"Edinburgh is a city whose physical development has been strongly linked to philosophical thought and literary movement," says the blurb for The Lighthouse's latest exhibition. "However, beneath this sedate image, Edinburgh has a schizophrenic character, caught between the rational and the irrational, between nostalgia and modernity, between the urban centre and the natural edge."

Bringing artists and architects into collaboration, The Lighthouse promises an investigation into these deep, dark seams of Edinburgh's buried unconscious, made all the more alluring with quotes from Jekyll And Hyde. Like RL Stevenson's famous tale of split personality, Edinburgh's mediaeval Old Town is to be set in sharp contrast to the enlightened boulevards of the neoclassical New Town.

That's the theory. But on the whole, the artists and architects, chosen for their past involvement in explorations of urban space, seem to be far more in tune with the ordered innovations of the Enlightenment than with the disordered accretions of Edinburgh's deeper past.

Even more apparent is their debt to Patrick Geddes, the Edinburgh-based pioneer of town-planning who was active a century ago. Geddes was a holistic thinker, insisting that an understanding of ourselves and our surroundings was only possible if we saw everything from the smallest detail up to the bigger picture. Way ahead of his time, he extrapolated the findings of botany into large-scale town-planning, recognising the organic growth patterns in both.

When he bought the camera obscura on Castlehill, it was to create an Outlook Tower which would give Edinburgh citizens a multi-faceted view of their own town and its place in the land. On their way up the stairs, they would read about Edinburgh and its place in the wider world, and at the top, a 360-degree panorama opened out before them, from the distant hills of Fife to the Pentlands in the south.

Inside the camera obscura, that same view was condensed, live, onto a concave table. Even today, the experience of bending over this real-life globe, scooping up the reflections of tiny little figures in your hands, is unique. It is that combination of an internalised vision with an external panorama that lies at the heart of Northern City.

This dichotomy of inside and out is expressed most explicitly in Northroom, an ambitious work by artist Victoria Clare Bernie and architects Metis. They're inspired by Robert Adam's neoclassical memorial to David Hume on Calton Hill, which contains a curious northern room open only to the sky. The artists have turned the sealed monument inside out, by filming details from the outside of the tomb and displaying them in a circle facing inwards.

Like the monument itself, the idea is more powerful than its realisation. Standing inside a wiry forest of miniature DVD players, you see tiny details of stone, lichen and delicate spiders' web, with sunlit sky and full moon lurking around shin level. There's no real sense that you're in an inside-out monument, but the greatest effect is the feeling of time passing, at all its different speeds.

Dalziel + Scullion, working with architects Sutherland Hussey, have created something equally ambitious technically, which, again, achieves something different from the artists' original intentions. A souped-up version of their GoMA installation, slowly panning views of Edinburgh, slicing at a tilt through 360 degrees, is projected onto a screen that is also tilted and spinning.

The basis for these angles and rotations is Edinburgh's latitude, its place on our planet. But while this astronomical demonstration does little for me, I am captivated by the oddness of the experience. The film was captured from a single view point but is played back on an ever-moving arc. So while I inhabit the role of static viewer, I find myself chasing the image around the room, never quite owning it. It's a strangely jarring effect, cutting me out of the loop, counter to Geddes's inclusive intentions.

Nathan Coley's quote in fairground lights - We Must Cultivate Our Garden - is in tune with Geddes's botanical bent, and with his motto that "by living we learn". But aside from the choice of Voltaire's words, this is a rehash of a previous work made for Mount Stuart in Bute. Brought into a sterile gallery space, the work is stripped of its power.

Finally, architects Gross. Max. have put together an amusing melange of commentaries on Edinburgh's architectural future and its geological present, bringing humour into an otherwise quite serious affair.