The house that Ludwig built was not cosy. Wittgenstein forbade carpets and curtains. Rooms were to be lit by naked bulbs, and door handles and radiators were left unpainted. The floors were of grey-black polished stone, the walls of light ochre.
The Wittgenstein House, in the unfashionable and ugly-sounding Kundmanngasse in Vienna, was a stark cubic lump devoid of any external decoration. In this, the house the philosopher designed was true to the architectural principles of Wittgenstein's close friend Adolf Loos, who once wrote a paper called Ornament and Crime, in which he argued that the suppression of decoration was necessary for regulating passion.
The Unknown Wittgenstein, at the Royal Academy, features photographs and a model of the house that indicate just how far the most difficult yet rewarding 20th century philosopher went in suppressing decoration. Built between 1926 and 1928, the Wittgenstein House made the contemporaneous architecture of Bauhaus seem as jaunty as Art Nouveau. Indeed, it could be seen as a reaction against the sexy decadence of Art Nouveau: there were no curves, little in the way of joie de vivre, and probably no scatter cushions.
The Wittgenstein House was very Viennese - its absence of decoration came from a conviction that Austrian ornament had become as unhealthy as Viennese sachertorte cake. Fin de siècle Vienna was a city of aesthetic and moral decay and, at the same time, of creatively frenetic reaction against that decadence: Schoenberg's atonal music insisted that everything that could be expressed had been expressed by tonal music; Loos's architecture railed against decoration; Freud argued that unconscious forces seethed below a purportedly ordered and elegant society. Established values were being turned upside-down in Vienna. According to Karl Kraus, Vienna was a "research laboratory for world destruction".
The Wittgenstein House was a laboratory for living. For some, though, it was an experiment that didn't work. Wittgenstein's sister, Hermine, wrote: "Even though I admired the house very much, I always knew that I neither wanted to, nor could, live in it myself. It seemed indeed to be much more a dwelling for the gods than for a small mortal like me, and at first I even had to overcome a faint inner opposition to this 'house embodied logic' as I called it, to this perfection and monumentality."
It was just as well, then, that Hermine didn't live there. But Wittgenstein's other sister, Gretl, did - both before and after the Nazi Anschluss - and apparently found it fitted her austere temperament perfectly. She and Viennese architect Paul Engelmann had invited Ludwig to collaborate with Engelmann on the design of her new house. Gretl did not issue the invitation lightly: she was no philistine and indeed, like the rest of the Wittgenstein family, was immersed in the world of arts (when she married in 1905, for instance, Gustav Klimt painted her portrait; Ravel wrote Concerto for the Left Hand for her brother Paul, a great pianist who lost an arm during the first world war).
At the time of the commission, Wittgenstein was at one of the many fraught transitional stages that pitted his life. He was fighting against depression and struggling to find a vocation worthy of his genius. He had abandoned philo-sophy in 1918, believing (wrongly) that he had solved all its problems with his Tractatus Logico- Philosophicus, whose ideas he had developed while serving as a soldier and later as a prisoner of war.
After the first world war, Wittgenstein had rid himself of his vast inherited fortune (his father had been a wealthy Viennese industrialist), sharing it among his brother and sisters. And, while philosophers around the world were realising that the Tractatus was the work of a genius, Wittgenstein became a primary school teacher in Trattenbach, in remote rural Austria. But after a classroom incident (the highly-strung Wittgenstein hit a pupil so hard the boy passed out), he quit. In despair, he contemplated becoming a monk - but instead took up gardening at a monastery.
But it couldn't last. There had to be some outlet for his visionary spirit. So the commission to work on his sister's house came at an opportune moment.
Colin St John Wilson, one of the organisers of the RA exhibition and architect of the new British Library at St Pancras, suggests that we can best understand Wittgenstein's architecture by seeing it as an extrapolation from the Tractatus. There Wittgenstein wrote that his philosophy was disposable: "My propositions are elucidatory in this way: he who understands me finally recognises them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder after he climbed up on it)...Whereof one cannot speak, thereof one must be silent."
For Wittgenstein, it was precisely the most important things - God, ethics, aesthetics - that could not be put into words. They could not be said, only shown. Wilson writes: "It was as if Wittgenstein's first attempt to deal with his predicament after the ladder had been thrown away was instinctively to make things (architecture, sculpture, photography) whose essence is that they cannot be 'said' but must be 'shown'."
According to Ray Monk, one of Wittgenstein's biographers, the philosopher's work on the house focused on the design of windows, doors, window-locks and radiators. "This is not so marginal as it may at first appear, for it is precisely these details that lend what is otherwise a rather plain, even ugly house its distinctive beauty."
Wittgenstein spent much time on these details. He took a year to design the door handles, and another year to design the radiators. Instead of curtains, each window was shaded by metal screens each weighing about 150kg, but easily moved by a pulley system designed by Wittgenstein. Bernhard Leitner, author of The Architecture of Ludwig Wittgenstein, hailed this "aesthetic of weightlessness": "There is barely anything comparable in the history of interior design. It is as ingenious as it is expensive. A metal curtain that could be lowered into the floor."
Ah, the expense. Bugger (one hears Wittgenstein saying as one studies his handiwork) the expense. When the house was nearly complete, he insisted that a ceiling be raised 30mm so that the proportions he wanted (3:1, 3:2, 2:1) were perfectly executed. "Tell me," asked a locksmith, "does a millimetre here or there really matter to you?" "Yes!" roared Wittgenstein.
Wilson praises the resulting house for having "none of that blatant self-satisfaction of minimalism" (something which, incidentally, is equally true of his British Library building). But then Wittgenstein was the least self-satisfied of men.
He probably wouldn't have been very satisfied with the little exhibition that has been set up on the landing and stairs to the Royal Academy's library, dangling over librarians trying to get on with their work. Wilson wants it to "act as a celebration of, and a focus for discussion around, a unique body of work". Wittgenstein might well have seen it as a ladder - and one to be kicked away before ascending - so irksome would he have found its insistence that he was an all-round genius of Renaissance proportions.
As well as display cases of that unlikely stuff - Wittgenstein memorabilia - the exhibition features drawings by Tom Phillips inspired by his reading of Wittgenstein, and a series of 12 silkscreen prints by Eduardo Paolozzi called As Is When, made in 1965.
The exhibition is dominated by the ticking of a machine that Wittgenstein devised while working in Newcastle during the second world war, in a research group studying blood loss through so-called wound shock. It's an ingenious instrument for measuring continuous pulse rate - and probably drives the librarians crackers.
But then Wittgenstein was no slouch at mechanical design. He originally trained as an engineer and retained a lifelong fascination for mechanical things (he once took great delight in repairing a fellow philosopher's toilet). He wasn't just a thinker, but also a doer - something few philosophers have managed. To clinch this point, the exhibition includes models of a kite and an aeronautical engine he made while a student in Manchester before the 20th century reached its teens. That engine - it was driven by jets on the tips of the propeller and so exerted no torque on the fuselage - proved revolutionary to the later development of helicopters.
Shortly after he finished work on the house, in 1928, Wittgenstein returned to Cambridge University and philosophy, developing a new philosophical vision that deconstructed his earlier work. It remains hugely influential today.
The Wittgenstein House had a less distinguished future. After the 1938 Anschluss, Gretl fled to New York. In 1945, Russian soldiers used it as barracks and stables. In the 1950s, it was bequeathed to Gretl's son who sold it to a developer for demolition. It was saved by the Vienna Landmark Commission and made a national monument in 1971.
Today it is home for the Cultural Department of the Bulgarian Embassy. Wittgenstein would have hated what they have done to it. Room dividers have been removed to form L-shaped rooms, walls and radiators have been painted white, the hall has been carpeted and wood-panelled. Wittgenstein would have preferred demolition to the cosy, human touches and changes Bulgarian vulgarians have inflicted on his unloveable, unliveable house.
The Unknown Wittgenstein: Architect, Engineer, Photographer is at the Library Print Room, Royal Academy of Art, London W1, until January 28. Details: 020-7300 8000.