Re: Will Vanheim Ever Become Spayed?
 

The first game I played I had huge problems with a Van AI. I eventually prevailed by liberal use of magic and summoned creatures. My progress had been impeded to the point that others eventually crushed me, but I did not feel that the Van were too tough. I simply did not understand how to handle them. Perhaps I was wrong?

Re: Will Vanheim Ever Become Spayed?
 

Look at glasses/contact lenses. We'll be able to "see" unaided... see badly, but well enough to find the glasses on the table.

Re: Will Vanheim Ever Become Spayed?
 

I was referring to the Aesop fable, speaking metaphorically...

Re: Will Vanheim Ever Become Spayed?
 

Ooh! Since this way off topic anyway--

The tortoise starts with a lead of a foot.
After a given period of time, the hare, traveling faster than the tortoise, will have made up this lead. But the turtle will have moved forwards, creating a new gap, which must be filled in a given time, after which the tortoise again has move, ad nauseum.

Re: Will Vanheim Ever Become Spayed?
 

Actually, that only works only up to a certain point. You see, you are measuring ever shorter and shorter and shorter amounts of time, and thus, won't actually cover more time of the hare's run than what is needed for the first few leaps. You aren't thinking of what happens once the hare gets to where the tortoise already is, and it will get there - that point is the first one you are ignoring with your time-trick!

Re: Will Vanheim Ever Become Spayed?
 

I'm ignoring much more. That is one of Zeno's paradoxes, ancient problems of the greeks.

The problem here is actually a misunderstanding of infinites. The series is actually convergent to 1/0, not 0. I don't really want to go over the math here, but suffice to say that my conclusion is totally wrong.

Re: Will Vanheim Ever Become Spayed?
 

I'm really interested in knowing what series is "convergent to 1/0" in the Zeno's paradox story. The way I see it, the time series is simply convergent to a finite, non-zero value, which is exactly the time where the arrow (hare) will catch up with the runner (tortoise).

Re: Will Vanheim Ever Become Spayed?
 

I'm not sure what are you trying to say here. The serie obviously converges to {lead}/({speed of hare}-{speed of tortoise}) (that's obvious because it's just the gap divided by speed of gap reduction). I'm not sure if the original mentiones that hare travels faster than tortoise, but I think it's implied. So there isn't any infinities involved here. If one wants to express it through the serie, as in fable, that's a simple geometric serie and the limit was known very long time ago, not sure if the fable predates this knowledge or not.

Re: Will Vanheim Ever Become Spayed?
 

Actually, the mathematical status of series, and infinites, and limits, was a problem until surprisingly recently. One version of the story was from Jean de La Fontaine, a 17th century French fabulist; at the same time, mathematicians knew how to take limits of sequences and series, but typically did not do this rigorously.

Re: Will Vanheim Ever Become Spayed?
 

Wasn't geometric progression considered by Euclid? Unlike most serie analysis it doesn't require rigorous definition of limits and infinities. Rather obvious multiplication by (1-p) allows to find the limit through other means, but I'm again uncertain when those techniques were developed.