = 1000
Const reports As Integer = 30
For report = 0 To reports
wins = 0
For i = 0 To samplesPerGo
prize = Random(0, 3) ' the prizedoor is decided
choice = Random(0, 3) ' the initial choice of contestant is decided
For j = 0 To 2 ' monty shows the empty door
If j <> choice And j <> prize Then
montysemptydoor = j
End If
Next j
For j = 0 To 2 ' switching to the other closed door
If j <> choice And j <> montysemptydoor Then
choice = j
End If
Next j
If choice = prize Then
wins = wins + 1
End If
Next i
Text1 = Text1 & (wins & "/" & samplesPerGo) & vbCrLf
Next report
End Sub |
The result:
532/1000
518/1000
514/1000
518/1000
615/1000
606/1000
613/1000
580/1000
555/1000
556/1000
559/1000
555/1000
551/1000
559/1000
521/1000
506/1000
509/1000
546/1000
588/1000
585/1000
575/1000
560/1000
565/1000
541/1000
...
Now when disabling the switching part:
If j <> choice And j <> montysemptydoor Then
' choice = j
End If
335/1000
340/1000
388/1000
400/1000
398/1000
373/1000
350/1000
352/1000
356/1000
333/1000
325/1000
328/1000
340/1000
386/1000
384/1000
383/1000
381/1000
380/1000
373/1000
288/1000
291/1000
292/1000
355/1000
374/1000
377/1000
348/1000
323/1000
321/1000
315/1000
291/1000
288/1000
291/1000
362/1000
370/1000
367/1000
...
I still find it odd myself, and yet logical... |
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Kemosabe-TBC
Intellectual
Joined: 06 Dec 2008
Posts: 1217
Location: Portugal
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| Posted: Thu Apr 29, 2010 1:21 pm Post subject: |
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I still find it odd myself, and yet logical...
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Your program is not correct, your "random" choices are not represented equally likely. When you run your program the following happens:
- Monty's empty door
. Door 0 is chosen about 22,2% of the time
. Door 1 is chosen about 33,3% of the time
. Door 2 is chosen about 44,4% of the time
(They all should be chosen 33.3% of the time)
Choice after switching
. Door 0 is NEVER chosen
. Door 1 is chosen about 44,4% of the time
. Door 2 is chosen about 55,5% of the time
This is easy to see using a truth table
| Code: |
CHOICE | PRIZE || EMPTY DOOR | CHOICE AFTER SWITCHING
-----------------------------------------------------
0 | 0 || 2 | 1
0 | 1 || 2 | 1
0 | 2 || 1 | 2
1 | 0 || 2 | 1
1 | 1 || 2 | 1
1 | 2 || 0 | 2
2 | 0 || 1 | 2
2 | 1 || 0 | 2
2 | 2 || 1 | 2
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Choice and Prize are your inputs here. No matter what happens, in your program, the empty door (chosen by monty) and the choice after switching can ALWAYS be directly calculated using the values of "choice" and "prize". There are only 9 possible situations.
There are several mistakes in the program. The first one is using a loop to calculate the empty door. By doing this you're ensuring that the last door will always be chosen more often, even if the expression (j <> choice And j <> prize) had already evaluated to true in a previous iteration. In the second loop you do the same thing, but it's even worse, because the value of "choice" changes in each step of the iteration, and it's used in the expression (j <> choice And j <> montysemptydoor).
Example:
choice = 2
empty_door = 1
Iteration 0
(j <> choice And j <> montysemptydoor) is true
choice = 0
Iteration 1
(j <> choice And j <> montysemptydoor) is false
Iteration 2
(j <> choice And j <> montysemptydoor) is true
choice = 2
If you break the loop, after the expression evaluates to true, you will get the correct value of ~66,6% wins. But still your program won't be correctly simulating what happens in the real show. Playing with numbers like these is not a good way to make statistical simulations IMO... Try to mimic EXACTLY what happens in the real game. Each door exists, it is a physical door, it is not a random number. I would use an array, and each element of the array would represent a different door. Also I would never iterate the array until I get the value I want, everything must be RANDOM. Here's an example of a C program, I wrote a while ago, that does this:
| Code: |
#include <stdio.h>
#include <time.h>
#define NUM_DOORS 3
#define GOAT 'G'
#define CAR 'C'
typedef enum _door_number {FIRST_DOOR=0, SECOND_DOOR=1, THIRD_DOOR=2} door_number;
typedef enum _result {WIN, LOSS} result;
// Headers
int reveal_goat(char* doors, int non_picked_door1, int non_picked_door2);
double play_ntimes(char* doors, int n);
result play_game(char* doors);
int main(int argc, char** argv)
{
double observed_percentage;
char doors[NUM_DOORS];
int wins;
srand(time(0));
// 1 million tries
observed_percentage = play_ntimes(doors, 1000000);
printf("\nThe observed result of 1 million tries is: %f\%\n", observed_percentage);
return 0;
}
result play_game(char* doors)
{
int random_car = rand() % NUM_DOORS;
int random_guess = rand() % NUM_DOORS;
int guess_after_switching;
switch(random_car)
{
case FIRST_DOOR:
doors[0]=CAR;
doors[1]=GOAT;
doors[2]=GOAT;
break;
case SECOND_DOOR:
doors[0]=GOAT;
doors[1]=CAR;
doors[2]=GOAT;
break;
case THIRD_DOOR:
doors[0]=GOAT;
doors[1]=GOAT;
doors[2]=CAR;
break;
}
switch(random_guess)
{
case FIRST_DOOR:
guess_after_switching = reveal_goat(doors, SECOND_DOOR, THIRD_DOOR);
break;
case SECOND_DOOR:
guess_after_switching = reveal_goat(doors, FIRST_DOOR, THIRD_DOOR);
break;
case THIRD_DOOR:
guess_after_switching = reveal_goat(doors, FIRST_DOOR, SECOND_DOOR);
break;
}
if(doors[guess_after_switching] == CAR)
return WIN;
else return LOSS;
}
double play_ntimes(char* doors, int n)
{
double observed_percentage;
result res;
int wins=0, i;
for(i=0; i<n; i++)
{
res = play_game(doors);
if(res == WIN) {
wins++;
}
}
observed_percentage = (double) wins / n * 100.0;
return observed_percentage;
}
int reveal_goat(char* doors, int non_picked_door1, int non_picked_door2)
{
if(doors[non_picked_door1] == GOAT)
return non_picked_door2;
else return non_picked_door1;
}
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PS: Visual Basic? Blergh  |
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