can be read

An experiment in presenting geometry


However complex figure may be
prose is always ready.


However long prose may be
figure is always present.

Euclid, ~300 BC.
Newton, 1687
Archimedes, ~200 BC.
Galileo, 1638.
Descartes, 1637


This is a clip from a geometry book. Particularly a translation of the 2300 years old Elements. Reading it requires going back and forth between the figure and the prose multiple times in most of the sentences. Which gets rather tedious and borderline torturous when you need to read again. Coloring it would help greatly.

This is from Oliver Byrne’s work(a digital version can be found at About 180 years ago he made use of colored print and made a phenomenal contribution. That brings a question: Now that we have digital displays that gets refreshed 60 times every second, what more can be done?

The usual answer is to record a video. Which dictates a rhytym, isolates fragments, strains potential participation and often turns ridiculous under production costs. Surely films are awesome but their teaching of technical material is not the strong aspect.

Now follow this: And press j/k or right/left on keyboard or use the gray buttons at the bottom of the page. That should move a cursor along the prose and highlight the figure for symbols. You can also click on sentences.

The human eye can't distinguish between more than a handful of colors and picking colors for all the lines is somewhat difficult; Equivalent to a naming scheme with different symbols than an alphabet. But with differential brightness for resonate highlights the complexity of the figure is not an issue as long as it is a reasonable figure. Color can be reserved for further development like the presentation of symbolic expressions.

Also, i tried to keep the figure visible in a separate column as the prose gets scrolled, which seems like a more fundamental issue for digital books. But it is impossible to argue for when the software is taken to be generic money making machine of vanishing marginal costs or simulation of absolute laws. Proper utilization of screen space will have to wait for a new generation.


As for ancient geometrical analysis and modern algebra, even apart from the fact that they deal only in highly abstract matters that seem to have no practical application, the former is so closely tied to the consideration of figures that it is unable to exercise the intellect without greatly tiring the imagination, while in the latter case one is so much a slave to certain rules and symbols that it has been turned into a confused and obscure art that bewilders the mind instead of being a form of knowledge that cultivates it.

— R. Descartes, A Discourse on the Method, 1637

This is mathematics at the beginning of modernity from the perspective of the inventor of Analytic Geometry; Introduced as "my method" later in the same book.

Screens are part of the computers for about fifty years now. But couple thousand years of imaginative work on paper determined that screens be an imitation of paper, for the most part. Basic container of data was inherited as files and folders. Much of the private computer was put together in a company that makes photocopy machines. Within which the preview of a print had monumental benefit along with a pointer device and a virtual catalog. Word processors, spreadsheets and slides came to be the most used software and suggested a future as typical products. And we come to look at web pages that were conceived to be available versions of physical documents.

Imitation is mostly effective but it can also be frustrating. But frustrations are a bit difficult to demonstrate. First, It is not obvious how information technology should leave the office and become relevant to life besides facilitation of bureaucracies or consumption of packaged entertainment. Second, criticism of digitized paperwork(i.e. finance) seem to fall on deaf ears. And i will not try to point out that relevance at a time anarchy and chaos are synonymous. Nor will i be an impotent reactionary and define a principal in negation to concentration of power. Instead, the new medium is taken as ground to experiment around prevailing institutional dependence and brute specialization that beats their imagination out of people.

Of course, this alone can't leave a dent in the curricular consumption called education. But the institution of school is so busy besides the washed out education. With the temporary custody for parent relief, introduction of the media for the other institutions, imposition of specialization to cope with the complexities, indoctrination to make up for the deficiencies, uniformization for the broken socialization, provision of outcasts from the cracks it can't cover and keeping a facade of professionalism with minimal funding for an essentially caring occupation. All of which turns outright pathetic when the media depended on by most organizations for memory and configuration has been dissolved into the virtual. And the technology is nothing more than a tool for the financialization of education as a cost item in the institutional budget with the pretense of student aid. Cramming of scanned books, managing of documents, tracking of attendance, delivery of performances, programming of quizzes and evaluation of tests can only help the institution not the student.

The natural inclination is to ignore the depth of tremors or wish for a Beneveloent Dictator out of Artificial Intelligence to free us from attending to the constraints of mediating tools. But learning can't be a contreversial goal of education; Mentioned hypothetically after an obligatory recognition of the subjectivist foolishness unless an irrefutable measure to satisfy some committee can be conjured. Media, like the air we breath, became banal platitude over the course of history and one question has to be made explicit: What can be done better than on paper? So that we be aware of the cultural momentum and possibly see a course correction.

Being able to read the classic books of mathematics as careful investigations that show insight to carry questions in complex configurations would dismiss the cloud of obscurity surrounding them. Geometry, probably the most detested subject, would prevent a very early instance of specialization and the later fixation with suboptimal syntactic constructs for those broken survivors. It can relieve algebra from the heroic duty that it has served during a time people had to be conscious of every symbol inscribed on a page, every page wowen in an heavy and expensive volume, every volume that needs to be delivered by hand and every delivery that would need to be repeated for updates.

Brevity and utility gained from articulated symbolic expressions is beyond any argument. But it is easy to mistake the compression for intelligence and forget that people work with abstractions of all kinds all the time. It is easy to forget the pains taken to devise them, certain level of arbitrariness inheretent to them and the need for decades it takes to become comfortable with them. Let alone the grounding of languages in a perspective and their perpetual reinvention. Of course there will always be constraints on communication across time and space. The question is what to do with the tremendous increase in bandwidth and resolution. It can either shackle us to the known or free us to participate in the universe.

Complaining about the raw information available on demand as a pollution is the forerunner amongst the candidates for a cliche of this age. But its truth eludes the expansive dominion of finer and finer specialization. What we have is an opaque technology that brings all knowledge, raw and refined, within clicking distance. Nothing short of a recipe for confusion where accounting replaces work. As progress without articulation goes with the elevation of the known to dogma. Instead, we can consider that constraints of media was a factor on boundaries of specialties, that limits in communication faced by investigators and leaders had a cascading effect on what had to be left opaque, that the future can't be reached under borrowed light.

— ibrahim sagiroglu