Halc

Non-sequitur. All numbers have equal chance of winning, so no choice, popular or not, alters your odds, but as swansont points out, unpopular numbers yield better average payouts. You seem to presume N is less than 64, which is not always the case. Even if it is the case, your conclusion is again a non-sequitur. Picking five random numbers under 32 gives the exact same odds of winning as picking 5 random numbers in the range of say 33 to 40. This is the simplest of mathematics: Every possible choice has the same odds as any other if the draw is random.

Decelerating the rocket just wastes all the momentum it already had. If you have delta-V left over, accelerate more, not decelerate. This gives maximum momentum transfer to the thing, which is what is needed to deflect it. Of course, it's best to hit it more or less from the side, which is inefficent for something coming more or less straight at you. Indeed, but also the harder it is to tell if the effort is needed at all, or if the effort will actually make the trajectory worse, due to miscalculation. Look at all the news about some asteroid that's going to hit Earth, and then it misses it by a mere million km. You can't send a defection mission out to every big rock that might get that close, but by the time we know it will hit, it's too close that a small defection is enough. It's also harder to get something out to an incoming object quickly if its further away. Takes more delta-V to get out there, leaving less to actually impart momentum to the thing. I don't think nukes are very effective in a vacuum. It will leave a nasty stain and small crater and will defect almost not at all, unless you can get the thing to embed itself a ways in without destroying the mechanism in the process. There is armor-piercing technology that helps with that sort of thing. Look at the bunker-buster bombs they have, designed to penetrate a long way and still explode, sometimes even hours later. But those bombs are heavy and not too fast, hitting at far slower speeds than what would likely occur in a rocket/asteroid interception.

Yes, they'd be comparable. You're asking if a straight line (or a geodesic one) is a similar length to one with some minor curvature to it, and both are about 2000 years long, differing only in perhaps the 6th significant digit (a guess). The length of the actual worldline would be a tiny bit shorter than the interval between the two events. This is essentially the gist of the twins scenario where one twin has a shorter worldline than the one with the straighter worldline.

PBS space time is a pop science source. They can say what they want. Speed for one is relative, so for instance I am currently going very near light speed relative to a muon waiting for me to go by it. The universe is unaffected by my moving at this speed. The speed at which something goes relative to something else has zero effect on the geometry of the universe. It is possible, but a 3D torrid surface, sort of like the video game asteroids takes place in a 2D torrid surface. It means that there are preferred axis orientations, and that if you travel along any of these axes, you get back where you started. Any other direction and you don't. Your post seems to describe something like that. Such a universe would be unbouned, but finite in volume, very much like the surface of Earth, except retaining the flat curvature. The universe is much larger than the distance to the event horizon, and since one cannot reach the event horizon, one cannot traverse even one loop no matter the speed. Presuming that expansion wasn't accelerating (or happening at all, for simplicity), there would be no event horizon, and thus one could go all the way around. So in asteroids, the universe isn't expanding at all, and if one goes vertical, you get back to the staring point after 1 lap, in say 5 seconds. If you go diagonal at the same speed, it might take a minute to get back approximately to the center of the screen, the starting point. You seem to presume that one direction is longer than another, sort of like the asteroids screen not being square. That's fine, but it isn't necessarily the case. If two depart from the center at the same speed and time, the vertical guy gets back before the one going the long way. If the aspect ratio is 3:4, then it will take 3 or 4 laps for them to meet each other again. Length contraction plays no role in this. For one, it is a coordinate effect, not strictly a physical one. A length contracted ship going at 0.9c still gets 3.6 light years from here in 4 years (as measured by 'here', the frame in which he is contracted). It being a coordinate effect, one does not experience length contraction. One is by definition always stationary relative to ones self, and thus there is no contraction to experience. And a paradox isn't something experienced either. You've not identified any paradox. You just say that there is one. What each person would see, if moving fast relative to stars, is a bunch of stars moving fast relative to him. They both see that. There is no paradox identified.

I can think of at least three kinds of time, and the distinctions are important. What clocks measure is proper time, which, in GR terminology, is the spacetime interval along the time-like worldline followed by the clock, completely analogous to proper distance being measured by tape measure following a space-like worldline. Proper time is an invariant (it is not frame dependent). It is physical and very real. Getting beyond strictly physical, there is also coordinate time. Coordinate time is the time coordinate assigned to events by a particular abstract coordinate system. It is purely abstract (a mental thing, not a physical one). It is very frame dependent, but still physics, not metaphysics. If we get truly down to metaphysics/philosophy, we get to the third kind of time, which is the progression of the present moment. It is 'that which flows'. When somebody asks if time is real, they're probably talking about this kind. It probably has an official name but I don't know it. I call it teapot time since like the teapot purported to be in orbit around the sun somewhere beyond Jupiter, there is zero empirical evidence for it, but its existence also cannot be disproven. So to give an example of the three kinds, we decide to throw Bob (and his watch) into a black hole. In some coordinate systems (say that of a distant observer), Bob takes forever to reach the event horizon. In a different coordinate system such as Kruskal–Szekeres coordinates, he falls right in in some finite time X. That's all coordinate time. Proper time is easy: Bob's watch reads time P upon reaching the event horizon. That value is the same regardless of choice of frame. As for proponents of teapot time, the only theory I know that includes it is forced to deny the existence of black holes at all since events within cannot exist, so any talk about falling into one is unsupported. This of course provides a semi-empirical test for presentism. If you jump into a large (at least say 15000 solar masses) black hole and find yourself inside, you've disproved presentism, but of course you cannot publish your findings in a science journal any more than you can publish your discovery of an afterlife. One has to die to test it, and the guy inside the black hole is, while not yet dead, certainly doomed.

You're asking two different questions: What is the most likely value of s when all of the list has been selected at least once? At which value of s will it be more likely than not that all of the list has been selected? The answer to the first question is seems necessarily lower than the answer to the second. Do you see why? I don't see an obvious way to derive either value right away.

It's a top, simple as that. Not clockwork at all. We had these as kids. They went under the brand name 'whizzers' or some such. This one is decorated as a bug. The wheels underneath drive an internal vertical-axis flywheel. You'd get quicker responses to your questions if the title actually gave any clue as to what the topic is about. You seem to give the same title to all your topics, however unrelated.

You got it all wrong Bufofrog. What kind of fool is going to believe that? Everybody knows it was last Tuesday, not Wednesday.

People can produce enough thrust to fly here on Earth, but it takes an athlete. Don't know the current record, but somebody flew over the English channel with human-powered flight. So sure, if you can do it at 1g, you can do it at lower g with less effort. I think your mistake is presuming it is just a matter of strapping on winds and arm-flapping. But our arms are situated nowhere near our center of gravity, so instead of flying horizontally like the pictures depict, you'd hang vertically if all your weight was born by your arms. I suppose it could work, but the aerodynamics would be horrible. All gliding done by humans is a different setup designed to support you everywhere, hence the funny flying-squirrel setup that the base jumpers use. I suppose that one could generate thrust by a more 'flappable' version of one of those. That (gasoline, electric, etc) would be powered flight. We also have that here on Earth, so again, doing it at low g would be easier. You can also strap on a rocket, something else a human can do here on Earth. What if the pressure was much higher? How much easier/harder would it be to fly at say 1g or less with thicker air. It has more mass to support you, but more drag as well. If it's dense enough, the buoyancy alone would be enough.

The velocity of the universe would be the change in its position relative to something that isn't the universe. It really makes no sense for a universe to have a velocity.= Velocity per second per megaparsec would be something like v/t/d (velocity, time, distance) which is d/t / t / d which is 1/t², something with different units than velocity at least. As for special relativity, that only applies to flat Minkowskian spacetime with zero energy and mass anywhere. For this reason, it is simply inapplicable to our universe except locally. Your equation adds values of different units, which makes it meaningless. You can't add meters to Pascals, and (in your case), you can't add H (units 1/t) to V/γ (units d/t) Another criticism: γ is the Lorentz factor of what exactly? It should be the factor for some speed, but "the Lorentz factor which is used in incorporating special relativity into the equation and using the laws of special relativity" is just a word salad.

Aspect dualism is effectively a violation of known physics. Such a violation would be required for any agency that is not tethered to physical causality. A non-deterministic interpretation of quantum mechanics does not open the door for this sort of thing since willed agency cannot emerge from the probabilistic description of quantum theory. One that claims such a relationship would need to demonstrate some structure in the privileged arrangement of matter (probably just humans) where a signal is generated purposefully (not randomly) without cause. There's no structure in a person that is seemingly designed to do anything like that. All structures at any scale seem to be evolved for repeatable (deterministic) operation, just as are transistors. I'm sure. Humans are excellent at rationalizing what they want to be true. Most are not so great at actual rational thought. Hence all the 'proofs' that not only does God exist, but a proof of exactly my version of God. All those proofs (but one at most) must be wrong, and even that statement doesn't pass rational analysis. This doesn't seem to make sense. It seems to suggest that MWI supports the existence of worlds where MWI is wrong, since MWI does not hold to PCD. None of those seem to be examples of counterfactuals. They're all states measured by Bob and/or Alice. The (one) universe as a whole is deterministic under MWI. I don't think the concept of a given world being deterministic is accurate there. It cannot be since any given world is the result of random events. Yes, Alice & Bob hook up in some worlds and not in others. In other worlds, one or both don't even exist. But as a whole, all those states exist in superposition. I don't think that qualifies as a counterfactual of any kind. Saying the cat is dead is a counterfactual. Saying the cat is in superposition of dead and alive is not. Then the robot should predict the indecision and play anything (the game does have a time limit you know), instead of losing by default. You've just pretty much proved Godel's theorem about the halting problem. It cannot do down either a single path or a finite distance. Events (such as my choice of footwear today) depend on many causes (the weather being but one), and those causes themselves have to have come about due to other states even prior. That 'chain' spreads both in width and depth all the way back to the big bang. This is true under determinism or not. The difference is that under nondeterminism, some of those causal branches stop. A choice I make might be partially a function of a beta decay somewhere. That particular piece of state (among the myriad of states that contributed to my choice) was uncaused, a true random occurrence under nondeterministic interpretations. The robots playing RPS is not a single event. I suppose their eventual choice is, but there's a lot of state that potentially contributes to its eventual choice (or lack of it). If the robots are identically constructed, then it would be like you trying to win RPS with your own reflection. I don't understand how any of that aids in the question of 'what definition of determinism is in play'. The definition is something along the lines of the complete lack of randomness: That identical closed systems in a given state will evolve the exact same way every time. Was there another definition that is fundamentally different than that? Only some systems exhibit this. You drop successive grains of sand from a fixed point and which way a given grain goes is fairly unpredictable, but the eventual conical hill of sand is very predictable. Most systems are chaotic, under which small perturbations result in macroscopic differences. The weather, the formation of galaxies from a uniform early state, are examples of this. Take the state of Earth just after the Theia event. From that state, life is unlikely to form, and if abiogenesis does occur, it will most improbably evolve into anything that would be recognized as a mammal.

It indeed seems not the case. The stanford page on libertarianism doesn't even mention determinism at all. I stand corrected on that point. There's the compatibilist view I suppose, but it requires a sort of soft determinism. Now I really wonder why 'free will' is a desirable thing.

I do believe the libertarians assert both free will and determinism, that the one is possible despite the other. Your stance, at last what I can make of it, doesn't look like that. I for one would I suppose qualify as libertarian, but only because I define free will in such a way that is 1) completely compatible with determinism, and 2) actually something that is desirable. A more typical definition of free will seems like something I'd not wish to have, and it is indeed often incompatible with determinism. Build two machines that play rock paper scissors. They are constructed so that each uses a completely deterministic in algorithm, and each has full access to the state and programming of the other. If the behavior can be predicted because it is deterministic, then each robot can predict the move of the other and always win. Since the machines can't both win, predictability cannot be had despite the deterministic nature of the situation. Godel did a simpler proof, but that one is a bit more on topic. I don't understand these comments or the relevancy to my comments to which they replied. Perhaps you don't grok what I said. I admit the lack of elegance in my conveying it. I think any non-local interpretation can be (but not necessarily is) consistent with counterfactual definiteness. Does determinism depend on counterfactuals? MWI for instance is considered fully deterministic but denies counterfactuals, but I'm not sure how a wave function can be properly expressed in the absence of counterfactuals. I lack the expertise to resolve that. You also mention a block universe, but I don't think a block universe necessarily implies determinism, so I don't see the relevance between one interpretation of time or another.

QM shows that it isn't predictable, but until the fully deterministic interpretations are falsified, QM does not kill determinism. If you can go back even a short time, then that prior state must be fully determined by the state shortly prior to that, and so on... Hence if we can go back a little and retain determinism, then we can go back all the way to the beginning. Of course there's no evidence of this short term determinism. For one, it presumes a meaningful state of a system, which is a counterfactual, and few interpretations of QM support counterfactuals. Don't confuse determinism with predictability. One can have a nice classical fully determined universe (such a Newton might have envisioned) and it would still not be predictable. It's pretty easy to show that. That's a good example of an uncaused thing. Bohmian mechanics (which supports counterfactuals) would I think assign hidden variables to the neutron system and a thousand identically set up systems would all decay after the same duration. MWI (also deterministic) would say that it decays after every possible duration. Copenhagen simply says we cannot know. Most of the others say something on the order of it occurring at some random time, which in some cases is 'God rolling dice'. None of the modern deterministic interpretations were out there during Einstein's time, and he seemed like a determinist type to me, so that's too bad. There are people (at least one of whom is contributing to this topic) which seem to spin a deterministic universe in a bad light, like it is somehow a thing to be avoided if possible, especially for decision making. I don't understand this aversion. I cannot conceive how a better decision can be made through a non-deterministic mechanism than through a deterministic one. All of evolution has favored structures that generate consistent output from identical inputs, despite leveraging quantum process in doing so. This shows that determinism is a good thing, even if it doesn't exist in reality.

Light from that star was emitted about 8 billion years ago when the star was about 5.5 billion light years away, both time and proper distance per the cosmic (expanding) coordinate system. That star, if it currently exists (unlikely), is a burnt out husk right now and doesn't shine at all. More likely it blew up and doesn't exist at all, or is a black hole or some such. Yes, it could not have been traveling for longer than that, and it doesn't need to. Such distances use an expanding coordinate system where light speed isn't constant. But also, absolutely nothing we see in the sky now was emitted further away than about 6 billion light years away (proper distance). Sure, the galaxy/quasar/whatever may be 40 billion light years away now, but we're seeing it where it was long long ago, which was much closer. The CMB light is the oldest, and that light was emitted from less than one billion light years away. That light isn't from any 'star', but it is from the formation of the first hydrogen atoms. You're going to have to unlearn this common misconception if you want to actually understand cosmology. The big bang happened literally everywhere and was never a 'point', and there is no rushing of material from a point into 'empty space' so to speak. Getting your information from peer-reviewed sources is a far better choice. I can find a 'doc' that states just about any nonsense I wish. Your source apparently claims to have measured something outside the observable universe, something which is by definition a contradiction.