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"Human beings," Powers began.
"Aha," said Rob. "I sense a bout of demiurge-splaining coming on. All right then, maestro, tell us about ourselves. We're all agog." He mimed disco dancing. "Agog a go-go, you might say."
"Children," Powers muttered darkly. "Human beings, as I was saying, possess the faculty of imagination, and that's a great thing. God, if god is anything, might be described as one vast and vivid imagination, and that's what the Bible means when it talks about you being made in God's image. Imagination is the central thing; all the rest is support mechanism. If you have one fault, and believe me you have many, it's your tendency to imagine that what you imagine is real, just because it helps you to deal with reality.
"Pi, the number, is a real thing. Circles exist in nature, though very few of them are perfect, and humans can create circles as well, and sometimes even they are perfect. Incidentally, that thing about the Bible saying pi is 3 is nonsense; all it's saying is that something was perfectly circular when it was actually ever so slightly oval and nobody had the heart to mention it. But wherever there is a perfect circle, the ratio between its diameter and its circumference will be a number expressed as pi in the units used for the two measurements. It's a real number. You could go into a supermarket and buy approximately pi ounces of cooked ham or something, though it would have to be approximate.
"i, on the other hand, is the result of imagination enabled by logic. All numbers have square roots, minus one is a number, therefore minus one must have a square root. And it's been very useful in helping you think about things like fluid dynamics and electromagnetism, which are real things. But it's not real. You can't go into a supermarket and get i ounces of cooked ham. i is not the same kind of thing as pi."
"Name, Ethan Powers," Zander murmured, "specialist subject, the frodding obvious."
"And you can imagine," the demiurge continued, "in a nebulous sort of way, a universe in which everything is simultaneously moving away from everything else, even though you have to reimagine that universe as something like the skin of an inflating balloon to do so. And that was the great discovery which lies at the heart of relativity; a brilliant effort of imagination. You didn't discover that there wasn't an absolute frame of reference; you imagined the universe without one and found that the sums still worked, and William of Occam did the rest.
"But the skin of a balloon metaphor still has a point of origin built into it; the centre of the volume of air inside the balloon. Anything that expands measurably in all directions has to have a point of origin from which that expansion starts. If everything in the universe were truly expanding at the same rate from its own centre, there would be no relative motion, and no way of detecting such expansion, because the measuring devices would be expanding at the same rate. Since there is relative motion, there must be a point at which all such motion began. If things are measurably moving apart, there was a time and a place when they were closer together.
"The expansion of the universe--all motion--is a pi thing. It's real and measurable. Relativity turns it into an i thing, a thing that can be imagined, like a TARDIS or a box that contains all boxes, but that doesn't make sense. The sums work to a point, of course they do, but that's because you're doing such limited things with them. Only when you get past relativity and its quantumy offspring, to the next great pi-type discovery, will some of the answers to the unanswered questions--and you know there are loads of those--start to fall into place. Want to know where all the missing matter is? Start by assuming that it isn't missing. That kind of thing. Imagination is the most important quality a scientist can have, it's the mainspring of all discovery, but it can lead you down alleys that leave you so blind you can't even tell you've stopped moving."
"Lacking an absolute frame of reference, perhaps," Rob murmured. "Some day," he told Zander, "you're going to find out that this chap is nothing but a cheap carnival fakir with a plausible line in patter. He obviously knows no more about science than you do."
"Yes, that would follow," Zander said. "But then, no more do you. I can imagine you both as experts, and listening to you argue certainly helps me think, but it's not real. Anyway, he's just miffed because the hedgehogs went on a two-year sabbatical to Angkor Wat and didn't invite him."
"I could have been invaluable," Powers muttered.
"Yes, but you so rarely are."
Powers was still trying to come up with a riposte when a mass of white, creamy goop impacted on his face, closely followed by the paper plate to which it was adhering. Zander tracked the object in motion back to its point of origin. At the flap of the tent, three small, lithe, tanned and above all spiky figures in Hawaiian shirts and sunglasses beamed, waved and went "whee!"
"They're back," Rob announced unnecessarily.
"Aha," said Rob. "I sense a bout of demiurge-splaining coming on. All right then, maestro, tell us about ourselves. We're all agog." He mimed disco dancing. "Agog a go-go, you might say."
"Children," Powers muttered darkly. "Human beings, as I was saying, possess the faculty of imagination, and that's a great thing. God, if god is anything, might be described as one vast and vivid imagination, and that's what the Bible means when it talks about you being made in God's image. Imagination is the central thing; all the rest is support mechanism. If you have one fault, and believe me you have many, it's your tendency to imagine that what you imagine is real, just because it helps you to deal with reality.
"Pi, the number, is a real thing. Circles exist in nature, though very few of them are perfect, and humans can create circles as well, and sometimes even they are perfect. Incidentally, that thing about the Bible saying pi is 3 is nonsense; all it's saying is that something was perfectly circular when it was actually ever so slightly oval and nobody had the heart to mention it. But wherever there is a perfect circle, the ratio between its diameter and its circumference will be a number expressed as pi in the units used for the two measurements. It's a real number. You could go into a supermarket and buy approximately pi ounces of cooked ham or something, though it would have to be approximate.
"i, on the other hand, is the result of imagination enabled by logic. All numbers have square roots, minus one is a number, therefore minus one must have a square root. And it's been very useful in helping you think about things like fluid dynamics and electromagnetism, which are real things. But it's not real. You can't go into a supermarket and get i ounces of cooked ham. i is not the same kind of thing as pi."
"Name, Ethan Powers," Zander murmured, "specialist subject, the frodding obvious."
"And you can imagine," the demiurge continued, "in a nebulous sort of way, a universe in which everything is simultaneously moving away from everything else, even though you have to reimagine that universe as something like the skin of an inflating balloon to do so. And that was the great discovery which lies at the heart of relativity; a brilliant effort of imagination. You didn't discover that there wasn't an absolute frame of reference; you imagined the universe without one and found that the sums still worked, and William of Occam did the rest.
"But the skin of a balloon metaphor still has a point of origin built into it; the centre of the volume of air inside the balloon. Anything that expands measurably in all directions has to have a point of origin from which that expansion starts. If everything in the universe were truly expanding at the same rate from its own centre, there would be no relative motion, and no way of detecting such expansion, because the measuring devices would be expanding at the same rate. Since there is relative motion, there must be a point at which all such motion began. If things are measurably moving apart, there was a time and a place when they were closer together.
"The expansion of the universe--all motion--is a pi thing. It's real and measurable. Relativity turns it into an i thing, a thing that can be imagined, like a TARDIS or a box that contains all boxes, but that doesn't make sense. The sums work to a point, of course they do, but that's because you're doing such limited things with them. Only when you get past relativity and its quantumy offspring, to the next great pi-type discovery, will some of the answers to the unanswered questions--and you know there are loads of those--start to fall into place. Want to know where all the missing matter is? Start by assuming that it isn't missing. That kind of thing. Imagination is the most important quality a scientist can have, it's the mainspring of all discovery, but it can lead you down alleys that leave you so blind you can't even tell you've stopped moving."
"Lacking an absolute frame of reference, perhaps," Rob murmured. "Some day," he told Zander, "you're going to find out that this chap is nothing but a cheap carnival fakir with a plausible line in patter. He obviously knows no more about science than you do."
"Yes, that would follow," Zander said. "But then, no more do you. I can imagine you both as experts, and listening to you argue certainly helps me think, but it's not real. Anyway, he's just miffed because the hedgehogs went on a two-year sabbatical to Angkor Wat and didn't invite him."
"I could have been invaluable," Powers muttered.
"Yes, but you so rarely are."
Powers was still trying to come up with a riposte when a mass of white, creamy goop impacted on his face, closely followed by the paper plate to which it was adhering. Zander tracked the object in motion back to its point of origin. At the flap of the tent, three small, lithe, tanned and above all spiky figures in Hawaiian shirts and sunglasses beamed, waved and went "whee!"
"They're back," Rob announced unnecessarily.