31–34 of 34 posts
Earlier quoted context omitted.
And also, I assume, because the concept of "species" isn't all that well defined?
It is well defined: a group of living organisms consisting of similar individuals capable of exchanging genes or interbreeding
My personal approach to magnitude is not based on category theory but rather based on weightings of a metric space. If your metric satisfies certain properties, you can obtain a measure of the 'effective number of points' of a metric space. This is particularly relevant when looking at the metric space from different scales---zooming in gives you a lot of disconnected points, while zooming out gives you clusters. Magnitude then captures the changes in the number of points in a principled manner.
Let's take the mammoth - it's basically a hairy elephant and the genetic material that could make one is 99+% present in Asian elephants ( possibly 100%, just not all in the same individual ) today.
A bit of selective breeding and you could probably produce one quite quickly [1]
ie the true measure of diversity is the pool of genetic diversity out there - rather than some arbitrary classifications.
[1] Look at the variety in shape and form of domestic dogs - they all came from the same stock a mere 20-40K years ago.
http://www.loujost.com/Statistics%20and%20Physics/Diversity%...