A proof in this context is, I think, I think, a series of formal statements, each one leading from the next that prove something to be always true. A kind of very formal argument with no holes in it at all. So you can say something you believe to be true, but that is no more than conjecture until you provide a 'proof', or a clear breakdown of 'how it works that this is true'.
An algorithm is, yes, a series of very clear instructions to solve a problem.
For a field so averse ambiguity in its work, there seems to be a great deal of ambiguity behind the scenes. There are a great many definitions of proof, and of algorithm. The difficulty of definition is referred to often in both cases. Malo's quote about astronomy is attributed to various people, and the foundation of binary seems to be discovered, rediscovered and debated for as long as humans have recorded their thought – including with reference to the i-ching, which is basically an ambiguity machine..
I find researching specific terms very difficult as any online explanation is very long, and defines many instances of the same thing, so I have to go through them all to find out the meaning in each context, then to cross check that a bit in case the source is whackery. They also contain a lot of other terms and symbols I do not understand, and I have to figure out some basic grasp of them to be able to work out what things are at a simpler level – particularly when looking at examples given. It's a definite language barrier. I do not understand what the symbols in the examples mean. But once I have picked that apart it begins to make sense, even if it is difficult to get my head around.
It is hard not to shy away when it becomes about numbers, because that has so many unfortunately negative connections for me from maths being wasted as an educational experience at school. The more I learn as I get older, the more similarities I see with art, and the more annoyed I am to have blipped stuff out just because it was a “maths” term, and therefore not to do with me. Whereas it is clearly simply another way of exploring and understanding the world. Numbers as a representative agent for me I find very hard to grasp because I don't naturally think in that way (any instance without something else defining it I find almost impossible to remember) but patterns, models and arrangements of arguments I find very compelling. There was definitely something very wrong with the approach towards maths in school as this weird disjointed, joyless period of learning tables and memorising numbers, and then never getting to the interesting stuff because of not being good at that bit. The response to “but why?” was usually an annoyed “because it is”, and just repeating it again. It's like teaching English by trying to make people remember lists of words before learning that they can join together to make stories, or learning to cook a risotto by counting grains of rice. Looking back on it, it seems so weird and short-sighted. I am very glad of this opportunity to see things differently.
Talking of seeing things differently, today I didn't see anyone at all! It turns out you need Skype Premium to have a conference video call, and that is something I don't have. So I had a conference audio call – also a first for me – with Malo, Chris Watkins and Matthew Hague. It's pretty tricky to know who is supposed to speak when, so we kept it short with a basic introduction – they asked about the project and gave a brief outline of their own specialities and interests.
Matthew Hague is working in software engineering and language .Checking that programs are correct. From the theoretical side, but also implementing. Building and analysing models – how exciting a model can we build and still be able to analyse it? The more complicated the model, the harder it is to analyse. This is the area I know least about and am very very keen to get to grips with at a theoretical level as it has tremendous use in terms of how it relates to writing, and how a computing or mathematical model differs from a physical one. A lot of terminology overlaps with art and literature but has very different meanings in this context and this is very useful.
Chris Watkins is working in machine learning, which I know a little more about, but not what he was specifically working on, which is how to visualise high dimensional data. Interpreting it so people (like me) who cannot comprehend numerical data can work with it in visual form. Also how to check that the visualisation is right and where it is misleading. This is machine learning overlapping with bio-informatics.
We will swap details and arrange individual conversations for next week in advance of my visit to talk about their work in more detail. I have also requested to read some of their papers so I can come to that with some reference.
I asked them all what they would like to get out of the exchange, and they were all keen to help with the project, and to share their knowledge. Malo added that alongside the desire for outreach, it was useful to be meeting with someone who sees the world in a different way. These people are being generous with their time and thought, and I hope I can find a way to feed back into their department in a useful way through this project.