ON the coastal path north-east out of Lochranza at the top of the Isle of Arran is a mysterious way-marker directing the walker to Hutton's Unconformity, along the route to the Fairy Dell. Although not exactly explained on the signage, it is an interesting juxtaposition of the fanciful and the scientific, the geologist James Hutton's 1787 discovery at Newton Point being an important point on the journey of the rational mind during the Enlightenment.

Many of the great thinkers of that crucial period of the 18th century gathered in Edinburgh, and Hutton was at the heart of the company, one of the founders of the Oyster Club, a company of scientists and philosophers, also including economist Adam Smith and chemist Joseph Black, who gathered weekly in the 1770s to discuss ideas, drink and eat shellfish. Hutton was a deep thinker, whose seminal work, 1785's Theory of the Earth; or an Investigation of the Laws Observable in the Composition, Dissolution and Restoration of Land upon the Globe was a tough read that was only brought to the notice of a wider public by his disciple John Playfair (brother and uncle of the capital's crucial architects). However our understanding of the geological development of the planet, and its formation rather longer ago that was generally accepted in his time, owes an enormous amount to Hutton, and it is nothing less than that legacy that will be celebrated in the free public opening event at this year's Edinburgh International Festival, which takes its title from Hutton's theory of Deep Time.

Ticket holders for Sunday's one-night-only performance of Deep Time – and there is a final release of tickets to personal callers only from 10am on Saturday at The Hub box office – will be witnessing the second collaboration between the Festival, academics from the University of Edinburgh, and digital video and scenic design company 59 Productions, following last year's Harmonium Project, which celebrated the Edinburgh Festival Chorus and illuminated the Usher Hall to a soundtrack of John Adams.

This time round, and beginning an association with sponsor Standard Life which will back work by 59 Productions at the Festival for a further two years, the soundtrack will be a selection of the music of Glasgow band Mogwai, and the subject is the last 350 million years of the cityscape, using the volcanic plug on which Edinburgh Castle is perched as the projection screen for the images 59 Productions founding director Leo Warner will create.

For Warner, the making of Deep Time is an important homecoming. He and Mark Grimmer began 59 Productions with early work at the Traverse on shows like Catherine Grosvenor's Cherry Blossom and as part of the Greyscale collective, in association with director Lorne Campbell, whose version of Get Carter for Northern Stage they recently helped realise. In between those jobs, the CV of 59 has also taken in work on the National Theatre of Scotland's world-conquering Black Watch, for the opening ceremony of the London 2012 Olympics, at the Sydney Opera House and the United Nations HQ, on the V&A's David Bowie Is exhibition, with New York Metropolitan Opera and on Broadway. Their stunning film of cellist Sol Gabetta launched this year's BBC Proms a month ago.

"It's fantastic to be working in Edinburgh, especially with the relationship we have with [Festival director] Fergus [Linehan]," says Warner, "We can be architects of our own brief, because the city is our blank canvas. We are rooted in Edinburgh and in Scotland, so we want to speak to Edinburgh as a city. The Castle is such a cultural and historical beacon you can't ignore it, and this is the ultimate story from the dawn of time!"

Hutton found "unconformities" that sustained his theories elsewhere than Arran, including at Jedburgh in the Borders and on the Berwickshire coast, and the molten rock that created Salisbury Crags at Arthur's Seat is labelled to this day as "Hunter's Section" if you look closely for the plaque. Warner will be working with imagery that runs from re-imagining the magma that formed the capital's skyline, to digital selfies that have been submitted for the Deep Time project by the capital's citizenry.

"There are also a few incredible Hutton quotes that we'll use," says Warner, "but he was not light reading."

"Last year the work was very rooted in the music and the musicians, and the shape of the images dictated by the digital process and the representation of the voices. This time I hope to be more painterly and artistic, with a plural narrative and different aesthetic styles, but I am always deeply inspired by the music – and the visuals will be driven by the music."

"I have loved Mogwai for many years, so this was an excuse to listen to my entire collection for pace, tone and instrumentation, raiding their early, middle and recent back catalogue."

Further enquiry yields the information that a total of four Mogwai compositions will feature in the three "chapters" of Warner's work, two pieces combining in the finale. If Rave Tapes or Hardcore Will Never Die But You Will are among your favourite albums, you may recognise a couple of tunes.

And if the band are looking for titles for future creations in their 20 year catalogue of molten rock, perhaps "Hutton's Unconformity" might suggest itself.

Deep Time,Castle Terrace, Sunday August 7, 10.30pm

www.eif.co.uk