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.