Characterising intelligence

In the final year of my undergraduate engineering degree, we completed a major project. I chose to explore whether we can characterise intelligence in the natural world. Specifically, to test the hypothesis of whether evolution produces branching structures with a higher degree of complexity.

My colleague and I compared the morphological structures of a selection of trees, as well as neurons from Drosophila Larvae, Pigeons and Humans, and a common animal neuron (Hippocampal neuron), using two measures: fractal dimension, and a new branching effectiveness method we derived.

Fractal Dimension

Fractal dimension (FD) characterises how well a structure fills space, and the box-counting method is used to estimate it. To do so, one can place an image on a coarser grid, as well as a finer grid, then count the number of boxes occupied by the image in both cases. For example, we can estimate the fractal dimension of a Koch curve, given below:

The number of squares occupied on grid 1: N1 = 27

The number of squares occupied on grid 2: N2 = 62

Grid 1 has 12 divisions along the width and height: S1=12

Grid 2 has 24 divisions along the width and higher: S2=24

Using the following formula to estimate fractal dimension:

We calculate D to be 1.2. This is close to the true answer of 1.26.

Branching Effectiveness

We introduced another measure, called branching effectiveness (BE), to provide another measure of the space-filling extent of a structure. It was developed to characterise branching structures, aiming to provide information such as how many generations (levels), nodes and branches there are, as well as the scale on which it exists.

Given a particular branching strucure, each branch is given an address, to assist in calculating the branching effectiveness.

After studying numerous tree-like branching structures, such as trees and neurons, and considering the scale on which they exist, the formula we developed was able to adequately characterise the structures, in terms of branching complexity.

Results

Overall, we find that the BE method is better than FD in regards to characterising intelligent structures in biology. A few of the main reasons are outlined below:

• BE has a more sensitive scale that covers a larger range of values. FD values are limited to the 1-2 range, whereas BE has no upper limit. By using the log(BE), it ensures the value will not be infinite

• BE recognises the number of individual branches, even if they are almost hidden behind another branch, whereas FD does not have a direct way of counting branches as it only measures the extent of space-filled

• As scale factor is taken into account there will always be an obvious separation between trees and neurons

Summary

In conclusion, the project compared how BE correlates with FD as well as how BE and FD both correlate with trees and neurons of various sizes from several species in order to measure intelligence. It was found that BE follows a more accurate relationship with respect to species of increasing intelligence than does FD, as they share a number of factors in common, such as how much length can be packed into a certain area, the scale that tree-like structures exist on, and how highly they are branched.

Further considerations

It is interesting to reflect back on this project in light of current developments in AI. In the context of attempting to characterise intelligence in the modern day, what further aspects are needed to characterise artificial intelligence? What is the difference between intelligence that has evolved in biological structures, versus intelligence existing on computer chips?