md65536

No, the "dream information" is not the same unless the dreamer knows that everyone else also knows the dream information, which they don't. The people can be ordered by, for example: Choose any one blue, let them choose any blue, etc. Obviously the order doesn't matter, and it will work the same for each blue I may choose, and each that each of those may choose, etc. No one dies on the first day. Say I see 99 blues. I can make an assumption that I'm not blue. If I'm brown, I'll learn by the 99th day that I'm right, when the blue islanders all leave/die. If I'm blue, I'll learn the next day, after realizing no one left as I assumed they would. If I'm brown, I know that the blues will leave on day 99 because they'll have realized after the 98th day that their assumption that there were 98 blues, is wrong.

This is one of those problems that I can't stop thinking about. More analysis: This is probably my favorite logic puzzle now too. Not a lot of mental math to do (the inductive solution is pretty light), but definitely some ideas to twist your brain up in understanding it.

Oh yes. I think the XKCD link presents it slightly more easy to think about. I think I see how it works, now.

If you're talking about only the case where there is one blue-eyed islander, then no: The brown-eyeds knew there was at least one blue-eyed, but the blue-eyed didn't know that. If the blue-eyed suicides, then the rest can deduce that there was only one blue-eyed. The interloper's comment provides new information only to a lone blue-eyed. No one else thinks anything too shocking of the comment. The blue-eyed's suicide provides new information to everyone else. Sorry if I'm off due to skimming the thread.

Isn't that a bit like saying "Planetary movement isn't possible without epicycles" some time in the past? Isn't QM considered just a model of reality (one with unprecedented predictive precision and accuracy), and not the mechanism that drives reality? Or is it more---Is QM also a label for the mechanism? If a better model was known (if one even is possible), then couldn't all those things work without QM? QM is our best understanding of phenomena, and hasn't been found inconsistent with reality (unlike epicycles), but that doesn't mean it's been proven correct or the only explanation possible. Sorry if I've wandered off topic. I suppose, none of those things could be explained by current knowledge, plus "electric universe", less QM.

Certainly a mind-bender. If you said that the physical laws were predictive, then you could argue that the laws are created by humans, and humans are physical things that obey the physical laws, so humans are not able to determine a set of laws that could predict the outcome of all experiments. Then you could use the "free-will" argument to prove it: If I know a law predicts that I will choose A, then I will instead choose B, violating this law that would otherwise contradict free-will. But if the laws don't have that degree of predictive power, then the choice of A or B could both be consistent with the laws (and the laws could be consistent with free-will). But then, even if the "necessary hypotheses" are satisfied so that Godel's theorem applies (I don't think it's been shown?), it still might only tell you that the physical laws cannot be used to prove their own consistency. I don't think that implies that there exists a physical phenomenon that is inconsistent with the laws.

As per Schrödinger's hat's point (a), what's stopping the PS from making contradictory statements while the PS itself doesn't break any physical laws? Doesn't using Godel's Incompleteness imply that given a "complete" set of laws, it's possible to derive a contradiction? Doesn't that then imply that you can always find an observable event that is inconsistent with any possible set of consistent laws? But can't you create a law for every observed event? So wouldn't your theory imply that reality is inconsistent? (I've likely made a mistake in my reasoning, or misunderstanding of Godel.) Edit: Just so I understand what we're talking about... By "phenomena" we're only talking about observable events, right? Laws are laws because (and only as long as) all observations are consistent with them. Laws don't necessarily "explain" stuff. So is it fair to say that by "Law(s) L explains phenomenon X" we mean "X is predicted by L and consistent with L"?

Why couldn't it be? I agree the hypothesis is "highly doubtful" but I don't think that assumptions based on Earth life either support or oppose it. Though, I suppose terrestrial assumptions can be used against other terrestrial assumptions (e.g. if it's assumed that aliens are like trees, then the argument that trees could not produce enough energy for locomotion is applicable). The Mars rovers. I'm not saying that alien life of any kind is plausible, just that the idea is imaginable.

Interesting idea. I disagree though. I think that if it is not necessary to become autotrophic (and it clearly isn't), then it isn't certain that a species will become autotrophic. It may be an advantage, but I don't think autotrophy is a required criterion for being "truly advanced". Green implies photosynthesis using chlorophyll? Aren't there other ways of obtaining energy? Why wouldn't they be black, and able to absorb a better range of wavelengths? Why not able to change color, and control absorption of light? Why be dependent on light at all? Why not engineer the body to be fusion-powered? Yes, but it wouldn't necessarily have to derive all of its energy from light. It wouldn't necessarily have Earth-like metabolism. Mobile light-powered creatures are conceivable. As well, it's conceivable that an organism could have multiple energy sources, and is able to survive on light only in some state of reduced mobility and energy consumption. I think making assumptions about what aliens "must" be like based on what Earth creatures are like, is not very reliable.

I'll go by that. I think the video and OP's others are very funny and I like the ironic, satirical sense of humor.

The numbers remind me of this: It's genius though! It's no wonder numbers have always boggled scientists! We've always been trying to find big numbers using just digits from 1 to 9. No one ever thought of using a 14 before! Troll though? Maybe we'll never know. It's not like one could just check the other videos uploaded by the same user on youtube. I think it's great. From "it's too much of a taboo subject" and "People couldn't work out... squares" to the closing inspirational thoughts, this is just enough like other serious crackpot theories that it's treated like one.

That's pretty big. At a glance, it certainly looks bigger than anything I've come across as a professional mathematician, but without knowing how you arrived at the number I can't be certain that it's the biggest. You'll probably have to publish your methods. If you're correct, it could be a pretty important finding.

Does it make sense to speak of the probability of detecting an electron on a certain side of the atom, such as say "the positive x hemisphere" or something? Or is the probability evenly distributed? By 'biased' I mean that the probability of an atom (or group of atoms) behaving as if the electron is more likely to be in one specific area of the atom (such as a pole) than another. Does an atom's behavior even depend on "where" an electron might be at any given time? Thanks for the reply.

MRIs temporarily align the magnetic field of some atomic nuclei. Electron spin resonance (ESR) is similar but affect the spin of electrons instead of nuclei. Does this in any way synchronize some probabilistic aspects of the atoms? I'm trying to imagine an experiment in which you could get a macroscopic object to display wavelike properties. All the electrons in the atoms of some piece of matter could be considered to be orbiting their atoms' nuclei in a random probabilistic cloud, right? Is it possible to align them so that the probabilities are temporarily biased all in the same direction? Or does that have nothing to do with spin, which is affected with MRI and ESR? If you had some mirror-like reflective material that could be affected by MRI or ESR, and you shone a light on it while it gets all resonated, is there any detectable difference in the reflected light? Could there be any interference patterns or anything visible?

Is that not allowed in other countries?

Funny, I was just looking up "loaded question fallacy" earlier today. False dichotomy also applies. I don't get it either.

No, they'd still be light nanoseconds (or smaller) apart. The speed of light is a constant and doesn't scale along with you, assuming you could be shrunk. So a being so large that she could view our observable universe on a tabletop, say, would still have light from different parts of the universe reach them with billions of years differences. This might not be so bad if the being's "brain cells" are spaced millions of lightyears apart and her thoughts occur on the order of quadrillions of years. Another aspect of light that's important is wavelength, I think. We can't directly image atoms with visible light because they're too small. I'm not sure what wavelengths of light you could absorb if you were that small, but I think things would look very different if you could shrink. Perhaps this fits well into your idea, as you speculate your lab may appear black and empty... not due to the travel time of light but perhaps due to the wavelengths of light. The speed of light's not such a limiting factor if you can change the scale of space itself. And you can do this, for example by using length contraction by traveling at near c relative to parts of the universe. A human-sized being who could somehow view our observable universe as a human-size thing might be able to observe the whole universe as we observe our immediate environments. Our experience is very different from what would be experienced at a subatomic level.

Ah thanks. They do state that the observed positrons are interpreted to be the result of photon-photon interaction. However it would be stupid for me to assume it must be something else, without good reason. I guess I have to throw out my assumptions and re-evaluate my understanding. So there is an example of light turning into mass, one interpretation of the original question in this thread.

I don't trust whomever it was who linked that article above. The above article isn't an experiment, but it theorizes a maximum laser energy, based on real experiments involving photons and electrons (edit: this isn't true. I should have read my own link, which says that photon-photon interactions happened after the photon-electron collisions). I didn't really think about it, but I realize now that it clashes with my understanding of light, which I now realize is based on some assumptions that might be dubious. Would it be correct to say that 1. Photon-photon collision has never been experimentally confirmed 2. There is no accepted theory that says that it's impossible So it may one day be determined that it is impossible (contrary to the predictions of the article I linked), or it may one day be experimentally observed (or neither)? I was extrapolating from the known in order to confirm my assumptions. Maybe not "too stupid", but a careless mistake nonetheless. A crackpot mistake.

Alright fine I don't know what I'm talking about. No collisions. I'm not sure if interference could be considered interaction. The wave function has interference but the photons haven't affected each other??? I'm not sure how to form this into a correct statement. Two photons may interfere and interact differently with their target, but they haven't directly interacted with each other. Alright fine I don't know what I'm talking about. I should have said, there are no interaction or principle (such as example Pauli exclusion) that allows for photon-photon collisions. ??? That also doesn't sound like the right way to say it.

The following story suggests doing the same with light: http://www.nytimes.c...-particles.html More stuff related to the last link: http://science.slash...intensity-limit However, the first link involves colliding photons and electrons (and I haven't read the second). So it still involves particles... not the "pure energy" I think you were thinking of? I suppose there would be no way to collide two photon beams, would there? Pauli exclusion doesn't apply to bosons such as photons, only fermions. So it should be possible for multiple light beams of any intensity to pass through the same space without "turning into matter". Light cannot act as an observer; it cannot receive light, so I suppose there's no way for two light beams to interact? Can a boson decay into a fermion by itself, or does it need to interact with another fermion? Edit: "Fermions are usually associated with matter, whereas bosons are generally force carrier particles" [http://en.wikipedia.org/wiki/Fermion], so I think boson to fermion decay is close to the idea of converting energy to mass... However I think that it's probably incorrect to describe it literally as such???

Yes, but it's interesting to figure out if it could be done any other way. What I mean with congruence is something like the first paragraph from http://www.highhopes.com/numberandgeometry.html (I don't know the reliability of this source.) "Counting was not always important. In fact, it was unnecessary when keeping track of such items as sheep. All that was needed was a one-to-one correspondence. If one had fifteen sheep and kept fifteen pebbles in a bag, it was a simple procedure to remove one pebble for each sheep to see if they were all present. An extra pebble meant a lost sheep. One doesn’t have to know how many sheep or pebbles one has – only to check the one-to-one correspondence between them. Using fifteen knots on a string or fifteen knicks on a stick could also do this. (One-to-one correspondence is a precursor of counting yet pervades much of mathematics.)" Similarly, it might not be necessary to express a length as a number if all you need to know is congruence. I can construct a circle by using congruent pairs of points, like the ends of a stick I'm given. I don't need numbers to do this, unless the stick is by definition representative of a number (its length, or the number r, or the number 1 in "stick units").

What is a ratio? How do you draw a circle? I know how to, using a given fixed length, but isn't that a measure or can count as a unit? Or if you're given a circle to begin with, how do you determine its center? Again I know how, but I don't think I could describe it without words like "of the same length", and wouldn't that be a measure? Perhaps congruence is enough to do all this, and wouldn't count as using numbers???

How would you describe the relative size of something without ratios? How would you express a ratio without numbers? (Pure analogy might do, I suppose.) How would you express area or volume without numbers? Perhaps you could describe some aspects of shapes without numbers. How would you describe a triangle (don't refer to numbers!)? "A number is a mathematical object used to count and measure." [http://en.wikipedia.org/wiki/Number] The word geometry comes from the words "Earth" and "measure". Even if you used only analogy -- for example your only measures were "Is it bigger than a breadbox? Is it bigger than an elephant?" -- the set of analogous objects might count as a system of numbers???

Well that makes sense, because inside the parenthesis of your limit you have something that approaches 0, and you're multiplying it by something that approaches infinity. You can't just change the thing that approaches 0, even slightly, and expect the limit to evaluate to the same thing. Basically you have two things that converge to the same value, and you're subtracting them. The limits of [math]\frac{1}{\sqrt{e}}[/math] and [math](1 - \frac{1}{2n})^{n}[/math] are the same, but for a finite n they differ by a specific amount which you're trying to find (or were given, really), which is proportional to 1/n. If you pull out one of those values and put in a different value, even if it converges on the same value, it will differ by some other specific amount for a given n. Anyway that doesn't tell you how to do it. mathematic tells you how. What does it look like when you expand (1-1/(2n))^n by the binomial theorem? (I don't know.)