The Alternative Guide to the Universe is a show set amidst a cultural scene that has never been more gripped by "outsider art". We are infatuated with this obscure artistic faction, and galleries are becoming increasingly concerned with giving this unrecognised, unvarnished art space on the walls. "Outsider art" is a tricky term, often used as a convenient umbrella expression for a broad ranging practice that is somewhat nebulous. This show at the Hayward however, has a more specific focus.

The works on display illustrate alternative perspectives on the world and re-imaginings of the conventions we all live by. The content is eccentric, deviant and idiosyncratic. The wackiness of the display screams "outsider". But, despite what the outsider aesthetic suggests, this exhibition is no cabinet of oddball curios. In fact, the unconscious flourishes of paint and compulsive scrawls so associated with outsider art have been set aside for a clean and highly-considered display of some carefully calculated works.

Take as an example Bodys Isek Kingelez's beautiful architectural models, which demonstrate skill, precision and sensitivity. These multicoloured cardboard constructions are entirely fictional realisations of alternative cityscapes and buildings formed in his mind. Yet the expertise and accuracy applied by Kingelez makes for some convincing structural maquettes.

Within this show of expert draughtsmanship, science is prevalent. It's a radical, imagined kind of science, which follows the artists' own outlandish logic. Paul Laffoley's complex diagrammatic paintings broach themes such as time-travel, alien visitations and other-worldly cosmologies. Eloptic Nohmagraphon, a complex diagram illustrating the modalities of the tulpodial urtraum, appears as a sophisticated form of mathematics, dense with mind-boggling information. The information is baffling. But the clarity of his compositions and his use of "technical" terms confuse the borders of what is science and what is myth.

Guo Fengyi is another artist who links the rationale of biology with the abstractions of thought and philosophy. Her large and complex pen drawings appear to be studies of the nervous system and its networks of veins and arteries. As a practitioner of ancient Chinese medicine, Fengyi believes her works are not art, but "painted prescriptions" and instruments for healing. As well as biology, physics crops up too. James Carter's "circlon synchronicity" theory offers an analysis of the universe in place of the more commonly accepted theories of relativity and the big bang. The Circlon Model of Nuclear Structure illustrates an unfamiliar kind of physics, presented like an alternative periodic table. And Jean Perdrizet's attempts to unpick the mysteries of the afterlife manifest themselves as complicated mechanical diagrams depicting strange technologies.

Despite the exhibition's science-based underpinnings, works of a less scientific nature are still given merit for their otherworldly and outlandish content. One particularly curious display is the work of Eugene Von Bruenchenhein, who spent years documenting his wife Marie in a vast collection of ethereal photographs. He would sit her upon a stage of floral drapes and extravagant wallpapers, decorating her with elaborate jewellery and materials; he once made her an elaborate crown using a coffee can. Von Bruenchenhein later went on to paint environments of where he and Marie might one day live as royalty.

Every artist in the show has his or her own wacky and individual belief system. Contrary to the general assumptions made about outsider art, many contributors in this show received formal education or were academically engaged with a variety of disciplines. Eugene Von Bruenchenhein for example was broadly educated in subjects from pre-Columbian art to Romanticism and Victorian design, and Laffoley studied architecture at Harvard. These artists are intellectuals of an alternative mode of thought, and the sheer draughtsmanship present in the exhibition is outstanding. In fact, in The Alternative Guide to the Universe, the "outsider" definition that has been attached to these works is arguably irrelevant. The artworks are technically impressive, conceptually strong and highly evocative in their own right.

So what then unites these artists as outsider? Is it the work's obsessive aesthetic? Is it their grounding in eccentric philosophies? Is it the lack of recognition given to many, whose works are "discovered" only posthumously? Or is it simply all the above? At The Alternative Guide to the Universe, outsider-ness is achieved by transporting the audience above the temporal realm to new, radical ways of thinking beyond our own earthly logic. There is a lot to take in here, but the exhibition is well paced. The Hayward has created a display of work, whether outsider or not, that is well-informed and carefully constructed, strongly grounded in both scientific and theoretical principles. The Alternative Guide to the Universe will prompt any visitor to re-imagine for themselves the possibilities of the realm we live in.

Alternative Guide to the Universe, at Hayward GalleryFrances Reed's review of The Alternative Guide to the Universe at Hayward Gallery, Southbank Centre, London.4