Essays
Collected here is a selection of some of my writings. It covers a wide range of topics, some technical, some general.
Abstract Mathematics and You
It often seems, to those with only a high school (or even basic university) education in the subject, that mathematics is largely a solved problem. Sure, the thinking goes, there are those arcane and abstruse little corners of irrelevancy with which academics busy themselves, but for the most part we know it all, right?
In fact there is a great deal that we simply do not know, and do not understand; and a lot of it is much simpler, and much closer to home than you might think. In many ways our understanding of the subject only really began very recently. Let's take a brief tour of some of what we don't know. Read More...
Proportional Representation
Originally intended for a Canadian audience where electoral reform is a growing issue
Electoral reform, and specifically proportional representation, is becoming an increasingly common topic in Canadian politics. As someone who lived and voted in a country as it transitioned from First Past the Post (FPP), as used here in Canada, to the Mixed Member Proportional electoral system (MMP), I would like to share my insights on the subject. Read More...
A Case for Formal Specification
Formal Specification helps build more robust, more maintainable software with fewer bugs and defects. It has a long history, but it is still a developing field. While it may not be suitable for all software projects, a case can be made that there are many projects not currently using formal specification that stand to benefit from it. As the methods and tools for formal specification develop it is increasingly becoming something that developers and software engineers should learn to use to their advantage. Read More...
Better Programming in Java
Sometimes ideas don't get the attention that they deserve. The Java Modelling Language (JML) is just such an idea. JML is something every Java programmer should know about. That does not mean every project in Java should make use of JML, only that developers should be aware of it so they can use it wherever it does make sense. The fact is that JML provides so many benefits for so little extra work that it deserves far more use than it gets. If you program in Java it could make your life a lot easier.Read More...
Introduction to Algebraic Specification
There are several different forms for formal specification. Algebraic specification, or property based specification, differs from model based specification systems such as Z, or VDM) in the degree of abstraction. Algebraic specification seeks to defer implementation decisions as much as possible, seeking to determine all possible models that fulfill the requirements. The theory of algebraic specification is grounded in universal algebra, category theory, and logic. This level of abstraction makes algebraic specification a powerful way of analysing system requirements. Read More...
What Happened to Mathematics Teaching?
As a university mathematics instructor I have found that there are some skills a lot of modern students seem to lack. This is not the usual complaint about poor algebra skills, a lack of decent calculus preparation, or any other specific item that might appear on a curriculum checklist, this is a deeper complaint. What many of the students I deal with seem to lack is a good understanding of formal reasoning and logic. This is troubling to me because I had always felt that this was one of the primary skills that mathematics was supposed to teach. Read More...
Uncaused Force, Teach the Controversy!
Yes, this is satire! Last time I published this quite a few people didn't pick that up!
It is time to closely and rigorously examine the prevailing ideas about gravity and force, its limitations and its failures. Our abilities to observe and record the very workings of the universe have improved astonishingly over the last hundred years. We now have space based telescopes, vast radio telescopes, and a stunning array of other equipment for astronomical observation. We also have at our disposal huge and expensive particle accelerators and other equipment to detect and observe interactions at the smallest possible scale. With these tools at our disposal, new observations bring an ever mounting weight of evidence that our very conceptions of gravity and force are deeply flawed. Read More...
Why the US Intelligene Reforms are Not Enough
Old news now, but I still feel it makes relevant points.
The US Intelligence Community is currently undergoing various reforms in the wake of events of September 11 2001, and issues of poor intelligence in the lead up to the Iraq war. These reforms include a new Intelligence Director to oversee all the agencies that make up the US intelligence community, but little real change to the existing structures. Read More...
The Elephants in the Living Room
Another older essay (dating from just after the 2004 election) that still has relevance today (many of the issues raised remain unaddressed).
The United States is facing the possibility of a severe economic correction. Yet most of the causes of such a correction are, for the most part, being completely ignored in preference to partisan bickering. It is the proverbial elephant in the living room - except it is not just one, but several elephants that everyone is doing their best to ignore. While the likelihood that any of these issues could result in disaster is low, these are issues worth taking the time to discuss. Read More...