A Pre-emptive Dialectic (to weed out the weaker objections)

Merlin,

The focus of this study is not cancer victims, it is on the doctors who attempt to answer the survey question about breast cancer and get it wrong 85% of the time.

In the original example, the false positive rate is 92.24%. If the number of actual cancer victims amounted to 50% of the total, then the false positive rate plummets to 10.7%.

What´s reasonable depends on context, but for some reason nothing beyond intuitive guesses seems reasonable to people including 85% of the doctors in these studies. Even when told the answer they either don't get it, don't believe it, or they believe it but then forget it some time later and fall back on intuition again.

Setting the number of cancer victims (who are not the focus of this study) at 50% makes the rate of true positives - 89.3% - appear intuitively correct. It's not the 1% or the 9.64% being focused on here, it's the 80% accuracy rate for the mammography.

So when you speak of reasonable expectations, I have to ask why the 80% figure is always focused on and not the 1% figure. Nobody should question changing the 1% to 50% if this is just a story problem. It could be that the women were hand-selected for the mammographies. It's not about that anyway.

Post 241

Thursday, January 21, 2010 - 5:05am

It's not the 1% or the 9.64% being focused on here, it's the 80% accuracy rate for the mammography.

Have I said otherwise? I said in post 237 they don't the recognize the significance of the 9.64%, since they are not focusing on it. I didn't say so as clearly in post 228, but it is what I meant.

(Edited by Merlin Jetton on 1/21, 5:31am)

Post 242

Thursday, January 21, 2010 - 6:56am

Merlin,

So did you solve the problem on your own?

Post 243

Thursday, January 21, 2010 - 7:29am

So did you solve the problem on your own?

Yes, it's an easy problem for an actuary.

(Edited by Merlin Jetton on 1/21, 8:47am)

Post 244

Thursday, January 21, 2010 - 1:52pm

Merlin,

Then what do you mean by, "and I believe doctors would expect to hear a reasonable probability"? I'm certain they are familiar with the population statistics. But they expectation involves the 80% accuracy and how it affects their judgment so that 85% of them come up with a statistic that is ridiculous based on the fact that 99% of the group does not have cancer.
(Edited by Robert Keele on 1/21, 1:53pm)

Post 245

Thursday, January 21, 2010 - 2:40pm

Robert Keele,

My saying "I believe doctors would expect to hear a reasonable probability" was mainly about your using a 50% probability of having (breast) cancer. (It doesn't look that way in post 239 because I broke up what you said in post 238. Stuff like that happens when posting quickly.)

As I showed in post 237, the doctors' intuition would have not been so wrong if the false positive rate had been much lower.

Post 246

Thursday, January 21, 2010 - 2:48pm

Our brains aren't well wired to consider base rates.

And it's very tempting to reverse terms here: to say "if positive, then big chance of having cancer," instead of "if cancer, then big chance of testing positive."

Jordan

Post 247

Thursday, January 21, 2010 - 4:33pm

Jordan,

I like your way of explaining the difference between X|A and A|X in the formula.

Merlin,

I raised the cancer rate to 50% to make the very point you're agreeing with. I'm sure you knew it all along. However, I'm just trying to argue Jordan's point of view about brains not being wired well to deal with these kinds of problems. Since that's the case, the answer is to avoid making assumptions which make an ass out of 'u' and 'mptions.'

The first doctor I quizzed who got the wrong answer still hasn't lived it down. But I'm not the one giving him a hard time about it. Really, I'm not. It's just that we get to work together twice a week, and...

Post 248

Thursday, January 21, 2010 - 5:18pm

What, exactly, is the point of saying that our brains aren't wired well to deal with . . . "X"? Should it be a surprise that certain types of problems are more difficult to solve than others? That understanding calculus is something that many people never achieve? That it took so long to demonstrate Fermat's last theorem? And that many people think even Fermat didn't solve it? Are brains or minds entities without specific natures, so that they should be able to do all things equally well?

And do not the people who understand how to calculate such problems in probability have brains that are, in fact, wired properly? Is your brain, Robert, not wired properly to understand this type of problem?

Our bodies aren't "designed" to allow us to fly across the English Channel under our own muscle power either. But it has been done. Humans are not "determined." It is effort that makes all possible accomplishments possible.

The fact that acquiring certain forms of knowledge requires more effort than others is surprising only to the mystic.

Post 249

Thursday, January 21, 2010 - 5:31pm

Ted,

The part where you wrote: What, exactly, is the point of saying that our brains aren't wired well to deal with . . . "X"? Should it be a surprise that certain types of problems are more difficult to solve than others? That understanding calculus is something that many people never achieve?

I made my point earlier. It's not just that people tend to rely on intuition. It's not just that some people don't know the method, it may be difficult but these are doctors who should know better such as Doctor #1 who is only 4 years out of college and has demonstrated to me his tremendous medical knowledge during that time.

It's that people rely on intuition relentlessly. I don't necessarily blame it all on wiring, I blame some of it on schools, but that using intuition as a fall-back position is entirely innate. Education can reduce this tendency but it cannot entirely eradicate it.

I was lucky and had a great algebra teacher who pounded methodology into our heads and would not tolerate the students who simply blurted out even correct answers without first demonstrating how they were achieved.

Post 250

Thursday, January 21, 2010 - 5:40pm

Ted,

I just noticed this: And that many people think even Fermat didn't solve [Fermat's last theorem]?

Fermat could NOT have solved the last theorem, it required a 20th-century solution based on mathematical theories that were not invented yet.

Post 251

Thursday, January 21, 2010 - 5:48pm

Robert, that is laughable. You do not have a proof that no simpler proof is possible.

Post 252

Thursday, January 21, 2010 - 5:54pm

I made my point earlier. It's not just that people tend to rely on intuition. It's not just that some people don't know the method . . . It's that people rely on intuition relentlessly. I don't necessarily blame it all on wiring, I blame some of it on schools, but that using intuition as a fall-back position is entirely innate. Education can reduce this tendency but it cannot entirely eradicate it.

Of course people rely relentlessly on intuition. There is no infinite regress. You must always rest somewhere. But that's not the problem. The problem is that they may only rely on intuition. You have made stronger claims than the complaint that physicians shouldn't rest on habitual intuition. You have said that this type of reasoning presents a problem for Objectivism. It does not. Objectivism does not hold that thought should be effortless or reason automatic, neither at first nor after long years of effort.

I was lucky and had a great algebra teacher who pounded methodology into our heads and would not tolerate the students who simply blurted out even correct answers without first demonstrating how they were achieved.

I'm glad you've come to the same conclusion as many before you:

One does not know a philosophy if ones knows merely its conclusions, but not the reasoning that led to them.

Post 253

Thursday, January 21, 2010 - 6:03pm

Fermat could NOT have solved the last theorem, it required a 20th-century solution based on mathematical theories that were not invented yet.

"Most mathematicians and science historians doubt that Fermat had a valid proof of his theorem for all exponents n: it is now considered unlikely that there is an elementary proof." (source) Unlikely, not impossible.

Post 254

Thursday, January 21, 2010 - 6:11pm

Ted,

It is a problem for Objectivism, at least of the ARIan variety.

It is a problem, to me at least, for an obvious reason, and it should be obvious to you by now if you've read all my posts on this topic.

It is obvious because the ARIan side makes reasoning itself into a moral issue. But if some aspects of reasoning are innate and can't be helped, then morality is no longer an issue.

But didn't I call it "intuition" and not "reason"? If intuition is just reason loosely applied, without set rules but only operating from experience, then intuition is just a (crude) form of reasoning.

That is why I said reason is more complicated than it appears, the Objectivist theory of reason is too simple and cannot account for the Bayes theorem or why the breast cancer problem stymies so many educated people.

Also, it is impossible for Fermat to have derived the solution to the Last Theorem unless he managed to live into the 20th-century.

Perhaps your meta-theory of math is also too simple to account for this. Because you are literally saying, by analogy, that Newton could have invented Relativity theory.

(Edited by Robert Keele on 1/21, 6:26pm)

Post 255

Thursday, January 21, 2010 - 6:15pm

Ted,

Laughable? So you're asking me to demonstrate a proof by negatives? You're asking me to prove that there is no simpler or more elementary solution?

Laughable? What has Objectivism come to?

Post 256

Thursday, January 21, 2010 - 6:50pm

Robert you are the one who made the claim to know that no other more eloquent proof is possible. My pointing out that you have made an unprovable claim, once you have already done so, does not amount to my asking you out of the blue to prove a negative. By your reasoning you could say a myriad of unprovable things but unreason would only arise if I pointed out that your claims were arbitrary.

As for your habit of acting as if your imagined refutations of an individual's arguments are refutations of Objectivism, you confuse people with philosophical positions, and your imagined refutations with valid arguments.

In plain English, Robert, you are a sophomore.

Post 257

Thursday, January 21, 2010 - 6:55pm

Robert,

***********
But if some aspects of reasoning are innate and can't be helped, then morality is no longer an issue.

But didn't I call it "intuition" and not "reason"? If intuition is just reason loosely applied, without set rules but only operating from experience, then intuition is just a (crude) form of reasoning.

That is why I said reason is more complicated than it appears ...
***********

Are you primarily an Arielyan (Dan Ariely's "Predictably Irrational"), or a Gladwellian (Malcolm Gladwell's "Blink") -- when you say that (I.E., that "reason" is "complicated")?

[there may not be a difference, but I'm curious as to your awareness/acceptance of such "new age talent"]

Ed
(Edited by Ed Thompson on 1/21, 6:57pm)

Post 258

Thursday, January 21, 2010 - 7:00pm

Ted,

Wow! That was a bit overboard, don't you think?

I have offered you a solution to the ARIan error of making reasoning itself into a moral issue. But I'm labeled a sophomore for making the effort.

Furthermore, I fully expect you someday to make use of that solution for your own purposes - albeit subconsciously, of course, it would never be intentional - without granting a mere sophomore such as myself even a small cite.

Anyway, if you'll look back, I was not the one who originally said anything about either a simpler or more complex solution to Fermat's Last Theorem. I simply stated that it required a 20th-century solution. One of your rebuttals challenged me to derive a proof by negatives involving a more elementary solution. But the burden of proof is on your shoulders, not mine. Once you find the more elementary solution, one that Fermat could have possibly accomplished without help from the 20th-century, I will relinquish the point.

You see, that's what happens when you cite Wikipedia.

Post 259

Thursday, January 21, 2010 - 7:02pm