Combinatory Analysis in the IChing

Combinatory analysis refers to a group of techniques that can be used to determine the number of elements in a particular setwith- out having to count them one-by-one. Theelements in question could be the results froma scientific experiment or the different potential outcomes of a random event. [...] Combinatory analysis has interestedmathe- maticians forcenturies.According toTakacs (1982), such analysis dates back to ancient Greece. However, the Hindus, the Per- sians (includingthe poet an...

 The Birth of Political Science in Ancient Greece

With the Greeks, education was an important part of polity. Men were formed for their country, much more than for themselves, or their family. This principle can only be embraced by commonities little populous, in which it is more pardonable to suppose a national interest, separate from the common interest of humanity. It is practicable only in countries where the most painful labours of culture and of the arts are performed by slaves. This branch of education was restricted almost entirely t...

 The 12-Note Octave is Too Good to be True

[Playing notes on a piano] One... Two... Three... Four... Five... Six... Seven... Eight... Nine... Ten... Eleven... Twelve... 12 different pitches, and then back to where we began. Incredible! Fantastic! The mystical number 12. There are 12 hours in the A.M. and 12 hours in the P.M. The new day begins at 12 midnight. There are 12 months in a year. Both the Western and Chinese Zodiac have 12 signs. Further, the Chinese use a 12-year cycle for reckoning time. There are 12 eggs in a dozen. 12 d...

 Biology is Too complex for Mathematical Explanation

There is a strange disparity between the sciences of inert matter and those of life. Astronomy, mechanics, and physics are based on concepts which can be expressed, tersely and elegantly, in mathematical language. They have built up a universe as harmonious as the monuments of ancient Greece. They weave about it a magnificent texture of calculations and hypotheses. They search for reality beyond the realm of common thought up to unutterable abstractions consisting only of equations of symbols...