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Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by landryraccoon on Thursday May 03, 2018 @03:18PM (#16988958)
> You’d certainly never run across such a program by chance—not even if you had a computer the size of the observable universe, trying one random program after another for billions of years in a “primordial soup”!

This is a remarkable claim, given that we did encounter this program by random chance, and it only took about 10 billion years (the estimated age of the universe) give or take a few billion years.

Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by a1369209993 on Thursday May 03, 2018 @03:29PM (#16989053)
We didn't encounter it by chance though; we encountered it by complex goal-directed physical processes that are known to produce extremely high distictiveness-to-kolmogorov-probability outputs.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by Someone on Thursday May 03, 2018 @03:37PM (#16989150)
But chance ‘built’ the machine that built the machine that… …that built the machine that can run such complex goal-directed processes.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by baddox on Thursday May 03, 2018 @04:34PM (#16989681)
I think it's clear that the author is simply referring to the odds of finding this program by trying random programs one after the other, not making any philosophical claims about whether the Universe is deterministic.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by lokedhs on Thursday May 03, 2018 @09:52PM (#16991630)
It's random, but the probability distribution is not uniform.

Just because you have a random process choosing between outcomes A and B doesn't mean that there is a 50/50 chance you'll see either outcome.

For a related interesting result relating to this see the recent paper where they analysed the Drake equation using probability distributions.

Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by sullyj3 on Friday May 04, 2018 @12:28AM (#16992187)
The universe doesn't try random states sequentially, it's governed by things like gravity that tend to lead to states where the forming of optimization processes is possible
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by naasking on Thursday May 03, 2018 @10:35PM (#16991806)
> But chance ‘built’ the machine that built the machine that…

Or perhaps this consists of (slight) evidence that favourable conditions for the evolution of intelligence are more common than we currently suspect.

Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by graycat on Thursday May 03, 2018 @11:25PM (#16991996)
IMHO Amazing: There's a boy in his room playing with his relatively large computer. He dreams up quantum mechanics and general relativity, types in the equations, clicks on the push button Big Bang, zooms forward 12 billion years of simulated time, and sees what he gets.

This was not his first try. His other efforts all ended in "Poof".

But this effort yielded life that figured out the equations! So, the equations generated life smart enough to figure out the equations.

So, the equations were both (1) general enough to generate life and (2) simple enough that the generated life could figure out the equations.

IMHO, amazing juxtaposition!

Is this set of equations essentially the only possible set of equations with both (1) and (2)?

Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by lisper on Thursday May 03, 2018 @04:10PM (#16989456)
No. Chance + selection. VERY important difference.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by SisypheanLife on Thursday May 03, 2018 @04:17PM (#16989516)
Is selection here not a byproduct of chance?
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by nmg on Thursday May 03, 2018 @04:31PM (#16989643)
If I aim a gun and pull the trigger, the results are not the byproduct of chance, excepting that in some sense everything is.

This was consciously aiming a gun at an explicitly-named remote target, ricocheting the bullet off an unprecedentedly-reasonable number of explicitly-chosen elements, and hitting the target.

Don't let semantics muddy the water about this achievement

Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by lisper on Thursday May 03, 2018 @04:22PM (#16989560)
No. The root of all selection is selection for reproductive fitness. That is decidedly non-random.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by mannykannot on Thursday May 03, 2018 @05:06PM (#16989978)
There is no selection for reproductive fitness until there is a replicator. Once a random process has stumbled upon a replicator, selection for reproductive fitness is inevitable, so long as some of the replicator's descendants survive. Reproductive fitness, therefore, is a feature of sufficiently large, complex and long-running random processes, not something additional that is imposed from outside. This is what Dennett called "Darwin's dangerous idea".
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by lisper on Thursday May 03, 2018 @05:21PM (#16990099)
No. The "dangerous idea" is that design might not require a designer.

As for the first replicator, we simply do not yet know how (or even when) that came about, though random chance does seem likely. So I guess if you add enough layers of "built the machine that..." then you do end up with pure randomness (probably). But I would conjecture that there's a lot less "informational distance" between the cosmos and the first replicator than there is between the first replicator and Adam Yedidia.

Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by mannykannot on Thursday May 03, 2018 @05:39PM (#16990222)
It might not be what Dennett meant, but I don't think issues of informational distance refute the claim that we can expect selection for reproductive fitness to be a feature in any random process that gives rise to replicators. After the appearance of the replicator, the random process continues to operate under the same rules (laws of physics) as before.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by a1369209993 on Friday May 04, 2018 @08:15PM (#16999462)
After the appearance (and sufficent success) of the replicator, it stops being a random process. Edit: or at least not a completely/primarily random process.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by lisper on Thursday May 03, 2018 @05:56PM (#16990354)
Oh, I certainly agree with that.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by PurpleBoxDragon on Friday May 04, 2018 @12:32PM (#16995871)
I think the selection is a byproduct of the underlying laws, thought one must rely on chance until a system complicated enough to engage in selection emerges. Now, are those underlying laws reliant upon chance? This requires understanding beyond that of the current universe, so maybe.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by dfee on Thursday May 03, 2018 @04:23PM (#16989581)
Etymological arguments for either position. Regardless, I wouldn’t claim the distinction exists, and would find it hard to justify that it’s VERY important.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by stan_rogers on Thursday May 03, 2018 @08:20PM (#16991179)
It's the difference between draw poker and a fresh hand every time.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by contourtrails on Thursday May 03, 2018 @04:39PM (#16989736)
It's not really that way.

The universe has produced things that basically must exist given the laws of physics (when certain chemicals exist together under certain conditions we know they will react in certain ways, etc).

We are one of those things, and the things we make are things that we are compelled to make by our very nature.

So it's not chance. Our universe as constructed necessarily gives rise to the things we see and experience.

Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by lallysingh on Thursday May 03, 2018 @04:51PM (#16989839)
So the universe is deterministic and nothing happens by chance? I think this is essentially arguing definitions of terms.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by gradys on Thursday May 03, 2018 @07:10PM (#16990842)
It doesn't need to be deterministic, it just needs to be biased.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by pdpi on Thursday May 03, 2018 @05:34PM (#16990185)
It's more akin to arguing for the anthropic principle.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by contourtrails on Thursday May 03, 2018 @10:20PM (#16991747)
I'm not arguing about anything, I'm just stating facts
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by coldtea on Thursday May 03, 2018 @03:55PM (#16989319)
>we encountered it by complex goal-directed physical processes

If you mean evolution, yes. But nothing about the big bang for example makes it a "goal directed process".

(In fact even evolution only looks that way from hindsight -- there's not some end goal there either).

Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by a1369209993 on Friday May 04, 2018 @08:12PM (#16999451)
Acually, the primary complex goal-directed physical process I was talking about was Scott Aaronson. Also various other mathematicians, and mathematics/mathematical research collectively. Evolution is goal directed with regard to locally maximizing inclusive reproductive fitness, but it's not particularly involved by this point.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by landryraccoon on Thursday May 03, 2018 @03:46PM (#16989218)
If a machine arises by chance that creates that goal directed process, that doesn’t seem any less interesting to me than if the output arose by chance instead. In some ways, it seems even more remarkable.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by osteele on Thursday May 03, 2018 @06:43PM (#16990694)
I'll play!

This distinction, between chance and goal-directed physical processes, is artificial, though.

It's artificial because it was produced by humans.

:-)

Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by makomk on Thursday May 03, 2018 @08:12PM (#16991141)
Ultimately, the thing that makes the complex goal-directed physical processes which make up life on this planet actually work is the inexorable, unavoidable increase of entropy. In some sense, living organisms are just a lucky arrangement that happen to make the direction in which entropy increases the one where life thrives, reproduces and grows in complexity. So I guess on some level maybe this is all the result of chance?
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by michaelsbradley on Thursday May 03, 2018 @03:40PM (#16989170)
At an observation scale of, say, our local supercluster, could the electromechanical activity of the processes employed be distinguishable from random physical processes throughout the rest of the observable universe? Honest question, if the question makes sense. If not distinguishable, then perhaps the parent of your comment has a good point.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by gowld on Thursday May 03, 2018 @03:39PM (#16989155)
It depends if you believe in free will, or if you think we are just entropic particles and waves.

The more precise statement is that you'd never encounter this number by uniform sampling within the range of objects of (some reasonable choice of finite size)

Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by burke on Thursday May 03, 2018 @03:40PM (#16989171)
No, it doesn't. "Random chance" in this context clearly implies the exclusion of goal-oriented interference from intelligent entities, whether you ascribe any special mystical meaning to "intelligence" or not.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by jepler on Thursday May 03, 2018 @09:31PM (#16991532)
I think the author intends to say something like: You'd never† run across such a program by uniform random sampling of programs of the appropriate length.

† or, rather, you'd have a vanishingly small probability of doing so

Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by adrianN on Friday May 04, 2018 @12:33PM (#16995889)
If you shuffle a deck of 52 cards and look at their sequence you're almost certainly the first person to see this particular sequence and, if you keep it a secret, almost certainly the last person to see it.
Re:The 8000th Busy Beaver number eludes ZF set theory (2016) by Ar-Curunir on Thursday May 03, 2018 @03:27PM (#16989030)
Wasn't really by chance; people put in a concerted effort to find it.