One of my recurring dreams is that I'm at an art exhibition with no clothes on and a crowd is gathering in front of me waiting to hear what I think about the work on show.

I'm struck dumb and the crowd starts to point and laugh. No, wait, that is real -

Welcome to my Dreamland.

Zoe Beloff grew up in Edinburgh and studied at Edinburgh College of Art before moving to New York, where she has lived and worked since 1980. Before I paid a visit to her first solo exhibition in her native land, I spent a few hours browsing online, watching strange little videos on her website purporting to be "dream films" made by the Coney Island Amateur Psychoanalysts, a society of which she claims to be archivist and last surviving member.

This was one of these exhibitions, I decided, that has to be seen to be believed/understood. Even the exhibition's title, A History Of Dreams Remains To Be Written – a quote by early-20th-century German cultural commentator Walter Benjamin, about the status of dreams as a product of social and cultural environments – belongs to a nether world in which nothing is as it appears. One of the panels here states that Beloff "considers herself a medium, an interface between the living and the dead, the real and the imaginary".

For this exhibition, the Talbot Rice Gallery has been transformed into Dreamland, a Freudian funfair complete with a discombobulating House of Mirrors, a projection booth showing a selection of "dream films" and a scale model of an unrealised theme park inspired by Sigmund Freud's visit to Coney Island in 1909. We are led to believe that Freud's visit had a significant impact on a small section of New York society, prompting the formation of the Coney Island Amateur Psychoanalysts, a group based in Brooklyn in the early days of the 20th century who got their kicks by exploring the nether world of our subconscious.

Beloff views her role in this world as archivist-in-chief. Since 2009, she has used it as a means by which to explore the unconscious by mapping one of the world's most famous amusement parks. Coney Island was best known as a holiday resort. It included Dreamland, the world's first enclosed amusement park, which was a seamless mix of family entertainment and lurid fantasies, not to mention clandestine sexual activity.

Working with a wide range of media, including film, installation, drawing and found objects, Beloff consciously allows the boundaries between historical fact and creative interpretation to blur, leaving the viewer to reflect upon what really happened and what might have been...

In the Upper Gallery, The Days Of The Commune, a new video work, is being shown for the first time alongside the props Beloff used to make it. Following the Occupy Wall Street protests in New York in late 2011, the artist restaged a play written by Bertolt Brecht about the Fourth French Revolution that took place in Paris in 1871. Using a cast of actors from diverse backgrounds, armed with handmade props, her re-enactment links two revolutionary movements, encouraging us to think about the role of the "everyman" in our hopes for a fairer world.

Beloff has acknowledged the profound influence of her family in her work. She has stated that the "character" of Albert Grass, leader of the Coney Island Amateur Psychoanalysts, is a homage to the Jews of her grandparents' generation, "working people who believed in social justice and the idea that on a personal level it was possible to change the world. I tell people who ask about him, that he [Grass] and I 'are as one'."

Beloff's interest in psychology and psychic phenomenon is bred in the bone as her parents, John and Halla Beloff, were both leading psychologists – although, interestingly, not Freudians. Her father, who died in 2006, was Britain's preeminent parapsychologist and a key player in setting up the University of Edinburgh's chair of parapsychology, thanks to a bequest set up for the purpose by his friend, Arthur Koestler.

The constructed societies John Beloff's daughter has created in this double-sided exhibition, based at the university in which he spent more than 40 years, have a curiously controlled feeling to them. She has overseen every aspect of their creation, drawing, filming, painting and remaking an alternative universe that is part freak show and part utopia – somewhere we can't help but feel a part of, even if we don't want to be in it.

Zoe Beloff: A History Of Dreams Remains To Be Written is at Talbot Rice Gallery, Old College, Edinburgh until February 16. 0131 650 2210, www.trg.ed.ac.uk