Let's firstly look at a list of the nine Muses and their respective arts:
Calliope - Epic poetry
Clio - History
Erato - Lyric poetry
Euterpe - Music
Melpomene - Tragedy
Polyhymnia - Choral poetry
Terpsichore - Dance
Thalia - Comedy
Urania – Astronomy/Astrology
Yes, there is a lot of poetry in the list but we also mustn't forget that in an age with few books or any other recording medium most knowledge was set down and transmitted in some poetic form so as to make it easier to remember. The rhythms and rhymes of poetry are just so much easier to memorize than long passages of prose. Having said that, there are two Muses that have always struck me as seemingly out of place: Clio and especially Urania. What is the Muse of Astronomy doing in the same family as her poetic sisters?
According to Hesiod's Theogeny (written in the seventh century BC) the Muses were the offspring of Zeus and Mnemosyne, the goddess of memory. Indeed, our words for 'memory', 'mnemonic' and even 'meme' are derived from Mnemosyne. This now starts to make much more sense. In the same Theogeny, we are told that kings and scholars receive their powers of knowledge from Mnemosyne and the Muses. Such memories are not just personal but collective. In an age with few written records the preservation and teaching of one's history is of prime importance in fostering one's identity. The history of the tribe, of this world and the next are encoded into the rhythms of the Muses, be they in poetic meters or planetary orbits.
In this new context what seemed to be the two ugly sisters are perhaps the two most important ones, with Urania, in the guise of astrology, being the history of the cosmos and Clio, the Muse of History, being the embodiment of everything the other arts aim to achieve – the preservation of history and hence identity. It is therefore also fitting that the word 'museum' is derived from 'Muse', as well as 'to muse' and 'amusement'.
As our modern physics and neurosciences show that both the universe and humans are ultimately composed of frequencies, the idea of the Muses as personifying the rhythms of memories brings the nine sisters back into being a meaningful part of our own culture.
I wrote the above piece last year and yet am sure it is a poor reflection of my original article,"The Muses of Mathematics", published in "Mathematics, Art, Technology and Cinema" (Springer, 2003) which are the proceedings of a conference in Venice on mathematics and culture. I have been able to find links online to purchase the book but, being Springer, have been unable to track down a readable digital version.
The original inspiration for the article came from my investigations into the iconography of mathematics and science throughout the ages. The icons of the seven Liberal Arts seemed to have been created in the late Hellenic period and transmitted through Arab and European culture until a sudden abrupt end during the early 19th century. Icons were important in terms not so much of transmitting knowledge but in making the general public aware that such knowledge may appear esoteric but is nevertheless important.
The inspiration for rewriting the article was that I came across the same theory in Wikipedia's page on the Muses, without reference to my article so assumed somebody else had had the same idea. However, that section has since disappeared and I have been unable to locate in their history pages when or why that took place.
However, given the elevated status of music in Greek philosophy and its links to mathematics, I feel that the Muses are more than mere symbols of inspiration, but rather the personifications of the rhythms of life.