That’s true tourists. St. Mary’s Island has plenty of them. Now they do not make this trip to pick up sea shells or worship palms — after all, they can do it on nearby Malpe Beach. So why do they get into those boats?
In three words: Columnarolytic lava. Truly just volcanic rock, it is not uncommon and has been found all over the world. Clue the word “pillar”. Rock formations are found on many other beaches throughout St. Mary’s Beach. But what you find here is surprising. Instead of lacking a distinctive shape, they are actually hexagonal. I mean thousands of hexagonal pillars with flat tops, together, rising from the sand and water.
Surprising, because these are not human creation. They formed naturally. Furthermore, every notion we have about nature tells us that such simple shapes are impossible. To be precise, bees produce hexagons in their hives. But hexagonal shaped volcanic rocks?
When the lava flows cold, they can produce such structures. I’ll be back to that. Geographically, the St Mary’s rocks tell the story of how India and Madagascar merged into an ancient supercontinent called Pangea millions of years ago. We know that there are similar typical rock formations in Madagascar. About 90 million years ago there was a volcanic hotspot in that part of Pangea — now southern Madagascar. Its lava really connects the six-sided pillars to each other, the highest being 6 meters.
The geographical history and connection with Madagascar itself is fascinating. I imagine anyone visiting St. Mary’s Island would be surprised: why the hexagonal shape?
Well, as you can imagine, mathematicians have followed a somewhat enlightening line of inquiry to that question.
To find out what they did, start with a sheet of paper. Cut with a straight slice so that you now have two pieces. Place one on top of the other and to get four pieces, slice straight through the pair again. Continue stacking, and then slice a few times at random.
When you have enough, do this exercise: Take each piece of paper you have produced and count the number of vertices and sides it has. Add these numbers and place the average on all the pieces. Here’s an estimate: on average, you end up with an average of four vertices and four edges per piece. What familiar shape has four vertices and four edges? A rectangle. On average, you made pieces of paper like rectangles.
No, all are equal rectangles with 90 degree angles and opposite sides. Of course, there is no such thing unless you deliberately make your cuts to produce rectangles. Also, there are no boomerangs or starfish, although you may have some triangles and pentagons. However, we are talking about “average” types and the average piece of paper you produce has a generally convex shape with four sides, four vertices and no indentations.
One way to get some perspective on this is to think about two consecutive pieces, i.e. how we get the tops. The angle at which they make each other ranges from 0 degrees to 180 degrees. So, on average, that angle is 90 degrees. A piece of paper with straight edges and angles at an average of 90 degrees … on all four sides. Like a rectangle.
Maybe you find all of this a little interesting? Well, what if you shred a three-dimensional object instead of a sheet of paper? Russian Nobel Peace Prize-winning physicist Andrei Sakharov once chopped cabbage with his wife. A similar question occurred to him: if you take sliced cabbage as an average piece, how many tops does it have? How many faces?
Well, in a paper published last year, three Hungarian mathematicians and an American geophysicist argued that it had eight heads and six faces. (“Plato’s Cube and the Natural Geometry of Fragmentation”, Gobor Domokos, Douglas J. Jerolmack, Ferenc Kun, and Genos Terock, Proceedings of the National Academy of Sciences, USA, 4 August 2020).
If you do not often slice the cabbage, think about chopping the onion, or French beans or cucumber into small pieces. Or think of smashing a stone with a hammer. What the paper refers to is the pieces you end up with, stone or vegetable, on average, eight heads and six faces.
They are cubes on average.
“In this study,” Domokos and his colleagues wrote at the beginning of their paper, “We draw inspiration from an improbable and ancient source: Plato, proposing that the earth is made up of cubes, because they can be so tightly packed. Reproduce the cube. “
So in effect, when stones are separated by natural processes, we have two intriguing results. On a two dimensional surface, they must necessarily be on four sides with four vertices: the rectangles mentioned above. Consider the third dimension and, more broadly, the fragments cubes.
But hold on. Scientist analysis has additionally shown that, from two angles, the fragments you get are usually quadrilaterals, with exceptions. Take fields that dry out in the summer heat, and then exhibit characteristic and familiar wide cracks. The individual cells of the soil are on six sides: a hexagon. Fascinatingly, there are also tectonic plates of the Earth — the crustal pieces of the planet that make up the well-known Earth mass — average hexagons. As scientists write, “Geometry [tectonic plates] 1) brittle fracture and evolution with episodes of healing or 2) fracture by thermal expansion. “And we know that the earth exists through those two processes.
Then there are rocks that form as a result of cold lava, starting solid at the surface and going down. The theory is that forces on these rocks work from the inside out, instead of other means (think of that hammer that crushes the rock, for example). “As a consequence of increasing energy release”, these rocks take on a familiar shape. Fact: Consider the horizontal section of these “pillar joints” — or look at the surface above them — and you will find that they are often … hexagonal.
A famous example of these hexagonal rocks is the Giants Causeway off the coast of Northern Ireland. The other is on our own St. Mary’s Island. All that remains is that the molten lava has cooled long ago after the eruption.
This is a unique and remarkable view, with these thousands of columns of “rheolitic lava” with these hexagonal surfaces. So visit St. Mary’s Island. While you are looking at the rocks, spend some time thinking about Madagascar. About Lava, Northern Ireland Hexagons. A world made of cubes.
In the wonders of mathematics.
Dilip D’Souza, once a computer scientist, now lives in Mumbai and writes for his dinners. His Twitter handle is DeathEndSfun