Just recently, I ran
across an article by a Japanese professor about the uniqueness of the number
6174. Being a math major, it piqued my interest and I was not disappointed. A
mathematician by the name of D. R. Kaprekar came up with an operation where you
would take any 4-digit number where not all the digits are the same, and make
the largest number out of the digits and the smallest number of the digits,
i.e. arrange the digits from biggest to smallest and from smallest to biggest
adding 0’s as necessary. If you subtract the smallest from the biggest, you get
another number. That is the Kaprekar Operation (hereby called KO). The amazing
thing is that if you then take the final result and do the KO on it and repeat,
you will eventually end up with the number 6174. In fact, we can say that it
will take you at most 7 times of doing that KO to reach 6174.
For example, let’s pick
5623. The biggest number is 6532 and the smallest is 2356. Subtracting, we get
4176. Repeating we get 7641 and 1467, then 6174. If we continue, we get 7641
and 1467 (look familiar?) and then 6174 again.
Another one, 40. Biggest
number is 4000 and smallest is 0004, or 4. Subtract, 3996. Then 9963 and 3699,
subtract, 6264. 6642 and 2466, subtract, 4176. Then 6174,
For me, this is the area
of Math that I really enjoy. It is called Number Theory. It gets into how you
can tell if a number is divisible by 3, 6, 9, 4, or 8? What is a pattern to the
decimals when you divide a number by 7? How can you find prime numbers? Etc. So
of course, this was so cool to me that I wanted investigate it. Now in math,
you can do this a couple of ways. First, you can try it out on a few numbers.
So I did and it worked. Then, since we only have 9999 numbers to try (actually
there are even less that we need to try but I was in a hurry), I wrote a quick
Excel Macro to run the operation and spit out the results. Boom, it worked like
a charm. After 72 lines of code, I had a spreadsheet that had all the possible
input numbers and the result of using the Kaprekar Operation on them
iteratively. By Joe, all of them ended in 6174 in 7 or less iterations. Thus,
this article called this number Beautiful in a mathematical sense. Yes, math
nerds have a different take on what is beautiful when it comes to numbers.
By the way, these are
called the kernel of the operation. If you use 3 digit numbers, the kernel is
495. There is no kernel for 2, 5 or 7 digit numbers and there are multiple
kernels for 6, 8, 9, or 10 digit numbers.
But that was not fully
satisfying to me as a Mathematician. I wanted to know why. What is going on behind
the scene? This is where the article burst my bubble. It said that we can show
that it works for all 4-digit numbers where the digits are not all the same; we
can show actually that we only need to check 30 numbers to ensure that it
works. But the one thing that no one can prove is why this works.
After mentioning a couple
of other of these type of beautiful numbers, the author made a comment that
seemed interesting to me. He said that we are drawn to these numbers “because
they are so beautiful. And because they are so beautiful we feel there must be
something more to them when in fact their beauty may just be incidental.”
While the analogy breaks
down a bit, I started thinking about prayer. Sometimes, we want to pray and
tell God to do what we want. When it works, we are happy. We think we found a
formula: we pray, God responds, we are happy. Beautiful, right? Yes, it is
beautiful but that does not prove why it works. Prayer works like that only
when we happen to want the same thing as God’s will. Incidental! We did not
discover some great truth. In a sense, we got lucky. If we want something
outside of God’s will and pray for it, we then can get disappointed when God
does not answer our prayers the way we want. We cannot manipulate God. We need
to rethink our attitude about prayer. As Carey Nieuwhof said in his blog,
“prayer is not a button to be pushed nearly as much as it is a relationship to
be pursued.”
But prayer is like the KO.
Where the KO changes the number, prayer is meant to change the person praying.
And just like eventually with the numbers, you will get to the kernel, with
prayer, eventually, we get changed into someone looking after God’s will and
not our own. Yes, it takes more than 7 times for this change to happen but if
we let the Holy Spirit work on us, it will happen.
How can we be sure of
that? Unlike with the KO, we do not have a finite number of cases to run to
verify that prayer works. In addition, we have no way to mathematically prove
that it works either. But, we can look at the Bible and see the pattern of God revealing
his will when his people submit to him. I know that I fall into the trap of
seeing prayer as a grocery list that we give to God. Instead, we need to see it
as a way for us to grow closer to Him. We may ask for our way but God gives us
something better: His Will. Just as the KO changes the number each time and
eventually gets to the kernel, may we use prayer to help us change to be more
conformed to God and His Will for our lives.
