What I’ve been up to

Kia ora. 2020, eh?

I haven’t posted here at all this year. This is (mainly) due to the crunch of postgraduate study taking away time from mapmaking — although certainly not helped by a global pandemic.

I’m also now the General Manager of Dunedin’s improv troupe Improsaurus! Improv!

This post will be an update of smaller mapping things that I’ve completed and other projects I’m halfway into, with the aim of keeping some momentum going on this blog (and to distract me from thinking about my exams and dissertation…).

I’ll also discuss some maths at the end, if you’re keen on paraconsistency in categories.

Mornington Cable Car Rack Card

This was a small project I did for the folks working on the restoration of the Mornington cable car. They’ve built a new Interim Cable Car Building that you can visit from time to time, where you can climb aboard the restored cars. I produced this rack card for them to use to market the attraction to tourists that happen to be in CBD:

Maps for Work

Before resigning earlier this year to focus on postgraduate study, I was working in the Student IT department at the University of Otago. While there, I used the University campus map as a base for a couple of maps for our staff. One shows the location of all student printers and their relevant toners, and the other draws out the routes for printer and computer checks.

Dunedin Tertiary Precinct Consultation

Late last year, the Dunedin City Council underwent consultation on the Tertiary Precinct project — a proposal between various organisations to redevelop the area surrounding the University of Otago and the Otago Polytechnic. This area of Dunedin is the location of thousands of jobs and where tens of thousands students study.

I created the following two maps to illustrate my points in my written submission — one showing what I perceived to be the missing walking and cycling connections, and one to show my suggestions. I’m no traffic engineer; these were just ideas that make sense to me from the perspective of someone who walked most days to work and study at the University.

Can’t Get There from Here

A few weeks ago, André Brett and I sent away the manuscript and maps for our book project Can’t Get There from Here: New Zealand’s shrinking passenger rail network, 1920 – 2020.

It’s such a bizarre feeling to send so much work away for review. Below, you can see me scrolling through my map spreadsheet — some 128 maps…

Stay tuned for more information on the book!

Auckland Metro 2030

Moving from completed to in-progress, I’m working on updating my Auckland Metro map to show ferries and other planned developments. Some snips:

…does this inverse drop shadow look stupid?

Orokonui Tracks

Over summer I spent a bit of time teaching myself how to make nice-looking geographical (as opposed to schematic) maps. When university started I suddenly had no more time, but hopefully I can get back into it soon — my plan is to make a map of the walking tracks in Orokonui Ecosanctuary using new aerial imagery… We’ll see how it goes!

Dunedin Bus Map v2…?

Yeah, I know, the goal was to have it done by this time last year. : (

Hopefully I can set aside some time to finish it soonish so it can be ready in time for the new Bee Card.


Mathematics

Below is some stuff on what I’m studying at the moment in case anyone’s interested!

The topic of my Honours project is something like: In Search of a Categorial Representation of Paraconsistency. Let’s break down what that means.

Paraconsistent Logic

In the logic used in most of mathematics research — so-called classical logic — funny things happen when you encounter a valid contradiction. Denote a statement as p and its negation as ~p (think p = “the ball is spherical”, ~p = “the ball is not spherical”). In classical logic, if the compound statement p and ~p is valid (i.e., both p and ~p are valid at the same time), then it turns out that any statement q can be logically deduced. If any statement is valid, no matter its contents, then we have reached triviality. Which is a Bad Thing.

The notion that contradictions lead to triviality is known as the principle of explosion, or ex falso quodlibet (EFQ), “from falsehood, anything”. A system of logic is paraconsistent if EFQ does not hold. You might think it’s a bit ridiculous to say that it’s okay to have contradictions, and fair enough, it does seem odd. But consider the following sentence:

If I tell you that I painted a spherical cube brown, you take its exterior to be brown …, and if I am inside it, you know I am not near it. (Noam Chomsky, The Minimalist Program, 1995)

Even though this sentence involves a contradictory object (spherical cube), we can still understand its properties and relations. The concepts of it being brown and being inside it still make sense. The contradictory nature of the object doesn’t lead to triviality of language, so there seems to be some use of paraconsistency.

Despite their potential use in understanding natural language and artificial intelligence, I’m more interested in paraconsistent logics for their allowance of inconsistent objects in maths (which I might ramble about in a later post, or on Twitter). You can read more about paraconsistency here.

Categories

Category theory is a rather new branch of mathematics (only about 70 years young). It concerns itself with structures called categories, which consist of objects and arrows where the arrows follow some structural rules.

There are special types of categories called toposes which turn out to represent intuitionistic logic. A system of logic is called intuitionistic if statements can be neither true nor false at the same time. Note that this is (kind of) dual to paraconsistency, where statements can be true and false at the same time!

So we can model intuitionistic logics (statements can be neither true nor false) in category theory with toposes, but can we model paraconsistent logics (statements can be true and false) with some other structure in category theory? That’s my research.

This explanation was very very rough but hopefully it’s understandable enough..! And my apologies to any mathematicians and logicians reading for my abuse of language. I’ve used some terms pretty loosely here.


That’s it from me for now! Stay safe, take care.