21–30 of 142 posts
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.
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 isn't a paradox at all. It's a slightly non-intuitive result.
a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true. "in a paradox, he has discovered that stepping back from his job has increased the rewards he gleans from it"
Earlier quoted context omitted.
As stated in the article, this is an example of a veridical paradox under Quine's classification of paradoxes. Which, a quick link following reveals as… A veridical paradox produces a result that appears absurd but is demonstrated to be true nevertheless. Amazing what philosophers will get up to.
The point is that it doesn't even appear absurd unless you have absolutely no number sense.
Took me ten seconds to get it. Takes most people (IME) a lot longer than me to get similar things.
Maybe "no number sense" is actually "other people's minds don't usually work like mine"?
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.
Earlier quoted context omitted.
As stated in the article, this is an example of a veridical paradox under Quine's classification of paradoxes. Which, a quick link following reveals as… A veridical paradox produces a result that appears absurd but is demonstrated to be true nevertheless. Amazing what philosophers will get up to.
The point is that it doesn't even appear absurd unless you have absolutely no number sense.
Neat. This bumps up my list of food-related maths from 3 to 4. So far: https://en.wikipedia.org/wiki/Ham_sandwich_theorem https://en.wikipedia.org/wiki/Pizza_theorem https://en.wikipedia.org/wiki/Layer_cake_representation
https://en.wikipedia.org/wiki/Ham_sandwich_theorem#/media/Fi...
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.
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.
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.
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.
