It started with a triangle and hasn't ended yet.
The short version. While reading a book the author described a hall with a triangle in the centre on the floor. My mind, being the free-thinking object it is, placed a circle in it, then tried to think about placing a hexagon inside and other shapes inside that. By the time I'd finished that train of thought, I'd written an equation, worked out the mathematical relationships between the shapes, linked in the holy trinity and the eleven dimensional universe and asked where matter comes from.
Needless to say I couldn't continue reading as I was so distracted and I now have an A4 sheet covered in scribbles and notes.
The long version. (WARNING: This contains algebra) I'm currently reading 'Gods of Atlantis' by Alan K Baker, a Blackwood and Harrington mystery. It's a steampunk book set the early 20th Century a few years after the failed Martian invasion of Earth. The two of them have been sent to Atlantis to retrieve a couple of scientists who've disappeared along with their machine. Blackwood has visited his mentor, Skala, and they uncover the tomb of Poseidon. A member of the team is a member of a masonic type lodge and in their entrance hallway is a triangle.
That got me thinking about a triangle with a circle in it and my mind decided to take a detour from the book and explore the triangle and shapes. It started with a circle then explored the idea of a hexagon within the triangle, followed by ever-multiplying numbers of sides to the shapes inside each other. It then proceeded to wonder how many sides there would be when the internal diameter of the shape was the same size of the smallest particle and called that the infinity particle, positing that if you had a rod the same diameter as the particle, you could press the particle and it would open a door to heaven.
After this, my mind then wondered if the particles on the way down to the smallest were of varying sizes and what the mathematical relationship between them is. It then got me to calculate what the relative circumference of the triangle and the hexagon etc are and I found out that the hexagon has exactly two-thirds the circumference of the triangle and the twelve sided shape has two thirds the circumference of the hexagon. I expressed this as Y = (X/3) x 2, where Y is the internal shape and X is the external shape.
I also calculated that the 10th inner shape would have 1536 sides, though I didn't calculate it's circumference or area.
While doing that lot, I remembered that you cannot fold a piece of paper, however wide or thin, more than 7 times and wondered if the same were true for the shapes, that there would always be the same number of shapes inside the triangle, however long the sides of the equilateral triangle were, and what would happen if it were and Isoceles triangle or an irregular one. Then my mind wondered if all the sub-atomic particles had this relationship of being two-thirds smaller/larger than each other.
As the book was about the rise of the Atlantean Gods, my mind also shifted to the holy trinity and posited something that I've thought for many years that the godhead is represented in the human body. God, Christ and the Spirit are analogous to the mind, heart and blood in us: Logic, Love and Life. The spirit is our essence our matter the basis of who we, and the universe, are. But where did that matter come from? Is it part of a temporal loop where it's created in the future, brought back and used to create life in the first place, or is it eternal?
Then I thought about the eleven-dimensional universe. Three dimensions of space, three of time, three of an ethereal nature, one that gives the universe its structure and cohesion and an eleventh that is a gateway to the universe outside our own, to heaven itself, the aforementioned infinity particle.
Which brought me back the the triangle. Why a triangle and not a square of a pentagon? A three sided shape is the first one with space in the middle. A one-sided shape has only an outside, like a dot. A two sided shape has a left and right (or top and bottom, whichever you choose), like a line and also has no internal area. The three sided shape is the first one with an internal area you can measure.
As a further thought, I then wondered if the reason we cannot create artificial intelligence is because we write programs in binary language, instead of trinary. In binary, it's true or false. In trinary it can be true, false or both which is more analogous to real life.
And that's where my mind stopped, for the time being, though I can feel further thoughts cooking in my subconscious waiting to jump out and disturb me. Probably as I'm just about to go to sleep tonight.
Welcome to the landscape of my mind.