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A circle with the center everywhere April 3, 2008

Posted by Alexandre Borovik in Uncategorized.

A collection of quotes:

Hermes Trismegistus, “thrice-great Hermes” “God is an infinite sphere, the center of which is everywhere, the circumference nowhere.” Book of the 24 Philosophers.

Alain of Lille “God is an intelligible sphere, whose center is everywhere, and whose circumference is nowhere.”

Pascal: “The whole visible world is only an imperceptible atom in the ample bosom of nature. No idea approaches it. We may enlarge our conceptions beyond all imaginable space; we only produce atoms in comparison with the reality of things. It is an infinite sphere, the center of which is everywhere, the circumference nowhere. In short, it is the greatest sensible mark of the almighty power of God that imagination loses itself in that thought.”

Also apparently, “Let him contemplate all nature in its awful and finished magnificence; let him observe that splendid luminary, set forth as an eternal lamp to enlighten the universe; let him view the earth as a mere speck within the vast circuit described by that luminary; let him think with amazement, that this vast circuit itself is only a minute point , compared with that formed by the revolutions of the stars…All that we see in of the creation, is but an almost imperceptible streak in the vast expanse of the universe. No idea can approximate its immense extent…This is an infinite sphere, the center of which is everywhere, but its circumference nowhere. In short, it is one of the greatest sensible evidences of the almightiness of God, that our imagination is overwhelmed by these reflections.”

In “Pascal’s Sphere,” Borges’ narrator lists dozens of variations of a single image, a circle that stands alternately single image, a circle that stands alternately for God, nature, the universe, infinity. Culminating his enumeration is Pascal’s image for the universe: “an infinite sphere, the center of which is everywhere, the circumference nowhere.” Indeed, Borges himself adds to the list in his story “The Library of Babel,” the Library is described as “a sphere whose exact center is anyone of its hexagons and whose circumference is inaccessible” (Labyrinths 52).

According to Borges, Pascal hated “the universe. He was sorry the firmament could not speak; he compared our lives to those of shipwrecked men on a desert island … and he expressed his fillings [saying nature] is an infinite sphere, the center of which is everywhere, the circumference nowhere.”

[Seems to me from the quotations, especially the second, that Borges had Pascal wrong.--D.C.]

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1. Seamus - April 20, 2008

A quick google search will also lead to places attributing that idea to Voltaire and Empedocles. I myself thought it was something Spinoza had said.

The moral of the story seems to be that that idea is voiced everywhere, but originated nowhere.

Pinaki - November 28, 2011

And whose quote is that? [Idea is voiced everywhere, but originated nowhere.]

Ian - September 22, 2012

Nice one:-) The quote seems to have been attributed to quite a few authors doesn’t it!

2. Seamus - May 20, 2008

Apparently Dietrich Mahnke’s book “Beitrage zur Genealogie der mathematischen Mystik” traces the history of the metaphor which compares God to an infinite sphere without center…

3. On the attribution of witty aphorisms « Sound and Fury - July 15, 2009

[...] third example is the idea of God as a circle whose centre is everywhere. I had it in my head that this was due to Spinoza, though it certainly seems to pop up in a variety [...]

4. Bob Pendell - April 12, 2010

Beg pardon, but seems to me that if we are talking about a sphere, it should have a surface rather than a mere circumference. Or in this case, no surface which = “surface is nowhere.” Yes, there is a circumference, but that applies only to a two-dimensional cross-section of the sphere, a circle. The proper boundary of a sphere would be its surface. I suspect the phrase originated in reference to an “infinite circle” and was later adapted to describe a sphere, with the word “circumference” retained by mistake.

With love under will,

Bob, Adastra,
The Wizzard of Jacksonville

5. Baz - April 29, 2010

A way for mortals to perceive the infinite is to see it as a circle which is a line without end or a sphere which is a surface without end.

We cannot perceive any more steps in this, yet, until we travel far enough in space to reach our starting point.

6. science and math - January 3, 2011

No thing in the universe is infinite.
If we determine some thing is infinite then that’s the sorrow of science.
Defining every thing is the victory of science.
No thing can be infinite.

Dr. Harry Doweiko - March 20, 2011

No thing “in” the universe is infinite. True. That the universe itself is not infinite remains to be proven or dis-proven. Our vision (electromagnetic, or visual light), is approximately 13.8 billion light years. Who knows what lies beyond that? Theories abound. But a thousand theories pale in the light of one observable fact that can be replicated.

Steve - January 3, 2013

Have you considered that “nothing” (i.e. no thing) could be considered infinite (not finite)? Likewise “zero”, that nothing boundary between pos. and neg? Also, Christ said “my Kingdom is not of this world” (i.e. not of this dualistic big bang duality.

Pinaki - January 4, 2013

Steve spoke my mind! That zero and infinity are one (i.e. equal). I also include in this equality minus infinity. Logically or Philosophically, minus infinity = zero = plus infinity. This concept is capable of solving “zero divided by zero” or similar indeterminate operations. Also this gives the result, “one by zero is zero”. This may be difficult to realize but it’s intriguing nonetheless. Consider the question: How many points does a Circle have? Think of Circles of every radius from zero to infinity. It illustrates the right half of the equality. Further for a zero-radius Circle, if you take the number of points to be one, it will establish equality between zero and one. You may avoid this zero-one equality by taking the number of points of a zero-radius circle to be zero arguing that zero-radius Circle is non-existent!

Steve - January 4, 2013

Another thought I’ve had is that infinity is much like a mobius strip (which is kind of figure eightish anyway, right?). If you pick a spot on the strip, traveling one direction towared the infinitely small or traveling the other toward the infinitely large, you will meet at the same place: infinity. Hindu mystics are said to have the ablility to be as large or as small as they like. Also, many mystical religions describe the bliss of God as being in the realm of “nothing” or, put otherwise, in the absence of things (which are indicative of duality rather than unity).

Come to think of it, if “the Lord our God is 1 God)” is true, and also that God is no thing (0), maybe 1=0! Hmmm.

Pinaki - January 4, 2013

Every religion converges on this description of God (what Steve pointed). Extremely large and extremely small, both quantities vanish at their limits. God is the mathematical extremum of two opposite approach.

7. Dr. Harry Doweiko - March 20, 2011

Insert words “limited to” between “is” and “approximately”. Shows what happens when you use the computer before you have a cup of coffee. Sorry!

8. vince czyz - June 28, 2011

How could you SO COMPLETELY misread Borges and Pascal?? I’ve read “Pascal’s Sphere” (twice) and PENSEES. Borges could not have been more right. Look again.

9. vince czyz - June 28, 2011

PS — There is no “narrator” in “Pascal’s Sphere”; it is an essay NOT a work of fiction. The “narrator” is Borges himself.

PPS — If you drop by my website you’ll see a brief note on Pascal & one of his pensees.

10. vince czyz - June 28, 2011

Ah … I see. Sorry. It seems you’ve misread Pascal because you haven’t actually read Pascal–aside from these two quotes. You’d have to read all or most of “The Pensees” to see why Borges is dead on: “He [Pascal] hated the universe and yearned to adore God. But God was less real to him [Pascal] than the hated universe.” Borges also has an essay called “Pascal” that you would probably find useful in this regard. Sorry for leaping to conclusions.

11. Metaxis « neurometaphysics - August 3, 2011

[...] microcosm of the self and the macrocosm are united in this symbol. The metaxis is the center of the circle whose center is everywhere and circumference is nowhere as the Hermetic axiom goes. The symbol of the circle with the point at the center is found in many [...]

12. Fred Faustroll - November 26, 2013

God is the tangential point between zero and infinity. – Alfred Jarry, 1898.

13. Lou Thomas - August 13, 2014

Nothing is the same as Everything. Including Nothing. That is, the argument that Nothing (an absence) is the same as Everything (an infinite diversity), simply because neither one is finite, is lacking in substance. Because Nothing has no substance, while Everything includes all substance. In other words, Being requires diverse content; if the Infinite were to be a big All-Nothing instead of a big All-Something, that would be a very bad cosmic joke. The formal proof of this is left as an exercise for the reader.

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