A Suitable Boy(109)

‘Er, I, have I, er, chosen a bad time – er –?’ he asked in his maddeningly slow voice.

‘Well, no – not, er, exactly –’ said Sunil. He liked Dr Durrani and was somewhat in awe of him. Dr Durrani was one of the two Fellows of the Royal Society that Brahmpur University could boast of, the other being Professor Ramaswami, the well-known physicist.

Dr Durrani did not even notice that Sunil was imitating his manner of speech; Sunil himself was still in an imitative mode after his kathak performance, and only noticed it himself after he had done it.

‘Er, well, Patwardhan, er, I do feel that, perhaps, I am, er, impinging?’ continued Dr Durrani. He had a strong square face, with a handsome white moustache, but scrunched up his eyes for punctuation every time he said ‘er’. This syllable also caused his eyebrows and the lower part of the skin on his forehead to move up and down.

‘No, no, Dr Durrani, of course not. Please do join us.’ Sunil led Dr Durrani to the centre of the room, planning to introduce him to the other guests. Dr Durrani and Sunil Patwardhan were a study in physical contrast despite the fact they were both rather tall.

‘Well, if you are, er, certain, you know, that I’m not going to, er, er, be in the way. You see,’ went on Dr Durrani more fluently but just as slowly, ‘what has been troubling me for the last day or so is this question of what you might call, er, super-operations. I – well, I – you see, I, um, thought that on the basis of all that, we could come up with several quite surprising series: you see, er –’

Such was the force of Dr Durrani’s innocent involvement in his magical world, and so uncensorious was he about the indecorous high jinks of his juniors, that they did not seem greatly put out by the fact that he had intruded on their evening.

‘Now you see, Patwardhan,’ – Dr Durrani treated the whole world on terms of gentle distance – ‘it isn’t just a question of 1, 3, 6, 10, 15 – which would be a, er, trivial series based on the, er, primary combinative operation – or even 1, 2, 6, 24, 120 – which would be based on the secondary combinative operation. It could go much, er, much further. The tertiary combinative operation would result in 1, 2, 9, 262144, and then 5 to the power of 262144. And of course that only, er, takes us to the fifth term in the, er, third such operation. Where will the, er, where will the steepness end?’ He looked both excited and distressed.

‘Ah,’ said Sunil, his whisky-rich mind not quite on the problem.

‘But of course what I am saying is, er, quite obvious. I didn’t mean to, er, er, trouble you with that. But I did think that I, er,’ – he looked around the room, his eye alighting on a cuckoo-clock on the wall – ‘that I would, well, pick your brains on something that might be quite, er, quite unintuitive. Now take 1, 4, 216, 72576 and so on. Does that surprise you?’

‘Well –’ said Sunil.

‘Ah!’ said Dr Durrani, ‘I thought not.’ He looked approvingly at his younger colleague, whose brains he often picked in this manner. ‘Well, well, well! Now shall I tell you what the impetus, the, er, catalyst, for all this, was?’

‘Oh, please do,’ said Sunil.

‘It was a, er, a remark – a very, er, perceptive remark of yours.’

‘Ah!’

‘You said, apropos the Pergolesi Lemma, “The concept will form a tree.” It was a, er, a brilliant comment – I never thought of it in those terms before.’

‘Oh –’ said Sunil.

Haresh winked at him, but Sunil frowned. Making deliberate fun of Dr Durrani was lèse majesté in his eyes.

‘And indeed,’ went on Dr Durrani generously, ‘though I was, er, blind to it at the time’ – he scrunched up his deep-set eyes almost into nothingness by way of unconscious illustration – ‘it, well, it does form a tree. An unprunable one.’

He saw in his mind’s eye a huge, proliferating, and – worst of all – uncontrollable banyan tree spreading over a flat landscape, and continued, with increasing distress and excitement: ‘Because whatever, er, method of super-operating is chosen – that is, type 1 or type 2 – it cannot, er, it cannot definitely be applied at each, er, at each stage. To choose a particular, well, clumping of types may, may… er, yes, it may indeed prune the branches but it will be too, er, arbitrary. The alternative will not yield a, er, consistent algorithm. So this, er, question arose in my, er, mind: how can one generalize it as one moves to higher operations?’ Dr Durrani, who tended to stoop slightly, now straightened up. Clearly, action was required in the face of these terrible uncertainties.