Learning Some Logarithms (2023) (opens in new tab)

A colleague asked how many digits of \(\pi\) I can recite from memory. I realised I still remember the 27.3 digits I memorised in my childhood11 Wait, what does it mean to remember 0.3 digits? I know the digit after the last one is in the range 0–4, which is one bit of information, and the full digit would be just over three bits. Hence, 1/3 or 0.3 digits. Okay but why do I know the digit after the last is in the range 0–4? I deliberately picked a cut-off point that didn’t force me to round t...