No. Whenever you are done with all strings of length n, you still have to check all strings of length n+1. So that moment you identify by "eventually" can never be reached.
If something can be proven there is a finite length proof, and if you check lengths one by one eventually you will reach a high enough length for a valid proof.
> Do note that during the pilot phase, the new system runs in parallel with Microsoft 365 rather than replacing it outright. That's okay, I think.
Well I think it's not ok without at least a fixed deadline for removal of MS365. People usually have work to do and learning new ways to get it done means extra work, and (almost) nobody takes upon extra work if they don't have to. So the new software will be largely ignored by default.
That's the problem, nobody is going to test the new software unless they have to, it will sit unused until the end of the pilot period as long as the old software is available too. Those people are no cs nerds who like testing new software, they are office people and learning new tools is stressful for (most of) them. I have been there.
I worked in Switzerland for 5 years in the 1980’s before Windows when the IBM PC/AT’s I ordered ran DOS with my own menu software. (And my father who fought in WW2 asked “Didn’t the Swiss allow sealed troop trains through their country?”, but that’s not my topic.) Anyway, I once installed a new version of WordPerfect alongside the old version, guess which version was never used? And the poor secretary who accidentally ran the new version couldn’t work with her old files & went home crying for 3 days. I was blamed for not explaining things, but I was sure anyone could tell the difference between the old & new versions - no, they evidently could not.
>... proposed that mass/energy in a parent universe collapsed to form a black hole (thus leaving the bubble of space-time that was the parent universe). It then “bounced” at the singularity, and expanded in a Big Bang, to form a new universe...
So any universe expanding within a black hole of ours has to exist with only the mass that fell into it? How would it produce black holes itself with so little mass?
Yes, this is a very common, and understandable, question; I get asked it a lot. But in fact new (child) universes aren't constrained in size by the initial energy/mass entering the parent black hole. Actually, that's one of the most attractive aspects of the theory. Universes have a huge reproductive advantage over, say, animals.
We know that in our own universe, the (positive) mass energy of matter and its (negative) gravitational energy net out to zero. But that means the amount of energy required to build a universe like ours is essentially… well, none. (See Laurence Krauss’s book, A Universe from Nothing; or Stephen Hawking and James Hartle’s 1983 paper, The Wave Function of the Universe, and Hawking’s later book with Leonard Mlodinow, The Grand Design, etc.)
Child universes are therefore effectively free to produce. Thus, over time, evolution will favor making more (and smaller) black holes from the same amount of matter. Yes, the black holes will get smaller – but the universes they give birth to, through Big Bangs, will still be full sized.
And universes aren’t constrained by a shared environment with limited resources – newborn universes aren’t all competing in a valley with a limited amount of grass. Indeed, each new universe is entirely self-contained and self-sufficient, being both organism and environment – it supplies its own energy for its own development, efficiently and frugally, through stellar fusion, gravitational collapse, et cetera.
This means evolution should ultimately favour runaway black hole production. (And that checks out: in the most recent estimate, in 2022, by a team from the International School of Advanced Studies in Trieste, our universe was estimated to have already generated up to a trillion supermassive black holes – and 40 quintillion stellar-collapse black holes.)
But since the mass that entered the black hole continues to produce gravitational pull in our universe, the child universe must still be anchored within ours, at least gravitationally, and we should feel the pull from all the additional mass the new universe generates?
Not convinced you've got evolution there. You've got adaptive radiation, but where's the natural selection?
The low-black-hole universes aren't going to stop "procreating" because high-black-hole universes exist. At most, all you can say is that if you select a universe at random, it's likely to be a high-black-hole universe.
And I think you can use that fact to argue the theory's wrong: because surely our own universe is an LBH universe? A trillion is rookie numbers. There must be universes that produce vastly more black holes than ours, so the chances of us ending up in such an LBH universe at random are vanishingly small.
> And universes aren’t constrained by a shared environment with limited resources – newborn universes aren’t all competing in a valley with a limited amount of grass.
Yeah, that's what I'm trying to say. Without competition, it's not evolution.
Evolution doesn't specifically require competition, just for replication rate to vary depending on some property of the thing replicating. Competition for finite resources is only one way to create that variation.
"just for replication rate to vary depending on some property of the thing replicating"
That's a heritable trait, not selection pressure. Remember, we're talking about an infinite population size here, but if the pop. size was capped then the mechanism that decided who got to replicate and who didn't would be the selection pressure.
Can you ELI5 why you think the varying replication rate is, by itself, a selection pressure? Because your point's obviously going over my head, and your last comment did nothing to communicate it more clearly.
> At most, all you can say is that if you select a universe at random, it's likely to be a high-black-hole universe.
Yeah, that's sufficient when it's caused by their heritable properties. The proportion of high-black-hole to low-black-hole universes will approach 1:0.
Extinction is not part of the definition of selection pressure. Even in biology we still call it selection when a species merely gets pushed to the margins of an environment instead of driven extinct, or when a trait merely becomes uncommon instead of disappearing.
This is not a simple y/n question. Computers have been superhuman at playing chess for decades now. Reading this article, I guess they are superhuman at understanding code now as well.
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