How to find a sunken ship of gold
Countless ships and planes have gone down somewhere in the ocean, and finding them is not mean feat. One such vessel was the SS Central America, which sunk in 1857. It was known as the Ship of Gold, and when it went down it had 14,000 kg of gold on board. Obviously a LOT of people were quite keen to find it, but it remained undiscovered. Until, that is, a team of people decided to use something called Bayesian Search Theory, which involves making a map of probabilities using all available data. Larry Stone from Metron Scientific Solutions was involved in this search, and he explained hwo they did it to Georgia Mills.
Larry - The way we went about this search was using this Bayesian Theory. The information available was the last recorded position form Captain Herndon, who was the Captain of the ship SS Central America, who actually went down with the ship by the way, but he hollered his position across to a passing ship about 6 o'clock at night. The ship went down at 8 o’clock. There were passing ships that saw the Central America. Survivors were recovered the next morning at about 8 o’clock. We had a position for that ship that recovered them.
So you put together all this information in this Bayesian framework and the way you do this is by quantifying uncertainties and terms of probability distributions. And then, combining the information into your probability map using something called likelihood functions and likelihood functions are the common currency of information in this Bayesian analysis. You put together all these clues, and that’s part of the trick here because the Bayesian approach is the principle approach for incorporating all the information available to you, both objective and subjective to produce a probability map for the location of the wreck. What the probability map tells you is those places that are high probability for the location of the wreck and those that are low. The high probability areas are where you want to search
Georgia - Let’s break this down. You’ve lost your favourite hat - you idiot! So how can Bayesian Theory help you find it?
Well, you know you often leave it in your bedroom so it’s quite likely to be in there. But you also sometimes wear it in your kitchen and a friend tells you he last saw it in your study. You draw up a grid of locations using all the data available to work out the probability of finding the hat in each location. Maybe taking everything into account it’s got a 70% chance of turning up in your bedroom but only 20% of being in the bathroom.
But what makes this special is you can update your data as you go. For example, another friend says they heard a rumour it was in the attic so you increase the probability of it being there. Or you search a room once and don’t find it so the probability it’s there reduces. And this is key, even if you’ve looked in a place, it can still have a higher probability than being somewhere else. So, according to your model, it sometimes makes sense to search somewhere twice before searching somewhere else.
Now, imagine you’ve got a lot more data, a lot more places to look, a few more computer processes to play with, and that’s largely how Bayesian Theory is used to find wrecks full of gold on the bottom of the sea. Speaking of which…
Larry - In the case of the SS Central America this worked out. We found the wreck and they recovered a ton of gold bars and coins and sailed back into the harbour in Norfolk. There were bands, and newspapers, and television showing their arrival.
Georgia - It’s the find of the century. Maths of all things is used to find a ship lost for hundreds of years. And everyone ends up rich and lives happily ever after…
Larry - Well, sadly it didn’t end quite that way.
Georgia - Ah. First off the old insurance companies who’d paid out when the original ship demanded, and were rewarded, in court a substantial amount of the gold recovered. And then it was up to Tommy Thompson, the team leader, to divvy up the rest between the investors.
Larry - But no. For some reason he didn’t do that. He didn’t sell the gold, he didn’t give the investors any information about what he was doing with the money. He borrowed a lot of money and finally the investors asked him to show up in court to explain what he did with the money. Instead of showing up in court in Ohio, he fled to Florida for a couple of years and was finally arrested down there, and he’s now in jail until he will tell people, the investors, what he did with the money. That’s the sad end to that story, unfortunately.
Georgia - Well, this story doesn’t have a particularly happy ending; Bayesian Theory is still used all the time in modern day search operations…
Larry - We did this, also, for the search for the Air France 447 flight that crashed on it’s way from Rio to Paris. The people in charge of that search were the BEA (the French Bureau of Enquires and Analyses) and they had, for two summer seasons, searched unsuccessfully for that wreck. Then they contacted Metron and me and said would you use all the information available from this search. Not only the last reported position of the aircraft, but the debris that drifted and was picked up, and all the unsuccessful search that was done. So we incorporated all that into a probability distribution for them and the next summer, beginning of the early spring season, they began a search looking in the high probability region of that probability map that we delivered to them and they found the wreck within one week of search. So that’s a big success story.
Georgia - Oh Wow!
Larry - It doesn’t always happen that way but it’s very satisfying when it does.