The Unorthodox Engineers

‘You know, Fritz, I’m beginning to get sorry I came.’ Jacko looked at Van Noon appealingly. ‘Can’t I just go home and sleep it off?’

‘Try closing your eyes, Jacko. Maybe it’ll go away.’

‘I tried that,’ said Wooley. ‘But it comes back every morning, large as sunrise.’

‘Well, what is the Ixion problem?’ Van Noon asked. ‘The one thing I haven’t been    able to    do is    get anyone to talk about it.’

‘Wait till you’ve seen it for yourself. I don’t think you’ll want to talk about it either.’

They were approaching a stockpile of carefully classified girderwork, part of the Ixion turntable structure recovered from spacedrop capsules. Wooley consulted a parts list, then drew a few sections from the stockpile and dropped them on the ground.

‘A simple demonstration. Girder A measures two metres exactly between hole centres. Don’t take my word for it—check it out.’

Jacko produced a steel tape from the recesses of one of his pockets and made the necessary measurement.

‘Two metres—check!’

‘Girders B and C each measure one metre between hole centres, yes?’

‘Check!’ Jacko looked at Fritz as if seeking release from the infantile nature of what    was    being demanded.

‘Very well!’ Wooley was unperturbed. ‘If you assemble girder B to girder C, end to end with a suitable rivet, the total length between extreme hole centres should be two metres. Right?’

‘Right.’

‘Wrong,’ said Wooley sadly. He dropped a rivet on to the ground and waited while Jacko moved the components into line and fitted the fastening loosely into the holes. ‘If you don’t believe me, measure it yourself.’

There was no need for measurement. Even viewed from a standing position the combined length of the two half girders was obviously much less than that of the whole one. Refusing to believe the evidence of his eyes, Jacko knelt and carefully measured the combined length of girders B and C.

‘One point five seven,’ he said hopelessly. Again refusing to accept the sum, he kicked the girders apart and checked each carefully before re-assembly. Fritz, who had watched the whole performance with detailed interest, seemed to have withdrawn into a state of deep concentration. At last he took the offered measuring tape from Jacko and repeated the whole ritual for himself. Intrigued by the situation, he found several other objects and measured them individually and together. Then he straightened.

‘Incredible,’ he said, ‘but very definitely true.’

‘Then explain it to me,’ said Jacko. ‘In all my books twice one is two—and it’s never before been in dispute.’

‘But your books were written on Terra, not Getawehi. On Getawehi they don’t apply.’

‘But that’s insane!’ Jacko was adamant. ‘Mathematics is merely a system for expressing the properties and relations of quantities. It’s universal, not a local phenomenon. Once one is one, twice one is two…

Van Noon rapidly reviewed his previous calculations.

‘Not on Getawehi. It seems to be different here. Once one is one… but twice one is only a bit over one and a half—one point five seven zero eight, to be more exact. And three times one is about two point three six.’

‘Wooley, you don’t agree…?’ Jacko was still fighting. The look on Wooley’s face, however, convinced him that the battle was lost. ‘I still don’t see how it’s possible,’ he finished lamely.

‘It’s long been suspected that our mathematics may not be universal,’ said Fritz. ‘Dimensionless numbers, for instance, although having an accepted value in the part of the universe where we customarily use them, are more likely to be local coincidences than physical absolutes. But on Getawehi we seem to have hit on something even more fundamental.’

‘Such as?’

‘I’m not sure yet, but for my money it’s something to do with unity.’

‘Unity?’

‘Yes. Unity… one… a whole. I’m no mathematician, but it seems to me there’s a darn great hole in our idea of the structure of numbers. We’ve explored number structure up to infinity and several orders beyond—but something we’ve always taken for granted is the constant mathematical value of unity.’

‘But it has to have a constant mathematical value.’ Jacko’s voice was ragged. ‘Once one is one… It can’t be otherwise by its very definition.’

‘So we’ve always assumed. But what if we happened to be wrong? What if there’s a difference between the value of one as representing a whole thing—and the value of one as a mathematical factor. They seem both to be the same in the corner of the universe where our books were written—but one used as a factor on Getawehi is demonstrably only point seven eight five of what it was on Terra.’

‘You’re not right, you know, Fritz. I’ll prove it to you.’

‘How?’

‘Take a metre length of iron, cut it in half and then join it together again. By your reasoning we should finish up with a total length only a little above three-quarters of what we started with.’

‘Let’s try it,’ said Van Noon. ‘We have to settle this one way or the other before we all go merrily insane.’

Wooley provided welding equipment, and they tried it. The final measurement was a little over point seven eight of a metre.

‘But I still don’t see how you can reconcile it with the law of conservation of matter,’ said Jacko.

‘Where do you keep the Scotch?’ asked Fritz Van Noon.

‘So what are we going to do with Project Ixion?’ asked Jacko the next day.

‘I’ve been thinking,’ said Fritz. ‘It’s not going to be easy even if it proves possible. The Ixion assembly is a pretty complex girderwork construction. Every part has to be accurate if it’s going to fit. My first thoughts are to take every girder, cut it in half, and re-join. In that way we might be able to construct what is, in effect, a scaled- down version of the original design.’

‘Is that acceptable?’ asked Jacko. ‘Surely some of the parts have a critical size.’

‘I don’t know. I tried to put this question to the Tycho Brahe, but I don’t think my message was received. Apparently the pinnace can hold our position by line of sight, but it’s not easy for us to track the pinnace because of its unstable orbit. Anyway, I suspect this is a problem for the design team on Terra rather than something which can be settled on the Tycho.’

‘Then you want me to try cutting and joining the girders?’

‘We’d better have a go. We certainly can’t make matters any worse than they are. I’ve a suspicion, however, that the problem isn’t going to be solved that simply.’

‘You’re the boss!’ said Jacko. ‘I still can’t convince myself that it happens at all, but at least we’ll go through the motions.’

Six hours later Jacko found Van Noon crouching at the laser terminal trying to maintain sighting on the pinnace. Such was the relative crudity of the ground terminal that sighting on a small and erratic spaceborne target such as the pinnace was so precarious as to be nearly impossible.

Jacko shook his head wearily. ‘Project Ixion’s no go, Fritz. We’ve tried cutting and joining the girders, but it doesn’t help. Where the assembly calls for a total span to be formed of thirty components along one edge and only five in another, the whole scheme falls down. Short of cutting every girder into the total number of parts required to form the entire project—and then re-joining them—we don’t stand a chance of getting anything to fit.’

Van Noon stood up. ‘I was rather afraid of that. We’d need God-knows how much computer down here to calculate the operations needed to resurrect the original design, and even then we’ve no guarantee that the final de-scaled assembly would do the job it was designed to do.’

‘Is it worth continuing with the work?’

‘No. Abandon the whole thing. There has to be a more rational way out of this. As far as I can see, Ixion in its present form is destined to be a dead duck. I wonder where the heck they found a name like that for it anyway?’