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Sat 24 Sep, 2005 08:47 am
Hey everyone...
...I need someone (other than supposed expert, Brandon) with a good deal of expertise in probability and statistics to get involved in a disagreement over the use of probability in an ongoing thread.
Lemme know if you have such expertise...and I'll link you to the thread.
And when you quote me, be sure to quote me accurately.
I think it's a red herring, Frank.
On his own terms, it's true enough -- but invasions should not take place on such flimsy pretenses (30% chance). Inspections should. Sanctions maybe. All-out invasions are an entirely different kettle of fish, for a number of reasons.
sozobe wrote:I think it's a red herring, Frank.
On his own terms, it's true enough -- but invasions should not take place on such flimsy pretenses (30% chance). Inspections should. Sanctions maybe. All-out invasions are an entirely different kettle of fish, for a number of reasons.
These other points are separate from the present issue of whether I have misrepresented the meaning of probability. I would be grateful if we could resolve that before dividing this into other discussions.
I will not quote you, Brandon...I intend to link the person to the start of our discussion.
Peace!
Frank Apisa wrote:I will not quote you, Brandon...I intend to link the person to the start of our discussion.
Peace!
And I don't want their judgement about whether they agree with me politically - just the one mathematical question.
Why don't you all pose the mathematical question devoid of political meaning.
I have a good academic understanding of probability and statistics... but I don't need to get into another debate on the topic I am assuming you all are involved on. I would be happy to comment on a purely mathematical query.
((BTW Frank, I trust Brandon's math (much more than I trust his politics))
ebrown_p wrote:Why don't you all pose the mathematical question devoid of political meaning.
I have a good academic understanding of probability and statistics... but I don't need to get into another debate on the topic I am assuming you all are involved on. I would be happy to comment on a purely mathematical query.
((BTW Frank, I trust Brandon's math (much more than I trust his politics))
Likewise.
If you toss a fair coin and fail to achieve heads, then you may get heads the next time. If you don't get heads on the second toss, nonetheless you can expect to get it about half the time. Not getting heads on one occasion doesn't mean that you might not get it the next toss. This is the molehill that has been blown up into a mountain.
Brandon9000 wrote:ebrown_p wrote:Why don't you all pose the mathematical question devoid of political meaning.
I have a good academic understanding of probability and statistics... but I don't need to get into another debate on the topic I am assuming you all are involved on. I would be happy to comment on a purely mathematical query.
((BTW Frank, I trust Brandon's math (much more than I trust his politics))
Likewise.
If you toss a fair coin and fail to achieve heads, then you may get heads the next time. If you don't get heads on the second toss, nonetheless you can expect to get it about half the time. Not getting heads on one occasion doesn't mean that you might not get it the next toss. This is the molehill that has been blown up into a mountain.
Wow...and you were worrying that I would misquote you.
YOU misquoted YOU.
I'll be back with a synopsis of the argument.
Brandon wrote:
Quote:As usual, you misunderstand. The theory is that if the general category of rogue states which have WMD programs are not treated seriously, then eventually a WMD will be used, at least for blackmail. If WMD were no longer in Iraq by the time we invaded, then the next time we have the same situation, or the next, the WMD will still be there. That's what it means to talk about a probability. Even one such device used in a population center could exterminate a half million people. It would be one thing if you folks quoted my position accurately and then argued with it, but you almost always quote it inaccurately.
I replied:
Quote:Quote:As usual, you misunderstand. The theory is that if the general category of rogue states which have WMD programs are not treated seriously, then eventually a WMD will be used, at least for blackmail.
Okay...I'll buy the essence of this comment.
Rogue states have to be "treated seriously."
Quote: If WMD were no longer in Iraq by the time we invaded then the next time we have the same situation, or the next, the WMD will still be there.
Respectfully as possible, Brandon...there is not enough logic in that passage to fill a flea's ear...and flea's don't even have ears.
Whether we found WMD in Iraq or not will not influence whether we ever find them anywhere else.
This sentence fails every test of logic.
Quote:That's what it means to talk about a probability.
C'mon! This has even less logic involved. You might just as well have said, "That's what it means to talk about homemade pasta."
Quote:Even one such device used in a population center could exterminate a half million people.
Unfortunately...all too true. And my guess is that this will happen at some point...no matter whether this incredibly incompetent administration or one as incompetent as it handles matters...
...or an administration much, much, much more competent comes along.
I think that at this stage of our difficulties...a mega event is almost a certainty no matter what.
But I do agree that we have still got to do as much as possible to minimize its chances.
Quote:It would be one thing if you folks quoted my position accurately and then argued with it, but you almost always quote it inaccurately.
Well...here I have cut and pasted your position...and your words.
[/quote]
I also said:
Quote:Frank Apisa wrote:By the way, Brandon...
...the "particular logic" you are using with regard to "probability"...namely that since we did not find WMD in Iraq we have increased the probability that we will find them when we invade some other country...
...reminds me of an old expression that seems very quint these days.
It use to go something like this: If you are afraid to fly because you think someone might bring a bomb on board your plane...consider that the chances against that happening are tens of millions to one against it happening. But if you don't even like those odds...simply pack up a bomb and bring it on board with you, because the chances of two people bringing a bomb on board any particular flight is tens of hundreds of millions to one against.
In any case...if your logic held up in any way...we probably should invade ten or twelve fifth world countries looking for WMD...Mali, Chad, Andorra, Benin, Eritria, Panama, Mauritania, etc. Then we would really improve our chances.
Brandon replied:
Quote:Brandon9000 wrote:Frank Apisa wrote:By the way, Brandon...
...the "particular logic" you are using with regard to "probability"...namely that since we did not find WMD in Iraq we have increased the probability that we will find them when we invade some other country..."
Frank, that was not what I said. I meant something quite different.
Let's say you find a dictatorship that once had WMD and claims to have eliminated them, but you consider there to be a probability of .3 that it is merely hiding them. You invade and find nothing. A year later, you find a country in a similar situation, with a .3 probability that it is concealing WMD. You invade this other country, but find nothing. Now a few years later, you find a third country in the same situation and invade....etc.
I am saying that if the probability is .3, eventually you will run into one that is hiding WMD from you. In fact you will do so 30% of the time.
I am certainly not saying that your success or failure to find WMD in one exerts influence over what you will find in the next one. You know I do have a couple of Physics degrees, and they do make us take probability and statistics courses before we get the diploma.
Brandon then said:
Quote:I am 100% correct. My reference to statistics is elementary. I have said nothing more exotic than if you toss a fair coin and fail to get heads the first time, then you may get heads the second time, but, if not, you will likely get heads sooner or later. This is not really subject to debate, since it is so simple. Let me try to be even more explicit:
You invade a series of countries each of which has a chance of .3 of having WMD hidden. The first one may be clean the second one may be clean, etc., but if for each, the probability is really .3 of hidden WMD, then you should, from time to time, encounter countries for which the proposition is true - WMD are hidden. As the number of invaded countries approaches infinity, the fraction you have found with hidden WMD approaches .3.
Therefore, if we are confronted every few years with countries which have a probability about that large of having hidden WMD, it is to be expected that even if the first, second, and third turn out to be clean when we get in, some of them will not be clean.
Go get the whole Courant Institute, this is barely more than the definition of probability.
That...except for a few "no you didn't" "yes I did" things...is where things stand.
No politics...just some supposed logic and probability...and a charge that both the logic and the probability are defective.
Hee! Hee! Well, Frank, what are the probabilities of you and Brandon agreeing on everything. Just kidding. As a matter of fact, I had to take Statistics to get my masters. What would you like to know?
Frank,
If you agree with Brandon's statement about the fair coin, then we can be done with the Mathematics of your argument.
Arguing about the what the argument is isn't any fun.
In my opinion Brandon's math is fine.
I don't think it has anything to do with the underlying political argument which in my opinion is pure hogwash.
Math is too pure to be sullied in this argument.
ebrown_p wrote:Frank,
If you agree with Brandon's statement about the fair coin, then we can be done with the Mathematics of your argument.
Arguing about the what the argument is isn't any fun.
I have no problem with the fair coin...but if you read his statement...you will see that it has no impact on the probability fallacy in his original statement...nor in the logic which he applies.
The fair coin argument is truly a red herring. He might just as well have offered that 2 + 2 = 4 as an argument that his original statement...and the way he is applying it...is correct.
If we assume something occurs 30% of the time then Brandon is correct. A 10 side die will come up 3 or less 30% of the time over a large number of rolls. The problem is that it requires a fairly large number of rolls to be reasonable sure of having your totals be 30%. It is possible to roll it 100 times and never have it be 3 or less. It is unlikely but possible.
His argument is specious since it assigns a 30% figure to something that is unknown and assumes that every country has a 30% chance.
The failure in logic is that we don't know the number of sides of the die each time it is rolled or even if the die has the numbers 3 or less on them. We can reasonably assume that at some point the number 3 or less will come up but we can't begin to figure out how many rolls it will take before we can be reasonably assured of having a measurable %.
The next problem with the example is we have a limited number of rolls of the die. (There are a limited number of countries that we can invade.) Because of this limited number of rolls there is no way to reasonably guarantee the 3 or less in our limited number of rolls.
All I intended to say is that if an event, X, has a probability p of occurring, then failure to observe p on the first few trials does not imply that X will not occur on the next trial. Similarly, when we invaded Iraq, there was a probability, p, that we would find WMD. It was probablistic because our knowledge of the truth was incomplete. If you knew all the facts connected with tossing a coin, you could predict the outcome, but your incomplete knowledge renders the result probablistic. Should we again invade another country under similar circumstances, we might very well find hidden WMD. I most certainly did not say that the real probability was .3. That was an absolutely arbitrary number used to facilitate the discussion. You folks have now succeeded in wasting a lot of time and energy over something that is virtually self-evident.
Let's take it out of the realm of politics.
Some people that swim in the ocean drown.
Hypothetically - lets say you have a 30% chance of drowning.
therefore if you swim in the ocean enough eventually you will drown.
Would you use the hypothetical as a reason to not go swimming?
parados wrote:Let's take it out of the realm of politics.
Some people that swim in the ocean drown.
Hypothetically - lets say you have a 30% chance of drowning.
therefore if you swim in the ocean enough eventually you will drown.
Would you use the hypothetical as a reason to not go swimming?
What I am saying is that the fact that you don't drown the first time you go swimming does not imply that you won't drown the second time, and that the fact that you don't drown the first time does not imply that there wasn't a very real chance of drowning. The reasoning, "I went swimming once, and I didn't drown. Therefore, there is no danger," is false. Go ahead, make me post this a thousand times. It will change nothing.