[unusualmonkey]

> 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.

[beltsazar]

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.

[unusualmonkey]

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.

[beltsazar]

> 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.

[unusualmonkey]

> 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).

[beltsazar]

> 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.

[unusualmonkey]

> 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

[_wire_]

>> 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.

[stouset]

> 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.

[Retric]

> 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.

[pests]

> 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.

[pfortuny]

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

[unusualmonkey]

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.