Well, it is on a plane with electronics, an atomic clock perhaps?
That’s right. The Hafele-Keating Experiment. I’m not sure who the suit is, but I love the look on his face.
I darned near spewed on my laptop!
There’s a theme in some ancient near eastern writings of “the kingship”, meaning the rule/reign by the monarchs of the preeminent city, that partakes of this a little bit, as though the kingship is bestowed in just one location and when it goes to another city it’s almost a case of the entire Earth being shifted so this next city is in the spot where the kingship dwells.
That doesn’t surprise me. Paul Stathern has a book I enjoyed listening to on 10 cities that led the world. There was a wild quote at the end with a double entendre for the New Jerusalem. I’ll dig it up and I know still need to get back to you on the Lion and Lamb passage.
Here it is:
If this is a reductio ad absurdum, I concur. Infinity cannot have a limit such as a size, hence instead of a point expanding to ten light-years across after the passage of one second, an infinity of such points each expanded to ten light-years across within that first second.
There appears (my mental limit) to be no way to distinguish between these two propositions. The finite version implies edges while the infinite version doesn’t need them, can’t even have them.
Cosmologists doing math on the mass and energy implicit in their Big Bang moment, as it expands outward, have found specific values for those; they are required for the behavior we see. In which case multiple such incipient universes would defeat any attempt to find an edge, even though a priori all of them should have edges.
I actually encountered a cosmologist (online) arguing that this accounts for inflation: that the initial singularity splintered from a single point to infinite points, and that each of those points splintered into an infinity of points, and that this kept happening until things had cooled enough from the initial state that the next generation of points “forgot” the singularity and settled into a more moderate multiplication of points.
Interestingly this serves to account not only for hyper-inflation but for the homogeneity of an infinite universe.
Careful – inifinities can be bounded or unbounded, and can for that matter have different densities (the simplest illustration being that the set of all fractions between zero and one is infinite, but that is less dense than the set of all decimals in the same interval.
Bounded infinities is one of those things I best understand while listening to a good explanation, and only can sometimes think clearly about when not listening to that good explanation.
I’m wondering if that is only a conceptual exercise, like in geometry where there is a ‘virtual’ infinity of points in a line segment, but not an infinity of real things that can be counted.
Not necessarily. I’m thinking of the density of a universe that is infinite in extent: while a universe with just one hydrogen atom in each volume V may be the same order of infinity as one with an atom of tungsten per V, I think that the tungsten universe would count as denser, and one with an atom of each element from the periodic table denser still. Though come to think of it, in math terms there might be no difference between the first two universes since one atom is just one element of a set regardless of its mass, so perhaps counting the (basic) subatomic particles would make the comparison work.
On the other hand, since it;s been shown that this seems to be a “Goldilocks universe”, a universe just right in size and density for there to be observers, the idea of other kinds of universes might just be nothing more than a conceptual exercise – and if we’re setting Genesis 1 as a parameter, then universes with observers are the only ones that matter.
Excuse me, but I’m pretty sure those are just conceptual universes.
The point was to illustrate that density is a legitimate concept with regards to infinity, even when infinity isn’t tied to a number line.
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