*Guest post by Vincent Kelly*

“*I often looked up at the sky an’ assed meself the question – What is the moon, what is the stars?*”

I saw the film “Melancholia” last night. Not your classic, Friday-night date movie. Its primary story concerns the discovery of a new planet – “Melancholia” – which, since pre- history, has been in orbit the other side of the sun to Earth, and hence undiscovered. Its existence is revealed when it moves from this “Dance of Death” orbit and spectacularly occupies the night sky along with the moon. Scientists declare that in days its orbit will take it within a couple of hundred thousand kilometres of Earth, a chin-hair in the context of the span of the universe. The world gets ready to set out its deckchairs and enjoy the show. Alas, much embarrassment ensues when the scientist egg-heads realise they have made a mistake in their initial calculations and, oops, it is going to hit us after all… and, incidentally, end the world forever.

Of course, the story and images are metaphorical – I’ll need to think a bit longer about what exactly. But it set me thinking about how little we know about the universe, and how little we *can* know of the universe from our little fishbowl in orbit of a star. The universe is so strange that the film’s storyline isn’t that inconceivable. Despite the advances of science, the utterances of Séan O’Casey’s loquacious gobdaw Captain Boyle, quoted above, remain as relevant now as they ever did.

His sentiment isn’t new. Throughout the ages the stars have been the focus for mankind’s wonder and speculation. Because we live in a fishbowl, because our senses can’t comprehend or observe the scale, or timescale, of the cosmos, our understanding of the universe is now necessarily explored in the language of mathematics. We can admire the rings of Saturn, but we can only infer the existence of blackholes or the Big Bang or X-rays through a mathematical framework.

As a mathematician of sorts, I have always been equally curious as to the role the night sky had on the development of mathematics.

For much of human history, arguably until the 18^{th} Century, mathematics and astronomy were essentially the same subject. And astronomy itself appears to have arisen from the astrology and religion of the pre-historic peoples. The main Sumerian God was “Anu”, which literally translates to “Sky-God”, sub-deities included “Utu”, the Sun-God, “Nanna”, the Moon God, and “Inanna”, the “lady of the sky” and believed to be the celestial planet Venus, whose unpredictable movements reflected the God’s character.

The study of the heavens to predict rain, drought, destiny or luck, eventually led to a body of observations, and attempts to create frameworks to predict seasons, tides and eclipses. It is thought that monuments like Newgrange and Stonehenge were built for both religious and astronomical reasons, serving as a guide to the changing seasons. The Egyptian pyramids are all aligned to the Pole star.

Most of the great mathematicians of the world were also astronomers: Hipparchus, Archimedes, al-Khwarizmi, Fibbonaci, Abu Nasr Mansur, al-Biruni, Kepler, Newton, Galileo, Euler, to name but a few.

The drive to produce a reliable calendar led to the first proposal of a “heliocentric” model by the Babylonians around the 5^{th} century BC. The Greeks developed this further and proposed a geometrical, three-dimensional model to explain the apparent motion of the planets. Seasons were defined relative to the motion of these heavenly bodies. This led to discoveries in spherical trigonometry. The development of ever more complex models of the celestial sphere required more complex calculations, and more sophisticated geometry to back them up. Latitude and longitude were described (in the Babylonian’s base-60), and based on this development the astrolabe was invented. This invention, constantly improved upon for the next millennium, was used to predict the positions of the moon and sun, and thus determine the local time given latitude, or vice versa. It was the single most important advance in maritime navigation in human history. Columbus used one when sailing to the Americas.

The Indians perfected a calendar model. In attempting to solve explain astronomical observations, the Kerala School of Astrology and Mathematics in India in the 14^{th}-16^{th} Century discovered a series expansion of trigonometric functions, a precursor of calculus. Calculus is the foundation of modern mathematics, and forms the basis for myriad applications in the modern world in the fields of engineering, economics, architecture and computing.

These but scratch the surface of the developments in mathematics inspired by the heavens.

And so, pondering upon Twinkle, Twinkle, Little Star, has actually borne remarkable fruit for human endeavour – although, as “Melancholia” would remind us, ours is a fragile existence, and doom could just as easily fall from the heavens as inspiration.

**Vincent Kelly** works as an actuary in Dublin, and is interested in science and mathematics, particularly applied mathematics. He has a BSc in Financial and Actuarial Mathematics from DCU.

*The 6th annual Maths Week Ireland which is an all island celebration of mathematics runs from tomorrow.*

_{Top image: Dmitry Brant}_{ / Wikimedia Commons }

Great article. I’m certainly not a math person, so I respect anyone who is, and furthermore can apply the principles to space exploration. A recent article on the topic got me thinking about it lately, and I discovered your blog as a result. I’d love to know your thoughts on how this could play out for young students. All the best, -rsmithing

Thanks for your comment rsmithing! I think this would definitely be a good angle to get students interested in maths. The Blackrock Observatory in Cork (Ireland) has put on a lot of events to do just that during maths week. These took place over the past week: http://www.bco.ie/2011/09/maths-week-2011/