Mr Skeptic

Good point I should be a little more observant. The fact that he thinks he knows how to deal with "hot things" probably is even worse. 4500 degrees F and melting through metal is probably hotter than most things he has dealt with. Seanattikus, may I recommend you read some of the dangers of thermite before using it?

I will give an example to clarify my idea. Suppose that there were 1,000,000 light years between galaxy A and galaxy B, which are stationary with respect to each other except for the expanding universe. Then at a (much) later time, you measure the distance again, and find that the distance is now 2,000,000 light years. You can conclude that they are twice as far apart, or that a light year is half what it used to be. What I am suggesting is that we examine the second possibility, that the speed of light (and therefore all distances as measured by light) is changing, rather than that the distance itself is changing. I think that either changing distance or changing constants would be equivalent and indistinguishable. But I'm pretty sure that other constants would also have to change if the speed of light were changing, and I'd like to know which and how many.

As I was saying, the original problem in post #1 made no reference to the radius of the cylinder, nor put any restrictions on how the hole related to the sphere other than that it passed through the center. In particular, it never said the cylinder was centered where the sphere was centered, nor that the endcaps of the sphere would get discarded, nor that the radius had to be such that the circles of the cylinder are on the surface of the sphere. True, I could have guessed all this, but I prefer not to solve a problem if I'm not sure it is the right one. Despite what John Cuthber says, in my example the cylinder is 6 inches deep (not zero), and 6 inches wide, so that the entire sphere would be contained in the cylinder. If that seems wrong to you, imagine a sphere infinitesimally larger than 6 in diameter, so that there would be an arbitrarily small ring and endcaps left. If there wasn't a restriction on the radius of the cylinder, the answer would be arbitrary. Of course, it is much clearer now that ishmael explained in post 14. Then, for a sphere of radius R, the radius r of the cylinder will be [math]3^2 + r^2 = R^2[/math] (where 3 inches is half the height of the cylinder) Actually, that is the same as MrMongoose said. At first I thought his was for a specific sphere, but he has the general solution, so I won't redo it.

Well, most people at least expect the singularity inside the black hole to be eliminated.

Well, here is an idea that I just had. Suppose that instead of the universe expanding, some of the constants of physics were changing. Ie, I think it is possible to change the constants of physics rather than the distance between galaxies. Depending on how many constants have to be fiddled to fit in, it might be an interesting idea or an ugly one. It should be more or less equivalent to the expansion, just an alternate explanation. For example, if the speed of light were decreasing, it would mean that distances (at least as measured by light) would be increasing. It would also mean some things have less energy, and might account for red shift. I'm not sure if any other constants would have to change in order to not violate known observations. Can anyone tell me what else would have to change? And yes, I do realize this is a completely ad hoc hypothesis, but it might be interesting.

I drink a lot of water too, cause I feel thirsty. I also sweat a lot, but I'm not sure whether it's because I drink a lot or the reason that I drink a lot.

Well, you can use it as meat tenderizer, but that is probably not what you wanted to know. Perhaps it also serves to break down some of the poisons that are made of protein?

DrDNA, while I agree that most of what calls itself nanotech is just there for the free money, I do think at least some good will come of simply making things smaller. In the end, there will have to be completely different methods to do things, but we need something to start from. My own view of this is that we could consider proteins to be nanotech, and start from there. The advantages are that we already have self-replicating, hardy cells that could be used, as well as a rather easy method for constructing them (just put the proper DNA in the proper place, and it will make your protein for you). It's a tried and tested system, and it works very well already.

I agree with what Severian said, and that was exactly the reason why I voted yes. However, an infinite universe has all sorts of uncomfortable theological and philosophical implications. Basically, it has all the attributes that the "parallel worlds" interpretation of QM has, but in a single world. For example, if it were at all possible for life to evolve, it would have done so infinitely many times, and infinitely many times in every possible way. And if it were at all possible for a more or less omnipotent/omniscient entity that is interested in your sex life to form/evolve/whatever, it would also have done so infinitely many times. Likewise, there would be a world much like our own, where you are a president, criminal, or cyborg, etc, etc. Quite disturbing to think about, so I too would much rather the universe be finite. At the very least, our own portion of the universe is completely cut off from the rest of the (potentially infinite) universe, so we probably wouldn't see the more improbable of the possibilities mentioned above. However, if our universe is cut off from the rest of the universe, would we not say that the universe (as defined by everything we can see, ie everything that could affect us) is finite, but a part of a larger metaverse that is infinite. Then the difference from the "many worlds" QM is that our universe intersects with many more universes which intersect with many more universes, etc.

You don't need to do electrolysis to get rust. Just scrape some off the bottom of my car... or grind some iron nails to a powder, or put some steel wool in a jar of water. The non-oxidized aluminum will be harder, as it will oxidize on contact with air.

Careful though. If we are talking about the differences between humans, only the genetic differences between them count for the "nature" portion. To put it another way, it is the question, "What is the probability that this human have attribute A given that his genetic composition is B?" If it is more than 50%, then we have a positive correlation, and if it is less than 50% then we have a negative correlation. The question is similar for the "nurture" portion, but much harder to study. With genes, you can look at identical twins, but no one has an identical upbringing. I think that if you look at identical twins you will also find that there are many things that cannot be explained by genetics.

Wouldn't this mean that smaller black holes have more gravity than larger ones? As I understand it, the smaller ones give off more Hawking radiation than the larger ones. What about quantum tunneling? I'm unfamiliar with it, but I understand it allows for particles to occasionally cross an impossible barrier.

That's a really clever question. I think the answer is that you are mixing GR gravity with quantum gravity. So far, we haven't figured out how to get these two to play nice.

The reason I gave my example is because it is a valid solution, and shows that whoever said the problem gave the same answer for every sphere is wrong. Unless there is a restriction or relation between the size of the sphere and the radius of the cylinder, than I can choose any I please. Was there a picture that further restricted the problem? Perhaps you can tell me what part of the problem forbids my solution?

Cute idea. To be a hypothesis, it has to make predictions. So, does this make any predictions? The best predictions are ones that have not been tested yet, but I'd be happy with just predictions that are logically derived from your theory (according to my definition of logic).

This is one of the types of problems we get from the federal and state government having too much say in local things. Without such interference, the problem would solve itself.

Lucky you

That's doubtful. We know neither the size of the sphere, nor the radius of the cylinder. Are you sure you're not forgetting something? Example: drill a 6 inch hole with radius 6 inches through the center of a six inch diameter sphere. Zero volume is left.

Pangloss, keep in mind that there is a somewhat negative effect for money leaving the country (it is the same effect as importing stuff), whereas if money stays in the country it will eventually find its way into the average American's pocket, no matter how badly it was spent. (Not that I disagree with your point, just saying there actually are some good effects of wasting money in your own country)

But how would the antimatter get separated from the matter?

That seems about right, so long as the late developers don't end up taking over and so leaving the whole colony defenseless. I'd agree that it would work somewhat at the group level, but I'd suggest that the warriors would go to extra trouble to protect their own family. If there were social expectations, this could complicate things too.

I don't think it is possible to have the finest and insanely advanced technology that civilization has to offer, yet have the chief engineer routinely double the efficiency of this or that in the space of a few hours, as needed.

You have two times, and one distance, and you know the acceleration is constant. To figure out the acceleration, you will want to know how fast the train was going when the person entered the tunnel. That's all I will say for now.

Only electric cars that use capacitors instead of batteries and get their electricity from non-chemicals sources are not chemically powered.

We need to change our voting system so that it doesn't by near-necessity result in two major parties. Or we could go the hard way, and educate people so that they actually care and can work around the problems caused by "first past the post" voting.