## Mathematicians to find MH370 Debris?

Australian authorities have announced that satellite images taken of a stretch of ocean 1,550 miles southwest of Perth, Australia, are believed to show floating debris that could be part of missing Malaysia Airlines Flight 370. “It is probably the best lead we have right now,” said John Young, a spokesman for the Australian Maritime Safety Authority. Confirmation of the material’s provenance will likely have to wait, however. While a merchant vessel has arrived in the area to help with the search, poor visibility has prevented search aircraft from locating the debris, and the nearest Australian Navy ship is several days’ sail away.

The search for Air France 447 offers a useful template for how investigators can whittle away at the seemingly unsolvable mystery of a midocean airliner disappearance. After the Airbus A330 went missing over the middle of the equatorial Atlantic in 2009, search aircraft took just one day to locate the first pieces of floating wreckage. The recovery of the black box, however, took another painstaking two years, and a full assessment of its implications another year after that.

The first step after determining the debris’ location is to call in the mathematicians. Based on all the data available—the aircraft’s last known position, route of flight, altitude, prevailing winds, sea currents, ocean depth, and so on—a probability is assigned to each variable, and a distribution map of probable locations on the sea floor is generated. Searchers can then deploy their underwater assets to scour the vastness of the deep, working back and forth along grid lines laid out in the areas of maximum probability.

There’s a deep problem inherent in this approach, however, and it’s that the probabilities are themselves only guesses. Searchers are uncertain even as to the extent of their own uncertainty. In the case of Air France 447, the set of base-set assumptions turned out to be wrong, and the first two search seasons scoured thousands of square miles in vain.

What turned the tide for AF447 searchers, in the end, was better math and better undersea technology. A recalculation of the location probabilities using a different mathematical approach led to the redrawing of the search grids much closer to the site of the plane’s disappearance. And a new type of autonomous undersea vehicle—a robot sub, in other words—became available for the first time. Called Remus 6000, these subs were able to navigate on their own along precise grid lines, ascending and diving to match the contours of the undersea terrain. On April 3, 2011, less than a week after the refined search began, one of the three submersibles deployed in the search returned to its mother ship bearing images of a debris field scattered across an abyssal plain. AF447 had been found. A month later another type of unmanned submersible brought the black boxes to the surface.

# Math equation could help find missing Malaysian plane

Bayes’ Theorem helped researchers locate Air France Flight 447’s black box in 2011

(Video: How Bayesian Search found the USS Scorpion)

Days after a Malaysian airliner with 239 people aboard went missing en route to Beijing, searchers are still struggling to find any confirmed sign of the plane. Authorities have acknowledged that they didn’t even know what direction it was heading when it disappeared.

As frustrations mount over the failures of the latest technology in the hunt for Malaysia Airlines Flight MH370, some scientists say an 18th-century mathematical equation – used in a previous search for an Air France jetliner’s black box recorder – could help pinpoint the location of the Malaysian plane.

Indonesian Air Force officers examine a map of the Malacca Strait during a briefing following a search operation for the missing Malaysia Airlines Boeing 777, at Suwondo air base in North Sumatra, Indonesia, on Wednesday.

In 2009, Air France Flight 447 en route to Paris from Rio de Janeiro vanished over the Atlantic Ocean, triggering the most expensive and exhaustive search effort ever conducted for a plane. After two years, officials could only narrow the location of the plane’s black box down to an area the size of Switzerland.

But Flight 447’s black box was found in just five days after authorities contacted scientific consultants who applied a centuries-old equation called Bayes’ Theorem.

## What is Bayes’ Theorem

Mathematically, Bayes’ theorem gives the relationship between the probabilities of A and B, P(A) and P(B), and the conditional probabilities of A given B and B given A, P(A|B) and P(B|A). In its most common form, it is: (Wikipedia)

$\displaystyle\boxed{P(A|B)=\frac{P(B|A)P(A)}{P(B)}}$

## Proof of Bayes’ theorem (Theorem useful for finding MH370 plane)

The proof of Bayes’ theorem is actually relatively simple, the only requirement is to know the formula for conditional probability (Learnt in H1/H2 Maths): $\displaystyle \boxed{P(A|B)=\frac{P(A\cap B)}{P(B)}}$

From this, we have $\displaystyle \boxed{P(A\cap B)=P(A|B)P(B)}$

Similarly, $\displaystyle \boxed{P(B\cap A)=P(B|A)P(A)}$

But since $\displaystyle P(A\cap B)=P(B\cap A)$, we have $P(A|B)P(B)=P(B|A)P(A)$. Dividing throughout by $P(B)$ gives Bayes’ Formula: $\displaystyle\boxed{P(A|B)=\frac{P(B|A)P(A)}{P(B)}}$

Sincerely wishing that the MH370 plane will be found soon, and hopefully the passengers are still alive.

Also see: Bayesian search theory (Bayesian search theory is the application of Bayesian statistics to the search for lost objects. It has been used several times to find lost sea vessels, for example the USS Scorpion. It also played a key role in the recovery of the flight recorders in the Air France Flight 447 disaster of 2009.)

# Deepest condolences to the loved ones of Math major Philip Wood on board Malaysia Airlines Flight MH370

“We extend our deepest condolences to the loved ones of those on board Malaysia Airlines Flight MH370,” U.S. State Department spokeswoman Jen Psaki said. “Officials from the U.S. Embassies in Kuala Lumpur and Beijing are in contact with the individuals’ families. Out of respect for them, we are not providing additional information at this time.”

Among them is Philip Wood, who graduated from Oklahoma Christian University in 1985 according to school spokeswoman Risa Forrester. He earned a bachelor of science degree, concentrating in math and computer science, and belonged to the Delta Gamma Sigma service organization, Forrester said.

On Oklahoma Christian’s Facebook page, one woman lamented the “heartbreaking news” while a man remembered Wood as “gentle, kind, had great taste in music and was a wonderful artist.”

“Philip Wood was a man of God, a man of honor and integrity. His word was gold,” his family said in a statement. “Incredibly generous, creative and intelligent, Phil cared about people, his family, and above all, Christ.

Malaysia Airlines is asking for prayers from around the world for Flight 370.