Solve for x: two sailboats cruise up and down the New England coast all summer, spending one night each at any of the region’s approximately 3,900 islands. The odds that the two boats, in a 24-week season, will drop anchor off the same island are 1 in x.

David Collins ’59 estimated the odds at a million to one. But he had a serendipitous moment in the middle of August when his stately sailboat, Next Dimension, pulled into Camp Island, near Stonington, Maine. Soon after, an old friend came along and dropped anchor for the night alongside him.

The old friend was Collins’s former sailboat: X Dimension, a 43-foot ocean racing yacht that he gifted to MIT in 2011.

Collins, best known for his pioneering work on barcode technology, has a good eye for detail. As he approached Camp Island that afternoon, he spotted X Dimension’s unmistakable red hue, then spied its familiar sail number. It was uncanny.

“It’s not exactly Times Square up there,” Collins says. “It was highly coincidental.”

After both boats anchored, Collins boarded a skiff and motored over to greet the crew of his former yacht. On board X Dimension, three MIT alumni and a former MIT staff member were relaxing after the day’s sail. Captain Eric Brown ’81 and Bonny Kellermann ’72 welcomed Collins aboard.

“Of all the harbors in the world!” says Kellermann, who was sailing on a three-day leg of a two-week long excursion offered to all MIT students, alumni, and staff. “It was a fabulous experience. On that leg, there were the three of us who were alums, one current grad student, one current undergrad, one staff member, and one guest.”

The mix of students, alumni, staff, and friends of MIT on board suited Collins’s vision perfectly in making his 2011 gift.

“I learned to sail at MIT and I wanted to give back to this community an experience that had been a benefit to me there. Sailing’s ability to clear your mind over a short period of time when you have a lot of stuff to think about gives you some balance as a student. There has to be a balance.”

While thousands of MIT students have taken to the six generations of Tech Dinghies since the Jack Wood Sailing Pavilion was built in 1935, for some the lure of deeper water beckons. X Dimension, at 43-feet long, satisfies that craving.

Sailing Master Fran Charles, who first raced against Collins in the 1970s as a teenager in Scituate, estimates that over a thousand students and at least 20 alumni have sailed on X Dimension in its first three years as a vessel in MIT’s 100-boat fleet. “It’s essentially booked for all trips we offer, just about every weekend from spring till November,” Charles says.

“It’s a different style of sailing than what we can teach students in the Charles River,” he says. “They learn navigation, teamwork, responsibility, all of which are important in bluewater sailing.”

Collins learned those skills on the 1957 version of Tech Dinghies, the first ones built of fiberglass. “They were rugged and tough, and they had to be. You didn’t want to flip over in the Charles back then. You didn’t know what was in the water.”

Collins went on to buy his first boat in 1966, and he has upgraded several times. He bought X Dimension in 1991, sight unseen, after his previous boat sank in Marion Harbor during Hurricane Bob. Collins loved racing the boat—with it he earned first place in the 2002 Edgartown Yacht Club race and the 2011 Vineyard Cup Regatta.

When he came across X Dimension at Camp Island, Collins was pleased to find such variety in its crew.

“That’s one of the great things about sailing,” he says. “It cuts across every demographic group. To see seven people on board with such different relationships to MIT isn’t unusual at all.”

{ 6 comments… read them below or add one }

Nice story and although I knew that MIT has many sailboats especially the ones on the river, I had no idea that it had 100 of them.

But with 3,900 islands, common sense tells us that at worst, on any given day, the odds are 3,899 to 1 against mooring on the same island as a certain boat. And given a season of 24 weeks, there are then 168 chances to get a match, resulting in odds that are more like 24 to 1 against. (If some islands are more popular than others, which they almost certainly are, then the odds of a match become even better. Unless one of the boats is deliberately trying to hide by mooring at little-visited islands.)

Back to MIT’s “fleet”. If we were permitted to count all of those boats, a fleet of 100 would give MIT the 27th largest naval fleet in the world, behind Taiwan and ahead of Denmark.

http://www.globalfirepower.com/navy-ships.asp

Granted, it’s a silly way to measure a navy; that same list puts Cambodia at #8 in the world (and North Korea at #1, with 1,061 naval vessels).

This does sounds like a great trip indeed. Wish I was there…

Now to the math (this is MIT after all): Since each of the two boats is moored there only once per season (and not on every one of the 168 days), the chances are 1/3900 * 1/168, which is indeed closer to 1 in a million than to 1/24.

Cheers

Sascha

Wish I was there too…

But back to the math. As mkt24 noted, on the first day alone, there is a 1/3900 chance of two boats mooring at the same island. Even if the odds for subsequent days somehow drop to zero, you still have a 1/3900 chance to meet for the season, so if you keep trying, the odds must get better than 1/3900.

If we assume that boats can visit the same island twice, the odds are exactly 168/3900. Since they can’t repeat, the problem is a little more complicated. But we can bookend the odds as between 1/3900 and 1/24.

I did a simulation of 1 million seasons, and the two boats met at least once per season 42,293 times out of the million, so the odds are pretty close to 1 in 24.

Steve and mkt24, judging from the words “chances”, “subsequent days” and “keep trying”, I think you both assume that each boat goes out to those specific islands more than once. In fact, you assume both boats go out there every day of the season. Then your math is of course correct.

Of course, they both sail a lot during the season. But they sail all over the coast. As I read it, the original poster on the other hand assumes that each boat only goes out to those particular islands once per season. It says “spending one night each”. Under those assumptions, the odds are 1/3900 * 1/168 = 1/655,200, because it is the conditional probability of A, given B (http://en.wikipedia.org/wiki/Conditional_probability).

As an example, if you and I both flip two coins, what are the odds that we both get the exact same ordered result? The possible set of results are these four 2-tuples: {(H,H),(H,T),(T,H),(T,T)}, with H = heads and T = tails. I hope you agree that the odds are 1/4 for both of us to throw let’s say (H,T). The odds are calculated by multiplying the odds that you flip H on the first one (1/2) with the odds that you flip T on the second one (1/2), i.e. 1/2 * 1/2 = 1/4, because it’s the odds of T given H (and not also of H given T).

Now let’s throw two really weird dice. One with 168 sides, and the other one with 3900 sides. We both only throw each die once. The result set is 168 * 3900 (=655,200) 2-tuples {(side1,side1), … , (side168,side1), (side2,side1), … , (side168),(side3900)}. And only one of those tuples represents what I throw. So your odds to throw the same combination is 1 out of the 655,200 possibilities.

Those are the odds of meeting on the same island, given that we both sail on the same day, and assuming we both only sail there once.

Also, I think nobody else cares about this other than you and me. I suggest we take this offline. I’m at sboehme@alum.mit.edu if you like to continue this stimulating conversation 🙂