231–240 of 335 posts
Is there a joke or double entendre to the misspelling of 'counterintuitive' in the HN title (the article title is correct) that I'm missing?
> 16. If you let a 100g strawberry that is 99% water by mass dehydrate such that the water now accounts for 98% of the total mass then its new mass is 50g: https://en.wikipedia.org/wiki/Potato_paradox I really like this one. It's a perfect combo of intuitive from one perspective and mind bending from another. > 18. A one-in-billion event will happen 8 times a month: https://gwern.net/Littlewood This one, on the other…
#16 is something video games taught me, particularly Path of Exile. In PoE resistance are a flat multiplier to incoming damage. Eg monster does 100 damage per attack and you have 60% resistance then you take 40 damage. The interesting thing is that the higher your resistances the more effective each additional percentage point of resistance is. Let's say a monster does 100 damage per attack. If you have 0% resistance…
One point of resistance gives 1% effective extra health no matter how much you already have.
100 armor give 50% reduction (100/100+100) while 200 armor give 66% (100/100+200)
The percentage 50 -> 66% is shown ingame and players often think the value per point of armor drops.
What does actually happen is your effective bonus health changes from +100% to +200% and every additional point will be worth the same
Earlier quoted context omitted.
> Both the stellar day and the sidereal day are shorter than the mean solar day by about 3 minutes 56 seconds. This is a result of the Earth turning 1 additional rotation, relative to the celestial reference frame, as it orbits the Sun (so 366.25 rotations/y). https://en.wikipedia.org/wiki/Earth's_rotation
So we would need 367 unique date identifiers … but we’ve only got 366 (Feb 29th being the non-annual one). I get I may be being unintelligent, but isn’t the author confusing the rolling coin paradox with an obscure astronomical reference system and coming up with a ‘mistakenly technically correct’ result that doesn’t match experienced reality?
Earlier quoted context omitted.
Wait, how is 95% effective twice as effective as 90%?
just as going from 98% effectiveness to 99% effectiveness halves your risk (you go from 2% chance of falling ill to 1%) its a common concept in games in which armor follows a linear formula (each point of armor is more effective than the last when calculating effective health)
Number 19 is a clinker. Banach-Tarski applies only to objects in real-number space, but there are no such objects. For that to work, objects have to be infinitely divisible, but all of our objects are made out of atoms. Real-numbered space is a good enough approximation to our experience that we hardly ever encounter a model failure like this one.
I'd deny that our objects do not live in a real space. Spacetime is real-valued. The issue isn't the reals, but that "solid object" isn't defined properly, ie., the sets under question don't have well-defined volumes. As soon as you fix that problem, via measure theory, the paradox resolves. You dont need to ditch real numbers.
> 15. Two 12-inch pizzas have less pizza than one 18-inch pizza. That is surprising, because it's not true. Any calculator will confirm that 2 (2 π×6) > 2 π×9. Or am I missing something?
it's true but really what they're missing is the number and variety of toppings on these pizzas.
Earlier quoted context omitted.
16 is like the money hall problem. I understand the answer, the answer makes sense to me. And yet but when I think of it how I think of it initially ... it still makes no sense.
The way to make sense of this is not to think about the water weight but the solid matter. By changing the proportion of water from 99% to 98%, you're also doubling the proportion of solid mass from 1% to 2%.
And the final step is then, that the solid mass didn't change and therefore the liquid must be halved, instead of the solid doubled.
> Knowing just slightly more about the value of your car than a potential buyer can make it impossible to sell it: https://en.wikipedia.org/wiki/The_Market_for_Lemons From that Wikipedia page: > This means that the owner of a carefully maintained, never-abused, good used car will be unable to get a high enough price to make selling that car worthwhile. This is bullshit-- the word "enough" was sneaked in there without…