Her work isn't an area I know a lot about, but I know that using gravitational lensing to measure dark matter distribution is an important technique in astronomy these days.
I use to love reading popular science books, but the trouble is that the more you learn about a subject the less interesting the popular science books are. You start wanting books that are more detailed.
@xcodeking When you say write an integral as a power series isn't this just Taylor expanding the function you're trying to integrate, then doing a term by term integration on the power series?
@JingleBells Do you really think the value of everything one works out is decided by how much money it is paid? I never think money has its intrinsic value. When I was in undergraduate ethic course group discussion, an issue is like donating money to poor people to see a doctor, I just argued:" why not ask the doctor to be kind in not charging money from poor people?"
@xcodeking so the problem is simply how you can take a power series and write in a closed form.
And I think in general you can't i.e. there are only a small subset of power series that correspond to a function that can be written in a closed form.
@JingleBells I don't understand the raising campaigns are everywhere for dementia, poor children lacking food. Just ask the doctors specializing in dementia and food manufacture to exempt from charging money from these poor people is a good solution, I think.
@JohnRennie or if these workers really like money so much, just ask the government to print more billnotes to those poor people.
In the UK everyone who has an income pays a small percentage of that income to support doctors who treat people for free i.e. we pay tax to fund the NHS. This seems an excellent thing to me.
Charities ask people to voluntarily give a little extra so the NHS can be supported even more, and I see nothing wrong with this.
I think doctors are generally far wealthier than a lot of people, if they lack money from treating poor patients, they wouldn't have much economical problems.
our Chinese government is very strange in asking everyone to have compulsory health insurance whether one has adequate income or saving or not.
Doctors are well paid but not among the top earners - in the UK at least - and they work very hard for their money. I don't begrudge doctors their salaries. It isn't a job I would want to do. I certainly wouldn't ask them to treat people at their own expense.
when I was in my MSc school, the stipend I got was barely enough to pay for basic living and tuition, but the government charged me for the premium for the compulsory health insurance.
The reason governments require everyone to have health insurance is that it isn't considered humane to watch other people die just because they can't afford to be treated. Well, in most countries it isn't.
The UK doesn't use the health insurance model, but I believe it is quite widely used. I don't know how it works in China.
@JohnRennie really? In my impression, doctors are one of the most wealthiest professions in this world. When I was a child, adults told me doctors are the most wealthy and admirable.
My aunt was a pediatrician and his home was very wealthy and even hired maid, who cooked very delicious dishes every meal.
I think top surgeons in the UK earn less than £100K/year though that's from memory and I would have to check to be sure of that. Most directors of big companies earn more than that.
The National Health Service (NHS) is the umbrella term for the publicly-funded healthcare systems of the United Kingdom (UK). Since 1948 they have been funded out of general taxation. There are four systems, one for each of the four countries of the UK: The NHS in England, NHS Scotland, NHS Wales and Health and Social Care in Northern Ireland. They were established together in 1948 as one of the major social reforms following the Second World War. The founding principles were that services should be comprehensive, universal and free at the point of delivery—a health service based on clinical need...
One of the very few things of which the UK can be proud.
@JohnRennie In india if you can have a government medical college seat which is filled by a exam like Jee called neet
You get free education plus+you will called as resident doctor
With some pay
Around 30 thousand per month which 2000 US dollar
But in case you have not got a chance in medical college you will have to pay million of rupees for a year ,which is what a private college fees which so expensive that even upper middle class cannot afford
in my observation, doctors are very wealthy and have a lot of free time unless they are research physicians and those medical professionals who are really heavily loaded by works and have very low salary are nurses.
@JackRod the problem in India is that there are far more students wanting college places than there are places, and you need some way of filtering them. In a perfect world there would be a place for every student who wanted one.
The problem is that providing so many places is too expensive for any government to afford. In the UK there is a place for any student who wants one, but you gave to pay £9K/year for a university place.
@JackRod exams are an easy way to filter students ...
there are too many universities here for too few students, so almost everyone here can go to university; the problem is whether one can afford to pay tuition and whether there are research fields one is interested in working in.
but we have international graduate student program providing high stipends compared to other PhD programs; this program attracts a lot of Indians to come here to study.
but international graduate student program only has application-oriented research fields, none of which interests me.
Folks, say I've got an optical grating. It will disperse light into the spectrum, and it will create several orders. How is the total light energy distributed between the orders? Say, the incoming light is white, if that simplifies things.
I even don't quite know the educational system in medical department. Not until I went to see a doctor earlier this year did I found doctors are distinguished into generalists and specialists, and generalists seem to generally only have BSc but I still don't know whether specialists have MSc or PhD.
it differs greatly from physics department - physics graduate with only BSc can't almost find a job as a physicist.
sorry, in the above, I meant my uncle, Father's brother, not my aunt.
For a grating with infinitely thin slits the intensity is independent of the angle of diffraction. For real gratings with non-zero slit width the intensity falls in a sinc function.
@JohnRennie the government here actually only imposes compulsory health insurance to people who are affiliated with most organizations who adequately pay them to work, because the organization extracts a small part of the salary to pay the premium of the health insurance even before it issues the salary to the worker. For people who are not affiliate with any organization, they can actually choose to have health insurance or not though the government stipulates everyone to have health insurance.
I Googled healthcare in China and I'm surprised to see most people use private healthcare. I would have guessed a notionally communist state would have something like an NHS.
@JohnRennie The government may send a letter to your home if they find you don't have the national health insurance, but if you still don't insure, they send a follow-up letter again, and if you still don't insure, they send again, and again and again, until finally they stop probably because they forget or get tired. But if you don't have national health insurance, you need to pay on your own to see a doctor, so the government doesn't actually execute (compulsory) national health insurance.
People who are unaffiliated with any organization and don't pay to the health insurance on their own may still not afford to see a doctor.
I am not sure if all universities pay the premium of health insurance for graduate students now because the stipends of a lot of graduate students are very low and some of them are even not paid.
and national health insurance may not be useful for everyone because it doesn't cover all medical expenses one needs.
Often when we solve an equation we do a Fourier transform. Then we often end up with an equation for every $k$, and these equations are decoupled. Why are not the equations for distinct $k$'s coupled? Does the initial equation have to be linear or is it something else?
@B.Brekke The Fourier transform turns differentiation into multiplication - if your initial PDE contains differentiation w.r.t. a variable $x$ but no multiplication, you can therefore reduce the number of different partial derivatives by one by Fourier transforming that variable
that's what we do e.g. in the wave equation - we Fourier transform the spatial parts so that the equation is essentially turned into an eigenvalue equation for the remaining time derivative
When people say that photon is an excitation of the field, do they necessarily mean that it is an excitation of a plane wave mode, ie an eigenstate of the Hamiltonian with eigenvalue $1\hbar\omega$? Or can it mean any mode, as long as it is an eigenstate of the number operator with eigenvalue 1?
In principle you can write the field as a sum of any states you want, but we would normally write it as a sum of momentum eigenstates because that's how we think of particles and we want our states to correspond to particles.
Yes. If I make an analogous “wavepacket creation operator” by a linear combination of old creation operators, then operating that on the vacuum should look like a wavepacket that’s created. Right?
@skullpatrol now do one with additionally a) the proclaimed climate goals (e.g. Paris agreement, Kyoto protocol and predecessors) and b) the reductions necessary to meet various maximal increases in temperature
@skullpatrol No. Germany is currently shutting down all of its nuclear power plants – including the best nuclear power plants in the world. Therefore, the CO2 curves will go up again.
what I'm saying is all these "look how much we've done" emission reduction graphs are meaningless unless you place something on it that tells you how bad (or good) that still is compared to meaningful targets
@Charlie It's odd how the "MP3 player" was a pretty large phenomenon where everyone wanted one and now you don't see them anymore at all because everyone just uses their smartphone.
If we consider a quadratic Hamiltonian of two canonically conjugate variables, is it guaranteed that eigenstates when represented in one of the variables will be a Gaussian times an appropriate Hermite polynomial in that variable?
@SuperfastJellyfish then the answer is yes - it's the same Hamiltonian after all, just with different variables in it which doesn't change anything about how you solve the TISE for it
@abhas_RewCie I don't think they're parsing what you type here into chats. I'm guessing you've looked at or at least searched for the iPad you want to get recently?
Also, the ads aren't "Twitter" - ad providers are typically separate entities from the platforms serving the ads, and will track you with various methods across all sites you visit where they can do so
@abhas_RewCie On the pages where you see ads, probably. The ad networks fingerprint your browser with various methods and can essentially track you across all sites where you've loaded an ad from that network
Okay, few hours ago, I searched and compared prices of iPad on Phone on Flipcart, (my Phone and PC both have same accounts opened), so, probably, that's why they are showing up in my PC too....
and most data you enter on the internet isn't "safe", and never has been. The moment you send anything in plain text (or only weakly encrypted) over the net, it can be read by someone determined enough
"safe" always is relative to what sort of threat you're trying to defend against - small-time scammers? multinational corporations? state secret sercvices?
@JohnRennie the more common word for moon is selene, but yes, the classical pronounciation is pretty certain - the 'e' sounds like the 'e' in English RP 'bed', 'm' and 'n' are just like you'd expect.
the classical accent was likely a pitch accent, so you'd have to speak the first syllable with a rising tone
(note that not all Greek 'e' are like this long 'e' - this is $\eta$ in Greek, but we transcribe $\epsilon$ also with 'e')
@bolbteppa there's plenty of scholarly difference over the finer points for sure, and there were different periods (e.g. Old Latin, Classical Latin, Vulgar Latin) where pronunciation shifted
but actually our understanding of Latin and Greek pronounciation is pretty comparatively good for both languages being dead because there's many texts of speakers of one Language transcribing words from the other in their alphabet
@abhas_RewCie a bachelor's degree is a bachelor's degree in some specific field, no one cares "of what" it formally is. Some universities give out BAs in math, others BScs in math, for example
@JackRod I first heard of him when The Elegant Universe came out. I read it when it was released and I thought it was very good as popular science books go.
The algebraic approach to spinors finally clicked I think. In four-dimensions for example, a Dirac spinor is a four-component column vector \begin{align} \begin{split} \Psi(x) = \begin{bmatrix} \Psi_1(x) \\ \Psi_2(x) \\ \Psi_3(x) \\ \Psi_4(x) \end{bmatrix} \end{split} \end{align} If we view this as the first column of a $4 \times 4$ matrix \begin{align} \begin{split} \Psi(x) = \begin{bmatrix} \Psi_1(x) & 0 & 0 & 0 \\ \Psi_2(x) & 0 & 0 & 0 \\ \Psi_3(x) & 0 & 0 & 0 \\ \Psi_4(x) & 0 & 0 & 0 \end{bmatrix}
Furthermore, since any $4 \times 4$ matrix can be expressed as a linear combination of the $4 \times 4 = 16$ Clifford algebra basis elements $\{I,\gamma_{\mu},\sigma_{\mu \nu},\gamma_5,\gamma_5 \gamma_{\mu} \}$ we can equivalently define a spinor as a minimal left-ideal in the Clifford algebra generated by the $\gamma^{\mu}$'s.
In general relativity, Schwarzschild geodesics describe the motion of particles of infinitesimal mass in the gravitational field of a central fixed mass
M
{\textstyle M}
. Schwarzschild geodesics have been pivotal in the validation of Einstein's theory of general relativity. For example, they provide accurate predictions of the anomalous precession of the planets in the Solar System, and of the deflection of light by gravity.
Schwarzschild geodesics pertain only to the motion of particles of infinitesimal mass
m...
Hello all and John Rennie. I have one question about vector (magnitude) in rotating 2D non-orthogonal coordinatie system could be different axes ratio.
I thought vector magnitude is independent of choice of coordinate system. But i have seen vector magnitude is changing when rotating orthogonal coordinate have different axes ratio let say 1:2.
Also in skew coordinate system any axes ratio change the magnitude of vector when rotating the coordinate system. Any reason and physical significance of changing vector magnitude in these cases. It should be independent of axes choosen.
A vector will have the same magnitude only for those linear transformations which preserve the value of the inner product $\mathbf{v} \cdot \mathbf{v}$, e.g. in 3D a rotation of the coordinate system will do this. In general a linear map can alter the value of the inner product. For example a map projecting a given vector onto a vector pointing along one of the coordinate axes will in general produce a vector having a different magnitude than the original vector, it's just a projection.