Schrödinger's hat

Yes, I think any remaining disagreement comes down mostly to semantics. The one minor difference of opinion may be that I still entertain the possibility that there is a perception of thinking without though occurring. I do not know what this would entail, but I can't find a good reason to rule it out either. If the laws of logic are not as we perceive them, then I sort of run into a brick wall. I'm reasonably certain of the statement that some kind of entity/place/event occured/is/was/some other atemporal verb, and that this verb produced the perception of thought. We very quickly get into shaky territory (differing definitions of thought/mind/perception etc) and somewhere along this line lies a semantic issue, as with most philosophy. Read the whole thing (again?), or just the letter at the front of that copy. Unless I am completely missing some heavy irony, he is talking specifically about the Christian God (although the deceiver is a generic character). Most of the latter chapters are dedicated to the ontological argument for said god. At some point he abandons the idea that he might be being deceived with no justification than that certain thoughts are 'clear and precise'. He then uses this to argue for god, then uses this to finally dismiss the deceiver completely. If I have misread this I would be interested to know. I don't quite care enough to trawl through it myself and find any misinterpretation I have, but if you could point one out it would be appreciated. I must say I do/did let my personal opinions of the man colour my opinion of his work more than it should. The more I learn about the intellectual environment, the more I come to respect (or at least stop disrespecting) him. Also, it doesn't appear to be in this edition, but one of the others I read opened with letter in which he was complaining about someone having translated some of his earlier works into French, and how this allowed unworthy people to read them.

Conceptually, I think this is somewhat of an improvement over the traditional pop-science interpretation. The idea that the stretching/curvature of the surface is intrinsic to it rather than merely as a result of embedding is more aparrent. I like the metaphor of there being more space piling up near a dense object. It gels well with the way things take infinite time cross event horizons in the types of coordinate frame that we're accustomed to. You'd have to be careful what you meant by inertial motion here though, it's not really at all apparent in this metaphor, and I think a straight line (outside the sheet) would represent acceleration not only of the wrong amount, but in the wrong direction. If you consider a line that is straight with respect to a grid you drew before stretching the sheet then things are still somewhat off. Without some way of representing the temporal direction you're unlikely to do well in this regard This being said, this is just a metaphor, and bears only a passing relation to the full theory.. Maybe if your sheet looked like this to begin with, you might make some progress in making some of the numbers line up. But then you'd have to supress another spatial dimension and just have one direction as distance, and one as time. Not quite sure how to answer this, or interpret displacing space-time. The presence of matter will mean that distances and straight lines or still/inertial paths will change. Mass does effect space-time. I don't know what you mean by 'at near ligh speeds'

I think what ydoaps was getting at -- and this is a path I have gone down many a time -- is that the only thing one can know for sure is that the perception of thinking exists. I do not know off hand whether I have seen it written elsewhere before or since, or if it was entirely original/independantly come up with. So I know that something is thinking (or mimicking thinking, or at the very least that _NOUN_ _VERB_), but I cannot be certain that it is the entity I consider 'me', or of the tense of the action it is taking. I could, for example, be part of a dream of this entity, or a fiction or simulation it is writing (or has written). This may just be an issue of semantics, but I don't think Descarte was talking about some general thing when he said me/I. It also seems I had projected these thoughts onto Descartes. I was under the impression that he acknowledged this briefly before moving on, but I was mistaken, he either does not consider this possibility, or has a broader definition of 'me' than I give him credit for. I was exaggerating somewhat and being facetious, but there is a grain of seriousness there, let's see if I can back it up. He takes sooo long to say anything, but I think the gist of it is summed up here (spoiler tags to save wall of text): This follows from some stuff about having ideas that must have come from external to himself because he cannot seem to alter their truth or his perception of them. To paraphrase the whole lot as one statement: If I am not being deceived, then there's all these ideas of perfection and therefore God exists. (let's assume the ontological argument is valid for now) Then If God exists and is perfect etc he will not deceive me. There's more there if I/you have the patience to dig further, Using this copy which seems to match the paper copy I read at some point in the past.

I'm glad I'm not the only one who was frustrated by the cheating. I seem to recall the full argument was something along the lines of: I believe I am thinking, therefore I either exist or I am being decieved. BUT GOD EXISTS AND HE WOULDN'T TRICK ME SO I EXIST, AND BECAUSE I EXIST THEREFORE GOD. The philosophers I have discussed this with usually say this second part was more of an anti-excommunication/execution clause than something he would have included otherwise (regardless of his spiritual beliefs). Indeed.

[math]\left(i\hbar\frac{\partial}{\partial t} + \frac{\hbar^2}{2m}\nabla^2 + \frac{e^2}{4\pi\epsilon_0 r}\right)\Psi(\mathbf{r},\,t) = 0[/math]

Hmm, this whole truth business is dangerously close to dogma. Such matters are usually best left to philosophers and theologans. Science is more about being less wrong. It's the only knowledge-seeking discipline where it is implicit that the explanations/theories are wrong. In fact that's the whole point if you think about it. A good scientist doesn't sit back and say, 'There, I have a hypothesis. It looks pretty much right; it must be the truth. Time to go home.' Instead they sit and poke it. Trying to find the rough edges or outright prove it wrong. In light of this the null hypothesis is just the simplest possible explanation of: "There's nothing interesting happening here." If we manage to disprove this, we run with the best available explanation (whatever the alternative to the null hypothesis) until we can disprove it. Hopefully by then something better will have shown up. This being said: A long standing theory -- while being wrong -- is usefully wrong. If we can find the edges of the wrongness, we have a fairly good idea of when it's good enough. I use the flat-earth model all the time. From informing my short distance travel plans, to building things (by assuming things at right angles to a line of constant gravitational potential are parallel). Newtonian physics is sufficient for 99% of human endeavour (a bit less now with constant use of computers and GPS, I suppose). There's nothing special about general relativity and the standard that mean they are any more likely to be The Truth than any of the preceeding theories. I don't need Truth. I'm perfectly satisfied with being less wrong, and peeling away another layer to see what lies underneath. This is the true wonder of science. It's wrong. Gloriously, wonderfully wrong. But a little less wrong all the time.

I was merely presenting a weaker form of the same argument. Regardless of whether or not a natural generator were found (I agree that this is highly unlikely given current knowledge), the fact we have not done so would make one interesting even if one did not assume there were intelligence behind it initially. As such, further investigation would be likely and any intelligence behind it would become more apparent. Well you said ignore it, but I didn't notice until I had already written a response, so here it is anyway as I thought it might be interesting. Obviously such numbers would have to be truncated at some point. A good way around the beginning thing is to repeat it. If I had reason to believe someone was trying to communicate with me, and I identified some kind of restricted character set, one thing I would try is a variety of number bases. Here's one for you to try dfhfaachdcgehhcdeahbdehgafhdf Granted you already know the general scheme, but it's not too much of a head start for a proof of concept. This would probably be a very poor scheme, especially with longer sections of transcendental numbers, as they could appear very much like noise. Alternatively I could encode something like pi as a series of rational approximations ... - ............. ---- ................ ----- ................... ------ ...................... ------- ................................................................................................................................................................................... --------------------------------------------------------- and so on. This is much more clearly a message, and would probably be about as effective as the prime numbers at getting the point across. Although it lacks the advantage of perparing the reader for the use of composite numbers to delineate area-like and volume-like entities (such as images).

Would have to is possibly slightly strong, but it would be a very clear signal that something interesting was happening. Exponentials (I include both [math]2^n[/math] and the fibonacci sequence in this, as it can be described as the sum of two numbers, each raised to the same exponent) on the other hand pop up all over the place. Even if some alien race had discovered natural phenomena that generated prime numbers they would probably still illicit interest. There are many other sequences we could use (ratios of masses of the most fundamental particles we know of for example, or something involving common fractals, or some encoding of pi¹), but it's a fairly good bet anyone advanced enough to have a radio telescope (or any hobbiest looking through one in a civilisation where they are more widely available) would recognise prime numbers, and not relate them to common natural phenomena. Anything we pick would potentially look terribly naive to some highly advanced race, including the use of radio waves. If they were interested in responding I doubt our primitive mathematics would be any further deterrant. ¹These would require some higher level encoding. Integers such as primes could be a series of beeps, or some other discrete part of the signal. Decimals or irrationals require further context. You can't just assume they use base ten. Any race as or more advanced would not have too much trouble recognising these numbers in any base if they were looking, but they would not stand out from the noise nearly as well as a sequence of integers. Other advantages of primes are they are monotonically increasing, increase quite rapidly in size (exponentials share this one), and once you get across the idea of primes you can use composite numbers to try and get across the idea that you're sending an image.

Where's your attempt? If you haven't made a start, why not? This is not a homework answers forum. We're happy to help if you're stuck but we need your working so far (even an attempt you know is wrong is fine). If you don't know where to start, help us by explaining which concepts you do/don't understand and any ideas you have.

Not quite sure what you're asking/stating here. It is often useful to represent light as spherical waves travelling out from their origin, is this what you're getting at?

Psst he already got the answer in chat. Although bailed before I could show him the graph.

Life isn't an entity or quantity in physics (or science in general). It's merely a label that is applied to certain types of systems. The most formal/nicest definition I've seen is: Life is a self-sustaining, reproducing, local entropy minimum. This is possibly a slightly broad definition

This is most certainly not the case. If I do not correct for light delay there will be further distortions, but they are location dependant. If you were moving towards me you would actually appear stretched. Any experiment I do (including momentarily trapping you in a container as long as I open the doors in time to let you out) will show your size in one dimension to be smaller. This is all a relic of us having a different definition of what constitutes time and space. If you consider all four dimensions, then the analogue of length (interval) remains constant

The fibonacci sequence comes up a lot in nature. Or at least sequences (or continuous things) that are very similar mathematically. Look up logarithmic spirals. Objects that are self-similar will generate these and it wouldn't take much of a coincidence for the growth rate to approximate the fibonacci sequence. Anything that is changes in a way proportional to itself will have a doubling time, and if that doubling time happened to match up with some other timing, you could easily get 2,4,8... or similar. Many patterns that come from a simple recurrence relation or differential equation will tend to pop up in nature. Prime numbers on the other hand are notoriously hard to weed out. Other than some advanced methods, some of which which aren't deterministic, the only way to find prime numbers is to start with some prime numbers, then use those to figure out which numbers aren't prime and cross them off to find more (and thus repeat the process). They don't arise easily from feedback loops and the nice (and sometimes not quite so nice, but still fairly tidy in the scheme of things) types of equation that natural phenomena tend to follow.

You clearly haven't hung around with enough mathematicians.

Hmm, I have an anecdote which may be relevant. The way I process mathematics, geometry, logic, and related concepts may be relevant. I would consider mathematics a language, when I do algebra in my head I most certainly do not use english. Most frequently I process it visually, symbolising it in much the same way I write it down. Although some operations have a decidedly tactile feel, I often find my eyes or hands move around when I'm rearranging equations and not paying attention. The motions match the spatial arrangement of the symbols in conventional notation. I can think about and plan actions/spatial activities without anything that maps to any formal language I know. It's hard to describe the exact process. It's certainly symbolic to a degree, but the symbols are not exclusively (or sometimes at all) audo or visual. It may involve the impression of a weight, a torque, heat etc, or some combination of some of those and/or sounds/sights. Least frequent is a smell or taste. I am not imagining all the details of the action, and sometimes the symbols don't match up exactly (ie. an impression of warmth may apply to an engine that hasn't been started in some time). Back to mathematics, some operations are decidedly visual. If I am dealing in vectors/multivectors, or tensors I understand the geometric meaning behind I will imagine something that visually resembles the symbol I'd use to write it down, but it carries a lot more information. If it is a bivector, for example, it will have a sense of squareness (I don't know why squareness rather than ellipseness or parallelogramness, I gues that's just the symbol for two dimensions) or sometimes circleness, and if it has known components it will have a sense of size (although the visual symbol doesn't change size) or perhaps more appropriate would be mass (even if it represents some other quantity). I'll deal with a cross product in much the same way I deal with real algebra (as described above), but a wedge product will be dealt with in this more intuitive manner. It will twist (again, this twist doesn't apply to the visualisation of the picture-symbol, but to the ...tactile symbol) everything it applies to as it distributes itself across a set of brackets. If I'm dealing with vectors/matrices which are in component form I operate differently again. This is almost purely visual. For example: If there is a multiplication involving a column vector it will move, rotate 90 degrees, then merge with a row of a matrix or a matrix vector. The final arithmetic calculations are then mapped to english/audio, although carries are processed/stored visually as if I were to write them down. Numbers do not have any extra information associated with them, when doing arithmetic I use my visual memory almost exactly as I would use a piece of paper for multiplication/addition. Although intermediate results are often stored as sounds. All these representations are very closely tied to the language(s) and abstractions I used when first encountering these concepts. So I think that thought and language both inform each other to a large degree. In response to some of Tar's comments. This is a selection of some of the highest level abstractions I could think of. Some of my thoughts are much less abstracted, the visualisation/other imagination may be close to an exact simulation of the event. Or at least the details I am interested in. I would agree that thought is difficult without some level of abstraction, but I don't know quite where I stand on whether or not any level of abstraction constitutes language. One should be careful of getting into issues of semantics. I'm in danger of veering off topic and/or falling into a recursive loop, but what exactly is language? If it were just abstraction we wouldn't have a separate word for these two concepts. Edit: Another thought. What do you define as thinking? Some of the things I do, do not involve any abstract thinking -- be it visualisation, thinking in english or other -- these are usually very simple tasks, or things I've done many times. In spite of me paying almost no attention to these things they can be very complicated if you actually think about them. Take walking for example. If we exclude this kind of processing what are we left with as our thesis? Abstract thought requires abstraction? It seems somewhat tautilogical at this point. Few more thoughts rolling around, but it's well and truly someone else's turn. If anyone is interested ask me about intuition and I'll remember what I wanted to say.

One. Muahaha Two. Muahaha Three. Muahaha Three! There are three sentences in the wall of text. Joking aside. We appreciate it if you break your thoughts down into readable chunks (lots of both sentences and paragraphs ). We also appreciate it if you would post non-mainstream ideas in the speculations forum (don't start a new thread, a mod will move it for you).

I have seen this both as recommendation from coaches/trainers and empirical studies. I don't know the mechanism behind it, but in addition to Perpetual Motion's suggestion, here is some conjecture: Cold fluid dissolves gas more readily, perhaps CO2 or oxygen transport into and out of the cells is the limit rather than what the blood can carry? In this case cooling could be beneficial. If the body needs to perform some exothermic (heat releasing) reaction in order to recover the ATP or do something with some other chemical in the muscles it could be limited by the temperature (ie. more heat would mean more damage so it slows the rather of the reaction). If this somehow resulted in the muscles spending longer metabolizing anaerobically it could result in more atp. Most proteins are very temperature sensitive. Some of the damage to muscles in exercise could be related to the increased temperature (not just lactic acid). Ice baths would stop this if it were occurring.

Okay, I'll use a particle model of a fluid for this explanation. Imagine it as a bunch of slippery balls which are jiggling about a little bit and can slide past each other freely. I might also re-order your questions a bit to try and answer them coherently. Imagine some sand (or our balls) being placed into a container in a big stack in the middle. Give it a bit of a shake, anywhere the balls aren't pushing against something (the edges or another ball) they'll tend to move out. This will keep happening until they are pushing against something, so the end result is they'll spread out and flatten until they are bumping into the container everywhere below the surface, and the top is flat. Pressure is the force acting inward from all directions on something in the fluid. Imagine all our balls bumping and pushing against each other. If there is more pushing on one side than another, the ball will move. Eventually things will reach an equilibrium where everything is bumping into everything else equally so there is no net force (although there are many forces acting inwards ie. pressure). Let's ignore gravity for the moment. If I exert a force on some part of the fluid (let's say with my hand), one of two things will happen: The fluid will get out of the way. I'll momentarily but an uneven force on some of the balls, they'll move, bump into others and so on until things are in equilibrium again. Or the fluid will have nowhere to go. In this case my hand will not move into the fluid, I'll meet resistance. I'll push balls I am touching which will push harder on the balls they are touching and so on until they are all pushing on each other or the walls of the container by the same amount. If this didn't happen then the balls would move, but they cannot move (well, individually they can, but there'd just be another ball there to take its place if the fluid as a whole has nowhere to go) so the pressure increases. You can modify our model a bit for a gas. Instead of having the balls mostly touching, they're all whizzing about at roughly the same speed (on average). When they bang into something and turn around they exert a small impulse (force for a tiny bit of time). This happens so often that the result is a fairly steady average force. The faster they move, the stronger each individual force (so high temp = more pressure). Also if you confine them to a tighter space, they bang into the walls more often, so there are more impulses, increasing the average force. Back to liquids: Before with my no-gravity example, all the forces from the bumping exactly cancelled. Once we include gravity, this can't be the case. If we had the same force on a ball from every direction (excluding gravity), it would still accelerate downwards. So the bumping from below must be stronger than the bumping from above (you can see that this must be true for the top layer in a liquid because there is nothing on top). Then the next layer down has enough pressure on it to hold up the stuff above it and keep itself still, but then it has to hold itself up as well, so there is even more pressure on the layer below. And so on. A slightly different picture/way of wording is that all the horizontal forces cancel out exactly, but there has to be more force from the layer below than from the layer above to cancel gravity. From the explanation above we have that the increase in pressure as you go down matches the weight of the fluid. So the bumping on the bottom part of an object would be more than the bumping on the top part. If the object is lighter than the fluid, then this will be more than is required to cancel the gravity, so it will accelerate up. If the object is heavier, it will be less than is required to cancel gravity, so it will accelerate down. This force comes from the fluid coming into equilibrium (not accelerating on average), so the force (difference in pressures, or difference in force) must be exactly enough to cancel something the same density as the fluid (ie. the buoyant force is equal to the weight of the fluid displaced). Hmm, I can't think of a good way to fit this one into my analogy. The best explanation comes from conservation of energy. If you look at all the types of energy in a fluid (pressure, gravitational potential, kinetic energy) then the total must remain constant. So if one increases (kinetic) then another must decrease. If any of this is still unsatisfying, feel free to ask some more. Further questions may help improve my explanation

You'd need to know something about its motion as well. Either its velocity/momentum in your frame or its acceleration or semi-major axis of its orbit or similar. If you had very precise instruments (or c was slower) you could compare its length to a reference ruler which is co-moving, or check its colour somehow (arguably measuring redshift requires a clock of some kind too). This would tell you its velocity without having to have access to a separate clock.

Well once you have known distances and (predictably) moving objects, you've made yourself a clock. Ditto goes for known times. If you were very quick (or c was slow) you might be able to do a direct measurement of time with a ruler using relativity, but only someone else's time. Other interesting and relevant fact: c is now defined as a ratio. So distances are actually measured with clocks (and light, or some other speed of light phenomenon). We do this because our clocks are very very good, while our distance related apparatus are merely very good.

I haven't looked at this from a quantum perspective before, but classically you can do something along the lines of replacing the monochromatic wave: [math]e^{ik(x-ct)}[/math] With something multiplied by some step functions, ie. [math]u(t0-t)u(t-t1)e^{ik(x-ct)}[/math] If you want to recover the spectrum of the truncated just take the fourier transform of the new function. The main potential problem I can see with this simplistic approach is the hard edge may introduce un-physical artefacts where -- were you to consider your shutter/barrier as a potential and treat it as a scattering problem --you'd have tunnelling.

Simply interrupting a beam to turn a (near) monochromatic wave into pulses is enough to change the bandwidth.

I'd be inclined to think it would only work once, too. But I don't know this for certain, I do know that the increased speed would make it much harder (and less useful energetically) each time so I put a rough upper bound of a small handful of times.

The simplest answer is that putting the light into the loop will change both the energy bandwidth (uncertainty) and position uncertainty.