Most of us are aware of the golden ratio, approximately 1.618. A rectangle whose larger side has such a ratio with its smaller size is called a golden rectange. A 5 x 8 picture frame comes close.

This ratio is related to the Fibonacci sequence 1,1,2,3,5,8,. . . where each number is obtained by adding the previous two. The ratios of two adjacent numbers approach the golden ratio, and these numbers are often found in nature.

**Now one can find two ratios of lengths between special points in the human skull are both 1.6. **

These special points on the cranium correspond with important underlying neural structures and junctions in both humans and other animals.

Our brains are even more complex than we imagined and **advanced mathematics is being employed to understand what’s going on** in that fabulous three pounds of matter. Scientists have long known our skulls contain billions of neurons and that thinking and experiencing involve synapses between them. Now they are finding it useful to study cliques of neurons that interact with each other. A neuron can belong to more than one clique. Imagine for each clique, a neuron is represented by a dot on a sheet of paper and if one neuron can transmit to another, draw an arrow. Such a picture is called a graph and there is an area of mathematics called graph theory, which is a subset of algebraic topology, an area of advanced mathematics. Brain researchers are finding it useful to try to understand the ways our minds work by using this mathematics to study the connections in these cliques. The article that alerted me to this use of algebraic topology made the strange claim that our brains contain structures only realized in eleven dimensions. Thinking of the physicists theory that space may be eleven dimensional and algebraic topology is useful in trying to determine the shape of the universe, I was fascinated. However, digging deeper into **the source of the article** there seems to be inconsistency on the definition of dimension. In one case it refers to it as the number of neurons in the clique, but then cliques with larger numbers of neurons are discussed so I am confused, but as a retired mathematician, I am always delighted that highly theoretical mathematics turns out to be useful in understanding the world we live in.