Big Numbers in Context¶

\(2^{256}\)¶

\(2^{256}\) is an unfathomably large number. It's \(\sim 10^{77}\) in decimal. The (observable) universe is estimated to contain \(10^{80}\) atoms.

It is many orders of magnitude larger than the estimated number of grains of sand on Earth, which is around \(5.23 \times 10^{23}\).

\(2^{128}\)¶

The number of seconds that have elapsed since the Big Bang is believed to be around \(10^{17}\). Even if every second of the universe's existence had been used to generate a new, unique value, we would still be far from exhausting \(2^{128}\) possibilities.

\(2^{128}\) = \(\sim 3.4 \times 10^{38}\)

How much entropy¶

Dice

\(\frac{1}{6} \cdot \log_{2} 6 \cdot 6 = 2.58\) bit

Latte Macchiato

\(2^{83}\) = \(\sim 8.36 \times 10^{24}\)

Ca. 16 times all the sand grains on planet earth are in one cup^^ (in regards to bits of entropy)

Card deck shuffle

\(36! = 2^{138}\)

links: AC1 TOC - Randomness - Index