Nice summary, although it has a rather glaring "thinko" in an early paragraph, where it points out that, because of the age of the visible universe being around 13 billion years, a naive calculation of the universe's diameter would be 26 billion light years across, but that because of cosmic inflation, it's "46 billion light years across [sic]." That should be ~46 bly in radius, in other words, ~93 bly across.
Small compared to infinity, mostly. Or maybe compared to the observable universe, i.e. how much stuff exists that we cannot see versus how much we can?
More or less, although the paper is talking about somewhere between "a few times larger than the currently observable size" (p.3) to "not more than a few orders of magnitude larger" (p.6) Either of which counts as "small" in comparison with the generally infinite size implied by current solutions of our flat curvature models.
(Totally unrelated question: How are you getting proper open-closed quotes?)
How infinite is "generally infinite"? Are we talking infinite enough it's not productive to talk about its size, or so infinite there are physical copies of the solar system, earth, and everyone it it by sheer chance?
My apologies. By "generally infinite" I merely meant "generally thought of as infinite," not like I was invoking some special class of nigh-infinitude. By the way, I wouldn't say an infinite universe doesn't necessarily imply that everything exactly repeats. Take any irrational number like pi. We know for a fact that it doesn't repeat itself exactly because if it did, it would not be irrational. Although it seems likely that pi is "normal" and that any finite segment of it will repeat infinitely many times, that is not a requirement of all infinite numbers. One could imagine a number called pu where every 9 but the first is replaced with a 0. So, 3.1415926535807032, etc. What can we say about pu? It a) is an actual number with a precise definition, b) is infinitely long, c) is aperiodic thus irrational, but d) only has one 9 in its entire infinitely long decimal expansion. Similarly, the cosmos might conceivably have some "one off" features that never repeat, even if it is infinite.
But I still haven't answered your question. My answer is, yes, if spacetime curvature is exactly 0, then it's my understanding (as a non-cosmologist) that the equations imply that the universe is that infinite such that conceivably everything could in principle repeat an infinite number of times. Although I myself am curious what the estimated size of just the non-repeating part would be.
Whether the creation/generation of the universe created copies of highly specific configurations like our solar system, given an infinite volume of space, wont quantum fluctuations spontaneously produce copies of it out of empty space?
If you do not want to use key combinations all the time, and just want real quotes always.
macOS latest: Settings -> Keyboard -> Text Input area, hit edit next to input sources "use smart quotes and dashes", you can turn it off or choose which quotes you want to use.
previous macOS: Settings -> Keyboard -> Look around in here, there is a smart quotes & dashes or Replacements area you can choose the real quote characters.
OK, thanks. I was imagining that perhaps the person had composed their reply in Word and then copy-pasted it as a comment, which seemed like overkill for an HN comment.
> On that note: a good typographer will use single quotes for quoting ‘single’ words.
Really? I find that surprising. At least in the US, the majority of style guides only recommend using single quote marks when embedding a quote within a quite.
