'I think it's truer to say he discovered himself,' Hannant answered. 'It's as if he's only recently woken up to his town potential. A late starter, so to speak.' 'But one who's all set to overtake the rest of the runners in a flash, eh?'
'Ah!' said Hannant. Since Harmon hadn't yet said: anything about the results of Keogh's tests, he had half-feared that the boy had failed. Being called down here had reassured him a little, and now Harmon's remark about Keogh 'overtaking the rest' had clinched it. 'He passed then?
'Hannant smiled.
'No,' Harmon shook his head. 'He failed — miserably! ' The English paper let him down. He tried hard, I believe, but-'
Hannant's smile faded. His shoulders slumped a little. ' — but I'm taking him anyway,' Harmon finished, grinning again as Hannant's wide eyes came up once more to meet his. 'On the strength of what he did with the other papers.' 'What he did with them?'
Harmon nodded. 'I admit that I gave him the most difficult questions I could find — and he made mincemeat of them! If he has any fault at all, I'd say it was his unorthodox approach — if that in itself is a fault. It's just that he seems to dispense with all the customary ' formulae.'
Hannant nodded, made no comment, thought: / know exactly what you mean! And when he saw that Harmon was waiting, he said out loud, 'Oh, yes — he does that.'
'I thought it might just be Maths,' said the other, 'but it was just the same with the other paper. Call it "IQ" or "spatial" or whatever, it's mainly designed to test the potential of the intellect. I found his answer to one of the questions especially interesting; not the answer itself, you understand, which was absolutely correct anyway, but the way he arrived at it. It concerned a triangle.'
'Oh, yes?' Ah! Trig, Hannant thought, forking a piece of chicken into his mouth. / wondered how he'd do with that.
'Of course, it could have been solved with simple trigonometry,' (Harmon had almost read his mind,) 'or even visually — it was that simple. Indeed it was the only simple question in the batch. Here, let me show you:'
He pushed his plate aside, took out a pen and sketched on a paper napkin:
'Where AD is half AC, and AE is half AB, how much greater is the larger triangle than the smaller?' Hannant dotted the diagram so:
and said: four times greater. Visual, as you said.'
'Right. But Keogh simply wrote down the answer. No dotted lines, just the answer. I stopped him and asked: "How did you do that?" He shrugged and said: "A half times a half is a quarter — the smaller triangle is one quarter as great as the big one.'"
Hannant smiled, shrugged. 'That's typical of Keogh,' he said. 'It's what first attracted me to him. He ignores formulae, jumps gaps in the normal reasoning process, leaps from terminal to terminal.'
Harmon's expression hadn't changed. It was a very serious expression. 'What formulae?' he asked. 'Has he done Trig yet?'
Hannant's smile slipped. He frowned, paused with his fork half-way to his mouth. 'No, we were just starting.'
'So he wouldn't have known this formula anyway?'
'No, that's true,' Hannant's frown deepened.
'But he does now — and so do we!'
'Sorry?' Hannant had been left behind somewhere.
Harmon went on: 'I said to him, "Keogh, that's all very well, but what if it wasn't a right-angled triangle? What if it was like… this?"'
Again he sketched
‘ And I said to him,' Harmon continued, '"this time AD is half AB, but BE is only a quarter of BC." Well, Keogh just looked at it and said: "One eighth. Quarter times a half.' And then he did this
'What point are you trying to make?' Hannant found himself fascinated by the other's tense expression, if not by his subject. What was Harmon getting at?
'But isn't it obvious? This is a formula, and he'd figured it out for himself. And he'd done it during the examination!'
'It may not be as clever or inexplicable as you think,' Hannant shook his head. 'As I said, we were going to be starting on Trig in the near future. Keogh knew that. He may have done some reading in advance, that's all.'
'Oh?' said Harmon, and now he beamed, reached across the table and punched the other on the shoulder. 'Then do me a favour, George, and send me a copy of the text-book he's been swotting from, will you? I'd very much like to see it. You see, in all my years of teaching, that's a formula I never came across. Archimedes might well have known it, Euclid or Pythagorus, but I certainly didn't!'
'What?' Hannant stared again at the diagram, stared harder. 'But surely I know this? I mean, I understand Keogh's principle. Surely I've seen it before? I must have — Christ, I've been teaching Trig for twenty years!'
'My young friend,' said Harmon, 'so have I, and longer. Listen: I know all about sines, cosines, tangents — I fully understand trigonometrical ratios — I am as familiar with all the common or garden mathematical formulae as you yourself are. Probably more familiar. But I never saw a principle so clearly set forth, so brilliantly logical, so expertly… exposed! Exposed, yes, that's it! You can't say Keogh invented this because he didn't — no more than Newton invented gravity — or "discovered" it, as they say. No, for it's as constant as pi: it has always been there. But it took Keogh to show us it was there!' He shrugged defeatedly. 'How might I explain what I mean?'
'I know what you mean,' said Hannant. 'No need to explain further. It's what I told Jamieson: this thing of Keogh's for seeing right through the trees to the wood! But a formula…?' And suddenly, in the back of his mind:
Formulae? I could give you formulae you haven't even dreamed of…
'…Oh, but it is!' Harmon insisted, cutting in on Hannant's wandering thoughts. For a specific sort of question, certainly, but a formula nevertheless. And I ask myself, where to from here? Are there any more "basic principles" in him — principles we simply never stumbled on before — just waiting for the right stimulus? That's why I want him here at the Tech. So that I can find out.'
'Actually, I'm glad you're taking him,' said Hannant after a moment. He found himself on the verge of mentioning his disquiet concerning Keogh, then changed his mind and deliberately lied: 'I… don't think he can realise his full potential at Harden.'
'Yes, I see that,' Harmon answered, frowning. And then, a little impatiently: 'But of course we've already made that point. Anyway, you can rest assured that I shall do my utmost to develop his potential here. Indeed I will. But come on now, tell me about the lad himself. What do you know of his background?'
On his way back to Harden, at the wheel of his '67 Ford Cortina, Hannant reflected on what he'd told Harmon of Keogh's origins and upbringing. Most of it he'd had from the boy's aunt and uncle, with whom Keogh lived in Harden. His uncle had a grocery shop in the main street; his aunt was mainly a housewife, but she also helped out in the shop two or three days a week.
Keogh's grandfather had been Irish, moving from Dublin to Scotland in 1918 at the end of the war and working in Glasgow as a builder. His grandmother had been a Russian lady of some note, who fled the Revolution in 1920 and took up residence in an Edinburgh house close to the sea. There Sean Keogh met her, and in 1926 they'd been married. Three years later Harry's uncle Michael was born, and in 1931 his mother, Mary.
Sean Keogh had been hard on his son, apparently, bringing him into the building business (which he'd hated) and working him hard from the age of fourteen; but by comparison he had seemed literally to dote on his daughter, for whom nothing had ever been good enough. This had caused some jealousy between brother and sister, which came to an end when Michael was nineteen and ran off south to set himself up in a business of his own. Michael was the uncle Harry Keogh now lived with.