Our place of worship, Frisco Bible Church, is about an 11-minute drive from our home; on this morning all three of my boys were riding with me in my vehicle, and I had one of the most eclectic 10 minute conversations I could have possibly imagined.
It started innocuously enough: Matthew piped up and mentioned how much he is into puzzles right now, and he mentioned that he has figured out most of mathematics is like a puzzle to solve. Which it is. (My degree was in mathematics, which has served us well as we homeschool our boys). I then told them about one of my favorite stories from math, about how Gauss developed the formula for summing a sequence of consecutive positive integers.
If you don't know the story, Gauss was, like most geniuses, not doing very well in primary school, and was assigned by the master to add up all the numbers from 1 to 100 as a form of punishment. (It is the mathematical equivalent of writing lines, and it should take a good while to complete when done manually). The young Gauss, however, solved it as a puzzle and returned with the correct answer in a matter of minutes. And his formula is still used today...
After that little foray into math history, the conversation then turned to the great unsolved conjecture from computational theory, P versus NP. Yes, it really did. Just a few days before, I had been watching an episode of "Numb3rs" with my boys, and the mathematician in the series, Charlie, had retreated to his garage during a time of emotional duress and worked on the PvNP problem as a way of holding his emotions at bay.
And so now, Matthew wanted to know what it was all about. Talk about opening a can of worms: I only have a B.S. in Math, and I'm not Charlie Epps... or Gauss.
So, with only my basic understanding of what the PvNP problem even entails, I endeavored to explain it to my sons. (In a nutshell, the idea is to prove that if a computer can be used to verify a solution to problem, then the computer ought to be able to be programmed to find a solution as well; if this thing is ever proven {you can win $1,000,000 if you do}, it will have a huge impact on the computer sciences).
Obviously, this wasn't making sense to them (did it make sense to you?), so I struggled to find an analogy that would help them understand the difficulty often faced when creating algorithms that can be used in computer programming to solve problems. Even the simplest things that humans can do without much effort or thought (such as sorting items) require an algorithm and multiple lines of code... all to teach the computer how to do these things, so the computer can do them very, very fast.
Then I remembered an old motivational demonstration I had heard about, designed to teach people about improving their communication techniques: making a PB&J sandwich. I told them I had a loaf of bread, a jar of peanut butter and a jar of jelly, and a knife. I asked them to tell me how to make a PB&J sandwich. (Most people will immediately start with 'put the peanut butter on the bread', so you put the jar of PB on top of the loaf of bread.... you get the idea). The creation of the 'algorithm' is the outlining of the very specific steps to get the 'computer' to properly assemble the sandwich.
Since, in this instance, my audience is made up of pre-teen and teenage boys, moments of hilarity ensued and filled out the remainder of our drive. "I'm spreading the jelly all over the plastic bag of the bread loaf!"
It was a very packed and interesting 10 minutes.
So......
What's the point of this otherwise-incredibly-nerdy-post-that-will-bewilder-most-folks?
Far too often, when my sons try to engage me in conversation, I do not give it the effort I really should. You know what I mean, the 'uh huh' syndrome... or the 'I haven't got time to get into that right now', or 'Dad would like a few minutes of no questions'. Guilty on all counts, plenty of times. Especially since I tend toward the curmudgeonly, a card-carrying G.O.B.
This morning, for some reason, I didn't. And it was a wonderful time... and will be a lasting, precious memory for me.
Every now and then, really listen to your kid's questions, no matter what your mood or the situation. Whether it's unsolvable math problems, sports, the dating habits of their favorite musician, or the intricacies of Spongebob. They asked, so it's something that interests them. Discuss it with them and they will feel special.
And you might find out that you do too.....
Thanks for sharing. I can so picture that conversation. That's not quite my understanding of the P=NP problem, but I understand the need to simplify. I've also used a recipe analogy to explain programming to my kids, but with not quite so much of a fun element. I should try that.
ReplyDeleteI also once saw the light go on when I explained basic algebraic variables as roles in a play. Different people (numbers) can play that role at different places and times.
It is absolutely amazing to me the conversations my brothers get into :)
ReplyDeleteThat said, tell me more about that $1M...