[beltsazar]

> 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.

[Retric]

> 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.

[beltsazar]

> 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.

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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.