If we accept the idea of a dynamic, changing, evolving Universe (Big Bang Theory), must Infinity remain entirely conceptual?

If the Universe is changing and evolving, this necessarily implies borders and constraints, or there is nothing which can change or evolve.

If so, there would seem to be 'no room' for any sort of Infinity in such a Universe. It seems to me that only a 'Steady State Universe' can potentially contain an Infinity.

  • I'm not sure if this question really belongs here. This seems more like a matter of physics/mathematics rather than philosophy. See here maybe: physics.stackexchange.com/questions/64197/…
    – David H
    Commented May 12, 2013 at 4:18
  • "If the Universe is changing and evolving, this necessarily implies borders and constraints, or there is nothing which can change or evolve." Why? Commented May 13, 2013 at 23:37
  • I am surprised that some as astute as yourself should ask this question - I believe it is elementary: Change, at the least, means moving through time from point A to point B. (or some analogous sort of movement or change of state) Therefore point A is DISCREET, as is point B, and there is of necessity a boundary between them. - all change requires boundaries. Otherwise, we have a state of perfect entropy, in which no change can occur.
    – Vector
    Commented May 14, 2013 at 0:28

2 Answers 2


Assuming that in your understanding

  • In "steady state" universe practically (in a large enough time period) things would repeat itself, and, in this sense, nothing new happens. But this would call some kind of finiteness. Just the opposite of your inferrence.Maybe you need to justify why only a steady-state universe would allow infinities? Actually even in a steady state universe, things can still "change" as in the way i will describe below allowing infinities.

  • Just assume that the way things change in an "always-changing universe" (or even in a "steady-state universe") happens to be related with decimal expansion of Pi (3.141592...). We know that there will be no repetition in this sequence no matter how long you count (or wait). Isn't this a room for a kind of infinity in both kinds of universes? The sequence of Pi decimal digits starts with a 1 and this may (for the sake of discussion) correspond to the "big-bang" moment. Still, you miss the other end. Kind of infinity, even if one-sided? Probably.

I would say that steady-stateness seems to have nothing to do with allowing or disallowing infinities. In both cases, for instance, the space itself or its geometry, or the fabric of the matter, would allow infinities.

  • "things would repeat itself, and, in this sense, nothing new happens" ?? No need for repetition if we have infinity!
    – Vector
    Commented May 14, 2013 at 1:58
  • Exactly. However, not all infinities dismiss the need for repetition but some certainly do. Even the repetition itself , if it is there, can be infinite. The point is that to have an infinity you don't need a steady-state universe. Both repetitious and ever-changing stuff leave room for infinities. Even in a universe with boundaries, you could have infinite entities within the boundaries.
    – mami
    Commented May 14, 2013 at 8:08
  • 'Even in a universe with boundaries, you could have infinite entities within the boundaries.' This is new and interesting territory to me and perhaps you have convinced me - at least sufficiently so for me to accept your answer. Your example of Pi in connection with this subject and the concept of repeating infinities are very interesting.
    – Vector
    Commented May 14, 2013 at 17:56

If the universe is everything that we see then according to current cosmological theories it is bounded. That is it is bounded spatially (as determined by General Relativity). It has been an open question as to whether it is unbounded in the future, current measurements indicate that it is unbounded in the future. But time unlike space we can only probe the present and memory & knowledge of the past. At every present moment what we see is a bounded, but expanding universe to the future and spatially.

But one can speculate - and plenty do - that there are other universes or all that we see is not the whole of the universe. For example the multiverse.

Where should one place the universe of mathematics? Is it in this universe. Is it elsewhere? Surely that is an infinite realm of thought.

Perhaps one can use a Turing Machine to enumerate every possible axiom system - certainly it wouldn't halt.

But why mathematics? Why not biology. The space of possible biological species is infinite too. As is all the possibilities of languages, and scripts and all the poems and essays and jokes that could be written.

Should mathematics have that high role that is traditionally awarded by it by philosophy? As a glimpse of the eternal.

Aristotle denied the possibility that humans can ever grasp a whole infinity, they can see only the potential. Since this has nothing to do with the nature of the universe - it applies whether the universe is steady-state or a big-bang. It rests upon an analysis of what infinite means. He states that the infinite is not an object or a thing. So it can't be identified with the universe.

  • 1
    Within the lambda-CDM model, the latest measurements from WMAP indicate a spatially infinite (i.e. unbounded) universe with very high certainty, and very likely temporally unbounded in its future as well if dark energy is as important as we believe it to be. I'd suggest revising your first paragraph.
    – David H
    Commented May 13, 2013 at 3:15
  • @DavidH: Ok, but I have a few questions first. How is it possible to measure an infinite spatial extent? Surely the most they can say is that it extends to such or such a distance. My understanding of the Big Bang is that both spacetime & matter unfolded at the same time which means that spacetime must be bounded. But of course experimental results trumps empirical theories. So how exactly does the WMAP experiment indicate a spatially unbounded universe, I can go along with the temporal unboundedness in the future. Commented May 13, 2013 at 3:37
  • Also, you might enjoy skimming NASA's online summary of WMAP: map.gsfc.nasa.gov/universe/uni_shape.html
    – David H
    Commented May 13, 2013 at 4:39
  • @DavidH: The exact form of the equation isn't important. I'll correct for temporal unboundedness. But the situation is more subtle than this as time is itself subtle. So, you agree that your statement 'the latest measurements from WMAP indicate a spatially infinite universe with very high certainty' is mistaken? Commented May 13, 2013 at 6:34
  • Nope, I'm not mistaken. Any mistake here is WMAP's. Experiments at the moment are overwhelmingly in favor of a flat geometry, and flat geometries are spatially infinite under typical topological assumptions.
    – David H
    Commented May 13, 2013 at 7:23

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