If you have 9,999 grains of sand, it's not a heap. A heap is at least 50 million.
The Heap Paradox
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Techniqueengambit88 wrote:
If you have 9,999 grains of sand, it's not a heap. A heap is at least 50 million.
Thanks for correcting me! With this new number, would 49,999,999 grains of sand be a heap?
Mar 24, 2026
0
#5
49,999,999 grains is also a heap. Also why are you talking like that
It is problem of language because it is not defined exactly what is heap so this is not real paradox. Do you have other paradoxes?
Techniqueengambit88 wrote:
49,999,999 grains is also a heap. Also why are you talking like that
Talking like what? Sorry if I sound robotic 😅
I have a better paradox
You have a hotel with infinite rooms and all the rooms are full do you have room for another guest?
Ooh, interesting.
#9 that paradox is broken because if a hotel has infinite rooms all the rooms can't be full.
Yeah true
Here's one, known as Fredkin's paradox:
Let's say you go to the animal shelter to pick out a dog. You narrow it down to two dogs. The paradox goes that the better both options are, the harder it is to choose between them. There's also the paradox that the more good options you have, the harder it is to pick one 🤔
burkechessing wrote:
You have a hotel with infinite rooms and all the rooms are full do you have room for another guest?
You have circle with infinite dots. All of them are red. Do you have empty space on that circle for black dot? Answer: no
Daughter-Of-Galahop wrote:
Here's one, known as Fredkin's paradox:
Let's say you go to the animal shelter to pick out a dog. You narrow it down to two dogs. The paradox goes that the better both options are, the harder it is to choose between them. There's also the paradox that the more good options you have, the harder it is to pick one 🤔
Because you must reject good options
The traffic paradox:
If you add a shortcut to a very busy highway, it will actually make traffic MORE congested, because all drivers will choose the 'shorter' route. Lots of large cities like New York have actually closed major roads to improve traffic.
This begs the question: should we restrict individual freedom of movement to improve collective efficiency?
Daughter-Of-Galahop wrote:
The traffic paradox:
If you add a shortcut to a very busy highway, it will actually make traffic MORE congested, because all drivers will choose the 'shorter' route. Lots of large cities like New York have actually closed major roads to improve traffic.
This begs the question: should we restrict individual freedom of movement to improve collective efficiency?
Yes
I was looking up more paradoxes and I came across the one burkechessing shared earlier. It also includes some of the reasoning behind the paradox:
An infinitely large hotel that is full can still accommodate more guests, even an infinite number of them, by moving guests to new rooms based on formulas like 2n or n+1
It's a little bit confusing, but wanted to show reasoning for the other side.
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Daughter-Of-Galahop wrote:
I was looking up more paradoxes and I came across the one burkechessing shared earlier. It also includes some of the reasoning behind the paradox:
An infinitely large hotel that is full can still accommodate more guests, even an infinite number of them, by moving guests to new rooms based on formulas like 2n or n+1
It's a little bit confusing, but wanted to show reasoning for the other side.
.
No way
This one is fairly simple. Let's say you have a heap of sand. In this heap of sand you have 10,000 grains of sand. If you remove one grain, is it still a heap? If not, then what is the exact moment where a pile of sand turns from 'heap' to 'non-heap'?
This is hurting my brain.