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Lyle Zapato

Walking Downhill Perpetually To Prosperity

Lyle Zapato | 2004-05-29.0000 LMT | Technology

In The Two Towers, Treebeard the talking, walking tree muses that he always likes going south because it somehow feels like going downhill. While meant as folksy humor, this actually isn't far from the truth (at least in the northern hemisphere, where presumably all the talking, walking trees live).

As one walks across the surface of a spinning planet toward its equator, one is moving farther away from the planet's axis of rotation, meaning one is traveling at a greater speed around it and is thus experiencing stronger centrifugal force -- the pseudoforce pushing objects away from the center of rotation that is really the consequence of the conservation of momentum. As the centrifugal force increases, the centripetal force of gravity remains relatively constant (in reality, planets bulge at the equator, so gravity is slightly greater,) resulting in a decrease in gravity's subjective effect. Therefore, walking south while in the northern hemisphere becomes progressively easier since one weighs less with each step (that is until one hits the equator, then it gets progressively harder until one hits the south pole and it becomes impossible). The difference in effort is, of course, not consciously perceptible to us, although it may be to massive, tree-sized creatures. So Treebeard might really have felt like he was going downhill afterall.

In M. C. Escher's famous illustration "Ascending and Descending," hooded figures perpetually ascend or descend a staircase that loops continuously on itself. This seemingly impossible situation was illustrated by Escher using geometric slight of hand, but could it not be possible in reality? In fact, it could, and Treebeard was 90° from the secret of Escherian perpetual downhilledness: he should have gone east!

When walking eastward on Earth, you are walking with the rotation of the planet (your planet may vary). Since your momentum would send you at a tangent to the surface if not for Earth's gravity, you are falling somewhat with every step east -- in other words, you are going downhill. Contrariwise, when going west you are stepping into the Earth as it rotates at you, requiring extra effort to lift yourself on top of it -- exactly like going uphill.

To realize Escher's impossible staircase, we would need only to build stairs circling the globe along a line of latitude. The stairs would need to have a very low rise to run ratio, and be slightly curved toward the Earth at a radius to balance gravity and linear momentum when traversing them. The effect would be most pronounced at the equator; however, budget concerns may force the stairs to be built farther north or south, with grippy soled shoes used to compensate for the necessarily angled runners. Much like the planned space elevator, this project would be one of both international cooperation and global economic benefit from energy savings -- imagine armies of moving men and stevedores from all the nations of the world harmoniously carrying crates down the stairs ever eastward, satisfied in the knowledge that they are doing less work than if they were going the other direction.

Can humanity even afford not to build the stairs? I think not.

End of post.