Blogtrek

10890

I used to record and analyze my dreams a lot. I still record them but don't get as much time to look at them. My dream last night, though, was really interesting. I dreamed that I was looking at some calendars, from the 20th and 21st centuries, until I found a calendar for the year 10890. I thought when I saw the calendar that the people of that time would have to contend with another digit in the year. Soon after I woke up I realized the significance of that number. Take any four-digit number. Reverse the digits and subtract the smaller from the larger number. Then take the remainder, reverse its digits and add it to the remainder. The result will almost always be 10890. Once in a while you get zero, and sometimes you get 9999. But usually you get 10890. I may write up a paper or column for my mathematics page about it. The analysis would be somewhat complex, as it would itemize exactly how the carries and borrows would occur. I am usually not that interested in problems like this for they seem artificial and based on our base ten system of numeration. But this one has links to automata theory, which examines systems in which a string of symbols becomes another string according to some rules. Automata can get quite complicated, as in the Game of Life. Adding and subtracting numbers have their counterparts in automata by interpreting the symbol strings as the digits of numbers. So I find a problem like this interesting. I had first found out about it when I was a child, and now I suddenly dream about it.