If you want to make the longest boat trip in the world, but no oars have, which way would you take? Five years ago, a Reddit user suggested that a crossing from South Pakistan to northeastern Russia would mean a journey of 32,090.3 kilometers – the longest straightforward journey on earth. Now a team of scientists has finally proved him right.
The Red Dot post came from user kepleronlyknows, also known as Patrick Anderson, an environmental lawyer in Decatur, Georgia. He says he was first fascinated by the question when he scrolled through Wikipedia. The line – nothing but a series of coordinates – appeared in an entry titled "Extreme Points of the Earth". Anderson mapped the dots and released a video to show that the line was in fact straight. "You may be a little disappointed because I did not discover the path, but thought it was cool enough to make a map," he says.
Rohan Chabukswar also thought it was cool. But the physicist at United Technologies Research Center Ireland in Cork City, Ireland, wanted more. "There was no proof," he says. To achieve this, he and his colleague Kushal Mukherjee, an engineer at IBM Research India in New Delhi, began using data from the ETOO1 Global Relief Model of the National Oceanic and Atmospheric Administration over the Earth's surface, which spatially resolves the entire planet approximately 1.8 kilometers, which means that the smallest features covered by the map would be 1.8 kilometers in size. Since the model also contains elevation data, the duo could be relatively sure which points are on land and which at sea.
With these data, finding the longest straight-line path over the ocean became a matter of geometry. All linear paths along a sphere form a shape called a great circle. Large circles always traverse the maximum circumference of the sphere and are therefore always in the same plane as the center of the sphere. The equator, for example, is a large circle.
First, the researchers tried to force the answer by examining every possible large circle on the planet. At a resolution of 1.8 kilometers, they had 233,280,000 potential large circles, each with 21,600 points on land or at sea. That meant a total of 5,038,848,000,000 points that needed to be verified, a calculation that was just too exhausting.
So, instead, the team turned to an optimization algorithm called "branch and bound," a computer program that has only a few subgroups of all possible big circles. Subsequently, the search is repeatedly tuned to seemingly promising lines with the longest paths. A standard laptop took only 10 minutes to find the optimal solution. When the results came back, Anderson and his Wikipedia muse proved correct, the team reported last week on the preprint server arXiv.
In full length, the voyage would take a boat from the sandy shores at Sonmiani, Pakistan, through the gap between Madagascar and continental Africa passing through the needle between South America and the Antarctic and finally north-northwest across the Pacific Ocean Dodge the Alaskan archipelago until it lands on the cold beaches of the Karaginsky district in Russia.
In spite of the fact that this line looks crooked, it is not really, when transferred to a globe, like the three azimuthals Projections show above
Chabukswar and Mukherjee then performed the same algorithm with the inverse parameters to find the longest such way over land without crossing large waters. This took longer to complete the computer – 45 minutes – but eventually led to an 11.241-kilometer route through 15 different countries, starting near Quanzhou in eastern China and ending in the town of Sagres in western Portugal.
Keith Clarke, geographer at the University of California, Santa Barbara, says the study is an interesting application of optimization. But he points out that the earth is not a perfect sphere; The gravity and rotation of the planet cause it to bulge slightly around the equator. With the sea squeezing through such a narrow gap between Antarctica and South America, Clarke wonders if even the slight camber could pave the way. On land, the model is limited by the resolution of the record. Because the data does not show details smaller than 1.8 square kilometers, the model may lack tiny amounts of water that could appear on the China-to-Portugal path, Chabukswar says. He and Mukherjee do not recommend driving.
As for Anderson, he admits that mathematics is "mostly over my head". But he calls it an excellent end to the search. The next task? Back to the top to find out who made this Wikipedia post.