31–40 of 142 posts
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.
This is only confusing because of the potatoes. If you said you had a pool that was 99% water, that changed to 98% water, the massive weight drop would be much less surprising.
How is that clearer?? :-) In fact, it's not even the same thing. A 100-gallon pool (for very small people) that is 99% full has 99 gallons. 98% full has 98 gallons...
This is only confusing because of the potatoes. If you said you had a pool that was 99% water, that changed to 98% water, the massive weight drop would be much less surprising.
How is that clearer?? :-) In fact, it's not even the same thing. A 100-gallon pool (for very small people) that is 99% full has 99 gallons. 98% full has 98 gallons...
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.
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 o…
You mean 40 kg and 9960 kg (so the sum is 10000 kg)?
Your program is slow so you profile it, and find out that f() takes 99% of the time. So you work a lot to optimize f(), and re-profiling shows that now f() takes 98% of the time.
Doesn't seem that impressive after all the work you've put into optimizing f(), but your program is actually twice as fast :)
Another angle on this problem: How much water must you add to the potatoes to make them 100% water? Of course, you can add all the water in the universe and they'll still not be 100% water. The water-percent increment just gets smaller and smaller, the more water you add. This "potato paradox" illustrates the same effect, but in the other direction, where a small relative decrease yields a large absolute decrease.
I think it is the fact that they used potatoes that makes it counterintuitive. Had it instead been a glass of water that had 1% of dissolved salt in it, it would have been very straightforward.
Why is this a "paradox"? Not sure what this applies to either. It's not even counterintuitive.