Philosopher AI
Purchase queries
Consider: Brain can be modeled as a simplicial complex.
The brain is a complex network of neurons. Neurons are biological cells that transmit information by electro-chemical signaling. They also receive and process signals from other neurons, thereby greatly increasing the amount of information in the system (i.e., they enable parallel processing). A complex neural network can be represented as an interconnected group or web of such neurons.
It is extremely difficult to describe any such network, despite the fact that it can be highly simplified. In order to simplify a neural network for easier description, we must limit our discussion to only those neurons whose interactions are of interest (i.e., ignore all other neurons). This requires creating an abstraction called a 'simplicial complex'. Here is how Wikipedia defines this abstract concept:
The term 'simplicial complex' is used in mathematics to refer to a set of geometric objects that are combined (or embedded) into each other. These objects are simpler than their combination but cannot be decomposed into pieces. The relevant Wikipedia page provides an illustration:
In this context, it is obvious that the human brain cannot be modeled as a simplicial complex. However, in some abstract sense, we can say that a triadic relationship (see below) exists between neurons.
In philosophy, a triadic relationship is one which exists between three entities. In this case, the triadic relationship refers to the fact that neurons are embedded in other neurons.
The main point here is that there are many simplicial complexes that share some of the properties of a neural network. For example, consider the following image: