I will admit that most of the math is beyond me as well. I used to be fascinated with this level of mathematics, and I felt that it held deeper truths to the universe. This may be true to a small extent, if viewed through the lens of physics, but I have doubts about universal truths being stored here.
I read a fascinating book about quantum physics and string theory that dealt with how the different universes in the multiverse have different numbers of uncurled superstrings that determine the number of dimensions that universe has. The book (
The Elegant Universe by Brian Greene) claimed that our universe has three visible dimensions from three uncurled superstrings in all matter, along with a dimension of time and six or seven "curled up" superstrings that make up all matter in the smallest way possible.
So essentially, when you wave your hand through the air, you are moving through length, width, depth, time, and six or seven tiny, curled up dimensions. During the formation or "Big Bang" of other, alternate universes, it is possible that a different number of strings uncurled, leading to that universe having a different number of perceivable dimensions than ours.
However, calculus does have the concept of "hyperspace." Keep in mind this is probably not the same as the hyperspace we talk about so often on the Nexus!! If you haven't seen a
3D graph before, it's just like a 2D graph with another axis "sticking out of the page" added in. Mathematicians run into a challenge when they try to add another dimension to the mix. You may know y = x appears as a line on a 2D graph, and something like 1 = x^2 + y^2 + z^2 appears as a sphere in a 3D graph. But what about when you add another variable (thus adding another axis)? How could we represent 1 = x^2 + y^2 + z^2 + w^2? This is where the concept of hyperspace comes in.
Unfortunately humans naturally have no spatial conception of dimensions beyond the third. It really requires some creative thinking to get there, and mathematicians basically add more 3D graphs onto each of the corners of the current 3D graph to create a 4D graph. I personally don't like this, but it's how they do it.
I prefer just imagining different values stored within different values at each point of the 3D graph, but this isn't visually helpful.
Anyway these concepts are what help physicists shape their ideas and perceptions about what happens at subatomic scales. Mathematics derives from philosophy, and the article you shared seems to combine the two by using some more advanced math (including the idea of hyperspace) to discuss analysis or possible origins of consciousness.
While quantum theory is fascinating, and I would have eaten this article alive about a year-and-a-half ago, I now doubt that there is much true meaning hidden within these complex systems. I think that a lot of the more advanced math and science is just a reflection of our perception and brains at deeper and deeper levels rather than universal truths among all organisms and conscious beings. But it's still interesting and helpful to think more critically about consciousness.
"Think for yourself and question authority." - Leary
"To step out of ideology - it hurts. It's a painful experience. You must force yourself to do it." - Žižek