Interesting to read this article again now, after the raise of LLMs. The bot vs. bot then could perhaps be read as llm vs. llm today?
"The paradox is that this bot glut could eventually push most human interaction offline again; news (real news, that is) will be shared by talking, jobs will be found through connections, and friends will discover major life updates about one another at events and reunions. This is the best case. Another option is that we will have bot-free zones online."
"As more components of our lives become automated, we may want to give some extra thought to which of our routine human interactions are ok to reduce to a bot, and which are worth doing the old-fashioned way, with our own voices, hands, and eyes."
In the distribution of the number of steps needed to reach Kaprekar's constant (6174), I observe an unexpected distribution pattern, with three steps being the most common number of steps required. I cannot think of why this is the case. Has anyone done some though about this phenomenon?
You must post a (auto)translated version! My spider sense tell me I'll get like 30 points here. (Obviously, I can't guarantee that, only 1 upvote.) I guess even some interesting comments, and perhaps a solution.
I read it. (I studied German in Primary School. I don't remember too much, but enough to skim the texts in Norwegian.) I'm also mathematician, so it's the kind of stuff I like. My guess is modulo 9 and then some bounds should explain most of it, but life is never so easy.
If you post the (auto)tranlated version and nobody gives an answer, I promise to try to solve it. (Obviously, I can't guarantee a solution.)
(In my experience, autotranlations does 90% of the job, but you need to polish it a little and in particular ensure the technical words are the correct ones.)
Title: Distribution of the Number of Steps to Kaprekar's Constant
We are trying Kaprekar's routine.
I choose a four-digit number with at least two different digits: 2345. We find the largest possible variant 5432 and the smallest possible variant 2345 from the digits and begin the routine...
This distribution seems a bit strange and not entirely intuitive. I immediately feel that the distribution should have been more evenly distributed.
Perhaps not evenly, but I think that one step to 6174 should be rarer than seven steps, shouldn't it? It has to do with the calculation i guess. There are a limited number of combinations where the result is 6174 on the first attempt. It feels a bit obvious and matches the diagram above. It slowly rises towards seven steps, is that to be expected?
What I find most strange is that three steps tops all others. Why is that? Why is there such a large presence of three? What does it mean? I would very much like to find an explanation for this.
That what I understood. It's interesting. After the second step in your example, they are congruent with 3 modulo 11, but I'm not sure if it's just a coincidence...
Anyway, I think that if you copy this to a new entry in your blog and then post it here, it may get traction and hopefully an answer.
On the side, from the title I was picturing actual knitted parachutes, which isn't the first time. At work, we had a student cansat team who did just that. To everyone's surprise, it worked better than regular ones. Here is a video where she explains it.
