[rhinoe]

The scientific paper isn't designed for people who need explanation/visualisation of a logarithmic curve. People who read that paper should be able to quickly decipher what the authors have written – their writing is consistent with normal mathematical instruction.

The electrical drawing would be obvious to anyone who is used to working with them.

There are obvious places where this would work– dissemination of material is always useful in many different forms. But this is NOT an answer to a question that is being asked. Rather, it is an alternative form of dissemination to an alternative audience.

[lstamour]

Fully admitting I've only read the website's summary bullets: I disagree. The point to me is not as much dissemination of material but thinking through materials in a language other than left to right words or symbols. It harkens back to renaissance books in which words and scribbles mixed together in what was, for the times, a coherent mixture. We're talking note-taking for instruction, tools to think about and optimize problem solving ... tools for thinking rather than sharing, even if the source appears to be sharing or instruction right now. That may not be true in the future... I, for one, am sick of OneNote being "the best thing since lined paper" and living otherwise with notepad.exe alternatives. What, precisely, will bring the tablet from its consumption roots into a true work/thinking device? There's a lot of room for more visual note-taking apps, and eventually that will be the new low-hanging fruit of computer vision and natural language input. Someday, for some tasks, at least.

[floatrock]

How did the people who read that paper get to the point that they are able to quickly decipher what the authors had written? Brute force repetition.

Back in high school I played a musical instrument. I practiced my scales, was quizzed on them, then practiced them some more for years. I got pretty high-school-good at this instrument, enough to earn a small scholarship. I never continued it into engineering school though, and one of the milestones I never reached was the ability to improvise within a key. You see, despite practicing the fingerings of the different keys hundreds of times, it wasn't enough to gain the intuition needed to just feel it out on my own.

Those people who read that paper and could decipher what the authors had written HAD practiced their scales enough times to develop that intuition.

Bret isn't trying to provide the most compact representation out there. He's trying to present the best model that helps you build that intuition the fastest. In music, you had to spend hours repeating the same scales so your fingers would get hard-wired into the valid combinations for a specific keys... the question is how can we build tools and techniques that help us reach that level of effortless mastery faster.