An introduction to graph theory

By Gordon Rugg

Graph theory is an extremely powerful approach that is based on a handful of elegantly simple concepts. It was invented by Euler in the 1740s, and is a central part of modern mathematics and technology. Among other things, it plays a key role in handling traffic on the Internet.

It’s invaluable for representing knowledge, because it combines flexibility with formalism. In particular, it’s useful for representing different facets and viewpoints; for representing hierarchies of goals and values; for representing successive layers of explanations; and for formal taxonomies. Continue reading

An introduction to facet theory

By Gordon Rugg

This is a brief overview of an invaluable concept. It links closely to graph theory, which we describe in another recent article, and to laddering, which we will describe in a later article. All three of these concepts are powerful, simple and elegant, and all three are not as widely known as they should be.

Facet theory in the strict sense is a concept from librarianship and information science. The core concept is that you use several different ways of categorising the things that you’re categorising. This lets you organise the same set of entities in different ways for different purposes. Continue reading

The Verifier approach: part1

By Gordon Rugg

The central theme in Blind Spot, the new book by myself and Joe D’Agnese, is the Verifier approach. The Verifier approach is a way of spotting errors in human reasoning; in particular, spotting errors made by experts dealing with long-standing problems where it looks as if the experts have ground to a halt and can’t see where to go next.

Its starting point is simple. Human beings make pretty much the same types of mistakes, regardless of their level of expertise, or of the field in which they’re working. If you know what those types of mistakes are, then you can go hunting for them.

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Truth

By Gordon Rugg

Truth, according to Vance, is a precious jewel, the more precious for being rare. It is not a researcher’s job to keep the price up by keeping the supply down.

From Rugg & Petre (2010) The Unwritten Rules of PhD Research (2nd Edition) p. 120. Open University Press/McGraw-Hill, Maidenhead, UK.

This is a counterpoint to our earlier article about the three golden rules of public speaking, just in case any over-zealous readers felt tempted to over-use the Third Golden Rule…

The Vance reference, for any science fiction fans reading this, is to Jack Vance’s book Star King.

The Voynich Manuscript: why should anyone care?

By Gordon Rugg

It’s a valid question. Why should anyone care about an undeciphered hand-written manuscript that almost certainly contains nothing more interesting than mediaeval recipes?

There are various answers. One is simple curiosity. Another is the challenge: millions of people do crosswords every day, which involve challenges with even less meaningful content than a mediaeval recipt. A more potent reason is fame – the first person to crack a long-standing problem gets their time in the limelight.

There’s another reason, though, which has much bigger implications. Modern civilisation depends on safe, secure codes – they’re at the heart of the Internet, e-commerce and online banking, among other things. The best modern codes are impressively good, but they’re reaching the end of their shelf life, as increasingly powerful hardware and software make it possible to crack codes that would have been impregnable just a year or two ago. Code-makers are now searching for entirely different approaches to security: types of code based on utterly different principles to anything currently known, that could resist the best modern codebreakers not just for months, or for years, but for decades.

Like, maybe, the Voynich Manuscript.

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The three golden rules of public speaking

By Gordon Rugg

These rules have been floating around for a long time, under various attributions. One version says that this is what US Air Force pilots are told if they have to testify to external inquiries after something very bad has happened. Whatever their origin, these rules now crop up in situations ranging from PhD vivas to interviews in politics. When you know why the third rule doesn’t necessarily contradict the first rule, then you see the world in a new light…

First golden rule:       Don’t lie.

Second golden rule: Don’t try to be funny.

Third golden rule:     Above all, don’t panic and blurt out the truth.

Subsystem optimisation and system optimisation

By Gordon Rugg

When a politician or a manager tells you that they’re going to take a “common sense” approach to a problem, they usually mean that they’re about to take a concept that works in one area, and apply it to a different area on the unstated assumption that it will work there too. Once in a while, it actually does. A lot of the time, though, it ends less than well.

There’s a technical description for one common way in which this approach comes to grief.

Sub-system optimisation does not necessarily lead to system optimisation.

It’s not exactly the most catchy line ever written, which might be why it’s not as widely known as it should be. This article is about what it means, and why it’s important.

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