A love of maths
This comes from my love of maths. Crazy, I know.
There is something lovely about being able to write down a relationship. A few symbols can hold an idea that would take several sentences to explain, and then let me do something with it. I can rearrange it, try a value, draw a graph or ask what happens as something changes.
The symbols give me somewhere to begin. Understanding comes from working out what they allow me to say, and why.
That is what I wanted this image to hold: the pleasure of learning something, and the pleasure of helping someone else understand it too.
On the board
The imagery had a few obvious requirements. A chalkboard, equations and plots. Somewhere a thought could be written down and worked on.
In the finished image, dark surfaces overlap at different angles. There are fractions, matrices, curves and small marks scattered across them. Some are faint enough to disappear into the background. Others catch the light.
A bright curve rises towards a glowing point where two lines cross. Loops turn through the space below it. Near the bottom, a small sphere rests on one of the surfaces, surrounded by more working. The board seems to have opened into a room made of mathematics.
I like that there is more here than I can take in at once. My eye follows one curve, then notices another shape behind it. The image gives me the feeling of arriving partway through a thought, with enough visible to become curious about the rest.
Leaving something out
Abstraction sounds rather grand for something that often begins by leaving details out.
If I draw a triangle, I can ask about its angles without deciding what it is made of. It might describe part of a roof, a folded piece of paper or three points on a screen. For that question, the material can wait.
There is a kind of generosity in this. Once I understand a relationship, I can recognise it somewhere else. I do not have to begin again with every new object. Something I learned in one setting becomes useful in another.
That is part of what I mean when I think of mathematics as a universal language. The same relationship can be expressed and examined by people who speak different languages. The notation still has to be learned, but it gives us something precise to share.
It also asks me to pay attention to what I have left out. A triangle might help me describe the shape of a roof. It will not, by itself, tell me whether the roof leaks.
The simplification is useful because of the question I am asking. Change the question, and I may need to bring some of the details back.
Both sides of the chalkboard
This scene represents my interest in learning, both as a student and as a teacher.
Those roles belong close together. Learning asks me to follow an explanation until the steps make sense. Teaching asks me to consider how those steps will look to someone who does not yet know where they lead.
There can be a surprisingly large gap between being able to use an idea and being able to explain it. A step that feels obvious may contain several smaller steps I have stopped noticing. Putting it into words makes those gaps visible again.
Where did that term come from? Why am I allowed to move it? Would a picture help?
I like the care involved in those questions. An explanation needs somewhere for another person to place their feet. If the distance between two steps is too large, I can look for an intermediate one, try a smaller example or draw the relationship differently.
The chalkboard has room for all of that. A diagram can sit beside an equation. An attempt can be rubbed out. There can be arrows, corrections and a second way of approaching the same thing.
Understanding something well enough to share it gives me another way of learning it.
More than one answer
Consider something as small as x + y = 10.
It tells me something definite about the relationship between two quantities. It does not tell me what each quantity must be. Six and four will work. So will seven and three. Without another condition, I have room for many answers.
I can still learn something from it. If one quantity increases, the other must decrease by the same amount to keep the total at ten. I know how they relate even though I have not settled on a pair of values.
There is a useful distinction there. Knowing a relationship and knowing a single answer are different kinds of understanding.
When I turn that thought towards myself, I have to be more careful. I cannot assign a number to every feeling and expect the arithmetic to explain my life. But I can notice relationships. I can ask what changes with a situation, what keeps recurring and what information I might be missing.
Sometimes that gives me enough to understand a little more. I do not always need to force the remaining uncertainty into one answer before the observation becomes useful.
The next line
In Source Code, an idea became something I could run and revise. Here, I am interested in the working that makes an idea understandable: choosing what to represent, following a relationship and finding a way to explain it.
The image leaves that working spread across the board. There are marks I can follow and others I cannot quite make out. There is still space in the darkness.
I might use it for another example. I might need to go back and explain a step I skipped. Or someone else might ask a question that sends me reaching for the chalk again.
That would be a good reason to keep some room on the board.