'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.'
'Are you sure it's the same thing?' Marvin asked.
'It has to be. After all, an equation is an equation. Solving from one end may take longer than from the other end, but cannot affect the outcome. In fact, we are really quite fortunate to know nothing about Cathy. Specific data sometimes has a way of interfering with the well-wrought operation of a theory. But we shall suffer no such discomfiture in this instance.'
They marched steadily upwards, across the steepening face of a mountain slope. A bitter wind screamed and buffeted at them, and patches of hoar-frost began to appear underfoot. Valdez talked about his researches into the Theory of Searches, citing the following typical cases: Hector looking for Lysander, Adam questing after Eve, Galahad reconnoitering for the Holy Grail, Fred C. Dobbs' seeking the Treasure of the Sierra Madre, Edwin Arlington Robinson's perquisitions for colloquial self-expression in a typically American milieu, Gordon Sly's investigations of Naiad McCarthy, energy's pursuit of entropy, God's hunt for man, and Yang's pursual of Yin.
'From these specifics,' Valdez said, 'we derive the general notion of Search and its most important corollaries.'
Marvin was too miserable to answer. It had suddenly occurred to him that one could die in this chill and waterless wasteland.
'Amusingly enough,' Valdez said, 'the Theory of Searches forces upon us the immediate conclusion that nothing can be truly (or ideally) lost. Consider: for a thing to be lost, it would require a place to be lost in. But no such place can be found, since simple multiplicity carries no implication of qualitative differentiation. In Search terms, every place is like every other place. Therefore, we replace the concept Lost with the concept of indeterminate placement, which, of course, is susceptible to logico-mathematical analysis.'
'But if Cathy isn't really lost,' Marvin said, 'then we can't really find her.'
'That statement is true, as far as it goes,' Valdez said. 'But of course, it is merely Ideal notion, and of little value in this instance. For operational purposes we must modify the Theory of Searches. In fact, we must reverse the major premise of the theory and reaccept the original concepts of Lost and Found.'
'It sounds very complicated,' Marvin said.
'The complication is more apparent than real,' Valdez reassured him. 'An analysis of the problem yields the result. We take the proposition: "Marvin searches for Cathy." That seems fairly to describe our situation, does it not?'
'I think it does,' Marvin said cautiously.
'Well then, what does the statement imply?'
'It implies – it implies that I search for Cathy.'
Valdez shook his nut-brown head in annoyance. 'Look deeper, my impatient young friend! Identity is not inference! The statement expresses the activity of your quest, and therefore implies the passivity of Cathy's state-of-being-lost. But this cannot be true. Her passivity is unacceptable, since ultimately one searches for oneself, and no one is exempt from that search. We must accept Cathy's search for you (herself), just as we accept your search for her (yourself). Thus we achieve our primary permutation: "Marvin searches for Cathy who searches for Marvin." '
'Do you really think she's looking for me?' Marvin asked.
'Of course she is, whether she knows it or not. After all, she is a person in her own right; she cannot be considered an Object, a mere something-lost.We must grant her autonomy, and realize that if you find her, then, equally, she finds you.'
'I never thought of that.' Marvin said,
'Well, it's simple enough once you understand the theory,' Valdez said. 'Now, to ensure our success, we must decide upon the optimum form of Search. Obviously, if both of you are actively questing, your chances of finding each other are considerably lessened. Consider two people seeking one another up and down the endless crowded aisles of a great department store, and contrast that with the improved strategy of one seeking, and the other standing at a fixed position and waiting to be found. The mathematics are a little intricate, so you will just have to take my word for it. The best chance of you/her finding her/you will be for one to search, and the other to allow himself /herself to be searched for. Our deepest folk wisdom has always known this, of course.'
'So what do we do?'
'I have just told you!' Valdez cried. 'One must search, the other must wait. Since we have no control over Cathy's actions, we assume that she is following her instincts and looking for you. Therefore you must fight down your instincts and wait, thereby allowing her to find you.'
'All I do is wait?'
'That's right.'
'And you really think she'll find me?'
'I would stake my life on it.'
'Well … all right. But in that case, where are we going now?'
'To a place where you will wait. Technically, it is called a Location-Point.'
Marvin looked confused, so Valdez explained further. 'Mathematically, all places are of equal potentiality insofar as the chances of her finding you are concerned. Therefore we are able to choose an arbitrary Location-Point.'
'What Location-Point have you chosen?' Marvin asked.
'Since it made no real difference,' Valdez said, 'I selected the village of Montana Verde de los Tres Picos, in Adelante Province, in the country of Lombrobia.'
'That's your home town, isn't it?' Marvin asked.
'As a matter of fact, it is,' Valdez said, mildly surprised and amused. 'That, I suppose, is why it came so quickly to my mind.'
'Isn't Lombrobia a long way off?'
'A considerable distance,' Valdez admitted. 'But our time will not be wasted, since I will teach you logic, and also the folksongs of my country.'
'It isn't fair,' Marvin muttered.
'My friend,' Valdez told him, 'when you accept help, you must be prepared to take what one is capable of giving, not what you would like to receive. I have never denied my human limitations; but it is ungrateful of you to refer to them.'
Marvin had to be content with that, since he didn't think he could find his way back to the city unaided. So they marched on through the mountains, and they sang many folksongs, but it was too cold for logic.
Onwards they marched, up the polished mirror face of a vast mountain. The wind whistled and screamed, tore at their clothing and tugged at their straining fingers. Treacherous honeycomb ice crumpled under their feet as they struggled for footholds, their buffeted bodies plastered to the icy mountain wall and moving leechlike up its dazzling surface.
Valdez bore up through it all with a saintlike equanimity. 'Eet ees deefecult,' he grinned. 'And yet – for the love which you bear for thees woman – eet ees all worthwhile, sí?'