Re: The socks have it
> the Pyke scale should be logarithmic
Tricky one, for two reasons.
First of all, is the scale additive or multiplicative? If one has a box in the
lab shed marked "lasers: misc." that puts you somewhere on the scale. Likewise if you just happen to own a mass spectrometer (or have a penchant for high altitude balloons), you would also be on there, somewhere. However if you have both does that make you a boffin by the sum of those devices "boffinism" or does it imply a greater area of boffinism, hence multiplying (or adding the log()'s) of the individual contributions.
Secondly, how would a logarithmic scale denote a person with zero boffinism? log(0) is not a defined value and there are no log()'s of negative values and log(<fraction>) comes out to be < 0.0.
In the spirit of making things as complicated as necessary a logarithmic scale would need to be calculated something like:
($value == 0 ? 0 : sign($value) * log(abs($value+1))/log(2))
Where the log(2) is a normalisation, so that a 1 Pyke boffin gets assigned a value of 1.0 - we wouldn't want them to be too Pyke-y, would we?