“Let the universe have only two dimensions, and let it be the surface of an india rubber ball. It is only the surface that is the universe, not the ball itself. …Let there be specks of dust fixed to the surface to represent the different galactic systems. If the ball is inflated, the universe expands, and these specks of dust will recede from each other, their mutual distances, measured along the surface, will increase in the same rate as the radius of the ball. An observer in any one of the specks will see all the others receding from himself, but it does not follow that he is the centre of the universe. The universe (which is the surface of the ball, not the ball itself) has no centre.”

— Willem de Sitter

Kosmos (1932)

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Willem de Sitter 44

Dutch cosmologist 1872–1934

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“The cosmos is extremely complex… Earth is nothing but a speck of dust, and it is insignificant. Yet within this expanse there are innumerable and complex structures of dimensions. What are these structures of dimensions like? … Which level of dimension does our humankind live in? We live in the surface matter comprised of the biggest layer of molecular particles; we live in between molecules and planets—a planet is also a particle, and within the vast cosmos, it, too, is a trivial speck of dust. The Milky Way Galaxy is also a trivial speck of dust. This universe—the small universe I just described—is also but a trivial speck of dust. The largest particles that our human eyes see are planets, and the smallest particles visible to humankind are molecules. We humans exist in between the particles of molecules and planets. Being in this dimension, you think it’s vast; from a different perspective, it’s actually extremely narrow and tiny.”

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“The surfaces of three-dimensional space are distinguished from each other not only by their curvature but also by certain more general properties. A spherical surface, for instance, differs from a plane not only by its roundness but also by its finiteness. Finiteness is a holistic property. The sphere as a whole has a character different from that of a plane. A spherical surface made from rubber, such as a balloon, can be twisted so that its geometry changes…. but it cannot be distorted in such a way as that it will cover a plane. All surfaces obtained by distortion of the rubber sphere possess the same holistic properties; they are closed and finite. The plane as a whole has the property of being open; its straight lines are not closed. This feature is mathematically expressed as follows. Every surface can be mapped upon another one by the coordination of each point of one surface to a point of the other surface, as illustrated by the projection of a shadow picture by light rays. For surfaces with the same holistic properties it is possible to carry through this transformation uniquely and continuously in all points. Uniquely means: one and only one point of one surface corresponds to a given point of the other surface, and vice versa. Continuously means: neighborhood relations in infinitesimal domains are preserved; no tearing of the surface or shifting of relative positions of points occur at any place. For surfaces with different holistic properties, such a transformation can be carried through locally, but there is no single transformation for the whole surface.”

Hans Reichenbach (1891–1953) American philosopher

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http://thinkprogress.org/lgbt/2012/03/29/454470/santorum-friends-dont-let-friends-use-pink-balls/
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“I was on par with the Creator of the Universe there in the dark in the cocktail lounge. I shrunk the Universe to a ball exactly one light-year in diameter.”

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Breakfast of Champions (1973)
Context: I was on par with the Creator of the Universe there in the dark in the cocktail lounge. I shrunk the Universe to a ball exactly one light-year in diameter. I had it explode. I had it disperse itself again.
Ask me a question, any question. How old is the Universe? It is one half-second old, but the half-second has lasted one quintillion years so far. Who created it? Nobody created it. It has always been here.
What is time? It is a serpent which eats its tail, like this:
This is the snake which uncoiled itself long enough to offer Eve the apple, which looked like this:
What was the apple which Eve and Adam ate? It was the Creator of the Universe.
And so on.
Symbols can be so beautiful, sometimes.

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Willem de Sitter 44

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