As far as Numerology goes, I refer you to my comment above.
I checked, you're right about the squirrel, the Target Transformation for Squirrels isn't affine.
I don't get your Indian tutors. If it's without arithmantical rigour, what's the use? Sure, it might help you in your day-to-day life, but if you want day-to-day use, you can take Charms.
Yeah, that's well and good if you're dealing with a polygon, but since our generating function is of degree 5, there's a 5th-or-less-dimensional polytope corresponding to it (of which a 2-dimensional projection is our celebrated polygon). Now, the beauty of that is that !Nuxab's Theorem (yeah, we haven't covered it, but that's because it's post NEWT-level) shows that there's a set of wand movements associated with any 5-dimensional set of rational verticies of a convex hull (with the fourth and fifth dimensions being wand orientations and timings, respectively), and that for any orientation of the hull which doesn't have any two verticies whose temporal components are equal, the wand movements are magically identical.
But here's the rub: Depending on your orientation, you get different polygonal projections (in other words there's no mapping from 5-dimensional polytopes to 2-dimensional projections, only mappings from 5-dimensional polytopes and 2-dimensional hyperplanes in the 5th dimension to 2-dimensional projections). So pretty much any properties of polygons derived from the polynomial for this sequence can't be derived on the polygonal level.
So it's possible you've sussed out what's going on, but if you have, it was in part by guesswork.
Continuing with your above comment as well, since two conversations about it seems a little silly!
Squirrels are quite irritating for spellwork, aren't they?
I suppose the lines of divination and arithmancy get a bit blurry. Numerology has been helpful in examining past lives and where we might end up in the next ones, assuming we don't make significant changes until that comes to pass. Since the Western World isn't exactly interested in that sort of thing, I can understand why it's not part of Western Arithmancy-- especially with the need for a clear delineation between divination and academia.
Oh, bother! I quite forgot to consider the generating function! No wonder it didn't seem right! !Nuxab's Theorem is a bit controversial, I must say, but it really does make a difference. I never remember to use it since it hasn't been brought into our coursework. It completely changes the results when we factor in orientation and timing.
It's quite irritating that we don't cover !Nuxab's Theorem. If we're going to take Arithmancy, shouldn't we cover something as vital as that? I don't suppose you'd mind tutoring me on it, considering the questionable lessons taken from my old tutors?
It wasn't by guesswork, Terry, but I can absolutely see now that I didn't take my analysis far enough.
I checked, you're right about the squirrel, the Target Transformation for Squirrels isn't affine.
I don't get your Indian tutors. If it's without arithmantical rigour, what's the use? Sure, it might help you in your day-to-day life, but if you want day-to-day use, you can take Charms.
Yeah, that's well and good if you're dealing with a polygon, but since our generating function is of degree 5, there's a 5th-or-less-dimensional polytope corresponding to it (of which a 2-dimensional projection is our celebrated polygon). Now, the beauty of that is that !Nuxab's Theorem (yeah, we haven't covered it, but that's because it's post NEWT-level) shows that there's a set of wand movements associated with any 5-dimensional set of rational verticies of a convex hull (with the fourth and fifth dimensions being wand orientations and timings, respectively), and that for any orientation of the hull which doesn't have any two verticies whose temporal components are equal, the wand movements are magically identical.
But here's the rub: Depending on your orientation, you get different polygonal projections (in other words there's no mapping from 5-dimensional polytopes to 2-dimensional projections, only mappings from 5-dimensional polytopes and 2-dimensional hyperplanes in the 5th dimension to 2-dimensional projections). So pretty much any properties of polygons derived from the polynomial for this sequence can't be derived on the polygonal level.
So it's possible you've sussed out what's going on, but if you have, it was in part by guesswork.
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Squirrels are quite irritating for spellwork, aren't they?
I suppose the lines of divination and arithmancy get a bit blurry. Numerology has been helpful in examining past lives and where we might end up in the next ones, assuming we don't make significant changes until that comes to pass. Since the Western World isn't exactly interested in that sort of thing, I can understand why it's not part of Western Arithmancy-- especially with the need for a clear delineation between divination and academia.
Oh, bother! I quite forgot to consider the generating function! No wonder it didn't seem right! !Nuxab's Theorem is a bit controversial, I must say, but it really does make a difference. I never remember to use it since it hasn't been brought into our coursework. It completely changes the results when we factor in orientation and timing.
It's quite irritating that we don't cover !Nuxab's Theorem. If we're going to take Arithmancy, shouldn't we cover something as vital as that? I don't suppose you'd mind tutoring me on it, considering the questionable lessons taken from my old tutors?
It wasn't by guesswork, Terry, but I can absolutely see now that I didn't take my analysis far enough.
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