The electrical circuit analogy

The Hilbert space, as explained in chapter 1, provides an abstract conceptual framework that can be used to describe any object or system in terms of selected parameters or functions.

The problem with this framework is that it contains all possible combinations of the dimensions, without any means of locating any particular object in the space. This is not a problem with conventional information systems - such as databases - because the space is first formatted with the dimensions (parameters) and the objects then placed inside the space afterwards - in a way that allows them to be easily located by reference to the dimensions (parameters).

The human brain cannot be designed to operate in this way because the the number of possible dimensions (parameters) are virtually limitless and, anyway, there is no way to format the neural space prior to recording information.

This might be visualized easier by using electrical circuits as analogies. First, imagine a space to be crisscrossed with many wires and wherever one or more of the wires crossed, a switch is installed that would light up a bulb only when power is connected to all of the wires that are connected to the switch. The space would then be filled with a multitude of bulbs, each of which will light up according to which particular combination of wires had a voltage applied to them.

This analogy could be used to describe how a conventional database locates information in its memory space - with the wires representing the values in fields and the bulbs representing the records in the database memory.

Many people think of the memory in the human brain working in a similar way. Subsituting neurons for the bulbs and electrical wires, you will have a picture of activated neurons energizing particular neural locations in the brain according to which combination of neurons have been activated. By rapidly altering the combination of neurons activated, different areas of the neuron space will be energized. However, a little though will tell you that this system is not realizable without first pre-formating the brain - which it is not possible to do.

In the human brain, you can think of networks of neurons that are activated according to various combinations of sensory inputs. Each of these combinations will energize a particular location (or locations) in the neural space and this energized location then serves as the memory that identifies a particular combination of sensory inputs. But you have to give the enegized areas in the brain names retrospectively - after the area has been energized - to identify particular combinations of sensory inputs that are activated when a particular image or sound is sensed.

To get away from the database analogy, try a paradigm shift. Instead of thinking about the parameters or dimensions pointing to an object or system in a space, think about an object or system in the space pointing to its parameters or dimensions. In other words, instead of the parameters describing an object or system, think of the object or system describing its parameters. This paradigm shift is like imagining a database where there are no common fields. Each object has its own unique set of fields.

From a computer system point of view, this makes no sense whatsoever - which is why a computer mind set is inappropriate here.

Consider now, a situation where there are millions of neurons that are interconnected in a complex neural network and these millions of neurons are each separately energized by different sensory cells in the body. This would result in different parts of the neural network being energised according to which particular combinations of signals from the sensory cells are sending signals to the brain. In other words, it would be functioning as a pattern recognition system - where the name of the pattern is provided retrospectively.

This simple model provides the essence of a learning machine.