The importance of being (Error!)
 

To get started I'm going to pose a hypothetical.

Fred Astaire is always right. He never makes a mistake. If you give him a problem that he can solve, he will solve it correctly 100% of the time. But Fred can't handle differential equations. Starting somewhere around basic calculus, he just can't wrap his mind around the problem. Fred's a logical person, he's right where all of the common-sense stuff is concerned, and he's a great poker player.

Ginger Rogers makes mistakes. She makes lots of mistakes. In fact, in every problem she tries to solve, she has a 50% chance of [censored] up. What's 3+3? "7." What's the largest mammal? "The shrew." How many fingers am I holding up? "Erk - NaN." But Ginger can handle any kind of problem. She consistently scores 60 on the Putnam exam, and if she sets out to prove the Goldbach conjecture, she has a 50% chance of success. Yes, no matter what the problem is, Ginger has a 50% chance of solving it. Ginger is often seen as irrational due to her mistakes, and she frequently hemorrhages money in poker.

So, who's smarter?

Re: The importance of being (Error!)
 

madnak, Ginger of course. Everyone knows Ginger did everything Fred did in heels going backwards. [img]/images/graemlins/grin.gif[/img]

Re: The importance of being (Error!)
 

Ginger is an impossibility.

It would take a parlay of many 50% error free steps (on 3+3 =7 type ones) for her to solve difficult problems.

D

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I voted fred, since there's so much he is infallible on. If you increase Ginger's chance of success to 80% or something it gets harder for me.

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I don't think its even close. Because Ginger never knows if she's right.

For Ginger to exist, she cannot be aware of her limitations.

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Ginger is an impossibility.

It would take a parlay of many 50% error free steps (on 3+3 =7 type ones) for her to solve difficult problems.

D

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this is why i couldn't vote.

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Ginger appears to be some sort of freakish idiot savant.

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Ginger appears to be some sort of freakish idiot savant.

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ROFL [img]/images/graemlins/laugh.gif[/img]

Re: The importance of being (Error!)
 

Fred is smarter because he's more likely to know his limitations on what problems he is qualified to weigh in on with certainty.

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Ginger is an impossibility.

It would take a parlay of many 50% error free steps (on 3+3 =7 type ones) for her to solve difficult problems.

D

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this is why i couldn't vote.

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It's a hypothetical. Suspend this. How she solves the problems is irrelevant, it's the results that matter.

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Ginger and it's not close

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Fred is smarter because he's more likely to know his limitations on what problems he is qualified to weigh in on with certainty.

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This was my thinking exactly.

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Ginger. Ginger is the one that has the courage to take the risks to have real experiences. So she has a better life than Fred. Life really isn't about being rational all the time.

Re: The importance of being (Error!)
 

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Fred is smarter because he's more likely to know his limitations on what problems he is qualified to weigh in on with certainty.

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Agreed and to quote Socrates "The only true wisdom comes in knowing you know nothing"

Re: The importance of being (Error!)
 

For almost all real-world problems, it is exponentially easier to "check" a solution than it is to "generate" a possible solution.

So Fred is smarter than Ginger on easy problems, but as the problems get harder, Ginger becomes asymptotically more intelligent.

Once we reach a really hard problem such as finding the longest cycle in a graph, Ginger is infinitely more intelligent than Frank.

Re: The importance of being (Error!)
 

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Ginger. Ginger is the one that has the courage to take the risks to have real experiences. So she has a better life than Fred. Life really isn't about being rational all the time.

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Welcome to the thread.

Re: The importance of being (Error!)
 

does ginger get the same answer everytime she attempts the same problem?

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does ginger get the same answer everytime she attempts the same problem?

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I'd imagine no, but thats a good question.

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If she doesnt get the same answer that means she is smartest by far because she can do the problem until she sees an answer repeating itself and then know the answer for sure

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If she doesnt get the same answer that means she is smartest by far because she can do the problem until she sees an answer repeating itself and then know the answer for sure

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no, she'll make the wrong conclusion about which answer is right 50% of the time.

Re: The importance of being (Error!)
 

i think i misunderstood at first but get it now.

So you're saying, Fred can solve the easiest 80% of problems, 100% of the time every time, but he can never solve the hardest 20%.

Ginger has a 50% chance at solving anything, no matter how hard.

Given that, ginger is smarter and its not close.

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i think i misunderstood at first but get it now.

So you're saying, Fred can solve the easiest 80% of problems, 100% of the time every time, but he can never solve the hardest 20%.

Ginger has a 50% chance at solving anything, no matter how hard.

Given that, ginger is smarter and its not close.

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I doubt many people would call someone stupid just because they cant do differential equations. However, if they cant even add single-digit integers?

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i think i misunderstood at first but get it now.

So you're saying, Fred can solve the easiest 80% of problems, 100% of the time every time, but he can never solve the hardest 20%.

Ginger has a 50% chance at solving anything, no matter how hard.

Given that, ginger is smarter and its not close.

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does not compute. If she's wrong 50% of the time and can never distinguish when she's wrong, I don't see how she can be smarter.

50% of the time she is always wrong and has not ability to distinguish what she right about, what her strengths are, etc.

She's a nightmare.

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Ginger. Ginger is the one that has the courage to take the risks to have real experiences. So she has a better life than Fred. Life really isn't about being rational all the time.

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Would you be so kind as to go to the SSNL 6 max thread and give some analysis on some hands posted. I thinks that forum could use some laughs.

Your contributions could be legendary.

Re: The importance of being (Error!)
 

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i think i misunderstood at first but get it now.

So you're saying, Fred can solve the easiest 80% of problems, 100% of the time every time, but he can never solve the hardest 20%.

Ginger has a 50% chance at solving anything, no matter how hard.

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That's correct.

To clarify, Ginger can't just repeat until she gets the correct answer. Once she gets it wrong, she will never get it right.

Another clarification - this is a matter of problem solving (and generally a matter of analytical tasks). There's nothing preventing Ginger from completing ordinary tasks in a rote way. Most importantly (wrt this discussion), Ginger can communicate with other people. I won't go into concerns of Ginger's lifestyle, that's beyond the scope of the thread - the important thing is that while she can't tell when she's right, other people are able to do so.

So if she tries to tackle the Millenium Prize Problems, she won't know which ones she got right, but it should be apparent to any competent mathematician who sees her work that she solved 3 of the problems (on average).

Re: The importance of being (Error!)
 

^^ Yes, I had assumed that also, both that if she got something wrong she couldn't just keep attempting it until she got it right, and also that if she did get something right that she should be able to explain her solution to others who can confirm that she is correct.

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Ginger is an impossibility.

D

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So is Fred. Anyone who can do math questions up to differential equations perfectly, is not going to all of a sudden hit a wall if he tackles harder subjects. Especially since most, if not all, math problems can eventually be broken down into simple logic.

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Especially since most, if not all, math problems can eventually be broken down into simple logic.

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Not true, not even close unless you mean by exhaustive search (which no human can do) and even then its not true.

chez

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Ginger is a genius.

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Ginger is useless because you can never know if she is right, unless you know the answer from before. Fred is useless after a certain point, but what he does know you can take for face value.

(like People have said before me, I know)

This sounds like a clever version of belief vs logic debate. [img]/images/graemlins/smile.gif[/img]

Re: The importance of being (Error!)
 

Ginger is going to go on and solve 3 of the 7 Millenium prizes winning $3 million dollars which she hemorrhages away regularly in high stakes games. She has to drop down to the micros where Fred is grinding making a steady $12 an hour. Fred explains to Ginger that the game is different at the lower level because the players play and think differently. Ginger stays down in the micros grinding with Fred until the next set of Millenial questions roll around. Now who's the genius?

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Especially since most, if not all, math problems can eventually be broken down into simple logic.

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Not true, not even close unless you mean by exhaustive search (which no human can do) and even then its not true.

chez

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Who is correct here?

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Especially since most, if not all, math problems can eventually be broken down into simple logic.

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Not true, not even close unless you mean by exhaustive search (which no human can do) and even then its not true.

chez

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Who is correct here?

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The proof I'm right is beyond simple logic.

chez

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Ginger is useless because you can never know if she is right, unless you know the answer from before.

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but you could use her answers as testable predictions. if you keep trying and keep asking her questions you would have amazing potential.

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Ginger is useless because you can never know if she is right, unless you know the answer from before.

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but you could use her answers as testable predictions. if you keep trying and keep asking her questions you would have amazing potential.

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True enough, though I suspect if we apply '3rd party' agents to the example it will become slightly different, so looking at it in a 'vacuum' might be better. I don't know, but anyways; it is a good point.

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It seems to me that Fred knows something, while Ginger knows nothing.

Am I smarter than my computer?

Or should I feel dumb for not getting this. [img]/images/graemlins/grin.gif[/img]

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Fred and Ginger sound like caricatures of my parents.

When I was young the three of use used to play card games. My mother was capable of showing deep understanding of the game, and pull of some brilliant plays where it was clear she knew what she was doing. She also often needed to be reminded of the rules and made elementary blunders. A week later she would have forgotten how to play and need to have it explained again.

My father would not forget the rules, unfortunately he is dead now. He had a very logical but more limited mind. He would play the obvious first level strategy flawlessly, but not progress beyond that.

In most real life situations my fathers plodding logical mind was more effective however I am in no doubt that my mother is more intelligent.

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Ginger is useless because you can never know if she is right, unless you know the answer from before.

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No. Think about things like prime factorization and differential equations.

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Saying who is smarter is somewhat arbitrary. Some savants can do amazing calculations but are horrible at other things. It is tough to say if they are smarter than an average person.

What you can say is who is more useful and it is Ginger hands down. Computers exist that can do everything Fred can (I think just mathematica alone could be enough) so he would add pretty much nothing.

Re: The importance of being (Error!)
 

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Saying who is smarter is somewhat arbitrary. Some savants can do amazing calculations but are horrible at other things. It is tough to say if they are smarter than an average person.

What you can say is who is more useful and it is Ginger hands down. Computers exist that can do everything Fred can (I think just mathematica alone could be enough) so he would add pretty much nothing.

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Computers can't do one percent of what Fred can. They can't do word problems.

The tough part about math is not knowing how to solve equations. Its about knowing what equation to solve.