Mobius

There are plenty of relationships between pi and phi. First of all if you have a circle of diameter phi then the circumference is pi*phi and is known as the golden circle. Ancient Egyptian's wondered about the relationship between phi and pi, their ancient measurement the cubit was about pi/6 of a metre. they also found this was phi squared / 5. to be fair, as mentioned, any number can arbitrarily be made into another number without any special connection. The thing is pi and phi do seem to have some unusual properties. For example the Phibonacci brick (length and heigth phi units, width 1 unit). Now if this brick is placed exactly inside a sphere the radius of that sphere is 1 and the surface are is 4*pi.... Just google all this stuff to find out more....

My goodness Martin..... this proof of infinite prime numbers was done by Euclid many a moon ago.... with regards to the important of large prime numbers and their importance.... just ask a computer security expert.....

Going back to the original post. this is not quantum mechanics..... Quantum mechanics is based on probabilty... However if you think of an infinite universe or a universe that has infinite time... then if something has a non zero probability of happinning then it WILL happen (an infinite number of times). Crazy world we live in.... Many worlds inturpretation indulges in this.....

this is completly vague as you pointed out... 8 is standard for 'normal' paper, but it really depends on what type of paper it is and how you fold it....

Hmmm I prefer to measure heat in Joules. Light is measured by wavelengths and amplitudes as Kyrisch said. The wavelength is related to the frequency as wavelength * frequency = speed. Red and yellow are the low frequencies of (visible) light while blue and violet are the high frequencies of (visible) light.

weight is a force... The force we exert on the ground due to our mass and gravity. In freefall we still have mass but we are weightless as the force is causing us to accelerate.

Okay from a logical point of view. All bulbs are turned on. then every second 1 is switched off. All multiples of 2 are switched off, this means that 2 squared i.e. is off. Now it will be turned on when we come to every 4th bulb. After this these earlier numbers are left alone. now look at the 3rd bulb, this will turn every 3rd bulb off which includes 9. This one will be turned back on when we get to switch every 9th light bulb. All the numbers have a corresponding square number which will be off until it is turned on when it is time to switch that number. All the other bulbs will end up being switched off. This is not so much a mathematical proof but a logical one....

Okay, I wrote a program to map out the results (well the first 100 anyway). It seems that the only bulbs left on are the square numbers... So light bulb 1, 4, 9, 16, 25.... are on while the rest are off. As yet I have no proof...

Actually my original post is incorrect. I over simplified the sum. In the situation of 10 light bulbs only 1 and 4 are on when you are finished. I will work on this some more.

this is a good question and I don't like answers that state the impraticallity of the question when we should only consider the maths. Light bulb number 1 is obviously on, so are all the prime numbers. Lightbulb 2 is off (as you won't be coming back to it after flipping every second bulb), 3 is on, 4 is off... therefore all the odd light bulbs will be ON and all the even bulbs will be OFF.

Well, I didn't think this thread would turn into a discussion on the eath-moon orbital decay, my fault probably for mentioning it in the original post. It does seem that the question of the earth losing energy was a bit more subtle than I had originally anticipated....

Well if 4 of them have to be picked up then there are 2 left, we now group the 4 as 1, so the choices are basically, how many combinations of 3 items can you have....? More to the point how many ways can you rearrange 3 itmes?

OK, so the moon is slowing down and getting further away from the earth all the time. So back to the original question: I am really trying to find out if the world is losing energy overall??? And the questions I raised in the 4th post!

So it would seem from the global warming that we receive more energy from the sun then we re-radiate back into space. So the moon is taking energy from us due to tidal forces. Our magnetic field is losing energy. What about the using ouf our natural resources. If all the energy is converted without escaping into space then the overall energy loss is nill??? therefore nuclear energy and burning of fossil fuels should not effect the earths energy. I am really trying to find out if the world is losing energy overall. Maybe because of the 2nd law Thermodynamics, it is a must that we are losing energy... Also does the internal heat energy of the earth eventually escape the atmosphere?? I know loads of questions....

Just thought I'd get your thoughts on this. Is the earth overall losing energy. It loses energy from tides, however the earth-moon system remains at constant energy. Our magnetic field is losing energy. Are we losing energy in our rotation? We gain energy from the sun but is the loss of this heat energy more or less than our gain....? All responses welcome

Don't mean to bumb this thread but I have just read about the problem in John D. Barrow's The infinite book. The light bulb is known as Thomson's lamp. Barrow pointed out that the question is unanswerable. He replaced the 'on' and 'off' with +1 for on and -1 for off. The problem is then reduced to the infinite sum S = 1 - 1 +1 - 1.............. this sum does not converge, the answer is either 1 (odd number) or 0 (even number) but interestingly could be a 1/2 S=1 - (1 - 1 + 1 - 1............) S=1-S S=1/2 i.e. the bulb is half on!!! The point is that as this is an infinite series there is NO result. It is like asking whether the last number in the natural numbers is odd or even. The book itself is pretty good, I recommend it.....

I'm with gib65 on this thread what is everyone talking about. As far as I can see your links are talking about resolving the twin paradox in special relativity for a universe with at least 1 compact dimension. Apart from a relatively (pardon the pun) interesting read, what is your point???

No, your idea is correct... If our universe was infinite (in the sense of extent and time) then there would be another person like you typing the same thing as you are now, and another person like you typing something completely different and indeed an infinite number of 'yous' doing everything that is infinitly possible... You see if anything has a non-zero probability of occuring in an infinite universe then it will occur an infinite number of times regardless of how small a chance. It is known as "infinte replication". It is very controvercial. However if this is the case we would never observe it as it would be beyond our visible horizon of the universe.

Hmm, even in a multiverse no universe could have any effect on another so the fact that there are an infinite number of them would not make any difference. this makes no sense, "functionally infinite", either the universe is OR is not infinite. We could never reach the end of a boundless finite universe, doesn't mean it's infinite. It is still debatable over the nature of the universe.

Hmmm, haven't read Brian Greene's Fabric of the cosmos, but Greene is a string theorist so I would recommend a more conventional introduction to cosmology before moving on to the more modern theories. I did read the Elegent Universe. I have to say Brian Greene is a very good writer and makes his work in string theory accessable and exciting, but he tends to keep things vague perhaps to spare his readers from the very difficult maths behind the theories. His explanation of General relativity and quantum mechanics is very good. If you want a history of ideas about the cosmos read Dennis Danielson's The book of the cosmos If you are a bright spark, you may want to challenge yourself with a bit of maths behind the theories. This is a good book but it is fairly complex in maths and physics for people who have not been exposed to it before, but it is a good reference book all the same. Roger Penrose's Road to reality.

I recommend Martin Rees' Before the beginning Although the book (in my oppinion) lacks excitement, it is a very good read to introduce concepts (pretty much all of them) in astronomy and cosmology. I did research in cosmology in college and I know how confusing it can be to get introduced to all the theories in cosmology. This book would have been a great help. Martin Rees himself is Britian's Astronomer Royal so is well qualified to talk about space.

Actually a 1000 * 1000 is only a million years, you have to multiply it by 1000 again to get the billion. Multicellular life has only been around for about 500 million years. So there is still a fair bit of time to sort ourselves out (escaping of course other disasters). I can't see us beeing able to move our planet and it may still be difficult to move to a new planet able to sustain our life. The best bet may be to colonise space and live in space stations close to some stable star for a source of power.

Also, seeings as most of us do not get the opportunity to travel at close to light speeds relative to others (I presume no one but just making sure), it is quite straightforward to synchronise our watchs to an acuracy that suits us.

this is a strange comment. Surely you should be able to see time in a 'cause and effect' way. Evolution, chaos, Entropy are also examples of time. It is not just a human concept. Our percecption of time however is different. This is more shady. It is widely beleived that time started at the big bang, as for its ending, it may never end depending on the future of our universe. A clock is a device with continually moving parts, usually oscillating in a periodic way and is therefore able to show lengths of 'time'. What we choose to read on our clocks is the time we have defined to be the 24 hour day. however we could set our watchs to read anything. Time does not stop when people die. however that person is not able to register the passing of time. The atomic clock is a clock that uses atoms as the oscillators so it is similar to any other type of watch, it is just really acurate. Whatever time they set to it, does not really matter, what does matter is that it will remain acurate to a high degree over a long period of time. If you want to seriously consider this idea then I suggest you read Julian Barbour's 'The end of time' If you want history of how we decided to register time in say the 24 hour day etc.. Then you should read Alexander Waugh's book 'Time'

neutrinos (if they have no mass). Only massless particles can travel at the speed of light. The question over neutrinos mass is debatable, Fermi proposed it was massless but modern theories suggests it does have a very small amount of mass.