440 Can You Appreciate a Good Paradox?

Brainden.com gives several examples of paradoxes as well as this definition: “A paradox is a statement that contradicts itself or a situation which seems to defy logic.”

Alan Parr suggested I write no more than the fact that 440 is the sum of consecutive prime numbers. It may seem to defy logic that he would want to try to figure out what those consecutive primes are without any hints, but he proved yesterday he is up for the challenge. Check the comments to see if he (or somebody else) can figure out what those prime numbers might be. I am waiting to see if he can again defy logic and figure them out. In the meantime, the factors of 440 will be listed at the end of this post.

I remember watching the episode of Star Trek in which several androids malfunctioned because they couldn’t handle paradoxes, but most humans seem to be able to handle paradoxes just fine. I’ve written one myself that I hope you will enjoy:

I overheard a pair of docs in the middle of a heated argument. One of them said, “As I have stated hundreds of times before, no matter what I say, YOU ALWAYS contradict me!” The other doc shook his head saying, “No, no. That’s not correct at all. YOU’RE the one who’s always contradicting ME!” I hate to hear arguing, so I left, but I have to wonder if they ever worked it out or are they still arguing about contradicting each other even today?

You might not expect to find paradoxes in the The New Testament, but crosswalkblogdotcom describes several of them beautifully in I-will-take-paradox-for-200-alec.

Shakespeare and Wordsworth used them as well. See examples in Is-this-phrase-grammatically-and-semantically-correct?

When I first joined twitter, this is part of the first conversation I had:

Steve Morris has written about paradoxes on several occasions including his very popular post titled Failure-to-fail. If we fail to fail, we become the biggest failure.

It is a paradox to have to be willing to fail in order to really succeed. As Michael Jordan stated in a Nike commercial: “I’ve missed more than 9000 shots in my career. I’ve lost almost 300 games. 26 times, I’ve been trusted to take the game winning shot and missed. I’ve failed over and over and over again in my life. And that is why I succeed.”

We will face setbacks, trials of faith, and other paradoxes in our lives, but we must not give up. All of them are opportunities for us to learn and grow. We actually ought to be grateful for them, because as we face them, we become stronger and more successful. Zeno’s paradox would have us believe that we can never reach our goals. That is simply not true. We can reach them if we keep them in our sights and keep going toward them relentlessly.

Here are the factors of 440:

  • 440 is a composite number.
  • Prime factorization: 440 = 2 x 2 x 2 x 5 x 11, which can be written 440 = (2^3) x 5 x 11
  • The exponents in the prime factorization are 3, 1, and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1)(1 + 1) = 4 x 2 x 2 = 16. Therefore 440 has exactly 16 factors.
  • Factors of 440: 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440
  • Factor pairs: 440 = 1 x 440, 2 x 220, 4 x 110, 5 x 88, 8 x 55, 10 x 44, 11 x 40, or 20 x 22
  • Taking the factor pair with the largest square number factor, we get √440 = (√4)(√110) = 2√110 ≈ 20.9762

Since 440 = 20 × 22, we know that 441 = 21 × 21.