George's black eye was almost perfectly oval, as if he'd made himself up as a mime artist. He stood there in his empty flat, frozen somewhere in between meaningful gestures. After a dozen or so meetings, the young psychiatrist visiting him still hadn't been able to work out his patient. What he felt now was a nagging irritation at George's inability, or refusal, to explain how he'd got the black eye.

The psychiatrist had come across George a few months earlier. The two men looked oddly alike - both in their mid 30s, the same height, a similar wiry build and some faint quality of mutual recognition. George had once been an estate agent. But the sharp suits had become crumpled, the behaviour increasingly erratic, and he had ended up in a locked ward after ransacking one of his offices at night.

By the time he was referred to the young psychiatrist, George had written pages of notes gleaned from estate agents' windows and websites - equations of property prices, postcodes, square footage, distance from tube stations. George claimed he could identify a set of codes for what he called his "caste system" for Londoners. Properties under £75,000 would condemn their owners to "untouchable" status; over £5m, and they would belong to a secret sect whose members possessed mystical powers.

The psychiatrist might want to perceive in this a distorted response to the stress of the London property market, but George's mindset probably belonged to a more general form of paranoia and solipsism common to schizophrenia. Prescribed the anti-psychotic drug quetiepine, George's more extreme symptoms abated, and he moved out of hospital into a small flat in an area he might previously have described as "untouchable".

Yet the psychiatrist was frustrated by his inability to find some point of empathy with George. The German philosopher-psychiatrist Karl Jaspers had distinguished between two kinds of madness: that which could be understood, and that which could only be explained. In some kinds of mental illness it is possible to recognise familiar emotions, even if exaggerated and distorted, and it is therefore possible to feel for the sufferer. Yet there are other kinds in which the sufferer is propelled into an unreachable mental orbit. Jaspers called such states "autochthonous".

What does it mean to know how someone else feels? Sometime after leaving hospital, George had stopped taking his medication. But instead of again being beset by delusions, he had disappeared into the "negative" symptoms of schizophrenia. Glancing around George's flat, the young psychiatrist looked for a point of conversation. There was a mattress and an old suitcase, nothing else. The young psychiatrist found himself tilting sideways into the same awkward posture as George. "It's a nice place you've got here," he said.

Unexpectedly, George jolted out of position. "I introduced myself to the neighbours last night," he said.

"Oh really? What time was that?"

"About three."

"In the morning?" The young psychiatrist pointed to George's black eye. "Did someone hit you?"

George ignored the question. "I think I might be getting sick again."

The young psychiatrist and his patient looked at each other, as if they were both standing in a hinterland between what made sense and what didn't. "How have you been feeling recently?" the young psychiatrist asked.

"I don't know," George replied. "I can't remember. I think my problem is actually a memory problem."

Then he shuffled over to the suitcase in the corner and began pulling out his notebooks. The psychiatrist drew breath, anticipating a cascade of distorted estate agents' data. Instead, George handed him a piece of paper with a couple of lines neatly written on it.

"I read this somewhere, and I thought you might like it," he said.

What George had written was: if in life we are surrounded by death, so too in the health of our intellect we are surrounded by madness.

It was a quotation that the young psychiatrist knew well; but now it wrong-footed him. When George wrote it down, he hadn't been thinking of his own condition; he'd been thinking of his psychiatrist's. Schizophrenics find empathy as difficult as it is for others to understand them. Thinking about someone else was a good sign.

"Would you like to come back to hospital for a bit?" the young psychiatrist asked.

"OK," George replied.

· Names and details have been changed.