# Hardcore Finger Counting

Earlier today, @elnomoteta mentioned in twitter that if you count with your fingers you are in trouble, because at least you have overflows.

That got me thinking. Not about whether there is an overflow, since there is always an overflow, even if you count by electron quantum states using the whole universe, because infinity, dude, but about how high you can finger-count.

Sure, the naïve answer is ten, but that's trivial to improve. For example, here is a very simple system to count to 99 but even that is very simplistic.

If you are a computer nerd, you may think you are clever by now saying $2^{10}-1$ but really, how unimaginative is that? It's unimaginative enough that it has its own wikipedia page.

One thing I do (and I recognize it as one of my most annoying traits) is to consider unorthodox answers to questions. Because often they will show that the one asking the question has only a very vague idea of what he is asking, and exposes a ton of unexpressed assumptions.

So, computer geek, $2^{10}-1$, that is 1023. Congratulations, you have done much worse than the Venerable Bede, who in 710AD described in De Computo vel Loguela per Gestum Digitorum a system to express numbers up to 9999 using both hands.

So, let's think about the unexpressed assumptions here.

Is a finger a bit?

Hell no. A finger is a finger. Sure, it can express a bit, but it can also (in some cases) express more. For example, I have 6 fingers I can bend independently in more than one place (thumb, index, pinky).

So, I could use those to have a ternary digit (if you pardon the pun), and count to $3^6 2^4-1$ (or 11663)

If we consider it hand counting instead it's much better. For example, I could hold each hand palm-up or palm-down for 2 extra bits. That's $3^6 2^6-1$ (or 46655)