Some 3 weeks or so after the disappearance of MH370 in 2014, I reverse-engineered the satellite BTO data. Back then, there was a huge effort from people all over the world to try to contribute something to finding MH370. I guess I wasn’t willing to wait for either Inmarsat or Malaysia to release the actual data, so I took it upon my self to at least estimate it, trying to see if I could decode the location of MH370. Malaysia finally released the data underlying the ping rings, and I found out I didn’t do too bad as far as estimating, given what I had to work with.
I would argue without the ping data, there would have been no subsurface search at all. Other than the actual subsurface search to date, which tells us a substantial swath of ocean where the plane is likely not, and has invalidated many hypotheses, I rank the BTO ping rings as our most important data. Back in 2014, a lot of people thought if we could decode the clues in the satellite data, we could find the plane, even without finding debris clues. It was simply a matter of unlocking the secrets contained therein. I had always thought you’d be better off trying to find an “X” on the last ping ring.
Now it’s 2018 and official search efforts have found the secrets of the ping rings to be elusive and really haven’t put much investigative effort into hints of an “X.” If you’re willing to buy my arguments that multiple “X” exist at the Waypoint Hypothesis and convince Malaysia to repost the “no cure, no fee” $75 million award for finding it, the Waypoint Hypothesis remains unsearched.
This post, however, isn’t concerned about the various “X” but instead asks: Are there secrets in the ping rings we have missed? Well, yes, I believe there are and it has taken over four years to find them. This post poses a riddle for you to decode, and I will post the answer in the next post.
Review Bayesian Occam’s Razor
To wade through the rest of this post, it would help to have a vague understanding of Bayesian Occam’s Razor. I discovered it existed in 2018 and have become fascinated with it. Most people have heard of Occam’s Razor, but what is less know is it is not just a saying or intuition, but it has a basis in mathematics of the Bayesian kind. It seems to be a fundamental property of our existence. After thinking of it for some time, I think I can explain why and why it matters to the search for MH370. First, a refresher on the principle of Occam’s Razor, which Swinburn formulated best:
… the simplest hypothesis proposed as an explanation of phenomena is more likely to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it is an ultimate a priori epistemic principle that simplicity is evidence for truth.
and how Bayesian Occam’s Razor works from Jefferys and Berger in Sharpening Ockham’s Razor on a Bayesian Strop:
Ockham’s razor is usually thought of as an heuristic, that experience has shown to be an effective tool. It is less widely known that under some circumstances, it can also be regarded as a consequence of deeper principles.
Bayesian Occam’s Razor is simply a mathematical way of computing a number to quantify “simple.” Given two or more competing hypotheses, one can compare them with Bayesian Occam’s Razor.
A Thought Experiment: Catching an Escaped Prisoner Riddle
We now go to an alternate reality to perform a thought experiment. Don’t worry if alternate realities exist – this is just a thought experiment and I am using alternate reality because I want to use familiar references to our reality, but change some details for illustration purposes. However, the experiment is intended to mimic the problem of finding MH370. Have you absorbed the lessons of Bayesian Occam’s Razor well enough to lead a team to find this escaped prisoner?
The setting is the United States, which is like the one we know, but different, and a prisoner has escaped from somewhere in the east-central US. The prisoner stole an official unmarked prison vehicle. In this reality, the US is completely cashless. We know the prisoner did not have access to electronic value of any kind, and even if he did, he could not have accessed the fuel tank to refuel it because we are certain he didn’t have the access code. Unbeknownst to the escapee (we believe), each prison car is tracked by Inmarsat satellite – via periodic handshake pings, and because the satellite wobbles, the resultant doppler shift. Experience has shown the doppler shift is near useless for locating the car, but the science team has assured you the Doppler at least rules out the possibility that the car headed towards the western interior of the US – it must have headed eastward. The curious thing is that the last (7th) ping ring tells us the escapee traveled quite a distance away from the prison, because the ping ring is centered over the central US (please don’t argue that a geostationary satellite would be at the equator – this is alternate reality). The seventh ping ring just happens to catch the Florida Keys, arcs into the Atlantic Ocean and back towards land right through New York City, then upstate New York and Canada. Since we believe he did not drive into the Atlantic Ocean, that basically leaves two destination towns that the ping ring intersects: Key West, Florida and New York City. Canada has built an impenetrable wall to keep Americans out and for reasons I won’t try to make up, we can rule out upstate New York. Stranger still, we know the air turbine deployed to generate power because the engine must have quit and then we never received another transmission. The experts insist this indicates the car ran out of fuel in one of these two cities and gradually coasted to a stop and the prisoner must still be close to that point. Which city do you send your team to, if you can only choose one?
Aside: At this point, the problem is pretty analogous to the problem of finding MH370 that we are faced with now. In the case of MH370, by virtue of having searched the middle area of the 7th arc, we are left with only one point at the extreme south end (The Waypoint Hypothesis) and the far north.
At this point, without more information or incorporating your own subjective biases on human intent, you would have to say it’s a coin flip (50% / 50%), right? Would you still attempt to reason about the problem? What if I told you that if I ended the experiment at this point and simply flipped a coin to decide the answer, would you still try to reason about the outcome? What if I told you this was a real example, but it’s known the escapee had no preference on destination and simply might have flipped a coin to decide which way to head? I hope that most people can see that while you might act on a hunch about human nature in deciding where to send your team, your expected outcome is at best 50/50 given the information we have. If I relaxed the criterion and allowed you to split your team, what percent split would you use? I would argue for 50/50 as there simply is no other logical answer.
Let’s see if we have more information to help us. Your technical team notices a couple of key things. The geometry of the satellite, the location of New York City, Key West and the prison all conspire to create the following situation: The travel distance from the prison to New York City is relatively short, and the most direct pathways to New York City that match the ping rings generally result in too much fuel and/or relatively slow speeds. In contrast, the distance from the prison to Key West is relatively long and there is only one, virtually direct pathway to Key West for which the car conceivably could have made it. Your engineers explain fuel mileage is related to air drag which is proportional to the square of velocity and any short burst of excess speed would eat up fuel and therefore the speed had to be pretty constant ….yada, yada. They go on to explain they calculated it would likely involve driving the car without the air conditioner on through the heat of Florida to even make it as well as driving at an efficient (but slightly fast) speed, virtually no more or no less to match the timing of the ping rings and stretch the fuel supply.
In contrast, there are a plethora of possible pathways to New York City that work, with a complex network of roads that connect multiple towns along the way. Each town might have six roads leading out to the six closest towns. Because there is plenty of fuel, your data modelers simply need to pick random pathways through this maze, and vary the average travel speeds between ping rings to match the satellite data. Does this additional information change where you send your team?
Aside: Again, we mimic the MH370 problem. The Waypoint Hypothesis faces extremely tight tolerances and there was only enough fuel to make it there (barely). The Waypoint Hypothesis essentially predicts the airpacks had to be turned off to have enough fuel. Further, MH370 had to be flown at or near a relatively specific, but common speed to arrive there, match all of the rings and just run out of fuel at the 7th arc. In contrast, more northerly paths typically require curvy spaghetti paths to reach latitudes on the northern portion of the arc, have plenty of fuel to get there and typically utilize slower speeds. It’s difficult to generalize all possible paths for more northerly destinations, because there are so many, but these are their general characteristics favored by the modelers.
At this point, if you have absorbed Bayesian Occam’s Razor or have been following this blog, you realize you have an edge (better than 50/50 odds) and know which city to send your team to that maximizes your chance of capturing this escapee. I can say this knowing that I haven’t even given you the ping ring data yet, but rather have simply told you general characteristics about them. If you had only one choice of city to send your whole team, you could confidently send them now without knowing anything else.
However, there is much more to Bayesian Occam’s Razor that I have discovered in just the last few days. Let’s explore.
You look at some of the path solutions your technical team has come up with. Some modelers restrict the speed changes as much as possible (constant speeds) and try to search for road pathways between ping rings that match. Some don’t worry about speed changes as much and allow the speed to vary from extreme top speed to very slow speed. They all tell you it’s actually fairly hard to match the ping rings except by picking random paths and adjusting the average speed to match. The most direct routes must necessarily use slow speeds but end up using very little fuel, but your data modelers tell you they assume the driver jettisoned fuel or wasted it in some way, driving in circles, perhaps, or driving way out of the way before heading towards New York City to assure the car runs out of gas at the 7th ring. Some even sacrifice ping ring fit for more “normal” and “natural” paths. You realize each modeler is injecting some opinion about human nature regarding path selection into their solutions.
Aside: Yet again, we mimic the state of the MH370 search. Modelers still propose searching further north on the 7th arc past the last block searched by Ocean Infinity requiring ever-curvier spaghetti paths and encountering the “too much fuel problem.” I’m not sure at this point modelers even bother fitting paths anymore as it has become apparent that if you search long enough, you will find one that fits, especially at the more northern latitudes. Constant speed and constant direction of turning paths seems to be the most popular. Few choose zigzag paths or highly variable speed, but lets be honest – those paths could be conceived and will fit satellite data just as well and if not too extreme lie within B777 performance limits. I’ve tried to argue that slow curvy spaghetti paths are against human nature for a flight I believe was planned by a human intent on disappearing the plane, but nobody seems to listen. So if you want to use a zigzag, variable speed paths between the rings, you go right ahead and you can quote the Big Lebowski if anyone claims it’s not what the perpetrator would do:
One of your modelers seems to have missed a memo and never realized there are intermediate ping rings, but only the last (7th) one, so they have only been fitting paths only to that one. The paths mostly look as reasonable as any of your other modeler’s paths, however, and this modeler has a lot easier time generating them since there is only one fit instead of seven. One thing is certain, however, none of these ever fit the existing intermediate ping rings exactly, except for one path. They mostly exist in an alternate, alternate reality or realities, ones that are clearly possible, but simply did not happen, according to the data. They mostly generate sets of rings that are entirely different from each other (excluding the seventh). It’s as if this modeler is exploring multiple alternate realities that all finish on the same 7th arc, rejecting the ones that are not plausible considering car performance and range and keeping the ones that are.
Can you guess why most paths never fit the real (well, real for our alternate reality)intermediate ping rings, and why only one path fits all of them? Can you see the implications of that? Now do you realize even more clearly exactly where to send your team? Have you decoded the secrets of the ping rings? It only took me a bit over four years to realize the nature of the problem in this detail, but I finally discovered the answers, and will share them in the next post.