KipIngram

I'm hesitant to get back into this one, but I can't help noting other situations where we label physical things using coordinates. I can note that a hot object and a cold object have a "temperature separation," but I don't think that "the temperature scale" has an innate physical existence. Green and red are of different frequencies, but "the frequency scale" doesn't have an innate physical existence. Same with heavy and light objects re: "the weight scale," and so on. It really seems to me that spatial coordinates are just labels we give things that we've found useful. The difference is that we're our brains have a different way of presenting spatial separation. Our vision sense just "works in a different way" from our senses of touch or hearing. The things we perceive as "occupying space" have relationships amongst themselves which our senses have evolved to perceive, and our science has been developed to express. I think it's those relationships that are real, irrespective of the sensory structures and analytical tools we use in connection with them. "Empty space" is just what we perceive when there is nothing there to attach that range of coordinates to. It's a creation of our mind, tied tightly to the nature of vision, and it just so happens that our other senses don't operate in a way that gives us that same "it's there but empty" message. Please don't take this as denying the whole virtual particle thing - I'm very aware that we believe space is foaming everywhere with "events," but I'm not qualified to enter into that part of the discussion with you.

Oh my, that is fun.

You're incorrect. J.C. MacSwell gave precisely the condition for applying momentum conservation to this problem, and we've stated it several times above. However, in a completely strict sense you are right - the answer we obtain using J.C.'s approach is an approximation. A very very good one, in my opinion, but an approximation nonetheless. The block is not fixed. It is free to move. Like I pointed out, we absolutely know that it moves, because the original problem statement tells us exactly how far it moves - the "amplitude." That provides a spring energy which can be used to calculate block/bullet velocity immediately following the collision. But you cannot get the initial bullet velocity from energy conservation, because the total energy to which the pre-impact bullet's motion contributes has not been conserved. The only way to get initial bullet velocity is with a momentum conservation, and that requires you to assume an instantaneous impact event, per J.C. We even have confirmation that trying to use energy conservation alone to get the bullet velocity doesn't work - the OP tried and he couldn't get the right answer. That's why he posted here in the first place. I'm letting this one go now - we have all the salient points the OP should need to help him along.

Ok, you are correct, but the block is not rigidly fixed; we're told how far it's moved when the spring reaches maximum compression. It moves. The other end of the spring is assumed to be rigidly fixed. And in the strictest possible sense momentum is not conserved once the block has moved at all, because the spring is now slightly compressed and has produced a force. But if you follow J.C. MacSwell and neglect that, which truly will be reasonably negligible in a real situation of this type, then you can conserve momentum over that time range. It's really the only way you can get an answer to this problem without understanding the deep and gory details of the ballistic impact physics. To remove that assumption you'd need a model for precisely how the relative velocity between the bullet and the block dropped to zero during the impact event. With such a model in hand you could solve the problem exactly.

I second Scott's explanation of Shor's algorithm. I was in high glee when I ran across that - it's fantastic. One of the comments provides an alternative way of viewing the quantum Fourier transform - I won't comment on its rigorous correctness but it surely felt like a nice visual aid to me.

Of course you can. Only one end of the spring is rigidly fixed - the other end is attached to the block. J.C. MacSwell had the key insight into this problem - what you neglect is the time spent by the bullet "halting" in the block. Just as the bullet makes initial contact with the block, the spring is uncompressed. We assume that the compression that occurs between then and the time the bullet comes to a halt is negligible, so we neglect force exerted on the block during that tiny initial period of compression. At that point in time momentum conservation requires (bullet mass)*(initial bullet velocity) = (bullet mass + block mass)*(velocity of block/bullet system) That still has unknowns in it. But the kinetic energy of the block/bullet system right then is what compresses the spring, and that has to match the energy obtained from the given amplitude later when the spring reaches maximum compression. So 0.5 * (bullet mass + block mass) * (velocity of block/bullet system)^2 = (spring energy at max compression) That lets us solve for (velocity of block/bullet system), and then we can use the momentum conservation equation I listed first above to solve for (initial bullet velocity). The point of my last reply is that you are not allowed to neglect losses if you treat the bullet and block as one object with one velocity after the collision. It just doesn't work. Obviously momentum is not going to be match the initial momentum total once the spring has significant compression; some of the momentum has been absorbed by force applied by the spring on the block/bullet system. That's why you have to make that assumption of negligible collision duration.

I think you're meant to assume that the other end of the spring is rigidly fixed. Otherwise there's no way even to start. Losses are inevitable, once you assume the bullet comes to a stop in the block. You must conserve momentum in the instant of collision (while you're neglecting the spring compression). Energy is conserved only in the case of a completely elastic collision (when the bullet rebounds). If the bullet becomes embedded in the block you now only have one free velocity to play with so you can't conserve both momentum and energy. With an elastic rebound you are assuming no loss and you have two free velocities to work with so you can conserve both momentum and energy.

Well, certainly no computer that you go out and buy right now would survive a hacksaw very well. But if you challenged me to build a computer system that was resilient in that way, and you gave me specifications about what sort of cuts you wanted to make (I mean general specifications - it would be too easy if you told me exactly where you were going to cut) I could at least make a run at it. It would involve a lot of redundancy and information storage with error correcting codes and things like that. My current job involves this on a very small scale - we design enterprise grade flash memory based data storage systems. It turns out that modern NAND flash memory is actually pretty crappy stuff - it just "spontaneously forgets" to some extent. We error correcting data encoding techniques and multiple levels of RAID redundancy to overcome that. The idea is to avoid having to just have full copies of the system (mirroring) in order to get the reliability we need. I enjoyed your answer - not trying to tear it down. But I think it's no surprise at all that evolution favored the development of brains that show redundancy.

Yes, you're right - I was trying to convey a general point and was a little loose in my wording. Thanks very much.

Ok, fair enough. It doesn't look terribly useful for practical purposes, though. But you're right - there it is.

Hmmm. that link someone posted above says this: In 1887, mathematicians Heinrich Bruns[4] and Henri Poincaré showed that there is no general analytical solution for the three-body problem given by algebraic expressions and integrals. That's what I meant by "no closed form solution." Seems that a number of specific solutions, for specific cases have been found.

Because kinetic energy goes as v^2, the energy being delivered by the first increment of force (just as the rocket begins to move), is zero "approximately." The velocity can experience a "first order change" while the energy experiences a "second order" change. In the limit of the "very first instant" your ratio of velocity change to energy change approaches infinity. That said, the rocket is delivering a lot of energy to the exhaust - that mass is flying at exhaust speed out the back, and so has significant kinetic energy. That gets you back to inefficiency at low speed - significant energy is being given to the exhaust, while insignificant energy is being given to the rocket. Over any small but not infinitesimal window of time beginning at t=0 the energy delivered to the rocket is small but not zero, so it will get itself underway. And after that the faster the rocket is going the more rocket v the force has to work with to produce delivered power. I remember watching Apollo launches when I was a kid, and always marveled at how gradually the rocket first lifted away from the pad. Then later it seemed to speed up faster and faster. But it all makes great sense given the math.

Yes, if all the masses are free to move. The three body problem I'm most familiar with is a satellite moving in the Earth / Moon system, where you can neglect the mass of the satellite. I don't think the fully general three-body problem has a closed form solution, does it?

The big question that someone asked above and I didn't notice an answer for is whether or not M1 and M2 are fixed. If you have to consider their motion as well this gets a lot more complicated. If they're fixed then 1) if M1=M2, your test body should stay on the centerline at all times - it will accelerate until it gets to the vertical centerline through M1 and M2 and then decelerate. If it's velocity is high enough it will go on off to infinity, slowing down the whole time. If it's not high enough, it will oscillate back and forth along the horizontal centerline. For non-equal M1 and M2, the test object path will curve toward the heavier one. If it's velocity is high enough it will follow a curved path to infinity. The really interesting case is for unequal M1 and M2 without escape velocity - your test object will enter some kind of orbit, and I suppose it's possible that orbit might hit M1 or M2 (more likely the lower mass one). But you'd have to calculate that.

J.C.McSwell seemed to be on the right track to me. You know the energy of the system "block with embedded bullet" from the spring constant and the amplitude. If you neglect the "collision time" (basically that means the bullet has come to a halt in the block before the block has moved very far), you note that the spring is uncompressed at that point, and all the energy has to be kinetic energy of "block + bullet." That gives you the velocity of "block + bullet," and that lets you calculate the momentum. That momentum must equal the momentum of the bullet prior to collision, from which you can ascertain the bullet speed. I was given a similar question in an interview once, only in an electrical system. There were two equal capacitors, one charged to a voltage V and one with no voltage, with a switch between them. I was asked what the voltage would be after the switch closed. I used charge conservation to come up with V/2. But energy conservation gives a different answer, because it presumes no energy was lost. Even with no resistor in the circuit, energy is still lost. A thorough analysis would show that it was radiated away, since there's no loss component in the (ideal) circuit to consume it. But there's no way for charge to escape, which is why it's appropriate to use charge conservation. Energy is always conserved, but energy can change form on you in tricky ways. Momentum is always conserved, and it's easier to keep track of it - none of it "sneaks away."

Thanks - this line from there: While Maxwell's equations are invariant under Lorentz transformations, the GEM equations were not. The fact that ρg and jg do not form a four-vector (instead they are merely a part of the stress–energy tensor) is the basis of this problem. was particularly helpful.

One of my books on EM theory brings the theory forth by starting with Coulomb's Law and special relativity and then proceeds to show how those things together require the existence of a magnetic field and so forth. Coulomb's Law and Newton's formula for gravity are both inverse square laws, so it seems an entirely parallel development could be done starting with Newton's formula and special relativity. And yet in sense EM and gravity are very different, with one being a "real" force field in GR terms and the other being an aspect of spacetime geometry. How valid is this, and how far can it be taken? Is it off track from the start because Newton's theory isn't really "right" but is rather just a good approximation? Does it "work up to a point," and give us a correct derivation of gravity waves and so on? I've also seen some references to early work on unifying EM and gravity (Kaluza's 5D approach, and so on). How worthwhile is a study of that material? I guess reviewing any work is educational, but would it really lead me forward, or more off into the weeds? Thanks, Kip

dimreepr: First of all, your post wasn't exactly friendly, though I've certainly seen worse in my day. But more pertinently, what my post really asked for, more than anything else, was ideas regarding how consciousness might emerge from brain complexity that I haven't run across before. Just saying "it does," or "why couldn't it?" isn't really helpful. I'm absolutely interested in reviewing new material on that front. Also, the link you posted just went to a web page on the "for whom the bell tolls" poem, and I didn't really see a connection. I knew when I wrote the post that "spirit" is a dangerous word to use, though it seemed better than "souls." Maybe I should have referenced Hoffman and said "conscious agents," but like I said, the point of the post wasn't to argue for the whole spirit/soul/conscious agent thing - it was to seek new reference material on the emergent consciousness premise. On a separate thread that referenced machine consciousness someone noted that the GEB book notes the idea that a logical system can contain unprovable truths. That was helpful - I knew that about GEB, but I'd never pondered it in connection with emergent consciousness. I was of the opinion that since the emergent consciousness premise puts consciousness entirely within the material realm, that science then MUST eventually be able to explain it. But the GEB connection has caused me to see that's not as obviously true as I had presumed. It gives me something new to think about, and that was my goal. Let's not have ill will between us, ok? I promise I'm not here to try to slip religion in through the back door or anything like that. I'm legitimately curious about these things - I just want have the best understanding I can of how my own self-awareness (which is the most undeniably real thing I can observe about the world) can be fit into the grand scheme of things.

funker, let me try to give an "inside view" of what's going on in the stick. You referred to it as "perfectly solid," but that's where you're getting off track. What the stick really is is a 3D "grid" of atoms / molecules. For simplicity, just imagine that it's a nice regular grid and that you're hand is pushing the back end of the stick rather than holding it in the normal manner: Hand | | | | | | | | | | 8-ball In that depiction each | character represents a one atom/molecule "slice" of the stick. The atoms/molecules in the slice are connected to one another via chemical bonds, and the slices are each connected to their neighboring slices by chemical bonds as well. These chemical bonds behave sort of like springs - they try to maintain a natural separation distance between the atoms/molecules. So when your hand pushes on the leftmost slice, that slice moves to the right. That "compresses the spring" between the first and second slices. That causes "the spring" to push the second slice to the right, which compresses the "spring" between the second and third slices. The process repeats all the way down the line until finally the right-most slice is pushed to the right. This process is actually how force is transferred to the 8-ball as well; the right-most slice pushes the 8-ball atoms/molecules it's in immediate contact with to the right, which compresses chemical bond springs inside the 8-ball - eventually you get the whole 8-ball into motion. Previous replies made reference to the speed of sound - that's the speed with which this spring compression wave moves through the material. That's why there is a speed of sound - it's calculated from the nature of the atoms/molecules in a material (their mass, primarily) and from the strength of the chemical bonds connecting them. Hope this helps. Basically, what you need to know here is that there is no such thing as a "perfect solid" as you phrased it - no such thing as a perfectly rigid extended object.

Eise, thank you for the very thorough reply. After posting the message earlier that referenced GEB I was actually thinking that perhaps the book was much more focused on consciousness-related things than I'd initially recalled. I haven't always been as interested in "nature of mind" issues as I am these days, and I imagine when I read the book the first thing my interests were in other areas. The bit about all logical system containing truisms that can't be proven is just something that "stuck in my memories." I will re-read. Also thank you for the kind words regarding post quality. I try. It's a great hope of mine that before I die I'll achieve a tier 1 understanding of theoretical physics. When I was in graduate school (engineering) I deliberately took more math than my program required with that goal in mind - I felt I should take advantage of available training opportunities while I had them. Also, we had one particularly superb math professor during that period at The University of Texas at Austin - sitting in his lectures was always a pleasure. Since then I've tried to read as much as I can and I think I've gradually absorbed some knowledge, but I have a long way to go. I'm hoping that when I retire I can kick the process up to a higher pace.

Maybe I need to go back and find that and re-read it. On first reading I thought it seemed like stuff was leaving the two ends - just more through one end than the other. But it's been a while. And it definitely involved physics I'm only partially knowledgeable about. I'm really just an engineer. A PhD educated one, and I did try to load up on math and physics in graduate school, but I'm still not "professional grade" in those areas. Still in the "little learning" category of your signature quote (which I love, by the way).

Thank you - you're the first person that ever mentioned (to me) GEB in connection with emergent consciousness, and I've asked around about this a lot over the years in various places. Usually all I get is proposals of more layers of data structures and so on - nothing that really addresses my very fundamental misgivings about possibility 1. But that's food for thought. I did read GEB, but it was along time ago and I may now need to re-read it with this specific context in mind. Of course, I guess that would make emergent consciousness as unfalsifiable as conscious agents - the GEB point was that something can be true without being provable, and if it's true it's not falsifiable because it's not false. I do suspect that possibility 3 is unfalsifiable. I wrote a long post here yesterday asking for new thoughts re: possibility 1 like the one you just gave me, but I put it in Speculations for that very reason.

There are three possibilities here: 1) there is the material universe only, and consciousness arises from brain complexity, 2) there is the material universe, but in addition to that consciousness exists as a fundamental, unexplainable "given," and 3) there is consciousness only, and the material world we perceive is just that (a perception). Possibility 1 I'm a digital electronics person by profession, with "heavy for an engineer" math and science education, and I haven't yet gotten comfortable with this position. People have lots to say about it, but in the end it just comes down to transistors that are on or off and logical 1's and 0's in the software data representation - I've yet to figure out how a data pattern can have the self-awareness that I have (and presume you have as well). Position 2 Possibility 2 could be correct, but loses the Occam's Razor contest to possibilities 1 and 3. For this reason, I really haven't spend much time on this one, and probably won't unless I give up on #1 and #3. Possibility 3 Possibility 3 (see Donald Hoffman's "conscious agents") doesn't have to explain consciousness, since it takes it as a given, but before it can claim to be fully developed it has to be able to provide a reasonable program for how the perceived material world would match what we've actually observed. This possibility may be just as problematic as position 1 - it could just be that I don't have the background to appreciate the problems. However, it seems to me that if we endow conscious agents with the power to control the outcome of some subset of quantum events, it's feasible that a mechanism for free will could result. In laboratory experiments related to quantum theory, the normal practice is to collect results from an ensemble of equivalently prepared samples, and we expect the proper probability distribution to emerge. But the quantum events that a conscious agent would control to implement free will would each occur only once. Any outcome, corresponding to any of the superposed possibilities, is valid, does not violate quantum theory, and therefore is "fair game." The choice mechanism would be internal to the conscious agent and explaining it would likely be outside the realm of science - it's part of the "given" of conscious agent theory. Basically the action of consciousness would be "behind the wall" of quantum uncertainty - beyond the reach of experimental investigation. Summary This feels a little like "stacking the deck" in favor of possibility 3, but that's just how the cards fall. Possibility 1 claims to live entirely within the realm of science, and therefore science must produce (eventually) a full explanation for the entire process. The whole shebang is on "our side" of the uncertainty "wall." Possibility 3 very nicely puts the unexplained stuff on the far side, out of reach. But sometimes the simplest explanation is the best one. Given my current state of knowledge I find myself most comfortable with possibility 3. I asked a question here earlier today in hopes of getting "new input" (new to me) about how possibility 1 might work. I also need to look more deeply into Hoffman's conscious agents materials. This is all fascinating stuff, and in my opinion represents one of the biggest "unknowns" we still face.

3blake7, kudos for your effort to make your science fiction "hard." Accurate technology doesn't eliminate the need for a great story, but it's always added a lot of enjoyment to science fiction for me.

Ethan, all the points others have made above are entirely valid. Electromechanical energy conversion is the field of my graduate research (though I spent most of my career in my undergraduate field, digital electronics), and I can assure you that an enormous number of man-years have been invested in honing our abilities in the area. In general conversion efficiency can be quite good, but they are certainly less than 100% - there is no free lunch. The geometry you suggested feels crude to me - most generators use continuous circular motion. I'd be happy to discuss this with you further, either here or via private messages, if you like. One of the other members here has a nice quote in her signature about the dangers of "a little knowledge"; maybe I could help you gain more in this area.