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Comment by NooneAtAll3 | Hacker News Reader

Reminds me of Titius–Bode law[1], where simple equation correctly gave orbits of all the known planets, while predicting one more in asteroid belt and correct distance to Uranus. Only was considered disproven when Neptune didn't work.

I would not trust these relations even existing (other than by pure chance). Even less I'd trust any intelligent design behind it

[1]https://en.wikipedia.org/wiki/Titius%E2%80%93Bode_law

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I thought that, absent perturbation, accretion rings and planets would form at mathematical intervals due to orbital resonance effects. It’s just a very low energy state. Similar to how vibrational modes tend to be integer harmonics (actual overtone patterns are not perfect integer harmonics due to nonlinearities).

If I use classical language, this is the claim that there are harmonies in math itself that manifest as harmonies in the physical cosmos [1]. Arguably, it’s more weird that we don’t see more physical harmonies — it seems this is due to the incredible complexity of the nonlinear interactions.

[1] https://www.sciencedirect.com/science/article/pii/S240587262...

> other than by pure chance

Barring intelligent design, there's an extremely good chance that at least one of these systems exist, and an equally good chance that only one exists, and we're just lucky enough to have observed it.

Why would it be an equally good chance that only one exists?

It depends on what priors you put on things like planetary size and orbital periods. If your prior is uniform, then it is just as likely for this configuration to exist as any other and because the probability mass is uniformly distributed (e.g. every outcome is equally likely) then there's probably only one of it.

> there's probably only one of it.

I fail to see how you arrived at this conclusion give the text that precedes it.

Every value being equally likely does not mean we expect every value to appear only once.

Throw a d6 seven times and we expect a configuration to come up twice, even though the distribution is uniform.

Throw a d6 seven times and the pigeonhole principle requires that a configuration will come up twice. The example is weakening your argument; it's still true that if you throw a d6 five times, you expect a configuration to come up twice.

A better example wouldn't involve a probability that can achieve 1; maybe ask about the probability of rolling a 3, or of rolling another 3 given you've already observed one 3.

None of those will match the comment above; it isn't well posed.

Throw a d6 six times and you probably won't see each value exactly once.

Yes, I mentioned that in my comment, unless you believe that after seeing five rolls including a duplicate, adding a sixth might bring the total to six rolls with no duplicates.

I refactored your comment. :)

> Throw a d6 seven times and the pigeonhole principle requires that a configuration will come up twice. The example is weakening your argument; it's still true that if you throw a d6 five times, you expect a configuration to come up twice

Even that isn't as strong as you could make it; rolling a die 5 times is basically the birthday paradox but instead of asking 30 people their birthdays to find a duplicate, you're asking 300.

In the case of life supporting planets though, it feels like we're trying to talk about the likelihood of rolling a given value when we haven't even determined whether the die has unique values on each face or not. If you're assuming that only one of the sides has a 3 on it, the interesting part is already over.

why you guys all rolling d6? d20 is the queen of dice!

I don’t understand how one follows from the other there?

And with mathematically significant orbits, there is also the chance that some process stabilises to them which increases the chance of seeing them significantly. It is like being impressed by fractal designs in plants. The plant isn't intelligent and doesn't know about fractals, it is just that repeating patterns are easier for evolution to stabilise on.

But hey, if the job is staring at planets they may as well stare at these interesting planets.

The non-clickbait studies suggest that this is expected with planet formation.

What makes this one unique is that it seems to have avoided disruptive events. Intelligent design and aliens get the pop science web hits while unperturbed defaults do not.

"The current delicate configuration of the

planetary orbits in HD 110067 rules out any violent event over the billion-year history ...making it a rare “fossil” to study migration mechanisms and the properties of its protoplanetary disk in a pristine environment."

https://arxiv.org/abs/2311.17775

That law reads like a good starting point for the lifetime evolution of matter around a star, but too simple to be expected to capture the full range of possibilities. Probably shouldn’t be used to refute hypotheses.

I'd suppose the astronomers behind this study know that "law" also, and ruled it out.

Not very far fetched, in my opinion.

What's the correct distance to Uranus?

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