Jeff, to what extent are espiri "protected" from their own magic? To be specific, the Scirus gleam allows the espiri to perform mathematical calculations. What happens when the espiri tries to: A) Calculate the ratio between a circle's diameter & circumference; B) Calculate the even-numbered root of a negative number; C) Divide by zero? For B & C, I could see the spell simply failing, but with A, or any other attempt to calculate an irrational number, could the espiri become trapped in a sort of infinite loop of calculation? Andrew ---------------------------------------------------------------- To unsubscribe, send mail to celandra-off@phoenyx.net.
Andrew Janssen wrote: > Jeff, to what extent are espiri "protected" from their own magic? To be > specific, the Scirus gleam allows the espiri to perform mathematical > calculations. What happens when the espiri tries to: > > A) Calculate the ratio between a circle's diameter & circumference; > > B) Calculate the even-numbered root of a negative number; > > C) Divide by zero? > > For B & C, I could see the spell simply failing, but with A, or any > other attempt to calculate an irrational number, could the espiri become > trapped in a sort of infinite loop of calculation? First, see the story "Sweetness and Light" (http://www.meanspc.com/~jeff_wilson63/fiction/Sweetness.html) For case A) any calculation or measurement rite requires an espiri to define how much accuracy is acceptable. If he or she fails to define that, the result is a series of numbers which the espiri's mind cannot contain. In gaming terms, this is a critical failure of the rite. Depending on the espiri's ability he may babble numbers, fall unconscious, or simply realize the mistake and accept the backlash to stop the rite in mid-progress. I suppose an espiri could attempt to control the spell past the number of digits his mind can hold and end up taking physical damage, but I can't see that happening on Celandra. For cases B) and C) you must remember that the calculation rite doesn't add mathematical ability. An espiri can only perform those calculation quickly which he could otherwise do by hand. So, in these cases, the result is more dependent on the results the espiri would get if he made the calculations by hand. Since imaginary numbers are mystically useful I'd be surprised if that idea didn't exist on Qaiyore, but I'm almost positive that the calculus to properly handle C) doesn't exist yet. Jefferson http://www.picotech.net/~jeff_wilson63/rpg/Exq_Main.html ---------------------------------------------------------------- To unsubscribe, send mail to celandra-off@phoenyx.net.
Jefferson wrote: > Andrew Janssen wrote: > > >>Jeff, to what extent are espiri "protected" from their own magic? To be >>specific, the Scirus gleam allows the espiri to perform mathematical >>calculations. What happens when the espiri tries to: >> >>A) Calculate the ratio between a circle's diameter & circumference; >> >>B) Calculate the even-numbered root of a negative number; >> >>C) Divide by zero? >> >>For B & C, I could see the spell simply failing, but with A, or any >>other attempt to calculate an irrational number, could the espiri become >>trapped in a sort of infinite loop of calculation? > > > First, see the story "Sweetness and Light" > (http://www.meanspc.com/~jeff_wilson63/fiction/Sweetness.html) > > For case A) any calculation or measurement rite requires an espiri to > define how much accuracy is acceptable. If he or she fails to define that, > the result is a series of numbers which the espiri's mind cannot contain. > In gaming terms, this is a critical failure of the rite. Depending on the > espiri's ability he may babble numbers, fall unconscious, or simply realize > the mistake and accept the backlash to stop the rite in mid-progress. I > suppose an espiri could attempt to control the spell past the number of > digits his mind can hold and end up taking physical damage, but I can't see > that happening on Celandra. Ok, so in other words, if the espiri casts "Calculate the square root of two to seven decimal places," he or she is okay, but saying "Calculate the square root of two," without limiting it, could cause some form of backlash. > For cases B) and C) you must remember that the calculation rite doesn't add > mathematical ability. An espiri can only perform those calculation quickly > which he could otherwise do by hand. So, in these cases, the result is more > dependent on the results the espiri would get if he made the calculations > by hand. Since imaginary numbers are mystically useful I'd be surprised if > that idea didn't exist on Qaiyore, but I'm almost positive that the > calculus to properly handle C) doesn't exist yet. Ok, that answers *that* set of questions. I would imagine that Mir is well on its way to developing the calculus. I had some other concerns, like how the Scirus gleam handles the fact that number theory is omega-incomplete (a fancy way of saying that you can make true statements of number theory which cannot be proven using number theory), or how it deals with Euclidean v. Non-Euclidean geometry, but that's probably too esoteric. Andrew > Jefferson > http://www.picotech.net/~jeff_wilson63/rpg/Exq_Main.html > > > ---------------------------------------------------------------- > To unsubscribe, send mail to celandra-off@phoenyx.net. > ---------------------------------------------------------------- To unsubscribe, send mail to celandra-off@phoenyx.net.
Andrew Janssen wrote: > Ok, so in other words, if the espiri casts "Calculate the square root of > two to seven decimal places," he or she is okay, but saying "Calculate > the square root of two," without limiting it, could cause some form of > backlash. Yep. Of course its one of the first things espiri are taught about that set of rites, but it's possible to get in hurry and forget. > I had some other concerns, like how the Scirus gleam handles the fact > that number theory is omega-incomplete (a fancy way of saying that you > can make true statements of number theory which cannot be proven using > number theory), or how it deals with Euclidean v. Non-Euclidean > geometry, but that's probably too esoteric. Another yep. It's not that I don't understand what's involved as that I don't understand the _implications_, and so have no idea how Feroze would handle that sort of authority. If it becomes important I'll make a decision then. Jefferson http://www.picotech.net/~jeff_wilson63/rpg/Exq_Main.html ---------------------------------------------------------------- To unsubscribe, send mail to celandra-off@phoenyx.net.
Jefferson wrote: > Andrew Janssen wrote: > > >>I had some other concerns, like how the Scirus gleam handles the fact >>that number theory is omega-incomplete (a fancy way of saying that you >>can make true statements of number theory which cannot be proven using >>number theory), or how it deals with Euclidean v. Non-Euclidean >>geometry, but that's probably too esoteric. > > > Another yep. It's not that I don't understand what's involved as that I > don't understand the _implications_, and so have no idea how Feroze would > handle that sort of authority. If it becomes important I'll make a > decision then. Well, to summarize in reverse order, the Euclidean v. Non-Euclidean geometry has to do with the parallel postulate and the shape of space. Take a line and a point not on the line, A. In Euclidean or plane geometry, there is exactly *one* line which passes through point A and does not intersect with the first line. In Non-Euclidean spherical geometry, there are *zero* lines which pass through point A and do not intersect the first line. In Non-Euclidean hyperbolic geometry there are *at least two* lines which pass through point A and do not intersect the first line. Another way to describe it is that in plane geometry, the sum of the angles of a triangle is *exactly* 180 degrees; in spherical geometry, the sum of the angles of a triangle is *greater than* 180 degrees; in hyperbolic geometry, the sum of the angles of a triangle is *less than* 180 degrees. For most purposes, Euclidean geometry is fine, but when you're working with the surveying of meridians on a planetary surface, you're getting into spherical geometry. Hyperbolic geometry is just plain weird, and is used mostly by mathematicians and theoretical physicists. As for the omega-incompleteness of number theory, it boils down to the fact that no matter how sophisticated your theory there will always exist at least one true statement which cannot be proven using the theory--it's the mathematical equivalent of saying, "This statement is false." Paradox is inescapable. However, I doubt most espiri will ever run across this barrier--at least, not in the near future. Andrew > Jefferson > http://www.picotech.net/~jeff_wilson63/rpg/Exq_Main.html > > > > ---------------------------------------------------------------- > To unsubscribe, send mail to celandra-off@phoenyx.net. > ---------------------------------------------------------------- To unsubscribe, send mail to celandra-off@phoenyx.net.
