Proof

I think I have another way to prove that every linear symbolic space is constructible as a numeric space. It is by induction on number of boundaries, and assumes a numeric cospace is constructible from a numeric space. By classification of the numeric cospace, the symbolic space has a symbolic cospace. To complete the proof I must prove every section of the symbolic space is a region in the symbolic cospace. Using a perspective, sections have sidedness wrt vertices. Consider a section of the symbolic space. I must show the section’s region in the cospace is not empty. Choose a point in the numeric cospace corresponding to a region in the symbolic cospace, a numeric, and a symbolic boundary in the space. Move the point across attached boundaries matching to section sidedness wrt vertices in the space. In some region of the cospace, the considered section is the same as the moved boundary wrt space vertices of attached cospace boundaries. Assume for contradiction that the point differs from the considered section wrt some vertex, called the contradiction vertex. In the cospace, choose a perspective that puts the contradiction boundary and an attached boundary on the same side of the attached region. That perspective in the space puts the contradiction vertex and a vertex attached to a region, in the considered section, divided by the moving boundary, on the same side of the considered section and moving boundary. This contradiction completes the proof.

Graphics

I wanted to eliminate my geometry shader so I could brag that my microcode runs fast, but I also wanted to show off my facets. The idea of decorating facets with pictures gave me an aha when I realized it would make rotation about the normal more useful. But for some time I could not figure out how to feed texture coordinates to the vertex shader. Note that duplicating the points was unacceptable to me, not because of memory constraints, but for aesthetic reasons; duplicating points violates topological reality. Since limiting planes to have at most one facet is acceptable to me, disallowing kissing vertices is ok, and facets separate polytope regions from non-polytope regions, I can limit vertices to have at most 3 facets in 3 dimensions. Then the challenge was to get the vertex shader to choose the correct texture color, texture weights, and texture coordinates. I wondered if each facet could be assigned a tag valid for all of its vertices. All the vertex shader need do is lookup its texture vectors by a uniform tag. Assigning a tag to each facet is a graph coloring problem. Using a greedy algorithm, no more than n+1 graph colors are needed, where n is the maximum degree of the graph nodes. Here, graph nodes are polytope facets, graph connections are shared polytope vertices, and graph colors are facet tags. A facet can have any number of vertices, but in 3 dimensions, it can be decomposed into 3 vertex facets. Modify the greedy algorithm to assign the same tag to facets in the same decomposition. Triangle facets have 6 vertex sharing neighbors, so 7 tags are needed. Thus each vertex needs 3 texture vectors, and the tag uniform needs to be changed 7 times.

Minimalism

There are several kinds and fields of minimalism. I know enough art theory and history to claim ignorance about art minimalism. Minimalism with a capital M has come to mean small houses or few possessions. But small and few are poorly defined; say small or few to a mathematician, I dare you. Minimalism in software language means Lua and such. Minimalism in software design means user interfaces like double dash files that melt the distinctions between automation, configuration, and interaction. Minimalism in backpacking can mean ultra-light and/or general purpose. Backpacking mores can be applied to behavior in general. Leave only footprints and take only pictures translates to minimize your carbon footprint and respect indigenous priority. Does one opt for high tech or tried and tested. Does one prefer expert approved or do it yourself. Does one keep a clean living space or minimize the amount of manintenance. Does one emulate a storage, workshop, or ship? Engineers claim to admire simplicity, but each interprets the word differently. Some lean towards architecture, and adopt descriptive identifiers and formulaic comments. I lean away from architecture, and opt for shorter identifiers, fewer lines of code, and imaginative comments. I take a similar approach to society. Corporate life is a bath of deception and secrecy. The claimed merit is productivity, but in practice that means toeing the line. Methodology claims to enhance reuse, but actually just makes marketing easier by reducing innovation. Similar dynamics occur in other hierarchical parts of society. Trickle down economics claims to raise all boats, but actually just crams more sardines into the same can.

Double Dash

I've become disillusioned. Open source is ugly; IDEs are ugly; big data is ugly. The only UI that brings me joy is my double-dash syntax. Only files are a way to communicate to a command line program that reads files with .-- extensions. If you want to change the mode that the program is running in, then you have to append to a .-- file that was given to the program at invocation. Every -- in a .-- file starts a command, no matter where it occurs. If a -- occurs before a command gets all the arguments it expects, then the interrupted command fails. Anything not matching the argument format is ignored. Stop trying to make computers more like people. Just find a common denominator. One command opens one window. Multiple instances of that command can share, or own, files given to the command on its command line. Only files are given on a command's command line; command line arguments that are not files are ignored. Obviously, simultaneous commands can share files, so I do need pthreads to read files as they are appended to. No other overhead is necessary. Everything else is innovation. Stop reinventing the wheel. No matter how profitable reinvention is, and how unprofitable true invention is, just express.

Innovation

Innovation is not a football in the battle between libertarian and socialist. Innovation is the field. Let’s give libertarians some intellectual credit, and assume they know that what socialists refer to as innovation comes from government and universities. Libertarians have as many words for profit as escimoes have for snow, and to a libertarian, innovation is a form of profit. They may quibble that innovation is a source of profit, but just as snow is a source of ice, it is all profit to a libertarian. When libertarians argue for less government, they are arguing for less of what socialists call innovation. Both libertarians and socialists have a point. Government gave us fracking as well as internet. Big government is imperialist, because building up alternatives before tearing down traditions accumulates advantage. Let the ideologues argue over more or less; the future is what kind. Until government stops being timid and greedy, and starts destroying as well as feeding corporations, we will stay on the current track to climate breakdown.

Meaning

I piled onto an author’s Twitter post, he blocked me, I bought his book, and I am not sorry he blocked me. In a sense, Roy Scranton is a humanist. Humanism can be good when it manifests as anti-fascism, for example, but when it manifests as anti-life, it is bad. Intellectually, humanism can be lazy. Scranton’s first essay used the word “meaning”, I’m estimating, twenty times. Using a word so many times robs it of meaning. Mathematicians adapt to the need for frequent references by defining things. Scranton would be hard pressed to define his use of the word “meaning”. Humanists also overuse words like “purpose”, and “belonging”. Personally, I’m nothing's tool or belonging. The Twitter debate was about whether we can or can’t solve global warming. I believe we can, because oil companies are ephemeral, and hurricanes are concrete. I find it presumptuous when people claim that human systems are set in stone. It is possible that some emergent properties of society are inevitable, but to assume they are inevitable because they presently exist is unscientific at best. In my opinion, assuming society cannot change is manipulative and reactionary. Thus, a putative humanist can in fact be conservative. For example, when a humanist uses the word “life” to refer to day to day activities of humans, he is dismissing the importance of ecological systems. Even the word “social” is often misused as a euphemism for popular. Some people have excuses for not thinking for themselves, but I loose patience with highly educated conservatives.

Values

Ian Morris would like to explain non-physical things with physical things. Why is that? The rebuttal Morris ignored is the most telling. Morris is essentially a capitalist. His values guide his explaining. I am a contrarian. Because capitalism rules, I am not a capitalist. My explanation for values is independent of the material world. Values are memes that battle it out in our brains. Morris’ observation about accelerated value change is explained by accelerated intercourse. If memes that favor intercourse win out, memes that favor consumption need not. We each have a responsibility to keep our mental homes orderly, by favoring memes that do not threaten our existence. In particular, the meme of climate denial should be eviscerated. How does the physical world affect memes? Why not ask how paper affected communication? Quite a lot. But not in a simple way like natural selection. The medium affects the message in counterintuitive ways. Morris does not go very far beyond intuition, so his theory helps no one but himself. More helpful would be a system dynamic model of the brain. Then because scientific method scientists understand such models better than do intuitionists, such as Morris, Morris’ capitalist meme would be quashed. The key feature of sustainable media is that they are significantly simpler than the universe. The reason humans are in so much danger is that they are an especially complex medium. It is by understanding the medium that artists are able to be constructive. And it is by understanding why we have values that we will put oil companies out of business, and thrive in a high intercourse world.