"Anton" <anton.txt@[EMAIL PROTECTED]
> wrote in message
news:Xns9AC597C358915antontxtgmailcom@[EMAIL PROTECTED]
>> This means 10*10*10 = 1000. This is just
>> This is just the degenerate case of X*Y*Z.
>> A square is still a rectangle, and a cube is still a box.
> A rectangle is not a square and a box is not a cube!
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.
> The base doesn't matter much.
It shows explicitly how a multiplication is taking place.
Log_b( b^n ) = n.
So n is the count of times b is being multiplied with itself.
> It is neither multi-dimensional nor consists of several variables...
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
>> Instead of using b*b*b -- a cube,
>> wouldn't it be more interesting to use b*c*d -- a box?
> Now that the variables are different, to assume their high
> correlation becomes ungrounded.
Perhaps we should use random numbers, to make the point clear.
Let x and y be random linear variables in the range 0..1.
So by definition, there is a 0% correlation between x and y.
Plotting points (x,y) fills a plane with random noise.
Now let z = x * y, and plot in three dimensions.
The unit cube is not filled with random noise,
but instead displays this graph:
http://home.comcast.net/~anglewyrm/thread/f(xy).png
The curved central diagonal line is the degenerate (and optimal) b*b*b...
case
within the surface of all b*c*d... possibilities.
>> "Such as Character Level, Armor class, Damage output, etc.
>> Perhaps you'll invent a replacement for these."
> In your 'article', you never mention several functions and all
Sorry, and this is really good information for me, thank you.
I will have to fix the page on this matter, so that it's clear
about what kind of situations the subject applies to.
> [both] models will be great as long as they'll be what their authors
> wanted them to be.
Wish that were true more often, which is why I'm working on this page.
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