As George Lakoff and Mark Johnson made clear in their touchstone book Metaphors We Live By, metaphors are the basis of all human thought and reasoning. The metaphors we use to speak about the web are not simply linguistic trivia – they determine how we understand it on a fundamental level. It determines what we think the web is capable of, what risks, opportunities, and challenges it poses. Which means the metaphors we use to think about the web profoundly influence what we think the web is, what we think we can do with it, and how we might change or evolve it.
…Out of all of these metaphors [for the web], the two most enduring are paper and physical space.
Digital gardening is the Domestic Cozy version of the personal blog. It's less performative than a blog, but more intentional and thoughtful than our Twitter feed. It wants to build personal knowledge over time, rather than engage in banter and quippy conversations.
An open collection of notes, resources, sketches, and explorations I'm currently cultivating. Some notes are Seedlings, some are budding, and some are fully grown Evergreen.
Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.
In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.