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shminux comments on Pascal's Muggle (short version) - Less Wrong
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If you really, honestly can't tell the difference between that and an xrisk reduction charity, you're probably not reading LW in the first place. Or if you mean something else by this question, could you ask with a different example instead?
Sorry, I'm just an amateur asking what is probably a stupid question. Given the leverage N and the prior probability 1/n, where N>>n>>1, what is the optimal investment amount, in whichever units you prefer? Say, in percent of the resources available to you.
I can't offhand see how to translate the given numbers into a Kelly betting criterion. My own heuristic is something more along the lines of "Find the best thing that looks like it might actually work and do it." Things that won't actually work are not done anyway even if the current state of the search calls them "best", but I try to avoid Enrico-Fermi-style "ten percent" underestimates about what might actually have an impact. No holes have actually appeared in the sky, and I'm not presently working with any N larger than 10^80, and there's no reason to worry about small probabilities of affecting that when it's easy to find several different medium-sized candidates. I'd only want to complicate my reasoning any further if I ended up in a more complicated situation than that.
(I also don't think that perpetual motion machines have N>>n.)
But as gwern and other commenters showed, your characterization of accessible chain reactions as an easily drawn implication of then-known physics was wrong.
The best case for bias on Fermi's part in that post is the partially (but not very) independent claim that:
But you didn't give a citation or quote for that.
And you suggest that
But you only present evidence that they cared about a 10% probability (and Szilard was selected from history in part because of his right-tail estimate).
I'm still suspicious that Fermi could truly not have done better than "ten percent", and wonder if people are trying a little too hard not to give in to hindsight bias and overfitting, at the cost of failing to learn heuristics that could indeed generalize. Agreed that if +chain reaction implied a new fact of physics in the sense that it tells you about a previously unknown heavy element which emits free neutrons and is splittable, the standard heuristic "does the failure of this prediction tell us a new fact of physics" does not work in the vanilla sense. This doesn't mean that a fair estimate of the probability of at least one not-yet-examined element having the desired properties would have been ten percent. Chain reactions were not just barely possible for a large barely-critical fission plant 50 years later, rather they were soon achieved at a prompt supercritical grade adequate for nuclear explosions by two distinct pathways of U-235 refinement and P-239 breeding, both of which admittedly required effort, but was the putting-in of that effort unpredictable? But this should be continued in the other post rather than here.
They could realistically only breed enough Pu239 by starting with U235 fueled reactor. Everything that you can do in 1945 goes through U235 , which we have only because it has unusually long half life (350x the next stablest fissile isotope, Np-237) . On top of that, they didn't even know that fission released prompt secondary neutrons at all - those could of simply remained in the fission products and convert to protons via beta decay.
I know they got a critical reaction with a big heap of unrefined uranium. This makes no mention of uranium needing to be isotopically refined for plutonium production on the Manhattan Project. As you are generally a great big troll, I am afraid I cannot trust anything you say about isotopic refinement having been used or required without further references, but I will not actually downvote yet in case you're not lying. Got a cite?
Federation of American Scientists:
Discussion of the particle accelerator route which would enable the bootstrapping of a non U-235 route eventually (producing a critical mass of 10+ kg of plutonium using superconductors and huge amounts of energy and accelerator time), but only with much increased difficulty:
The original giant heap of uranium bricks with k=1.0006 (CP-1 the first pile) - was that chain reaction all due to U235? Maybe the spontaneous fissions are mostly U235, but are the further fissions mostly neutrons hitting U235? This doesn't correspond with my mental model of a pile like that - surely the 2-3 neutrons per fission would mostly hit U238 rather than U235. I also know there were graphite bricks in the pile and graphite bricks are for having slow neutrons being captured by U238.
Let's suppose U235 didn't exist any more. We couldn't build a huge heap of pure U238 uranium bricks, and throw in a small number of neutrons from somewhere else (radium?) to get things started?
EDIT: Okay, I just read something else about slow neutrons being less likely to be absorbed by U238, so maybe the whole pile is just the tiny fraction of natural U235 with the U238 accomplishing nothing? This would indeed surprise me, but I guess then the case can be made for all access to chain reactions bottlenecking through U235. Still seems a bit suspicious and I would like to ask some physicist who isn't frantically trying to avoid hindsight bias how things look in retrospect.
EDIT2: Just read a third thing about slow neutrons being more easily captured by U238 again.
U238 is essentially only fissioned by fast neutrons (only fast neutrons are not dramatically more likely to be simply captured than to fission it), and overall tends to capture neutrons without being fissioned (that's how you get Pu-239: U-238 absorbs a neutron, becomes U-239, then after one beta decay becomes Neptunium-239, then after another beta-decay, Plutonium-239).
So, while it does fission and does release neutrons when it fissions, it doesn't sustain chain reaction. Fission doesn't imply chain reaction even with secondary neutrons.
Fortunately U238 has small enough capture cross section that you can make a reactor work with natural uranium, but only if you use graphite to slow neutrons down. You need graphite because http://www.whatisnuclear.com/articles/fast_reactor.html (scroll down to graphs, note that U235 fission cross section increases faster with decrease in neutron energy than U238 capture cross section so even though both are larger at lower energies, u235 fission wins over u238 capture. Also note nice almost-fractal peaks and valleys (resonance) which very much get in your way when you try to figure anything out from real data. This is a true extreme miracle of actual human rationality that this stuff was figured out sufficiently to build anything).
U-235 has a higher neutron absorption cross-section than U-238, so more U-238 than U-235 doesn't necessarily mean more neutrons hitting U-238 than U-235.
In a natural uranium fuelled reactor, the actual fuel (at startup) is U235, present in the natural uranium at a concentration of about 0.7%. No U235 in nature = no easy plutonium.
Those two "distinct" pathways both rely on properties of 1 highly unusual nucleus, U235, which is both easy to fission, and stable enough to still be around after ~5 billion years. How unusually stable is it? Well, from the date of, say, 40 million years since explosion of the supernova that formed Solar system, it was for all intents and purposes the only one such isotope left. (Every other fissile isotope was gone not because of fizzling or spontaneous fission but because of alpha decay and such)
I explained it in greater detail here .
Depends on your opportunity costs.