View original postHello everyone. It's good to see you again. I mean, I see you often, but normally from the dark corner where I sit, not letting anyone see me.

View original postAs you may or may not be aware, I've been hard at work these last two years on novels (I have two of them on the go). They're coming together fairly well I think; the fourth draft of one of them, which is my current effort, is easily the best thing I've written to date.

View original postHowever, I've encountered a fantasy math problem. I believe I've solved it, but the answer is counter-intuitive and I would be very grateful if you would let me go over it with you. It would be wonderful if anyone could either confirm my work or point out my fatal error.

View original postThe background -- my fantasy world consists of a very large city, and by large I mean large. This one city is only a little smaller than the entire nation of France. It's somewhere between a square and a circle in shape, and the farthest edge of the city is about 800 miles from the center. In the center is a very tall clocktower. Astonishingly tall. Impossibly tall. Don't worry about the physical logistics of such a tall tower; in reality I'm well aware that it would collapse under its own weight. In the story, people believe that God created this clocktower in the days before history, and therefore it doesn't have to follow the rules of mortal building materials. There's a deeper answer, but I'm not at liberty to spoil it. Suffice it to say that this clocktower exists.

View original postDue to the nature of my world, it is possible to see the clocktower from even the farthest edge of the city, 800 miles away. Again, don't worry about that part. Within the context of the world's rules, this is possible.

View original postThe question is, how high should the tower be? Both so that it can be seen at that distance above other buildings and so that the highest clockface is clearly visible and comparable to the size of our moon? In addition, the top must be higher than airplanes can fly, because reasons.

View original postAngular diameter can be determined by the quick and dirty method of taking the actual size and dividing by the distance away, then converting the answer from radians to degrees. In this case, actual size is 10, distance away is 800. Divide to get 0.0125 radians. To convert to degrees, multiply by 57.2957795, equaling roughly 0.7 degrees. This is 40% larger than the moon, which is close enough that I can live with it.

View original postBut I'm having trouble reconciling this math with how I imagine the reality. Would something ten miles wide really appear to be bigger than the moon when viewed from 800 miles away? The math seems to say that yes, it would. Is my math correct?

View original postI'm thinking that my difficulty in imagining this comes from the fact that in reality we can only see something 800 miles away if it's in space. The curvature of the Earth hides anything 800 miles away on the surface, no matter how wide it is. But even so, it seems counter-intuitive that something 10 miles wide would still look so large from such a great distance.

View original postHelp me, Obi-wan RAFObi, you're my only hope.