Dave, you write: *The third discussion is of the "Rarity of the Commonplace" — how the mundane reality about us is so improbable. Part of this discussion deals with causality (another frequent FRIAM topic, but not so much recently), part with the fact that only 4% of the Universe is ordinary matter, and part that is corollary to the discussion of infinities. Part of the latter: a Real Line is made up of the rational and the irrational numbers, both of which are infinite in number. The rationals are infinitely dense and so take up zero percent of the Real Line. Again, mathematicians, a bear of little brain asks for an explanation.*
What it means to say that the rationals are infinitely dense on the real line, is say that in any neighborhood of a point on the line you will find infinitely many rationals. Despite their fecundity, there are still infinitely more non-rationals on the line (by Cantor's argument). Still, by Diophantine Approximation we can formally talk about how well we can approximate any real number with a rational. There is a killer book by Ivan Niven on the subject. For the record, when you ask for a random number between zero and one and another gives you back a number you can imagine, you can reasonably assume that other is biased :) Jon
-- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ... FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
