Image above by Kevin from The Beginning at Last
Freedom to Roam Everywhere
When I was a kid, I used to roam around a lot, in the forest and on the mountains, and I liked to swim and fish in the rivers and the famous deep lakes in the Swedish countryside. Sweden has 97,500 lakes larger than 2 acres and many of them are deep lakes with clean and clear water surrounded by forests, typically coniferous forests. A small deep clean forest lake is referred to as a “tjärn”. I can add that there are no alligators or venomous water snakes in Swedish lakes.
Sweden offers a type of freedom that is rare in the world, and it does not exist in the United States and certainly not in Texas where I live. It is the freedom to roam or more specifically allemansrätten. Whether the land is public or private you have the right to roam, to hike, to camp, to swim, to pick wild berries, to pick wild mushrooms, to fish, and no one can stop you. Landowners are not allowed to tell you to get off their land and they cannot put up fences to stop you or animals from roaming on their land. Everyone has the right to roam and swim everywhere. It is a freedom Swedes love, and if you one day come to experience it you will know why.
Allemansrätten
The Swedish freedom to roam or allemansrätten, is a right for all people to travel over private land in nature, to temporarily stay there and, for example, pick wild berries, mushrooms, flowers and certain other plants. It is important to point out that you must respect the landowner’s property. You can pick wild berries but not anything the landowner is growing. You cannot destroy or break things or start fires, use ATVs, cut branches off trees, etc. You also need to stay 70 meters or 230 feet away from any dwelling.
As a landowner in Sweden, you can buy land and use it for farming and forestry, and you have the right to prevent people from damaging or stealing your crops. You can buy land for mining, and you have the right to your proceeds and the right to prevent people from stealing from your mines. In addition, people don’t have the right to get close to your house. However, you do not have the right to prevent anyone from roaming on your land.
Other countries with similar laws are Norway, Finland and Iceland. Limited forms of allemansrätten exist in Austria, Germany, Estonia, France, the Czeck Republic, and Switzerland. In the United States, where allemansrätten does not exist, 63% of all land is private and in Texas 93% of all land is private. Since there is no law in the US protecting your freedom to roam there is noticeably something missing, especially if you are an outdoors person.
Concentric Circles
In addition to evoking my memories of Swedish lakes and allemansrätten, Kevin’s picture tickles my mathematical sense, specifically regarding concentric circles. Concentric circles are beautiful, dreamy, and interesting mathematical phenomena. I could watch concentric circles in the water all day long.
When you jump and play in a lake, when raindrops fall on a lake or a pond you’ll see concentric circles. You see concentric circles on a tree stumps, when you cut an onion, some flower petals, spiderwebs, etc. Concentric circles are everywhere in nature. Light can create concentric circles due to diffraction called an airy disk. Gravitational waves originating from, for example, two black holes colliding create 3D gravitational concentric circles/spheres traveling at the speed of light through space.
Concentric circles are very common in nature. You can see them in Kevin’s picture above. You can see them below my son as he falls into the Swedish lake, and you can see them in the pictures of light below. Whenever waves originate at a point and spread outward you get concentric circles.
There are many kinds of waves, water waves, sound waves, surface waves, seismic waves (earthquakes), mechanical waves, light are waves, electromagnetic waves, matter is both particles and waves, gravitational waves, and they can all make concentric circles. If the waves are moving outward with the same velocity in all directions, you will get equidistant concentric circles.
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