The unbearable brightness of boating

July 2008

By Tom Snyder

I’m a talker on a boat. I know that. I share countless words, except when I’m being quiet, at which time I only say a lot of words. I find my ideas fascinating and generally won’t quit until the crew experiences a comparable thrill.

On a recent delivery with Sandy Marsters, from Boston to Portland, we resolved a lot of thorny issues. Democracy is now the better off for some of our breakthroughs. We put the human condition up on the lift, took a look at the underside and made a few adjustments. (You should all be feeling the benefits over the next few decades.) We read aloud from Dodge Morgan’s book, thereby deciding – for all humans of any age – on the requisite of setting challenging life goals. We came up with a few goals for people who will surely be pleased to hear about them.

I was confident, a day out of Gloucester, that we were on a conceptual roll that would never end. Until at dusk , sitting in the cockpit, I introduced the irresistible conversation starter that my breath was visible. I was prepared to expand the subject to include vapor pressure, when Sandy said, “Yeah, like I’ve never seen someone’s breath before.” (You probably know Sandy as the founding editor of this magazine. I know him as a guy who has seen enough visible breath.) This was a clear signal to me that everyone, except me, has their threshold with nonstop speculation and enlightenment.

To say that I retreated to an inner world, pouted, and retired to my cabin would be a wild exaggeration and only superficially true. But I did decide to hold my next speculation close to the chest. I had, in fact, been nurturing a highly charged line of thought for a few hours, preparing its compelling introduction, but sadly for Sandy, he would never experience it. It had to do with boat speed and with making decisions about how long to let one’s boat idle in light winds. But a bit more rumination on the topic exposed the mother load of all cerebral adventures. Again, Sandy, sorry you had to miss this one, because I found a doozey, better than drugs. (Actually anything is better than drugs. Woody Allen reports that the only time he tried a recreational substance, he tried to take his pants off over his head.)

The doozie of all brain food emerged after I, by happy accident, alone in my cabin, gave myself what I thought would be a simple trip-planning problem to solve. After filling a notebook with sketches and formulations – after narrowly escaping from a conceptual black hole – I can now present this bizarre marvel to you. (Sandy, I think it’s only fair for you to skip this section. I’ll let you know when you can return.)

Say you want to cruise from point A to point B. Anywhere to anywhere. And say that when you arrive at point B you want to be sure to have averaged 10 knots. Now, say when you reach the halfway point, you realize that you have so far only averaged five knots. How fast will you have to travel for the rest of your trip to average 10 knots?

Make a guess. Say it out loud. How confident are you in your answer? What if I allowed your answer to be off by 100 knots? A thousand knots? Ready to put a couple of bucks on the table?

If you are putting money down, you’re giving it to me. If you guessed 15 knots you were wrong. Or 500, or a million, or seven trillion. The answer is that you could never go fast enough on the last half of your trip to get the average up to 10 knots.

An interesting point here is that we all assume in most areas of computation that, even if we don’t know the exact best method to solve a problem, we can always use intuition and common sense to come up with a reasonable guess, or even a somewhat unreasonable guess. But to have our guess be off by infinity (a very large number) seems strange. I asked about 15 random people in Harvard Square yesterday to make a guess on this little problem. Doctors, lawyers, professors, waitresses, graduate students, consultants – they all got it wrong. The consultants were the most likely to quickly change the subject.

Here is the arithmetic. Let’s give the story some real world numbers. You are going 100 miles from Boston to Portland and you want to average 10 knots. That means you will be going 100 nautical miles in 10 hours. At the halfway point, you calculate that you have averaged only five knots. That is, you have gone 50 miles in 10 hours. Wait. Do you recognize that number – 10 hours? You have gone halfway, but you have used up all of your time. There’s no way you can possibly go the entire 100 nautical miles in 10 hours. Those 10 hours are gone.

Why is this so hard to understand instinctively? It most likely has to do with the indirection of the question. The problem at its core is really about time and distance, but by presenting itself in terms of speed and average speed, we get carried away.

Several years ago some researchers from Harvard asked a series of simple math and science questions to hundreds of students at a high-school graduation. The researchers were thrilled to prove that the students were consistently wrong and thus woefully taught. To my ear, all of their “simple” questions had that sleight-of-hand quality of indirection that we just experienced above. This is an area worth more study.

Sandy, you are free to re-enter now. Thanks for your patience. We have been chatting about seeing someone’s breath on a boat, but we are just finishing up. What shall we talk about next? One area that I’ve been toying with is my adolescence. Fun?