Hedos

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1. I have a problem with theory of relativity

In the frame of reference of ruler A, the ruler B will be shorter. In the frame of reference of ruler B, then ruler A will be shorter. You might be interested in the ladder paradox for a conceptual application of this phenomenon. That's a very good question indeed. I am really not sure, but I would take the point of view that it is "real" (whatever that means), rather than just an illusion, because length contraction is analogous to time dilation which is clearly very "real". Moreover, the ladder paradox above suggests that length contraction IS real and not a mere illusion.
2. I have a problem with theory of relativity

Confusing stuff... But you are saying that the guy left on the planet will read 15 years on the same clock? What happens when you land your spaceship? Will the decelleration make the clocks "synchronize", otherwise guy A on planet and B on the ship will have a big problem deciding on a time to meet eachother... If you never land, but have some kind of way to communicate, would guy A and B start to argue about what time the clock is showing? Or would communication be impossible? [/quote] The observer on the planet will read 15 years on the ship's clock, when the ship arrives, yes. This is the same time that the ship-based observer read on the ship's clock. The ship-based observer reads 20 years on the planet's clock and the planet-based observer reads 20 years on the planet's clock. The two observers are in complete agreement. Whether you land the spaceship or not doesn't matter! Nothing would change at all. There is no synchronization involved and there is no contradiction either. Time has indeed been shorter for the observer travelling on a spaceship, there is asymmetry in this situation (because the spaceship undergoes changes of velocity but the planet does not). Keep in mind that when the spaceship has just been launched from Earth, then the reference frame of the Earth and the reference frame of the spaceship disagree about when the clock on the destination planet was started relative to when the ship-based clock was started. But that's because the ship-based clock and the destination planet's clock are physically separated. When the ship arrives at its destination, then because the two clocks are at the same location, it doesn't matter at all which frame of reference you choose, they will all be in agreement about the two clocks.
3. I have a problem with theory of relativity

How on earth is this synchronisation achieved (no pun intended)? [/quote] If you know the distance between the planets, you can easily achieve that (in theory). Suppose the distance is 1 light-year. Send a beam of light from planet A to planet B and wait 1 year. After exactly 1 year, immediately start the clock on the spaceship and launch the spaceship (assuming the spaceship can be given a high acceleration burst such that the desired velocity is almost instantaneously achieved). On planet B, start the clock exactly when the light beam is received from planet A. This only synchronizes the watches in the reference frame of the planets, however.
4. I have a problem with theory of relativity

Okay, I think I understand your confusion. For simplicity, let's assume that the ship is going at speed 0.661c relative to the two planets, hence the time and space dilation factor is gamma = 3/4. From the reference frame of the two planets, the ship is moving, hence the ship's clock is ticking slower. With a speed of 0.661c the clock on the ship will show approximately 15 years when it arrives at the destination planet due to time dilation. As others have pointed out, an observer on the planet will read the ship's clock as indicating 15 years too and an observer on the ship will also read the clock on the ship as indicating 15 years. Now, from the reference frame of the ship, however, it is the destination planet that is moving. Hence, the clock on the planet is ticking slower. So at a speed of 0.661c, it is correct to say that the clock on the planet will only have ticked for 15 years throughout the journey and in the reference frame of the spaceship. I think your mistake is to assume that the clock on the planet will read 15 years from the observer on the spaceship. That is wrong, the clock will read 20 years from the observer on the spaceship, as others have pointed out. The problem lies with the notion of simultaneity of events. In relativity, there is no such thing as absolute simultaneity of events. So you cannot say without ambiguity that the two clocks were started at the same time. You need to specify in which frame of reference the clocks are being synchronized. So if the clocks were started at the same time in the reference frame of the planets, then in the reference frame of a spaceship that has just been launched from Earth, the two clocks were not started at the same time, in fact the clock on the destination planet was started earlier. This explains why the clock on the destination planet reads 20 years from the ship-based observer, even though he knows the clock must have only been ticking for 15 years since the ship left Earth. It's because from the ship's reference frame, the two clocks were not started at the same time and the clock on the destination planet has been started 5 years before the ship's clock was started. This part can be calculated using a Lorentz transformation to compare the space-time coordinates of an event in different inertial reference frames.
5. Game programming vs Girls

Just a tip but why don't you ask her out instead? It's a lot less awkward and it achieves essentially the same goal. Moreover, you can make the date as casual as you like which puts a lot less pressure on both of you than telling her about your feelings before you even went on a first date! And think about it from her perspective, if you confess your "love" out of the blues, what is she supposed to respond? Anyway, my advice is to try and go out with this girl as soon as possible so that you can gauge if there is any mutual attraction. So, just ask her out! It's really not worth your time obsessing about a girl if it's not meant to be anyway.
6. Steve Jobs

This is a huge loss of a truly brilliant man. RIP steve.
7. Mini-Contest: ASCII Fishtank

Good job everyone! I enjoyed playing with everybody's fish tanks! Thanks to capn_midnight for organizing this contest, it was fun!

10. simple ebay question

I don't think eBay has the capabilities to mix an AND and an OR in a single search, you can only do either. What I recommend is that you do three distinct searches with the option "All words, any order" for: blue cat, brown cat and finally green cat. Then just combine the results together.
11. How long would a zombie apocalypse last?

You might be interested in the following (actually serious) articles written by a mathematics professor modeling zombies population using differential equations based on assumptions made from popular zombie movies: When zombies attack!: Mathematical modelling of an outbreak of zombie infection.
12. Mini-Contest: ASCII Fishtank

Alright, here it is: Hedos' Fishtank Hint: The game can become quite a bit of a huge mess if you drop too much food One fun way to play this game in fact is to not do anything at all and just watch the fishtank evolve given the initial setup. There should cycles where the population of fish alternate between going almost extinct and then growing very large. It's interesting to see how long your fish can survive without any intervention. If you do that however, make sure to toggle on the fast mode. Anyway, the fact that the fishtank behaves as some kind of an ecosystem with population cycles is what I'm most proud of! I really regret not adding the remaining features I had in mind. I wanted somehow to be able to export or visualize statistics (number of fish, quantity of plankton, etc.) so that one can see clearly the alternating cycles that the ecosystem goes through (inspired from the prey-predator cycles, where both populations oscillate but the predator population always lags the prey population). Also, I really wanted to add algae! I couldn't figure a proper way to have the algae grow or interact with the fish though.
13. Mini-Contest: ASCII Fishtank

Unfortunately I wasn't able to work on my fishtank in the last few days and hence missed the deadline. The game is far from finished, but I'd like to submit it anyway so that people can have a look. I have however to make a few very quick final adjustments to the game (otherwise it won't be playable) and then I'll submit it in the next hour or so. I totally understand if that means I'm out of the contest, that's okay.
14. My reasoning is more than yours

For Question 1, I thought of cutting a giraffe into pieces at first, but then I realized that the better idea is just to find a large enough refrigerator and put the giraffe in. My answer for question 2 was the same, which I stand is correct, because the question asks "How do you put an elephant into a refrigerator?". The assumption that you have to put the elephant in the same refrigerator as the giraffe is just arbitrary and plain wrong! I got question 3 right, I thought this was pretty obvious given the provided answers to the two previous questions... For question 4 though, I have to admit I completely missed the point, but my idea was if there is a bridge, just cross it, and otherwise ask the locals how they do it. Edit: Yes I do realize the quiz is silly
15. Mini-Contest: ASCII Fishtank

I'm going to enter this contest. I have some free time this month, plus this looks like fun I strongly suggest anybody that's willing to participate to have a look at Benryves' Windows Console tutorial to learn how to setup a 80x25 or 80x50 console window without a scrollbar, with no flickering and with user input. So far I have bubbles and one type of fish that only moves in a straight line