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The general lack of space-going aliens suggests that getting into space is harder than it sounds.
Or there are fewer civilizations than we expect, or something is wiping out civilizations once they go to space, or most species for whatever reason decide not to go to space, or we are living in an ancestor simulation which only does a detailed simulation of our solar system. (I agree that all of these are essentially wanting, your interpretation makes the most sense, these examples are listed more for completeness than anything else.)
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Open thread, Oct. 12 - Oct. 18, 2015
There might be an alien civilization building stuff in its solar system.
If this turns out to be aliens rather than a low-probability astronomical event, does it imply that getting out into space is a lot harder than it sounds?
Anyone want to take bets on whether or not this will turn out in ten years to be natural?
If you're at the state where the worst thing about a proof is that it relies on the axiom of choice, you're practically at the finish line (at least compared to here). Once proofs has been discovered, mathematicians have a pretty good track record of whittling them down to rest on fewer assumptions. From my (uninformed dilettante's) perspective, it's not worth limiting your toolset until you've found some solution to your problem. Any solution, even ones which rest on unproven conjectures, will teach you a lot.
Ah, yes, I think that makes sense. And obviously a proof of say Friendliness in ZFC is a lot better than no proof at all.
Sure, I know he is not taken very seriously. That is his own point, too.
In the time of Carl Sagan, in the year 1986 or so, I became an anti Saganist. I realized that his million civilization in our galaxy alone is an utter bullshit. Most likely only one exists.
Every single astro-biologist or biologist would have said to a dissident like myself - you don't understand evolution, sire, it's mandatory!
20 years later, on this site, Rare Earth is a dominant position. Or at least - no aliens position.
On the National Geographic channel and elsewhere, you still listen "how previously unexpected number of Earth like planets will be detected".
I am not afraid of mathematicians more than of astrobiologists. Largely unimpressed.
I'm not sure what your point is here. Yes, experts sometimes have a consensus that turns out to be wrong. If one is lucky one can even turn out to be right when the experts are wrong if one takes sufficiently many contrarian positions (although the idea that many millions of civilizations in our galaxy was a universal among both biologists and astro-biologists is definitely questionable), but in this case, the experts have really thought about these ideas a lot, and haven't gotten anywhere.
If you prefer an example other than Wildberger, when Edward Nelson claimed to have a contradiction in PA, many serious mathematicians looked at what he had done. It isn't like there's some special mathematical mob which goes around suppressing these things. I literally had a lunch-time conversation a few days ago with some other mathematician where the primary topic was essentially if there is an inconsistency in ZFC where would we expect to find it and how much of math would likely be salvageable? In fact, that conversation was one of the things that lead me along to the initial question in this subthread.
I am not afraid of mathematicians more than of astrobiologists. Largely unimpressed.
Neither of these groups are groups you should be afraid of and I'm a little confused as why you think fear should be relevant.
If there's any sort of inconsistency in ZF or PA or any other major system currently in use, it will be much harder to find than this.
Indeed, since you can prove ZFC consistent with the aid of an inaccessible cardinal. And you can prove the consistency of an inaccessible cardinal with a Mahlo cardinal, and so on.
I'm not sure that's strong evidence for the thesis in question. If ZFC had a low-lying inconsistency, ZFC+an inaccessible cardinal would still prove ZFC consistent, but it would be itself an inconsistent system that was effectively lying to you. Same remarks apply to any large cardinal axiom.
I would think it faster to search for proofs of any kind, then simplify to an elementary/constructive/machine verifiable proof.
What do you mean?
Yes. It's not the Choice axiom which is problematic, but the infinity itself. So it doesn't mater if ZF or ZFC.
I doubt that any proof in FAI will use infinitary methods.
I'm not sure why you think that. This may depend strongly on what you mean by an in infinitary method. Is induction infinitary? Is transfinite induction infinitary?
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Simulations Map: what is the most probable type of the simulation in which we live?
It could be that the 'external' world is completely different and way, way bigger than our world. Their world might be to our world what our world is to a simple game of life simulation.
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Simulations Map: what is the most probable type of the simulation in which we live?
If the hypothetical external world in question diverges from our own world by a lot then the ancestor simulation argument loses all force.
What can one expect after this super-task is done to see?
Nothing?
At a meta level, if there were this basic a problem, don't you think it would have already been noticed?
It has been noticed, but never resolved properly. A consensus among top mathematicians, that everything is/must be okay prevails.
One dissident.
Wildberger's complaints are well known, and frankly not taking very seriously. The most positive thing one can say about it is that some of the ideas in his rational trignometry do have some interesting math behind them, but that's it. Pretty much no mathematican who has listened to what he has to say have taken any of it seriously.
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Highly speculative thoughts off the top of my head (only with what little I can remember from my high school physics):
The main factor that determines escape velocity is the mass of the planet (there's also atmospheric drag, but it's generally manageable unless the world is a perpetual hurricane hell, in which case I doubt it has any civilization). After a certain mass threshold, the planet is likelier to be gaseous than rocky. I don't think Neptune-like or Jupiter-like worlds are suitable for life (but their moons are another story). In general, I'd say if the world is too big to jump out of, it's too gaseous for anything to have walked on it anyway. Edited to add: Inhabited moons of Jupiter-like worlds would also need to take into account the planet's escape velocity, even if it's lower where they are.
If the planet is a big Earth (that is, quite massive but still mostly rocky), the greater gravity will result in a thicker and denser atmosphere, but I don't know enough aerodynamics to tell how much, if any, this detail will add to the problem of escape velocity. But this difference may change the rules as to which fuels will be solid, liquid or gaseous under that planet's normal conditions.
Another, related problem is payload. For example, if the planet's intelligent species is aquatic, the spaceship will need to be filled with water instead of air; this will increase the total mass horribly and require a much more potent fuel (but all this is assuming that an aquatic species has had the opportunity to discover fire in the first place).
In worlds too big to escape by propulsion, people may come up with the idea of the space elevator, but the extra gravity will require taking into account the structure's weight. The counterweight at the upper end will need to be heavier and/or farther. Issues related to which material is best suited for this building scenario and whether there's a limit to how big a space elevator you can build are beyond my knowledge. According to Wikipedia, nanotubes appear to be a workable choice on Earth.
Some world out there may have a ridiculously tall mountain that extends into the upper atmosphere. Gravity at the top will be lower, and if a launch platform can be built there, takeoff will be easier. Of course, this is an "if" bigger than said mountain.
India has a huge coastline, but for mythical/cultural reasons, Hinduism used to have a taboo against sea travel. In the worst scenario, our heavy aliens may stay on ground, not because they can't, but because they won't; maybe their atmosphere looks too scary or their planet attracts too many meteorites or it has several ominous-looking moons or something.
Good analysis! A few remarks:
In practice even for a planet with as thin an atmosphere as Earth, getting past the atmosphere is more difficult than actually reaching escape velocity. One of the most common times for a rocket to break up is near Max Q which is where maximum aerodynamic stress occurs. This is generally in the range of about 10 km to 20 km up.
Getting enough mass up there to build a space elevator is itself a very tough problem.
Whether gravity is stronger or weaker on top of a mountain is surprisingly complicated and depends a lot on the individual planet's makeup. However, at least on Earth-like planets it is weaker. See here. Note though that if a planet is really massive it is less likely to have large mountains. You can more easily get large mountains when a planet is small. (e.g. Olympus Mons on Mars).
This would require everyone on the planet to take this same attitude. This seems unlikely to be common.