No solution · The numbers
Why a completely lost phrase is never recovered
Many people assume it is a matter of power: that with a big enough computer, or in a few years’ time, it could be done. The numbers say no, and it is worth seeing them, because that is what protects you from whoever is about to charge you for trying.
The size of the problem
A twelve-word phrase is chosen from a number of possibilities written with about forty digits. To put that in scale:
| Quantity | Approximate digits |
|---|---|
| People on Earth | 10 |
| Seconds since the Big Bang | 18 |
| Grains of sand on Earth | 20 |
| Stars in the observable universe | 22 |
| Atoms in a human being | 27 |
| Possible 12-word phrases | 39 |
Each extra digit multiplies by ten. The difference between the second-to-last row and the last isn’t «a bit more»: it is a trillion times more than all the atoms in your body.
Why it doesn’t improve with time
This is the point almost nobody explains. Even if computers doubled in speed every year — and they no longer do — each doubling only removes one of those thirty-nine digits every three years or so. It would take more than a hundred years of continuous doubling to make a dent, and long before that we would hit physical limits of energy: there isn’t enough energy in the solar system to run that count, however efficient the computer.
Where the exact boundary is
All of this applies to the whole phrase. The gap between that and a workable case is enormous and worth seeing side by side:
| Situation | Combinations to check |
|---|---|
| 1 word missing of 12 | about 128 |
| 2 words missing | hundreds of thousands |
| 3 words missing | hundreds of millions |
| The whole phrase | a 39-digit number |
The first three rows are ordinary work. The fourth isn’t «very hard work»: it is a different category. It is expanded in I’m missing one word of my 12-word phrase.