Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Conterintuitive facts in mathematics, CS, and physics

axisofordinary.substack.com

Post reply on HN
Print view View original

201–210 of 335 posts

Re: Conterintuitive facts in mathematics, CS, and physics

#201

Post by foldr »

londgine wrote: post #105
adenadel wrote: post #98

Earlier quoted context omitted.

Hm, I'm not so sure that just because the definition of a bijection is technical that it is not intuitive. I'll start an enumeration of the rationals 1 1/3 2 1/4 3 1/5 ... If you can prove that you can do this, is that really so non-colloquial? It is certainly what we mean by "as many" for all finite sets, so what is wrong with doing this for infinitely many sets?

If every whole positive number is a fraction, but not every fraction is a whole positive number, then colloquially, I wouldn't define them as having "as many" elements as each other. Now, if you want to say they have the same cardinality (and you define cardinality as existing a bijection), then I would agree fully.

The thing is that you could also use this kind of logic to show that there are more natural numbers than there are natural numbers. For example, you could associate 1 with all of the numbers from 1 to one million, and still have enough numnbers 'left' to associate each of 2,3,... with distinct natural numbers above one million.

Re: Conterintuitive facts in mathematics, CS, and physics

#202

Post by implements »

rawling wrote: post #190
implements wrote: post #187

Number 7: “The Earth makes 366.25 rotations around its axis per year.” Errr, the Earth doesn’t ‘roll around the sun’ - hence the author’s (+1) is wrong, I think (hope!). It’s 365.256 according to Wikipedia.

> 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?

Re: Conterintuitive facts in mathematics, CS, and physics

#203

Post by throwaway8451 »

Aerroon wrote: post #200
6gvONxR4sf7o wrote: post #11

> 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…

OK, let's assume you have 75% elemental resistance. You also take 15% reduced damage and 10% less damage. You have 5% chance to avoid elemental damage and 10% to dodge it and are under the effect of Elemental Equilibrium and Gluttony of Elements. How much better is it to just kill everything before it can kill you?

Re: Conterintuitive facts in mathematics, CS, and physics

#205

Post by niklasbuschmann »

6gvONxR4sf7o wrote: post #11

> 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…

The strawberries remind me of the pricing of long-term bonds.

Let’s say newly issued 100yr Treasuries pay a 1% coupon today, but tomorrow the coupon will be 2%, how much does the price of the older bond change?

The answer is a near 50% loss, simply because this is required to bump the yield of the older bond to 2%.

(If we include the discounted principal payment the exact answer becomes a 41.3% loss)

Re: Conterintuitive facts in mathematics, CS, and physics

#207

Post by _Microft »

1f60c wrote: post #204

> 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?

Area is calculated using pi*r^2:

2 * pi * 6^2 < pi * 9^2

Re: Conterintuitive facts in mathematics, CS, and physics

#208

Post by bryanrasmussen »

1f60c wrote: post #204

> 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.

Re: Conterintuitive facts in mathematics, CS, and physics

#209

Post by 1f60c »

detaro wrote: post #206
1f60c wrote: post #204

> 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?

That's the formula for circumfence, not area.

Ahhhh, of course. facepalms

Re: Conterintuitive facts in mathematics, CS, and physics

#210

Post by 1f60c »

_Microft wrote: post #207
1f60c wrote: post #204

> 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?

Area is calculated using pi*r^2: 2 * pi * 6^2 < pi * 9^2

Thank you. I feel kind of stupid now.
Post reply on HN