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For the past thirteen years, I have been interested in Geometric Algebra (GA, real-valued Clifford Algebras with geometric interpretation), which gives a standard formalism for all sorts of problems, including a more comprehensible QM, Gauge Theory Gravity, as well as practical applications in graphics and path planning for robots and machine tools. What I most like about it is that nearly every paper is written to be understood, starting from scratch and assuming little prior knowledge. It is also coordinate-free, terse, visualizable and just general enough to represent anything physical. Clifford spectra of tree structures is a current application that I find particularly interesting.
Another of my interests is a computer language called "Frink", created by Alan Eliasen. The most radical thing about it is that it is physically-typed, so that every quantity can have physical units, and it will recognize virtually any sort of units, no matter how obscure. (For instance if you want to calculate orbital energy as "roods / microfortnight^2", it can do it.)
Frink runs on anything with a JVM, has both simple terminal-like interactive desk-calculator and full programming modes, and has many other advanced and convenient features for all sorts of practical purposes, including arbitrarily large integers and precise rational numbers, interval arithmetic, exact time computations in various time systems, currency conversion and inflation-adjusted value calculations, natural language translations, regexp, self-evaluation, fast number theory functions, convenient built-in data structures, and some modest symbolic math capabilities. I use Frink all the time and hope some of you will try it out. It also has some of the best documentation I have ever seen.
Working with Frink led me to try to figure out the patterns in the factors of the various unit classes (a unit class would be something such as "area" rather than a specific unit such as "hectare"). It turns out that there is a pattern that lets the vast majority of the different unit classes be mapped out in a coherent arrangement that fits on a single page, and gives new insight into how physical quantities relate to each other. I'll post more on this soon.
More relevant to Azimuth is the idea of "seed factories", minimal toolsets sufficient to produce the tools that make the tools ... that make as large a fraction as possible of products in the economy. The software used for materials, tooling and product routing, scheduling and accounting, and the co-design of products together with all the processes needed to make them is the biggest challenge. Similar software will be needed for off-planet industrial ecologies and for product-producing molecular nanotechnology, so this software will be some of the most critical infrastructure of the future.
Great gains in efficiency and sustainability are possible with seed factories, and the lend themselves to decentralized ownership and organization that allows closely coupling demand to production and widely distributing the economic rents of productive machines.
I hope we will together think up and build things that have a big positive effect in the real world.