Something New Is Sometimes Something Old With A New Name

mathematical-graphs.png

Sunday, 9.06pm

Sheffield, U.K.

My journey is where I’m at right? It’s the monopoly board of my life, and I’m making my rounds. – Saint Jhn

We used to go to France every summer for a camping holiday.

Before the pandemic hit, of course.

Before one of those summers, the winter before, we went to a farm for a Christmas market. As we wandered around the stalls we came across one that had handmade armour – a helmet, mail chain and a sword. So the small people started trying these out and I looked around the stall and noticed some game boards with a strange pattern I hadn’t seen before.

These were handmade by the stall owner, I think, and were an old style of board with locations where pieces could stop and lines along which they could move. I thought this was a very interesting idea but I didn’t buy one at the time. I should have. We spent much of the summer in France creating boards on the lines of the one we saw with cardboard and pens. By the way, one of the reasons you had lines on the boards rather than squares like a chessboard or passages like a maze is that these games were often carved into tables and it’s easier to just make a line with a knife.

Okay, it’s now three or four years later and I’m reading research and thinking about how to remember this stuff I’m reading. A few days ago I wrote about coming across the work of Vera F. Birkenbihl and thinking this was new and cool. As a reminder an ABC list is when you write down the letters of the alphabet vertically on a page and then write down words that capture the essence of what you’re reading.

Something like this.

ABC-list.jpg

The idea is that writing down these words will help you remember what you read better when you look back at the words. I still need to get my head around the theory behind that but if it’s a memory thing I thought why not create “123 lists”. This is for numbers and you put down figures that you want to remember. I have a 123 list that I’ll come back to in a few weeks to see if this works.

But, if you have ABC lists, then what happens if you connect related words – draw a word, circle it, draw a related word and connect the two? Something like the image above. I thought I could call that an “ABC Connect”. Pretty cool, yes?

Now, we can draw these diagrams but when they get bigger it’s probably easier to use software and my go to software for drawing words and connections is Graphviz. If I use that to create this kind of connection you’ll get something like this.

ABC-connect.png

I was on the Graphviz website and idly browsing through the theory of graphs when I came across a paper titled A Short Note on the History of Graph Drawing so of course I had to read that. The paper has a definition:

“A mathematical graph consists of a set of nodes and a set of edges. An edge connects to a pair of nodes.”

So… this is my “ABC Connect”. Ah well, it sounds good anyway and is a little less confusing than the word “graph” might be.

But, even better, the paper starts by talking about how nodes and edges can be seen in Morris gameboards from the thirteenth century.

If you drew one out, it might look like this.

nine-mans-morris.png

And these are the same boards we stumbled across in that market stall all those years ago.

Anyway, mathematical graphs help you see patterns in data – family trees in genealogy is one of the best known examples of applying these techniques. My own work uses these extensively but now I have a few names for what I do – old ones and new ones.

Cheers,

Karthik Suresh

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