Ummm... are the "most logical minds" going to be drawn to a contest where, given that your skill is an unknown, your odds of winning are 1 over all the participants?
Most people do not go to such a contest with the sole purpose of winning. It would be quite logical to attempt such a contest even if you had no chance of winning, e.g. if you wanted to see an interesting puzzle, and see how you compare to other enthusiasts.
You can expend considerably less labor at many other endevours, and expect a much greater return.
You seem to assume people who think logically are motivated by nothing more than monetary gain. Perhaps a better characterization of the behavior of a logical thinker would be someone who knows what would maximize his or her overall happiness, and sets about achieving that. One should consider the possibility that gathering wealth is not on the top of everyone's list of things that make them happy.
Prediction: they will attract a lot of people who love puzzles, and the most logical mind within that subset will have a good chance of winning, but they will most certainly not attract the most logical minds of all, unless...
That sounds like a good prediction, so far. I suppose the contest organizers are making the implicit assumption that logical thinkers enjoy the logical thinking associated with puzzle-solving.
So, unless you are the ubermind, why bother?
Why bother doing anything at all if you can't be the best in the world at it? I guess the 99.99% of us who are mere mortals should just sit on our collective asses instead of enjoying life. That sounds like the logical solution to me.
The electron doesn't just take up a point. It exists in all those points at once.
The fact that an electron has nonzero amplitude everywhere does not imply that it takes up all the space in the universe. There is an important distinction to be made between the region a particle is likely to be and the region it occupies. Thus far, there has been no experimental evidence for electrons having nontrivial volume. Incidentally, if an electron were some kind of black hole, the region enclosed by the event horizon would be much too small for us to measure, or even distinguish from a point.
The energy of that light wave is typically absorbed as a packet by *all* the electrons in the conductor. But it also can be absorbed by each of the electrons in the conductor.
You're not making yourself very clear here. It looks like you are saying something about electrons obeying Fermi statistics and interacting with the EM field. Both properties are pretty much unrelated to size, e.g. protons (which do take up volume) also obey Fermi statistics and interact with the EM field.
That is because the structure of the nucleus involves a bunch of quarks continuously decomposing at the boundaries of the nucleus.
As another poster noted, this does not seem to make much sense. What are the decay products of these quarks, and what happens to them? Are you referring to the parton model? That does involve lots of quarks in some kind of confinement, but no decomposition, and no definite boundary.
Electrons are stable particles, and do not spontaneously decay. Black holes of that size are highly unstable.
Really? What would be the decay products of a charged black hole with the mass of an electron? I haven't heard of any charged particles with less mass.
The article was about how precisely astronomers were able to measure b and c (they are very close), and thus determined that a (not some mystical term 'delta') = ~.3m.
Not really. The estimate of 0.3m comes from a general physical principle, stating that events that are synchronized to within a short amount of time (say 1 ns) are usually triggered by processes that take up very little space (e.g. 0.3m), since larger triggering processes have a speed-of-light obstruction to getting the necessary information to all of their parts in a timely fashion. This is how astronomers first concluded that pulsars are compact objects - repeated millisecond pulses are unlikely to be triggered by anything bigger than 300km.
It isn't clear what the parent was trying to say, since he never made his point very clear. I think the idea was that if the surface of the pulsar were somehow absolutely flat (say it was a cube), with normal vector facing us dead-on, and the pulsar managed to produce some kind of instantaneous pulse that took zero time in our rest frame, he could place some kind of bound on the size of the side facing us (about 4 times the diameter of the sun) via the pythagorean theorem.
It was quite a calculational tour de force, but I can't really see why it would be useful.
The danger is that soon enough an Intel processor will get hot enough to trigger a fusion reaction in atmospheric hydrogen, turning Earth into a small star.
Fortunately, Intel is working on this as we speak! Here is a Register article with VP Gelsinger's predictions. Here is a nifty photo of an overclocking experiment gone awry.
I assume you are referring to prewarp or average tech starts. In the advanced game scenario, Creative is pretty much essential, even though it costs 8 points. If you don't have it, chances are, you will have a large research/production disadvantage, because the game selects a random set of earlier technologies for you.
Unification, Tolerant, +1 Production eats any creative race's lunch.
... and Unification, Telepathic, Omniscient, Rich Artifact Homeworld eats the Unification Tolerant for lunch and only gets stronger. An early (i.e. turn 60-70) cruiser with MIRV nukes will take out almost anything you can throw against it.
Unification Tolerant and other high-production races perform quite stunningly against the computer, but they are weak enough in research that there is a vulnerable period between the time they start colonizing en masse and the time the consequent high population allows them to erase the technology gap. Similarly, races such as Democracy, Lithovore, Artifact Homeworld can stay on their homeworld for about 100 turns before building a Guardian-killing fleet when playing against the computer, but they can expect interference if there are other human players.
For prewarp and average starts in multiplayer situations, balanced races such as Subterranean, Lithovore, Large Artifact homeworld, and the canonical Telepathic blitz races work much better.
I tend to agree here with the grandparent about not mixing physics with sociopolitics.
While it may be poor judgment to say that sociopolitics and quantum physical systems exhibit the same behavior, it is often valid to say that they can be treated with similar mathematical models. Sometimes, observed phenomena in one area can provide insight into the behavior of the other, even if they are as disparate as the two aforementioned fields.
This Bose Einstein example itself seems ridiculous to me. I don't see the lowest state as "winning over and monopolizing over" all the other states. What happens is that the other states can take in only so many particles.
The grandparent never mentioned any sort of "winning over and monopolizing over" action. The analogy was on the level of using a mathematical model. A Bose-Einstein condensate happens in systems with indistinguishable, non-excluding particles (i.e. they exhibit Bose statistics). It is necessary for the thermal energy in the system to be low enough that most or all of the particles settle into the lowest energy state. Your description is poor because other states can accept arbitrarily many particles (up to certain macroscopic constraints, e.g. gravity), and the reason for condensation is that it is not energetically favorable for the particles to jump to those levels.
Although the phrase, "winner take all," is a bit overused, there does not seem to be any evidence that the author of the book seeks to anthropomorphize bosons.
Additionally, if the two photon are emitted exactly 180 degrees opposite of each other, and both are traveling at velocity c, the transmission of data has a theoretical velocity of twice the speed of light.
Unfortunately, there is no information transmitted from Photon Receiver A to Photon Receiver B in your scenario, so no information travels faster than light. Schrodinger and Heisenberg are pretty much irrelevant here.
You may be trying to describe teleportation via quantum entanglement, which has been done in the
laboratory. This involves some surprising correlations between measurements of widely separated particles, such as the photons in your example (although a black body is a terrible source). However, the correlations in question do not represent any sort of information transfer, and this phenomenon has been explained quite well by theory which keeps everything at light speed or less, despite the wishes of various crackpots and science fiction fans.
But if gravity were not instant, how could things orbit one another? in my minds eye, I see the earth pulling on the moon.. and the moon pulling on earth, but the moon is falling past the earth. If the speed of gravity weren't instant, it is hard to imagine circular or elliptical orbits..
Try not to think of gravity as a force, but as a geometric phenomenon. The earth and moon are not really "pulling" on each other so much as the presence of their mass, momentum, energy, etc... are shaping spacetime, and the curvature that results makes their paths appear to orbit each other. For objects which don't move too much relative to each other, this looks a lot like an instantaneous force, and that's why Newton's theory was proposed in the first place.
However, for elliptical orbits such as Mercury's, Einstein's theory predicts a precession of the axes, and it deviates enough from Newton's instantaneous force theory that the differences are testable from Earth. The observations in question agreed with Einstein's prediction much better than they did with Newton's. This is one of several pieces of experimental evidence favoring Einstein's theory.
Einstein's principle of equivalence says (among other things) that uncharged objects in space will follow what is basically a straight line path (strictly speaking, a geodesic). However, when spacetime is curved (usually due to stuff being nearby), that path can appear bent to a distant observer. Hence, planets, satellites, and thrown objects feel no external gravity, and are actually travelling in "straight" paths, while we are being accelerated upward from our natural trajectory by our contact with the ground.
The matter would become energy.. and energy doesn't create gravity.. so.....
According to general relativity, energy does make a contribution to gravitational effects. Einstein's field equations include the stress-energy tensor, which for each point in spacetime gives information about the energy (including mass-energy) density, momentum density, and stress (e.g. pressure) associated to all forms of matter and all non-gravitational fields [MTW].
The problem is that if you assume Einstein's field equations, you automatically get the assertion that gravity "travels" at c, the speed of light in a vacuum. Any alternative theory regarding speed would have to include some change in the field equations, which have made some very strongly verified predictions in the last 85 years. On the other hand, if you had some alternative theory that did not have the same dependence on the stress-energy tensor, and if it predicted a gravitational change from an annihilation event, then you might be able to test its validity using such an experiment.
Don't forget to factor in my displacement
device and damper field.
I did. Without the defensive devices, only one missile would be necessary, as MIRV zeon missiles do 4*30 damage.
And where are you getting the 120 damage b4
it explodes?
If you scan a ship on the battle screen, you will get a display of various systems, such as engine, computer, etc... On the top right of each such box, there will be a fraction, e.g. 56/120, indicating the health of the system in question. I don't recall the exact numbers for engine hit points, but it is 10 for battleships and 40 for doomstars, with reinforced hull tripling everything. Note that these numbers are completely independent of your armor technology, and they tend to be rather small (which is why ion pulse cannon is so annoying). Engine damage will cause the ship's mobility to deteriorate according to some formula I don't recall, and at something like 25%, the ship is immobilized. When the engine loses all of its hit points, the ship disappears in a big explosion, damaging everything within 2 or 3 squares.
Attack the Guardian once you've got ships with graviton guns or better, and zortrium armour at least. The best combo in the mid-game is a volley of grav cannon to knock down the shields, then a volley of ion cannon to demolish internal systems. A couple of Titans with this setup can destroy the Guardian without giving it a chance to return fire.
This is gross overkill. The Guardian can be killed with two cruisers and 4-6 frigates fitted with a mixture of appropriately typed merculite missiles (another poster described these - I'd omit the FST mod). It requires just zortrium armor, merculite missiles, emissions guidance system, and fast missile racks. Note that it does not need any beams or computers (making it good for non-creative races by eliminating research tree problems), and the construction takes about half the production needed to build single titan. A custom democracy-lithovore-artifact race often can send off such a fleet within 100 turns of a prewarp start, and several other races can perform similarly. If you're quick enough killing the Guardian, you can just use the Avenger to kill off everyone else.
Death rays and particle beams are heavily overrated
Particle beams have a defensive use: they are the most powerful beam that can be placed in a fighter. While fighters on ships are quite inefficient, they provide rather good defense in a fighter garrison, where they can produce up to 1400 points of damage. Death rays are very good if you can kill the Guardian early, as there are no comparable weapons until the phasor. Unfortunately, both are very expensive to produce.
At the end? HV AF SP Phasors w Achilles Targeting System. 'Nuff said.
If you build smart, you don't need to get much further than MIRV nuclear missiles at the end. Given a pre-warp or average start, it is quite possible to win at "impossible" level before the opponents get either radiation shield or powerful beams to counter the missiles.
As it happens, the most efficient ship-to-ship weapon is the plasma cannon, not the phasor. However, if you are attacking a well-shielded planet, neither weapon will do any damage whatsoever.
Also, it's worth investigating the potential of phasing cloaks and timewarp facilitators.
That and stasis fields make the late game rather silly. There is something wrong with the game mechanics when you can defeat the Antarean home fleet with a single frigate by piling plasma webs on the star fortress and ships.
BTW, did you know what you can avoid war all
together by simply ignoring the diplomats?
This is definitely not true in general, at least not on the "impossible" difficulty level. Occasionally, the computer players, especially the repulsive ones, will declare war for no apparent reason.
The parent's story doesn't sound like the same MoO2 game I've played. I've never seen a CP demand either surrender or more than 10% tribute (it's not an option on the diplomacy screen), and I've never seen a CP offer tribute, no matter how dire the circumstances.
400? That assumes you only put 1 converter per ship. Bollucks! I recall doing over 10k damage with stellarconverters...
Stellar converter does 400 enveloping damage, meaning 400 points for each of four shield faces. If you shoot an unshielded planet with 7 convertors, you will do 11200 damage. If you have structural analyzer, those same weapons will do 22400 damage to unshielded ships.
While this sounds impressive, the stellar converter is one of the least efficient high-level weapons, since it is bulky and does not benefit from beam bonuses like high-energy focus and hyper-X capacitors. An optimized ship full of plasma cannons will be able to do over 150,000 damage to unshielded ships in one turn, about six times the stellar converter's efficiency. The plasma cannon is in fact the most efficient weapon in the game, followed by disruptor, gauss cannon, phasor, and mauler device. Naturally, the presence of shields, especialy on planets, will shift the balance in favor of the heavier weapons, e.g. disruptor and mauler.
reflection field + damper field + energy
absorber + displacement device + inertial nullifier
+ wide area jammer + automated repair unit
damn near impossible to destroy.
A ship like this is rather trivial to destroy, using MIRV EMG ECCM missiles, as unshielded ships are quite vulnerable to the emissions guidance system. Even a doom star with reinforced hull can only take 120 points of damage to the engine before exploding. If the enemy has sensor technology, your evasion becomes (130% [WAJ]+ 50% [IN] - 70% [Sensor] )/2 [ECCM] = 55% so 11 or 12 missiles should suffice, and that can fit on a mere cruiser with enough tech advancement.
If you are playing in a multiplayer game, you will find that no ship is anywhere near impossible to kill. Unfortunately, the AI does not know how to build efficient ships.
This did not completely solve the problem. If the enemy does not have PC/TWF tech, it is still possible to attack with impunity if you appropriately time your attacks with the "wait" button. Thus, it is still possible to defeat the Antarean home fleet using a single frigate fitted with with Phasing Cloak, Time Warp Facilitator, and a plasma web.
what happens if the existing "sarcophagus" fails after the bigger one is built over top of it?
If the existing sarcophagus fails inside the new one, the dust and debris that are kicked up will remain inside the outer structure. The purpose of the outer structure is to prevent this dust from being picked up by the wind and contaminating the surrounding countryside.
I don't specialize in dynamical systems, but I do know what a queue is.
Fractal box counting will show that the fjords have a boundary that is approximately 1.4 dimensions (rather than the typical 1-dimensional boundary of a circle or square) and thus, can not be measured with a finite 1-dimensional measure such as length.
Both the land and water are made of atoms, so your approximation breaks down at small scales, and you end up with a finite path length. The problem is that you are applying fractal box approximation, a mechanism suited to morphological representations, to a calculation of length, for which it was not designed.
Thus the coastline length can be approximated by infinity.
Instead of approximating the length, you just extrapolated a pattern from limited data to well outside its applicable domain. Here's an analogous example. Suppose I have one dollar in my wallet at time 0, two dollars at time 1 minute, 4 dollars 30 seconds later, and 8 dollars 15 seconds after that. Clearly, my wealth is doubling at an asymtotic rate. Would you approximate my wealth at 2 minutes by infinity? Everybody knows that anything remotely close to infinity is still infinity, thus I have infinite wealth, at least in your imaginary world.
The best one is time: there are now 50 seconds in a minute, so we can move 2 minutes to one, then we get 26 minutes in an hour, by quadrupling the hour to 100 minutes we now get 6 hours in a day, halving the length of a second will now give us 10 hours in a day. We have just decimalised time without significantly changing the base unit.
Perhaps a more global treatment would prevent errors such as poorly multiplying minutes. Note that one day has "42000" of our normal seconds, so we must either shorten a second by a factor of about 3 (actually "60/21"), or lengthen it by a factor of "4.2" in order to get a power of "10"
I still favor binary, or base e when exact representations are unnecessary. Division in binary takes more space, but is less prone to errors, since the operations involve less thinking. You can count very high on your fingers in binary, if you use your knuckles appropriately. The downside (other than looking bad in front of aliens) is people around you might think you have palsy.
yet within this small region may be over 10 solar masses of material.
Had you read the article, you would have seen that neutron stars are thought to contain the mass of about 1.4 suns. Barring certain speculative theories of exotic matter, no cold (i.e., not undergoing fusion) stellar configuration can have a mass greater than 5 suns. See, for example, Misner, Thorne, Wheeler, page 627.
The result is a gravitational field at the surface of a neutron star about 70 trillion times stronger than that on Earth.
Given that neutron stars have mass about 500,000 times that of the earth, and radius about 1/400 earth radius, one can use the Newtonian inverse-square law approximation to get a factor of about 80 billion, which is considerably less than your figure. Where did you get these numbers?
Its core consists mainly of densely-packed neutrons, with a sprinkling of protons and typically 3 times as many electrons as protons, in a liquid-like state known as neutronisticis.
Do you have a reference for this? Most models of neutron stars treat the core as a degenerate Fermi gas, and as another poster noted, your star seems to have a net negative charge. Where did the protons go? Also, this is the first time I've encountered the word "neutronisticis". A Google search turns up nothing but this very post.
As a neutron star cools and grows, strains develop in the crust so that it buckles, causing starquakes equal to 1000 on the richter scale.
Starquakes are thought to be possible, but if our time frame is more than a few seconds after formation, the cause is probably not due to thermal stresses. This is because the thermal contribution to pressure and density is negligible as long as the temperature of a neutron star is below the Fermi energy of matter at nuclear density (about 30MeV, or 3*10^11 K - see MTW page 599, referenced above), and neutrino radiation brings the temperature well below this level very rapidly.
The Richter scale is logarithmic, based at 105 Joules for a degree 0 quake (reference), and growing by a factor of 1000 for every two degrees. A quake registering 1000 would have to release 1.05*10^1502 Joules, which is much more than the mass-energy contained in the observable universe. Indeed, it is quite impossible for any stellar-scale phenomenon to register more than 40 on the Richter scale, simply because stars don't have enough mass to release that kind of energy.
Weight is the measure of gravitational attraction between two bodies... nothing more.
Merriam Webster's definition is fundamentally flawed, as it does not specify a frame of reference for measuring the force, which is not Lorentz-invariant (N.B. there is a relativistic analogue of force, called 4-force, but it would be zero in this case). Furthermore, it is contradicted by a more authoritative source: MTW's Gravitation,
page 13, first paragraph of section 1.3.
Free fall is synonymous with weightlessness: absence of any force to drive the object away from its normal track through spacetime.
Indeed, the fundamental principle behind Einstein's general relativity is the fact that gravity does not exert force. Rather, the presence of mass-energy bends space-time, and can cause the trajectories of distant objects to converge.
A scale is just one limited method for measuring weight. I say limited because it functions by measuring the normal force... caused by the ground holding the scale at rest, thus giving an inertailly fixed reference frame...
Weight is just the force applied to an object, and in the case of objects on the Earth's surface, this force is supplied by the ground, which is in our way, accelerating us from our natural path toward the Earth's center. Thus, a scale is a very good way to measure weight, as it is transferring the normal force from the ground to the object we are weighing, and measuring the force applied in the instantaneous reference frame of the object. Incidentally, the ground is not an inertially fixed reference frame, for the very reason that it is not in free fall.
Coastlines are fractal: the closer you look, the longer they get.
Both the ocean and the continent are made of atoms, so the fractal approximation breaks down when you look too closely, and you end up with a finite path length. For the purposes of aerial photography, you might as well take a minimal cover of the coast using discs of radius ~1km and sum their diameters. Small crinkles are completely irrelevant.
It's one of the few really fundamental mathematical discoveries of the last century.
This sounds like a troll, but there is a shred of truth hidden inside. There have been plenty of deep, fundamental mathematical discoveries in the last century, and I doubt you can find many mathematicians who would agree with your sentiments. All of the people appearing on this page have done very impressive work, and you may notice that fractals are not featured at all. Unfortunately, fractal geometry is one of the few recent advances which can be understood even superficially by people lacking a background in mathematics, and this seems to raise the public profile of the field substantially.
Imagine you have a cannon. You fire a cannonball out of it, and it follows a parabolic path until it hits the ground (Boom).
The path looks like a parabola in the same sense that the surface of the Earth looks flat. From a Newtonian standpoint, the path is not a parabola, but the end of an ellipse, one of whose foci is at the center of gravity of the the Earth-cannonball system. Since the Earth is essentially a homogeneous ball, we can pretend (as long as the cannonball is above the surface) that it is a point mass at its center of gravity, so the cannonball and the Earth are briefly mutually orbiting each other.
Unfortunately, the ellipse will not be followed beyond the intersection of the trajectory with the Earth, even if the cannonball were made out of some kind of weakly interacting matter that could pass through atoms. This is because the gravitational force inside the Earth decreases in proportion to the distance from the center, instead of following the inverse square law.
For instance, treat c as a singularity in the complex-mathematical sense and integrate around it.
Perhaps you are referring to analytic continuation. Unfortunately, whatever extended function you produce is only guaranteed to be single-valued in special cases, like rational functions. As it happens, if you somehow got your velocity to move around c in a loop, your mass and length would become negative, because the Lorentz contraction formula contains a square root. You'd have to make a second loop to get back to normal.
This
appears to be the abstract for the announced results. Note the lack of words like "round" in the abstract and article. You may need a subscription to Physical Review Letters to reach it and download the paper.
This appears to be the abstract of the paper of Miller and Frank attempting to explain the phenomena. You will have to accept cookies to get any sort of information out of the APS site.
This
seems to be the experimental project page. It doesn't appear to be an informative resource for the uninitiated.
I'd never read a nuclear physics paper before, so I wasn't sure what to expect. It looks like straight pQFT calculation with the Feynman diagrams, etc. would be computationally intractible for these problems, so people are always looking for reasonable approximation schemes. I guess the ones that had been used in the past didn't factor in relativistic effects as much as they should have, and the recent models corrected this.
Slashdot Mirror
Ummm... are the "most logical minds" going to be drawn to a contest where, given that your skill is an unknown, your odds of winning are 1 over all the participants?
Most people do not go to such a contest with the sole purpose of winning. It would be quite logical to attempt such a contest even if you had no chance of winning, e.g. if you wanted to see an interesting puzzle, and see how you compare to other enthusiasts.
You can expend considerably less labor at many other endevours, and expect a much greater return.
You seem to assume people who think logically are motivated by nothing more than monetary gain. Perhaps a better characterization of the behavior of a logical thinker would be someone who knows what would maximize his or her overall happiness, and sets about achieving that. One should consider the possibility that gathering wealth is not on the top of everyone's list of things that make them happy.
Prediction: they will attract a lot of people who love puzzles, and the most logical mind within that subset will have a good chance of winning, but they will most certainly not attract the most logical minds of all, unless...
That sounds like a good prediction, so far. I suppose the contest organizers are making the implicit assumption that logical thinkers enjoy the logical thinking associated with puzzle-solving.
So, unless you are the ubermind, why bother?
Why bother doing anything at all if you can't be the best in the world at it? I guess the 99.99% of us who are mere mortals should just sit on our collective asses instead of enjoying life. That sounds like the logical solution to me.
The electron doesn't just take up a point. It exists in all those points at once.
The fact that an electron has nonzero amplitude everywhere does not imply that it takes up all the space in the universe. There is an important distinction to be made between the region a particle is likely to be and the region it occupies. Thus far, there has been no experimental evidence for electrons having nontrivial volume. Incidentally, if an electron were some kind of black hole, the region enclosed by the event horizon would be much too small for us to measure, or even distinguish from a point.
The energy of that light wave is typically absorbed as a packet by *all* the electrons in the conductor. But it also can be absorbed by each of the electrons in the conductor.
You're not making yourself very clear here. It looks like you are saying something about electrons obeying Fermi statistics and interacting with the EM field. Both properties are pretty much unrelated to size, e.g. protons (which do take up volume) also obey Fermi statistics and interact with the EM field.
That is because the structure of the nucleus involves a bunch of quarks continuously decomposing at the boundaries of the nucleus.
As another poster noted, this does not seem to make much sense. What are the decay products of these quarks, and what happens to them? Are you referring to the parton model? That does involve lots of quarks in some kind of confinement, but no decomposition, and no definite boundary.
Electrons are stable particles, and do not spontaneously decay. Black holes of that size are highly unstable.
Really? What would be the decay products of a charged black hole with the mass of an electron? I haven't heard of any charged particles with less mass.
The article was about how precisely astronomers were able to measure b and c (they are very close), and thus determined that a (not some mystical term 'delta') = ~.3m.
Not really. The estimate of 0.3m comes from a general physical principle, stating that events that are synchronized to within a short amount of time (say 1 ns) are usually triggered by processes that take up very little space (e.g. 0.3m), since larger triggering processes have a speed-of-light obstruction to getting the necessary information to all of their parts in a timely fashion. This is how astronomers first concluded that pulsars are compact objects - repeated millisecond pulses are unlikely to be triggered by anything bigger than 300km.
It isn't clear what the parent was trying to say, since he never made his point very clear. I think the idea was that if the surface of the pulsar were somehow absolutely flat (say it was a cube), with normal vector facing us dead-on, and the pulsar managed to produce some kind of instantaneous pulse that took zero time in our rest frame, he could place some kind of bound on the size of the side facing us (about 4 times the diameter of the sun) via the pythagorean theorem.
It was quite a calculational tour de force, but I can't really see why it would be useful.
The danger is that soon enough an Intel processor will get hot enough to trigger a fusion reaction in atmospheric hydrogen, turning Earth into a small star.
Fortunately, Intel is working on this as we speak! Here is a Register article with VP Gelsinger's predictions. Here is a nifty photo of an overclocking experiment gone awry.
I assume you are referring to prewarp or average tech starts. In the advanced game scenario, Creative is pretty much essential, even though it costs 8 points. If you don't have it, chances are, you will have a large research/production disadvantage, because the game selects a random set of earlier technologies for you.
Unification, Tolerant, +1 Production eats any creative race's lunch.
... and Unification, Telepathic, Omniscient, Rich Artifact Homeworld eats the Unification Tolerant for lunch and only gets stronger. An early (i.e. turn 60-70) cruiser with MIRV nukes will take out almost anything you can throw against it.
Unification Tolerant and other high-production races perform quite stunningly against the computer, but they are weak enough in research that there is a vulnerable period between the time they start colonizing en masse and the time the consequent high population allows them to erase the technology gap. Similarly, races such as Democracy, Lithovore, Artifact Homeworld can stay on their homeworld for about 100 turns before building a Guardian-killing fleet when playing against the computer, but they can expect interference if there are other human players.
For prewarp and average starts in multiplayer situations, balanced races such as Subterranean, Lithovore, Large Artifact homeworld, and the canonical Telepathic blitz races work much better.
I tend to agree here with the grandparent about not mixing physics with sociopolitics.
While it may be poor judgment to say that sociopolitics and quantum physical systems exhibit the same behavior, it is often valid to say that they can be treated with similar mathematical models. Sometimes, observed phenomena in one area can provide insight into the behavior of the other, even if they are as disparate as the two aforementioned fields.
This Bose Einstein example itself seems ridiculous to me. I don't see the lowest state as "winning over and monopolizing over" all the other states. What happens is that the other states can take in only so many particles.
The grandparent never mentioned any sort of "winning over and monopolizing over" action. The analogy was on the level of using a mathematical model. A Bose-Einstein condensate happens in systems with indistinguishable, non-excluding particles (i.e. they exhibit Bose statistics). It is necessary for the thermal energy in the system to be low enough that most or all of the particles settle into the lowest energy state. Your description is poor because other states can accept arbitrarily many particles (up to certain macroscopic constraints, e.g. gravity), and the reason for condensation is that it is not energetically favorable for the particles to jump to those levels.
Although the phrase, "winner take all," is a bit overused, there does not seem to be any evidence that the author of the book seeks to anthropomorphize bosons.
Additionally, if the two photon are emitted exactly 180 degrees opposite of each other, and both are traveling at velocity c, the transmission of data has a theoretical velocity of twice the speed of light.
Unfortunately, there is no information transmitted from Photon Receiver A to Photon Receiver B in your scenario, so no information travels faster than light. Schrodinger and Heisenberg are pretty much irrelevant here.
You may be trying to describe teleportation via quantum entanglement, which has been done in the laboratory. This involves some surprising correlations between measurements of widely separated particles, such as the photons in your example (although a black body is a terrible source). However, the correlations in question do not represent any sort of information transfer, and this phenomenon has been explained quite well by theory which keeps everything at light speed or less, despite the wishes of various crackpots and science fiction fans.
But if gravity were not instant, how could things orbit one another? in my minds eye, I see the earth pulling on the moon.. and the moon pulling on earth, but the moon is falling past the earth. If the speed of gravity weren't instant, it is hard to imagine circular or elliptical orbits..
Try not to think of gravity as a force, but as a geometric phenomenon. The earth and moon are not really "pulling" on each other so much as the presence of their mass, momentum, energy, etc... are shaping spacetime, and the curvature that results makes their paths appear to orbit each other. For objects which don't move too much relative to each other, this looks a lot like an instantaneous force, and that's why Newton's theory was proposed in the first place.
However, for elliptical orbits such as Mercury's, Einstein's theory predicts a precession of the axes, and it deviates enough from Newton's instantaneous force theory that the differences are testable from Earth. The observations in question agreed with Einstein's prediction much better than they did with Newton's. This is one of several pieces of experimental evidence favoring Einstein's theory.
Einstein's principle of equivalence says (among other things) that uncharged objects in space will follow what is basically a straight line path (strictly speaking, a geodesic). However, when spacetime is curved (usually due to stuff being nearby), that path can appear bent to a distant observer. Hence, planets, satellites, and thrown objects feel no external gravity, and are actually travelling in "straight" paths, while we are being accelerated upward from our natural trajectory by our contact with the ground.
The matter would become energy .. and energy doesn't create gravity .. so .....
According to general relativity, energy does make a contribution to gravitational effects. Einstein's field equations include the stress-energy tensor, which for each point in spacetime gives information about the energy (including mass-energy) density, momentum density, and stress (e.g. pressure) associated to all forms of matter and all non-gravitational fields [MTW].
The problem is that if you assume Einstein's field equations, you automatically get the assertion that gravity "travels" at c, the speed of light in a vacuum. Any alternative theory regarding speed would have to include some change in the field equations, which have made some very strongly verified predictions in the last 85 years. On the other hand, if you had some alternative theory that did not have the same dependence on the stress-energy tensor, and if it predicted a gravitational change from an annihilation event, then you might be able to test its validity using such an experiment.
Don't forget to factor in my displacement device and damper field.
I did. Without the defensive devices, only one missile would be necessary, as MIRV zeon missiles do 4*30 damage.
And where are you getting the 120 damage b4 it explodes?
If you scan a ship on the battle screen, you will get a display of various systems, such as engine, computer, etc... On the top right of each such box, there will be a fraction, e.g. 56/120, indicating the health of the system in question. I don't recall the exact numbers for engine hit points, but it is 10 for battleships and 40 for doomstars, with reinforced hull tripling everything. Note that these numbers are completely independent of your armor technology, and they tend to be rather small (which is why ion pulse cannon is so annoying). Engine damage will cause the ship's mobility to deteriorate according to some formula I don't recall, and at something like 25%, the ship is immobilized. When the engine loses all of its hit points, the ship disappears in a big explosion, damaging everything within 2 or 3 squares.
Attack the Guardian once you've got ships with graviton guns or better, and zortrium armour at least. The best combo in the mid-game is a volley of grav cannon to knock down the shields, then a volley of ion cannon to demolish internal systems. A couple of Titans with this setup can destroy the Guardian without giving it a chance to return fire.
This is gross overkill. The Guardian can be killed with two cruisers and 4-6 frigates fitted with a mixture of appropriately typed merculite missiles (another poster described these - I'd omit the FST mod). It requires just zortrium armor, merculite missiles, emissions guidance system, and fast missile racks. Note that it does not need any beams or computers (making it good for non-creative races by eliminating research tree problems), and the construction takes about half the production needed to build single titan. A custom democracy-lithovore-artifact race often can send off such a fleet within 100 turns of a prewarp start, and several other races can perform similarly. If you're quick enough killing the Guardian, you can just use the Avenger to kill off everyone else.
Death rays and particle beams are heavily overrated
Particle beams have a defensive use: they are the most powerful beam that can be placed in a fighter. While fighters on ships are quite inefficient, they provide rather good defense in a fighter garrison, where they can produce up to 1400 points of damage. Death rays are very good if you can kill the Guardian early, as there are no comparable weapons until the phasor. Unfortunately, both are very expensive to produce.
At the end? HV AF SP Phasors w Achilles Targeting System. 'Nuff said.
If you build smart, you don't need to get much further than MIRV nuclear missiles at the end. Given a pre-warp or average start, it is quite possible to win at "impossible" level before the opponents get either radiation shield or powerful beams to counter the missiles.
As it happens, the most efficient ship-to-ship weapon is the plasma cannon, not the phasor. However, if you are attacking a well-shielded planet, neither weapon will do any damage whatsoever.
Also, it's worth investigating the potential of phasing cloaks and timewarp facilitators.
That and stasis fields make the late game rather silly. There is something wrong with the game mechanics when you can defeat the Antarean home fleet with a single frigate by piling plasma webs on the star fortress and ships.
BTW, did you know what you can avoid war all together by simply ignoring the diplomats?
This is definitely not true in general, at least not on the "impossible" difficulty level. Occasionally, the computer players, especially the repulsive ones, will declare war for no apparent reason.
The parent's story doesn't sound like the same MoO2 game I've played. I've never seen a CP demand either surrender or more than 10% tribute (it's not an option on the diplomacy screen), and I've never seen a CP offer tribute, no matter how dire the circumstances.
400? That assumes you only put 1 converter per ship. Bollucks! I recall doing over 10k damage with stellarconverters...
Stellar converter does 400 enveloping damage, meaning 400 points for each of four shield faces. If you shoot an unshielded planet with 7 convertors, you will do 11200 damage. If you have structural analyzer, those same weapons will do 22400 damage to unshielded ships.
While this sounds impressive, the stellar converter is one of the least efficient high-level weapons, since it is bulky and does not benefit from beam bonuses like high-energy focus and hyper-X capacitors. An optimized ship full of plasma cannons will be able to do over 150,000 damage to unshielded ships in one turn, about six times the stellar converter's efficiency. The plasma cannon is in fact the most efficient weapon in the game, followed by disruptor, gauss cannon, phasor, and mauler device. Naturally, the presence of shields, especialy on planets, will shift the balance in favor of the heavier weapons, e.g. disruptor and mauler.
reflection field + damper field + energy absorber + displacement device + inertial nullifier + wide area jammer + automated repair unit
damn near impossible to destroy.
A ship like this is rather trivial to destroy, using MIRV EMG ECCM missiles, as unshielded ships are quite vulnerable to the emissions guidance system. Even a doom star with reinforced hull can only take 120 points of damage to the engine before exploding. If the enemy has sensor technology, your evasion becomes (130% [WAJ]+ 50% [IN] - 70% [Sensor] )/2 [ECCM] = 55% so 11 or 12 missiles should suffice, and that can fit on a mere cruiser with enough tech advancement.
If you are playing in a multiplayer game, you will find that no ship is anywhere near impossible to kill. Unfortunately, the AI does not know how to build efficient ships.
Yes, they changed the extra-turn sequence
This did not completely solve the problem. If the enemy does not have PC/TWF tech, it is still possible to attack with impunity if you appropriately time your attacks with the "wait" button. Thus, it is still possible to defeat the Antarean home fleet using a single frigate fitted with with Phasing Cloak, Time Warp Facilitator, and a plasma web.
what happens if the existing "sarcophagus" fails after the bigger one is built over top of it?
If the existing sarcophagus fails inside the new one, the dust and debris that are kicked up will remain inside the outer structure. The purpose of the outer structure is to prevent this dust from being picked up by the wind and contaminating the surrounding countryside.
I don't specialize in dynamical systems, but I do know what a queue is.
Fractal box counting will show that the fjords have a boundary that is approximately 1.4 dimensions (rather than the typical 1-dimensional boundary of a circle or square) and thus, can not be measured with a finite 1-dimensional measure such as length.
Both the land and water are made of atoms, so your approximation breaks down at small scales, and you end up with a finite path length. The problem is that you are applying fractal box approximation, a mechanism suited to morphological representations, to a calculation of length, for which it was not designed.
Thus the coastline length can be approximated by infinity.
Instead of approximating the length, you just extrapolated a pattern from limited data to well outside its applicable domain. Here's an analogous example. Suppose I have one dollar in my wallet at time 0, two dollars at time 1 minute, 4 dollars 30 seconds later, and 8 dollars 15 seconds after that. Clearly, my wealth is doubling at an asymtotic rate. Would you approximate my wealth at 2 minutes by infinity? Everybody knows that anything remotely close to infinity is still infinity, thus I have infinite wealth, at least in your imaginary world.
The best one is time: there are now 50 seconds in a minute, so we can move 2 minutes to one, then we get 26 minutes in an hour, by quadrupling the hour to 100 minutes we now get 6 hours in a day, halving the length of a second will now give us 10 hours in a day. We have just decimalised time without significantly changing the base unit.
Perhaps a more global treatment would prevent errors such as poorly multiplying minutes. Note that one day has "42000" of our normal seconds, so we must either shorten a second by a factor of about 3 (actually "60/21"), or lengthen it by a factor of "4.2" in order to get a power of "10"
I still favor binary, or base e when exact representations are unnecessary. Division in binary takes more space, but is less prone to errors, since the operations involve less thinking. You can count very high on your fingers in binary, if you use your knuckles appropriately. The downside (other than looking bad in front of aliens) is people around you might think you have palsy.
yet within this small region may be over 10 solar masses of material.
Had you read the article, you would have seen that neutron stars are thought to contain the mass of about 1.4 suns. Barring certain speculative theories of exotic matter, no cold (i.e., not undergoing fusion) stellar configuration can have a mass greater than 5 suns. See, for example, Misner, Thorne, Wheeler, page 627.
The result is a gravitational field at the surface of a neutron star about 70 trillion times stronger than that on Earth.
Given that neutron stars have mass about 500,000 times that of the earth, and radius about 1/400 earth radius, one can use the Newtonian inverse-square law approximation to get a factor of about 80 billion, which is considerably less than your figure. Where did you get these numbers?
Its core consists mainly of densely-packed neutrons, with a sprinkling of protons and typically 3 times as many electrons as protons, in a liquid-like state known as neutronisticis.
Do you have a reference for this? Most models of neutron stars treat the core as a degenerate Fermi gas, and as another poster noted, your star seems to have a net negative charge. Where did the protons go? Also, this is the first time I've encountered the word "neutronisticis". A Google search turns up nothing but this very post.
As a neutron star cools and grows, strains develop in the crust so that it buckles, causing starquakes equal to 1000 on the richter scale.
Starquakes are thought to be possible, but if our time frame is more than a few seconds after formation, the cause is probably not due to thermal stresses. This is because the thermal contribution to pressure and density is negligible as long as the temperature of a neutron star is below the Fermi energy of matter at nuclear density (about 30MeV, or 3*10^11 K - see MTW page 599, referenced above), and neutrino radiation brings the temperature well below this level very rapidly.
The Richter scale is logarithmic, based at 105 Joules for a degree 0 quake (reference), and growing by a factor of 1000 for every two degrees. A quake registering 1000 would have to release 1.05*10^1502 Joules, which is much more than the mass-energy contained in the observable universe. Indeed, it is quite impossible for any stellar-scale phenomenon to register more than 40 on the Richter scale, simply because stars don't have enough mass to release that kind of energy.
Weight is the measure of gravitational attraction between two bodies... nothing more.
Merriam Webster's definition is fundamentally flawed, as it does not specify a frame of reference for measuring the force, which is not Lorentz-invariant (N.B. there is a relativistic analogue of force, called 4-force, but it would be zero in this case). Furthermore, it is contradicted by a more authoritative source: MTW's Gravitation, page 13, first paragraph of section 1.3.
Indeed, the fundamental principle behind Einstein's general relativity is the fact that gravity does not exert force. Rather, the presence of mass-energy bends space-time, and can cause the trajectories of distant objects to converge.
A scale is just one limited method for measuring weight. I say limited because it functions by measuring the normal force ... caused by the ground holding the scale at rest, thus giving an inertailly fixed reference frame...
Weight is just the force applied to an object, and in the case of objects on the Earth's surface, this force is supplied by the ground, which is in our way, accelerating us from our natural path toward the Earth's center. Thus, a scale is a very good way to measure weight, as it is transferring the normal force from the ground to the object we are weighing, and measuring the force applied in the instantaneous reference frame of the object. Incidentally, the ground is not an inertially fixed reference frame, for the very reason that it is not in free fall.
Coastlines are fractal: the closer you look, the longer they get.
Both the ocean and the continent are made of atoms, so the fractal approximation breaks down when you look too closely, and you end up with a finite path length. For the purposes of aerial photography, you might as well take a minimal cover of the coast using discs of radius ~1km and sum their diameters. Small crinkles are completely irrelevant.
It's one of the few really fundamental mathematical discoveries of the last century.
This sounds like a troll, but there is a shred of truth hidden inside. There have been plenty of deep, fundamental mathematical discoveries in the last century, and I doubt you can find many mathematicians who would agree with your sentiments. All of the people appearing on this page have done very impressive work, and you may notice that fractals are not featured at all. Unfortunately, fractal geometry is one of the few recent advances which can be understood even superficially by people lacking a background in mathematics, and this seems to raise the public profile of the field substantially.
Imagine you have a cannon. You fire a cannonball out of it, and it follows a parabolic path until it hits the ground (Boom).
The path looks like a parabola in the same sense that the surface of the Earth looks flat. From a Newtonian standpoint, the path is not a parabola, but the end of an ellipse, one of whose foci is at the center of gravity of the the Earth-cannonball system. Since the Earth is essentially a homogeneous ball, we can pretend (as long as the cannonball is above the surface) that it is a point mass at its center of gravity, so the cannonball and the Earth are briefly mutually orbiting each other.
Unfortunately, the ellipse will not be followed beyond the intersection of the trajectory with the Earth, even if the cannonball were made out of some kind of weakly interacting matter that could pass through atoms. This is because the gravitational force inside the Earth decreases in proportion to the distance from the center, instead of following the inverse square law.
For instance, treat c as a singularity in the complex-mathematical sense and integrate around it.
Perhaps you are referring to analytic continuation. Unfortunately, whatever extended function you produce is only guaranteed to be single-valued in special cases, like rational functions. As it happens, if you somehow got your velocity to move around c in a loop, your mass and length would become negative, because the Lorentz contraction formula contains a square root. You'd have to make a second loop to get back to normal.
This appears to be the abstract for the announced results. Note the lack of words like "round" in the abstract and article. You may need a subscription to Physical Review Letters to reach it and download the paper.
This appears to be the abstract of the paper of Miller and Frank attempting to explain the phenomena. You will have to accept cookies to get any sort of information out of the APS site.
This seems to be the experimental project page. It doesn't appear to be an informative resource for the uninitiated.
I'd never read a nuclear physics paper before, so I wasn't sure what to expect. It looks like straight pQFT calculation with the Feynman diagrams, etc. would be computationally intractible for these problems, so people are always looking for reasonable approximation schemes. I guess the ones that had been used in the past didn't factor in relativistic effects as much as they should have, and the recent models corrected this.