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imatfaal

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1. A question about black holes

3-26, I think Hawking originally said that the information was retained in new black holes in baby universes - but has retreated from that position and now believes that the information is retained within this universe. Susskind, I think, was responsible for the string theory development that AJB referred to.
2. Why I Believe Einstien's Equation for Gravity is Wrong

Boboe - not sure about why you would call your first idea Density, it seems to be a measure of occupancy, and a slightly strange one at that. Personally I would say the rug occupies area_rug/area_floor and not any form of the square root. I think you also need to engage with lorenz boosts rather than just time dilation. Both x and t are transformed by lorenz boosts in a very similar way (x' = (x-vt)gamma and t'=(t-vx)gamma - but they are not the same. The second formula you give is not an equation - as you give it, but does seem to be the factor for calculating proper time through g
3. A question about black holes

This question has taxed the greatest minds - Stephen Hawking and Kip Thorne had a long running and public bet with John Preskil on whether information was lost or maintained (hawking said lost, preskill maintained.) Hawking has paid up and he now believes that the information is retained within the universe. I don't believe the solution has been found yet; although a group claimed to have done so a few years back.
4. Resistance of a hollow sphere

Further to cypress; could I suggest a thought about units of resistivity and how they come to be what they are.
5. Helpful Maths Trick

Could you run that method past me - I only know Euler Matrices as the result of a three dimensional rotation. I hope there is some other Euler Matrix - cos long multiplication is easier for two digit numbers than messing around with Euler Angles/matrices
6. Double-slit Experiment Questions

is this a dastardly combination of heresy and hearsay? Michel and RMW - if you have access to JSTOR then you can find thomas youngs original write up here http://www.jstor.org/pss/107135 . the later experiments showing destruction of the interference when pathway is known are easier to find. And whilst we must be careful to avoid anecdotalism and defending the paradigm merely for its own sake; we must also acknowledge that science is enabled by "standing on the shoulders of giants". QM is remarkably well evidenced, and rigorous.
7. Angular relationships between Two Tangent Spheres

Hello Wick, not sure which angles you mean. The angle of the two surfaces where they touch is by definition zero. I understand the setup (I think) just not sure of the question
8. How long would you live for in space (with no gravity)?

I had always assumed that the extended life in science fiction was merely that the author presumed that by the point in history that we become space-faring we will be better at preventing and curing disease and possibly have some form of gene therapy to combat natural ageing in our genes (telomere extensions or some such) whilst avoiding cancer. Everything I have heard about life in zero gravity tallies with above posts that it is not particularly good for you.
9. counting triangles

I think this problem is the same as arranging the points in a nice symmetric pattern; ie around the edge of circle - and it is much easier to visualize the relations If you imagine numbering each point 1,2,..n around the circle then a triangle of a single colour is formed when you complete an entire circuit in three legs (ie from point 1 to point 4, point 7 and back to point 1 again). Alternatively you can see this triangle as a journey around in which the total steps add up to n. Example for seven points 1 to 2 to 4 to 1 is three legs making a triangle and the steps (1+2+4 = 7) add
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