How can it be that there are still properties to numbers that we are ‘discovering’, even in this era that we like to call the modern age? Well, apparently there are and I for one am delighted that this is the case. How boring it would be to live in a world in which we think we know everything.
I came across a number the other day that rather surprised me. It has a certain quality of the inescapable about it, and in fact I’ve heard it refered to as The Black Hole Number.
It was first announced in 1949 and is named after the self-taught Indian mathematician D.R. Kaprekar who discovered it, now known as “Kaprekar’s Constant”. It’s an odd beast, so be sure to remember it for your next cocktail party trick.
Follow this simple little game, with only one rule: use any four digit number, so long as at least two numbers are not the same.
Write that number down any way you want. I’ll give you a random sample just to show you how clever I am (no really, it’s random):
8451
Now, rearrange those 4 numerals in order, highest to lowest:
8541
Below that, arrange the numbers lowest to highest:
1458
Subtract lowest from highest:
8541
1458
7083
Next, take the result of that first iteration, your 7083, and do the process again with the same rules. First:
8730
0378
8352
becomes 8532
2358
6174
And that’s it. You’ve hit the number 6174. If you try to play that same trick with the number “6174”, you’ll always end up with “6174”. No matter the starting four digit number, you’ll get here after no more than 7 iterations. In my sample, it took three.
It’s a recursive number, so it repeats itself infinitely and is useful in the study of other mathematical and physical systems that have their own built-in codes for repetition.
In fact this same process can work on different scales – so there is in fact a formula for arriving at 495 using three numbers
What does it mean? Fixed reference points like this suggest a larger symmetry in number theory that’s way beyond me. To make sense of it, some people fall into the mysticism of numerology, suggesting that secret numbers are embedded in the destiny of all mankind. Please don’t fall down that rabbit hole.
But it does remind me of one of my favorite egg-head jokes.
Question: What does the middle letter ‘B’ in ‘Benoit B. Mandelbrot’ stand for?
Answer: Benoit B. Mandelbrot
Get it?
