Please read the below carefully because it's very difficult
for me to participate in a conversation when my intercolluctor
ingores half of what I write and tends to distort the other
half. Don'r respond to any fragment of my text not having read
the rest. Don't draw my words out of context.
"These two sentences do not match; the reversal was not
implied. x*x*x is the degenerate case of x*y*z, where y and z
happen to equal x."
I just thought -- and still think -- it was. Let me explain.
All the graphs on your page are those of a funciton of one
variable raised into different powers. And those are all
you're discussing.
You don't pay attention to the fact that with many variable
the situation can (and probably will) be very different. You
say the one-variable case is a specific case of the
multi-variable product, which is right. But then you project
the properties of the former onto the latter, thus making a
fundamental logical error.
Here's exactly how you say it:
1. "This means 10*10*10 = 1000. This is just the degenerate
case of X*Y*Z."
2. "Instead of using b*b*b -- a cube, wouldn't it be more
interesting to use b*c*d -- a box?"
I don't find it interesting, and although you are free to
analyse the "rectangle" case (which I wouldn't call so!) you
must do it correctly. Most of what you say about a particular
case (naturally) will not apply to the general case.
So, please, reconsider who of us is reversing the antecedent
and the consequent...
"It is correct to say only one variable is being used. But I
cannot fully agree that it is not multi-dimensional. I argue
that b^n is n-dimensional with 100% correlation between
dimensions"
It's kinda a philosophical argument, but look: we measure the
experience as follows: Exp = Const*Tact. As simple as that.
And that's is the definition of experience in my model.
Where's the multidimenstionality?
Then I just want one thing: if someone gets twice more
experieced I wanna him to be one skill level higer. I just
look at it from this viewpoint...
Would you call the number of nuts in a heap a multidimensional
number? I hope no. Then if I attach all the nuts to a nodes of
a binary tree? They will still be the same nuts of the same
number. Why do you want to consider the number of nuts in a
heap a normal value and the same number of the same nuts in a
binary tree multidimensional? That's how I see it.
"So by definition, there is a 0% correlation between x and y.
Plotting points (x,y) fills a plane with random noise."
Right.
"Now let z = x * y, and plot in three dimensions. The unit
cube is not filled with random noise, but instead displays
this graph:"
Right. So what? You meat I wasn't right when speaking about
you wrongly assuming the presence of a high correlation? But I
was speaking only about the correlation between the variables
that you multiply. Of course the prodict thereof will be
correlated with them! No surprise, it's evident. But my
argument still holds because there's no reason for a
correlation between the variables. And since there's no
correlation, they won't behave like x^n.
"Wish that were true more often, which is why I'm working on
this page."
Thats how you turn my critics of your views into your own
sup****t. You better respond to the whole paragraph.
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