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Grand mosaic of the Milky Way is now larger than ever

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Re: Grand mosaic of the Milky Way is now larger than ever

#51

Post by danbruc »

omnicognate wrote: post #48
rsj_hn wrote: post #46

Earlier quoted context omitted.

Doesn't this require a continuum? I don't think you get there with a measure on a countable set. That would make this an unphysical argument, IMO.

Yes, it requires uncountability. It could be that physics is ultimately best modelled with countable sets, but that hasn't been established and our current best physical theories are certainly full of uncountability. 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 thin…

Just out of curiosity, is there are short answer why it requires uncountability? Naively something like pick a random natural number would also seem to lead to probability zero. I can see that pick a random natural number might be problematic, how would you do this? Pick on digit and then with some probability either stop or continue and pick another digit, but it is at the very least not obvious that one could make this work without larger numbers just having smaller and smaller probabilities and there might also be issues with termination. On the other hand it is not obvious to me why one could not work with uniform distributions over the set [0, n) and then look at the limit as n goes to infinity.

Re: Grand mosaic of the Milky Way is now larger than ever

#52

Post by rsj_hn »

omnicognate wrote: post #48
rsj_hn wrote: post #46

Earlier quoted context omitted.

Doesn't this require a continuum? I don't think you get there with a measure on a countable set. That would make this an unphysical argument, IMO.

Yes, it requires uncountability. It could be that physics is ultimately best modelled with countable sets, but that hasn't been established and our current best physical theories are certainly full of uncountability. 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 thin…

> It could be that physics is ultimately best modelled with countable sets

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.

Re: Grand mosaic of the Milky Way is now larger than ever

#53

Post by rsj_hn »

danbruc wrote: post #51
omnicognate wrote: post #48

Earlier quoted context omitted.

Yes, it requires uncountability. It could be that physics is ultimately best modelled with countable sets, but that hasn't been established and our current best physical theories are certainly full of uncountability. 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 thin…

Just out of curiosity, is there are short answer why it requires uncountability? Naively something like pick a random natural number would also seem to lead to probability zero. I can see that pick a random natural number might be problematic, how would you do this? Pick on digit and then with some probability either stop or continue and pick another digit, but it is at the very least not obvious that one could make…

If you have a measure on a countable set, lets number it 0, 1, 2, .. then you must have: m(i) >= 0 (since it's a measure).

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

Re: Grand mosaic of the Milky Way is now larger than ever

#54

Post by danbruc »

rsj_hn wrote: post #52
omnicognate wrote: post #48

Earlier quoted context omitted.

Yes, it requires uncountability. It could be that physics is ultimately best modelled with countable sets, but that hasn't been established and our current best physical theories are certainly full of uncountability. 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 thin…

> It could be that physics is ultimately best modelled with countable sets 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.

It seems to me, the question is, how do we assign probabilities to the existence of life. One way I can imagine is the following. We think of the universe as a classical system, then there is a phase space for the entire universe. Now we can look at each trajectory through phase space and classify it as either having or not having life at at least one point. Then we can obtain the measure of the set of trajectories classified as having life. With this view it seems at least possible that life could have measure zero even though it does not seem likely to me and there might even be [non-]obvious reasons why the set could not have measure zero. I am not sure how the argument would change if one would try something similar but with a quantum mechanical instead of a classical description of the universe.

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.

Re: Grand mosaic of the Milky Way is now larger than ever

#55

Post by HotHotLava »

foobiekr wrote: post #32
pfp wrote: post #25

Earlier quoted context omitted.

He's selling (up to A2 or so) prints via https://astroanarchy.zenfolio.com/ . Maybe you can contact him & ask for something larger.

I would absolutely buy something larger.

The largest option in his shop is actually 5m x 75cm, divided into 5 panels. But that also comes at a price of 7.5k EUR, or 12.5k EUR for a glicee print.

Re: Grand mosaic of the Milky Way is now larger than ever

#56

Post by omnicognate »

dotancohen wrote: post #42
omnicognate wrote: post #26

Earlier quoted context omitted.

Strictly speaking our own existence doesn't even tell us the probability is greater than zero. For an event to have probability zero doesn't imply it can't occur. If a number is chosen from a uniform distribution on the reals between zero and one, whatever the result is the probability of that exact result occurring was zero.

> For an event to have probability zero doesn't imply it can't occur. The distinction in meaningless. We exist, ergo intelligent life can develop in this universe.

> The distinction in meaningless. We exist, ergo intelligent life can develop in this universe.

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.

Re: Grand mosaic of the Milky Way is now larger than ever

#57

Post by mensetmanusman »

danbruc wrote: post #45
dotancohen wrote: post #42

Earlier quoted context omitted.

> For an event to have probability zero doesn't imply it can't occur. The distinction in meaningless. We exist, ergo intelligent life can develop in this universe.

It is correct, if you split 100% across infinitely many possible outcomes, each outcome will have probability zero, still one of the possible outcomes will occur.

Infinity times zero might be meaningless in a quantized reality

Re: Grand mosaic of the Milky Way is now larger than ever

#58

Post by mensetmanusman »

beezle wrote: post #38
mensetmanusman wrote: post #35

Earlier quoted context omitted.

Of the sticker? Very clean, because the adhesive is built to stick together like a command strip.

No, was thinking how does the wall look after removal? Does the adhesive take paint or other parts of the surface off?

I have worked with this type of material.

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.

Re: Grand mosaic of the Milky Way is now larger than ever

#59

Post by danbruc »

rsj_hn wrote: post #53
danbruc wrote: post #51

Earlier quoted context omitted.

Just out of curiosity, is there are short answer why it requires uncountability? Naively something like pick a random natural number would also seem to lead to probability zero. I can see that pick a random natural number might be problematic, how would you do this? Pick on digit and then with some probability either stop or continue and pick another digit, but it is at the very least not obvious that one could make…

If you have a measure on a countable set, lets number it 0, 1, 2, .. then you must have: m(i) >= 0 (since it's a measure). 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

There is probably something wrong with this, but I was thinking something like the following.

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.

Re: Grand mosaic of the Milky Way is now larger than ever

#60

Post by rsj_hn »

danbruc wrote: post #59
rsj_hn wrote: post #53

Earlier quoted context omitted.

If you have a measure on a countable set, lets number it 0, 1, 2, .. then you must have: m(i) >= 0 (since it's a measure). 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

There is probably something wrong with this, but I was thinking something like the following. 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 u…

No, you can't interchange limits like that.

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.

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