Yoruichi-san

Okay, yes, I agree that males tend to do better than females at these tasks and there are more famous male physicists than females, etc. In fact, that is kind of the whole point of this thread. Females are under-represented in these areas. My question is WHY? Why females in general are worse off at 3-dimensional problems, etc. I think it is due to social pressures, not to fundamental differences. I.e. boys are encouraged to play with Legos and girls are encouraged to play with dollhouses by culture and society, so guys get a better handle on spacial problems. I myself played with Legos, and I have been at least on-par with my male associates all my life ;P.

What, no guesses after that MAJOR hint? ;P

Yeah, and that higher probability is 1. XP You may be getting confused about the Uncertainty Principle, which says you can't know the exact position and velocity, but you can know position if you give up trying to determine velocity. It's a trade-off, just like margin of error and confidence level, as I pointed out in my earlier post. And my position is summarized by this: your interpretation of frequency theory is incorrect. I already pointed out based on your own quotes from your book that you are confusing confidence level with error, and that you are trying to say A->B means B->A, which is not true. I don't really care about your poke in the eye, as I have landed several hard blows in your other areas ;P. (I don't mean to be offensive, just responding in the spirit of fun and debate in the same way you responded to me )

Lol...PG, Slick, you're the one reminding us to behave? Anyways, great intro! Although I can't get Mohinder the Sith Lord out of my mind from the last episode...;P

Y-san smiles..."I see...";P

Lol...I'd say his power is...

I'm not much of a movie person, since I usually go for plot/character development, which requires longer media, but here are some I like: Sin City Match Point Crash My Sassy Girl (Korean) Battle Royale (Japanese)

Err...too late to edit, but just to be clear... The confidence level and the margin of error are inversely related, so that by increasing N, you can make one of them converge, i.e. get the confidence to 100% or the error to 0, but not both.

Thank you, I do appreciate your viewpoint, like you said, it's a very good "way of getting there" from a thinking perspective, but mathematically, it does not prove the answer. I would "give you kudos" for your answer but not your proof ;P. And thank you for showing that quote, however from a logical perspective, I have to disagree with your interpretation: "There are several common theories of probability. In the frequency theory of probability, the probability of an event is the limit of the frequency with which it occurs in repeated, independent trials under the same circumstances.(...) According to the subjective theory, probability is a measure of how strongly we believe an event will occur." From a logical perspective, it says that the frequency in repeated trials will approach the probability, i.e., as I said before, that the probability is a good predictor of the frequency. But it does not say frequency of an outcome is probability. We all know that A->B does not mean B->A. Your approach involves looking at a data set after a large number of trials, and saying that the frequency will approach 1/6, which I do not disagree with. But I disagree that this proves the probability is 1/6. This may verify your prediction that the probability is 1/6 to within a certain degree error, which brings me to my second point, your other quote: Actually, it says neither: "(I)n repeated, independent trials, all having the same probability p of an event, the chance that the relative number of events differs from the probability p by more than a fixed positive amount, e > 0, converges to zero as the number of trials N increases." Like you did with some of my earlier posts, you highlighted the parts you thought were important and dismissed other parts of the same sentence. Looking at the part in red, it is apparent that the quote does not say that the difference b/w probability and frequency converges to 0, but that the probability that this difference is greater than "a fixed positive amount, e>0" converges to 0. I.e. statistically, you predict that p is within some interval [p-e,p+e] and your confidence level approaches 100% as N->infinity, but not that e->0, i.e. not that the frequency approaches p. *For those who may not know as much about statistics, just want to say: Using statistical analysis, you can predict a factor (such as probability) to a degree error (e in this case), and with a certain % confidence. I.e. if I draw colored balls out of a bag, I can say "the percentage of blue balls is 15+/-.1, at a 95% level of confidence", or equivalently, "the percent of blue balls is within the interval [14.9,15.1], at a 95% level of confidence". So you have shown that statistically, you can get your level of confidence to 100% as N->0, but you can't get the error to 0 at the same time. I hope I'm not coming off as too harsh. It's just that I have had way more probability and statistics than I ever wanted, and so I can't help myself from responding when I think there is a misunderstanding. ;P

The title and the OP. "Intelligence" as in females being under-represented in intellectual circles, i.e. fewer famous female physicists, fewer females who do well in intellectual competitions, etc.

Yes, I actually agree with most of what you said. I definitely agree that there are differences b/w males and females physiologically, but I have seen no evidence that this causes differences in "intelligence", or the capability for intelligence. And I apologize if I sounded harsh, but my point was that if "intelligence" were truly coded in our DNA somehow differently for men and women, like on the Y-chromosome or whatever, then it should apply to all men and women, with the exception of a few genetic "mutants". I.e., if men are genetically coded to be better at math, then men should always be better at math than women. However, the fact that there are women who are just as good as men, and, as Prof. Templeton pointed out earlier, the number of women in traditionally men-dominated fields keeps increasing, proves that the differences can't be in coded into our DNA.

More like cold plasmas and particle accelerators ;P...jk...but my dad did occasionally bring home a superconductor or two from work .

No, I don't think it is not self-evident. I never said I thought the male/female differences caused differences in particular skills that would be tested for in IQ tests or any other tests. I said I thought we had different hormones, i.e. brain chemicals, and as we all know ;P, those mostly cause different emotional states, but I have yet to see evidence that this causes different scores on IQ tests or any other sort of intelligence tests, or directly cause women to be under-represented in intellectual circles. And when you say they tend to focus on areas where men excel, my question is why do men excel in these areas? Show me science that suggests that this has to do with the differences in male and female brains, not what seems to me to be circular reasoning that men do better in areas that men do better in...;P And parents do set an example for their children, even without outside influences. Even if the parents don't tell the children how they should react, the children still see what their male/female parent does and are influenced by that. Edit: And I know I'm an exception, but the question is why am I an exception? Is my brain somehow built more like a male's than a female's? Why? I have female DNA, so that can't be it...it only takes one counter-example to prove a theory false...;P

either way i'm really confused I think the watch meant Nice story, Woon! I love it! Hehe...the curse of the detective ;P.

Then I must be misunderstanding your notation, because it seems to me that p(x)^p(x) is splitting it (x^(x^(x^...)^(x^(x^(x...), i.e. putting a parenthesis between the two infinite series whereas the original only puts parentheses around higher exponents... But I agree that a condition is that the series actually converges for a particular x. However, I don't necessarily agree that 2^(0.5)>100^(0.01), it depends on whether you're using a positive/negative/complex root for each...100^(0.01) has 100 roots

Awesome . Actually, as I think more about what you and Octopuppy said, I'm thinking that guys doing better in math and girls being better at tasking may have to do with the fact that boys are encouraged to play with, like, Legos, and girls are encouraged to play with dolls and tea sets...(guess which one I played with? ;P)

lol is any of this even close? -you're getting there, doing well ;P

Well, I think we're using the assumption, as Octupuppy said, that if a series converges to some value at infinity then the infinity-1 series also converges to that value, i.e.... if the series converges then the differences between adjacent values in the series become smaller until they stop changing. For a series to converge, the slope, i.e. the change in the values, of the series has to approach 0, so that yinf/yinf-1 ->1. Your values in your example series do not converge, they just change between 0 and 1. The differences between adjacent values never gets smaller and never approaches 0. Anyways, thank you for helping me convince myself that my earlier work actually works ;P.

Thank you for sharing your opinions, I hope more ppl will do so as well, some thoughts I have: I agree that we are different, we definitely have different hormones (which are brain chemicals) ;P, but I have yet to see a study that shows that these differences actually effect our intelligence, whether measured by IQ or otherwise... And your math teacher never met me... But I agree the ability to visualize helps with math, that's why I tested out of geometry and love Calculus , but I haven't seen anything that proves that that ability is related to our DNA or brain structure. It could be attributed to women having too much of their brain power used up on social stresses. And I didn't say men don't have social stresses, just that women tend to have MORE social stresses, much more...they have the same stresses of social relationships but add to that the stresses of maintaining society's standard of beauty... That's interesting. While I'm sure you and your wife tried your best to treat your children equally, unless they were kept in a bubble ;P, there were probably social influences that you couldn't control, such as television and of course, peer pressure...i.e. if your son's peers are playing with cars or he sees boys playing with cars on TV, he may think be influenced by that. Also, does "stereotypically feminine" or "stereotypically masculine" behaviors change someone's level of intelligence? Does being outwardly affectionate make one less likely to do well in math than not being outwardly affectionate? I guess what I'm trying to say is that while I have no doubt there are inherent differences in males and females, none of these inherent differences seem to explain why females tend to be under-represented in intellectual circles, so I believe, as some others, that it has to do with society and culture.

Umm...I don't think we can use this substitution. This series is created by adding a base each time, and it can't be split in half that way along any exponent in the middle...i.e. (3^3)^(3^3) is not equivalent to 3^(3^(3^3)). But I myself am still iffy on using inf=inf-1...

O_o o_O You misread my statement, I never said probability is not having knowledge of probability, I said that probability is not having knowledge of complete results. Analyzing the result set is statistics.

No, we can't. The frequency with which an outcome occurs over time is related to the probability, i.e. the probability is a good predictor of that, but they are not the same, there's always some probability that the probability and the frequency of an outcome is different. The frequency with which an outcome occurs falls under statistics. Your discussion about chi-squared charts and statisticians and Large Numbers is true, but also falls under statistics. I think you have some good ideas and a lot of knowledge, but the fact is that you just cannot prove probabilities inductively from data sets, no matter how LARGE. You can estimate to a high level of confidence and a small error, but it still does not prove the probability is equal to that. And my PDEs were talking about electron wavefunctions ;P. Edit: Probability talks about the chance of something occurring, meaning that there are different possible outcomes and you don't know which one it is. After the data set is known, the probabilities all become 0 or 1, you know what occurred and what didn't occur, there's no chance for it to be any different, and then you use the frequency of occurrence instead of the probability. I tried (unsuccessfully) to bring in the example of the collapse of the wavefunction because I think it demonstrates this fact the best. A complex wavefunction collapses into a delta function once the event is observed, i.e. the result is known, and gives no information about the actual wavefunction.

I've been reminiscing about the past, and I remember one incident that had a huge impact on me: I used to do math contests, where you went in and took a test and then they had an awards ceremony where they called the top ten on stage and then gave out the awards from starting from 10th place. I'd always be fine when taking the test, but when it came time for the awards ceremony I'd get really really nervous, because I always felt like if I didn't do well, my parent's wouldn't love me... Anyways, since I was so nervous, I'd never pay attention to the other contestants, I'd always be focused on listening to the announcer call out the names. After one particular time (which I succeeded in attaining 1st place ), I was walking off-stage when this woman came up to me. She congratulated me and told me how nice it was to see a girl up there on stage and winning, and I realized that I had been the only girl in the top ten. I had never really thought about it before, but from then on out, I paid more attention, and I noticed the ratio was always in favor of guys. Where I went to college, the ratio was 2:1 guys to girls. Since I don't believe that guys are inherently smarter than girls, especially since scientist have not found any significant differences in the male/female brains that would suggest such, I wondered why it is that females are often under-represented in intellectual circles. (Here at BrainDen, however, we have definitely proven that girls can be just as smart as guys ;P) One of my theories is this: Society pressures females to put extra time and energy into superficial concerns and stresses, such as makeup, clothing, dieting, etc, which occupies their minds and makes it difficult to focus on larger issues and more intellectual problems, whereas males have much less of these stresses and can spend more of their thought ability and focus on thinking about intellectual problems. The fact that I've never really cared about said things may be what has given me an advantage compared to some of my fellow females ;P. I'm wondering what other BrainDenizens' takes on the issue are...