How did Fermi arrive at a 90% confidence for the false proposition that there weren’t enough neutrons? What was the clever technical argument he immediately saw that Szilard and Rabi didn’t, and why did it not work on Reality?
Fermi was not misleading Szilard. It was easy to estimate the explosive force of a quantity of uranium, as Fermi would do standing at his office window overlooking Manhattan, if fission proceeded automatically from mere assembly of the material; even journalists had managed that simple calculation. But such obviously was not the case for uranium in its natural form, or the substance would long ago have ceased to exist on earth. However energetically interesting a reaction, fission by itself was merely a laboratory curiosity. Only if it released secondary neutrons, and those in sufficient quantity to initiate and sustain a chain reaction, would it serve for anything more. “Nothing known then,” writes Herbert Anderson, Fermi’s young partner in experiment, “guaranteed the emission of neutrons. Neutron emission had to be observed experimentally and measured quantitatively.” No such work had yet been done. It was, in fact, the new work Fermi had proposed to Anderson immediately upon returning from Washington. Which meant to Fermi that talk of developing fission into a weapon of war was absurdly premature.
Many years later Szilard succinctly summed up the difference between his position and Fermi’s. “From the very beginning the line was drawn,” he said. ”. . . Fermi thought that the conservative thing was to play down the possibility that [a chain reaction] may happen, and I thought the conservative thing was to assume that it would happen and take all the necessary precautions.”
(Even if he had an elegant technical argument, doesn’t mean he would be right. Heisenberg had a short elegant argument for why the uranium critical mass would be 1 ton, but it was actually more like 10 pounds.)
There’s something else. Most nuclei that will fission when irradiated with high energy neutrons (such as the ones from the neutron sources of the time) actually will not sustain chain reaction! That’s the distinction between “fissile” and “fissionable”. More here .
edit: Curiously enough, U238 can fission with neutrons produced by it’s own fission, it just that most neutrons slow down before they fission any nucleus, and U238 can only be fissioned by fast neutrons. Had U235 had a bit shorter half life, or had evolution taken longer to make us, or had Sun formed later in the cloud, or the like, bench-top fission would still have been discovered (using neutrons from radium&lithium and U238) but we wouldn’t have bomb anywhere near 1945 . This is quite interesting because of it’s potential impact on Fermi’s paradox. Nukes could be a lot harder to make.
There are at least four materials capable of sustaining a fission chain reaction, and any change to nuclear physics that is barely large enough to take those away would replace them with others. We are not even particularly near the boundary of it being possible.
1: When you only know that one fissions to begin with, you can’t use that.
2: You need something naturally abundant enough, and (correct me if I am wrong) there’s only one, it’s U-235, with an outstandingly long half life for a fissile isotope, of 700 millions years, which is still not very long (other stuff doesn’t hit even a million years). I wouldn’t be surprised in the slightest if small adjustments to fundamental constants can change it to 2 and other small changes, 0.
edit: basically. No U-235, no bomb until you can bootstrap some sort of breeder using a particle accelerator, like, after decades and decades and decades of engineering, when all countries know the principle, but its too expensive.
But they made Pu-239 in time for WW2. Did that rely on reactor-grade U-235? Even if they did use reactor-grade U-235 to make it, could they have just stuck it near some other neutron emitter?
Yes, Fermi engineered the nuclear reactor (and very carefully too, with very well thought out safety system for it, just in case there would be a positive feedback of some kind), using natural uranium and graphite. Other neutron emitters would be very very very expensive. edit: e.g. an accelerator would need ridiculous amounts of electrical energy. The lab emitter used radium in combination with lithium, beryllium, or some other light nuclei, which isn’t a viable route either.
It’s a little sad that Fermi can correctly assume the worst in engineering his reactor and overengineer his precautions against a small chance of runaway feedback, and yet when it came to him estimating 10% for the possibility of an atomic bomb which he knew could be on the scale of city-obliterating and society-killing (because that calculation was so easy a journalist could do it), he apparently didn’t do much of anything. Near vs Far, I guess.
What do you think he should/could have done about it? Try to prevent it’s creation? Try to speed up it’s creation? It’s 10% on the fission releasing secondary neutrons, I’d think. Successful bomb requires other conditions to be met.
Easier to illustrate on example of hypothetical hafnium isomer initiated bullet sized thermonuclear bombs. What is the probability those are possible? That those will be made in next 5 years? Are you buying stocks on basis of that probability?
He could have done either, yes. He was a famous scientist, his Nobel in 1938 massively increased his credibility, his work was cited in the Einstein-Szilard letter which triggered the American bomb project and the first meeting of the bomb committee was to fund more work by Fermi. If Fermi could not have either slowed down or sped up the development of the bomb, it’s hard to think who could have!
Are you buying stocks on basis of that probability?
I wasn’t aware I assigned 10% either to their possibility or to the possibility of a critical but as-yet unknown requirement for their possibility.
Precisely. Now, which he should have done on basis of 10% possibility? There’s a non-negligible cost as well, and ‘business as usual’ still leads to update from 10% to much larger probability, just a bit later, and arguably counter balanced by potential returns of other research done on the way. It’s really easy to misestimate expected utility differences here by re-use of hindsight.
I wasn’t aware I assigned 10% either to their possibility or to the possibility of a critical but as-yet unknown requirement for their possibility, a bit later but somewhat counterbalanced by various probabilities of discovering something else of interest.
Suppose you did assign 10% probability to hafnium triggering. You still have rest of the mini-nuke as a big conjunction, which is far clearer than for the nuke because for the nuke there’s all this pop sci that makes it sound a lot easier than it actually is, plus having cherry picked the nuke that was actually made in time as an example, a lot of bad learning can be done.
Now, which he should have done on basis of 10% possibility?
I’m not sure what would be the best tack to take; knowing everything I do about the subsequent course of history, I think delaying the bomb program as much as possible would have been best, but I don’t know if that was the best decision one would’ve made at the time.
and ‘business as usual’ still leads to update from 10% to much larger probability, just a bit later
Secrecy was already a major issue; business as usual could well lead to a fatal leak of information to the Germans who still were probably the first or second greatest physics establishment in the world and who Fermi must have known were also working on nuclear issues and were aware of the possibility of nuclear explosives; relevant papers were being kept secret and classified, etc. No, anyone at the time knew perfectly well that this was not a harmless issue with no consequences or actions which could be taken.
Well, anyone at the time if they weren’t pulling a Fermi and essentially acting as if the 10% possibility didn’t exist… Whether one decided to retard or advance the bomb, it seems highly unlikely to me that acting exactly as if he hadn’t figured ~10% would just happen to turn out to be the right decision! Listen, I’m not the one claiming Fermi ignored the possibility, it’s right there in the reference:
Many years later Szilard succinctly summed up the difference between his position and Fermi’s. “From the very beginning the line was drawn,” he said. ”. . . Fermi thought that the conservative thing was to play down the possibility that [a chain reaction] may happen, and I thought the conservative thing was to assume that it would happen and take all the necessary precautions.”
I don’t criticize him for any sort of Pascal’s wager, because 10% is a really effing big probability. Moving on...
Suppose you did assign 10% probability to hafnium triggering. You still have rest of the mini-nuke as a big conjunction
Suppose I did assign 10%. Then you cannot defend my inertia and ostrich attitude at 10% because the actual probability is lower! So make up your mind, is Fermi right to put his head in the sand at 10% or is the actual probability lower and he should be doing something else? Or are you arguing that 10% is a magical threshold at and below which head-in-the-sand is always the right response?
I think that is taking anti-Pascal-mugging way too far: if a doctor told me I had a 10% chance of dying this year of a rare disease, I would hysterically shove all the money I had at the doctor to make it go away and start drawing up my will and drafting letters for my family, I wouldn’t go ‘hm, this is very interesting, perhaps I should apply for more government money grants to study this fascinating possibility.’
I’m not sure what would be the best tack to take; knowing everything I do about the subsequent course of history, I think delaying the bomb program as much as possible would have been best, but I don’t know if that was the best decision one would’ve made at the time.
This is another issue with wagers on speculative propositions, its unclear what actually should be done, besides secrecy which they’d already apply to any results involving secondary neutrons upon obtaining said results. edit: though, French obtained and published these results anyway. Which leaves the issue of carbon’s neutron absorption cross-section, which Fermi measured as late as 1940 , after secondary neutrons (and thus well after the quote, at the point when self sustaining chain reaction was much less speculative).
Sure, the expected |utility| is huge, but expected utility is only huge when you can make predictions of what’s best with good accuracy.
Suppose I did assign 10%. Then you cannot defend my inertia and ostrich attitude at 10% because the actual probability is lower!
And how’d you know that, I wonder? You have gamma ray emitting nuclear isomer that you can maybe trigger with x-rays. You have another nuclear isomer that can be triggered like this. It’s not like fission’s unknown-at-the-time secondary neutrons which are maybe released promptly (or maybe stay in the decay products which then undergo beta decay).
By the way, right here is your problem. “actual probability”, which doesn’t even meaningfully exist in such cases. You guys flip between subjectivist probability that lets you assign arbitrary numbers to the end of the world, and some intuitive notion of actual probability which is under which acting upon probabilities is the sanest thing.
if a doctor told me I had a 10% chance of dying this year of a rare disease
But the doctor did not tell that. Secondary neutrons do not necessarily imply the self sustaining chain reaction, which doesn’t necessarily imply the bomb, which doesn’t necessarily imply any effect on the course of the war! (Specifically the war that these European scientists cared about). This makes me wonder what exactly they were even talking about—maybe Szilard was worried they’d irradiate themselves fatally or blow themselves up doing experiments, and Fermi was like “Nuts!”.
edit: also some background on quote is necessary—exact date down to the day, as the conclusions were moving really quick at that point.
It’s wise to consider how non-hindsight might have been harder. It’s even wiser to consider, for each training example, what general heuristics might’ve helped anyway.
But such obviously was not the case for uranium in its natural form, or the substance would long ago have ceased to exist on earth.
But there ought to be some unstable elements that hadn’t fizzed by themselves in natural aggregations and purities, and many such, and these might be manipulated by humans. If something doesn’t happen naturally, are you in a situation where you’re likely to be learning about a randomly placed lower bound that’s probably randomly far above you, or in a case where you’re learning about a nearby lower bound that probably has some things right above it?
However energetically interesting a reaction, fission by itself was merely a laboratory curiosity.
Sounds like an absurdity heuristic; this is a bad general lesson to learn. “Laboratory curiosity” foresooth.
Only if it released secondary neutrons, and those in sufficient quantity to initiate and sustain a chain reaction, would it serve for anything more.
Which it did. So why should one have been confident that they didn’t...?
“Nothing known then,” writes Herbert Anderson, Fermi’s young partner in experiment, “guaranteed the emission of neutrons. Neutron emission had to be observed experimentally and measured quantitatively.”
The good old confusion between negative information and positive information of falsehood, perhaps?
Again, trying to avoid hindsight bias is not best done by inventing new cynical contrarian ideas that serve to steer your mind in the opposite direction of each training example. It would be better to look for truths that are hard to see, and not plausible falsehoods that by golly you ought to have believed. “It would have been just as easy to think Y as X, given Z” is a powerful argument against an alleged heuristic Z that supposedly could’ve told you X. “But it would have been perfectly rational to think Y!” is not how you want to train yourself.
But there ought to be some unstable elements that hadn’t fizzed by themselves in natural aggregations and purities, and many such, and these might be manipulated by humans. If something doesn’t happen naturally, are you in a situation where you’re likely to be learning about a randomly placed lower bound that’s probably randomly far above you, or in a case where you’re learning about a nearby lower bound that probably has some things right above it?
This doesn’t actually work...
There’s only 3 isotopes to choose from. Th232 , U238 , U235 . Evidence that fission occurs probably came from U238 being fissioned by fast neutrons (or could just as well have). You can’t make a bomb out of U238 , though, because it doesn’t get fissioned by slow neutrons, and neutrons slow down quite rapidly, before they fission it enough. You need a nucleus so unstable, that it fissions when it captures a neutron. It must also fission immediately—if it fissions with a delay (if the mechanism of fissioning is that it captures the neutron, transmutes into something unstable that fissions later. Because neutrons do not leave tracks you don’t immediately know that this is not what is going on).
There’s precisely one naturally abundant isotope that you can use, it is U235 . Forget about plutonium, it’d be very expensive to make any without a reactor. Without naturally abundant U235 , no bomb anywhere near 1945 . It’d be something akin to an antimatter bomb—you need to make the material in a particle accelerator, which is ridiculously inefficient. (One could maybe make some plutonium in the particle accelerator, then use that plutonium in a breeder reactor to kick-start breeder economy, but the energy requirements for production of the seed plutonium are still utterly insane)
There’s very little U235 because it has half life of 700 millions years. It is still ~4400 times the half life of the next most stable isotope that you could blow up, though (U233). Which has ~7x the half life of the next stablest (Pu239) , which has 3.2 x the half life of the next stablest (Am-243) . Which suggests to me that it’s like “this cylinder will land with it’s axis horizontal” prediction for something that turns out to be a coin rather than a pencil. (Frankly I do not understand why we even have any U235 at all. Could be some really weird anthropic reason that we don’t know enough to deduce)
edit: doh, a correction. Neptunium-237 , albeit never used in bombs (critical mass 60kg—ish), can maybe be made into one, no doubt with great difficulty due to the size. It has half life of 2 million years. So the sequence of relative half-life becomes 3.2, 7, 12.5, 350
“But it would have been perfectly rational to think Y!” is not how you want to train yourself.
Well of course, but when 2 dice rolled sixes, you can’t go on how it was irrational of Fermi to think the probability of such is 1⁄36 before anyone ever looked at the dice.
On the other hand, if you want a general heuristic that could’ve led Fermi to do better, I would suggest reasoning that previous-historical experimental proof of a chain reaction would not be strongly be expected even in worlds where it was possible, and that to discover a chain reaction to be impossible would imply learning some new fact of physical science which was not already known.
It’s wise to consider how non-hindsight might have been harder. It’s even wiser to consider, for each training example, what general heuristics might’ve helped anyway.
I think the comments have done a good job showing that learning that a chain reaction was possible would have also implied new facts of physical science, e.g. about neutron emission of the available isotopes, so the heuristic in the OP doesn’t help much.
Yes. Essentially, “they were still the default projection from what was already known.” was dramatically untrue at the time of 10% assessment, when it was not known that any neutrons are produced in fission, or any similar processes. And once it became true, Enrico Fermi did rapidly do a very difficult calculation of the neutron multiplication factor, and concluded that self sustaining chain reaction is possible.
The imaginary world where people of Enrico Fermi calibre are unable to follow simple steps due to the extreme conclusions, is a shared fantasy of many, many crackpots.
How did Fermi arrive at a 90% confidence for the false proposition that there weren’t enough neutrons? What was the clever technical argument he immediately saw that Szilard and Rabi didn’t, and why did it not work on Reality?
From your reference:
(Even if he had an elegant technical argument, doesn’t mean he would be right. Heisenberg had a short elegant argument for why the uranium critical mass would be 1 ton, but it was actually more like 10 pounds.)
There’s something else. Most nuclei that will fission when irradiated with high energy neutrons (such as the ones from the neutron sources of the time) actually will not sustain chain reaction! That’s the distinction between “fissile” and “fissionable”. More here .
edit: Curiously enough, U238 can fission with neutrons produced by it’s own fission, it just that most neutrons slow down before they fission any nucleus, and U238 can only be fissioned by fast neutrons. Had U235 had a bit shorter half life, or had evolution taken longer to make us, or had Sun formed later in the cloud, or the like, bench-top fission would still have been discovered (using neutrons from radium&lithium and U238) but we wouldn’t have bomb anywhere near 1945 . This is quite interesting because of it’s potential impact on Fermi’s paradox. Nukes could be a lot harder to make.
Most don’t, that’s true. It only takes one.
There are at least four materials capable of sustaining a fission chain reaction, and any change to nuclear physics that is barely large enough to take those away would replace them with others. We are not even particularly near the boundary of it being possible.
1: When you only know that one fissions to begin with, you can’t use that.
2: You need something naturally abundant enough, and (correct me if I am wrong) there’s only one, it’s U-235, with an outstandingly long half life for a fissile isotope, of 700 millions years, which is still not very long (other stuff doesn’t hit even a million years). I wouldn’t be surprised in the slightest if small adjustments to fundamental constants can change it to 2 and other small changes, 0.
edit: basically. No U-235, no bomb until you can bootstrap some sort of breeder using a particle accelerator, like, after decades and decades and decades of engineering, when all countries know the principle, but its too expensive.
But they made Pu-239 in time for WW2. Did that rely on reactor-grade U-235? Even if they did use reactor-grade U-235 to make it, could they have just stuck it near some other neutron emitter?
Yes, Fermi engineered the nuclear reactor (and very carefully too, with very well thought out safety system for it, just in case there would be a positive feedback of some kind), using natural uranium and graphite. Other neutron emitters would be very very very expensive. edit: e.g. an accelerator would need ridiculous amounts of electrical energy. The lab emitter used radium in combination with lithium, beryllium, or some other light nuclei, which isn’t a viable route either.
It’s a little sad that Fermi can correctly assume the worst in engineering his reactor and overengineer his precautions against a small chance of runaway feedback, and yet when it came to him estimating 10% for the possibility of an atomic bomb which he knew could be on the scale of city-obliterating and society-killing (because that calculation was so easy a journalist could do it), he apparently didn’t do much of anything. Near vs Far, I guess.
What do you think he should/could have done about it? Try to prevent it’s creation? Try to speed up it’s creation? It’s 10% on the fission releasing secondary neutrons, I’d think. Successful bomb requires other conditions to be met.
Easier to illustrate on example of hypothetical hafnium isomer initiated bullet sized thermonuclear bombs. What is the probability those are possible? That those will be made in next 5 years? Are you buying stocks on basis of that probability?
He could have done either, yes. He was a famous scientist, his Nobel in 1938 massively increased his credibility, his work was cited in the Einstein-Szilard letter which triggered the American bomb project and the first meeting of the bomb committee was to fund more work by Fermi. If Fermi could not have either slowed down or sped up the development of the bomb, it’s hard to think who could have!
I wasn’t aware I assigned 10% either to their possibility or to the possibility of a critical but as-yet unknown requirement for their possibility.
Precisely. Now, which he should have done on basis of 10% possibility? There’s a non-negligible cost as well, and ‘business as usual’ still leads to update from 10% to much larger probability, just a bit later, and arguably counter balanced by potential returns of other research done on the way. It’s really easy to misestimate expected utility differences here by re-use of hindsight.
Suppose you did assign 10% probability to hafnium triggering. You still have rest of the mini-nuke as a big conjunction, which is far clearer than for the nuke because for the nuke there’s all this pop sci that makes it sound a lot easier than it actually is, plus having cherry picked the nuke that was actually made in time as an example, a lot of bad learning can be done.
I’m not sure what would be the best tack to take; knowing everything I do about the subsequent course of history, I think delaying the bomb program as much as possible would have been best, but I don’t know if that was the best decision one would’ve made at the time.
Secrecy was already a major issue; business as usual could well lead to a fatal leak of information to the Germans who still were probably the first or second greatest physics establishment in the world and who Fermi must have known were also working on nuclear issues and were aware of the possibility of nuclear explosives; relevant papers were being kept secret and classified, etc. No, anyone at the time knew perfectly well that this was not a harmless issue with no consequences or actions which could be taken.
Well, anyone at the time if they weren’t pulling a Fermi and essentially acting as if the 10% possibility didn’t exist… Whether one decided to retard or advance the bomb, it seems highly unlikely to me that acting exactly as if he hadn’t figured ~10% would just happen to turn out to be the right decision! Listen, I’m not the one claiming Fermi ignored the possibility, it’s right there in the reference:
I don’t criticize him for any sort of Pascal’s wager, because 10% is a really effing big probability. Moving on...
Suppose I did assign 10%. Then you cannot defend my inertia and ostrich attitude at 10% because the actual probability is lower! So make up your mind, is Fermi right to put his head in the sand at 10% or is the actual probability lower and he should be doing something else? Or are you arguing that 10% is a magical threshold at and below which head-in-the-sand is always the right response?
I think that is taking anti-Pascal-mugging way too far: if a doctor told me I had a 10% chance of dying this year of a rare disease, I would hysterically shove all the money I had at the doctor to make it go away and start drawing up my will and drafting letters for my family, I wouldn’t go ‘hm, this is very interesting, perhaps I should apply for more government money grants to study this fascinating possibility.’
This is another issue with wagers on speculative propositions, its unclear what actually should be done, besides secrecy which they’d already apply to any results involving secondary neutrons upon obtaining said results. edit: though, French obtained and published these results anyway. Which leaves the issue of carbon’s neutron absorption cross-section, which Fermi measured as late as 1940 , after secondary neutrons (and thus well after the quote, at the point when self sustaining chain reaction was much less speculative).
Sure, the expected |utility| is huge, but expected utility is only huge when you can make predictions of what’s best with good accuracy.
And how’d you know that, I wonder? You have gamma ray emitting nuclear isomer that you can maybe trigger with x-rays. You have another nuclear isomer that can be triggered like this. It’s not like fission’s unknown-at-the-time secondary neutrons which are maybe released promptly (or maybe stay in the decay products which then undergo beta decay).
By the way, right here is your problem. “actual probability”, which doesn’t even meaningfully exist in such cases. You guys flip between subjectivist probability that lets you assign arbitrary numbers to the end of the world, and some intuitive notion of actual probability which is under which acting upon probabilities is the sanest thing.
But the doctor did not tell that. Secondary neutrons do not necessarily imply the self sustaining chain reaction, which doesn’t necessarily imply the bomb, which doesn’t necessarily imply any effect on the course of the war! (Specifically the war that these European scientists cared about). This makes me wonder what exactly they were even talking about—maybe Szilard was worried they’d irradiate themselves fatally or blow themselves up doing experiments, and Fermi was like “Nuts!”.
edit: also some background on quote is necessary—exact date down to the day, as the conclusions were moving really quick at that point.
edit2: a timeline: http://oznucforum.customer.netspace.net.au/ANFINFO8.pdf
For others’ reference: this begins on page 280 of The Making of the Atomic Bomb.
It’s wise to consider how non-hindsight might have been harder. It’s even wiser to consider, for each training example, what general heuristics might’ve helped anyway.
But there ought to be some unstable elements that hadn’t fizzed by themselves in natural aggregations and purities, and many such, and these might be manipulated by humans. If something doesn’t happen naturally, are you in a situation where you’re likely to be learning about a randomly placed lower bound that’s probably randomly far above you, or in a case where you’re learning about a nearby lower bound that probably has some things right above it?
Sounds like an absurdity heuristic; this is a bad general lesson to learn. “Laboratory curiosity” foresooth.
Which it did. So why should one have been confident that they didn’t...?
The good old confusion between negative information and positive information of falsehood, perhaps?
Again, trying to avoid hindsight bias is not best done by inventing new cynical contrarian ideas that serve to steer your mind in the opposite direction of each training example. It would be better to look for truths that are hard to see, and not plausible falsehoods that by golly you ought to have believed. “It would have been just as easy to think Y as X, given Z” is a powerful argument against an alleged heuristic Z that supposedly could’ve told you X. “But it would have been perfectly rational to think Y!” is not how you want to train yourself.
This doesn’t actually work...
There’s only 3 isotopes to choose from. Th232 , U238 , U235 . Evidence that fission occurs probably came from U238 being fissioned by fast neutrons (or could just as well have). You can’t make a bomb out of U238 , though, because it doesn’t get fissioned by slow neutrons, and neutrons slow down quite rapidly, before they fission it enough. You need a nucleus so unstable, that it fissions when it captures a neutron. It must also fission immediately—if it fissions with a delay (if the mechanism of fissioning is that it captures the neutron, transmutes into something unstable that fissions later. Because neutrons do not leave tracks you don’t immediately know that this is not what is going on).
There’s precisely one naturally abundant isotope that you can use, it is U235 . Forget about plutonium, it’d be very expensive to make any without a reactor. Without naturally abundant U235 , no bomb anywhere near 1945 . It’d be something akin to an antimatter bomb—you need to make the material in a particle accelerator, which is ridiculously inefficient. (One could maybe make some plutonium in the particle accelerator, then use that plutonium in a breeder reactor to kick-start breeder economy, but the energy requirements for production of the seed plutonium are still utterly insane)
There’s very little U235 because it has half life of 700 millions years. It is still ~4400 times the half life of the next most stable isotope that you could blow up, though (U233). Which has ~7x the half life of the next stablest (Pu239) , which has 3.2 x the half life of the next stablest (Am-243) . Which suggests to me that it’s like “this cylinder will land with it’s axis horizontal” prediction for something that turns out to be a coin rather than a pencil. (Frankly I do not understand why we even have any U235 at all. Could be some really weird anthropic reason that we don’t know enough to deduce)
edit: doh, a correction. Neptunium-237 , albeit never used in bombs (critical mass 60kg—ish), can maybe be made into one, no doubt with great difficulty due to the size. It has half life of 2 million years. So the sequence of relative half-life becomes 3.2, 7, 12.5, 350
Well of course, but when 2 dice rolled sixes, you can’t go on how it was irrational of Fermi to think the probability of such is 1⁄36 before anyone ever looked at the dice.
I think the comments have done a good job showing that learning that a chain reaction was possible would have also implied new facts of physical science, e.g. about neutron emission of the available isotopes, so the heuristic in the OP doesn’t help much.
Yes. Essentially, “they were still the default projection from what was already known.” was dramatically untrue at the time of 10% assessment, when it was not known that any neutrons are produced in fission, or any similar processes. And once it became true, Enrico Fermi did rapidly do a very difficult calculation of the neutron multiplication factor, and concluded that self sustaining chain reaction is possible.
The imaginary world where people of Enrico Fermi calibre are unable to follow simple steps due to the extreme conclusions, is a shared fantasy of many, many crackpots.