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How do you think it possible for the ancients to be satisfied with the concept of FINITE SPACE, with "fixed stars" at its limits? To our minds, the idea of infinite extension comes so naturally, without the slightest effort, even for the mathematically unsophisticated. So what is really hiding here?

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  • $\begingroup$ Never read Alexandre Koyré's From the Closed World to the Infinite Universe (1957) ? The "conceptual transformation" was not natural nor easy at all. $\endgroup$ – Mauro ALLEGRANZA Jun 13 '17 at 11:15
  • $\begingroup$ You must take into account that ancient do not have "modern" concept of space; for them the relevant concept was that of "finite cosmos". $\endgroup$ – Mauro ALLEGRANZA Jun 13 '17 at 16:15
  • $\begingroup$ What infinite extension? If you believe in the Big Bang then the universe is finite. $\endgroup$ – Mikhail Katz Jul 13 '17 at 13:04
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    $\begingroup$ @MikhailKatz ... A "big bang" singularity is consistent with unbounded space. $\endgroup$ – Gerald Edgar Jul 13 '17 at 13:48
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    $\begingroup$ Off-topic here but try physics.stackexchange.com/questions/150666/… ... from questions there is seems this misconception is common among amateurs $\endgroup$ – Gerald Edgar Jul 13 '17 at 13:51
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Who believed in a closed world? The fathers of science, the Old Greek, did not.

Anaxagoras 499-428 BC knew: Of the great there is no greatest but there is always a greater.

Anaximander of Milet 611-547 BC already said: The infinite (apeiron) is not exhaustible. Wherever the warrior stays, he can stretch out his spear farther.

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    $\begingroup$ I am not much of an expert in astrophysics but it seems to me that modern science tells us quite the opposite: space is finite. As far as the spear objection is concerned, the rebuttal is that you may eventually stab yourself in the back. $\endgroup$ – Mikhail Katz Jul 13 '17 at 13:03
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    $\begingroup$ The geometry described in Euclid's Elements is certainly unbounded. The parallel postulate shows that. And it is said that geometry was studied by the ancients as a model for the actual world, not (as today) some abstraction. $\endgroup$ – Gerald Edgar Aug 12 '17 at 14:20
  • $\begingroup$ I believe the OP is referring to the idea of the firmament as " the structure above the atmosphere, conceived as a vast solid dome." (Upvoted regardless for your two very excellent references;) $\endgroup$ – DukeZhou Oct 12 '17 at 20:28

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