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Orthogonality... yeah, nice features. Since a few months I've been grinding orthogonality in the sense of principal component analysis (single value decomposition) - mind you, I'm not a mathematician, I just apply stuff on physiology.

When I read your post Masem it occurred to me that good sets of functions are just the opposite of principal components. For you who are not familiar with this (intriguing) subject, principal components are a set of orthogonal axes of data that are chosen (like rotating and scaling the 3D euclidian space) in such a way that as much of the variability as possible goes into the first axis, from the remaining data as much as possible in the 2nd component etc etc. Moreover, all these components are orthogonal. Apart from the physiological applications I'm familiar with, there are also mathematical implications, like matrix rank, finding solutions and so on.

A good set of functions is the opposite of principal components.

You don't want as much functionality as possible crammed into a single function and all remaining bits scattered around a bunch of insignifant code. You want each function to have a clear and confined scope, so that each of the functions is as meaningfull and concise as possible without a lot of flags and parameters and other confusing stuff.

I don't know the opposite of single value decomposition in a statistical sense, but it probably is an ill-posed problem. You can recombine orthogonal axes into an infinite number of other orthogonal axes (coordinate systems) but only one set forms the principal components. The reverse, equal division of information over all axes is possible in many different ways and therefore it is hard to come up with a solution (I figure, but I don't have hard proof for this... does anyone?).

This compares nicely with writing code. There are a lot of ways to write orthogonal functions, but it is hard to divide the functional space equally over functions.

Is there a name for this? Rural components maybe?

Jeroen
"We are not alone"(FZ)

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