We can't as far as I'm aware even get a strongly non-trivial result of the form for some explicit constant C, "No NP complete problem can be solved in polynomial time with a polynomial of degree at most C."
I'm curious to know the best lower bound for any decision problem. I don't even know any good lower bounds for problems where the output must be at most linear in the size of the input.
NP is a set of problem. The main issue is about two subsets of NP: P and NP-complete. We have lots of examples of problems in each subset. We think that these subsets are disjoint, but no one has proven that fact. We have proven that if they are not disjoint then they are equal. Therefore one way to prove that they are equal is to show a problem is both in P and NP-complete.
Also, I'm not sure we want labor controlled by the free-market.
There is no magic reason that the free market will pay people a decent
wage. It's easy to envision a future where industry does not profit
by paying a decent wage for most labor. Real capitalism comes from
being an owner, and in such a future only the owners would survive
with the existing free market labor model.
Re:What would the impacts of this be for cryptogra
on
Claimed Proof That P != NP
·
· Score: 4, Informative
You don't need to simulate the Turing machine. You just need to encode it as a boolean formula. That's part of what Cook's theorem shows; it shows how to encode a non-deterministic Turing machine as a boolean formula with at most a polynomial increase in size. Now that the problem is in a NP-complete form just follow the reductions until you get to the NP-complete algorithm that has a P algorithm. In this way you can solve any NP problem in P time as long as you solve one NP-complete algorithm in P time.
The bottom 50% of the population still don't pay any taxes at all.
Any references for this? Make sure it includes payroll and sales taxes. Also remember that many payroll taxes are effectively doubled since the employer matches the amount.
at best you're just cotton-headed naive, at worst your in danger of
ethnocentric and prejudicial thinking
He's asking for evidence to justify your human psychology theory.
If you don't have any real evidence then fess up. It's not enough to
give anecdotes that don't really address the issue. It's even worse
to come up with some bizarre theory on his thought process that
doesn't seem to amount to more than an ad hominem attack.
I find it interesting how this is essentially a way to use waste
heat generated by sunlight. I wonder if the design takes extra
advantage of that fact.
For example, one could have the fans drive long shafts to put the
generators closer to the cold air inlets. Not only would this be
beneficial in keeping the generators cooler, the excess heat generated
would create even more power. Another idea is to add some heat
intensive industrial process near the inlet. The waste heat from the
facility would just add to the energy. If the process runs on
electricity one could again boost the effective efficiency by using
the solar tower's electricity to power the process. A computer center
might be a decent source of waste heat, but I don't know if silicon
technology gets hot enough to be practical. Maybe if it's used in a
pretty cold environment.
I'm more interested in what's right for the future, as in what
would be interesting technology to develop, but I'll try to stick to
the present.
You mention geothermal piping. This is expensive, but if done
right would work even for your climate. The temperature below 7m is
pretty constant at around 50 degrees; heat pumps work well at that
temperature. A far cheaper solution is to use an air based heat pump.
It will not work well during your cold winters but modern units
include a gas heater. Still if you've currently got a 95% efficient
furnace the costs are probably not worth it.
As for cogeneration, this is not something you can do directly.
It's more popular in urban settings and in other countries. Jumping
to the future, what I mentioned is a way to do local cogeneration.
Instead of the electricity company creating a bunch of waste heat, you
create that waste heat in your own house. The electricity you get at
your house is at best 50% efficient. This means at least half the
energy turns to heat before it gets to your house. Assuming that heat
is just being wasted, during the winter it makes sense to generate
that electricity at home and use the waste heat. In some sense, your
generating electricity at 95% efficiency since you would need to use
the gas anyway to heat the house. If you can sell the electricity
back to the power company at a reasonable rate then you can probably
shave around 40% off your power bill. (The "efficiency" would be
around 85% if you sell since it would suffer some transmission
losses.)
Again this is just a possibility. There are several issues to be
resolved. It also probably doesn't make sense if you live in a
climate more suitable for a heat pump or if your place is big enough
to justify a ground based heat pump. However, it does show why your
95% efficiency, while technically correct, is not useful when
comparing heating options.
To get back to the original topic of discussion, the point of my
original post was to show that it is possible to run SETI on your
computer in the winter at the same efficiency as a gas furnace. You
replied
If it were possible to recover all of the waste heat
from a reciprocating engine and do something useful with it, we'd be
living in a different world right now, and would not be having this
conversation.
Meanwhile, here in reality, I think I'll keep my 95% efficient
natural gas furnace, and try to turn electronics off when not in
use. Thanks.
This seemed to imply my claim was breaking some thermodynamic law.
I proceeded to explain why this is wrong. You then changed the topic
to why it doesn't make sense for heating your house. While this
tactic might work in a conversation, it doesn't work in print. Admit
you were wrong and that you learned something; no one else is
watching. Or don't.
There's just no fucking way this will begin to approach the total monetary efficiency of the inexpensive and simple heating system I already have. It's already at 95%, not accounting for transmission losses (but those exist no matter what). Squeezing anything more out the remaining 5% is going to be expensive enough that it's simply not worth considering.
These statements show that you don't know what your talking about. Why do you think people in certain climates use heat pumps instead of gas furnaces? It a large part of the USA it's by far the cheapest way to heat your house. Also cogeneration techniques are currently being used and are much better solutions than simple furnaces. Yes a modern furnace can extract almost all the heat out of gas, but that is not the only way to heat a house. You can use waste heat from a nearby industrial process. You can extract heat from the outside air or the ground.
I know you want to defend what you decided to do for your house, and it might be the best solution for you, but it's definitely not the best solution for everybody, and in the future, it might not be the best solution for anybody. There's a much bigger margin than 5% to be exploited.
I just want to use the waste heat to heat the house. The heat has to go somewhere. The reason that natural gas furnace is 95% efficient is that all it generates is waste heat, but it doesn't let much escape out the flue. In principle it should possible to run a gas turbine without letting much heat escape through the exhaust. Once the turbine reaches a temperature equilibrium most of the heat stays in the house. It's just a matter of distributing it.
This is just a cogeneration technique. These types of techniques have existed for a long time.
http://en.wikipedia.org/wiki/Cogeneration
It is mainly used on a large scale to distribute heat to nearby locations. This of course causes loss of heat during transportation. Local generation would be better, but I assume the capital costs are high given our infrastructure. (It would be nice if the excess power could feed the grid in the winter...)
And it's crazy to spend BTUs fold proteins for sport, where the same energy is available cheaper in the form of gas, oil, or wood.
It should be possible to do both. Run a generator/furnace to make electricity from the gas. The electricity will heat the house and the heat from the generator can be used to heat the house. Any excess electricity can be put on the grid or used in resistive heating.
They never claimed each statement or function call had a 79% chance of success, they said the program had a 79% of success. This is fine for a randomized algorithm. Check out
http://en.wikipedia.org/wiki/Monte_Carlo_algorithm for more information.
AMD processors are still beating Intel in the performance/cost ratio.
Only if you ignore Intel processors which cost more than $200, right?
The best AMD (Phenom II X4 965) is about on par with the i5 and they cost about the same. As the CPU gets faster the price performance gets worse for Intel CPUs.
To be fair, if your buying a whole system that extra CPU cost becomes less significant. An i7-860 might be worth it if it increases the cost of the system by at most 30%. Even an i7-960 can be OK if it increases the price by at most 60%. Given that a good AMD computer costs maybe 600 then the i7-860 is probably worth it, but the i7-960 is overpriced when you factor in the motherboard.
Of course, Intel wouldn't have such good prices without AMD, so in the long run it's good to support AMD. Also most people don't really need the extra speed. If you need a new machine then a midrange AMD for around 500 is probably your best bet.
If you are really concerned about speed then just use the money you save to upgrade more often. Given Moore's law, on average, you'll have a faster machine (or at least a machine with more cores.) Also, when just upgrading, the AMD price/performance gap gets even better.
Even in bandwidth, 10Gb ethernet is still orders of magnitude smaller than RAM access speeds in a supercomputer. At least use InfiniBand which can be configured to 96Gb bandwith with much better latency.
The debate has been politicized and therefore forever tainted. The
science has been lost and those involved pushed to their respective
sides so much so that the truth is getting lost. We're all citing our
science celebs in some kind of battle royale of evidence. The
scientific debate will hopefully go on, as it should. Let's hope the
political debate is stifled until some meaningful consensus can be
reached.
This is an effective strategy for anyone who would like to maintain
the status quo. Just throw enough random mud and speculation around
to disturb any claims of consensus. Since most people don't have the
background and time to understand the research, a handful of "experts"
that are promoted by the media can cast a lot of doubt.
However, it seems that this strategy has run its course. Perhaps a
long draw out court case is the next step. When the case is over,
they might get lucky and find a more receptive presidential
administration. This might be able to buy them another 12 years.
But that's not the end to the story. All of that money has to go
somewhere. It goes into businesses. Banks that hold their mortgages (I
can't believe any would still have mortgage payments, but they don't
seem to be the most responsible group), auto manufactures, airlines,
restaurants, etc. As those businesses profit from this expense, that
will spur new investment in those businesses, and the profits and/or
revenues from the baby boomers will go into the pockets of the people
running the businesses, who will then want to invest it. If that place
is still the stock market (bonds seem to be out of vogue but could
come back, commodities seem to only be a safe haven), then the net sum
is not bad--the stock market won't crash.
Money is just a convenient tool for trading goods and services.
The real problem is that with the boomers retiring there will be less
people working and creating wealth. My guess is that this will have
negative implications for investing in the stock market.
An interesting question on energy is can we provide the energy
needed for people to live while still have a small amount left over
to increase the standard of living in terms of technology.
Why do you think we can't? The current state is that we are
successfully expending tremendous resources to improve the
standard of living. If we can do that, we should be able to
implement this far more timid approach.
I think we can, but I haven't done any research on the numbers
involved. I would guess the US could eventually bring its energy
consumption down to 25% of the current level and still maintain a good
standard of living. With the current population, this might be
sustainable using various forms of solar energy (biofuels, wind,
photovoltaic...) Of course, while possible it's not politically
realistic.
Also, energy is very cheap. I don't understand the rational for such
extreme rationing of it. It's unnecessary and actually hurts our
more important efforts (like improving the standard of living or
advancing the state of human knowledge).
The current use of energy is not sustainable and involves various
negative externalities. This has many dangers. Our society can
become dependent on that cheap energy and when it runs out our society
could collapse. We can devastate our environment to the point that it
excessively damages our standard of living and/or damages the
economy.
The problem is increased efficiency demands increased
complexity. This complexity implies that that the cost increase of
a more efficient system is actually exponential, not linear, such
that, going from 10% efficient to 50% efficient is pretty cheap,
but it gets way more expensive after that.
Let me save you a summer. Your model utterly fails when you apply
it to integrated circuits.
While the GP tries to defend his model for integrated circuits, I
don't think it's necessary. There are different types of
efficiencies, and his model only needs to deal with energy. People
need a certain amount of energy for our current standard of living,
and thermodynamic limits make it impossible to continually increase
energy efficiency. In fact, the problem is not that the cost grows
exponentially, but that one can't do better than 100% efficiency.
While computers might get exponentially faster (even faster per
watt) it still takes a certain amount of energy to grow and move food
around the planet, to heat and cool our homes, to light our businesses
and houses...
Of course, our economy is not only based on energy but on products
built with that energy that use various raw materials and information.
Fortunately, there are fewer thermodynamic limits on the performance
of these types of products. Many of these products can cheaply
increase in complexity because the thermodynamic constraints on
computation are very low. http://en.wikipedia.org/wiki/Reversible_computing
This equivocation of energy efficiency and general efficiency is
often a source of confusion. Most people would agree that a human is
much more complex than an electric motor; however, a good electric
motor is more efficient in terms of energy. Complexity is better
modeled by information theory independent of energy.
An interesting question on energy is can we provide the energy
needed for people to live while still have a small amount left over to
increase the standard of living in terms of technology. It seems the
primary constraint is on the population and the energy that they need
to live comfortably. This energy requirement can definitely be shrunk
based on all the inefficiencies in the developed world.
Unfortunately, a large percentage of the world is in the opposite
situation. They need more energy to get a reasonable standard of
living. However, as long a the population does stabilize at a point
where we can sustainably supply enough energy to live, we should have
enough left over to continue our economic growth in terms of
information based products.
There has been some recent noise about low levels of vitamin D being a possible cause of autism. People are so worried about skin cancer that they can't make enough vitamin D from the sun. While they get enough vitamin D to prevent scurvy, it's far from an optimal amount.
Did I miss something here? The GP was talking about the "free market" capitalism we have in the US. I never saw him talk about the insignificant fraction of our government made up of free-market libertarians. This has nothing to do with his point, and nothing to do with the way the government is currently run.
Well I was more interested in exact computation or at least relative error bounded computation. An ill-conditioned matrix is going to give problems for any type of elimination based algorithms. Perhaps iterative techniques can give decent bounds on relative accuracy while still using double precision floats. If I want exact answers, it might be the case that the best algorithm is exponential if I use rational numbers to represent the inputs. Of course, if I start using infinite precision computation, I could use an elimination algorithm and just extend the precision enough to compensate for the lost bits.
Not to be pedantic, but matrix inversion is not exponential in n, the size of the matrix. If you want to solve Ax=b, LU decomposition is roughly 3 times faster than matrix inversion. Perhaps your thinking of Crammers method which is exponential. Also, it can be hard to solve Ax=b exactly, and I vaguely remember that the size of the answer as rational numbers can require exponentially more bits than the input, though I can't find a reference.
Looking at WHO's methodology, what a joke. "Fairness of financial
contribution?" And of course, Cuba is a police state. Not exactly an
open, transparent society. So how is WHO they getting open access to
information?
That's just one measure, and Cuba didn't do so great in it either.
As for how WHO gets their information, they gave up after 2000 as it's
too complicated to do this type of assessment. Luckily we still have
you.
Plus, Americans are unhealthy because they are fat and don't exercise
and drive everywhere. Cubans, who are starving most of the time and
have to walk everywhere obviously have some "advantages" that have
nothing to do with healthcare.
There's still the matter of those 36 countries above us. Are they all
third world countries?
Any ranking that puts Canada ahead of the US is one I give little
credence to. The US is where rich Canadians go to get their
healthcare, LOL.
I'm sure rich Americans get great health care too. That doesn't
mean the country has a good health care system.
There is no other country in the world that I would rather be that
America when I get sick. Not Cuba, not Canada, not the UK, not
France. The USA. Because some part of the population here 1) are
illegal aliens or 2) would rather drive late model cars instead of
paying for the privilege of heath care (lets face it, the poor already
have medicaid), does not affect the 80% of Americans who have kick ass
healthcare.
Just hope you don't get a chronic condition. If your job lays you
off and the Cobra runs out your stuck with a pre-existing condition
and premiums that are through the roof. Hopefully it won't happen to
you, but it's probably happening to someone. That's not what I call
insurance. Matters are even worse if you're close to the poverty line;
it's estimated that 58% of Americans will spend at least one year in
poverty. (Hacker, J. S. (2006). The great risk shift: The new
insecurity and the decline of the American dream. New York: Oxford
University Press (USA)) and it's estimated that approximately 60
percent of poor Americans are not covered by Medicaid
http://www2.citizen.org/hrg/medicaid/assets/reports/2007UnsettlingScores.pdf
The ranking I care about isn't compiled with some silly left wing
methodology. It's called mortality rates for diseases like cancer and
heart disease. And the US does a lot better than most of those
socialized medicine countries in survivability of those diseases,
those which I am most likely to get. You can take your free abortions
in Cuba.
So there are universal healthcare systems that do better than the
US in the narrow statistic you care about. So what's your point again?
Slashdot Mirror
I'm curious to know the best lower bound for any decision problem. I don't even know any good lower bounds for problems where the output must be at most linear in the size of the input.
NP is a set of problem. The main issue is about two subsets of NP: P and NP-complete. We have lots of examples of problems in each subset. We think that these subsets are disjoint, but no one has proven that fact. We have proven that if they are not disjoint then they are equal. Therefore one way to prove that they are equal is to show a problem is both in P and NP-complete.
Also, I'm not sure we want labor controlled by the free-market. There is no magic reason that the free market will pay people a decent wage. It's easy to envision a future where industry does not profit by paying a decent wage for most labor. Real capitalism comes from being an owner, and in such a future only the owners would survive with the existing free market labor model.
You don't need to simulate the Turing machine. You just need to encode it as a boolean formula. That's part of what Cook's theorem shows; it shows how to encode a non-deterministic Turing machine as a boolean formula with at most a polynomial increase in size. Now that the problem is in a NP-complete form just follow the reductions until you get to the NP-complete algorithm that has a P algorithm. In this way you can solve any NP problem in P time as long as you solve one NP-complete algorithm in P time.
Please don't feed the trolls.
Any references for this? Make sure it includes payroll and sales taxes. Also remember that many payroll taxes are effectively doubled since the employer matches the amount.
He's asking for evidence to justify your human psychology theory. If you don't have any real evidence then fess up. It's not enough to give anecdotes that don't really address the issue. It's even worse to come up with some bizarre theory on his thought process that doesn't seem to amount to more than an ad hominem attack.
I find it interesting how this is essentially a way to use waste heat generated by sunlight. I wonder if the design takes extra advantage of that fact.
For example, one could have the fans drive long shafts to put the generators closer to the cold air inlets. Not only would this be beneficial in keeping the generators cooler, the excess heat generated would create even more power. Another idea is to add some heat intensive industrial process near the inlet. The waste heat from the facility would just add to the energy. If the process runs on electricity one could again boost the effective efficiency by using the solar tower's electricity to power the process. A computer center might be a decent source of waste heat, but I don't know if silicon technology gets hot enough to be practical. Maybe if it's used in a pretty cold environment.
I'm more interested in what's right for the future, as in what would be interesting technology to develop, but I'll try to stick to the present.
You mention geothermal piping. This is expensive, but if done right would work even for your climate. The temperature below 7m is pretty constant at around 50 degrees; heat pumps work well at that temperature. A far cheaper solution is to use an air based heat pump. It will not work well during your cold winters but modern units include a gas heater. Still if you've currently got a 95% efficient furnace the costs are probably not worth it.
As for cogeneration, this is not something you can do directly. It's more popular in urban settings and in other countries. Jumping to the future, what I mentioned is a way to do local cogeneration. Instead of the electricity company creating a bunch of waste heat, you create that waste heat in your own house. The electricity you get at your house is at best 50% efficient. This means at least half the energy turns to heat before it gets to your house. Assuming that heat is just being wasted, during the winter it makes sense to generate that electricity at home and use the waste heat. In some sense, your generating electricity at 95% efficiency since you would need to use the gas anyway to heat the house. If you can sell the electricity back to the power company at a reasonable rate then you can probably shave around 40% off your power bill. (The "efficiency" would be around 85% if you sell since it would suffer some transmission losses.)
Again this is just a possibility. There are several issues to be resolved. It also probably doesn't make sense if you live in a climate more suitable for a heat pump or if your place is big enough to justify a ground based heat pump. However, it does show why your 95% efficiency, while technically correct, is not useful when comparing heating options.
To get back to the original topic of discussion, the point of my original post was to show that it is possible to run SETI on your computer in the winter at the same efficiency as a gas furnace. You replied
This seemed to imply my claim was breaking some thermodynamic law. I proceeded to explain why this is wrong. You then changed the topic to why it doesn't make sense for heating your house. While this tactic might work in a conversation, it doesn't work in print. Admit you were wrong and that you learned something; no one else is watching. Or don't.
These statements show that you don't know what your talking about. Why do you think people in certain climates use heat pumps instead of gas furnaces? It a large part of the USA it's by far the cheapest way to heat your house. Also cogeneration techniques are currently being used and are much better solutions than simple furnaces. Yes a modern furnace can extract almost all the heat out of gas, but that is not the only way to heat a house. You can use waste heat from a nearby industrial process. You can extract heat from the outside air or the ground.
I know you want to defend what you decided to do for your house, and it might be the best solution for you, but it's definitely not the best solution for everybody, and in the future, it might not be the best solution for anybody. There's a much bigger margin than 5% to be exploited.
I just want to use the waste heat to heat the house. The heat has to go somewhere. The reason that natural gas furnace is 95% efficient is that all it generates is waste heat, but it doesn't let much escape out the flue. In principle it should possible to run a gas turbine without letting much heat escape through the exhaust. Once the turbine reaches a temperature equilibrium most of the heat stays in the house. It's just a matter of distributing it.
This is just a cogeneration technique. These types of techniques have existed for a long time. http://en.wikipedia.org/wiki/Cogeneration It is mainly used on a large scale to distribute heat to nearby locations. This of course causes loss of heat during transportation. Local generation would be better, but I assume the capital costs are high given our infrastructure. (It would be nice if the excess power could feed the grid in the winter...)
It should be possible to do both. Run a generator/furnace to make electricity from the gas. The electricity will heat the house and the heat from the generator can be used to heat the house. Any excess electricity can be put on the grid or used in resistive heating.
They never claimed each statement or function call had a 79% chance of success, they said the program had a 79% of success. This is fine for a randomized algorithm. Check out http://en.wikipedia.org/wiki/Monte_Carlo_algorithm for more information.
The best AMD (Phenom II X4 965) is about on par with the i5 and they cost about the same. As the CPU gets faster the price performance gets worse for Intel CPUs.
To be fair, if your buying a whole system that extra CPU cost becomes less significant. An i7-860 might be worth it if it increases the cost of the system by at most 30%. Even an i7-960 can be OK if it increases the price by at most 60%. Given that a good AMD computer costs maybe 600 then the i7-860 is probably worth it, but the i7-960 is overpriced when you factor in the motherboard.
Of course, Intel wouldn't have such good prices without AMD, so in the long run it's good to support AMD. Also most people don't really need the extra speed. If you need a new machine then a midrange AMD for around 500 is probably your best bet.
If you are really concerned about speed then just use the money you save to upgrade more often. Given Moore's law, on average, you'll have a faster machine (or at least a machine with more cores.) Also, when just upgrading, the AMD price/performance gap gets even better.
Even in bandwidth, 10Gb ethernet is still orders of magnitude smaller than RAM access speeds in a supercomputer. At least use InfiniBand which can be configured to 96Gb bandwith with much better latency.
However, the main problem with a 100 core chip for supercomputing is not the network bandwidth but the memory bandwidth. The cores will starve for data with the limited memory bandwidth. http://spectrum.ieee.org/computing/hardware/multicore-is-bad-news-for-supercomputers
This is an effective strategy for anyone who would like to maintain the status quo. Just throw enough random mud and speculation around to disturb any claims of consensus. Since most people don't have the background and time to understand the research, a handful of "experts" that are promoted by the media can cast a lot of doubt.
However, it seems that this strategy has run its course. Perhaps a long draw out court case is the next step. When the case is over, they might get lucky and find a more receptive presidential administration. This might be able to buy them another 12 years.
Money is just a convenient tool for trading goods and services. The real problem is that with the boomers retiring there will be less people working and creating wealth. My guess is that this will have negative implications for investing in the stock market.
I think we can, but I haven't done any research on the numbers involved. I would guess the US could eventually bring its energy consumption down to 25% of the current level and still maintain a good standard of living. With the current population, this might be sustainable using various forms of solar energy (biofuels, wind, photovoltaic...) Of course, while possible it's not politically realistic.
The current use of energy is not sustainable and involves various negative externalities. This has many dangers. Our society can become dependent on that cheap energy and when it runs out our society could collapse. We can devastate our environment to the point that it excessively damages our standard of living and/or damages the economy.
While the GP tries to defend his model for integrated circuits, I don't think it's necessary. There are different types of efficiencies, and his model only needs to deal with energy. People need a certain amount of energy for our current standard of living, and thermodynamic limits make it impossible to continually increase energy efficiency. In fact, the problem is not that the cost grows exponentially, but that one can't do better than 100% efficiency.
While computers might get exponentially faster (even faster per watt) it still takes a certain amount of energy to grow and move food around the planet, to heat and cool our homes, to light our businesses and houses...
Of course, our economy is not only based on energy but on products built with that energy that use various raw materials and information. Fortunately, there are fewer thermodynamic limits on the performance of these types of products. Many of these products can cheaply increase in complexity because the thermodynamic constraints on computation are very low. http://en.wikipedia.org/wiki/Reversible_computing
This equivocation of energy efficiency and general efficiency is often a source of confusion. Most people would agree that a human is much more complex than an electric motor; however, a good electric motor is more efficient in terms of energy. Complexity is better modeled by information theory independent of energy.
An interesting question on energy is can we provide the energy needed for people to live while still have a small amount left over to increase the standard of living in terms of technology. It seems the primary constraint is on the population and the energy that they need to live comfortably. This energy requirement can definitely be shrunk based on all the inefficiencies in the developed world. Unfortunately, a large percentage of the world is in the opposite situation. They need more energy to get a reasonable standard of living. However, as long a the population does stabilize at a point where we can sustainably supply enough energy to live, we should have enough left over to continue our economic growth in terms of information based products.
There has been some recent noise about low levels of vitamin D being a possible cause of autism. People are so worried about skin cancer that they can't make enough vitamin D from the sun. While they get enough vitamin D to prevent scurvy, it's far from an optimal amount.
http://www.vitamindcouncil.org/health/autism/vit-D-theory-autism.shtml#hd1
http://timeofgrace.wordpress.com/2009/03/14/low-vitamin-d-linked-to-autism/
I've also never had a problem with CDs, but the issue is with DVDs. DVDs are much worse, presumably because of the higher data density.
Did I miss something here? The GP was talking about the "free market" capitalism we have in the US. I never saw him talk about the insignificant fraction of our government made up of free-market libertarians. This has nothing to do with his point, and nothing to do with the way the government is currently run.
Well I was more interested in exact computation or at least relative error bounded computation. An ill-conditioned matrix is going to give problems for any type of elimination based algorithms. Perhaps iterative techniques can give decent bounds on relative accuracy while still using double precision floats. If I want exact answers, it might be the case that the best algorithm is exponential if I use rational numbers to represent the inputs. Of course, if I start using infinite precision computation, I could use an elimination algorithm and just extend the precision enough to compensate for the lost bits.
Not to be pedantic, but matrix inversion is not exponential in n, the size of the matrix. If you want to solve Ax=b, LU decomposition is roughly 3 times faster than matrix inversion. Perhaps your thinking of Crammers method which is exponential. Also, it can be hard to solve Ax=b exactly, and I vaguely remember that the size of the answer as rational numbers can require exponentially more bits than the input, though I can't find a reference.
That's just one measure, and Cuba didn't do so great in it either. As for how WHO gets their information, they gave up after 2000 as it's too complicated to do this type of assessment. Luckily we still have you.
There's still the matter of those 36 countries above us. Are they all third world countries?
I'm sure rich Americans get great health care too. That doesn't mean the country has a good health care system.
Just hope you don't get a chronic condition. If your job lays you off and the Cobra runs out your stuck with a pre-existing condition and premiums that are through the roof. Hopefully it won't happen to you, but it's probably happening to someone. That's not what I call insurance. Matters are even worse if you're close to the poverty line; it's estimated that 58% of Americans will spend at least one year in poverty. (Hacker, J. S. (2006). The great risk shift: The new insecurity and the decline of the American dream. New York: Oxford University Press (USA)) and it's estimated that approximately 60 percent of poor Americans are not covered by Medicaid http://www2.citizen.org/hrg/medicaid/assets/reports/2007UnsettlingScores.pdf
So there are universal healthcare systems that do better than the US in the narrow statistic you care about. So what's your point again?