Length of a moment of eternity

dendros · Feb 26, 2020

I have read a short story by the Grimm Brothers, named "The Sheperd Boy" and there is a riddle that sounds like this:

"The third question is, How many seconds does eternity have?"

The little shepherd boy said, "The Diamond Mountain is in Lower Pomerania, and it takes an hour to climb it, an hour to go around it, and an hour to go down into it. Every hundred years a little bird comes and sharpens its beak on it, and when the entire mountain is chiseled away, the first second of eternity will have passed."

So we have a mountain made of pure diamond, and it takes 1 hour to climb it, 1 hour to go around it and 1 hour to go down into it (I assume from its peak to its base). And every 100 years a little bird comes to sharpen its beak on it and after the entire mountain is reduces to dust in this way, a second of eternity would have passed.

So, using this info, is it possible to deduce the dimensions (in meters) of this mountain and how long a second of eternity would be? Of course, by using math and the actual laws of physics (e.g the physical properties of diamond and the bird's beak, the friction, the speed of a walk, etc. For this problem, ignore the problem of the lifespan of that bird).
Just for fun.

BvU · Feb 26, 2020

The Grimm brothers wrote fairy tales. Grim ones

But they don't say it's the same bird. Just "a little bird"
If the mountain's circumference is 5 km, it doesn't take one hour to climb it -- unless it's a sky scraper.
And diamond doesn't wear from a bird's beak.
And the first second of eternity lasts exactly one second. So does the second.
etc.

russ_watters · Feb 26, 2020

dendros said:

Length of a moment of eternity

Roughly 1/infinity.

256bits · Feb 26, 2020

BvU said:

... lasts exactly one second. So does the second.

Makes sense. The second second lasting a second. So does the third, fourth, fifth,.. second last a second.
Not sure about the second to last second.

dendros · Feb 27, 2020

Well, the sheperd boy equates the length of the first second of eternity with the amount of time required to completely wear that diamond mountain. I'm not a native English speaker but I think that in this text "second of eternity" means "a moment of eternity".
The question was: it's possible to calculate that amount of time? Assuming that the diamond does wear when the bird sharpens its beak on it, because of friction (albeit very slowly, losing perhaps a few hundred molecules at every 100 years).
That's all.

phinds · Feb 27, 2020

Even if you COULD make such a vague calculation (and I don't think you can), what would be the point? Make up a number that satisfies you and be happy with that.

Chris Miller · Mar 4, 2020

The description is obviously metaphorical.

SPL · Apr 10, 2020

(t Big Bang 1 - t Big Bang 0) * 365 days * 24 hours * 60 minutes * 60 seconds = # of seconds.
Don't forget adjustments to account for the expanding Universe, leap years, and other minor things.

But you have to define *eternity* to begin with.

some bloke · Apr 11, 2020

Your first step is to work out how much the surface of a diamond is eroded when rubbed by the material of a birds beak - I doubt it is even a tangible amount.

Cooky Monstr · Sep 15, 2021

Heaven Sent brought me here. How many seconds in eternity? The powerful metaphor of the fable is admired by many. In some versions the mountain has dimensions of 2,5 miles. Being a mountain let's assume it is not a cube, but a pyramid. Its volume then would be (2.5³)/3 i.e. about 5.208333 cubic miles or 21.71 km³. Which is a fairly big diamond. Now the only thing missing is to estimate the volume of one-beak-sharpening-worth of erosion. Conventional unit of the diamond crystal lattice is a cube of an edge length 0.3567 nm. [https://lampx.tugraz.at/~hadley/ss1/crystalstructure/structures/diamond/diamond.php]
Which corresponds to the volume of 0.045384685263 nm³ or 0.045384685263*10^-1728km³. Let the birdie take this minimum amount each 100 years. Now divide the volumes and we get 4.7835519568313812325313425849327*10¹⁷³⁰centuries or roughly 5*10¹⁷³² years. For comparison, our universe is about 1.4*10¹⁰ years old. So, to sum it all up, one second of eternity is very roughly about 10¹⁷²³ ages of the universe.

DaveC426913 · Sep 15, 2021

some bloke said:

Your first step is to work out how much the surface of a diamond is eroded when rubbed by the material of a birds beak - I doubt it is even a tangible amount.

Dr. Locard disagrees with you.

He's the guy who said any contact between a perpetrator and a scene will leave some traces of the scene on on the perp.

phinds · Sep 15, 2021

If you were a normal human, this

Cooky Monstr said:

Now divide the volumes and we get 4.7835519568313812325313425849327*101730centuries

would astound me with its precision but since you were sent here by god, well ...

256bits · Sep 15, 2021

DaveC426913 said:

Dr. Locard disagrees with you.

He's the guy who said any contact between a perpetrator and a scene will leave some traces of the scene on on the perp.

And contact with a perp and a scene will leave traces of the perp at the scene.
The mountain of diamond could end up to stay as a mountain, but a mountain of bird beak

Cooky Monstr · Sep 16, 2021

It felt right to leave silly amount of decimal places in a silly calculation. "Heaven Sent" is an episode of Dr. Who.

willem2 · Sep 16, 2021

Cooky Monstr said:

Which corresponds to the volume of 0.045384685263 nm3 or 0.045384685263*10-1728 km3

Something went wrong here, it's only a factor 10^(-36) to go from nm^3 to km^3

Cooky Monstr · Sep 16, 2021

willem2 said:

Something went wrong here, it's only a factor 10^(-36) to go from nm^3 to km^3

Right. I got carried away :-) It would be only 5*10⁴⁰ years. Eternity is quite bearable after all.

DaveC426913 · Sep 16, 2021

Whew!

Ivan Seeking · Sep 17, 2021

dendros said:

Length of a moment of eternity

1 / [Jeremy Bearimy]

Length of a moment of eternity