ForumGeneral Discussion ► would you rather have a million dollars or a penny that doubled every day?
what would you do with the thing you chose, be it the money or the penny?
The penny that doubles every day. Let's break it down like this:
The wealth function W(t) = 2*W(t-1)= 2*2*W(t-2) = ... = 2tW(0) where W(0)=1

With me so far? W(t) = 2t means we can figure out how many days it takes to make 1million dollars (100,000,000 pennies) as follows:

Let W(x) = 100,000,000 = 2x
this implies: Log22x = x Log22 = Log2(100,000,000)
therefore x = 26.57 days

In under a month I would have $1000000
Unless he's implying that only the original penny doubles, and none of its duplicates have that power. Which would mean..... you get one penny every day.

So either the doubling penny is extremely valuable, or practically worthless.
I would take the lump sum because I know I would never get around to depositing my endless pennies due to anxiety over the poor bank teller's reaction.

I would buy a house. Lol no. I would put down a deposit on a house. And... That's it. Save the rest? Pay off my uni debt?
I'd go with the exponential pennies, but I don't think I'd take the money to a bank and I'd try not to let the IRS figure out that it exists.
If we have the exponential penny sitting in some random place, imagine what sort of antics that could cause.

You go to one of those coin machines and deposit a portion of those coins. The next day, the machine has broken because the pennies doubled inside overnight. You try to deposit the pennies, but once they get back into circulation, cash drawers in random places start exploding with copper. You try to hide the duplicating doubloon in your house, but soon that copper can't be contained.

A volume that doubles every day can cause quite a havoc. I wonder what happens if you melt down the material too; does that double?
I'm no physicist, but assuming that one penny has 2.5g of mass in it, and using the trusty old E=mc2, that's 2.25E14 J of energy being created on the first day. 200 Fat Man's being pumped out of nowhere. And that amount DOUBLES every day.

It would only take three months before the penny-mageddon would outweigh the Earth itself.

I don't want a nuke penny, thank you very much. I'll take a lump sum
could we save ourselves by launching the penny into space?

edit, would it form it’s own rogue planet? maybe one of the pennies would land on a planet in space and they would accumulate, and one day become so massive that it forms a black hole.
I did the calculations and in less than 100 days the volume of the pennies would overtake that of the earth.
This turned from "What would you do with a penny that doubled every day?" to "The pennies have consumed the earth. All is lost."
the mass of all the pennies would probably increase the gravitational pull of the earth as well. the moon would crash into the earth, so there’s that to look forward to.
I'd go with the million dollars, personally. invest in the stock market. have some extra money when I'm ready to go off to college.
dude, maybe that’s how scp 1689 was created! it’s like that, but for pennies
The sudden shift away from the monetary value to possible causes of Armageddon is really cool discussion.
one day become so massive that it forms a black hole.

Quick calculations by setting the Schwarzschild radius on one side and the radius of a sphere with a given volume on the other, and solving for the number of pennies indicates that by day 140 by the latest the penny black hole would form. Earlier, if the mass of the pennies causes the core to melt and collapse.

With a event horizon radius of 1 million km, it would certainly be a threat to the solar system, if it fell out of orbit.

Within 5 months, your monetary thought experiment has become an existential threat for the solar system.
false penny decay

it will eventually be expanding faster than the universe. faster than light. there will be no stopping the penny. the penny is all and all is the penny.

there will be no more heat death. no more great rip. there will only be penny. an infinite penny, “with no recourse to the fecundity that once termed within the boundaries of creation.”
Well we can't break the speed of light. The question, then, is how these duplicate pennies are forming.
Quantum foam. Or virtual particles. I can never remember if they're the same thing or not.

Which means there's a pile of identical anti-pennies forming somewhere else in the universe. They will eventually meet and annihilate in a spectacular fashion.
it means that 300 million miles worth of pennies are being generated every second

25920000000000 pennies every day would be enough to break the light barrier
would only take 45 days of penny duping

edit: assuming each penny was a mile wide. i gotta redo these calculations

there are 84480 pennies in a mile so 57 days

i feel like my math is still off
From what I understand, the title infers that it is a single penny duplicating each day, and not it's copies.
ebag you would be correct

god how i hate typing on a phone
i’m not good at math but the penny planet would be frickin huge
i feel like my math is still off

Mass would cause the pennies to collapse into a singularity at that stage. Hence the penny black hole.
The event horizon would grow bigger, but not the actual size of the ball itself.
Forum > General Discussion > would you rather have a million dollars or a penny that doubled every day?