Good catch. That one is just a bit too obvious - a single, total "I'm a douchebag" post just to provide support for a frankly disproved argument through a single anecdote.
If games are available cheap and fast, no-one would bother pirating outside a few groups trying to demonstrate their skills. Remove DRM and there would be no point for anyone - I'd happily pay for a game that I can download quickly, play right away and wherever I am. Hell, the only thing that annoys me about Steam is that I can't play my games offline so easily (waiting in airports etc - I know that people complain about not selling used games, but I've never really felt the need. I'm sure it's annoying for people who do, though).
Actually, EFE have nothing to do with quantum physics - they're purely classical. Schrodinger/Heisenberg is where you want to really look for quantum physics (or the photoelectric effect, also an Einstein thing but nothing to do with the field equations).
That's not to say that EFE aren't awesome - they gave us the tools we needed for GPS etc, and tons of insight into cosmology, but technologically speaking we wouldn't be far behind if we still had a Minkowski space + Quantum Field Theory version of physics right now.
Totally with you in spirit, there definitely IS something there that we don't know about, and examining it is the first step towards developing something out of it. I just wish people would give us the money to look at it from all angles.
Could you cite a source for those numbers? I'm curious as to how they were measured, and what counted as a death caused for power generation (eg Miners for coal, also road/rail deaths in transport? Deaths from pollution? etc etc)
Where you've assumed constant acceleration throughout? And at the end of that time the car would be going 155mph - I highly doubt that acceleration is anything like constant from 0-60 and it certainly won't be at higher velocities, as drag is proportion at v^2. If it were, you could have one of these babies hit light speed in about a year and a half...
So I've both taken GR as an undergrad/grad student, and now taught it to both. My undergrad was in math, grad school physics. To understand modern GR (singularity theorems, black holes, cosmology, lensing effects etc) from a math background the subjects that really help are:
1) Special Relativity. This is an easier intro that really comes out of the end of electrodynamics courses (ie, why there's that pesky 'c' in Maxwell's equations that doesn't seem Gallilean invariant). There are outstanding lecture notes available from, say, oxford university on both SR and GR - see www.maths.ox.ac.uk and go to lecture notes for undergraduates and dig around a bit.
2) Differential Geometry. I started out with 2D shapes in 3D spaces (Geometry of surfaces) which actually taught me all I need to know about how the idea of a metric is formed etc. Then I moved on to general differential geometry (book: Differential Maniforlds by Hitchin: http://people.maths.ox.ac.uk/hitchin/hitchinnotes/hitchinnotes.html) . If you can wrap your head around Riemannian geometry, moving over to the Lorentzian case isn't too hard.
Anything you can get your hands on to do with tensors will help a LOT, as all modern interpretations are based on the abstract index notation which is written in tensors.
For learning GR itself, the standard book is Wald's General Relativity. Carrol's book is pretty good too, but Wald seems to be the one that just about everyone I know cuts their teeth on.
I found GR a hell of a leap from everything I'd understood so far, so I took a long, long time reading through notes again and again until I understood the ideas behind things like connections, covariant derivatives, tensors, Christoffel symbols etc. Don't expect to learn it quickly or easily like most concepts in statistics, but rather be prepared for it to take a long time. As you probably know by now, maths is a participation sport, so really flex those muscles by working through any examples/problems you can get your hands on - that was really what made concepts sink in for me.
Let me know if I've assumed too much background (to get to these you need prerequisites like topology, analysis, euclidean geometry etc). But I'm assuming that you want to understand the modern mathematical background of curved space-times rather than just the general philosophy (if so, as someone else suggested Einstein's original book on the special and general theories is a delight to read).
Tuition was included, otherwise I wouldn't have been able to afford it - I worked in physics, so tuition was really just a few classes in my first two years, and supervision of my dissertation. The 'support' provided was really just office space, access to libraries, computers etc with one member of tech support staff and a vastly over-worked department secretary.
Now, I'm sure all these things add up, but when you consider that there were four of us per (tiny) office, and around twenty shared the computer resources, secretary etc, it seems like an incredible amount of money for 'overhead'.
University overheads are ridiculous. As a grad student I made about 24K, though with fellowships in the last couple of years this got into the low 30s. However, the cost to my research adviser from his grant to support me was more like 65-70k. This is because the university charges an outrageous amount of money for the support services they provide, and it's pretty much the same everywhere from what I've seen. The rule of thumb is that the salary is about 40% of the cost of a grad student.
The WWI solution was indeed that deaths were reduced - I just thought the parallel interesting. Your solution about safety in numbers though, does indeed seem plausible.
It's not being a self entitled asshole to ask that IT do their job so that I can do mine. My job brings money into the company, and that is what keeps us all in business. We don't make money by having a little walled garden network which isn't any good - we make money by selling our products to other people. The asshole is the person who wants to rule his own little kingdom and in doing so inhibits the core function of the business - to make money.
You've lost an understanding of what your job is: You job is to help ME bring in money. So do that. Not make a pretty network that no-one can use, but provide the services that help me bring in money. Otherwise you're not worth having.
The problem with big bang/big crunch is that really what we're saying is the physical equivalent of "Here there be dragons". We simply don't know what physics looks like at the Planck scale yet. Big bang/crunch are what happens if we trust GR way into the regime where we expect quantum gravity effects to be strong.
Now there are various ideas about how a collapsing universe can transition into an expanding one - conformal cyclic cosmology, loop quantum cosmology, etc etc, and certainly within at least one of them (LQC) the connection - a bounce - would be survivable to a well built probe - see http://arxiv.org/abs/0901.2750 for example.
However, I must stress that we have no data anywhere near the Planck scale, so we cannot yet test any of these models. The best we can do is look at things like the cosmic microwave background and try to see if there are any artifacts of quantum gravity there, but so far nothing is proven.
String theory != cosmology. There's string cosmology, sure, examining the cosmological implications of string theory, but standard GR based cosmology has been tested - see WMAP, COBE, predictions of the cosmic microwave background.
In fact, XCKD based their entire "It works bitches" http://xkcd.com/54/ on the predictions of standard cosmology.
No, you really don't need quantum mechanics or GR to get to space, or even the moon. Newtonian physics is good enough to get you there, and in fact all the calculations done by NASA completely neglected relativistic effects.
Without GR you would be struggling to explain the perihelion advance of Mercury still, and you wouldn't have very accurate GPS devices, but you certainly would be able to hit the moon, or anywhere within our solar system with enough accuracy to get a rocket there.
Nope, you're born aged 0 and that's when you start your first decade. After 10 years (1 decade) you are 10 years old and starting your second decade. Etc.
You're missing out a couple of vital steps in your logic here: From someone who's done it, it goes more like this:
University administrators: We've signed up 4000 students for intro courses in physics this semester. We need qualified teachers and lab assistants, but are only willing to pay less than minimum wage, an amount for which we can't find any Americans with the qualifications willing to work.
So: Let's bring over the best and brightest the world has to offer. We'll pay them a pittance and claim that 'tuition' in the form of being told to do all our teaching duties and given all the grunt work of research with little to no guidance is part of their remittance. We'll not spend this money on an American because we could only afford one tenth of the qualified people we need if we did that.
Then, we'll kick the best and brightest and make them get a new visa to work here so that we can force them to keep working or their visa becomes invalid. Hence we can pay them less for their qualifications, and they have no job security.
Slashdot Mirror
Good catch. That one is just a bit too obvious - a single, total "I'm a douchebag" post just to provide support for a frankly disproved argument through a single anecdote.
If games are available cheap and fast, no-one would bother pirating outside a few groups trying to demonstrate their skills. Remove DRM and there would be no point for anyone - I'd happily pay for a game that I can download quickly, play right away and wherever I am. Hell, the only thing that annoys me about Steam is that I can't play my games offline so easily (waiting in airports etc - I know that people complain about not selling used games, but I've never really felt the need. I'm sure it's annoying for people who do, though).
One in a billion? Holy shit, there should be 7 Batmen running around now!
A quick google gave me this. God speed, good sir!
http://www.justinbieberzone.com/where-is-justin-bieber-right-now/
You wouldn't happen to know where I can find a concrete mixer, would you?
Actually, EFE have nothing to do with quantum physics - they're purely classical. Schrodinger/Heisenberg is where you want to really look for quantum physics (or the photoelectric effect, also an Einstein thing but nothing to do with the field equations).
That's not to say that EFE aren't awesome - they gave us the tools we needed for GPS etc, and tons of insight into cosmology, but technologically speaking we wouldn't be far behind if we still had a Minkowski space + Quantum Field Theory version of physics right now.
Totally with you in spirit, there definitely IS something there that we don't know about, and examining it is the first step towards developing something out of it. I just wish people would give us the money to look at it from all angles.
Could you cite a source for those numbers? I'm curious as to how they were measured, and what counted as a death caused for power generation (eg Miners for coal, also road/rail deaths in transport? Deaths from pollution? etc etc)
Where you've assumed constant acceleration throughout? And at the end of that time the car would be going 155mph - I highly doubt that acceleration is anything like constant from 0-60 and it certainly won't be at higher velocities, as drag is proportion at v^2. If it were, you could have one of these babies hit light speed in about a year and a half...
And that's presuming that there are no repeats - I'd wager there are people who object to more than one book at a time...
As a bonus, starting with The Sun and decreasing in quality helps people to learn about negative numbers...
So the backpacks are full of ropes and extra toys? That explains a lot, actually.
That I'd be willing to try. But I think joining the Boy Scouts at the same time would prove a bigger challenge ;-)
That's a LOT of things to do all at once...
A wall around the whole of China is 'viable'?
We've done big projects before...
So I've both taken GR as an undergrad/grad student, and now taught it to both. My undergrad was in math, grad school physics. To understand modern GR (singularity theorems, black holes, cosmology, lensing effects etc) from a math background the subjects that really help are:
1) Special Relativity. This is an easier intro that really comes out of the end of electrodynamics courses (ie, why there's that pesky 'c' in Maxwell's equations that doesn't seem Gallilean invariant). There are outstanding lecture notes available from, say, oxford university on both SR and GR - see www.maths.ox.ac.uk and go to lecture notes for undergraduates and dig around a bit.
2) Differential Geometry. I started out with 2D shapes in 3D spaces (Geometry of surfaces) which actually taught me all I need to know about how the idea of a metric is formed etc. Then I moved on to general differential geometry (book: Differential Maniforlds by Hitchin: http://people.maths.ox.ac.uk/hitchin/hitchinnotes/hitchinnotes.html) . If you can wrap your head around Riemannian geometry, moving over to the Lorentzian case isn't too hard.
Anything you can get your hands on to do with tensors will help a LOT, as all modern interpretations are based on the abstract index notation which is written in tensors.
For learning GR itself, the standard book is Wald's General Relativity. Carrol's book is pretty good too, but Wald seems to be the one that just about everyone I know cuts their teeth on.
I found GR a hell of a leap from everything I'd understood so far, so I took a long, long time reading through notes again and again until I understood the ideas behind things like connections, covariant derivatives, tensors, Christoffel symbols etc. Don't expect to learn it quickly or easily like most concepts in statistics, but rather be prepared for it to take a long time. As you probably know by now, maths is a participation sport, so really flex those muscles by working through any examples/problems you can get your hands on - that was really what made concepts sink in for me.
Let me know if I've assumed too much background (to get to these you need prerequisites like topology, analysis, euclidean geometry etc). But I'm assuming that you want to understand the modern mathematical background of curved space-times rather than just the general philosophy (if so, as someone else suggested Einstein's original book on the special and general theories is a delight to read).
Tuition was included, otherwise I wouldn't have been able to afford it - I worked in physics, so tuition was really just a few classes in my first two years, and supervision of my dissertation. The 'support' provided was really just office space, access to libraries, computers etc with one member of tech support staff and a vastly over-worked department secretary.
Now, I'm sure all these things add up, but when you consider that there were four of us per (tiny) office, and around twenty shared the computer resources, secretary etc, it seems like an incredible amount of money for 'overhead'.
University overheads are ridiculous. As a grad student I made about 24K, though with fellowships in the last couple of years this got into the low 30s. However, the cost to my research adviser from his grant to support me was more like 65-70k. This is because the university charges an outrageous amount of money for the support services they provide, and it's pretty much the same everywhere from what I've seen. The rule of thumb is that the salary is about 40% of the cost of a grad student.
The WWI solution was indeed that deaths were reduced - I just thought the parallel interesting. Your solution about safety in numbers though, does indeed seem plausible.
This reminds me of a question about helmets in the first world war:
http://www.geom.uiuc.edu/~lori/mathed/problems/sloanA307.html
Perhaps the solution is similar...
It's not being a self entitled asshole to ask that IT do their job so that I can do mine. My job brings money into the company, and that is what keeps us all in business. We don't make money by having a little walled garden network which isn't any good - we make money by selling our products to other people. The asshole is the person who wants to rule his own little kingdom and in doing so inhibits the core function of the business - to make money.
You've lost an understanding of what your job is: You job is to help ME bring in money. So do that. Not make a pretty network that no-one can use, but provide the services that help me bring in money. Otherwise you're not worth having.
The problem with big bang/big crunch is that really what we're saying is the physical equivalent of "Here there be dragons". We simply don't know what physics looks like at the Planck scale yet. Big bang/crunch are what happens if we trust GR way into the regime where we expect quantum gravity effects to be strong.
Now there are various ideas about how a collapsing universe can transition into an expanding one - conformal cyclic cosmology, loop quantum cosmology, etc etc, and certainly within at least one of them (LQC) the connection - a bounce - would be survivable to a well built probe - see http://arxiv.org/abs/0901.2750 for example.
However, I must stress that we have no data anywhere near the Planck scale, so we cannot yet test any of these models. The best we can do is look at things like the cosmic microwave background and try to see if there are any artifacts of quantum gravity there, but so far nothing is proven.
String theory != cosmology. There's string cosmology, sure, examining the cosmological implications of string theory, but standard GR based cosmology has been tested - see WMAP, COBE, predictions of the cosmic microwave background.
In fact, XCKD based their entire "It works bitches" http://xkcd.com/54/ on the predictions of standard cosmology.
No, you really don't need quantum mechanics or GR to get to space, or even the moon. Newtonian physics is good enough to get you there, and in fact all the calculations done by NASA completely neglected relativistic effects.
Without GR you would be struggling to explain the perihelion advance of Mercury still, and you wouldn't have very accurate GPS devices, but you certainly would be able to hit the moon, or anywhere within our solar system with enough accuracy to get a rocket there.
Nope, you're born aged 0 and that's when you start your first decade. After 10 years (1 decade) you are 10 years old and starting your second decade. Etc.
You're missing out a couple of vital steps in your logic here: From someone who's done it, it goes more like this:
University administrators: We've signed up 4000 students for intro courses in physics this semester. We need qualified teachers and lab assistants, but are only willing to pay less than minimum wage, an amount for which we can't find any Americans with the qualifications willing to work.
So: Let's bring over the best and brightest the world has to offer. We'll pay them a pittance and claim that 'tuition' in the form of being told to do all our teaching duties and given all the grunt work of research with little to no guidance is part of their remittance. We'll not spend this money on an American because we could only afford one tenth of the qualified people we need if we did that.
Then, we'll kick the best and brightest and make them get a new visa to work here so that we can force them to keep working or their visa becomes invalid. Hence we can pay them less for their qualifications, and they have no job security.
I dunno, in my late teens I had way more guys hit on me than girls - being gay would have been a plus back then...