Comment by aasasd | Hacker News Reader

Comment by aasasd | Hacker News Reader

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Thanks!

> no matter how far in the future you plant an observer, the speed of light is not fast enough for them to observe the entire observable universe

I'm guessing it's just ‘universe’ here, instead of ‘observable universe’—since afaiu the definition is that light inside the observable universe is able to reach us?

So, if I understand the whole comment right, a curved universe is guaranteed to have an edge, but with a non-curved one it's a toss-up because no one knows what it would look like.

Then, when the article says:

> It’s often said that the whole universe we can now observe was once compressed into a volume the size of a golf ball, but we should imagine that the golf ball is only a tiny piece of a universe that was infinite even then.

Does the author essentially mean that the smaller universe still had only a part of it observable? Or am I mixing things up here? In fact, if the universe expanded faster in the early days, I would guess it was less observable than now (even disregarding all the matter getting in the way).

> if I understand the whole comment right, a curved universe is guaranteed to have an edge, but with a non-curved one it's a toss-up because no one knows what it would look like.

A curved universe doesn't "have an edge," I'm referring to Euclidean and non-Euclidean geometry [1]. As in, if the curvature is truly and perfectly zero, then the space-time we live in goes on forever. If it has even the tiniest curvature, then it curves back onto itself and is non-Euclidean.

If it is truly and perfectly zero, then all I'm trying to say is that it goes on forever like an "ideal" 2D plane or 3D space.

[1] https://en.wikipedia.org/wiki/Plane_(geometry)

> A curved universe doesn't "have an edge"

Ah, indeed, quite a brain fart moment from me there, since you explained the structure right in the previous comment. Pondering cosmology while sleep-deprived is suboptimal, I guess.

Though now I'm curious about this:

> If it has even the tiniest curvature, then it curves back onto itself and is non-Euclidean

Would it be possible in theory that the three dimensions are curved like a helix—so they have constant curvature but don't intersect themselves? This way the universe would still stretch infinitely in most directions, but would be non-Euclidean, and you'd need to know where the ‘axis’ is to be able to see in a direction that shortcuts to another one.

Just hypothetical 3D curved spaces here, not saying this has any physical reality -

If the X axis curves into Y (i.e. wraps around the Z axis) and also has a slight negative Z component (i.e. to move in a helical fashioin) each of those curvatures would mean a line segment eventually intersected itself.

It's the nature of the curvature: the space is not sheared (like a rhombus), it is curved (like latitude and longitude), which is why the line segment eventually intersects itself.

> Does the author essentially mean that the smaller universe still had only a part of it observable?

No, I think John C. Mather there is focused wholly on the concept of infinity. So even if the whole observable universe (30 billion light-years across) got squished to the size of a golf ball, the whole universe (infinity light-years across) would still be infinite, because multiplying infinity by some small constant still equals infinity.

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