It's sad to say that the destruction of the WTC was prossibly the single most important thing that finally forced the IRA to really join the peace process. Suddenly Americans discovered that terrorism isn't something that happens in funny countries and can be ignored, or even funded and the IRA almost certainly saw a big reduction in funds coming in.
No - photons cannot account for the "missing mass". It's called "dark matter" because we know that it (whatever it is) does not interact with the electromagnetic force.
Indirectly, we can experimentally confirm that photons have a rest mass of zero from the fact that unless EM is exactly inverse square then there would be an electric field inside a hollow conductor. (proving this is relatively straight forward for a perfect sphere - I understand that it can be proved for a general closed conductor but that's maths far beyond what I'm capable of)
Basically it's a galvanometer connected between an isolated conductor that is inside a closed conductor and the closed conductor. The conductor is then driven with a few kV at the resonant frequency of the galvanometer. Any deflection at all would indicate that EM isn't exactly inverse square and one possible explanation would be that photons do not propogate at c.
However, any result like this would be so disruptive to all known physics that pretty much every physicist would assume that there was a fault with the experiment.
So, there is no magical disappearing of time or events or 4D cloaking of spacetime.
It's slightly more subtle than that. IIUC, it's impossible to detect something happening in the cloaked region of space. So in the chicken crossing the road scenario, to an outside observer, it looks like the cars travel at a constant speed and the chicken "magically" teleports from one side of the road to the other.
The idea that something is in one state or another without being able to detect intermediate states is not new to physics. If you attempt to "watch" the transition between two eigenstates you will always measure one state or the other. We can have a mathematical model of how the wave function evolves, we can do experiments that demonstrate that the wavefunction must have been in a state that our mathematical model describes as a superposition of eigenfunctions, but we can never measure that superposition.
In QM terms, I suppose the chicken would be described as "tunneling across the road"
(note that I have no reason to suppose there is any relationship between 4d cloaking and QM tunneling - it's merely an analogy that came to mind)
I can't speak for people from a hypothetical universe and about what their naming conventions would be, but I can tell you that, given the known laws, the "anti-matter" universe would behave in exactly the same way as ours does.
No, this isn't true (unless time also runs backwards in the anti-matter universe).
Neutral Kaon decay violates CP - You can distinguish K0 decay in our universe from the anti-K0 decay in an antimatter universe.
It is conjectured that CPT symmetry does hold (therefore CP violation implies T violation)
No, I'm afraid there is no "get a loan" scenario that can beat simply saving money at approximately the payment rate, if you simply use your wits.
This didn't work when house price inflation was rampant. Despite my salary increasing by substantially more than inflation (compounded) it's only been in the last four years or so I would have been able to buy with a mortgage the properties I own outright because house prices rose so much faster than inflation.
I, of course, used my above inflation salary increases over the years to pay off my mortgages.
Borrowing money to buy my second car was also a good move. The reduction in fuel and maintenance charges more than paid the interest on the loan (in fact the reduction paid the interest plus the repayments so for three years I saw no net cash flow change and then on year four I had an extra 190GBP/month). At that time in my life there is no way I could have saved enough money to buy the car outright when I needed it. I was never desperately short of money but for the first three or four years of working life I was definitely not flush with cash.
The only negative impact from a helmet is on hearing
Drivers pass helmeted cyclists closer than unhelmeted cyclists.
I'm very glad that I wasn't wearing a helmet when I was hit by a car wing mirror passing me at 60+ mph. Couple of inches closer and instead of an impressive bruise on my arm I'd probably be dead.
Actually, as I understand, scientific research shows that wearing a helmet has a tremendous benefit in prevent the sorts of injuries that leave people brain damaged for the rest of their lives.
Case controlled studies showed that HRT reduced coronary heart disease. It is now recognized that HRT increases the risks of coronary heart disease.
Case controlled studies have shown that cycle helmets reduce head injury rate. Whole population studies have failed to show any benefit whatsoever.
What the Nyquist theorem misses is that the mind is not just taking a single sample, but a time series of many samples. A good listener or an observant viewer can see qualitative differences in a square wave and a smoother sine wave, even near the limits of resolution.
No. This fundamentally misunderstands the Nyquist theorem.
If you low pass filter a signal and then sample it at at least twice the frequency of the highest frequency passed by the low pass filter then you can _exactly_ reconstruct the original low pass filtered signal by low pass filtering the digital signal generated from the samples.
Of course, CDs do not permit storing the samples at infinite precision so the theoretically perfect reconstruction does not occur but that's not due to the finite sampling frequency and the ear just isn't sensitive enough to changes in amplitude for the quantization of the samples to matter in normal circumstances.
Higher sampling frequencies allow the low pass filtering to be moved into the digital domain. Ideally we want a brick wall low pass filter but building a filter like this in the analogue domain is hard. Simple filters with a nice flat pass band have a relatively gentle 6 or 12dB/octave cutoff. Simple filters with a sharp cutoff introduce lots of non-linearity in the pass band.
It's the UK rather than the US but this really can happen. (And the rules are changing every year so you have to keep on the ball to avoid unnecessarily getting caught by these things)
Salary 149999. Pension contribution of 50000. Tax rate 40% (we'll assume that the tax rate applies across the whole band because this doesn't affect the calculations)
Tax is paid on 99999 @ 40% = 39999 (it rounds down) giving 50000 in the pension and 60000 in your pocket.
Salary 150001. Pension contribution of 50000. Tax rate 40% as before.
Because salary >150000 only the first 20000 of pension contribution attract 40% relief, the rest attracts 20% relief
Tax is paid on 100001@40% plus 20% on 30000 (the excess over 20000 paid into the pension) = 46000 giving 50000 in the pension and 54001 in your pocket.
So you earn 2GBP more but end up 6000 poorer.
(In fact, someone earning 150001 can "sneak" under the barrier by making a charitable donation. A 2GBP donation would get you under this years threshold)
Tim.
p.s. For anyone in the UK actually affected by this - the calculations above leave out a lot of subtleties about how much tax relief you get on pension contributions. If you are potentially affected by this then don't use the calculations above but seek professional advice.
Huh? Liquid fuel is a hell of a lot safer. Seriously, how often do you hear about massive fires and explosions involving gas stations and/or gasoline-fueled vehicles?
(I used to work sufficiently close to this plant that I could see these tanks from my desk)
A hydrogen leak probably wouldn't have ignited (would have dispersed too quickly). If it had ignited would probably not have exploded (outside so it's pretty hard to get enough H2 in one place) and would probably have just destroyed the one leaking tank and burned out within minutes.
The only reason Buncefield didn't have dozens to hundreds of fatalities was that it happened very early on a Sunday morning.
1e15 kg or approximately the mass of 9-10 billion Mount Everests
That can't possibly be right!
10billion is 1e10 which would mean that Mount Everest only weighs 1e5kg or 100 tonnes!
1e15kg of water would be 1e12 m^3 or a cube 10km on a side. That's not far off the size of Mount Everest. Allowing for rock having a higher density than water I'd day roughly the mass of Mount Everest.
The solar constant is roughly 1.5e3W/m^2 at Earth's orbit. Earths orbit is roughly 1.5e11m. Surface area of sphere at Earth's orbit would be roughly 2.7e23m^2. So the sun outputs roughly 4e24W per second.
1e32J would be roughly 3 million seconds worth of output or roughly 1 month of the suns output.
Generating 1e15kg of anti-matter is far beyond us today but it's not beyond belief. Jupiter has a mass of roughly 1e27kg so a Dyson sphere at Earth's orbit would have 100kg/m^2 to play with. Obviously, Jupiter is mostly hydrogen so it would have to be fused to more useful elements first. ISTM that the only real technical problem we would have to overcome to build a Dyson sphere is a net positive energy controllable fusion reaction. Once we have that we could slowly syphon off Jupiter's upper atmosphere, fuse it and build the sphere. It might take thousands of years but it's fundamentally doable.
One was browsing this story in one's library on one's iPad when one showed it to one's butler, Charles, as he was handing one a snifter of brandy. He assured me that "Sir is neither a 'selfish elite' nor a 'snob'."
But you're missing the point. At some point, one tiny change occurred from a non-chicken (which would have been pretty similar to a chicken) to a chicken.
There wasn't a "tiny" change that differentiated "non-chicken" from "chicken". The two classes will overlap.
Time--->>>--->>>--->>>--->>>--->>>--->>>--->>>--->>> Proto Chicken ---------------------
------------- Chicken -----
A B
At point A an animal evolved that can interbreed with today's chickens. At point B the "proto-chicken" branch diverged sufficiently from the chicken branch that it could no longer interbreed with the chicken branch
You cannot draw the line between chicken and non-chicken any more than you can draw the line between Herring Gull and Lesser Black-backed Gull (which do not normally hybridize) or the various subspecies of Ensatina salamander (which form a complete link of interbreeding sub-species although the extreme ends cannot interbreed)
At least in Europe, this is really Monsanto's problem. The fact is that "the people" have spoken and the vast majority have decided that they'd rather pay more than eat GM food. The majority of people don't want it, so the shops won't sell it, so the farmers won't grow it. There isn't a step in that chain that wouldn't jump at GM if they thought it would increase their profits and they could get away with it.
There isn't a restaurant in the UK that doesn't have a sign "We do not knowingly use GM ingredients". Quite frankly, if they could be sure to not use them accidentally then there would instead be a sign "We do not use GM ingredients".
It's somewhat refreshing that, for once, "the people" have chosen a path that I want to follow. My concern about GM foods isn't that they couldn't be safer, or even better, than non-GM foods but that the drive to GM is being driven by the search for profit.
BP was drilling in the Gulf in the quest for profit. It made the choices it made because it felt at the time that they had the best return on investment. It doesn't really matter whether they were criminally negligent, too laissez-faire, or just unlucky, the results are the same. There's no reason to suppose that a similar scale of accident couldn't happen with GM crops.
Corporations have too much power and too little interest in "doing the right thing". They have as little regard for their host, the human race, as the malaria parasite has for its host.
This is done exactly the way I would have done it - it's a fairly obvious extension to the standard way of preventing an incorrectly inserted battery doing any harm by "hiding" the positive connector.
My bigger question would be how they avoid momentary (or longer) shorts to the battery as you are inserting it.
It doesn't look too difficult to get both the -ve and +ve poles touching the "-ve" connector and a naive wiring would have these connected together.
With the standard battery compartment with the "hidden" +ve connector it's hard to do any harm. Worst that happens is that the device just does not work.
I'm not sure what point you're trying to make here but "and now that we have discovered the greenhouse effect from CO2" is rather odd.
Arrhenius http://en.wikipedia.org/wiki/Svante_Arrhenius realized that CO2 causes global warming. The arguments were happening at the turn of the 20th Century and by the end of the Second World War and the advent of high altitude aircraft the debate was settled.
Slashdot Mirror
As soon as *BUY ME* will stand for won't buy you... the adds will be gone. As long as they work they will stay.
If advertising a product ever had a significant negative impact on potential buyers then there would be adverts for competitors products.
Microsoft suing RedHat for claiming that Windows is the safest, best value, most secure operating system ever written ;-)
Tim.
Didn't the IRA phone in warnings of their bombings in advance so people could evacuate the area?
Yes - evacuate the area that the bomb wasn't to concentrate the people where the bomb really is.
http://en.wikipedia.org/wiki/Omagh_bombing
In many cases there either wasn't a warning at all or there was insufficient time to evacuate the area.
http://en.wikipedia.org/wiki/List_of_terrorist_incidents_in_London
It's sad to say that the destruction of the WTC was prossibly the single most important thing that finally forced the IRA to really join the peace process. Suddenly Americans discovered that terrorism isn't something that happens in funny countries and can be ignored, or even funded and the IRA almost certainly saw a big reduction in funds coming in.
Tim.
No - photons cannot account for the "missing mass". It's called "dark matter" because we know that it (whatever it is) does not interact with the electromagnetic force.
Indirectly, we can experimentally confirm that photons have a rest mass of zero from the fact that unless EM is exactly inverse square then there would be an electric field inside a hollow conductor. (proving this is relatively straight forward for a perfect sphere - I understand that it can be proved for a general closed conductor but that's maths far beyond what I'm capable of)
http://personal.rhul.ac.uk/UHAP/027/PH2420/PH2420_files/notes/04.pdf (page 6)
Basically it's a galvanometer connected between an isolated conductor that is inside a closed conductor and the closed conductor. The conductor is then driven with a few kV at the resonant frequency of the galvanometer. Any deflection at all would indicate that EM isn't exactly inverse square and one possible explanation would be that photons do not propogate at c.
However, any result like this would be so disruptive to all known physics that pretty much every physicist would assume that there was a fault with the experiment.
Tim.
So, there is no magical disappearing of time or events or 4D cloaking of spacetime.
It's slightly more subtle than that. IIUC, it's impossible to detect something happening in the cloaked region of space. So in the chicken crossing the road scenario, to an outside observer, it looks like the cars travel at a constant speed and the chicken "magically" teleports from one side of the road to the other.
The idea that something is in one state or another without being able to detect intermediate states is not new to physics. If you attempt to "watch" the transition between two eigenstates you will always measure one state or the other. We can have a mathematical model of how the wave function evolves, we can do experiments that demonstrate that the wavefunction must have been in a state that our mathematical model describes as a superposition of eigenfunctions, but we can never measure that superposition.
In QM terms, I suppose the chicken would be described as "tunneling across the road"
(note that I have no reason to suppose there is any relationship between 4d cloaking and QM tunneling - it's merely an analogy that came to mind)
Tim.
Being in the UK, who are currently on GMT, I can tell you that it's not yet 20:00 on 9th Nov. Not for another 2 hours.
If these times are local times then it's even worse.
Either there's been a mega screw up and the missile was launched early (or the announcement was late) or this is for something else.
Tim.
I can't speak for people from a hypothetical universe and about what their naming conventions would be, but I can tell you that, given the known laws, the "anti-matter" universe would behave in exactly the same way as ours does.
No, this isn't true (unless time also runs backwards in the anti-matter universe).
Neutral Kaon decay violates CP - You can distinguish K0 decay in our universe from the anti-K0 decay in an antimatter universe.
It is conjectured that CPT symmetry does hold (therefore CP violation implies T violation)
http://en.wikipedia.org/wiki/CP_violation
Tim.
It's ironic that, in order to actually believe your statement, one must not have a very firm grasp of probability.
I only know about the UK lottery. IIRC 50% of the income is paid out in prizes.
In the UK, in roulette, IIRC 36/37 of the money is paid out in prizes.
(I've never done the lottery and I've never been in a casino ...)
Tim.
No, I'm afraid there is no "get a loan" scenario that can beat simply saving money at approximately the payment rate, if you simply use your wits.
This didn't work when house price inflation was rampant. Despite my salary increasing by substantially more than inflation (compounded) it's only been in the last four years or so I would have been able to buy with a mortgage the properties I own outright because house prices rose so much faster than inflation.
I, of course, used my above inflation salary increases over the years to pay off my mortgages.
Borrowing money to buy my second car was also a good move. The reduction in fuel and maintenance charges more than paid the interest on the loan (in fact the reduction paid the interest plus the repayments so for three years I saw no net cash flow change and then on year four I had an extra 190GBP/month). At that time in my life there is no way I could have saved enough money to buy the car outright when I needed it. I was never desperately short of money but for the first three or four years of working life I was definitely not flush with cash.
Tim.
The only negative impact from a helmet is on hearing
Drivers pass helmeted cyclists closer than unhelmeted cyclists.
I'm very glad that I wasn't wearing a helmet when I was hit by a car wing mirror passing me at 60+ mph. Couple of inches closer and instead of an impressive bruise on my arm I'd probably be dead.
Tim.
Actually, as I understand, scientific research shows that wearing a helmet has a tremendous benefit in prevent the sorts of injuries that leave people brain damaged for the rest of their lives.
Case controlled studies showed that HRT reduced coronary heart disease. It is now recognized that HRT increases the risks of coronary heart disease.
Case controlled studies have shown that cycle helmets reduce head injury rate. Whole population studies have failed to show any benefit whatsoever.
Tim.
What the Nyquist theorem misses is that the mind is not just taking a single sample, but a time series of many samples. A good listener or an observant viewer can see qualitative differences in a square wave and a smoother sine wave, even near the limits of resolution.
No. This fundamentally misunderstands the Nyquist theorem.
If you low pass filter a signal and then sample it at at least twice the frequency of the highest frequency passed by the low pass filter then you can _exactly_ reconstruct the original low pass filtered signal by low pass filtering the digital signal generated from the samples.
Of course, CDs do not permit storing the samples at infinite precision so the theoretically perfect reconstruction does not occur but that's not due to the finite sampling frequency and the ear just isn't sensitive enough to changes in amplitude for the quantization of the samples to matter in normal circumstances.
Higher sampling frequencies allow the low pass filtering to be moved into the digital domain. Ideally we want a brick wall low pass filter but building a filter like this in the analogue domain is hard. Simple filters with a nice flat pass band have a relatively gentle 6 or 12dB/octave cutoff. Simple filters with a sharp cutoff introduce lots of non-linearity in the pass band.
Tim.
It's the UK rather than the US but this really can happen. (And the rules are changing every year so you have to keep on the ball to avoid unnecessarily getting caught by these things)
Salary 149999. Pension contribution of 50000. Tax rate 40% (we'll assume that the tax rate applies across the whole band because this doesn't affect the calculations)
Tax is paid on 99999 @ 40% = 39999 (it rounds down) giving 50000 in the pension and 60000 in your pocket.
Salary 150001. Pension contribution of 50000. Tax rate 40% as before.
Because salary >150000 only the first 20000 of pension contribution attract 40% relief, the rest attracts 20% relief
Tax is paid on 100001@40% plus 20% on 30000 (the excess over 20000 paid into the pension) = 46000 giving 50000 in the pension and 54001 in your pocket.
So you earn 2GBP more but end up 6000 poorer.
(In fact, someone earning 150001 can "sneak" under the barrier by making a charitable donation. A 2GBP donation would get you under this years threshold)
Tim.
p.s. For anyone in the UK actually affected by this - the calculations above leave out a lot of subtleties about how much tax relief you get on pension contributions. If you are potentially affected by this then don't use the calculations above but seek professional advice.
Don't be silly.
If that's your definition of agnostic then anybody with half a brain cell is agnostic on absolutely everything.
Even 2+2!=5 depends on a belief that ZFC is consistent.
An atheist is someone who puts belief in gods on the same level as belief in magic and belief in leprechauns.
Tim.
Huh? Liquid fuel is a hell of a lot safer. Seriously, how often do you hear about massive fires and explosions involving gas stations and/or gasoline-fueled vehicles?
http://en.wikipedia.org/wiki/Buncefield_fire
(I used to work sufficiently close to this plant that I could see these tanks from my desk)
A hydrogen leak probably wouldn't have ignited (would have dispersed too quickly). If it had ignited would probably not have exploded (outside so it's pretty hard to get enough H2 in one place) and would probably have just destroyed the one leaking tank and burned out within minutes.
The only reason Buncefield didn't have dozens to hundreds of fatalities was that it happened very early on a Sunday morning.
http://en.wikipedia.org/wiki/Lindsey_Oil_Refinery
IIRC this caught fire the day the Judgement was being released into the Buncefield disaster.
Tim.
4e24W per second.
Grrr.
J per second or W obviously. :-(
Tim.
1e15 kg or approximately the mass of 9-10 billion Mount Everests
That can't possibly be right!
10billion is 1e10 which would mean that Mount Everest only weighs 1e5kg or 100 tonnes!
1e15kg of water would be 1e12 m^3 or a cube 10km on a side. That's not far off the size of Mount Everest. Allowing for rock having a higher density than water I'd day roughly the mass of Mount Everest.
The solar constant is roughly 1.5e3W/m^2 at Earth's orbit. Earths orbit is roughly 1.5e11m. Surface area of sphere at Earth's orbit would be roughly 2.7e23m^2. So the sun outputs roughly 4e24W per second.
1e32J would be roughly 3 million seconds worth of output or roughly 1 month of the suns output.
Generating 1e15kg of anti-matter is far beyond us today but it's not beyond belief. Jupiter has a mass of roughly 1e27kg so a Dyson sphere at Earth's orbit would have 100kg/m^2 to play with. Obviously, Jupiter is mostly hydrogen so it would have to be fused to more useful elements first. ISTM that the only real technical problem we would have to overcome to build a Dyson sphere is a net positive energy controllable fusion reaction. Once we have that we could slowly syphon off Jupiter's upper atmosphere, fuse it and build the sphere. It might take thousands of years but it's fundamentally doable.
Tim.
(I am not a mathematician)
If a proof that P=NP is undecidable exists then P=NP is decidable.
If P=NP then there is a polynomial time reduction from a P problem to an NP complete problem. That algorithm is sufficient to prove that P=NP.
If P=NP is undecidable then no such algorithm can exist and therefore P!=NP.
Therefore a proof that P=NP is undecidable is sufficient to prove that P!=NP and therefore P!=NP cannot be proven to be undecidable.
(The only loophole I can see is that the algorithm could exist but could not be proven to run in polynomial time)
Tim.
For example, the problem "is a given integer n composite?" is in NP because...
While this is perfectly correct PRIMES is also in P.
http://en.wikipedia.org/wiki/AKS_primality_test
Tim.
One was browsing this story in one's library on one's iPad when one showed it to one's butler, Charles, as he was handing one a snifter of brandy. He assured me that "Sir is neither a 'selfish elite' nor a 'snob'."
Ha! Of course you need to view that timeline in a fixed width font.
But you're missing the point. At some point, one tiny change occurred from a non-chicken (which would have been pretty similar to a chicken) to a chicken.
There wasn't a "tiny" change that differentiated "non-chicken" from "chicken". The two classes will overlap.
Time--->>>--->>>--->>>--->>>--->>>--->>>--->>>--->>>
Proto Chicken ---------------------
------------- Chicken -----
A B
At point A an animal evolved that can interbreed with today's chickens. At point B the "proto-chicken" branch diverged sufficiently from the chicken branch that it could no longer interbreed with the chicken branch
You cannot draw the line between chicken and non-chicken any more than you can draw the line between Herring Gull and Lesser Black-backed Gull (which do not normally hybridize) or the various subspecies of Ensatina salamander (which form a complete link of interbreeding sub-species although the extreme ends cannot interbreed)
http://en.wikipedia.org/wiki/Ring_species
http://en.wikipedia.org/wiki/Ensatina
Tim.
At least in Europe, this is really Monsanto's problem. The fact is that "the people" have spoken and the vast majority have decided that they'd rather pay more than eat GM food. The majority of people don't want it, so the shops won't sell it, so the farmers won't grow it. There isn't a step in that chain that wouldn't jump at GM if they thought it would increase their profits and they could get away with it.
There isn't a restaurant in the UK that doesn't have a sign "We do not knowingly use GM ingredients". Quite frankly, if they could be sure to not use them accidentally then there would instead be a sign "We do not use GM ingredients".
It's somewhat refreshing that, for once, "the people" have chosen a path that I want to follow. My concern about GM foods isn't that they couldn't be safer, or even better, than non-GM foods but that the drive to GM is being driven by the search for profit.
BP was drilling in the Gulf in the quest for profit. It made the choices it made because it felt at the time that they had the best return on investment. It doesn't really matter whether they were criminally negligent, too laissez-faire, or just unlucky, the results are the same. There's no reason to suppose that a similar scale of accident couldn't happen with GM crops.
Corporations have too much power and too little interest in "doing the right thing". They have as little regard for their host, the human race, as the malaria parasite has for its host.
Tim.
This is done exactly the way I would have done it - it's a fairly obvious extension to the standard way of preventing an incorrectly inserted battery doing any harm by "hiding" the positive connector.
My bigger question would be how they avoid momentary (or longer) shorts to the battery as you are inserting it.
It doesn't look too difficult to get both the -ve and +ve poles touching the "-ve" connector and a naive wiring would have these connected together.
With the standard battery compartment with the "hidden" +ve connector it's hard to do any harm. Worst that happens is that the device just does not work.
Tim.
I'm not sure what point you're trying to make here but "and now that we have discovered the greenhouse effect from CO2" is rather odd.
Arrhenius http://en.wikipedia.org/wiki/Svante_Arrhenius realized that CO2 causes global warming. The arguments were happening at the turn of the 20th Century and by the end of the Second World War and the advent of high altitude aircraft the debate was settled.
Tim.
Yes, it's solved. That's why the problem got "demoted" to an M45 problem.
An M3 problem would be a mathematical problem you should be able to solve in your head without much thought.
Tim.