Pilot plants aren't supposed to produce commercial levels of output.
Fair 'nuff. I just wanted to know what the process is capable of.
... it's a bit strange to compare a single plant--pilot or production--to the output of an entire country.
A factory that can only increase production by 1% might not be a great investment. These guys were cited in the article as having 17% of the world's copper holdings.
Not mentioned in the article is how quickly the bacteria do their job. The sister project mentioned here:
Codelco also has a joint venture with BHP Billiton called Alliance Copper Limited, which uses another form of bioleaching to produce 20,000 tons a year of copper cathodes at a pilot plant in northern Chile.
Let's say I'm a Muslim in Oregon, and I'm accused of committing a terrorist crime in Cleveland. I have multiple people willing to testify that I was in Oregon at the time. But the police have three different RFID reads placing my car in Cleveland at the time. Which one of these has more credibility in a court of law? Which one should have more credibility?
Acoustic noise, yes. Electronic noise, no. Computers can add a lot of hum when they are near audio cables (at least, in my experience. Maybe others have found nifty shielding solutions?).
sample a 1 second clip of nothing and subtract it from your recording and you remove all system noise.
I've wondered about doing that but have not gotten around to really testing it. Do you get good results from it? Does it have an adverse impact on the tone of the signal?
An alternate approach that I've heard rumor of is to reverse the usual noise-reduction idea: instead of seeing the background noise as "noise" and the mic input as "signal", consider the mic input to be "noise" and filter it out; then invert the result and add back to the original. Results are claimed to be outstanding. I haven't figured out how to code for it yet.
Nice solution, except for the punch in the face part. My concern is the cost for a 4-channel, 24- or 32-bit, 44.1kHz sample rate stand-alone box, but maybe digital money could solve the problem? Kidding! Secret Service, it was only a joke.
Eliminating noise is a matter of degrees. You could easily move the tower outside the recording room -- but then you have longer cables, and you get noise from that. If you are playing an electric guitar, your pickups might grab stray signal from a monitor as well, which is really annoying when the amp is at "11". And, I recently discovered that flatscreens are much noiser than old CRTs in that regard.
Agreed on the propane issue. Disagreed on the understanding of the Middle Ages. I'm not a Catholic by any stretch, but the church actually did a fair amount of holding things together after Rome's collapse. This includes preserving ancient documents -- you would never have heard of Aristotle or Plato without the church -- building hospitals, and running a lot of local governments. Nor did the church in the early Middle Ages promote feudalism. Later on, perhaps even as early as Charlemagne, the church became much more enamored with top-down government. You might read, e.g., Cahill's "How the Irish Saved Civilization" for a non-Christian's take on the impact of the church. Another good readable history is Chadwick. Anyways, I'm digressing on a digression.
City of God gets a bad rap. Augustine's point was not to tell people to turn their backs on the city of man; after all, people live there! Instead, he was reacting against the idea that "Christendom" == "Rome". By telling Christians that their ultimate hope rested in the city of God, he was encouraging them that the failure of Rome was not an ultimate disaster. He was, in fact, advocating an early form of separation of church and state: two cities, interacting but not comingled.
When your talking about infinite value's your not talking strictly about numbers anymore because infinity is not a number.
Agreed.
You can only talk about what the number approaches.
Disagreed. The key here is to properly distinguish between numbers and sequences. Numbers are definite points on the number line; they have no fuzzy boundaries and do not approach anything. A sequence a(n), on the other hand, takes on different values for different values of n. As a result, a sequence can indeed approach some value -- a number! -- as n --> infinity.
Let's take a neutral example: What is the value of 0.333...? My students will sometimes naively say that it has no value, since we keep on adding on terms forever. However, they say, 0.333... "approaches" the value (1/3). This seems reasonable, but it is incorrect. The true value of 0.333... is 1/3; the only thing that is "approaching" is our approximation of 1/3. The trick to handling infinity is to find the right notation to do the job. The standard line, taken by mathematicians around the world, is as follows:
Let S(N) = Sum(i = 1, N, 3/10^i). It is clear that S(N) = 0.333...333 to the Nth place. But, if we evaluate that sum using the standard geometric series formula, we also get S(N) = (1 - (1/10)^N)/3. So, if we let N --> inf, we get the value of the infinite series 0.333...., which is 1/3.
You probably recognize this procedure from algebra or some other class. The point is that infinity is not handled loosely via common sense, but is instead handled with precise notation:
Assign a meaningful function which gives correct values for finite values of N, then
let N go to infinity. If the limit exists, then that limit is considered to be the value "at infinity".
That's the procedure I was taking in my first post: define a function which gives the correct percentage of twin primes for finite N, then let N go to infinity. The result is the only meaningful way to define the percentage of twin primes out of all of the primes, which are infinite in number. The advantage of doing it that way is that it avoids odd concepts like "infinitely small positive value", which doesn't have any concrete meaning.
Without us Sumerians, you wouldn't have writing! You hereby owe us 699.99 dinars per character... no, wait, wrong joke... umm... Soviet Russia... no... tinfoil hat... forget it.
Hmph. Numbers don't "approach"; they have well-defined values. That is, they are constants. On the other hand, functions (including sequences) approach values for different values of x or n or whatever variable.
I think I address your concern in the remainder of my first post. If you can sort through the terrible notation (sorry!), I think it will clear up the problem.
The flaw is in the word "percentage." It is certainly given that a positive number of primes differ by two: 3 and 5, 5 and 7, done.
But a percentage? Start with
% = part/whole x 100%.
Now, take the series a(n) = (# of primes.lt. n which have a prime twin)/(# of primes.lt. n) * 100.
Sorry about the FORTRAN notation; I can't seem to get a "less than" sign with HTML!)
We should all agree that this a(n) is reasonably able to be called the "percentage of primes.lt. n that have a prime twin." Now, let n --> infinity. If the number of prime twins is finite, then a(n) will approach 0, which is not a positive number.
From your post, I think you agree so far. Now go one step further: what is the most meaningful way to assign a value to "the percentage of primes who are twins"? Since there are an infinite number of primes, I would humbly submit that the only consistent way to do so is to assign it to
The backside of LeftOverture was pretty nice. And La Villa Strangiato (from Hemispheres) is still an all-time favorite. Almost anything off of The Yes Album or Fragile was a gem.
The important thing about those groups is that they inspired me and thousands of others like me to pick up a guitar and really learn to play. In that sense, they did significant art.
I totally agree. What's interesting is my students, who are reluctant to sing in public (and when they do, they try to imitate the grunge band sound). They know that they don't sound like what they hear, so they shut up. What they don't know is that the voices on CD don't sound like that, either, until they get chorused, reverbed, EQed, and pitch-fixed.
1) I am encouraged by the amount and quality of home-recording equipment around these days. For $500 or less you can get decent microphones, and for another $500 you can get decent editing and processing software which surpasses last decade's state-of-the-art. To my mind, this gives me as a musician a whole lot of freedom to make music the way I want to.
2) However, I couldn't make a living like that, unless I were to be picked up by someone. And the point of the Frontline show is that the "someones" willing to pick up new artists are diminishing in number. In the long run, I believe that the problem will be solved by a shift in the market; after all, musicians receiving patronage has a long and glorious tradition.
3) But, in the short run, the situation stinks. What is interesting here is that we have gotten exactly what we wanted, so to speak. Music marketers discovered what types of music people were willing to pay for. The majority of us said "Yes" to 3 minute singles with catchy choruses repeated ad nauseum, sung on video by sexy-looking stars, and we said "No" to 20 minute explorations created by groups like Yes, Kansas, or Rush. Which raises an interesting point: if majority rule and utilitarian thought produces such obvious garbage in the music realm, what garbage can it produce in other areas... like government, or ethics?
... but you rarely here about anybody supporting lower sentances for crimes.
Why, 20 years ago, you would have been held after class and forced to write the words "hear" and "sentences" a hundred times on the board. Now, you just get off with a warning...;-)
P.S. The above is strictly humorous, and any resemblance to grammar-naziism is strictly coincidental.
You're right about the ludicrous broadness of the term. However, the legal definition of value is a bit different from the philosophical:
VALUE, common law. This term has two different meanings. It sometimes expresses the utility of an object, and some times the power of purchasing other good with it. The first may be called value in use, the latter value in exchange.
2. Value differs from price. The latter is applied to live cattle and animals; in a declaration, therefore, for taking cattle, they ought to be said to be of such a price; and in a declaration for taking dead chattels or those which never had life, it ought to lay them to be of such a value. 2 Lilly's Ab. 620.
[1]
So it turns out that "value" is actually measured in terms of its fungibility, or "financial gain" -- which is a vicious little circle...
P.S. I hope you've never suggested charging your wife for the "I love you"s.;-)
Hm. In the first case, energy can be accounted for quite nicely:
at the top of the atmosphere, the meteor has potential energy and a small amount of kinetic energy; on the way down, it trades off potential for kinetic and thermal energy. I'm having trouble seeing the violation.
In the second and third cases, you are being fooled by thinking about a *person* as the actor. People have a complicated mechanism of applying forces that involves continual expansion and contraction of muscle fibers. As a result, a person can do no work and yet still expend energy; that energy shows up *not* as work, but as heat.
Take the person out of your example: imagine an object clamped to the wall. In that case, the object pushes against the wall but does no work, and it never gets tired. Or, imagine a rock on a string spinning in outer space, with no one turning it. The rock will continue indefinitely.
What would *really* help you here is some math, so I recommend from here that you take your questions to a physics book.
Do you see where I am confused? Yes. Your analysis of the meteor is correct: work is done. This is why the meteor speeds up *and* heats up on its way down.
Your analysis of the man pushing the wall is somewhat correct. The man does no net work, but his muscles do work internally as they continually expand and contract. Hence, man gets hot in a way that a brick never would.
Your analysis of the orbiting situation is incorrect because the "distance" traveled by the moon is never in the same direction as the gravitational force. Thus, it can never be gravity that does any work.
So, why does the moon keep spinning? Because it is *already* in motion. Newton drew this cool diagram showing a man shooting a gun from the north pole. As the muzzle velocity gets faster and faster, the arc of the bullet gets longer and longer. Eventually, the arc gets long enough so that as the bullet falls towards the ground, it follows the curvature of the earth. At that point, the bullet is in orbit. But, the energy needed to put the bullet in orbit comes from the gun, not from the earth.
Sorry...tried to post earlier and the browser barfed.
You asked
But the moon does constantly change direction (velocity), which does requires energy, does it not?
That's a fair question, but the answer is No. From a mathematical point of view, kinetic energy is solely a function of speed (K=(1/2)mv^2) with no regard for direction. Therefore, changing direction without speed requires a force, but no energy expended. This contrasts with momentum, which is has both magnitude and direction; therefore, changing direction *does* require an "impulse" (force * time).
Take an example from a martial arts situation: suppose a 100-kg man is moving towards me at 2 m/s. It would require a lot of energy to bring him to a halt. But it would require very little energy for me to stick out my foot and trip him, thus changing the direction of his motion.
Look at it another way: suppose you were correct, and the moon does acquire energy as it turns. But, after one month, it would be back at the same point in its orbit, moving with the same velocity. Yet by your reckoning, it would have accumulated a large amount of energy, even though it would be in the same state that it was a month ago. That's not possible.
Conclusion: the moon has no net change in energy as it moves in its orbit.
A much cleaner way to think about this is to take a couple of semesters of calculus. Then you can define
Force = -grad U
Work = Integral(F*dx)
and then it's trivial to show that work = 0 for motion along a circular path, or even any closed path.
IAAPT (Physics Teacher). It seems like what is bothering you is some confusion over force and energy. Imagine a brick resting on a table. In order for the brick to remain on the table, the table must exert an upward force on the brick to counteract the force of gravity. This force comes from the repulsion between electrons in the brick and electrons in the table. However, no energy is expended by the table in maintaining the brick's place. If those two objects were the only objects on Earth, they would continue indefinitely, with no need to recharge any batteries. So the existence of a force does not require the expenditure of any energy.
The orbiting Moon is a similar situation from an energy point of view. Assume first a circular orbit. As the moon moves around, its speed (which determines kinetic energy) remains the same, and its orbital distance (which determines potential energy) remains the same. As a result, the moon never expends any energy at all to remain in orbit. Instead, it maintains a constant level of total energy. If you are skeptical about this, think about the speed issue. If energy really were being pumped into the moon, it would change speed (or perhaps orbital distance), and something would have to lose a corresponding amount of energy -- the Earth, perhaps? -- and that doesn't seem to be happening.
Actual orbits for moons and planets are elliptical, but the difference between elliptical and circular orbits is that in an elliptical orbit, some potential energy is traded for kinetic energy on the near end of the orbit and then the same amount is traded back on the far end of the orbit. The total amount of energy of the moon never changes.
What about the cause of the gravitational force? There are two main theories out there:
standard general relativity holds that masses create "accelerated reference frames" around themselves which then behave like gravitational attractors. To understand this, imagine being in an elevator on a scale. Right as the elevator accelerates upwards (an accelerated reference frame), the scale reads a higher number. When it begins to decelerate, the scale reads a lower number. (Try this at home!). The accelerated reference frame acts just like a gravitational force.
The second model is quantum gravitation, which envisions masses sending out small virtual particles called "gravitons." My understanding is that as gravitons are absorbed, they exert gravitational force on the absorbing object. (this theory is out of my area, so better explanations are available). Quantum gravity sounds weird, but the idea is to parallel the Quantum Electrodynamic theory, which explains electrical forces in terms of absorbed and emitted photons. One reason that we want to do this is that the gravitational force F = Gm1m2/r^2 looks eerily like the electrical force F = kq1q2/r^2. Hence, we suspect that a similar mechanism is at work.
Finally, keep in mind that at the bottom of all of these theories will be undefined terms. What is "charge"? "mass"? Those terms cannot be defined in a non-circular manner. We simply have to agree that we all understand them well enough to use them.
A great reference is Albert Einstein's book on relativity. It's mostly non-technical, and has some great analogies.
That might be true for a small number of of obsessed geeks but the majority of people dont give a monkeys about who controls software.
They ought to give a monkey's $BODYPART about control. Condsider:
Software controls whether or not my car passes vehicle emmissions inspections. Someone who fails inspections will *never* know whether he really failed or whether he's being ripped off.
Software controls whether or not I'm flagged as a terrorist on a flight.
Software controls flow of goods and services around the world.
Software controls my bank account balances, and
Software may very well tally votes in the next election.
I want a non-vested party to be able to audit the code that controls those things.
Good responses all. I was unaware of third-party escrow, but it sounds like it solves some of the problems. Not as good as a thirty-day warranty, though:-)
I *did* in fact check out the ratings on the seller prior to the sale, but *didn't* bother to leave negative feedback after the sale because I was disgusted with the system as a whole (i.e., didn't figure my feedback would count for much).
Now, that may have been a premature reaction on my part, but it's also instructive: if e-bay can't get a high enough percentage of first-time buyers like me to have a positive experience, then they don't have a long-term viable business model.
Slashdot Mirror
Let's say I'm a Muslim in Oregon, and I'm accused of committing a terrorist crime in Cleveland. I have multiple people willing to testify that I was in Oregon at the time. But the police have three different RFID reads placing my car in Cleveland at the time. Which one of these has more credibility in a court of law? Which one should have more credibility?
Acoustic noise, yes. Electronic noise, no. Computers can add a lot of hum when they are near audio cables (at least, in my experience. Maybe others have found nifty shielding solutions?).
sample a 1 second clip of nothing and subtract it from your recording and you remove all system noise.
I've wondered about doing that but have not gotten around to really testing it. Do you get good results from it? Does it have an adverse impact on the tone of the signal?
An alternate approach that I've heard rumor of is to reverse the usual noise-reduction idea: instead of seeing the background noise as "noise" and the mic input as "signal", consider the mic input to be "noise" and filter it out; then invert the result and add back to the original. Results are claimed to be outstanding. I haven't figured out how to code for it yet.
Nice solution, except for the punch in the face part. My concern is the cost for a 4-channel, 24- or 32-bit, 44.1kHz sample rate stand-alone box, but maybe digital money could solve the problem? Kidding! Secret Service, it was only a joke.
Sorry ... Spinal Tap joke ...
Eliminating noise is a matter of degrees. You could easily move the tower outside the recording room -- but then you have longer cables, and you get noise from that. If you are playing an electric guitar, your pickups might grab stray signal from a monitor as well, which is really annoying when the amp is at "11". And, I recently discovered that flatscreens are much noiser than old CRTs in that regard.
Al Cicada! Now I understand the invasion going on in my back yard! Oh...wait...Al CIAda...sorry
Agreed on the propane issue. Disagreed on the understanding of the Middle Ages. I'm not a Catholic by any stretch, but the church actually did a fair amount of holding things together after Rome's collapse. This includes preserving ancient documents -- you would never have heard of Aristotle or Plato without the church -- building hospitals, and running a lot of local governments. Nor did the church in the early Middle Ages promote feudalism. Later on, perhaps even as early as Charlemagne, the church became much more enamored with top-down government. You might read, e.g., Cahill's "How the Irish Saved Civilization" for a non-Christian's take on the impact of the church. Another good readable history is Chadwick. Anyways, I'm digressing on a digression.
:-)
Reducing cow farts? Ha!
"pickmode" = "nit"
City of God gets a bad rap. Augustine's point was not to tell people to turn their backs on the city of man; after all, people live there! Instead, he was reacting against the idea that "Christendom" == "Rome". By telling Christians that their ultimate hope rested in the city of God, he was encouraging them that the failure of Rome was not an ultimate disaster. He was, in fact, advocating an early form of separation of church and state: two cities, interacting but not comingled.
"pickmode" = "off"
Let's take a neutral example: What is the value of 0.333...? My students will sometimes naively say that it has no value, since we keep on adding on terms forever. However, they say, 0.333... "approaches" the value (1/3). This seems reasonable, but it is incorrect. The true value of 0.333... is 1/3; the only thing that is "approaching" is our approximation of 1/3. The trick to handling infinity is to find the right notation to do the job. The standard line, taken by mathematicians around the world, is as follows:
Let S(N) = Sum(i = 1, N, 3/10^i). It is clear that S(N) = 0.333...333 to the Nth place. But, if we evaluate that sum using the standard geometric series formula, we also get S(N) = (1 - (1/10)^N)/3. So, if we let N --> inf, we get the value of the infinite series 0.333...., which is 1/3.
You probably recognize this procedure from algebra or some other class. The point is that infinity is not handled loosely via common sense, but is instead handled with precise notation:
Assign a meaningful function which gives correct values for finite values of N, then
let N go to infinity. If the limit exists, then that limit is considered to be the value "at infinity".
That's the procedure I was taking in my first post: define a function which gives the correct percentage of twin primes for finite N, then let N go to infinity. The result is the only meaningful way to define the percentage of twin primes out of all of the primes, which are infinite in number. The advantage of doing it that way is that it avoids odd concepts like "infinitely small positive value", which doesn't have any concrete meaning.
Without us Sumerians, you wouldn't have writing! You hereby owe us 699.99 dinars per character ... no, wait, wrong joke ... umm... Soviet Russia ... no ... tinfoil hat ... forget it.
Hmph. Numbers don't "approach"; they have well-defined values. That is, they are constants.
On the other hand, functions (including sequences) approach values for different values of x or n or whatever variable.
I think I address your concern in the remainder of my first post. If you can sort through the terrible notation (sorry!), I think it will clear up the problem.
The flaw is in the word "percentage." It is certainly given that a positive number of primes differ by two: 3 and 5, 5 and 7, done.
.lt. n which have a prime twin)/(# of primes .lt. n) * 100.
.lt. n that have a prime twin." Now, let n --> infinity. If the number of prime twins is finite, then a(n) will approach 0, which is not a positive number.
But a percentage? Start with
% = part/whole x 100%.
Now, take the series
a(n) = (# of primes
Sorry about the FORTRAN notation; I can't seem to get a "less than" sign with HTML!)
We should all agree that this a(n) is reasonably able to be called the "percentage of primes
From your post, I think you agree so far. Now go one step further: what is the most meaningful way to assign a value to "the percentage of primes who are twins"? Since there are an infinite number of primes, I would humbly submit that the only consistent way to do so is to assign it to
lim n-->inf a(n), which is 0.
The backside of LeftOverture was pretty nice. And La Villa Strangiato (from Hemispheres) is still an all-time favorite. Almost anything off of The Yes Album or Fragile was a gem.
The important thing about those groups is that they inspired me and thousands of others like me to pick up a guitar and really learn to play. In that sense, they did significant art.
I totally agree. What's interesting is my students, who are reluctant to sing in public (and when they do, they try to imitate the grunge band sound). They know that they don't sound like what they hear, so they shut up. What they don't know is that the voices on CD don't sound like that, either, until they get chorused, reverbed, EQed, and pitch-fixed.
1) I am encouraged by the amount and quality of home-recording equipment around these days. For $500 or less you can get decent microphones, and for another $500 you can get decent editing and processing software which surpasses last decade's state-of-the-art. To my mind, this gives me as a musician a whole lot of freedom to make music the way I want to.
... like government, or ethics?
2) However, I couldn't make a living like that, unless I were to be picked up by someone. And the point of the Frontline show is that the "someones" willing to pick up new artists are diminishing in number. In the long run, I believe that the problem will be solved by a shift in the market; after all, musicians receiving patronage has a long and glorious tradition.
3) But, in the short run, the situation stinks. What is interesting here is that we have gotten exactly what we wanted, so to speak. Music marketers discovered what types of music people were willing to pay for. The majority of us said "Yes" to 3 minute singles with catchy choruses repeated ad nauseum, sung on video by sexy-looking stars, and we said "No" to 20 minute explorations created by groups like Yes, Kansas, or Rush. Which raises an interesting point: if majority rule and utilitarian thought produces such obvious garbage in the music realm, what garbage can it produce in other areas
/ramble
P.S. The above is strictly humorous, and any resemblance to grammar-naziism is strictly coincidental.
P.S. I hope you've never suggested charging your wife for the "I love you"s.
Hm. In the first case, energy can be accounted for quite nicely:
at the top of the atmosphere, the meteor has potential energy and a small amount of kinetic energy; on the way down, it trades off potential for kinetic and thermal energy. I'm having trouble seeing the violation.
In the second and third cases, you are being fooled by thinking about a *person* as the actor. People have a complicated mechanism of applying forces that involves continual expansion and contraction of muscle fibers. As a result, a person can do no work and yet still expend energy; that energy shows up *not* as work, but as heat.
Take the person out of your example: imagine an object clamped to the wall. In that case, the object pushes against the wall but does no work, and it never gets tired. Or, imagine a rock on a string spinning in outer space, with no one turning it. The rock will continue indefinitely.
What would *really* help you here is some math, so I recommend from here that you take your questions to a physics book.
Regards,
Jeff Cagle
Do you see where I am confused?
Yes. Your analysis of the meteor is correct: work is done. This is why the meteor speeds up *and* heats up on its way down.
Your analysis of the man pushing the wall is somewhat correct. The man does no net work, but his muscles do work internally as they continually expand and contract. Hence, man gets hot in a way that a brick never would.
Your analysis of the orbiting situation is incorrect because the "distance" traveled by the moon is never in the same direction as the gravitational force. Thus, it can never be gravity that does any work.
So, why does the moon keep spinning? Because it is *already* in motion. Newton drew this cool diagram showing a man shooting a gun from the north pole. As the muzzle velocity gets faster and faster, the arc of the bullet gets longer and longer. Eventually, the arc gets long enough so that as the bullet falls towards the ground, it follows the curvature of the earth. At that point, the bullet is in orbit. But, the energy needed to put the bullet in orbit comes from the gun, not from the earth.
You asked That's a fair question, but the answer is No. From a mathematical point of view, kinetic energy is solely a function of speed (K=(1/2)mv^2) with no regard for direction. Therefore, changing direction without speed requires a force, but no energy expended. This contrasts with momentum, which is has both magnitude and direction; therefore, changing direction *does* require an "impulse" (force * time).
Take an example from a martial arts situation: suppose a 100-kg man is moving towards me at 2 m/s. It would require a lot of energy to bring him to a halt. But it would require very little energy for me to stick out my foot and trip him, thus changing the direction of his motion.
Look at it another way: suppose you were correct, and the moon does acquire energy as it turns. But, after one month, it would be back at the same point in its orbit, moving with the same velocity. Yet by your reckoning, it would have accumulated a large amount of energy, even though it would be in the same state that it was a month ago. That's not possible.
Conclusion: the moon has no net change in energy as it moves in its orbit.
A much cleaner way to think about this is to take a couple of semesters of calculus. Then you can define
Force = -grad U
Work = Integral(F*dx)
and then it's trivial to show that work = 0 for motion along a circular path, or even any closed path.
Hope that helps.
The orbiting Moon is a similar situation from an energy point of view. Assume first a circular orbit. As the moon moves around, its speed (which determines kinetic energy) remains the same, and its orbital distance (which determines potential energy) remains the same. As a result, the moon never expends any energy at all to remain in orbit. Instead, it maintains a constant level of total energy. If you are skeptical about this, think about the speed issue. If energy really were being pumped into the moon, it would change speed (or perhaps orbital distance), and something would have to lose a corresponding amount of energy -- the Earth, perhaps? -- and that doesn't seem to be happening.
Actual orbits for moons and planets are elliptical, but the difference between elliptical and circular orbits is that in an elliptical orbit, some potential energy is traded for kinetic energy on the near end of the orbit and then the same amount is traded back on the far end of the orbit. The total amount of energy of the moon never changes.
What about the cause of the gravitational force? There are two main theories out there:
standard general relativity holds that masses create "accelerated reference frames" around themselves which then behave like gravitational attractors. To understand this, imagine being in an elevator on a scale. Right as the elevator accelerates upwards (an accelerated reference frame), the scale reads a higher number. When it begins to decelerate, the scale reads a lower number. (Try this at home!). The accelerated reference frame acts just like a gravitational force.
The second model is quantum gravitation, which envisions masses sending out small virtual particles called "gravitons." My understanding is that as gravitons are absorbed, they exert gravitational force on the absorbing object. (this theory is out of my area, so better explanations are available). Quantum gravity sounds weird, but the idea is to parallel the Quantum Electrodynamic theory, which explains electrical forces in terms of absorbed and emitted photons. One reason that we want to do this is that the gravitational force F = Gm1m2/r^2 looks eerily like the electrical force F = kq1q2/r^2. Hence, we suspect that a similar mechanism is at work.
Finally, keep in mind that at the bottom of all of these theories will be undefined terms. What is "charge"? "mass"? Those terms cannot be defined in a non-circular manner. We simply have to agree that we all understand them well enough to use them.
A great reference is Albert Einstein's book on relativity. It's mostly non-technical, and has some great analogies.
They ought to give a monkey's $BODYPART about control. Condsider:
Software controls whether or not my car passes vehicle emmissions inspections. Someone who fails inspections will *never* know whether he really failed or whether he's being ripped off.
Software controls whether or not I'm flagged as a terrorist on a flight.
Software controls flow of goods and services around the world.
Software controls my bank account balances, and
Software may very well tally votes in the next election.
I want a non-vested party to be able to audit the code that controls those things.
Good responses all. I was unaware of third-party escrow, but it sounds like it solves some of the problems. Not as good as a thirty-day warranty, though :-)
I *did* in fact check out the ratings on the seller prior to the sale, but *didn't* bother to leave negative feedback after the sale because I was disgusted with the system as a whole (i.e., didn't figure my feedback would count for much).
Now, that may have been a premature reaction on my part, but it's also instructive: if e-bay can't get a high enough percentage of first-time buyers like me to have a positive experience, then they don't have a long-term viable business model.
Regards,
Jeff Cagle