Over the last thirty years, networks, alongside formal logic and classical mathematics, have come to play an increasingly important role in the scientific analysis. Coincidentally, that was also the period when the Internet became popular. But in fact, classical mathematics had already reached its limits at the start of the last century. Einstein used a four-dimensional geometry for his theory of relativity, de euclidian geometry with three dimensions did not suffice. He added the dimension of time. Time also plays a key role in the analysis of causation.
It is surprising that the logics for causation has been neglected that long, although David Hume stressed its importance his long time ago in his "Treatise of Human Nature, and An Enquiry concerning Human Understanding" (1739–1740). Why are formal logic and classical mathematics not sufficient? Essentially for two reasons. Firstly, because they are based on a binary view of reality. In formal logic, something is either true or false. The excluded middle is, of course, useful for proving things from the absurd, but formal logic and classical mathematics only work well for closed. They fall short when it comes to describing networks.
Initially, computer science, too, was limited to binary relationships. Data first had to be normalised in relational databases before it could be processed. That normalisation heterogeneous data was organised into tables showing unambiguous relationships between the data key and the other data. However, once relationships becomes complex, for example in a semantic network, this approach no longer works. The relationships within a network are ternary, not binary. In networks, triplets are used: a → b. The advantage of these triplets is that they are highly extensible and thus manage to describe a complex reality quite well without being constrained by the restructuring of the original data. It is no coincidence that XML, AI, neural networks and LLMs work with triplets. It was the only solution that produced results.
The second reason why classical mathematics falls short is that, whilst it copes well with homogeneous data, it soon runs into problems with heterogeneous data. In the field of ecology, for example, Robert E. Ulanowicz came across that problem after having spent a long time trying to analyse ecological networks using classical mathematics. It didn’t work. Too much heterogeneity. That problem also arose in biology, genetics, neurology, geography and numerous other sciences as they became more complex. More and more networks are also popping up there.
The building block of a network is a graph. And Edugraph can be used to visualise graphs. It also generates an adjacency matrix from each of these graphs. The adjacency matrix makes the bridge to classical mathematics. Internally, in computer programmes, these matrices are used for the processing.
Edugraph is intended as an introduction to network analysis for secondary education. It can help to demystify AI in this context. At an academic level, it is useful for presenting interdisciplinary research. As an example think about the language acquisition of the homo sapiens. It covers genetics, biology, neurology, phonetics, linguistics and anthropology, all of which are discussed. However, as the collection and processing of data varies from discipline to discipline, different scientific disciplines use different software programmes. In ecology, for example, Ecopath is used. In the Wikipedia you find a list of the various software applications used in different disciplines.
The three main advantages of Edugraph are that it can integrate images and HTML links into graphs. To do this, you would normally have to rely on expensive commercial software packages. Furthermore, it does not require much prior knowledge; an intuitive understanding of networks is sufficient. No new hardware is required. Even simple AI tools are resource-intensive. See for example PuppyGraph. It is immediately accessible to students in both the humanities and the arts. It can also be used in technical and vocational education. This means that science can still be presented visually without extensive knowledge of mathematics. Another advantage is that you can use the programme offline. No internet connection is required.
An additional objective, alongside the introduction of networks, is to demystify AI and LLMs. Not by attacking them, but by learning to engage with them critically. The example ‘From Text to Knowledge Graph’ explains how you can use LLM in a positive way without becoming a slave to it. One of the nodes includes a detailed example of how to get LLM to structure a text in such a way that you can turn it into a knowledge graph. See deze link
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