Marvin watched her leave, then sat down at the bar. 'One for my baby, and one for the road' he told the bartender.

'A woman's a two-face,' the bartender commented sympathetically, pouring a drink.

'I got the mad-about-her-sad-without-her blues,' Marvin replied.

'A fellow needs a girl,' the bartender told him.

Marvin finished his drink and held out his glass. 'A pink cocktail for a blue lady,' he ordered.

'She may be weary,' the bartender suggested.

'I don't know why I love her like I do,' Marvin stated. 'But at least I do know why there's no sun up in the sky. In my solitude she haunts me like a tinkling piano in the next apartment. But I'll be around no matter how she treats me now. Maybe it was just one of those things; yet I'll remember April and her, and the evening breeze caressed the trees but not for me, and-'

There is no telling how long Marvin might have continued his lament had not a voice at the level of his ribs and two feet to his left whispered, 'Hey, meester.'

Marvin turned and saw a small, plump, raggedly dressed Celsian sitting on the next bar stool.

'What is it?' Marvin asked brusquely.

'You maybe want see thees muchacha so beautiful other time?'

'Yes, I do. But what can you-'

'I am private investigator tracer of lost persons satisfaction guaranteed or not one cent in tribute.'

'What kind of an accent have you got?' Marvin asked.

'Lambrobian,' the investigator said. 'My name is Juan Valdez and I come from the fiesta lands below the border to make my fortune here in big city of the Norte.'

'Sandback,' the bartender snarled.

'What thees theeng you call me?' the little Lombrobian said, with suspicious mildness.

'I called you a sandback, you lousy little sandback,' the bartender snarled.

'That ees what I thought,' said Valdez. He reached into his cummerbund, took out a long, double-edged knife, and drove it into the bartender's heart, killing him instantly.

'I am a mild man, señor,' he said to Marvin. 'I am not a man quickly to take offence. Indeed, in my home village of Montana Verde de los Tres Picos, I am considered a harmless man. I ask nothing more than to be allowed to cultivate my peyote buds in the high mountains of Lombrobia under the shade of that tree which we call "the sun hat", for these are the bes' peyote buds in all the world.'

'I can understand that,' Marvin said.

'Yet still,' Valdez said, more sternly, 'when an exploitator del norte insults me, and by implication, defames those who gave me birth and nurtured me – why then, señor, a blinding red mist descends over my field of vision and my knife springs to my hand unaided, and proceeds from there non-stop to the heart of the betrayer of the children of the poor.'

'It could happen to anyone,' Marvin said.

'And yet,' Valdez said, 'despite my keen sense of honour, I am essentially childlike, intuitive, and easygoing.'

'I had noticed that, as a matter of fact,' Marvin said.

'But yet. Enough of that. Now, you wish hire me investigation find girl? But of course. El buen pano en el arca se vende, verdad?'

'Si, hombre,' Marvin replied, laughing. 'Y el deseo vence al miedo!'

'Pues, adelante!' And arm in arm the two comrades marched out into the night of a thousand brilliant stars like the lance points of a mighty host.

Once outside the restaurant, Valdez turned his moustached brown face to the heavens and located the constellation Invidius, which, in northern latitudes, points unerringly to the north-north-east. With this as a base line, he established cross-references, using the wind on his cheek (blowing west at five miles per hour), and the moss on the trees (growing on the northerly sides of decidupis trunks at one millimetre per diem). He allowed for a westerly error of one foot per mile (drift), and a southerly error of five inches per hundred yards (combined tropism effects). Then, with all factors accounted for, he began walking in a south-south-westerly direction.

Marvin followed. Within an hour they had left the city, and were proceeding through a stubbled farming district. Another hour put them beyond the last signs of civilization, in a wilderness of tumbled granite and greasy feldspar.

Valdez showed no signs of stopping, and Marvin began to feel vague stirrings of doubt.

'Just where, exactly, are we going?' he asked at last.

'To find your Cathy,' Valdez replied, his teeth flashing white in his good-humoured burnt-sienna face.

'Does she really live this far from the city?'

'I have no idea where she lives,' Valdez replied, shrugging.

'You don't?'

'No, I don't.'

Marvin stopped abruptly. 'But you said that you did know!'

'I never said or implied that,' Valdez said, his umber forehead wrinkling. 'I said that I would help you find her.'

'But if you don't know where she lives-'

'It is quite unimportant,' Valdez said, holding up a stern musteline forefinger. 'Our quest has nothing to do with finding where Cathy lives; our quest, pure and simple, is to find Cathy. That, at least, was my understanding.'

'Yes, of course,' Marvin said. 'But if we're not going to where she lives, then where are we going?'

'To where she weel be,' Valdez replied serenely.

'Oh,' Marvin said.

They walked on through towering mineral marvels, coming at last into scrubby foothills that lay like tired walruses around the gleaming blue whale of a lofty mountain range. Another hour passed, and Marvin again grew disquieted. But this time he expressed his anxiety in a roundabout fashion, hoping by guile to gain insight.

'Have you known Cathy long?' he asked.

'I have never had the good fortune to meet her,' Valdez replied.

'Then you saw her for the first time in the restaurant with me?'

'Unfortunately I did not even see her there, since I was in the men's room passing a kidney stone during the time of your conversation with her. I may have caught a glimpse of her as she turned from you and departed, but more likely I saw only the Doppler effect produced by the swinging red door.'

'Then you know nothing whatsoever about Cathy?'

'Only the little I have heard from you, which, frankly, amounts to practically nothing.'

'Then how,' Marvin asked, 'can you possibly take me to where she will be?'

'It is simple enough,' Valdez said. 'A moment's reflection should clear the matter for you.'

Marvin reflected for several moments, but the matter stayed refractory.

'Consider it logically,' Valdez said. 'What is my problem? To find Cathy. What do I know about Cathy? Nothing.'

'That doesn't sound so good,' Marvin said.

'But it is only half of the problem. Granted that I know nothing about Cathy, what do I know about Finding?'

'What?' Marvin asked.

'It happens that I know everything about Finding,' Valdez said triumphantly, gesturing with his graceful terracotta hands. 'For it happens that I am an expert in the Theory of Searches!'

'The what?' Marvin asked.

'The Theory of Searches!' Valdez said, a little less triumphantly.

'I see.' Marvin said, unimpressed. 'Well … that's great, and I'm sure it's a very good theory. But if you don't know anything about Cathy, I don't see how any theory will help.'

Valdez sighed, not unpleasantly, and touched his moustache with a puce-coloured hand. 'My friend, if you knew all about Cathy – her habits, friends, desires, dislikes, hopes, fears, dreams, intentions. and the like – do you think you would be able to find her?'

'I'm sure I could,' Marvin said.

'Even without knowing the Theory of Searches?'

'Yes.'

'Well then,' Valdez said, 'apply that same reasoning to the reverse condition. I know all there is to know about the Theory of Searches, and therefore I need to know nothing about Cathy.'