What kind of analysis is that? That's nigh on divinational. Are you just summing the digits or something? There's a reason the numbers aren't just 4,5,6,6,7,8.
If you had bothered, you would realize that they're a part of a quintic integer-representing polynomial. (Specifically f(x) = -0.225*x^5 + 4.25*x^4 + -29.375*x^3 + 91.75*x^2 + -122.4*x^1 + 60.0 ) Unfortunately, it's not an integer polynomial, and has no integer roots, and it's odd-ordered, so the clearest significance is going to be the other values it spits out. For instance, predictivitatively, the intercept (60) gives whatever is going on a strong valuing/caring/family/relationship component, as well as indicating that it has a lot of factors (1,2,3,4,5 and 6 (that's 6 factors, making a triple significance of 6. Add to that the fact that f(6)=42->{4+2=6} and it's clear that 6 is critical here) (the ultradecafactors, 12, 15 and 30 all summarily reduce to the first six as well, which means that the order of the summary reduction of the factors = the order of the infradecafactors = 7, and we all know what that means)). Also, I think you can probably either turn squirrels into ale and/or ale into thrash metal by enclosing the target in a structure arithmantically equivalent to the polygon equivalent to that polynomial. Possibly stop time, as well.
On the other hand, I'm not convinced that the numbers aren't just an encoding of some number with non-arithmantical significance.
Professor, do the numbers 46, -52 and -426 mean anything to you? How about 60? Or 308? 982? 2,445? 5,216? 46,732? -18,200,388? -125,901,984? Obviously, the most important ones are 60, 46 and -123,901,984.
Really, Terry, you are overcomplicating the sequence and misunderstanding what I do. First of all, summing is not a terrible method of determining initial properties, even if it isn't the most precise or gets into the greatest grain of detail, although I will agree that it's quite too related to divination to give us the complete picture-- but please don't forget that it's still elementary arithmancy. Or do you forget that Numerology is including in our textbooks? For one, when you're addressing someone who may not understand more complex arithmancy, it's gentler to start from the basics. Also, just because we can perform more complicated analyses doesn't mean leaping to them first thing.
And if you did enclose the target in a structure arithmantically equivalent to the polygon equivalent to that polynomial, you had better rebalance the equation to account for the fact that the slightest presence of a squirrel skews the results by at least a factor of 42. They wreck havoc on the proper order of operations, for one, and even if there was an integer pattern to these numbers (which there isn't) the squirrels would break it. And yes we all know what that means but Wenlock clearly established that seven squirrels would just be asking for a curse on the numbers.
Now, let's look again: 4, 8, 15, 16, 23, 42
Are you overlooking the fact that the sequence itself, before any higher arithmantical analysis, has two 1s, two 2s, and two 4s, and a number that is the square of the first-- 42 = 16, or the two 4s multiplied? You always like to go straight into the more complex calculations without first ruling out the simplest-- let's work with exponential operations and number of digits first. 11 * 22 * 42 = 64 reduced to 10 reduced to 1, which brings us back to the two 1s which further suggests starting with this analysis (not to mention that 11 * 22 * 44 = 1024 reduces to 7 which means we can use you-know-what) and yes I know you'll be irritated at that summing, but you must note that (42 * 82 * 152 * 162 * 232 * 422) / 6 = 9173296742400 which, reduced, is 54, which reduces to 9. The numbers summed equal 9, compute to 9, and 92 also reduces to 9.
Now, I'm sorry to be so irritable about this, Terry, but I don't appreciate you accusing me of practically relying on divination. That is what my sister does.
In this case, more like saying that despite your excellent fashion sense, you chose to buy off the rack because it was quicker and easier than going to a boutique and getting personally tailored clothing.
No, I'm upset and frustrated because your sister is doing bad arithmancy. How would you feel if someone made something up, gave it a half-arsed justification and called it divination to impress those who don't understand the deeper truth underlying the enterprise or for a quick buck? Oh wait, it's divination, never mind; I guess that question doesn't really make sense.
Terry, if I didn't perfectly understand the arithmantical operations you used, how could I say that there's a simpler way? Yes, I could just reject something I found too complex-- but I don't find it too complex. I am saying that there are other methods to attempt that still derive useful answers, even if they don't reach your preferred level of precision. Perhaps I failed to explain properly, but I did not make something up or give a "half-arsed justification" and you can take that to Professor Vector.
You wanted me to back up what I said. I laid out the process that I'd used. It's simpler to present these things as simple things, because people with less experience would be overwhelmed by describing the full process rather than just laying down the answer and the more general sense of it.
Of course it's going to seem vague and general when I just looked at the set itself. I didn't know the date the sequence was created, when it was used, when the bad things started. It certainly helps the analysis to have that context, because it can point out things we've missed.
I'm not saying my answer is the perfect answer, but it is still a valid, useful answer.
I've got a paper by Eodore K. Leedis, called 'The Magic of Arithmancy and the Arithmancy of Numerology' you should look at. Borrowing the terms from muggles, Leedis's thesis is that fundamentally, numerology is not mathematical, nor scientific, but it is, rather, hermeneutical. And, as a hermeneutic practise, its fundamental flaw is that, for any interpretation, there are other, equally valid interpretations that conflict with that interpretation. Ergo, the validity of an answer does not entail its soundness.
Look, consider a digit sum reduction of those numbers in octimal. 4 + 1+0 + 1+7 + 2+0 + 2+7 + 5+2 = 37 -{3+7 = 12 -{1+2 = 3}}. The octimal digit sum reduction of the squares = (2+0 + 1+0+0 + 3+4+1 + 4+0+0 + 3+3+4+4 + 1+0+2+1) = 33, which is a special case of 3, numerologically speaking. So why not 3? I bet I can find a number of other connections to 3 as well.
The basic difference between your position and mine is that I'm trying to plot out properties of the series of numbers, should they, qua numbers, have magical signficance, while you are engaging in speculation. Speculation with a justification, but speculation, nonetheless. And even if you don't buy Leetist's philosophical argument, consider this: You're not going to be able to brew a potion, chalk a magical barrier and construct a spellgorithm with your conclusions and come up with rigorously predictable outcomes, and that's telling.
Numerology is in our textbooks because we start arithmancy as young children, and we don't know better. Numerology, without the proper rigorous context, is the albatross of the Arithmantical profession. You don't see Professor Flitwick teaching us Shamanic Rain Dances to the anamistic spirits, do you? No, because there's a better way of doing it, and one that depends less on the accidental casting of a magic spell. Numerology is a tool of charlatans and divinators, and dispensing its bromides to the uneducated (among whom I would be hesitant to include Professor Snape) makes you no better than an astrologer or divinator. Especially when you take a number, look up the vague and broad meaning of it, and then try to turn that into a predicitive tool.
Look, you can compute the equation yourself, there's no integer values for x where f(x) isn't an integer. If you want to pretend that the inherent arithmantical sequence of those numbers isn't important, that's fine with me, but don't tell me that my arithmancy itself is wrong.
Oh, right, the Squirrel Theorem. Okay, well, then I'm not so sure about the squirrel part, it was a parenthetical conjecture anyway. It's still possible that the squirrel is properly isolated within the structure, of course, but I'm not going to bet anything on the results of putting a squirrel in such a polyhedron.
Creative summing of digits is still summing of digits. You and I both know Zerpinksi's Theorem, showing the relative arbitrariness of base ten digits, why do you cling to them as if they had basic arithmantical importance? The true form of the numbers in their relations to other numbers and to objects with an inherent arithmantical correspondence to those numbers, not to a form of representation. Sums of digits are a tradesman's tool, not an arithmatician's tool. The same goes for counting occurances of digits.
And you don't believe I'm exercising it in the proper rigorous context? I will admit that it's possible Parvati has been a negative influence and I'm more fond of Numerology than I ought to be, but I still think it's a valid tool when used correctly. It's unfortunately abused by charlatans and divinators, but that doesn't mean it is only used by them.
I'm not pretending that it's not important, Terry, and you are correct about the equation. I'm not saying your arithmancy is wrong, either-- your point about the integers does hold up now that I've computed it. I'm saying it's wrong of you to discount my reading just because you'd done a more complicated one. Although I still hold that it's wrong to not factor in the squirrel; otherwise, I don't have a problem with it.
Perhaps there's a difference in Indian and English arithmancy, as well. My tutors may have emphasized different aspects. We don't ignore the tradesman just because there's other (better) ways to do it. There is something of value even in the more generic readings, even though they can't be relied on.
Let me give me a much more predictive reading, then. You will find my work posted near the Ravenclaw Sandwich Bar, as you'll find it's too long to reproduce here, not to mention I'm not sure how I'd include the graphs on technology like this.
To summarise:
If you graph the polygon of these numbers and read it according to Nasutus's Theory of Wand Gestures (we really ought to cover that more thoroughly,) you will find that this wand movement is used for only two applications, both of which are significant to us: 1. The cursing of sets as they occur in a person's life, e.g. any of a sequence such as those in Professor Snape's life; 2. The summoning and formation of a horror that I only need two words to describe: Squirrel. Army. i.e. "completion, the end of things" should such ever be unleashed.
And as for the prediction, and I'm sorry to tell Professor Snape of this, but as a result of the circumstances given in number 1: On the seventh hour of the seventh day of the seventh month of his seventy-seventh year, Severus Snape will be set upon, slashed, and shredded by seventy-seven thousand seven hundred and seventy-seven squirrels summoned by the spouse of septuagenarian.
As he said: The numbers are bad. The numbers are cursed. But only for him.
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.
If you had bothered, you would realize that they're a part of a quintic integer-representing polynomial. (Specifically f(x) = -0.225*x^5 + 4.25*x^4 + -29.375*x^3 + 91.75*x^2 + -122.4*x^1 + 60.0 ) Unfortunately, it's not an integer polynomial, and has no integer roots, and it's odd-ordered, so the clearest significance is going to be the other values it spits out. For instance, predictivitatively, the intercept (60) gives whatever is going on a strong valuing/caring/family/relationship component, as well as indicating that it has a lot of factors (1,2,3,4,5 and 6 (that's 6 factors, making a triple significance of 6. Add to that the fact that f(6)=42->{4+2=6} and it's clear that 6 is critical here) (the ultradecafactors, 12, 15 and 30 all summarily reduce to the first six as well, which means that the order of the summary reduction of the factors = the order of the infradecafactors = 7, and we all know what that means)). Also, I think you can probably either turn squirrels into ale and/or ale into thrash metal by enclosing the target in a structure arithmantically equivalent to the polygon equivalent to that polynomial. Possibly stop time, as well.
On the other hand, I'm not convinced that the numbers aren't just an encoding of some number with non-arithmantical significance.
Professor, do the numbers 46, -52 and -426 mean anything to you? How about 60? Or 308? 982? 2,445? 5,216? 46,732? -18,200,388? -125,901,984? Obviously, the most important ones are 60, 46 and -123,901,984.
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And if you did enclose the target in a structure arithmantically equivalent to the polygon equivalent to that polynomial, you had better rebalance the equation to account for the fact that the slightest presence of a squirrel skews the results by at least a factor of 42. They wreck havoc on the proper order of operations, for one, and even if there was an integer pattern to these numbers (which there isn't) the squirrels would break it. And yes we all know what that means but Wenlock clearly established that seven squirrels would just be asking for a curse on the numbers.
Now, let's look again: 4, 8, 15, 16, 23, 42
Are you overlooking the fact that the sequence itself, before any higher arithmantical analysis, has two 1s, two 2s, and two 4s, and a number that is the square of the first-- 42 = 16, or the two 4s multiplied? You always like to go straight into the more complex calculations without first ruling out the simplest-- let's work with exponential operations and number of digits first. 11 * 22 * 42 = 64 reduced to 10 reduced to 1, which brings us back to the two 1s which further suggests starting with this analysis (not to mention that 11 * 22 * 44 = 1024 reduces to 7 which means we can use you-know-what) and yes I know you'll be irritated at that summing, but you must note that (42 * 82 * 152 * 162 * 232 * 422) / 6 = 9173296742400 which, reduced, is 54, which reduces to 9. The numbers summed equal 9, compute to 9, and 92 also reduces to 9.
Now, I'm sorry to be so irritable about this, Terry, but I don't appreciate you accusing me of practically relying on divination. That is what my sister does.
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Which you aren't, but that doesn't bother you, and I accept our differences.
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What a bastard.
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You wanted me to back up what I said. I laid out the process that I'd used. It's simpler to present these things as simple things, because people with less experience would be overwhelmed by describing the full process rather than just laying down the answer and the more general sense of it.
Of course it's going to seem vague and general when I just looked at the set itself. I didn't know the date the sequence was created, when it was used, when the bad things started. It certainly helps the analysis to have that context, because it can point out things we've missed.
I'm not saying my answer is the perfect answer, but it is still a valid, useful answer.
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Look, consider a digit sum reduction of those numbers in octimal. 4 + 1+0 + 1+7 + 2+0 + 2+7 + 5+2 = 37 -{3+7 = 12 -{1+2 = 3}}. The octimal digit sum reduction of the squares = (2+0 + 1+0+0 + 3+4+1 + 4+0+0 + 3+3+4+4 + 1+0+2+1) = 33, which is a special case of 3, numerologically speaking. So why not 3? I bet I can find a number of other connections to 3 as well.
The basic difference between your position and mine is that I'm trying to plot out properties of the series of numbers, should they, qua numbers, have magical signficance, while you are engaging in speculation. Speculation with a justification, but speculation, nonetheless. And even if you don't buy Leetist's philosophical argument, consider this: You're not going to be able to brew a potion, chalk a magical barrier and construct a spellgorithm with your conclusions and come up with rigorously predictable outcomes, and that's telling.
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Look, you can compute the equation yourself, there's no integer values for x where f(x) isn't an integer. If you want to pretend that the inherent arithmantical sequence of those numbers isn't important, that's fine with me, but don't tell me that my arithmancy itself is wrong.
Oh, right, the Squirrel Theorem. Okay, well, then I'm not so sure about the squirrel part, it was a parenthetical conjecture anyway. It's still possible that the squirrel is properly isolated within the structure, of course, but I'm not going to bet anything on the results of putting a squirrel in such a polyhedron.
Creative summing of digits is still summing of digits. You and I both know Zerpinksi's Theorem, showing the relative arbitrariness of base ten digits, why do you cling to them as if they had basic arithmantical importance? The true form of the numbers in their relations to other numbers and to objects with an inherent arithmantical correspondence to those numbers, not to a form of representation. Sums of digits are a tradesman's tool, not an arithmatician's tool. The same goes for counting occurances of digits.
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I'm not pretending that it's not important, Terry, and you are correct about the equation. I'm not saying your arithmancy is wrong, either-- your point about the integers does hold up now that I've computed it. I'm saying it's wrong of you to discount my reading just because you'd done a more complicated one. Although I still hold that it's wrong to not factor in the squirrel; otherwise, I don't have a problem with it.
Perhaps there's a difference in Indian and English arithmancy, as well. My tutors may have emphasized different aspects. We don't ignore the tradesman just because there's other (better) ways to do it. There is something of value even in the more generic readings, even though they can't be relied on.
Let me give me a much more predictive reading, then. You will find my work posted near the Ravenclaw Sandwich Bar, as you'll find it's too long to reproduce here, not to mention I'm not sure how I'd include the graphs on technology like this.
To summarise:
If you graph the polygon of these numbers and read it according to Nasutus's Theory of Wand Gestures (we really ought to cover that more thoroughly,) you will find that this wand movement is used for only two applications, both of which are significant to us:
1. The cursing of sets as they occur in a person's life, e.g. any of a sequence such as those in Professor Snape's life;
2. The summoning and formation of a horror that I only need two words to describe: Squirrel. Army. i.e. "completion, the end of things" should such ever be unleashed.
And as for the prediction, and I'm sorry to tell Professor Snape of this, but as a result of the circumstances given in number 1:
On the seventh hour of the seventh day of the seventh month of his seventy-seventh year, Severus Snape will be set upon, slashed, and shredded by seventy-seven thousand seven hundred and seventy-seven squirrels summoned by the spouse of septuagenarian.
As he said: The numbers are bad. The numbers are cursed. But only for him.
They better only be for him.
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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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