[eck]

A much more important example of this than "martian potatoes" is uranium enrichment.

Natural uranium is ~1% U235; bombs need 90+% U235. So when you've enriched it from 1% to 2% it doesn't seem like you've made a lot of progress towards 90.

If instead of enriching U235 you think of it as eliminating U238, though, then you've done half of the work.

[cperciva]

If instead of enriching U235 you think of it as eliminating U238, though, then you've done half of the work.

That's the wrong way to think of it though. The right way to measure progress is in terms of Separative Work Units: https://en.wikipedia.org/wiki/Separative_work_units

If you start with 10000 kg of natural (0.7%) uranium and you want to separate it into 45 kg of highly-enriched (90% U235) uranium and 9955 kg of depleted (0.3% U235) uranium, then you will have to do 8800 kg of "Separative work units".

On the other hand, separating that same fuel into 3000 kg of partially-enriched (1.4% U235) uranium and 7000 kg of partially-depleted (0.4% U235) uranium only takes 1790 kg of "Separative work units", even though the increased concentration of U235 means that "half the U238 has been eliminated".

Isotope enrichment is an area where, to borrow a line from software engineering, the first 90% takes 90% of the time, and the last 10% takes the other 90% of the time.

[mhartl]

45 kg … and 9960 kg

You mean 40 kg and 9960 kg (so the sum is 10000 kg)? <insert "Were you a Putnam Fellow?" joke here>

[cperciva]

blushes

Actually I meant 45 kg and 9955 kg. I adjusted the numbers several times looking for values which would come out with round-ish quantities but %U235 values in the right ranges for HEU and DU.

[disillusioned]

Annnnd just spent an hour reading that delightful Colin Percival Putnam thread. Thanks for the reminder on that. Man, people really loved to hate on Tarsnap because of his perceived arrogance.

[blacksmythe]

  >> people really loved to hate on Tarsnap

On the contrary, Colin is highly regarded on HN both for his technical ability, and his success in business (despite breaking from conventional wisdom in how to be successful in business).

[vecter]

Thanks for pointing this out. I've vaguely heard before that some nations (like North Korea) have difficulty building nuclear bombs because it's hard to enrich Uranium. This really quantifies that difficulty for me.

[gizmo686]

It is worth mentioning that eliminating the first half of the U238 is still easier then eliminating the second half.

[dsugarman]

as much as our brains are designed to understand logarithmic scales, this percentage problem never really feels intuitive for me. If you have 1 part U235 and 99 parts U238, to get to 2%, it is 50.5% (50/99) of the work to get to to 100% enriched. If all you need to get to weapon grade uranium is 90% enriched, you need to eliminate 98.88888 of the 99 units of U238 (1/1.11111 = .90). So there is no real significant difference in your progress, you are now 50.56% of the way there.

[eCa]

> then you've done half of the work.

So that's why the last 20% takes 80% of the time.