Hacker News Reader

> We do not have plausible mechanisms to generate structures on such a massive scale.

Actual structure no. But, random chance can make things look like a structure on this scale.

> But if you had 20+ stars arranged in a circle like that ring, no one would think it was a chance projection, you would demand a physical explanation.

I would generally assume it to be random. In galaxies stars move around far to much for any structure from their initial formation to remain for long, and forming a ring long after creation would just be happenstance.

> I would generally assume it to be random.

But its not, it has structure - it looks like ring or arc. The universe should be homologous at this scale.

Every formation of galaxies has structure.

Random processes can appear to have meaningful structure, but that’s just because we value some outcomes more than others.

> The universe should be homologous at this scale.

That doesn’t mean we’re going to perceive it as homologous. A true random number generator spitting out 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 would be freaky as fuck to see, but that doesn’t make it non random.

This is true, but at this scale, aren’t we looking at a moderate portion of the visible universe? This is hundreds of thousands or millions of galaxies appearing with some strong correlation, I believe. There are only a few trillion galaxies in the observable universe, so it’s not like we have 10^20 chances to observe random chance correlations like this.

I’m just talking without actually having done a close reading or done the statistics for myself, so I could be quite wrong.

Check out the preprint: https://arxiv.org/pdf/2402.07591

It’s less impressive when looking at the background data than how it’s described.

> Random processes can appear to have meaningful structure, but that’s just because we value some outcomes more than others.

No. It's because some structures are much much much less likely to form randomly than other structures.

If you throw 1000 dices, is it possible to get all one? Yes. Is it likely? Not at all.

Why do planets look like a sphere (approximately)? Because that's the most probable shape if things happen randomly. If a pyramid-shaped planet was found, scientists would freak out. This galaxy ring phenomenon is similar to that (but not that crazy).

Finding ~50 dots arranged in a (very loosely defined) circle, from any projection, of a dense set of 2 trillion of them is very plausible.

Actually, you would have a hard time producing this set in such way that no "circles" like that are found at all. It would have to be a very artificial distribution of points in space for you not to observe this, like all of them arranged in a single line, or a giant rectangle, idk.

> Finding ~50 dots arranged in a (very loosely defined) circle, from any projection, of a dense set of 2 trillion of them is very plausible.

It depends on the size of the circle, though. The smaller the size, the more likely the probability is. But that’s only for a particular combination of 50 dots. Now we have to average out of all possible circle sizes and all combinations of 50 dots. Can someone do the math (or the simulation)?

On a first glance it seems so, but ... could it be the opposite?

I'm thinking, the larger the space, the larger the number of points contained within it, so the larger the probability of them being arrange in such way that blah blah ...

We need a math guy to chime in. I have a hunch there may be a theorem about something like this already.

> If you throw 1000 dices, is it possible to get all one? Yes. Is it likely? Not at all.

That's literally as likely as any other possible outcome.

Let's simplfy this to a coin toss, which is more likely:

HHHHHH

or

HHTHTT

or

HTHTHT

They all have the exact same odds of appearing, we might just tell ourselves one formation is more special than any other.

Of course each instance has the same probability. But we're not talking about the probability of an instance, but rather that of a set of instances.

In the dice example, it's obvious that the probability of getting at least one dice facing two is much more likely than the probability of getting all dice facing one.

Similarly, in the planet shape example, I hope you don't think that a pyramid-shaped planet is as likely to form as a sphere-shaped planet.

Yes, a large set of instances is more likely than a single instance (all things being equal).

However that doesn't mean that a sphere is any more or less likely than any specific other structure. It's an small but important distinction.

No, a pyramid shaped planet is not as likely to form as a sphere shaped pyramid. Definitionally a pyramid shaped planet is impossible.

> However that doesn't mean that a sphere is any more or less likely than any specific other structure.

A shape/structure doesn't have an intrinsic probability. Your sentence is underspecified. Shape of what under what process?

In the context of the shape of galaxies, I think we can agree that if we found galaxies forming a shape like this sentence: "WE ARE COMING", everyone would freak out. So yeah, in this context, some shapes are more likely to form (randomly) than others.

> So yeah, in this context, some shapes are more likely to form (randomly) than others.

Again I think you are confused. Assuming random distribution, 'We Are Coming' is just as likely as any other similarly long structure to form. You just happen to care about that structure more than others - however that doesn't make it more or less likey to form.

That message, in morse code is .-- . / .- .-. . / -.-. --- -- .. -. --..

There are 200B to 2T galaxies in the obeservable universe. If you found lines of galaxies and interperated them as morse code, I'm sure you'd find some interesting words/phrases being said.

You'd expect that phrase in every 2^28 = 268,435,456 random 28 digit binary strings - which is not very many. Keep in mind a galaxy could be part of many, many strings (different index position, different orientation of string).

> Again I think you are confused. Assuming random distribution, 'We Are Coming' is just as likely as any other similarly long structure to form.

You are confused. How could we be back to square one? We've discussed it before. I'm not arguing that "WE ARE COMING" is more likely than, for example, "WE RAE COMING". Of course, they are as likely.

Suppose you have a machine that generates 15-char strings. Yes, "INTERCHANGEABLE" is as likely as "YSVQEPQVIGXOQSR" to come out—but that’s not the point. My point is that the probability of getting a proper English word is very unlikely. Most of the time, you'll get gibberish strings.

Also, I didn't say the sentence to be encoded in morse code. Instead, the galaxies form the literal shape of "W", "E", and so on. I hope you can see that in this case, it's borderline impossible to happen.

> My point is that the probability of getting a proper English word is very unlikely. Most of the time, you'll get gibberish strings.

Sure, but given a large enough sample both will likely exist. So the fact that one happens to be english should not surprise anyone nor does it suggest meaning.

> Also, I didn't say the sentence to be encoded in morse code. Instead, the galaxies form the literal shape of "W", "E", and so on. I hope you can see that in this case, it's borderline impossible to happen.

I used morse as its easy to reason about. There's no reason to think shapes are impossible - you just have to define what makes a shape and then look for patterns that match.

Humans have been finding patterns in clouds, stars and even toast since time immemorial.

https://svs.gsfc.nasa.gov/30505

> Sure, but given a large enough sample both will likely exist.

This applies to every event with nonzero probabilities. What's your point?

> Humans have been finding patterns in clouds, stars and even toast since time immemorial.

I knew this—humans love finding patterns. But our discussion is not about that. It's about the very basic thing in probabilities, which is some event is not as likely to happen as others. This is so trivially true.

The probability of getting a proper English word from a random string generator is much less likely than the probability of not getting it. Thus, getting a proper English word should be surprising. It is as surprising as getting any string from a set of gibberish strings with the same cardinality of English vocabularies.

> So the fact that one happens to be english should not surprise anyone

What should surprise you, then? I'm surprised that we need to talk about this very basic thing three times.

When the entire class of things are unlikely given the number of observations. The odds that I personally may win the Jackpot are low but the odds that someone at sometime wins is very high. So me winning would surprise me but someone winning wouldn’t. Applying that rule to research and a lot of people are looking for something interesting in many domains not just this particular one.

Similarly finding any shape in a random set of points is much more likely than the odds of any one shape.

So you need to adjust for both things people are looked for correlations and the entire class of things that would notice not just the odds of what you happened to see. A random process you run spitting out a famous quote would be low, but you would also be surprised Pi is 3,14 or Pi is 3.14 etc etc.

Thus someone else hitting a random process and getting “To be or knot to be” is now looking at the odds that anyone anywhere would get something that’s close to something memorable which should actually be quite high.

TLDR; https://xkcd.com/882/

> Similarly finding any shape in a random set of points is much more likely than the odds of any one shape.

Obviously. But that’s not the point (no pun intended). My point is that most of the "shapes" would be just an unstructured shape—if you can even call it a shape. "Familiar" shapes will be much much unlikely to form that "uncommon" shapes. (Hopefully this is obvious because the number of familiar shapes are much much fewer than uncommon shapes.)

Let me use another example to help you understand the point. Suppose a monkey is given a typewriter and a sheet.

Is the probability of getting The Declaration of Independence is as likely as the probability of getting one particular gibberish sequence of characters? Yes.

Should we surprise if the monkey types any proper one-page English essay? Yes.

In case it's not obvious, that's because the number of possible ways to write a proper one-page English essay, albeit humongous, is nothing compared to the number of possible ways to arrange characters in one page. In other words, it's very very very unlikely to happen.

> Should we surprise if the monkey types any proper one-page English essay? Yes.

You can’t exclude non English languages being you would still be surprised if it was in Spanish etc. If your test is if anything surprising happens, then you must consider every possibility that you would find surprising.

Also, this isn’t some mathematically perfect shape it’s a points in a clump that we’re classifying as a shape.

As such a monkey typing someone vaguely like a proper one-page essay in any language or encoding would still be surprising, but is probably 10^1,000 or so times more likely than any specific sequence.

> You can’t exclude non English languages being you would still be surprised if it was in Spanish etc.

I'm not saying that the only surprising result is an English esssay. But sure, let's add all languages in the world. Getting a proper one-page essay is still surprising, because the absurd number of ways to arrange characters in one page. It's much much much larger than even the number of particles in the universe.

> but is probably 10^1,000 or so times more likely than any specific sequence.

Obviously. Your point? If the probability of an event is so low, it doesn't really matter if it's 1 in 10^1000 or 1^1000000. If that event happens, it is surprising.

---

Anyway, I'm not arguing that the galaxy ring is a rare occurrence, hence surprising. I don't know even an approximate probability of it to happen.

I'm arguing against those who shrug and say "Well, it's random, so even a complex structure can form." Not necessarily. It all depends on the processes behind it.

Case in point: Darwin's evolution. The only reason that it's plausible that random processes can transform basic living organisms into complex ones like mammals is DNA replication.

Without DNA replication, random mutations between generations would be independent, just like random key presses by a monkey. You need to start over every time. This makes it essentially impossible to form complex organisms over time, considering how long DNA of complex organisms is.

> But our discussion is not about that. It's about the very basic thing in probabilities, which is some event is not as likely to happen as others. This is so trivially true.

Except that's not a given.

Any equally long random string is as likely as any other equally long random string.

Different length sets of random strings may differ in probability.

Finding what might appear to be meaningful structures in large data sets, e.g. shapes in 2T galaxies, doesn't inherently suggest anymore than chance.

I agree to almost all your points from the previous four comments, and I think so do you to my comments (because you didn't argue against my statements). We differs only on what to discuss.

Before I give up on this discussion that's always back to square one, maybe this question (that I've similarly asked) will help set a baseline:

What are a few examples of probablistic events that should surprise you?

You just don't understand probability, possibility and potential very well. Yes, you can get hung up where you are and we can argue semantics - the fact is that if I throw 1000 dice and get 1000 "1"s that is not the same as my being able to theoretically do that an equal % chance each throw.

The ring may be possible but, so far, it's the only example so despite being a potential random outcome of randomness, the sheer singularity of its existence proves it's incredibly low likelihood of occurrence - perhaps such a low % chance of actually occurring that it may be easier to believe that the ring had help in its formation, whatever that may be.

I'm not going to deny obvious things just bc they challenge my worldview - especially if I have to defend my viewpoint semantically

No: precisely that is the definition of randomness as “lack of information “ or “incompressibility”.

HH is just as compressible as HT or TH or TT.

You can easily build a compression scheme for any one of these values, but not one that encapsulates all values while using less data than the raw values themselves.

>> If you throw 1000 dices, is it possible to get all one? Yes. Is it likely? Not at all.

> That's literally as likely as any other possible outcome.

???

If you want any outcome, they're equally likely.

But the prev post chose a particular outcome, and any particular outcome is rare.

There's no contradiction.

So what's the insight?

This distinction is popularly represented by the "Monty Hall problem": should you take the offer of the other door.

The problem involves 3 doors with a prize behind only one, where you choose 1 of the three, then Monty shows you what's behind 1 of the remaining 2, which is not the prize, then asks you if you would like to switch to the remaining door.

You might think that your odds won't change because nothing behind the doors has changed, or might get worse because the offer is a second chance to pick the dud.

But instead of 3 doors, imagine 1000 doors. You pick 1. Monty shows you what's behind 998 that aren't the prize and asks you if you want to switch.

By switching, your 1-of-1000 odds become 1-of-2.

The particulars matter.

> But instead of 3 doors, imagine 1000 doors. You pick 1. Monty shows you what's behind 998 that aren't the prize and asks you if you want to switch. By switching, your 1-of-1000 odds become 1-of-2.

No they should become 999 out of 1000. If your door is 1 in 1000 then the other door must have all other possibilities.

Also, the Monty haul problem is counter intuitive because it depends on the exact rules under which he operates. Suppose the classic 1 in 3 odds of a win, but an evil Monty haul where he only gives the option if you would win, now swapping is a guaranteed loss. Mathematically the answer is obvious when all the rules are guaranteed, but people’s internal heuristics don’t automatically trust rules as stated.

> But the prev post chose a particular outcome, and any particular outcome is rare.

No, we first observed a particular outcome (the giant ring). This would be like running coin flips for long enough, spotting some interesting sequence that wasn’t decided beforehand, then deciding it must not be random because that sequence should have been incredibly rare.

Sure, that sequence was rare but it was just as likely as all the other sequences which we didn’t end up seeing.

> By switching, your 1-of-1000 odds become 1-of-2.

It's not 50/50. That means you had a 50% chance to get the door correct on the first guess out of 1000. By showing the non-winning doors, the odds collapse into the remaining door. You had a 1/1000 chance of getting it right the first time, after the reveal all 998 are now assigned to the remaining door.

> Why do planets look like a sphere (approximately)? Because that's the most probable shape if things happen randomly.

That has actually nothing to do with randomness, and everything to do with gravity. https://spaceplace.nasa.gov/planets-round/en/

which, to be clear, is the exact point the parent comment is making.

Randomness only favors something over noise if there is a non random process determining the structure

For any allegedly-random distribution, it's possible to statistically determine an upper-limit on the size of non-random-appearing structures. The upper limit for such structures in our universe is thought to be about 370 MPc, about 1/3rd of the size of this ring.

A lot of these questions are much more clearly addressed in the previous paper by the same authors, which is much more layperson-friendly: https://academic.oup.com/mnras/article/516/2/1557/6657809?lo...

I’m guessing the point is something along the lines of, if you have a page of randomly-distributed points, you would expect to see small features but a large circle spanning the page would be inexplicable.

That makes sense, thanks for actually explaining the core idea.

This isn’t how randomness works. Given enough points plotted at random on the surface of a sphere, you’ll find the entire written works of Shakespeare scribed across it.

That doesn’t mean it was put there intentionally, just that given enough random samples any pattern will appear.

> But, random chance can make things look like a structure on this scale.

You can never absolutely prove that something isn’t random. However:

Galaxy distributions are pink noise, not white noise. Large scale structures are less probable.

The Komolgorov complexity of large structures is lower than random noise, and lower Komolgorov complexity usually indicates some non-random process.

A random process is less likely to produce structure than a non-random process.

Thank you for taking the time to write such an informative response.

> But if you had 20+ stars arranged in a circle like that ring, no one would think it was a chance projection…

Of course we would? This is absolutely backwards.

A random plot of billions of points will have all sorts of coincidental shapes and clusterings. A uniform field might look more random but would actually demand explanation, as lacking those coincidental clusterings is strong evidence for structure.

And as I understand the topic, the scales involved preclude those galaxies physically interacting and being able to form structure. So they should appear randomly distributed.

Edit: To be clear I’m assuming my own ignorance here. I presume there is a reason this is significant, I just don’t understand it. But arguments like yours aren’t convincing to me because we should expect to see random structure, the same way a series of a billion coin flips is likely to have a giant run of alternating heads and tails.

I'm interested in the part about using quasars to illuminate the galaxies. Are quasars so common that they provide a uniform background to the whole universe? I always thought they were fairly sporadically distributed.

Actually I do have a plausible mechanism whose numbers have been sanity checked by a couple of cosmologists, but has never been published.

Here's the idea. The expansion of the universe is currently accelerating. If this continues indefinitely, we get the https://en.wikipedia.org/wiki/Big_Rip model. What happens if the Big Rip proceeds to the point where a lot of https://en.wikipedia.org/wiki/Vacuum_energy gets released, and that release stops the Rip by creating the next Big Bang? This could form a cycle since the next Bang creates cosmos that in turn will Rip.

It doesn't sound entirely crazy to me. The Casimir effect shows that you should release vacuum energy when you constrain the volume that a particularly bit of space can interact with. The incredible expansion of a Rip should constrain such interactions. So a large release of vacuum energy seems expected. And who knows how releasing vacuum energy interacts with the acceleration of the expansion of the universe?

Let's do a back of the envelope estimate. Theory estimates vacuum energy at something like 10^113 joules per cubic meter of vacuum energy. For comparison the visible universe is estimated at 10^53 kg. Using Einstein's E = mc^2, that's around 10^70 joules. Current cosmological models say that at the hottest part of the Big Bang, the universe must have already been larger than a cubic meter. Yes, there is a lot of energy not in the form of visible matter. Even so, there's a lot of room for a release of vacuum energy to explain the energy density needed at the beginning of a Big Bang.

We at least pass the most basic sanity check.

This would offer interesting answers to some key cosmological questions.

Current Big Bang models struggle with how a large volume started out very uniform. Inflation has been proposed for this, but it has some problems. But in this model, extreme uniformity over a large volume is predicted. If you add in quantum fluctuations starting the vacuum release, that have spread out before we go from Rip to Bang, then you can also explain arbitrarily large structures in the universe.

This also explains the arrow of time. How could we start off with such low entropy when entropy is always increasing? Well as the universe expands, entropy increases. But volume increases faster. We wind up with a giant universe filled with very low entropy/volume. When a small piece of that forms a new Big Bang, it again starts with very low entropy.

Unfortunately, this involves an insane lack of conservation of energy. But GR provides no easy way to even state what conservation of energy means. At least not outside of limited classes of models. Which this is not one of. So the idea of energy not being conserved at cosmological scales is at least not entirely unprecedented by current theory.