Tuesday, April 19, 2005
Surrogate factoring, mapping, hyperbolas
A sci.math poster has turned to just outright lying, putting up a thread claiming that surrogate factoring has completely failed.
Such behavior is the mark of desperation, and I figure I should be so kind as to just shut down avenues for rational claims against the SFT, so that you can see that those people arguing with me are basically, well, you come up with the word.
The surrogate factoring theorem (SFT) maps factors in rationals, which some have made a big deal out of, but those of you who know your mathematics, know that a factorization into two factors is just a hyperbola.
So when I have
f_1 f_2 = M^2 (M^2 - j^2)
and graph f_1 and f_2, I get a hyperbola, where by making them rationals, I just gap it, but not in a visible way. That is, the hyperbola is not continuous, but if you graph it, it looks continuous, even with just rationals.
Now the other number is
g_1 g_2 = j^2 (M^2 - j^2)
and again, you get a hyperbola, just like before.
The SFT maps f_1 and f_2 to g_1 and g_2, so guess what?
For each f_1 and f_2, you can put a dot on your graph, and you get g_1 and g_2, so you can put a dot for them as well.
If you trace out the graphs you get two hyperbolas.
The theorem requires that you get the full hyperbolas over rationals, and the most astute of you can look at the theorem and see that actually it would work over complex numbers to map two hyperbolas together over the complex plane.
So it's not rational to claim that you only get one type of factor that matters to human beings, as the connection is between two hyperbolas.
Posters are just lying, and in looking at the lying, I've found it fascinating not only that they do it, but that they seem to be confident in their lies.
Now for some of you visualization will be key, as mapping two hyperbolas, you can ask yourselves how can one hyperbola, map to another, perfectly, yet somehow be picky?
Such behavior is the mark of desperation, and I figure I should be so kind as to just shut down avenues for rational claims against the SFT, so that you can see that those people arguing with me are basically, well, you come up with the word.
The surrogate factoring theorem (SFT) maps factors in rationals, which some have made a big deal out of, but those of you who know your mathematics, know that a factorization into two factors is just a hyperbola.
So when I have
f_1 f_2 = M^2 (M^2 - j^2)
and graph f_1 and f_2, I get a hyperbola, where by making them rationals, I just gap it, but not in a visible way. That is, the hyperbola is not continuous, but if you graph it, it looks continuous, even with just rationals.
Now the other number is
g_1 g_2 = j^2 (M^2 - j^2)
and again, you get a hyperbola, just like before.
The SFT maps f_1 and f_2 to g_1 and g_2, so guess what?
For each f_1 and f_2, you can put a dot on your graph, and you get g_1 and g_2, so you can put a dot for them as well.
If you trace out the graphs you get two hyperbolas.
The theorem requires that you get the full hyperbolas over rationals, and the most astute of you can look at the theorem and see that actually it would work over complex numbers to map two hyperbolas together over the complex plane.
So it's not rational to claim that you only get one type of factor that matters to human beings, as the connection is between two hyperbolas.
Posters are just lying, and in looking at the lying, I've found it fascinating not only that they do it, but that they seem to be confident in their lies.
Now for some of you visualization will be key, as mapping two hyperbolas, you can ask yourselves how can one hyperbola, map to another, perfectly, yet somehow be picky?
# posted by James Harris @ 19:47 
