Prometheus

Thanks. I've handed this one in as I described so I'll just see how it goes for now.

In terms of the intuition, at the moment I just imagine the transform as a mapping onto another space because it is easier to perform certain operations in the space. Kind of like why we sometimes work in log space. I've seen a few books but they are all engineering books so they talk about quite specific mappings I'm not familiar with. Can you recommend any good non-engineering orientated books on the subject?

I managed to make some sense of it by letting [latex] g(s) = 1[/latex] in the first integral and playing around with the limits a bit.

Still, any intuition behind the convolution integral would be awesome.

If you're in the UK you could consider the Open University (one of those online/distance learning degrees John mentioned - in the UK it has a good reputation). For a physics degree you'd be paying £5000 a year instead of the £9000 a year at a bricks and mortar uni. You can also take on less modules per year there, allowing more time for you to work part-time.

I know some people who have given private tuition to senior high school kids in physics and maths - a good way to consolidate your knowledge too.

For part of a homework question I need to write:

[latex]

f(x,T)=\int_a^b G_{w^2}(x-s)ds

[/latex]

as a convolution integral, where:

[latex] G_{\sigma^2}(x) = (2{\pi}{\sigma^2})^\frac{-1}{2}e^\frac{-x^2}{2{\sigma^2}} [/latex]

So my understanding is that I need to express the above integral in the form:

[latex] \int_{-\infty}^{\infty} f(x-y)g(y)dy[/latex]

Is this the correct understanding? Also, is anyone able to give a little insight into these convolutions integrals - I find them very strange and do not understand them in the least.

Thanks to any and all help.

The ones who did die at the time of dying in their dreams aren't here to tell us about it.

If we're answering will dying in your dreams always cause real death, then based on the testimony here we can certainly say no. However, the question posed in the OP is can dying in your dreams cause death which is forever consigned to the realm of untestable hypotheses. However, given that there is no plausible biological mechanism (other than the fright given to someone with a 'weak heart', mentioned above, and even then I would rather attribute it to the weak heart than the dream) and the fact at least some have survived dream death lends more credence against the idea. So i wouldn't worry about it.

Really it is impossible to answer this question, because if someone dies in their sleep, you can't ask them if they were dreaming afterwards and what they were dreaming about.

 

But if someone dreams that they have died, then wakes up, we have evidence against the hypothesis. I have dreamt i have died several times. Include the fact that there is no plausible mechanism for death being induced by death in a dream, i would say don't worry about it.

Passion is just another predisposed (or cultivated at very early age) brain preference and can be viewed as part of the aptitude just like 'hard wire'. It is hard to conceive that one person is passionate at something that his brain rejects intellectually.

Keeping that passion up is what what makes a predisposed strength to shine. But it does not disprove that some predisposition is determinant.

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.

Can they?

 

He died more than 40 years ago...

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?

I can't see any objection to us killing animals. Animals kill each other all the time. Like lions killing wildebeests, and sperm whales killing giant squids.

These examples show that Nature is based on killing, So why should humans try to be aloof.

 

Killing is clearly natural. Shouldn't we just accept the fact. And stop pretentiously moralising about it.

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.

Maths is not a language. A language is something that expresses human communication, their expressions, what they want to say.. Anything that gives out numeric values and symbols as a result of an equation - therefore I would very vehemently say that maths is NOT a language.

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.

Perhaps the first thing to do in this case is look for falsifiability of the hypothesis. I can't think of a way to show that what you say isn't true, so this may never be scientifically testable.

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.

 

 

Does Buddhism not promote the concept of reincarnation where our spirits are reborn time and again on this planet? Is not the idea of life after death or spirits supernatural?

 

WHAT CAN BE MORE SUPERNATURAL THAN BEING BORN TIME AND AGAIN INTO DIFFERENT BODIES?

 

What about Karma? That is a popular part of Buddhist belief. If there is no deity then how is that supposed to operate exactly without some sort of mass consciousness or telepathy interactions?

 

The whole concept of Reincarnation should be enough to Satisfy INOW. We do not yet know if SwansonT will accept Buddhism as a religion qualified for this discussion.

 

Inow was kind enough to suggest Buddhism as a fine example so I have used that religion to show they had beliefs in meditation and mind over matter, telepathy, ESP, fortune telling, teleportation, remote viewing, and more.

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:

“The case provides evidence that the brain can adapt itself to a pathology that occurred earlier,” Dr. Feuillet told AFP. “Even if he has a slight intellectual handicap, this has not hampered his development of building social network,”

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.

Surely the simple statement "1" is the shortest possible, and considerably shorter than the shortest mathematical algorithm or calculation I can think of to generate a 1.

Whilst some would debate the null sequence can be a sequence or random, the sequence with just one term is perfectly admissible.

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.