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Spaceways, v. 4, issue 5, whole no. 28, June 1942
Page 22
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22 SPACEWAYS THE READERS ALWAYS WRITE be called the 4th., since a whole system of solid geometry has been built up which uses the three spatial dimensions as the first three, and to change around to calling them the 2nd., 3rd., and 4th., would serve no end other than to cause a huge amount of needless confusion). 2nd., then, is length; but you might just as well call it "width", because each of them is just a single spatial dimension in itself. Let two spatial dimensions intersect at any angle and you have a two-dimensional plane--existing, once more, in time. Let a third intersect the plane and you have a three-dimensional solid existing in the fourth dimension of time. That's the most convenient way of looking at it, I think. The simplest case, of course, occurs when the first two dimensions of length, represented by straight lines, intersect at right-angles; and the third dimension of length - call it "height" or "depth" if you will--intersects the plane thus formed at right angles. Fill in six planes in those three dimensions and you have a cuboid: a three-dimensional solid existing in a 4th. dimension of time. All this is as simple as ABC and not yet in the realm of the more complex subject called four-dimensional mathematics. " In what respects, then, does Fortier talk no sense at all? Firstly, as I said, time is more conveniently supposed to be the 4th., not the 1st. Secondly, width is a dimension exactly the same as length, and so, again, is height. A line--supposed, for the purposes of theory, to have no thickness--is the example of a one-dimensional object, existing in time. (JFF is quite entitled to call it two-dimensional if he likes, but it's only confusing.) Similarly a point--of negligible or (theoretically) no size--is a no-dimensional object (no spacial dimensions, that is) and yet could exist in time. To show most conveniently how length and width and height are interchangeable, consider a cube. Rotate it any way about any axis, and it's still the same. What was its "length" dimension before is now its "height" dimension. (This applies to any 3-dimensional object, of course, bu tis less easy to see.) Or take a one-dimensional line, with length but no thickness, pointing north. Rotate it 90[[degree symbol]], but keep looking N yourself. From that point of view it now has width (distance in an E-W direction--the same distance as was formerly its length), but no length (distance N-S). Now turn yourself round to face E and you can again (if you want) consider it as before. Same with height. All three spacial dimensions are of the same order--it's all in the point of view whether you label them "length", "width", or "height". This is an important fallacy in Joe's 1-2-3--5th. paragraph; important not in itself (it's elementary), but in that it shows he's given the matter only the most superficial thought and has no right to go blowing off his mouth as if he'd discovered something important. Of course we're living in four dimensions--any twirp can see that. The real problems are much more abtruse and interesting, which is why it annoys me so to see him kicking up such a fuss. " Oh, I could go on: he drivels like hell. But I daresay someone who knows the ground will have shown you the light. If no-one has, it's a bloody disgrace. This talk of flat-landers living in the "third" dimension, for instance. Nothing of the sort. Flat-landers would live on a world of two spatial dimensions, through the dimension of time, and not on a single dimension at all. And "volume is....the fourth". Tripe. Volume is a means of measuring the amount of space enclosed within a solid of three spacial dimensions; to say that it itself is a single dimension is ridiculous. And it's such an interesting subject, really--both the extensions of this and the interesting science of perception. Oh, I could weep. But maybe I'll tell you about it someday. Louis Russell Chauvenet, 1920 Thomson Road, Charlottesville, Virginia, remarks: Farnsworth's poem: 5. Lowndes poem: Also 5. Neither of these is satisfying; they are inadequate for different reasons. Farnsworth is trite in words and his meter limps haltingly. Lowndes is too arty; there is no genuine feeling or emotion perceptible in his sonnet. The idea is but an idle speculation of no apparent significance to the one voicing it. At least, none appears in the poem. The approach is too intellectual; the emphasis too heavily on the mere
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22 SPACEWAYS THE READERS ALWAYS WRITE be called the 4th., since a whole system of solid geometry has been built up which uses the three spatial dimensions as the first three, and to change around to calling them the 2nd., 3rd., and 4th., would serve no end other than to cause a huge amount of needless confusion). 2nd., then, is length; but you might just as well call it "width", because each of them is just a single spatial dimension in itself. Let two spatial dimensions intersect at any angle and you have a two-dimensional plane--existing, once more, in time. Let a third intersect the plane and you have a three-dimensional solid existing in the fourth dimension of time. That's the most convenient way of looking at it, I think. The simplest case, of course, occurs when the first two dimensions of length, represented by straight lines, intersect at right-angles; and the third dimension of length - call it "height" or "depth" if you will--intersects the plane thus formed at right angles. Fill in six planes in those three dimensions and you have a cuboid: a three-dimensional solid existing in a 4th. dimension of time. All this is as simple as ABC and not yet in the realm of the more complex subject called four-dimensional mathematics. " In what respects, then, does Fortier talk no sense at all? Firstly, as I said, time is more conveniently supposed to be the 4th., not the 1st. Secondly, width is a dimension exactly the same as length, and so, again, is height. A line--supposed, for the purposes of theory, to have no thickness--is the example of a one-dimensional object, existing in time. (JFF is quite entitled to call it two-dimensional if he likes, but it's only confusing.) Similarly a point--of negligible or (theoretically) no size--is a no-dimensional object (no spacial dimensions, that is) and yet could exist in time. To show most conveniently how length and width and height are interchangeable, consider a cube. Rotate it any way about any axis, and it's still the same. What was its "length" dimension before is now its "height" dimension. (This applies to any 3-dimensional object, of course, bu tis less easy to see.) Or take a one-dimensional line, with length but no thickness, pointing north. Rotate it 90[[degree symbol]], but keep looking N yourself. From that point of view it now has width (distance in an E-W direction--the same distance as was formerly its length), but no length (distance N-S). Now turn yourself round to face E and you can again (if you want) consider it as before. Same with height. All three spacial dimensions are of the same order--it's all in the point of view whether you label them "length", "width", or "height". This is an important fallacy in Joe's 1-2-3--5th. paragraph; important not in itself (it's elementary), but in that it shows he's given the matter only the most superficial thought and has no right to go blowing off his mouth as if he'd discovered something important. Of course we're living in four dimensions--any twirp can see that. The real problems are much more abtruse and interesting, which is why it annoys me so to see him kicking up such a fuss. " Oh, I could go on: he drivels like hell. But I daresay someone who knows the ground will have shown you the light. If no-one has, it's a bloody disgrace. This talk of flat-landers living in the "third" dimension, for instance. Nothing of the sort. Flat-landers would live on a world of two spatial dimensions, through the dimension of time, and not on a single dimension at all. And "volume is....the fourth". Tripe. Volume is a means of measuring the amount of space enclosed within a solid of three spacial dimensions; to say that it itself is a single dimension is ridiculous. And it's such an interesting subject, really--both the extensions of this and the interesting science of perception. Oh, I could weep. But maybe I'll tell you about it someday. Louis Russell Chauvenet, 1920 Thomson Road, Charlottesville, Virginia, remarks: Farnsworth's poem: 5. Lowndes poem: Also 5. Neither of these is satisfying; they are inadequate for different reasons. Farnsworth is trite in words and his meter limps haltingly. Lowndes is too arty; there is no genuine feeling or emotion perceptible in his sonnet. The idea is but an idle speculation of no apparent significance to the one voicing it. At least, none appears in the poem. The approach is too intellectual; the emphasis too heavily on the mere
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