Necroscope

'Oh, yes?' Ah! Trig, Ha

'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?' Ha

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.'"

Ha

Harmon's expression hadn't changed. It was a very serious expression. 'What formulae?' he asked. 'Has he done Trig yet?'

Ha

'So he wouldn't have known this formula anyway?'

'No, that's true,' Ha

'But he does now - and so do we!'

'Sorry?' Ha

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?' Ha

'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,' Ha

'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?' Ha

'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 Ha

Formulae? I could give you formulae you haven't even dreamed of...

'...Oh, but it is!' Harmon insisted, cutting in on Ha

'Actually, I'm glad you're taking him,' said Ha

'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, Ha

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.

By the time Mary Keogh was twenty-one, however, her father's doting had turned to a fierce possessiveness which totally shut her off from any sort of social life, so that she stayed mainly at home and helped with the housework, or assisted her aristocratic Russian mother in the small psychic circle she had built up, when she would attend and regularly take part in those stances for which Natasha Keogh had become something of a local celebrity.

Then, in the summer of '53, Scan Keogh had been killed when an unsafe wall he was working on fell on him. His wife, who for all that she was not yet fifty was already ailing, had sold the business and gone into semi-retirement, holding the occasional seance to eke out her living, which now mainly derived from the interest on banked money. For Mary, on the other hand, the death of her father had heralded a hitherto undreamed-of freedom; quite literally, a 'coming out'.