Though encoding names by their frequency in name lists from an old US census is a terrible way too do it, I shall use it here. Since I do not know the middle names of many of my ancestors, I will ignore them. Thus instead of using the unique descriptor for my full name, Douglas Pardoe Wilson, as 45, 80085, 8, I will only use Douglas Wilson, which is could be 45, 8. Obviously there will be many Douglas Wilsons.
Instead of a unique descriptor using the three numbers, I will use two of them plus my birthdate. Thus I am 45, 8, 1949, 8, 5. I think that is probably a unique descriptor, involving just five numbers. Now instead of using five numbers to describe me, I could add the sequences for my parents. Using the same encoding, my father is 19, 8, 1920, 6, 6. My mother was 14, 999999, 1920, 1, 1, where I have used 999999 to indicate that her maiden surname was not found in that census at all.
The result of doing this is to have a sequence of fifteen numbers to describe myself: 45, 8, 1949, 1920, 6, 6, 14, 999999, 1920, 1, 1. This is entirely plausible. I am in many ways like my father, in many other ways like my mother. Though using something based on name frequency is just plain wrong, the set of fifteen numbers is a better summary of me than the original five.
This can be done for my father and mother also. My mother would be not only the five given numbers, but the fifteen, 14, 999999, 1920, 1, 1, 85, 999999, 1885, 8, 29, 997, 1891, 4, 2. My father would be 19, 80085, 8, 1920, 6, 6, 131, 8, 1880, 10, 16, 256, 7238, 1886, 11, 2.
Having fifteen numbers for each of my parents, I would then have a 45 number descriptor, my own plus each of theirs. If we go back one more generation, I’d get a 135 number descriptor. Using a valid multimensional name space instead of just name frequency, one person might have ten numbers in their own description, thirty in the one including their parents, nighty in the next and 270 in the next. Having a legitimate 270 number vector description of a person would be very useful. In fact a single person may have hundreds of numbers in their description and the multiplication factor may be much higher. Instead of using just parents in multiplying the basic data for a person, birthplace could be used. Eventually megabytes of information could be found for each person existing today and nearly as much for all ancestors.
This is what Recursive Exhaustion is all about. It is one of the most powerful tools I have.