Grand mosaic of the Milky Way is now larger than ever(astroanarchy.blogspot.com) |
Grand mosaic of the Milky Way is now larger than ever(astroanarchy.blogspot.com) |
I think I might have a hallway that it could fit in, but wow that’s big!
Milky Way, 12 years, 1250 hours of exposures and 125 x 22 degrees of sky - https://news.ycombinator.com/item?id=26490579 - March 2021 (139 comments)
Imagine that in a museum, just a massive wall with 100 billion stars. It would be ridiculously cool.
Or, even at 1 in every 10 million, that could be 10,000 systems with life.
In a way I hate these photos. It's like showing a kid an ultra delicious looking candy, but telling them that they will not be able to taste it in their lifetime.
Sad and Scared... my life is over...
Japan is huge on making very large graphics from printing on sheets of white adhesive: https://youtu.be/ioyMec7YU0Y
If they added it to the ground it cheaper to install and then kids could run on it in the gym (could easily cover an entire Gym, lol): https://youtu.be/mBjSM783Tug
Would be fun with the retroreflectors added like in the latter video, as with the lights off and only head lamps on you could see stars below your feet.
It depends a lot on the strength of the underlying layers.
If it is just cement, it takes bits of dust/debris with. If it is stained wood, it can peel some of the stain off if it is left on for a while. If it is painted drywall, it can peel off any little bits of poorly primed paint unless a heat gun is used to gently remove it by softening the adhesive (even this can be tricky though…). On glass it’s perfect :)
For a robust epoxied wooden gym floor, it would be a clean removal.
> For an event to have probability zero doesn't imply it can't occur.
I didn't say anything contrary to this. I was just pointing out an interesting detail about probability theory.
It's impolite to edit your comment in such a way as to turn its existing replies into non-sequiturs. For the record, this comment initially cast doubt on the claim about zero probability events, hence the reply saying it was correct.
The distinction between "surely" and "almost surely" [1] is "just" a curiosity about probability theory though, albeit a rather fundamental one, and I only brought it up as such. It's interesting to think about, and if you do so it quickly brings you up against deep philosophical questions about what probability means.
And must also have
1 = m(0) + m(1) + ... (because it's a measure)
so
1 = Lim S(i)
Where S(i) is the partial sum going from 0 to i.
But if each m(i) = 0, then each partial sum is zero.
So 1 = Lim 0 = 0
That's not my argument. The issue isn't whether physics requires a continuum to model reality -- I'm certain it does. But just because a continuum is required to model the universe doesn't mean that the observables in the universe actually form a continuum. For that, I am certain that they don't.
EDIT: Additional thought and I might be totally wrong because of a lack of mathematical understanding. Pick a point on a trajectory classified as containing life and perturb it in a way such that it only affects parts of the universe far away from life. Then all trajectories through the perturbed points would also still be classified as containing life. But I think the resulting set of trajectories would still have measure zero because we allowed only perturbation far away from life.
So to grow a single trajectory classified as containing life into a set of trajectories classified as containing life of non-zero measure would require being able to pick a point on the trajectory and perturb it in all dimensions and still have all perturbed trajectories classified as containing life. Seems possible but not obviously so to me.
Take the sequence of sets M(n) = { 0, 1, 2, ... n - 1 } with measure m(n, i) = 1 / n. The m(n, i) are non-negative and the sum over all m(n, i) for a fixed n is 1. Then take the limit. The set M(n) will seemingly approach the natural numbers but I am not sure that this is valid. The m(n, i) will approach 0, I think that is uncontroversial. But I guess it might not be valid to argue that the sum remains 1 even though it seemingly equals n * 1 / n.
In your case, when you say "sum" of the n identical things, you just mean multiplying n by the integer 1/n.
So you have 1 = 1/n *n != lim(1/n)lim(n). The last is an indeterminate form of 0*infinity and so you don't get to conclude that it's one.
I agree that this does not work if growing the set and shrinking the measures are two independent limiting processes very similar to how integrating x dx from minus to plus infinity yields infinity if you have independent integration limits [2] but yields 0 if the integration limits are not independent [3].
I am still happy to accept that it requires uncountable sets but I am not convinced by the argument you provided, that the limit does not work out. I think there must be a different issue, some other property of probability measures that fails.
EDIT: I also finally did a little bit of searching and while I did not read much yet, it seems that the problems indeed arise from additivity as you hinted at with the partial sums. But I also found that there are actually ways to have uniform distributions on the natural number [4] if one uses non-standard axioms, but I only skimmed the paper for the moment.
[1] https://www.wolframalpha.com/input/?i=lim_%28n-%3E%E2%88%9E%...
[2] https://www.wolframalpha.com/input/?i=lim_%28a-%3E-%E2%88%9E...
[3] https://www.wolframalpha.com/input/?i=lim_%28a-%3E%E2%88%9E%...