For all that our bodies know and care, the earth is flat. We walk around and across a more or less flat world, of indefinite extent. We are geared to move forward in the direction of the gaze of our eyes: we have a front and back, and on either side, a left and right. We are not alone. All over the earth, animals have a similar bilateral symmetry: all kinds of creatures, from centipedes to elephants, have a front and back, a left and a right. This shapes our worldview. In a sense we are all good Cartesians. The idea that space itself is three-dimensional becomes easy. Everything is an extension of up-down, front-back and left-right.
Our bodily orientation neatly mirrors our terrestrial frame of reference. The basic gravitational pull of the planet gives us our basic up and down. This is the main force we experience, that pins many of us to the solid surface of the earth. Another force is the magnetic one which defines our north and south. If this is 'up' and 'down' on the map, then east and west are right and left, where the sun rises and sets. The significance of the four cardinal points is ingrained in our perceptions of night and day, summer and winter.
The ancient Chinese believed the Earth to be square. They built cities on a square grid pattern, in tune with the cosmos. The Romans aligned their main streets north-south and east-west. The Americans divided their whole territory into grid squares, ordering the layout of the country before the land itself was surveyed.
It is an easy step from a rectangular landscape to add the vertical dimension. In a sense our principal worldview is cubic. We are all positioned somewhere inside the cube: every point on earth has a latitude, longitude and altitude. You don't even need to believe in a flat earth for this rectangular frame to work.
But not everyone sees things in this way. We may find alternative points of view expressed in the annals of alien cosmology.
Consider, floating in an aqueous region of some planet, an alien jellyfish, more or less round, with a single eye on the top, looking directly upward. (This species is particularly known for stargazing, and advanced in astronomical sciences.) Our alien jellyfish can feel the vertical force of gravity and buoyancy, but has no particular conception of forward and backward, left and right. Everything is the same all the way round.
(Human readers are invited to imagine floating in a still swimming pool. If you can become detached from awareness of your bilaterally symmetrical body, you can start to imagine floating free of conception of left and right. The scientific experience is helped if your swimming pool does not have rectangular sides, and you are in the open air, staring directly into boundless space.)
The scientific culture of stargazing jellyfish species does not conceive of a cubic universe of three linear dimensions. These aliens conceive of no left and right, only degrees of rotation.
The most forthrightly anti-Cartesian alien jellyfish live in the condensed polar sea of an obscure gaseous planet. At the poles, 'normal' terrestrial geometry is confounded. There is no neat set of north, south, east and west as such. What is immediately west of the north pole? What is the opposite of south there? We cannot define anything except that North is 'here', South is everywhere else. East and West are not distinct opposites but just degrees of rotation clockwise or anticlockwise. Even the sun can be ambivalent, circling the horizon without distinguishing east or west.
Our pole-dwelling alien jellyfish, then, conceive of neither left and right nor east and west. Their eminent cosmologists cannot understand why earthlings insist on trying to rectanglify everything: to straighten out the horizontal disc of the world into two perpendicular axes. They see it as a rather arbitrary fabrication, a cheap local contrivance which just so happens to work for lazy species living on the flanks of solid planets.
Human scientists may protest; but the anti-Cartesian alien jellyfish point to the fact that when it comes to the bigger cosmological picture, even earthlings abandon their cubic fantasy and revert to a good old polar perspective of the universe: when it comes to mapping interstellar space, everything is imagined as part of a spherical projection, radiating outwards from Earth. Even the ancients who thought the earth was square believed the heavens to be round.
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