Say it ain’t so … narcissism in the Natural Numbers?

Thanks to the digital age, many people are slowly beginning to believe that everything they do has some special significance.  Whether it is what they had for lunch, how many times they yawned in meeting or the number of licks it took to get to the center of a Tootsie Pop, every boring fact of people’s lives has somehow become important.  To put it simply, thanks to technology, narcissism is running wild.

So, where can people go to escape this growing epidemic?  For a long time, I took refuge in the wonderful world of mathematics.  There, I cannot be bothered by the all important mundane facts of people’s lives.  I can focus my thoughts and energies on the mysteries of numbers, free from narcissism … or so I thought.

Unfortunately, for me and many people like me, even in the world of mathematics, we cannot escape narcissism.  It turns out that our very own Natural Number system has a problem with narcissism, or what mathematicians call Narcissistic Numbers!

What is a narcissistic number, you ask?  Well, the official definition is as follows:  a n-narcissistic number is an n-digit number that is the sum of the nth powers of its digits.

For example, take the number 1634.  Here, n = 4.  So, if 1634 is a narcissistic number, then it follows that:

1634 = 1⁴ + 6⁴ + 3⁴ + 4⁴

^or

1634 = 1 + 1296 + 81 + 256

Now, before you give up on escaping narcissism and start posting your own important facts involving the number of hairs you have on your kneecap, there is still hope!  As it turns out, there are only a total of 88 narcissistic numbers in our Natural Number system.  Further, it appears that there is no special mathematical significance to these numbers … narcissistic, indeed!  So, if you can find a way to avoid these numbers, you can still enjoy many hours of narcissistic-free entertainment in the world of mathematics.

(Thanks to MathWorld for the official definition of a Narcissistic Number: Weisstein, Eric W. “Narcissistic Number.” From MathWorld–A Wolfram Web Resource.http://mathworld.wolfram.com/NarcissisticNumber.html)