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avevale_intelligencer"Or," Powers went on, still giggling sporadically, "take imaginary numbers." He staggered over to a barrel of water in a corner of the tent, plunged his head in and made plumbing noises for a moment, then straightened up and shook his head, drenching Zander and Rob as his hair flew. "It's a tiresome old saw these days that you're entitled to your own opinions but not to your own facts. I think it's fairly safe to say that in the practical sphere there is no branch of mathematics in which making up your own numbers will do anything but get you into trouble. And yet, what is i? What is it but the ultimate made-up number, the quintessential fudge, a number which cannot exist even in the limited and semi-abstract sense in which other numbers exist? We can imagine huge whole numbers. We're okay with fractions. We have a dim, nebulous sort of idea about negative numbers. But a number that by the very laws of the universe cannot exist..." He shook his head again. "And then they say you can't make up your own facts. It's either wilful blindness or sheer hypocrisy."
"But, my dear old demiurgic sausage," Rob said patiently, "the fudge works. It's had practical applications, in electronics, aeronautics..."
"Oh yes, fudges often work," Powers sneered. "I can't see why anyone would use them otherwise; but they're short cuts, and people who get into the habit of taking short cuts often miss learning what the long way round can teach them. You invent a number to make your equations work out, and you never find out that there's a way to get the same result without flouting common sense and all logic--a way that might lead to new discoveries and new thinking." He snorted. "Laziness."
"Progress is made by lazy men trying to find easier ways to do things," Zander quoted. "Anyway, suppose there isn't another way?"
"Natural laws again," Powers said at once. "If there's no way to do something without breaking a natural law, such as the one that says that any two negative numbers multiplied must of force produce a positive result, then it can't be done. Since it can be done..." He spread his hands. "There must be a legal way to do it."
"And do you know this way?" Rob challenged, and had the satisfaction of seeing Powers look shifty.
"I was never mathematically minded," he said. "You want Dicecaster for that. But that's not my point." He rallied himself. "Suppose, then, that it's all all right, that imaginary numbers are actually part of the universal framework, a necessary part to make natural processes work. It doesn't make sense, but as a great showman once remarked, the universe is under no obligation to make sense to you or anyone."
"Well, then what?" Rob said into the lengthening silence.
"Then," Powers said triumphantly, "isn't that the final, clinching, conclusive and irrefragable proof that within and behind the great construction that is the real physical universe in which our friend here lives--as opposed to this mere secondary creation--there must also be, there has to be, an Imagination?"
Further discussion was shelved at this point as Timmaeus Agrael, Gautama R Melies and Magus A Realtime burst into the tent, closely followed by Grovel announcing lunch. The three archangels, who had expected to find Powers gone, were full of questions, expostulations and cheap jokes, each according to his way, and Zander and Rob allowed themselves to be distracted.
The hedgehogs waited patiently. Their time would come.
"But, my dear old demiurgic sausage," Rob said patiently, "the fudge works. It's had practical applications, in electronics, aeronautics..."
"Oh yes, fudges often work," Powers sneered. "I can't see why anyone would use them otherwise; but they're short cuts, and people who get into the habit of taking short cuts often miss learning what the long way round can teach them. You invent a number to make your equations work out, and you never find out that there's a way to get the same result without flouting common sense and all logic--a way that might lead to new discoveries and new thinking." He snorted. "Laziness."
"Progress is made by lazy men trying to find easier ways to do things," Zander quoted. "Anyway, suppose there isn't another way?"
"Natural laws again," Powers said at once. "If there's no way to do something without breaking a natural law, such as the one that says that any two negative numbers multiplied must of force produce a positive result, then it can't be done. Since it can be done..." He spread his hands. "There must be a legal way to do it."
"And do you know this way?" Rob challenged, and had the satisfaction of seeing Powers look shifty.
"I was never mathematically minded," he said. "You want Dicecaster for that. But that's not my point." He rallied himself. "Suppose, then, that it's all all right, that imaginary numbers are actually part of the universal framework, a necessary part to make natural processes work. It doesn't make sense, but as a great showman once remarked, the universe is under no obligation to make sense to you or anyone."
"Well, then what?" Rob said into the lengthening silence.
"Then," Powers said triumphantly, "isn't that the final, clinching, conclusive and irrefragable proof that within and behind the great construction that is the real physical universe in which our friend here lives--as opposed to this mere secondary creation--there must also be, there has to be, an Imagination?"
Further discussion was shelved at this point as Timmaeus Agrael, Gautama R Melies and Magus A Realtime burst into the tent, closely followed by Grovel announcing lunch. The three archangels, who had expected to find Powers gone, were full of questions, expostulations and cheap jokes, each according to his way, and Zander and Rob allowed themselves to be distracted.
The hedgehogs waited patiently. Their time would come.