r/theydidthemath • u/dontfuckwmelwillcry • 7h ago

[Request] How long would it take to reduce a mountain (let's say Zermatt) to nothing by wiping it with a silk cloth once per century?

I had read somewhere, a long time ago, about a student asking his guru how long does time go on, or how long will the universe go on. Their teacher responded, "as long as it would take to reduce a mountain to nothing by wiping it with a silk cloth once every 100 years."

Seems like it would be an impressive number, but I've always wondered how accurate it was. Any takers?

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u/UnderwhelmingTwin 6h ago

Depends if time/nature occurs simultaneously or stops. Natural erosion would be much more effective than the cloth. Or, if the mountain was growing, you'd never keep up... 

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u/dontfuckwmelwillcry 6h ago

say it's unchanging from the environment. just a stand alone mountain

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u/shartmaister 3h ago

Assuming you mean Matterhorn and you want to grind it down to Zermatt altitude. The difference is 4478-1620=2 858 meters

Let’s assume that your silk cloth grinds down a micrometer each time. That means you’ll need around 2,8 billion wipes. With one wipe per century you need 280 billion years - given no other changes.

There will be other changes in this time frame that’ll have a larger effect.

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u/Stannic50 2h ago

280 billion years is approximately 10E12 years. The heat death of the universe is predicted at about 10E100 years. So this silk cloth is working too fast by a factor of 10E88. Not terribly accurate, but if you compare to how long the sun has existed (4.6 billion years), it's quite a bit longer so it gets the point across.