northern Africa) as she could enclose with a bullâs hide. She cut it into a very long, thin strip and enclosed a circle. There she founded the city of Carthage. Why did she choose a circle? Because the circle is the shape with greatest area, for a given perimeter. In the same way, a sphere is the shape with greatest volume, for a given surface area; or, to put it another way, it is the shape with the smallest surface area that contains a given volume. A soap bubble contains a fixed volume of air, and its surface area gives the energy of the soap film due to surface tension. In the space of all possible shapes for bubbles, the one with the least energy is a sphere. All other shapes have larger energy, and are therefore ruled out.
You may not feel that bubbles are important. But the same principle explains why Roundworld (the planet not the universe, but maybe that, too) is round. When it was molten rock, it settled into a spherical shape, because that had the least energy. For the same reason, the heavy materials like iron sank into the core, and the lighter ones, like continents and air, floated up to the top. Actually, Roundworld isnât exactly a sphere, because it rotates, so centrifugal forces cause it to bulge at the equator. But the amount of bulge is only one-third of one per cent. And that bulging shape is the minimum-energy configuration for a mass of liquid spinning at the same speed as the Earthâs rotation when it was just starting to solidify.
The physics here isnât important for the message of this book. What is important is the âWorlds of Ifâ point of view involved in the application of phase spaces. When we discussed the shape of water in a pond, we pretty much ignored the flat surface, the thing we were trying to explain. The entire argument hinged upon non-flat surfaces, humps and dips, and hypothetical transfers of water from one to the other. Almost all of the explanation involved thinking about things that donât actually happen. Only at the end, having ruled out all non-flat surfaces, did we observe that the only possibility left was therefore what the water would actually do. The same goes for the bubble.
At first sight, this might seem to be a very oblique way of doing physics. It takes the stance that the way to understand the real world is to ignore it, and focus instead on all the possible alternative unreal worlds. Then we find some principle (in this case, minimum energy) to rule out nearly all of the unreal worlds, and see whatâs left. Wouldnât it be easier to start with the real world, and focus solely on that? No, it wouldnât. As weâve just seen, the real world alone is too limited to offer a convincing explanation. What you get from the real world alone is âthe world is like it is, and thereâs nothing more to be saidâ. However, if you take the imaginative leap of considering unreal worlds, too, you can compare the real world with all of those unreal worlds, and maybe find a principle that picks out the real one from all the others. Then you have answered the question â Why is the world the way it is, rather than something else?â
An excellent way to approach âwhyâ questions is to consider alternatives and rule them out. âWhy did you park the car round the corner down a side-street?â âBecause if Iâd parked outside the front door on the double yellow lines, a traffic warden would have given me a parking ticket.â This particular âwhyâ question is a story, a piece of fiction: a hypothetical discussion of the likely consequences of an action that never occurred. Humans invented their own brand of narrativium as an aid to the exploration of I-space, the space of âinsteadsâ. Narrative provides I-space with a geography: if I did this instead of that, then what would happen would be â¦
On Discworld, phase spaces are real. The fictitious alternatives to the one actual
You may not feel that bubbles are important. But the same principle explains why Roundworld (the planet not the universe, but maybe that, too) is round. When it was molten rock, it settled into a spherical shape, because that had the least energy. For the same reason, the heavy materials like iron sank into the core, and the lighter ones, like continents and air, floated up to the top. Actually, Roundworld isnât exactly a sphere, because it rotates, so centrifugal forces cause it to bulge at the equator. But the amount of bulge is only one-third of one per cent. And that bulging shape is the minimum-energy configuration for a mass of liquid spinning at the same speed as the Earthâs rotation when it was just starting to solidify.
The physics here isnât important for the message of this book. What is important is the âWorlds of Ifâ point of view involved in the application of phase spaces. When we discussed the shape of water in a pond, we pretty much ignored the flat surface, the thing we were trying to explain. The entire argument hinged upon non-flat surfaces, humps and dips, and hypothetical transfers of water from one to the other. Almost all of the explanation involved thinking about things that donât actually happen. Only at the end, having ruled out all non-flat surfaces, did we observe that the only possibility left was therefore what the water would actually do. The same goes for the bubble.
At first sight, this might seem to be a very oblique way of doing physics. It takes the stance that the way to understand the real world is to ignore it, and focus instead on all the possible alternative unreal worlds. Then we find some principle (in this case, minimum energy) to rule out nearly all of the unreal worlds, and see whatâs left. Wouldnât it be easier to start with the real world, and focus solely on that? No, it wouldnât. As weâve just seen, the real world alone is too limited to offer a convincing explanation. What you get from the real world alone is âthe world is like it is, and thereâs nothing more to be saidâ. However, if you take the imaginative leap of considering unreal worlds, too, you can compare the real world with all of those unreal worlds, and maybe find a principle that picks out the real one from all the others. Then you have answered the question â Why is the world the way it is, rather than something else?â
An excellent way to approach âwhyâ questions is to consider alternatives and rule them out. âWhy did you park the car round the corner down a side-street?â âBecause if Iâd parked outside the front door on the double yellow lines, a traffic warden would have given me a parking ticket.â This particular âwhyâ question is a story, a piece of fiction: a hypothetical discussion of the likely consequences of an action that never occurred. Humans invented their own brand of narrativium as an aid to the exploration of I-space, the space of âinsteadsâ. Narrative provides I-space with a geography: if I did this instead of that, then what would happen would be â¦
On Discworld, phase spaces are real. The fictitious alternatives to the one actual
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