Scuba Diving and Skiing#

Author: Steve Kieffer

Consider the set of all pages at Wikipedia as forming the nodes of a network. The nodes are connected by the links between pages. This gives us a network of related concepts, which we can choose to explore in different ways.

I’d like to talk about two ways of exploring, which we can call oceanic and alpine.

Oceanic exploration is free and undirected. The network of pages floats like a fishing net in the water. You can start reading any page, and when you come to a link, you can follow it if it interests you. As you read the next page, it may lead you onward to still other pages. As you continue to explore, you may eventually circle back around to a point you had already visited, or perhaps not. You may drift in an unexpected direction. A day of oceanic exploration is like a day of scuba diving, exploring a coral reef, and floating freely from one unexpected discovery to another, with no particular plan in mind.

Image credit: Randall Munroe, XKCD#

Alpine exploration, by contrast, chooses one page in the network and lifts it up, so the remainder of the network hangs below it. The network is now like a mountain, with the chosen page its summit. In this type of exploration, your goal is to understand the chosen page. This means you will need to understand some of the linked pages, i.e. the ones that now hang one level below it. There will be several of these, so you’ll have to pick a first one.

Of course, when you move to that page, it too will have several below it. So you will have to choose a certain path down the mountain, and go a certain distance along it before you run out of momentum. Then you’ll backtrack to a higher point already visited, and from there follow a different downward path a certain distance, before again coasting to a stop. A day of alpine exploration is like a day at the ski mountain, whooshing down one trail, before hopping on a ski lift to go back up, and whoosh down another.

Proofscape offers a way to manage “alpine” studies.

If a student wants to dive into some new concepts, Wikipedia is a great place to do oceanic exploration. But as teachers we need new tools to help us set up alpine studies. With its expandable and collapsable proof diagrams, which can be automatically navigated by linked annotations, Proofscape offers a way to manage this type of study.