Schrödinger's hat

If it's a consistent effect, that will be reproduced over all your measurements (or will change in a predictable (or even just biased) way over all your measurements) it's a systematic error. An example would be using a ruler which was mis-calibrated so that every milimeter on it was actually 1.01mm, and thus the whole ruler would be 1.01m rather than 1m. So if the light varied over space, and different samples were in the same spot between measurements, that would be a systematic error. A random error is one that is un-predictable, and will change each of your measurements independantly. in the ruler example, this would be the error due to not quite holding the ruler in the right place, or mis-reading it slightly. If the light was flickering or fluctuating between measurements (and not doing something like slowly getting brighter) then this would be a random error.

That's fine for individual objects, and this is where we use the term 'proper'. Ie. The proper time it takes me to go to the shops, is the time taken in a frame where I am at rest. The proper shape of earth is a (very very slightly oblate and bumpy) spheroid, not a highly oblate spheroid. The proper distance between the poles is however many thousands of km (~14000?). However, that doesn't mean the distance is always 14000. In some frames the poles might be 1km and a few seconds apart. Arguing over whose frame is right is like having two people on opposite sides of a table. They have two drinks on the table and are both arguing that the one on the left is theirs. Edit: Deleted response to Iggy written when my sarcasm detector failed.

(Note that the below uses the geometric interpretation of relativity, ie. space is four dimensional. To the best of my knowledge this is the only mainstream interpretation of the mathematics. There are others but I do not think they are relevant right now.) I think your logic is sound but you are acting on a faulty premise. Namely, that space and time are separate things. So you have two events on earth (an event is a point in four dimensions), in one frame they are at the same time, but the distance between them is 100cm. If you look at them from a different reference frame they might be 12.5cm and 1 microsecond apart. Neglecting the microsecond is where the apparent paradox comes in. This is highly counter-intuitive (like most of the universe once you get away from our nice, medium sized scale), but there are very good reasons for the adoption of this model. A two/three dimensional (Euclidean) analogue can be useful (ignore time being a dimension for now). Bear in mind this analogy won't stretch very far, but it illustrates a similar concept. Imagine you are constrained to a flat table on which you have been living your life and you can (somehow) see and interact with a circle which is floating above the table. If someone were to rotate the circle so it became (from your point of view) an ellipse, it would seem quite outrageous and counter to your normal expectations. The (2D) distance from one side to the other would be smaller in every 2D experiment you could perform. This is because you can't measure the difference in height between the two sides.

About 50 hours, a few times. Two were from insomnia, one was on purpose-ish (no-where to sleep and didn't feel like paying for a taxi). Was pretty delerious by the end of it, the weirdest thing is my memories of events (both short term at the time, and long term) were not in the correct order. I don't know if this is because I was micro-sleeping or if it was something else.

@mytechuniverse: Well, it depends on how fast you go. Realistically you're never going to get enough energy to make a noticeable difference, even if you had an anti-matter drive.

It's hugely complicated. KE isn't the only factor, I absorb more energy in a few minutes by standing in heavy wind, than would be contained in a bullet. We have pressure, time sustained, location and angle of hit, probably a whole host of things I can't even think of. The energy you can put into striking something is not completely determined by what is in the motion of the weapon. Follow through is very important, too. The line between an ineffective attack and a fatal one could be a matter of a few millimeters, or someone not expecting/knowing how to roll with the blow. You are probably better off using informed heuristics than anything you can glean from a physics textbook. Not only that, but a skilled fighter will constantly be looking for weak points, while attempting to get blows to land on his strong points. He wont just swing wildly at whatever is nearest. Go talk to your local medieval re-enactors, maybe a doctor.

Hmm? I was still only thinking of Minkowski space. The transformations are the same no matter how you represent the coordinates. I imagined it'd be rather a headache and involve a lot of affine transformations, rather than a straight matrix multiplication (possibly some trig/hyperbolic trig too). Rather like trying to do general 3D rotations and translations in cylindrical coordinates. At any rate, I've given up that idea now and gone on to other methods. Thanks anyway.

I dun no 'bout dat type 'f fing. I just do der maf an' alg'riv'ms. You talk to da Cap'n if you wan' dat. You c'd jus' upgrade browser.

Hahah, well. At least you can admit it. You are forgiven. Also, I think I'll blame you for my waning interest in GR (I'll get back to it sometime soon, I swear).

Does anyone know where I might be able to find a general boost formula like this one written in spherical coordinates (ct,r,phi,theta)? I really don't feel like expanding it all myself.

Water requires roughly 4 joules (actually 1 calorie if you want to look up more exact values) to head 1 mL 1 degree C So 200L is 800kJ/Degree You generally pay for electricity in kWh (one of the sillier units that people use, although not as bad as my pet hate kWh/year :/) so divide by 3600 gives 0.2kWh/degree

I would recommend something like python or pascal if you're just starting out. Usually the tutorials and things explain things more clearly and slowly.

Well you can use an addition table if you really want, and you don't even have to make the symbols match their binary representation. Ie. base 4 could be 0= 10, 1=11, 2=00,3=01 then you'd save a table of what the addition operation did and implement carry giving you the ability to do arithmetic. This doesn't involve binary arithmetic at all, at no point do you perform a base 2 carry. Realistically you use binary arithmetic, but you store the 'digits' of a massive number in something like a linked list or an array. let's take base 256 multiplication as an example say you had the numbers: 2 30 45 (equivalent to 138797 base 10), and; 3 200 120 (248928 base 10) First you calculate 45*120, you need 16 bits to store this gives you 24 with a carry of 21. and so on 1 23 35 14 21 2 30 45 * 3 200 120 ___________________ 254 37 24 1 167 147 40 00 +6 90 135 00 00 ___________________ 8 3 24 77 24 Edit: can't get it to align properly, should have looked up whatever tags make a table :/ Or 34411662616 base 10. This can be useful when dealing with numbers much larger than your word size. You will have to store these in some kind of structure regardless, so you take advantage of the fact that many cpus are optimized to do multiplications in one cycle. Using base 2 or base 10 in this case would be very wasteful. In this case you are using the base 2 optimized multiplication in lieu of memorizing a times table and the slower higher order operation as your actual multiplication algorithm. This could be achieved by making a 1 megabyte (256*256*16) (and thus no base 2 multiplication would be involved) hash table and looking up the value each step, but this would be no faster and you'd use up all your L1 cache. Naively using the square root of your largest int value as your radix seems like it would work best, but I think there is some reason to prefer smaller numbers (perhaps something to do with the addition step to avoid additional carries before starting to translate your answer to base 2 or 10). I think there is also a hack where you can take advantage of the way the 32 and 16 bit registers on a 32 bit x86 cpu overlap to optimize this a bit further, but I don't know much about assembly and can't recall where I saw this so I can't say for sure how it works.

Pinocchio does complicate matters, but I don't think it does so in a trivial way. If we observe his nose after he says that one of two things will be true: It is the same or smaller size; It is larger. Thus, after this observation his statement has a definite truth value which will be different to what has happened. The only resolution to this I can think of is that the outlined situation is absurd and we have disproved the existence of pinocchio. Also, this type of pinocchio would be the perfect oracle. You'd just have to break down any situation or set of situations or pieces of information down into a binary tree, and science would be solved within weeks. "Pinocchio, say 'P=NP'. Now say 'string theory is completely wrong'."

Well, the inner planets are mostly rocky because most of the gas got pushed away or escaped on its own. Depending on how big they were they cooled down and solidified at different rates. Mercury was tiny and couldn't hold on to much stuff at all, so it's mostly iron and other heavy stuff. Venus and earth were bigger, the surface constantly gets recycled by volcanism or plate tectonics, different thickness of atmosphere is the other major difference. Mars would be similar except that it was a bit smaller so it cooled down and solidified, the stuff on the surface has been there for a long time so the iron all reacted with oxygen, compare it to really old land on earth like central Australia or US. Also life on earth came and changed everything. Jupiter has lots of everything because it was one of the bigger clumps to begin with, but not big and close enough to either merge with the sun, or become a star itself. This sort of gave it a head start and allowed it to gobble up more of the available stuff faster than the other planets. Most of the stuff in the cloud was hydrogen and helium, so that's what it is composed of. (it has a fairly large core of metals as well). Saturn is similar, but it was originally smaller, so it's much less massive. It was, on the other hand, a bit further out so it got to hold on to more gas for its size. As a result it is less dense than Jupiter. It's a similar temperature and composition to Jupiter so it looks the same. Further out it's colder, so it's much easier to hold on to nitrogen/oxygen etc. so the outer planets/dwarf planets tend to be made out of ice and various other frozen compounds of hydrogen nitrogen, oxygen, hydrogen and carbon. Hydrogen and helium are pretty hard to hold on to so you get things like the dwarf planets and various moons of all the gas giants. I don't know the exact composition of Uranus/Neptune compared to Saturn/Jupiter, but I believe there is a higher proportion of oxygen/nitrogen in their atmosphere making them blue-er because of the lower temp. All in all it's a very complicated process and temperatures and sizes of planets at different times during their formation, along with what they hit and interacted with has a huge effect on composition.

I don't really understand the question. Umm, 'an orbit' is just a name for the path an object will take if it's trapped in a gravitational well and isn't on a collision course. They aren't distinct, individual things. If you accelerate for long enough you can enter a hyperbolic/parabolic trajectory which will never come back to the planet/star/whatever. Some people call these an orbit, too. Also, if you aim right you can hit a planet/other object.

I don't know what you mean by 'it's not friction', but I'll try to explain anyway. (watch the videos on centripetal acceleration, they will help a lot) Say someone is sitting in the middle of the space station or the shuttle or whatever not touching anything, why don't they hit the wall? (let's ignore Well the person and the space station were accelerated to the same speed originally by a rocket, so if there was no gravity or anything else accelerating them they could sit there just fine without bumping into anything. But gravity is accelerating them. It just so happens that there is the same force per unit mass on them as the space station. So they have the same acceleration. That means they will always be moving at the same speed as the space station. Watch the video, or find a book to read about circular motion if you want to know why moving in one direction, and accelerating at a right angle (what gravity does to something in a circular orbit -- elliptical orbits are a slightly more complicated version of the same thing) makes you go in a circle at constant speed. Or come on the chat and ask.

Umm, the current scientific theory is that the planets and the sun formed at about the same time. The idea is that there was a big cloud of dust and gas from a previous star exploding (it needs to be a supernova remnant for there to be metal in it, otherwise only a star and maybe a gas giant would be formed). The whole cloud is shrinking because of gravity and the cloud would have tiny imperfections in it, some bits are denser than others. What happens is the gravity from these dense bits pulls a tiny bit stronger than the gravity from the less dense bits, so more dust gathers there. Slowly they build up, and some of them merge together. The biggest one will eventually be a star, if there's another big one near it they tend to merge together and form one even bigger one. Eventually gravity pulls the gas together and it gets hotter and hotter, the star ignites. As this is happening the clumps close to the star can't hold on to the gas around them, the light and energy from the star, along with the heat from the condensing cloud push most of the gas away so that all that is left is the heavy stuff that sank to the middle and a thin atmosphere. Further out it's cooler and easier to hold on to light hydrogen, oxygen, nitrogen etc. so you get big gassy planets. Also if planets are big enough they can hold onto the gas better. I'm glossing over a whole lot of stuff about the role electrostatic attraction plays in the early stages, and theories on formation of hot Jupiters in other solar systems, but this is reasonably close to the current model.

One of the reasons we get things like cyclones and the reason air and water currents act the way they do is the coriolis effect. If you shoot a gun or throw a ball high enough it does come back in a different place. The best way of illustrating the physics involved in this effect is the .The reason you think that a ball or a bullet will come straight back down is that the earth is very very big, and so you can't throw a ball very high compared to its radius. With regard to your rocket experiment, I'm not quite sure how to explain orbital mechanics in a way that won't confuse the issue further. I think the best thing would be to think about for a while. A good example is Neptune's moon Triton. Another thing to understand is circular motion. (that and the next two videos). Then we can start discussing gravity.

Firstly, the flux density in orbit above earth is not much greater than at the surface (less than double iirc), the main difference is the distribution of frequencies. The harmful ionising (UV) frequencies are absorbed more than visible light and infrared. The main advantage of high altitude or orbital solar panels is that you aren't sitting in the shade of the earth for half of the day. Mile high posts and cables are at the edge of or beyond our ability to make, and even if we could they would be very expensive in energy and money. For the gain you get from doing this it is much cheaper to just make extra solar panels with the money and energy. There is no shortage of sunlight, with efficient solar panels a small fraction Australia's deserts alone could power the world (the money for such a project would be prohibitive though). Another project that has been seriously considered is putting solar collectors in orbit and beaming the energy down with microwaves. Although one or two countries could do this with very little effect, the ecological/weather impact of doing this on a global scale would have to be considered.

Check what your college allows in exams, many have restrictions on features or allowable models. Out of the models that my university allowed, I was quite enamored of the Ti-34. Puts me in mind of my second year SR exam. I'd left my bag/calculator in another building but still had time to go and get it if I ran. I asked my lecturer (who knew me quite well and had taught me before): "Do I need a calculator for this exam?" He responded: "Do you need a calculator for this exam.....hm....no." Turns out, he knew that I knew an algorithm for calculating square roots and how to calculate trig functions for arbitrary angles by hand :/

That's rather more complicated, for charging high voltage from DC you need a switched mode transformer or similar. It involves an oscillator of some kind, some transistors, some diodes, and an inductor. There will probably be an off the shelf part which will do this, or if you do a bit of browsing online/in a suitable library (your local university may have a publically accessable library) you may find schematics. Again I emphasize the importance of caution when dealing with high voltage electronics. Although a 9V battery is not dangerous on its own, it contains more than enough energy to kill you if you step up the voltage.

Well the issue is that we look at the universe, see that it's expanding and that the rate of expansion is increasing. If we think only about gravitational attraction between matter the rate would be slowing and you have one of two situations: Matter is not moving fast enough to escape, so eventually it stops and leads to a big crunch. Matter is moving at or above escape velocity and so will slow down, but approach a constant speed -- Not sure about the details of this one, if there is infinite matter in the universe then escape velocity is also infinite. At any rate a quick bit of modelling would show whether it could be the case. Armed with our prediction we looked at the universe and saw that the rate of expansion was increasing rather than decreasing. Exactly why this is the case is unknown, but it completely blew a lot of our understanding of the universe away. We have dubbed the cause of this repulsion dark energy.

I don't understand, perhaps a diagram?

Random aside: Computers sometimes use large bases for calculations. Especially those involving division or multiplication of numbers with 100s of digits. The idea is that you have to store each digit in a different place in memory in its own place in some form of data structure. As they have to be dealt with separately, and there are all sorts of optimizations and conveniences for dealing with things that are one word (frequently 64, 32, or 16 bits) long then it can be useful to use a base close to your word size. Ie. 65536 for 16 bit. It gets a bit more complicated than this and bigger isn't always better, but this outlines the basic idea.