# Largest-ever damages sought

Anton Purisma has launched a civil rights suit against an airport Au Bon Pain restaurant; he's asking for \$2,000,000,000, 000,000,000,000,000,000,000,000,000. That would be two undecillion dollars.

## Notable Replies

1. Heck, I'd be happy with 1/10 that amount.

2. Good gracious, that's more than the CEO of Goldman-Sachs earns in a month.

3. Stacked one on top of another, the pennies would make a stack 310,000,000,000,000,000,000,000,000,000,000 km tall. That's 3.1E32 km. For reference, the distance from Earth to the Andromeda Galaxy is about 2.3E19 km. Assuming the bottom of the stack was at a fixed place on Earth and you could avoid having the pennies slip on one another somehow (IE the stack was the most rigid rod ever made), the tip of the rod would be experiencing the most severe relativistic time dilation since the Big Bang.

Light emitted from the front porchlight of the US Mint at the time it forged the first penny would only be 0.00000000000000068% up the stack today. In fact the stack would reach further than it is possible to see in the universe. If it existed back when the Big Bang happened, light from the end of the stack would not have had time to reach our planet yet.

4. I'm guessing that a "\$Googleplex" might be: All of the money that Google will earn. Ever. And I would surely accept an out of court settlement for that amount.

A \$Googolplex would be a lot more money, however, and if it were on the table, I would be tempted to insist on the matter going to a jury.

5. The Schwarzchild radius RS for a black hole of mass M is RS = 2GM/c2

where

G = 6.67×10-11 m3 kg-2 s-1
c = 3×108 m s-1

and M is the mass of the material inside the sphere just before the black hole forms.

Assuming the payment is in pennies, the US penny has mpenny = 2.5 grams and Vpenny = 360 mm3. The density of the US penny is then ρpenny = 7600 kg/m3. (There's a geometric factor we should include here due to the space packing)

The mass of the pile of pennies needed to form a black hole is:

M=(4πRS3/3) ρpenny

and the radius of the black hole made of pennies is then:

RS = 8 G π RS3 ρpenny / 3c2

or rearranging:

RS = √( 3c2 / 8 G π ρpenny ) = 2.7×108 km

This black-hole forming sphere of pennies has a volume of:

Vblack hole = 4πRS3/3 = 8.25×1025 km3

It contains:

Ncoins = Vblack hole / Vpenny = 2.29×1041 pennies, to a value of:

\$black hole = 2.29×1039 dollars
\$black hole = 2,290,000,000,000,000,000,000,000,000,000,000,000,000 \$

A physical limit on the quantity of money that needs to be considered in litigation

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