Schrödinger's hat

Heh, that was a decent attempt, timo. I'll have a go as well. You'll get many different interpretations of QM if you ask many different people. A common interpretation of the phrase many-worlds is basically what timo described, privileging consciousness as some kind of magic wand which splits universes. This is similar in many ways to how the Copenhagen interpretation is/was often presented (with the experimenter/consciousness as some kind of magic wavefunction collapsing wand). The more coherent versions of each are as follows: The Copenhagen interpretation is a bit ambiguous to the objective reality of the wavefunction. It deals with it as a model or abstraction of reality, which may or may not be true. Measurement is a process which is very difficult to define (and as far as I am aware, left somewhat undefined except insofar as what the result will be), but easy to point to (it's the thing that guy in the lab did with those results). It collapses wavefunctions down into single possibilities with measurable results. The main objection to it is that the idea of measurement and quantum collapse is a poorly understood, complicated process that needs to be inserted into the theory, making it more complicated. There is room for some variations of interpretation within the Copenhagen interpretation, from completely denying the wavefunction as a way in which reality behaves and instead considering it a model with predictive power over large numbers of trials of an unknown but complicated process to ones where wavefunction collapse is an objective phenomenon. The many worlds interpretation comes from simply taking the wavefunction at face value. We observe that particles take on superpositions when interacting with other particles in superpositions. You insert some (often vague) argument about macroscopic objects being one of the distinguishable states of this superposition. Measurement and 'universe splitting' is simply the process of becoming entangled with a specific state of another superposition. There is no privileged system which can do the measuring. The main objection to this is, although it makes the theory simpler, it entails an absolutely preposterous number of universes (a split for every interaction that's ever resulted in a distinguishable difference). Re. the dice example, depending on how far back you go (maybe after it's thrown), that may just be a deterministic phenomenon insofar as there was nothing in superposition large enough to change the result of the roll Ie. there'd be universes where a photon bounced of the die in one direction, and universes where it bounced in another direction, but it might be showing 3 in all of them (if you go back to where some small change could alter the outcome, you would have splits with different rolls). Re. The quantum suicide, the experimenter would be just as dead in (n-1)/n universes as if they had committed suicide by any other means, so strikes me as an absurd way of going about testing MW. TL;DR There are lots of interpretations of QM, most sane variants of Copenhagen and MW have adherents within serious scientific circles (or at least people who will state that they use x interpretation when pressed), but Copenhagen is a lot more common. Most physicists just take a shut up and calculate approach as the maths works extremely well and doesn't care how you interpret it. Anyone who takes one or the other too seriously can probably be safely dismissed, esp. if they insert consciousness as a magic measuring-wand.

Foil only makes sense if you have already reduced conduction and convection. It's best to break the problem down into (and prioritize it with respect to) three categories. Conduction: Make sure it's not in direct contact with anything that conducts heat well. Low density, non-metallic substances (ie. air) work extremely well. Convection: If part of a fluid moves after it heats up, it can be replaced with another part at a lower temperature. This speeds up conduction greatly. This is the reason things like foam are good insulators -- although they conduct more readily than air, they significantly reduce or completely stop convection. Foam is generally better at insulating the lighter it is (and thus less better-than-air-conducting solid there is in it) along with being better if it has smaller pockets of air. The material does make some difference but is not as important. Conduction and convection are by far the most significant at moderate temperature differences, but if you have already controlled for these as well as you can, there is one more factor: Radiation: Even in a complete vacuum (no conduction and thus no convection either) objects will still lose heat to their environment by emitting heat in the form of light (at low temperatures mostly in the infrared range). If you can somehow place a reflector (such as aluminium foil) in the path of this light in a place where it will not be as hot as the source (ie. have a transparent insulator, ideally air or vacuum between the hot thing and the foil) this light will be reflected back into the object and (some of it will be) reabsorbed. Given this, and the household materials constraint I'd build something like this: If the shape of the bottle is controllable, make it as close to spherical -- or at least same height as width -- as possible, lower surface area to volume ratio means less opportunity for heat transfer. Also, bigger is better in this regard. Bottle -> thin to medium layer of foam with holes in it (ie. just enough foam to support the foil whilst leaving as much of the intervening space empty) or foam webbing (like that used for fruit packing) -> foil -> thick layer of foam Optionally a second layer of foil just over the bottle but under the foam might help (or might hinder). NB: use the smallest/thinnest amount of foil that does the trick, you don't want the region just around the bottle to have a high heat capacity. Pay special attention to the lid/opening to make sure air can't travel in or out. Also re. contact with the thick layer of foam, you want a close fit (to avoid convecting heat to a larger region of foam), but not a tight/smooth fit. Bumps and dents (the smaller but more numerous the better) on the contacting surface are good because they reduce contact area -- as long as they aren't big enough to encourage convection. One other note, if you have a supplied bottle or difficulty making the opening as good as the rest of it, you may be better off having a lid/plug of foam coated in foil/other opening on the bottom (with toothpicks or something to support the weight of the bottle and stop good contact) as hot fluid tends to rise. Final thought: If it needs to be opened regularly to check the temperature you might consider putting a separate, much smaller lid/openable hole for that purpose

Noone has attacked it because it is too incoherent. Very few or none of the technical terms you are using have their traditional meanings and you have said nothing specific enough that it would allow anyone to test your hypothesis against observed data.

Light propagation through a medium is a bit different. It can be viewed as the average speed of light which is being absorbed and re-emitted repeatedly. Although this doesn't describe the way phase velocity and group velocity can differ (and how phase velocity can exceed the non-medium-dependant constant c) without going into much more involved detail.

I guess it depends on what you mean by verification. We haven't gone to other galaxies to measure how long light takes to travel from point a to point b, but the speed of light is so intricately tied up in so many phenomena that it would require a large amount of special pleading to set a different value for c in other places. Things like absorbtion and emission spectra of stars and gas clouds, the energies at which nuclear reactions take place, etc etc depend on the constant c. I suppose one could argue that it's just a coincidence that photons travel at c in this location and travel at other speeds elsewhere, but that would require even more contorted reasoning re. ideas about massive and massless particles.

Well, perhaps we can speculate then, if it will stop the nonsense. yrreg. Assume someone/everyone has answered yes and respond accordingly. Then assume someone/everyone has answered no and respond accordingly.

Lowemack: I can't quite figure out the scenario you're explaining, but SR says: Two events, different places, same time in one frame -> Two events, different places, possibly different times in other frame (depending on direction of separation) Two events, same place, same time in one frame -> Two events, same place, same time in all frames (ie. actually same event). Four events, two pairs, two places (one for each pair), two durations (difference between times of pair of events) which are the same, two start times that are the same in one frame -> Four events, two pairs, two places (one for each pair), two durations (difference between times of pair of events) which are the same as each other but possibly different from the original, two start times that can change depending on frame So you can have two clocks that go out of synch, or two parts of one clock that go out of synch, but each individual clock or part of the clock will continue to have the same period as the other parts providing the whole thing is moving inertially. There's a stickied thread explaining the lorentz transforms. If you can understand it, try setting up some situations and seeing what they say.

I was attempting to be facetious for humor value. I realise choice of method and design of algorithm is far more important than the amount of computing power available. Apologies if I gave offense. I thought my note at the end made it clear that I didn't actually think that was a good technique.

There is also a presupposition that for every time '(some finite amount of time) before that time' is a coherent statement with an extant referent that is the same class if entity that we normally use when speaking of time. Or at the very least, the concept of 'always' is somewhat ill defined. This is yet another complicated and difficult question for which anyone who is not on the forefront of cosmology should answer "I don't know".

Slow? Just throw more computing power at it -- it's what everyone else does. javascript:(function(){var x = 1,xo = 0;while(x - xo){xo = x;x = 1.002 * Math.sin(x)};alert('Solution: ' + x)})(); (I was going to make it a hyperlink, but xss protections ruined my fun -- should work if you paste into URL bar unless your browser has similar anti-social-engineering protections) Also, another interesting note that this example brings up, is methods like these require a good guess for finding all of the solutions. A human is much more capable of finding the x=0 solution here than a computer using this method.

The line between not enough power and far more than you will ever use for any given problem is so thin that I would think it is hardly worth spending much money on performance. Especially if you are just dealing with toy projects for learning, you will just be able to turn down the number of steps/elements in your simulation. Save the larger investments for when you actually know enough that you are using your workstation for real work (or are you at this stage now?).

I don't know of any way to solve that analytically. Ewmon's method is as practical as any other numerical method in this case. You can formalize it somewhat, or use other formal methods if that is important -- they usually require calculus though.

You can update and fork someone else's fiddles, too. The number in the url just increases when you save it. It may do something fancy like ip checking and force you to fork, not sure

If you have n doors and the host only opens one goat-door, the probability boost from switching (to one of the n-2 doors) does decrease. If you have n doors, total and the host opens n-2 goat-doors, the probability boost increases. The frequentist rationale: There are n choices initially. For n-1 of these choices, the remaining door must have a car (because you picked a goat initially). For 1 choice, the remaining door has a goat. So given that you are about to pick a door: P(Car|Switch) = (n-1)/n P(Car|Stay) = 1/n Which approaches 1 as the number of doors increases. I can expand an analysis for arbitrary number of doors in the style of the Zomorodian paper if you wish. Modifying the asinine cretin's program to do so should also be fairly straightforward (change some 3s to ns and modify the revealing logic slightly). The program I wrote and posted -- not so much. I wrote it to be more interactive (and thus it's slightly more complicated) and didn't plan it at all so it's rather a mess. A hands on experiment can also be more convincing. I suggest the following refinement of my ace of spades example. Shuffle a deck of 52 (or n where n>=3) cards. Pick a card at random, give the rest of the deck to a friend (or pretend to be said friend). Ponder on the following questions (and maybe follow along on the analogous steps of one of the derivations): What is the probability you have the ace of spades? What is the probability that your friend has the ace of spades? Get your friend to sort through their 51 (n-1) cards, and put 50 (n-2) cards that are not the ace of spades in their shoe. Get them to hold the remaining card. What is the probability that the ace of spades is somewhere about their person? What is the probability that the ace of spades is in their shoe? What is the probability that the ace of spades is in their hand? Finally, given this information what is the probability that the ace of spades is in your hand? What is the probability that you would be holding the ace of spades if you swapped cards? Also, I apologise for the sober comment. It was somewhat insensitive.

I've been terrible at spelling lately, not sure why. :/

You'd get on well with Wolfram.

One point is that adult humans are bad at adapting their thought patterns. Society could easily get stuck in a rut. Whether this is viewed as a bad thing is more subjective. Another point is accidents. Even if we live forever, with no population growth, accidents could be bad. Catastrophe even more so if the technology to reverse the infertility is destroyed. A much less intrusive method of population control is greater levels of education. In areas with high levels of education (esp. of women) population growth slows or even goes negative.

I'm not 100% sure on what you asked me. Perhaps you could re-state the question, maybe adding a little redundancy just in case I still don't follow. I would be happy to attempt a formal answer if I knew exactly what was being asked. I think part of the issue here, is that the simplest way to proove this is by simple exhaustion. There are numerous tables and tree diagrams on the wiki page that constitute a proof from a frequentist standpoint. If you prefer symbol pushing, then you can throw Bayes theorem at it repeatedly, and there are a number of ways to approach the answer. The amount of exposition present is because the answer depends so much on the host's behavior. It's very important that he makes the same decisions every time, otherwise you get different priors, or a different distribution of outcomes. Also, many of us consider the proof to be rather trivial (as I stated, exhaustion is sufficient, or even pointing out the number of distinct states and outcomes) and that all of the difficulty to be had is in adjusting one's intuition. I think part of the reason you haven't gotten satisfactory clarification is that we (or I at least) are(am) having a great deal of difficulty understanding exactly what it is you are pointing out or what you're asking. This is probably due to an unstated assumption on someone's part, or an unstated knowledge differential. Perhaps you could break things down into much simpler statements (and over-explain slightly) until said confusion clears up. The reason we're concerned with your standpoint is that this community is here to help people learn and understand things. If we perceive you do not understand something we will endeavour to help you (even if we sometimes do it rather inefficiently). This is also an excellent example of how intelligent and mathematically experienced people can have difficulty understanding the Monty Hall problem or accepting the conventional answer. Ie. a good example of 'why is it so controvercial?'

Indeed, this is where the information comes from. Another interesting fact: If the host just picks the first (left-most) door he sees that has a goat, this also gives you information. If you see him open the right-most unopened door, you know the car is in the left one. If you see him open the left-most door, you have a 50/50 chance (i think? I'm very sleepy -- you can tell by my terrible code) Also, fixed my applet to reflect this, and added a x1000 and random button Edit, whoops: http://jsfiddle.net/uLzmY/3/

Here's an interactive javascript app I wrote that does it: http://jsfiddle.net/uLzmY/ Source code if it gets lost somehow, not a complete webpage as jsfiddle inserts some things for me. If you want to make it into a page but cannot, feel free to ask and I'll complete it: This goes in the body: This goes in a script tag in the head somewhere: Edit: Don't press the switch button before picking a door, that's the only bug i noticed and I'm too lazy to fix it. If clicking the buttons is too laborious, I can add a click 1000 times button on request. Xitten, when you get back, perhaps you could look at it this way: Go back to the 1 million doors example, 999,999 goats, one car. You pick a door. The host offers you something different this time. You can either stick with your door, or switch to the 999,999 remaining doors. If you switch, the host will then open 999,998 of the doors you picked, leaving one door as part of your selection, and the door you initially chose. You then open the remaining door of the 999,999 and keep a car if it is there. Is it now sensible to switch? If so (and if my previous 1 million doors example is a 50/50 chance of getting the car) what is different?

Xitten, go back to my 1 million doors example. Are you really saying that the remaining door has just as much chance of having the car? Perhaps this scenario might be easier to think about: Shuffle a deck of cards. Pick a card at random, put it in your pocket without looking at it -- This is your initial door. Go through the remaining deck and remove any cards that are not the ace of spades until you have one card left (ie. either the ace of spades if you found it, or the last card you looked at). Which card is more likely to be the ace of spades? The one in your pocket, or the remaining card? If this scenario is different, please explain the distinction.

This is unfortunate, because I still cannot tell what you are trying to say or even whether you are claiming switching is a good idea. Are you sober and in a state of good mental health? You are normally much easier to understand than this. Maybe break it down step by step and draw some diagrams?

Xitten, I cannot tell if you are joking, and if you're not, I cannot tell what you are trying to say. One thing that will make the normal conclusion of the Monty Hall problem incorrect is if the host is not forced to use his knowledge and open a goat door. Assuming he knows where the goats are, and he opens a goat door every time, do you then accept the conclusion (ie. it is the host transferring some of his knowledge to you that alters your probability estimate)? An alternative scenario that is often much more clear is the following: There are 1 million doors, with 999,999 goats and one car (assuming you want the car). You pick a door. The host knows where all the goats are. He opens 999,998 doors which all have goats (and he does this every time the game is played). Do you switch (or is switching a good idea if you want the car)? If switching does not improve your odds of getting the car. Please explain why. If switching does improve your odds of getting the car, please explain the difference between this and the 3 door version.

What is the nature of the wager? Is it a simple coin toss, or a game with more complex rules? Those two conditions aren't quite the same. Average of all bets may not match the average of every subset of 100 bets. If I picked rand(100) or even rand(1000) for my betting function and you ran it for a sufficiently long time, you could pick a subset with average less than 100.

This is one of the major problems with the Bohr model of the atom and was part of the argument that lead to the adoption of the quantum mechanical model of the atom. In the modern model, the electron is not considered to be a little ball orbiting the middle, instead it is a field that takes up the entire region and the shape, size and density of the field is determined by how much energy and angular momentum (and some other things) the field has.