They are numbers. But not just ordinary numbers. But before we try to explain why, I suspect there are among the readers who already know what they are. The explanation will not be for them. However, they might benefit from whatever insights they will read into why these numbers are special, along with several others more popularly, if not commonly, known. But I must hasten to wager that these numbers are rarely known to many.
First, we acknowledge that language, in every manner that they are used or exhibited, is the single and most special quality that separates us from all other creatures. It is what makes us human. Words - singly or part of a group - are what and how we communicate. They are spoken or written. In prose or poetry, in songs and speeches, in sad or happy tones, words are the meat and potatoes of language. But lest we forget, we have numbers that are significantly part of language as well, and they are what give superpowers to language.
One example of the superpowers of numbers are when they are employed in statistics; in polls (in about a month, numbers will decide the fate of a nation in crisis); in defining socio-economic issues because numbers can dominate in how goods are sold and purchased; inflation numbers affect the rich and the poor and sometimes the very viability of a business or how a family manages to make life livable, and so many other things too lengthy to list here.
Okay, so let's dive into these two numbers: 6174 and 495. Then we'll go into more insights on numbers later. Including zero, which technically is not a number but it is the most important fuel that provides numbers with unlimited energy because it not only can double up, it can exponentially increase the power of numbers. However, it too can literally render a number as powerless as a feather wafting in the air, practically reducing a number to inutility. We'll get to it later.
6174 is named after an Indian mathematician named D.R. Kaprekar who discovered it. It is now known as Kaprekar's constant.
The number will show up constantly when manipulating the digits of a four-digit number in a certain simple way of subtraction that will result in 6174 all the time.
"Take any four-digit number, with at least two of the digits to be different from each other (leading zeros are allowed).
Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.
Subtract the smaller number from the bigger number.
Go back to step 2 and repeat".
It's best to illustrate with an example. Take the number 8457. Arrange it in descending order to become 8754. In ascending order it becomes 4578. Now, subtract the lower number from the higher number.
8754-4578=4176, now, 7641-1467=6174
Let's try the number 1234:
4321-1234=3087, now 8730-378=8352, 8532-2358=6174
Try this on your birthday, using month and days, i.e. Dec. 7, as 1207. 6174 will always show up at the end, in as short as two steps but no more than seven. Remember though that at least there must be two different digits. It will not work, for example in 1111, or 0000. Which makes you special if your birthday is November 11. Your birthday thwarts the Kaprekar's constant.
Now imagine if you are tasked to determine the variety of numbers or number combinations that will give you the constant 6174? It is a huge number. That's why, even a combination padlock, shown below, poses a challenge. Put simply, four digit combinations are a formidable challenge even if we know that given the Kaprekar's routine, you will always come up with a constant, 6174.
495 is the constant when using the same operations on three digits (always keeping in mind that at least one digit is different from another. Sometimes, it only takes one routine to arrive at 495. The number 612 will give us 621-126=495. And on and on for any 3-digit number.
n+1... is a simple example of an algorithm instruction to add 1 to any number in a series, say 1+1, 2+1, 3+1. It can easily be made complex by simply modifying the definition of n or the value of 1 to something else.
The algorithm behind the Kaprekar's constant is just a tad more complicated.
Throughout our history since our ancestors discovered it, the role of numbers has gone from that of marking how many deer Grog the caveman had to his credit by scratching them on a piece of bone to treating numbers with superstition or fear. Before the Babylonians kind of invented zero, humans had gone on with their lives without it. But once known, the Greeks actually banned the use of it, while the Hindus worshipped it. We will not get into constants like the value of pi or the Hubble constant because they deserve more pages than merely be part of a musing.
Today, there is just no way we can conduct our lives and businesses without the zero. The zero to the right of any digit, and however many is added, gives power to that number and we had to come up with words like billion, quadrillion and gazillion when children run out of words in place of so many zeros. And don't forget the Googol (different from Google). On the other hand, when a zero is written to the left of a number with a decimal point before the zero, the number gets smaller and smaller and for the purpose of nomenclature we add 'th', say, to the million or billion to signify how small a number has become. But get this. Computers only understand zeros and ones when they do the gazillion calculations with "the speed of summer lightning" (from Henry Higgins, in My Fair Lady).
Then we invented infinity (∞) and every number became even a lot smaller, in comparison. We hear that the universe began with a huge explosion 13.7 billion years ago. With infinity to look forward to beyond today, the beginning of the universe might as well have started this morning, relatively speaking, that is. But (∞) is real to anyone who uses integral calculus.
But numbers too have gone on to influence our psyche. They have become tools for superstition. At one time there were no 13th floors in tall buildings. 8 is revered in Chinese culture but 4 is not. 666 is not to be written down or uttered by devout Christians. 7 and 12 are good numbers in both the Old and New Testaments but 40 seems to have a disastrous connotation as when it rained for 40 days and nights that floated Noah's ark. And nothing good came to the Israelites when Moses went to spend 40 days away from them. Before that they wandered through the desert for 40 years.
When I was in college my lucky number was 13. It annoyed my friends but what I was going for was that 13 is a prime number, the consecutive numbers 6 and 7 when added together is 13. 7 is a prime number but although 6 is not, the product of multiplying the consecutive prime numbers 2 and 3 makes 6. At the gym, the locker number I always use when it is not occupied is no. 67. It is not superstition but simply to help me remember every time I go to retrieve my stuff after swimming.
Now, if you are encountering it for the first time, you will not forget 6174 or 495. I know what you are going to do. You are likely to make number combinations from those two on your next lottery pick. If you win, I hope you remember to send me a commission. I'll take a small fraction because even with just a few zeros my share from $120 million will still be a windfall. GOOD LUCK !
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