This isn't homework, but it's complicated and I'm completely stumped.
It has to do with signals. There's a system with three nodes: xj(n), x'j(n), and yk(n). xj(n) has no input and outputs to x'j(n). x'j(n) gets input from xj(n) and yk(n), and outputs to yk(n). yk(n) gets input from x'j(n) and outputs to x'j(n). A simple feedback loop.
The connection from x'j(n) to yk(n) is considered as an operator, A. That is, yk(n) = A[x'j(n)]. The connection from yk(n) back to x'j(n) is similarly considered B.
Here's the bit I don't get. From the conception above:
- yk(n) = A[x'j(n)]
- x'j(n) = xj(n) + B[yk(n)]
According to the thing I'm reading, from this it can be found that yk(n) = (A/(1-AB))[xj(n)].
Now this makes sense if A and B are considered as numbers, but they're described as "operators". What am I missing here?
[1] This facsimile operated in part by synAC.Oh, those problems are a bitch. First you have to make sure that the bases are the same number hint, and then you take the logarithm of both sides.
[1] This facsimile operated in part by synAC.So, this is kind of lame following up all that crazy calculus shit, but I have to make graphs in Excel, and the instructions are for a newer version than I have. Most things translate easily enough, but does anyone know how to get the equation shown with the graph in the 2002 version?
Nvm, found it. =) It's an option when you add a trendline.
edited 29th Aug '10 12:33:18 PM by DaeBrayk
Anyone have some good articles on "Cogito ergo sum"
? I looked up stuff on Google and all I got was high-brow stuff that I have trouble understanding.
Basically, Descartes was reacting to the general climate of philosophical skepticism that was brewing in France by attempting to find at least one thing that is absolutely certain; he went about doing this by systematically doubting everything until he found something that could not be doubted; what he eventually settled on was that his own existence: according to Descartes, there is no way for him to doubt his own existence, because that would require him to be able to think, which in tun requires that he exists (this strategy of combating doubt by claiming that the doubt itself presupposes the doubted thing is called a transcendental argument, btw) . Thus, he thinks, therefore he knows that he exists. He later went on the use some truly idiotic reasoning to prove that God and everything else exist too, but that is tangential to the Cogito Ergo Sum thing. What's ionic about the whole thing is that because of this, he's often misunderstood to have been a solipsist, when really, that's the sort of thing he was trying to discredit. Don't know any good articles about it, though. Hope that helps.
edited 31st Aug '10 8:25:16 AM by Taelor
The Philosopher-King ParadoxTzetze: Are these logical operators? (AND, OR, NOR, NAND, XOR, XNOR, etc...)
I'm not sure I can help though...
My FF.net accountNo, they're multiplication operators. Or linear operators. Or something.
[1] This facsimile operated in part by synAC.Now this makes sense if A and B are considered as numbers, but they're described as "operators". What am I missing here?
Then you can work almost as if A and B were numbers: in brief *, since
y = A(x') = A(x + B(y)) = A(x) + AB(y)
it holds that
(1 - AB)(y) = y - AB(y) = A(x)
and from this and the invertibility of 1-AB it follows that
y = (A/(1-AB))(x).
However, the notation A/(1-AB) is kind of ambiguous here, since this "product" is not commutative: the intended meaning is the inverse of (1-AB) applied to A, that is,
(A/(1-AB))(x) = (1-AB)^{-1}(A(x))
and not the other way around.
If I can handwave things a little, when you calculate AB(y) you "assume that x=0", compute the value of x' corresponding to y under this hypothesis, and then use this new value of x' to compute the new value of y - if x were 0 we would have that y = AB(y), of course; more in general, you assume that the "control dial" x is set to 0 and you go through the feedback loop once more under this hypothesis.
Hence, (1-AB)(y) can be seen as the difference between the current value of y and the one that it would result after going through the loop once more if it held that x=0.
Furthermore, A(x) can be interpreted as follows: you take the value of x (the setting of the "control dial", so to say), assume that x' = x (that is, that no feedback is coming from y to x', for example because the system has just now been turned on) and you compute the corresponding value for y.
Thus, the formula
(1-AB)y = Ax
has a rather natural meaning: the difference between the value of the output y and the one that it would take after one cycle of feedback if the dial were set to 0 is precisely the value that the output y would take if no feedback existed from y to x' .
But in general, (1-AB) is not necessarily invertible, I think, unless there is some further hypothesis of the problem...
There are ways of finding approximate inverses of a non-invertible operator if need be, of course, but I am not sure if I remember enough of them to really go into it now (also, that's not really related directly enough with the problem at hand).
Hope this helps!
edited 4th Sep '10 3:19:04 PM by Carciofus
But they seem to know where they are going, the ones who walk away from Omelas.I just figured it out, thanks to my textbook. It's the number of lists with 3 elements you can make.
The first part is where they're all different, and "n" is where they're all the same.
The second part must be where two are the same, but I have to figure out how that works.
I should really read the "suggested textbook problems" section on my syllabus.
I need help. I need to find stuff about the genre Magic Realism and how it relates to the book we've been reading, but so far every single source I've visited has either given a different definition or no definition at all. What is Magic Realism?
Magical realism is a literary genre in which supernatural things happen in our world, but are not really explained. If a story provides a framework for why supernatural things happen (even a Fridge Logicy one), then it isn't Magical Realism. If it takes place in a world where such things are normal, then it is also not Magical Realism. Or at least, that's how it was explained to me when I was in high school, like, 4-5 years ago. I may be misremembering part or all of it.
The Philosopher-King Paradox

You know, I've been considering making a follow-up thread since school is almost back in and this one seems to be getting a bit cluttered. I wouldn't want to make two of the same thread though, and this one still pops up on the front page sometimes.