Prometheus

Since neither of us has provided any evidence we are just exchanging opinions. I'm not sure there is sufficient evidence at the moment to quantify the claims we are making.

If true (citation?), does it support the premise? The difficulty would be in defining 'emotional', and then quantifying it. Are certain mental health conditions sufficient proxy for the nebulous question 'why are women so emotional?' On a side note, the question itself demonstrates a degree of sexism. Given women constitute half the human population the question, 'Why are men so unemotional?' is just as valid? I believe this sort of sexism is the more dangerous compared to Dekan's overt misogyny, for the latter is easy to recognise while the former is what helps forms low ceilings to the aspirations of women.

That there is variability isn't being contested, only why. Factors such as fetal conditions may well play a part, but i think the greater variability comes from passions and interests. My physical education teacher said it well; 'sports is about 5% talent and 95% hard work'. I believe it's the same for maths/physics, certainly it's the only factor i can control.

Yes, i see now where all the zeros are coming from, thanks. The only way i can get the last single eigenvaluev is to use the fact that the sum of the eigenvalues is equal to the trace of the matrix and since all the other eigenvalues are zero, the last eigenvalue must be n. I was looking at the eigenvectors too. Its obvious that one eigenvector will be a vector of ones, corresponding to the eigenvalue n. For the other eigenvalues i just choose any vectors that are mutually orthogonal since the matrix is real symmetric. Is that reasoning sound?

I found the eigenvalues of a 2x2 matrix with all elements equal to one to be 2 and 0. The eigenvalues of a 3x3 matrix with all elements equal to one to be 3,0,0. A 4x4 matrix to be 4,0,0,0 I stopped at a 5x5 matrix. I was just wondering (as i'm rubbish generalising things) whether this results holds for any size matrix. Also, are there any links were this is explored, i couldn't find any.

Would a mass posting of (ostensibly inoffensive, but who knows what offends people) cartoons of the prophet Mohammed, be an appropriate response or merely inflammatory? Respect to those who died exercising their right to free speech.

How does the fact someone died 40 years ago invalidate the argument that psychedelics can provide insight?

The above is nearly correct, just a small typo. The bit missing from my understanding was simply realising that [latex] K^TW_t = ||K||^2 [/latex] Now stuck on a related question. I now have [latex] e^{iK^TdW_t}[/latex], where [latex]dW_t[/latex] is an infinitesimal Brownian increment. I want to find the Taylor expansion of this - I would know how to proceed in the univariate case, but i don't understand the multivariate case. Does anyone have any hints or good links?

So i want to find the expectation of a geometric Brownian motion: [math]E[e^{K^TW_t}][/math] Where K is a constant vector and [math]W_t[/math] is a vector of normal Brownian motions, both of length n. I assume that as [math]K^TW_t[/math] is a scalar I can just proceed in a similar fashion as the univariate case to get: [math]e^{\frac{1}{2}K^TK}[/math] But is it that simple or am i missing something as i suspect? As always, help very much appreciated.

Wasn't there a recent film called War Horse in which many horses were killed, alongside many humans (inevitable i guess, trying to re-enact WW1)? Was it banned?

The reasoning being that what is natural is right? Isn't there a similar argument against homosexuality? If we accept the latter is fallacious why not the former? Not everyone enjoys the thought of killing, but i agree that it is a part of our evolutionary past. That does not mean we have to accept it as part of our future - we have the choice, and in this we are unlike our cousins in the animal kingdom.

What if what I want to say is that the ratio of a circles circumference to its diameter is a particular number? I could express this using English, as i just have, or maths. Same expression but one is a language and one is not? I don't understand why you would restrict a language to only communicating 'human expressions' - by which i take it you mean emotions?

Just reading Schrodinger's book Mind and Matter and came across a description of evolution which is meme theory in all but name (under a section called behaviour influences selection). I thought the theory germinated with Richard Dawkins, but it seems the idea has been in the background from some time before. Schrodinger mentions Julian Huxley as an influence in the book a few times, of whom I know very little, and I was just wondering whether Huxley also had similar ideas.

Further, with no way to distinguish between hypotheses the question becomes moot. This world, whether you call it real or virtual still behaves in the way we observe. It is easier to suppose this is the real world rather than postulate the existence of others.

Just want to clarify some points on Buddhism. Buddhism teaches rebirth not reincarnation, the difference being in rebirth there is no soul, spirit, or any 'self' which leaves one body and enters another. The idea there is no true 'self' is central in Buddhism. Quite what gets reborn is another question and not for here. Karma, doesn't have to have mystical allusions in Buddhism, even though it often does. Buddhists very often do believe in supernatural things, and certainly the Buddha also appeared to. But the Buddha taught that is not what is important in his teachings. I've got limited net access at the moment, but can provide links later if you like.

Ah, wait. Are we only considering a sequence with one term here?

Hydrocephalus is hardly the same as having no brain. The last paragraph in the link is quite telling:

Did a quick search and found two articles: one finding a correlation between supernatural beliefs and religiosity and one finding otherwise. Could only read the abstracts so no idea them really - hopefully someone has access.

OK, but still if you always calculate A to be a certain value it can be expressed more compactly than a complete list and so it's still not a random sequence. I don't understand the relevance of the other statement, please explain.

Religious texts are full of supernatural happenings: water to wine, talking cats and dogs, invisibility... the list is pretty long. Therefore they are associated. Science is neutral in the matter - it is the evidence which does not support the existence of gnomes and ghosts. There is no conundrum. Religious people continue to make supernatural claims. I cannot understand the obsession religious people have with trying to understand physical phenomena through mystical hand-waving. We have a very good method of understanding such things which demonstrably works. One would think this would make religious people happy, for no longer do we have to worry about such physical questions, but can rather focus on the important questions such as how to be a better and happier person. Unfortunately religion cannot let go of its historical burdens and so has become a bane to humanity when it might have been a boon.

But if you always calculate A to be a certain value it can be expressed more compactly than a complete list, i.e. it's always one or it's always zero. Therefore it's not a random sequence, so it will be predeterminate.

Yes. Then asking what the probability is for exactly x=0 is meaningless in this context, and so should satisfy the OP. I was wondering about this problem though: I agree with Function that there is more chance of someone selecting 2 than of them selecting some irrational number. My initial thought was that we are not actually dealing with a continuous distribution, but a large discrete one. If someone states a number, they are not selecting from an infinite set - people would select from quite a narrow set (i imagine), and even if they tried to pick an irrational number, they couldn't - physically stating it would prove prohibitive. Then i considered the case where people are given a line measured 1 to 10 in some way and asked to pick a point. We could then consider it continuous, but the limits of precision in measuring that point would provide intervals to give a meaningful probability. Then haven't we in some way made the case discrete, each sample element some interval on a continuous scale?

Thanks for clarifying. I use the books Probability and Measure by Billingsley and A First Look at Rigorous Probability Theory by Rosenthal. So how do we interpret the OP in light of the above discussion? Let's take two continuous probability distribution functions: the normal and the uniform. This is the best image i could easily find, we want the pink and grey curves (U and N), ignore the rest. For small intervals around x=0 there is more chance that an outcome from the normal distribution would occur, but the chances of x=0 is zero, and so the same, for both distributions. Why? Because [latex]\int_a^a f(x)dx=0[/latex]. I still can't help feeling this is where the problem lies, and the chance /probability definitions are a red herring.

I've searched through my probability texts. In one the only time the word chance is used is when referring to gambling probability problems. In another it is used in several different ways one similar to how you have used it. Is there a firm consensus to how the words are used in scientific English?

Damn you go to a good school if you learn this at high school. By 'psychological chance' do you mean your personal degree of belief that it will land on a specific point? If so we are getting onto Bayesian probabilities (not my forte), which it sounds like you know about. But Bayesian probability is just as rigorous as traditional probability, they come from the same axioms, so the answer is the same. I've not read around the subject but my lecturer made a distinction between 'subjective' Bayesian stats and 'empirical' Bayesian stats. The former involves probabilities plucked from thin air, while the latter tries to justify why a particular probability was picked. So I would say it is still mathematics, but the end of mathematics that tries to meet with the real world. Physicists probably do this best - maybe one would like to comment.