A new aid to rapid - almost magical - learning has made its appearance. Indications are that if it catches on all the electronic gadgets will be so much junk.
The new device is known as Built-in Orderly Organized Knowledge. The makers generally call it by its initials, BOOK.
Many advantages are claimed over the old-style learning and teaching aids on which most people are brought up nowadays. It has no wires, no electric circuit to break down, No connection is needed to an electricity power point. It is made entirely without mechanical parts to go wrong or need replacement.
Anyone can use BOOK, even children, and it fits comfortably into the hands. It can be conveniently used sitting in an armchair by the fire.
How does this revolutionary, unbelievably easy invention work? Basically BOOK consists only of a large number of paper sheets. These may run to hundreds where BOOK covers a lengthy programme of information. Each sheet bears a number in sequence so that the sheets cannot be used in the wrong order.
To make it even easier for the user to keep the sheets in the proper order they are held firmly in place by a special locking device called a 'binding'.
Each sheet of paper presents the user with an information sequence in the form of symbols, which he absorbs optically for automatic registration on the brain. When one sheet has been assimilated a flick of the finger turns it over and further information is found on the other side.
By using both sides of each sheet in this way a great economy is effected, thus reducing both the size and cost of BOOK. No buttons need to be pressed to move from one sheet to another, to open or close BOOK, or to start it working.
BOOK may be taken up at any time and used by merely opening it. Instantly it it ready for use. Nothing has to be connected or switched on. The user may turn at will to any sheet, going backwards or forwards as he pleases. A sheet is provided near the beginning as a location finder for any required information sequence.
A small accessory, available at trifling extra cost, is the BOOKmark. This enables the user to pick up his programme where he left off on the previous learning session. BOOKmark is versatile and may be used in any BOOK.
The initial cost varies with the size and subject matter. Already a vast range of BOOKs is available, covering every conceivable subject and adjusted to different levels of aptitude. One BOOK, small enough to be held in the hands, may contain an entire learning schedule.
Once purchased, BOOK requires no further upkeep cost; no batteries or wires are needed, since the motive power, thanks to an ingenious device patented by the makers, is supplied by the brain of the user.
BOOKs may be stored on handy shelves and for ease of reference the programme schedule is normally indicated on the back of the binding.
Altogether the Built-in Orderly Organized Knowledge seems to have great advantages with no drawbacks. We predict a big future for it.
I used a book by Gordon M. Barrow (Physical chemistry, fourth edition), which derives the Second law using the gas laws
Oh, I see. I'm not familiar with it. That approach troubles me. A standard undergraduate statistical mechanics textbook that covers thermodynamics (and the 2nd Law) from a quantum statistical physics approach is F. Reif, Fundamentals Of Statistical and Thermal Physics. There's also voluminous material on the web.
Would you suggest that it is is not possible to use a system involving the freezing and thawing of ice [...] for converting thermal energy into electricity?
Yes, it is never possible to extract any useful work from a heat engine when there is no temperature difference (when Th=Tl in which case e=1-Tl/Th=0).
Your ice example is a very good one! There is a phase change between solid and liquid at T=0C=273K, and as you said the solid is significantly less dense than the liquid. So we might suppose in a thought experiment that it would be possible to extract work using two heat reservoirs, with Th=273+ (infinitesimally warmer than freezing) and Tl=273- (infinitesimally colder than freezing), respectively.
The cycle might be supposed to work in two steps as follows:
Step #1: decouple the engine from its drive element and bring the engine (filled with ice) into thermal contact with the reservoir at T=Th. An amount of heat, say Q, will be absorbed, the ice will melt to water, and the volume will contract to V1.
Step #2: couple the engine to its drive element (which exherts an extra pressure, say a constant p, which turns out to be optimal, on the water) and bring the engine into thermal contact with the reservoir at Tl. As the water cools, it turns to ice and expands to volume V2 (where V2 > V1). It does work W = p*(V2-V1) > 0 against the drive element (which we'll say is some kind of generator that creates electrical power during the stroke), and deposits the remaining heat (Q-W) into the reservoir at T=Tl. Go to Step #1 and repeat.
The efficiency is e=W/Q, by definition, and by very general considerations using the 2nd Law we know that e <= e_max = (1 - Tl/Th).
But if W > 0 (as we suppose) then there is a contradiction: e > e_max = 0. This is bad.
So where is the problem?
The problem is that the pressure p on the ice in Step #2 actually lowers the melting point temperature of the ice to below T=273K. The water will not freeze! You can demonstrate this yourself by taking an ice cube that is not too cold (very close to melting) and putting pressure on it. It will begin to liquify even if no heat can flow into it. Usually just the outer edge melts, because the inside of the ice cube is typically significantly colder than the surface. (In intro physics classes instructors sometime perform a demonstration wherein they suspend a weight from a block of ice using a loop of wire. Over time the wire will gradually pass through the block of ice! Each bit of ice below the wire melts, due to the pressure exherted by the weight, then it subsequently re-freezes.)
Therefore, in order to fix our heat engine and make it "work" (i.e. to make sure the water actually freezes under the extra pressure in Step #2), we must use a colder cold reservoir: Tl < 273K. Then small positive work W can indeed be done, but there is no contradiction now because e_max = (1 - Tl/Th) > 0 in this case, as Tl < Th.
It will still be impossible for e to become larger than e_max in this revised situation (with Tl now less than 273K). This is because H2O has a very large latent heat of fusion (L=334 kJ/kg) which must be overcome when absorbing heat Q. That is, the heat Q absorbed in Step #1 has to include a large L, while W is relatively small, so that e=W/Q will still be a small number.
Here is a sketch of a proof that e < e_max:
Consider the phase boundary line between the solid/liquid phases
But never ever come up with the Second Law again unless you're talking about a conversion involving gasses [...]
the second law was derived for GASSES.
The Second Law doesn't appear to say much more than that for a gas the energy content is linear with the temperature.
If one looks at how the Second Law is derived, one sees symbols like V1, V2, and R, the GAS constant in there.
This is simply not true. I wonder why you're thinking all this? These misconceptions really need to be cleared up...
I think perhaps you are mixing up the 2nd Law with something else, perhaps the calculation of the entropy of an ideal gas...
When you compute the change in entropy ("delta S") of an ideal monatomic gas that undergoes a thermodynamic process which takes it from temperature T1 and volume V1 to T2,V2 you find the change in entropy is
\delta S = n*R*( ln(V2/V1) + (3/2)*ln(T2/T1) )
Maybe this is the formula that you are thinking of? But I'm not using this formula, and it's irrelevant to the point!
In any case this is *NOT* the Second Law of Thermodynamics! It is merely the change in entropy for that particular system and process. Other systems and processes will have different formulas. There are well-known textbook formulas for the entropy of models of solids, liquids, non-ideal gasses, nuclear spin systems, plasmas, blackbody radiation, etc, etc. For example, the link I gave above (repeat: black hole thermodynamics) contains the formula for the entropy of a black hole! If you study big-bang cosmology, you'll even find approximate formulas for the entropy of the entire universe.
Calculating entropy of ONE particular system, such as for an ideal gas, is not "how the Second Law is derived".
The Second Law is a different thing entirely: It is the statement, confirmed through many observations and experiments, that ANY isolated system which undergoes a thermodynamic process will tend to increase in entropy: \delta S >= 0.
Now, how is this Universal Law really "derived"? Not with gas formulas. In quantum mechanics, if you enumerate all of the microstates (which are the distinct and equally probable detailed physical arrangements of all the constituents -- think of distinct quantum numbers) of a system that are consistent with each of its macrostates (which are the distinct course-grained values of the physically measurable system parameters such as total energy), you'll find that most microstates (by far) correspond to the system being near one particular macrostate: its equilibrium. Therein the entropy, which is essentially just the logarithm of the number of microstates consistent with a given macrostate, is maximal. This finding is a very general one. Therefore, so long as there is at least weak coupling between the microstates of a system, it will evolve with very high probability toward the most preferred macrostate = equilibrium = maximum entropy.
Now hopefully you can see that the calculation I made in my original post is valid for ANY system, not just gasses. The system I used is an *arbitrary* heat engine together with two heat reservoirs. And the only ingredients used were:
(i) The temperature reservoirs have a constant temperature: T1 and T2 stay fixed.
(ii) Due to (i) the net entropy change for ANY such heat engine (no matter what it is made of) is just \delta S = (Q-W)/T1 - Q/T2.
This is just the integral of dS = dQ/T quasi-statically over a cycle, where the integrand is piecewise constant because T is. Don't confuse this with an assumption about gasses -- it is universal as the reservoirs are held at constant temperature. Remember that entropy S is a state variable.
(iii) Second Law of Thermo: \delta S >= 0.
If you still don't see why these show that the efficiency for ANY heat engine is always bounded by e_max = (T2 - T1)/T2, then I suggest reading up on the Carnot cycle to understand why it gives such a profound universal bound.
I wish I didn't have to waste so much energy on (would be) physicists that don't realise that the second law was derived for GASSES.
Well I am an actual physicist, and the Second Law Of Thermodynamics is indeed a universal law of physics that applies to any closed physical system where at least some form of weak coupling exists between the possible states of the system. This is generally true, not just for gasses. The Law applies to all forms of matter, even to electromagnetic fields, black holes and the universe itself!
The efficiency of a carnot cycle makes no direct reference to gasses.
We will both agree agree that 100% is the max.
I do not agree. A main point of my derivation above was to show that the 2nd Law implies an efficiency that is necessarily bounded above by a theoretical maximum that is significantly less than 100%.
The Second Law doesn't appear to say much more than that for a gas the energy content is linear with the temperature.
Are you thinking about the equipartition theorem for the energy of an ideal gas? No offense, but your understanding of the 2nd law appears to be seriously confused.
My understanding is that if you try to simply strap on another heat engine like a thermocouple, you're working with a very low temperature differential which means low efficiency.
That's right. A lower temperature difference in the second engine does mean a reduced theoretical efficiency for that engine. Of course the two will still combine to give a higher "overall" efficiency. If e1 and e2 are respective efficiencies for two heat engines, then the "overall" efficiency e is then e <= e1 + e2 - e1*e2. (You can derive this pretty simply by inserting a third, intermediate-temperature T3 reservoir beween the hot and cold ones and extracting work via both engines.) Here e1 + e2*(1-e1) >= e1 but is limited in size by the small maximum value of e2.
Also, if you insert carnot efficiencies e1 = 1 - T3/T2 and e2 = 1 - T1/T3 into that expression, you'll still get the overall theoretical max efficiency bound e < 1 - T1/T2 as before. This holds regardless of whether T3 is close to T1, in particular.
One question though. Isn't a gas turbine just another heat engine that that is governmed by the limits of any thermodynamic cycle?
You can roughly think about it that way. The effective high-temperature "reservoir" isn't really at well-defined uniform temperature, though. Also, a sizable component of entropy increase in a combustion engine (as opposed to a pure heat engine) comes from the fact that the number of particles in a combustion chamber increases sharply since large (enthalpy-rich) hydrocarbon molecules are broken into several smaller (enthalpy-poor) CO2 and H2O molecules.
Unfortunately, thermoelectric converters based on the Seebeck effect are not going to help with efficiency by a large amount.
Firstly, there is a theoretical limit (Carnot Cycle) to the efficiency of any pure heat engine based on the Second Law of Thermodynamics.
If a quantity of heat Q is taken from a high-temperature reservoir at temperature T2, partially converted into useful work W, and the remainder (Q - W) is deposited into a low-temperature reservoir at temperature T1, then the net increase in entropy is at least
\delta S = (Q-W)/T1 - Q/T2 >= 0.
So the efficiency (useful work generated per unit energy input)
e = W/Q < (T2 - T1)/T2
The waste heat is ultimately deposited into the environment, so T1 can't be much smaller than say 300K.
In a steam engine T2 has to be greater than the boiling point of water (at whatever pressure it is operated), but it is limited by what the materials of which it is composed can withstand. Temperatures of order 1000K are typical. That gives a maximum theoretical efficiency of around 70%. The best steam engines barely reach about half that efficiency.
However, modern power plants (which are not pure heat engines) use a Combined Cycle that can do better by first generating electricity from their fuel with a combustion turbine and then using the waste heat from the combustion turbine to make steam to generate additional electricity via a steam turbine. Their efficiency can reach about 60% of the net calorific value of the fuel.
So you can see that one might be able to shave a few more percentage points off the waste, but it will not at all be the godsend we really need...
IMHO only nuclear power can fulfill that role today.
Prior to relativity the past was the past and the future was the future. There was a sharp divison between past and future and saying that event A had already happened was saying something significant that seemed to extend beyond just a feature of the coordinate frame in popular use. Now it doesn't.
With regard to relativity, I understand you're concerned about that because according to the Lorentz-boosted observer, who's here and now, the said event might lie anywhere on an invariant hyperboloid of one-sheet. And that sheet contains points with t'<0, t'=0, t'>0. And that's qualitatively unlike an event in the causal past, which would lie on an invariant lobe of a two-sheet hyperboloid with t'<0 always. I understand and agree.
I also agree that so far as we know physical laws can be formulated in a covariant way. They are invariant in form under the SO^+(1,3) Lorentz group in flat spacetime. Therefore they cannot hinge on an artifact of a spacetime coordinate system.
I also agree this means their retarded Green's functions vanish outside of the light-cone. Therefore the measurable values of physical observables can't depend on quantities at events outside the light cone.
To be perfectly clear, if I haven't been before, I wholeheartedly agree with all of this nuts-and-bolts stuff.
We also now statedly agree that despite its covariant formulation physics is actually done (measurements of real things must be made) in coordinate systems.
It makes complete sense to say that an event is in our future or past in our frame - but this is a completely uninteresting fact. Nothing hinges on this. Whether or not the event in question happens 1000 years in our future or 1000 years in our past is of little consequence, it's outside of our light cones either way. For example, it makes no difference to our ability to go and see the event in question.
We also agree it's not possible to reach and see up close events outside our light cone, in principle, not for technical reasons.
But it certainly does make a difference as to *exactly when* we (ie our terrestrial posterity) will actually be able to see evidence of the event in question, accounting for the finite propagation time of the light. ("the majestic pillars will appear intact to observers on Earth for another 1,000 years or so.")
That's because it matters where and when the said event lies on our spacetime manifold in relation to us. I read the article in this mindset, as using terms ("have already been" / "will be") to describe the physical *configuration* of events on our spacetime manifold, using an implicit but clearly understood coordinate system. (Ok, maybe the spacial orientation wasn't exactly fully spelled out but the time axis was clear enough: "observers on Earth") There's really no way to specify exactly where and when the events lie in a coordinate-free way. We *need* such talk to physically locate events, inside our light cone or not.
There's no need to wait 1000 yr for an event to be 7000 yr in our causal past in order to be able to legitimately conclude, then, that it's a 7000 yr old past event and therefore was chronologically 6000 yr in the past of our 1000 yr old selves. We can (contingently) do that now, because we can have some knowledge, based on theoretical extrapolations, of events located outside our light cone.
And if your choice of frame is clear then you're free to use coordinates in that frame, including talking about events 7,000 light years away.
And for the reasons given that is exactly what I feel the author was doing.
If the author had written something like "...the Eagle Nebula is located some 7,000ly to our left..." without spelling out any other context, he'd deserve a rebuke.
Past and future still have meaning in our relativistic SO^+(3,1) world in the same way that left and right still have meaning
as long as it's acknowledged that we're talking about something contingent
Well I'd certainly agree that the aforementioned destruction that has "already" happened is still *contingent* upon it actually being observed by a stargazer 1kyr our better. (Who knows, maybe somehow it turns out we knew nothing of supernova shockwaves.) But our ordering of events will be his historical timeline.
that we have an emotional attachment to,
I meant that I've acquired a rather unfortunate gravitational attachment to this frame.:-)
rather than something of physical significance
It's not a Lorentz covariant notion so it has no physical significance whatsoever.
I'm not using a classical model of time here. I'm arguing that noncovarient quantities (like the sign of the difference of the time coords of two events), though not covariant, can still be physical in the sense that they can be measured (with respect to a frame). Take it to momentum-space. Is the energy above the rest mass of an object physical? Sure, it can be determined in a frame. Or there's the frame-dependent electric field strength, or wavelength, speed, etc, etc..
Indeed I think the case can be well made that essentially *all* physical quantities are ultimately/implicitly determined by measuring frame-dependent coordinate differences. (Think about the Stern-Gerlach experiment, Millikan's Oil-Drop measurement of e, temperature on a thermometer, time elapsed on a stopwatch. It's all just x2-x1.)
then we're in agreement
I believe we agree on the causality of the nuts-and-bolts physics. maybe not philosophically.
about events 7,000 light years away
Hmmm.. a difference between space coords of two events. Yet another non-covariant quantity. Your hypothetical observer who's here and now, moving past us at high velocity, using English in the same way, would claim the event is actually not that far away. But it's fine, I knew exactly what you meant by that.:-)
Of course it's a frame-dependent ordering on the events, not Lorentz covariant at all, but it's not entirely useless nor devoid of meaning. I and about 6 billion of my closest friends have acquired quite an attachment to this particular (though, yes, arbitrary) frame of reference!
I appreciate your desire to inject some physicality into the discussion, just not the rhetorical way you went about it.
Really, when will people learn not to use the past tense for events outside of our past light cone!
Really, when will people learn not to post embarrassingly wrong "corrections"?
As a physicist who has studied General Relativity (but my area is quantum field theory), I can assure you most definitely that the condition for event #1 (t_1, x_1) to lie in the past of event #2 (t_2, x_2) is merely t_2 > t_1. It is not (t_2 - t_1) > |x_2 - x_1|/c . This is in flat spacetime where the coordinates of the events are measured in the same (arbitrary but consistent) inertial reference frame, or a reasonable approximation thereof (like ours). When the curvature of the spacetime is not negligible, you have to use the metric (g_mu,nu) to determine whether a future-directed *timelike* curve connects event #1 to event #2, not whether a future-directed *causal* curve connects them.
Just because an event is not in our absolute or causal past, does not mean that it is not in our chronological past!
What are compression waves? They are merely trillions of particles (atoms/molecules) moving in concert due to their interactions with other particles up and down stream.
Reduce this down to the atomic scale and think about it like this: atom #1 propagates through space at speed v (less than c) until it approaches atom #2. Atoms #1 and #2 then interact. In the context of quantum field theory, this means that one or more virtual photons are exchanged between the charges (electrons and protons) in atom #1 and atom #2. This interaction takes time (which is not negligible) for those photons to propagate. Through this interaction some momentum is transferred from atom #1 to atom #2. Now atom #2 has to propagate, and so on...
So what you said is not true. For compression waves to move faster than c, the constituent atoms (and virtual photons) would also have to.
There has been a speculative proposal by Miguel Alcubierre, in the context of General Relativity, that takes advantage of an imagined negative energy density in some region of spacetime to produce a metric (a special kind of curvature of the spacetime) that allows for superluminal transport of matter. That is, a warp drive.
The good news here is that there is a known phenomenon of quantum field theory (the Casimir effect) that causes the region in between two highly polished metal plates that are extremely close together to develop a measurable negative energy density. (Basically the plates filter out the zero-point energy of long-wavelength electromagnetic quantum fluctuations of the vacuum that would otherwise be present, but cannot fit between the plates.) The bad news is that the effect is utterly negligible in strength.
What you are describing is a truly rigid body, and unfortunately there is no such thing in nature. It would require instantaneous action at a distance. This is also why Newtonian physics ultimately fails.
There is always a finite propagation time for the the electric field of the moved charge of the first particle to reach and repel the next particle in the row, etc. These interactions are mediated by (virtual) photons (ie light).
It is indeed possible for the speed of sound to exceed that of light, not by increasing the incompressibility of the material (which increases the speed of sound) but by increasing the index of refraction (which decreases the speed that light travels in that medium).
A few years back, some Harvard physicists grabbed headlines by slowing down light in a Bose-Einstein condensate to 38 mph! More recently, just a couple of weeks ago, Japanese scientists fabricated nanocavities in solid state which slowed light passing through them to 5.8 km/sec.
...what fundamental principle would you have to violate...?
Incompressibility of a material is mediated by the electromagnetic force arising from the charges inside and between the atoms comprising a material. As such there is a fundamental limit to the magnitude of the incompressibility. You can always push those electrons closer together (until they disappear on you, creating a shower of new particles).
Irrelevant to the real world? Hmmm... I suppose one's definition of "real" depends on the limitations of one's experience, but a clearer understanding of what is and is not possible in principle should surely be recognized as relevant by anyone interested. Maybe you really just aren't. Studies of intractability in computability do not only show where the boundaries lie, but can be helpful and save time in practical ways. In the context of security, I've personally seen halting concerns arise in turing-complete grammar extensions to regular expression engines, for example. Ever heard of a DoS attack? You wouldn't want a devious user to trigger one of those on your modded PCRE engine, so what's the best prefilter/dectector? Doh! There isn't one! Good thing that expensive CS education helped to steer us clear of that pitfall. Why aren't there any good sendmail configuration security checkers? Answer. Honestly, there are an infinitude of real, practical examples. You need to check out Garey&Johnson's Classic, at least the introduction.:-)
uh... splint? Now you're just being silly on purpose.
Make it out of cheese? Talk about an irrelevancy.
Poor Russell and Gödel and Turing and Post and Church and Rice and.... All those mental masturbators! What wasted lives!
Congratulations, you have won today's "Ignorant undergraduate misunderstanding of the Halting problem" prize.
Man, it's annoying when someone accuses another of ignorance when the former is more wrong by an order of magnitude!
The parent poster wrote
You cannot write a program in a turing-complete language to determine if another program in a turing-complete language is 100% secure. It's trivially reducable to the halting problem. You can't automate it, at least not with 100% accuracy, in every case.
and that assertion stands as claimed.
He is arguing that there is no such (secure) algorithm which always answers (correctly) in every case (100% accuracy). His argument is perfectly fine: it's a routine and trivial application of Cantor's diagonalization method. If you really disagree, I challenge you to produce such an algorithm forthwith.
Your problem is that you have misunderstood the hypotheses in his proof sketch and tried to replace a universal quantifier with an existential one. Of course there is some limited program that can verify the security of some carefully specified others.
IsSecure() cannot return false when passed program A as input without violating the hypotheses.
Your changing the specification of the problem is analogous to removing the "not" in "This sentence is not true." and then claiming: Wow, no contradiction!
Dr. Dobson's Newsletter: February, 2005 Setting the Record Straight
Dear Friends:
If you had told me a month ago that Id be devoting my February letter to a cartoon character named SpongeBob SquarePants, Id have said you were crazy. Nevertheless, by now you probably know that I have been linked to that famous talking sponge by hundreds of media outlets, from the New York Times to "MSNBC" to "Saturday Night Live." The story of how this situation unfolded is somewhat complicated, but it must be told.
In truth, this tale has very little to do with SpongeBob himself, and everything to do with the medias ability to obscure the facts and to direct lies and scorn toward those of us who care about defending children. It all began on an evening in late January, during Inaugural Week in Washington, D.C. At that time, I spoke briefly to 350 guests attending a banquet hosted by Tony Perkins and the Family Research Council, Focus on the Family, and Gary Bauers American Values. I concluded by sharing a word of concern about a video that will be distributed to 61,000 public and private elementary schools across the nation, for use on the proposed "We Are Family Day," March 11.
The video, which millions of children will soon see, features nearly 100 favorite cartoon characters that kids will instantly recognize, including not only SpongeBob, but also Barney the Dinosaur, the Muppets, Dora the Explorer, Bob the Builder, Winnie the Pooh, Clifford the Big Red Dog, Jimmy Neutron and Big Bird.1 The video itself is innocent enough and does not mention anything overtly sexual. Rather, it features the childrens cartoon characters singing and dancing along to the popular disco hit "We Are Family."
But while the video is harmless on its own, I believe the agenda behind it is sinister. My brief comments at the FRC gathering were intended to express concern not about SpongeBob or Big Bird or any of their other cartoon friends, but about the way in which those childhood symbols are apparently being hijacked to promote an agenda that involves teaching homosexual propaganda to children. Nevertheless, the media jumped on the story by claiming that I had accused SpongeBob of being "gay."2 Some suggested that I had confused the organization that had created the video with a similarly named gay-rights group.3 In both cases, the press was dead wrong, and I welcome this opportunity to help them get their facts straight.
I want to be clear: the We Are Family Foundation the organization that sponsored the video featuring SpongeBob and the other characters was, until this flap occurred, making available a variety of explicitly pro-homosexual materials on its Web site. It has since endeavored to hide that fact (more on this later), but my concerns are as legitimate today as they were when I first expressed them in January.
So let us consider the evidence. One of the first resources to catch our attention on the foundations Web site was a booklet4 that lists a number of organizational "allies," including five of the largest pro-homosexual organizations in the nation: the Gay and Lesbian Alliance Against Defamation (GLAAD), the Gay, Lesbian and Straight Education Network (GLSEN), the Human Rights Campaign (HRC), the National Gay and Lesbian Taskforce, and Parents, Family and Friends of Lesbians and Gays (PFLAG). Also, the Web site made available school lesson plans that suggested teachers ask these questions of students: "How are you affected by homophobia?" "How would you be affected by your sexual orientation were it different than it is now?" "How will understanding these definitions change your thinking about compulsory heterosexuality and homophobia? "How will it change any of your behaviors?"5
From a handout entitled, "Talking About Being Out" there was this: "Do you know of any people in your school whose sexual orientation differs f
You seem to be seriously wondering about it. I've thought hard about this as well. This may seem like an overly simplistic or flippant answer. I didn't find it satisfying to begin with, but it does call for reflection:
Evil is simply anything that opposes the personal will of God, which must (for now) be axiomatically taken (ie "on faith") to be "good". Apart from the personal will of God the concept of evil really is ultimately meaningless. One could try to argue that there is a certain common sense of morality which is shared by most people, most of the time, but the notion breaks down on close examination. Individual hearts differ on what is needed or desirable. Only the existence of an absolute God can provide an absolute point of reference, otherwise everything descends into relativism.
What first impressed me to think about this was while reading through the Old Testament once: I noticed over and over it saying that "the righteous shall live by faith". (Righteousness, of course, being the antithesis of evil.)
This struck me because it was the exact opposite of what I had expected or wanted. Why was it *faith* that God demanded, if indeed there were a God, and not direct knowledge or action or experiece? Faith is so weak and unreliable in comparison to knowledge and experience. It took me two years of thinking about it to finally find a satisfying answer to that question. It's worth considering carefully for yourself.
small hint: Jung qb lbh ubcr sbe jura lbh cynag n zhfgneq frrq?
Actually texwtf is correct here. Following your "fencepost" reasoning consistently (by counting computers involved instead of their changes), the ratio would then only be 3:2 with market shares of 60% and 40% respectively, not 75%/25% (even though install bases are actually equal).
Over the long term however, the upgrade *rates* of 2 vs 1 purchaces every 3 years do imply a 66.7% and 33.3% market split.
Oddly, the infamous quote was actually made in response to Wolf Blitzer's question, "Why should Democrats, looking at the Democratic nomination process, support you [Gore] instead of [Senator] Bill Bradley...? What do you have to bring to this that he doesn't necessarily bring to this process?"
Also, in his response Gore said quite a bit more than the grandparent poster gives us, though the most relevant bits are all there.
If you want to view the question and Gore's full response for yourself grab this clip of the CNN interview:
(Get rid of any spaces in the link that are added by Slashdot. The file format is Real Video. The file size is less than 600 kBytes. Use an eDonkey client to download.)
In my opinion, if you take his statement at face value, the straightforward, unqualified way in which Gore makes it suggests that, even if he didn't believe that he actually "invented" the Internet, he seems to have genuinely believed that his own beaurocratic contribution was more important than any researcher's or network engineer's prior work!
Another noteworthy site is http://www.RatherBiased.com. Their motto is "Watching CBS News so you don't have to".:-)
But seriously, I have been checking it out it daily since the whole MemoGate controversy erupted. The blog is on top of this story; the operator of the site appears to have a number of internal contacts within CBS News. It also has deep archives that go back years, detailing previous spats between Dan Rather and the Bushes.
The grandparent poster seems to be confusing things a bit. Let's try to clarify...
Except for the Lorentz transformation, the most important equation in Special Relativity theory is the Energy-Momentum relation:
E^2 - p^2 c^2 = m^2 c^4
(This is true for all inertial reference frames, and embodies the fact that the contraction of the energy-momentum 4-vector for a particle is an lorentz invariant. The Dirac equation, the Klein-Goron equation, and much of modern quantum field theory is rooted in this equation.)
Another important equation of SR involves the velocity:
pc/E = v/c
From these, we can see that
(i) if v < c (sub-luminal), then pc/E < 1, so E^2-(pc)^2 > 0, which means m^2 > 0. This case is true for normal, boring matter. Note that the converse is also true: m^2 > 0 implies v < c .
(ii) if v = c (luminal), then E = pc, and m^2 = 0. This holds for (massless) photons and gluons, and used to be assumed true for neutrinos. The converse ( m^2 = 0 implies v = c ) is also true.
(iii) if v > c (super-luminal), then m^2 < 0. Conversely, m^2 < 0 implies v > c . There is no known type of matter that is described by this case, but physicists have given such hypothetical particles the name "tachyons". One could say that mass is imaginary in this case, as m^2 < 0, but physicists rarely actually speak like this.
Anyway, the parent poster is right in correcting the grandparent poster that it is negative mass *squared*, not negative mass, that makes something a tachyon (v > c). But this
I think negative mass just makes you accellerate in the 'opposite' direction in a gravitational field. Feel free to correct me, though. It's been a while.
is not quite correct. From F=ma, we can see that it is true a negative mass would cause a particle experiencing a force in one direction to actually accelerate in the *opposite* direction! (Imagine that. You push something away with your finger, but it comes closer, increasing the force you're exherting on it, which increases the acceleration, ad infinitum. Physicists really hate thinking about the instabilities involving negative inertia, so we don't like to talk about negative mass at all.)
The problem with the parent post's suggestion is that althought this strange behavior would happen with an electrical force (such as your finger), it need not hold for gravity! In boring old Newtonian Gravity, a particle a distance r away from another mass M feels the force F = GmM/r^2 . But the acceleration would be a = GM/r^2, whether the mass is negative or not, because m completely cancels out of the equation. A similar thing happens in General Relativity, Einstein's theory of gravity -- the particle still follows the local geodesic of the spacetime metric generated by M.
I think that's what most people mean: you can't transfer information faster than c such that you can view it sooner than information travelling at c. Or are tachyons different?
To get back on the topic of information transfer, it's pretty clear that without nontrivial spacetime topologies (eg, wormholes) superluminal information transfer shouldn't happen
except in the tachyon case. But does it really happen in this case?
The problem is that real life is quantum mechanical, wherein "particles" are described by evolving wavefunctions in a Hilbert space. A particle is a sort of propagating localized disturbance. The equation that should describe the propagation of a (scalar) tachyon is the Klein-Gordon equation. I quote the last paragraph from this discussion of the KG equation in the tachyon case:
Slashdot Mirror
LEARN WITH B.O.O.K.
- R. J. Heathorn
A new aid to rapid - almost magical - learning has made its appearance.
Indications are that if it catches on all the electronic gadgets will be
so much junk.
The new device is known as Built-in Orderly Organized Knowledge. The
makers generally call it by its initials, BOOK.
Many advantages are claimed over the old-style learning and teaching
aids on which most people are brought up nowadays. It has no wires, no
electric circuit to break down, No connection is needed to an
electricity power point. It is made entirely without mechanical parts to
go wrong or need replacement.
Anyone can use BOOK, even children, and it fits comfortably into the
hands. It can be conveniently used sitting in an armchair by the fire.
How does this revolutionary, unbelievably easy invention work? Basically
BOOK consists only of a large number of paper sheets. These may run to
hundreds where BOOK covers a lengthy programme of information. Each
sheet bears a number in sequence so that the sheets cannot be used in
the wrong order.
To make it even easier for the user to keep the sheets in the proper
order they are held firmly in place by a special locking device called a
'binding'.
Each sheet of paper presents the user with an information sequence in
the form of symbols, which he absorbs optically for automatic
registration on the brain. When one sheet has been assimilated a flick
of the finger turns it over and further information is found on the
other side.
By using both sides of each sheet in this way a great economy is
effected, thus reducing both the size and cost of BOOK. No buttons need
to be pressed to move from one sheet to another, to open or close BOOK,
or to start it working.
BOOK may be taken up at any time and used by merely opening it.
Instantly it it ready for use. Nothing has to be connected or switched
on. The user may turn at will to any sheet, going backwards or forwards
as he pleases. A sheet is provided near the beginning as a location
finder for any required information sequence.
A small accessory, available at trifling extra cost, is the BOOKmark.
This enables the user to pick up his programme where he left off on the
previous learning session. BOOKmark is versatile and may be used in any
BOOK.
The initial cost varies with the size and subject matter. Already a vast
range of BOOKs is available, covering every conceivable subject and
adjusted to different levels of aptitude. One BOOK, small enough to be
held in the hands, may contain an entire learning schedule.
Once purchased, BOOK requires no further upkeep cost; no batteries or
wires are needed, since the motive power, thanks to an ingenious device
patented by the makers, is supplied by the brain of the user.
BOOKs may be stored on handy shelves and for ease of reference the
programme schedule is normally indicated on the back of the binding.
Altogether the Built-in Orderly Organized Knowledge seems to have great
advantages with no drawbacks. We predict a big future for it.
Oh, I see. I'm not familiar with it. That approach troubles me. A standard undergraduate statistical mechanics textbook that covers thermodynamics (and the 2nd Law) from a quantum statistical physics approach is F. Reif, Fundamentals Of Statistical and Thermal Physics. There's also voluminous material on the web.
Yes, it is never possible to extract any useful work from a heat engine when there is no temperature difference (when Th=Tl in which case e=1-Tl/Th=0).
Your ice example is a very good one! There is a phase change between solid and liquid at T=0C=273K, and as you said the solid is significantly less dense than the liquid. So we might suppose in a thought experiment that it would be possible to extract work using two heat reservoirs, with Th=273+ (infinitesimally warmer than freezing) and Tl=273- (infinitesimally colder than freezing), respectively.
The cycle might be supposed to work in two steps as follows:
Step #1: decouple the engine from its drive element and bring the engine (filled with ice) into thermal contact with the reservoir at T=Th. An amount of heat, say Q, will be absorbed, the ice will melt to water, and the volume will contract to V1.
Step #2: couple the engine to its drive element (which exherts an extra pressure, say a constant p, which turns out to be optimal, on the water) and bring the engine into thermal contact with the reservoir at Tl. As the water cools, it turns to ice and expands to volume V2 (where V2 > V1). It does work W = p*(V2-V1) > 0 against the drive element (which we'll say is some kind of generator that creates electrical power during the stroke), and deposits the remaining heat (Q-W) into the reservoir at T=Tl. Go to Step #1 and repeat.
The efficiency is e=W/Q, by definition, and by very general considerations using the 2nd Law we know that e <= e_max = (1 - Tl/Th).
But if W > 0 (as we suppose) then there is a contradiction: e > e_max = 0. This is bad.
So where is the problem?
The problem is that the pressure p on the ice in Step #2 actually lowers the melting point temperature of the ice to below T=273K. The water will not freeze! You can demonstrate this yourself by taking an ice cube that is not too cold (very close to melting) and putting pressure on it. It will begin to liquify even if no heat can flow into it. Usually just the outer edge melts, because the inside of the ice cube is typically significantly colder than the surface. (In intro physics classes instructors sometime perform a demonstration wherein they suspend a weight from a block of ice using a loop of wire. Over time the wire will gradually pass through the block of ice! Each bit of ice below the wire melts, due to the pressure exherted by the weight, then it subsequently re-freezes.)
Therefore, in order to fix our heat engine and make it "work" (i.e. to make sure the water actually freezes under the extra pressure in Step #2), we must use a colder cold reservoir: Tl < 273K. Then small positive work W can indeed be done, but there is no contradiction now because e_max = (1 - Tl/Th) > 0 in this case, as Tl < Th.
It will still be impossible for e to become larger than e_max in this revised situation (with Tl now less than 273K). This is because H2O has a very large latent heat of fusion (L=334 kJ/kg) which must be overcome when absorbing heat Q. That is, the heat Q absorbed in Step #1 has to include a large L, while W is relatively small, so that e=W/Q will still be a small number.
Here is a sketch of a proof that e < e_max:
Consider the phase boundary line between the solid/liquid phases
This is simply not true. I wonder why you're thinking all this? These misconceptions really need to be cleared up...
I think perhaps you are mixing up the 2nd Law with something else, perhaps the calculation of the entropy of an ideal gas...
When you compute the change in entropy ("delta S") of an ideal monatomic gas that undergoes a thermodynamic process which takes it from temperature T1 and volume V1 to T2,V2 you find the change in entropy is
\delta S = n*R*( ln(V2/V1) + (3/2)*ln(T2/T1) )
Maybe this is the formula that you are thinking of? But I'm not using this formula, and it's irrelevant to the point!
In any case this is *NOT* the Second Law of Thermodynamics! It is merely the change in entropy for that particular system and process. Other systems and processes will have different formulas. There are well-known textbook formulas for the entropy of models of solids, liquids, non-ideal gasses, nuclear spin systems, plasmas, blackbody radiation, etc, etc. For example, the link I gave above (repeat: black hole thermodynamics) contains the formula for the entropy of a black hole! If you study big-bang cosmology, you'll even find approximate formulas for the entropy of the entire universe.
Calculating entropy of ONE particular system, such as for an ideal gas, is not "how the Second Law is derived".
The Second Law is a different thing entirely: It is the statement, confirmed through many observations and experiments, that ANY isolated system which undergoes a thermodynamic process will tend to increase in entropy: \delta S >= 0.
Now, how is this Universal Law really "derived"? Not with gas formulas. In quantum mechanics, if you enumerate all of the microstates (which are the distinct and equally probable detailed physical arrangements of all the constituents -- think of distinct quantum numbers) of a system that are consistent with each of its macrostates (which are the distinct course-grained values of the physically measurable system parameters such as total energy), you'll find that most microstates (by far) correspond to the system being near one particular macrostate: its equilibrium. Therein the entropy, which is essentially just the logarithm of the number of microstates consistent with a given macrostate, is maximal. This finding is a very general one. Therefore, so long as there is at least weak coupling between the microstates of a system, it will evolve with very high probability toward the most preferred macrostate = equilibrium = maximum entropy.
Now hopefully you can see that the calculation I made in my original post is valid for ANY system, not just gasses. The system I used is an *arbitrary* heat engine together with two heat reservoirs. And the only ingredients used were:
(i) The temperature reservoirs have a constant temperature: T1 and T2 stay fixed.
(ii) Due to (i) the net entropy change for ANY such heat engine (no matter what it is made of) is just \delta S = (Q-W)/T1 - Q/T2.
This is just the integral of dS = dQ/T quasi-statically over a cycle, where the integrand is piecewise constant because T is. Don't confuse this with an assumption about gasses -- it is universal as the reservoirs are held at constant temperature. Remember that entropy S is a state variable.
(iii) Second Law of Thermo: \delta S >= 0.
If you still don't see why these show that the efficiency for ANY heat engine is always bounded by e_max = (T2 - T1)/T2, then I suggest reading up on the Carnot cycle to understand why it gives such a profound universal bound.
Best regards.
I don't know if you're just trolling, but...
I wish I didn't have to waste so much energy on (would be) physicists that don't realise that the second law was derived for GASSES.
Well I am an actual physicist, and the Second Law Of Thermodynamics is indeed a universal law of physics that applies to any closed physical system where at least some form of weak coupling exists between the possible states of the system. This is generally true, not just for gasses. The Law applies to all forms of matter, even to electromagnetic fields, black holes and the universe itself!
The efficiency of a carnot cycle makes no direct reference to gasses.
We will both agree agree that 100% is the max.
I do not agree. A main point of my derivation above was to show that the 2nd Law implies an efficiency that is necessarily bounded above by a theoretical maximum that is significantly less than 100%.
The Second Law doesn't appear to say much more than that for a gas the energy content is linear with the temperature.
Are you thinking about the equipartition theorem for the energy of an ideal gas? No offense, but your understanding of the 2nd law appears to be seriously confused.
My understanding is that if you try to simply strap on another heat engine like a thermocouple, you're working with a very low temperature differential which means low efficiency.
That's right. A lower temperature difference in the second engine does mean a reduced theoretical efficiency for that engine. Of course the two will still combine to give a higher "overall" efficiency. If e1 and e2 are respective efficiencies for two heat engines, then the "overall" efficiency e is then e <= e1 + e2 - e1*e2. (You can derive this pretty simply by inserting a third, intermediate-temperature T3 reservoir beween the hot and cold ones and extracting work via both engines.) Here e1 + e2*(1-e1) >= e1 but is limited in size by the small maximum value of e2.
Also, if you insert carnot efficiencies e1 = 1 - T3/T2 and e2 = 1 - T1/T3 into that expression, you'll still get the overall theoretical max efficiency bound e < 1 - T1/T2 as before. This holds regardless of whether T3 is close to T1, in particular.
One question though. Isn't a gas turbine just another heat engine that that is governmed by the limits of any thermodynamic cycle?
You can roughly think about it that way. The effective high-temperature "reservoir" isn't really at well-defined uniform temperature, though. Also, a sizable component of entropy increase in a combustion engine (as opposed to a pure heat engine) comes from the fact that the number of particles in a combustion chamber increases sharply since large (enthalpy-rich) hydrocarbon molecules are broken into several smaller (enthalpy-poor) CO2 and H2O molecules.
Unfortunately, thermoelectric converters based on the Seebeck effect are not going to help with efficiency by a large amount.
Firstly, there is a theoretical limit (Carnot Cycle) to the efficiency of any pure heat engine based on the Second Law of Thermodynamics.
If a quantity of heat Q is taken from a high-temperature reservoir at temperature T2, partially converted into useful work W, and the remainder (Q - W) is deposited into a low-temperature reservoir at temperature T1, then the net increase in entropy is at least
\delta S = (Q-W)/T1 - Q/T2 >= 0.
So the efficiency (useful work generated per unit energy input)
e = W/Q < (T2 - T1)/T2
The waste heat is ultimately deposited into the environment, so T1 can't be much smaller than say 300K.
In a steam engine T2 has to be greater than the boiling point of water (at whatever pressure it is operated), but it is limited by what the materials of which it is composed can withstand. Temperatures of order 1000K are typical. That gives a maximum theoretical efficiency of around 70%. The best steam engines barely reach about half that efficiency.
However, modern power plants (which are not pure heat engines) use a Combined Cycle that can do better by first generating electricity from their fuel with a combustion turbine and then using the waste heat from the combustion turbine to make steam to generate additional electricity via a steam turbine. Their efficiency can reach about 60% of the net calorific value of the fuel.
So you can see that one might be able to shave a few more percentage points off the waste, but it will not at all be the godsend we really need...
IMHO only nuclear power can fulfill that role today.
With regard to relativity, I understand you're concerned about that because according to the Lorentz-boosted observer, who's here and now, the said event might lie anywhere on an invariant hyperboloid of one-sheet. And that sheet contains points with t'<0, t'=0, t'>0. And that's qualitatively unlike an event in the causal past, which would lie on an invariant lobe of a two-sheet hyperboloid with t'<0 always. I understand and agree.
I also agree that so far as we know physical laws can be formulated in a covariant way. They are invariant in form under the SO^+(1,3) Lorentz group in flat spacetime. Therefore they cannot hinge on an artifact of a spacetime coordinate system.
I also agree this means their retarded Green's functions vanish outside of the light-cone. Therefore the measurable values of physical observables can't depend on quantities at events outside the light cone.
To be perfectly clear, if I haven't been before, I wholeheartedly agree with all of this nuts-and-bolts stuff.
We also now statedly agree that despite its covariant formulation physics is actually done (measurements of real things must be made) in coordinate systems.
We also agree it's not possible to reach and see up close events outside our light cone, in principle, not for technical reasons.
But it certainly does make a difference as to *exactly when* we (ie our terrestrial posterity) will actually be able to see evidence of the event in question, accounting for the finite propagation time of the light. ("the majestic pillars will appear intact to observers on Earth for another 1,000 years or so.")
That's because it matters where and when the said event lies on our spacetime manifold in relation to us. I read the article in this mindset, as using terms ("have already been" / "will be") to describe the physical *configuration* of events on our spacetime manifold, using an implicit but clearly understood coordinate system. (Ok, maybe the spacial orientation wasn't exactly fully spelled out but the time axis was clear enough: "observers on Earth") There's really no way to specify exactly where and when the events lie in a coordinate-free way. We *need* such talk to physically locate events, inside our light cone or not.
There's no need to wait 1000 yr for an event to be 7000 yr in our causal past in order to be able to legitimately conclude, then, that it's a 7000 yr old past event and therefore was chronologically 6000 yr in the past of our 1000 yr old selves. We can (contingently) do that now, because we can have some knowledge, based on theoretical extrapolations, of events located outside our light cone.
And for the reasons given that is exactly what I feel the author was doing.
If the author had written something like "...the Eagle Nebula is located some 7,000ly to our left..." without spelling out any other context, he'd deserve a rebuke.
Past and future still have meaning in our relativistic SO^+(3,1) world in the same way that left and right still have meaning
I'm not using a classical model of time here. I'm arguing that noncovarient quantities (like the sign of the difference of the time coords of two events), though not covariant, can still be physical in the sense that they can be measured (with respect to a frame). Take it to momentum-space. Is the energy above the rest mass of an object physical? Sure, it can be determined in a frame. Or there's the frame-dependent electric field strength, or wavelength, speed, etc, etc..
Indeed I think the case can be well made that essentially *all* physical quantities are ultimately/implicitly determined by measuring frame-dependent coordinate differences. (Think about the Stern-Gerlach experiment, Millikan's Oil-Drop measurement of e, temperature on a thermometer, time elapsed on a stopwatch. It's all just x2-x1.)
I believe we agree on the causality of the nuts-and-bolts physics. maybe not philosophically. Hmmm.. a difference between space coords of two events. Yet another non-covariant quantity. Your hypothetical observer who's here and now, moving past us at high velocity, using English in the same way, would claim the event is actually not that far away. But it's fine, I knew exactly what you meant by that.Of course it's a frame-dependent ordering on the events, not Lorentz covariant at all, but it's not entirely useless nor devoid of meaning. I and about 6 billion of my closest friends have acquired quite an attachment to this particular (though, yes, arbitrary) frame of reference!
I appreciate your desire to inject some physicality into the discussion, just not the rhetorical way you went about it.
Really, when will people learn not to use the past tense for events outside of our past light cone!
Really, when will people learn not to post embarrassingly wrong "corrections"?
As a physicist who has studied General Relativity (but my area is quantum field theory), I can assure you most definitely that the condition for event #1 (t_1, x_1) to lie in the past of event #2 (t_2, x_2) is merely t_2 > t_1. It is not (t_2 - t_1) > |x_2 - x_1|/c . This is in flat spacetime where the coordinates of the events are measured in the same (arbitrary but consistent) inertial reference frame, or a reasonable approximation thereof (like ours). When the curvature of the spacetime is not negligible, you have to use the metric (g_mu,nu) to determine whether a future-directed *timelike* curve connects event #1 to event #2, not whether a future-directed *causal* curve connects them.
Just because an event is not in our absolute or causal past, does not mean that it is not in our chronological past!
What are compression waves? They are merely trillions of particles (atoms/molecules) moving in concert due to their interactions with other particles up and down stream.
Reduce this down to the atomic scale and think about it like this: atom #1 propagates through space at speed v (less than c) until it approaches atom #2. Atoms #1 and #2 then interact. In the context of quantum field theory, this means that one or more virtual photons are exchanged between the charges (electrons and protons) in atom #1 and atom #2. This interaction takes time (which is not negligible) for those photons to propagate. Through this interaction some momentum is transferred from atom #1 to atom #2. Now atom #2 has to propagate, and so on...
So what you said is not true. For compression waves to move faster than c, the constituent atoms (and virtual photons) would also have to.
There has been a speculative proposal by Miguel Alcubierre, in the context of General Relativity, that takes advantage of an imagined negative energy density in some region of spacetime to produce a metric (a special kind of curvature of the spacetime) that allows for superluminal transport of matter. That is, a warp drive.
The good news here is that there is a known phenomenon of quantum field theory (the Casimir effect) that causes the region in between two highly polished metal plates that are extremely close together to develop a measurable negative energy density. (Basically the plates filter out the zero-point energy of long-wavelength electromagnetic quantum fluctuations of the vacuum that would otherwise be present, but cannot fit between the plates.) The bad news is that the effect is utterly negligible in strength.
What you are describing is a truly rigid body, and unfortunately there is no such thing in nature. It would require instantaneous action at a distance. This is also why Newtonian physics ultimately fails.
There is always a finite propagation time for the the electric field of the moved charge of the first particle to reach and repel the next particle in the row, etc. These interactions are mediated by (virtual) photons (ie light).
A few years back, some Harvard physicists grabbed headlines by slowing down light in a Bose-Einstein condensate to 38 mph! More recently, just a couple of weeks ago, Japanese scientists fabricated nanocavities in solid state which slowed light passing through them to 5.8 km/sec.
Incompressibility of a material is mediated by the electromagnetic force arising from the charges inside and between the atoms comprising a material. As such there is a fundamental limit to the magnitude of the incompressibility. You can always push those electrons closer together (until they disappear on you, creating a shower of new particles).
Sound waves are ultimately constituted by moving particles, and according to relativity it is not possible for a particle (or even information!) to move faster than c=299792458 m/s (not to be confused with "the speed of light" which is only equal to c in vacuo). This is unless those particles are (hypothetical) tachyons, in which case they can never move slower than c (but even then, they cannot transmit information faster than c.)
Even inside a neutron star, the Pauli exclusion principle is insufficient to prevent the neutrons from compressing and collapsing into a black hole.
Irrelevant to the real world? Hmmm... I suppose one's definition of "real" depends on the limitations of one's experience, but a clearer understanding of what is and is not possible in principle should surely be recognized as relevant by anyone interested. Maybe you really just aren't. Studies of intractability in computability do not only show where the boundaries lie, but can be helpful and save time in practical ways. In the context of security, I've personally seen halting concerns arise in turing-complete grammar extensions to regular expression engines, for example. Ever heard of a DoS attack? You wouldn't want a devious user to trigger one of those on your modded PCRE engine, so what's the best prefilter/dectector? Doh! There isn't one! Good thing that expensive CS education helped to steer us clear of that pitfall. Why aren't there any good sendmail configuration security checkers? Answer. Honestly, there are an infinitude of real, practical examples. You need to check out Garey&Johnson's Classic, at least the introduction. :-)
.... All those mental masturbators! What wasted lives!
uh... splint? Now you're just being silly on purpose.
Make it out of cheese? Talk about an irrelevancy.
Poor Russell and Gödel and Turing and Post and Church and Rice and
Man, it's annoying when someone accuses another of ignorance when the former is more wrong by an order of magnitude!
The parent poster wrote
and that assertion stands as claimed.
He is arguing that there is no such (secure) algorithm which always answers (correctly) in every case (100% accuracy). His argument is perfectly fine: it's a routine and trivial application of Cantor's diagonalization method. If you really disagree, I challenge you to produce such an algorithm forthwith.
Your problem is that you have misunderstood the hypotheses in his proof sketch and tried to replace a universal quantifier with an existential one. Of course there is some limited program that can verify the security of some carefully specified others.
IsSecure() cannot return false when passed program A as input without violating the hypotheses.
Your changing the specification of the problem is analogous to removing the "not" in "This sentence is not true." and then claiming: Wow, no contradiction!
You're wrong on almost every significant point.
Indeed.
http://www.family.org/docstudy/newsletters/a003533 9.cfm
Dr. Dobson's Newsletter: February, 2005
Setting the Record Straight
Dear Friends:
If you had told me a month ago that Id be devoting my February letter to a cartoon character named SpongeBob SquarePants, Id have said you were crazy. Nevertheless, by now you probably know that I have been linked to that famous talking sponge by hundreds of media outlets, from the New York Times to "MSNBC" to "Saturday Night Live." The story of how this situation unfolded is somewhat complicated, but it must be told.
In truth, this tale has very little to do with SpongeBob himself, and everything to do with the medias ability to obscure the facts and to direct lies and scorn toward those of us who care about defending children. It all began on an evening in late January, during Inaugural Week in Washington, D.C. At that time, I spoke briefly to 350 guests attending a banquet hosted by Tony Perkins and the Family Research Council, Focus on the Family, and Gary Bauers American Values. I concluded by sharing a word of concern about a video that will be distributed to 61,000 public and private elementary schools across the nation, for use on the proposed "We Are Family Day," March 11.
The video, which millions of children will soon see, features nearly 100 favorite cartoon characters that kids will instantly recognize, including not only SpongeBob, but also Barney the Dinosaur, the Muppets, Dora the Explorer, Bob the Builder, Winnie the Pooh, Clifford the Big Red Dog, Jimmy Neutron and Big Bird.1 The video itself is innocent enough and does not mention anything overtly sexual. Rather, it features the childrens cartoon characters singing and dancing along to the popular disco hit "We Are Family."
But while the video is harmless on its own, I believe the agenda behind it is sinister. My brief comments at the FRC gathering were intended to express concern not about SpongeBob or Big Bird or any of their other cartoon friends, but about the way in which those childhood symbols are apparently being hijacked to promote an agenda that involves teaching homosexual propaganda to children. Nevertheless, the media jumped on the story by claiming that I had accused SpongeBob of being "gay."2 Some suggested that I had confused the organization that had created the video with a similarly named gay-rights group.3 In both cases, the press was dead wrong, and I welcome this opportunity to help them get their facts straight.
I want to be clear: the We Are Family Foundation the organization that sponsored the video featuring SpongeBob and the other characters was, until this flap occurred, making available a variety of explicitly pro-homosexual materials on its Web site. It has since endeavored to hide that fact (more on this later), but my concerns are as legitimate today as they were when I first expressed them in January.
So let us consider the evidence. One of the first resources to catch our attention on the foundations Web site was a booklet4 that lists a number of organizational "allies," including five of the largest pro-homosexual organizations in the nation: the Gay and Lesbian Alliance Against Defamation (GLAAD), the Gay, Lesbian and Straight Education Network (GLSEN), the Human Rights Campaign (HRC), the National Gay and Lesbian Taskforce, and Parents, Family and Friends of Lesbians and Gays (PFLAG). Also, the Web site made available school lesson plans that suggested teachers ask these questions of students:
"How are you affected by homophobia?"
"How would you be affected by your sexual orientation were it different than it is now?"
"How will understanding these definitions change your thinking about compulsory heterosexuality and homophobia?
"How will it change any of your behaviors?"5
From a handout entitled, "Talking About Being Out" there was this:
"Do you know of any people in your school whose sexual orientation differs f
Evil is simply anything that opposes the personal will of God, which must (for now) be axiomatically taken (ie "on faith") to be "good". Apart from the personal will of God the concept of evil really is ultimately meaningless. One could try to argue that there is a certain common sense of morality which is shared by most people, most of the time, but the notion breaks down on close examination. Individual hearts differ on what is needed or desirable. Only the existence of an absolute God can provide an absolute point of reference, otherwise everything descends into relativism.
What first impressed me to think about this was while reading through the Old Testament once: I noticed over and over it saying that "the righteous shall live by faith". (Righteousness, of course, being the antithesis of evil.)
This struck me because it was the exact opposite of what I had expected or wanted. Why was it *faith* that God demanded, if indeed there were a God, and not direct knowledge or action or experiece? Faith is so weak and unreliable in comparison to knowledge and experience. It took me two years of thinking about it to finally find a satisfying answer to that question. It's worth considering carefully for yourself.
small hint: Jung qb lbh ubcr sbe jura lbh cynag n zhfgneq frrq?
The angles given for the 4,5,7 triangle on page 1 of chapter 1 are incorrect to the number of digits specified. These values are quoted as
:-) j/k
theta_1 ~= 33.92 deg
theta_2 ~= 102.44 deg
theta_3 ~= 43.64 deg
But the accurate values (according to my trusty HP48SX) are
theta_1 ~= 34.05 deg
theta_2 ~= 101.54 deg
theta_3 ~= 44.42 deg
Maybe the author explored alternatives to traditional trigonometry, because he was not good at traditional trigonometry?
Over the long term however, the upgrade *rates* of 2 vs 1 purchaces every 3 years do imply a 66.7% and 33.3% market split.
Oddly, the infamous quote was actually made in response to Wolf Blitzer's question, "Why should Democrats, looking at the Democratic nomination process, support you [Gore] instead of [Senator] Bill Bradley ...? What do you have to bring to this that he doesn't necessarily bring to this process?"
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Also, in his response Gore said quite a bit more than the grandparent poster gives us, though the most relevant bits are all there.
If you want to view the question and Gore's full response for yourself grab this clip of the CNN interview:
ed2k://|file|Al%20Gore%20Created%20The%20Intern
(Get rid of any spaces in the link that are added by Slashdot. The file format is Real Video. The file size is less than 600 kBytes. Use an eDonkey client to download.)
In my opinion, if you take his statement at face value, the straightforward, unqualified way in which Gore makes it suggests that, even if he didn't believe that he actually "invented" the Internet, he seems to have genuinely believed that his own beaurocratic contribution was more important than any researcher's or network engineer's prior work!
Another noteworthy site is http://www.RatherBiased.com. Their motto is "Watching CBS News so you don't have to". :-)
But seriously, I have been checking it out it daily since the whole MemoGate controversy erupted. The blog is on top of this story; the operator of the site appears to have a number of internal contacts within CBS News. It also has deep archives that go back years, detailing previous spats between Dan Rather and the Bushes.
Of particular interest to me was this interview with former CBS correspondent Bernard Goldberg, whose recent op-ed in the Wall Street Journal is also an informative read.
To win in four moves pick middle row/right col, bottom row/middle col, bottom right corner, and upper right corner.
The grandparent poster seems to be confusing things a bit. Let's try to clarify...
Except for the Lorentz transformation, the most important equation in Special Relativity theory is the Energy-Momentum relation:
(This is true for all inertial reference frames, and embodies the fact that the contraction of the energy-momentum 4-vector for a particle is an lorentz invariant. The Dirac equation, the Klein-Goron equation, and much of modern quantum field theory is rooted in this equation.)
Another important equation of SR involves the velocity:
From these, we can see that
(i) if v < c (sub-luminal), then pc/E < 1, so E^2-(pc)^2 > 0, which means m^2 > 0. This case is true for normal, boring matter. Note that the converse is also true: m^2 > 0 implies v < c .
(ii) if v = c (luminal), then E = pc, and m^2 = 0. This holds for (massless) photons and gluons, and used to be assumed true for neutrinos. The converse ( m^2 = 0 implies v = c ) is also true.
(iii) if v > c (super-luminal), then m^2 < 0. Conversely, m^2 < 0 implies v > c . There is no known type of matter that is described by this case, but physicists have given such hypothetical particles the name "tachyons". One could say that mass is imaginary in this case, as m^2 < 0, but physicists rarely actually speak like this.
Anyway, the parent poster is right in correcting the grandparent poster that it is negative mass *squared*, not negative mass, that makes something a tachyon (v > c). But this
is not quite correct. From F=ma, we can see that it is true a negative mass would cause a particle experiencing a force in one direction to actually accelerate in the *opposite* direction! (Imagine that. You push something away with your finger, but it comes closer, increasing the force you're exherting on it, which increases the acceleration, ad infinitum. Physicists really hate thinking about the instabilities involving negative inertia, so we don't like to talk about negative mass at all.)
The problem with the parent post's suggestion is that althought this strange behavior would happen with an electrical force (such as your finger), it need not hold for gravity! In boring old Newtonian Gravity, a particle a distance r away from another mass M feels the force F = GmM/r^2 . But the acceleration would be a = GM/r^2, whether the mass is negative or not, because m completely cancels out of the equation. A similar thing happens in General Relativity, Einstein's theory of gravity -- the particle still follows the local geodesic of the spacetime metric generated by M.
To get back on the topic of information transfer, it's pretty clear that without nontrivial spacetime topologies (eg, wormholes) superluminal information transfer shouldn't happen except in the tachyon case. But does it really happen in this case?
The problem is that real life is quantum mechanical, wherein "particles" are described by evolving wavefunctions in a Hilbert space. A particle is a sort of propagating localized disturbance. The equation that should describe the propagation of a (scalar) tachyon is the Klein-Gordon equation. I quote the last paragraph from this discussion of the KG equation in the tachyon case:
1 kilowatt-hour = (1000*3600)/(e*10^12) = 2.25 x 10^13 TeV !!
(But concentrating even a GeV into a single particle's kinetic energy is rather difficult, today.)