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Math as art: what lies behind the numbers?
Material posted: Publication date: 10-11-2019
As you know, people are divided into "physicists" and "lyricists". According to popular stereotype, the first is austere scholars, alien to any sentimentality, the"geeks" in their spare time will appear on the cloth, not the first freshness high-rise equation. "Lyrics" — the writers, artists and people of art — have a monopoly on all kinds of manifestations of love. Meanwhile, mathematical calculations, which are usually associated with dry multipage figures and tables, can be very visual and very beautiful.

You just need to see what is hidden behind them. And of course, to show everyone else how it makes Chris Harrison, graduate student, Department of computer science at Carnegie Mellon.

"Programmers working in computer algorithms, usually write their own methods for other programmers, not caring about how they perceive the development of end users, said Chris Harrison, a PhD student in the laboratory for the study of human interaction with computers (Human-Computer Interaction). — I'm dealing with how people perceive all of this data. So, at the junction of these two worlds I have had the idea to display some figures in this unusual form. However, I consider it as a hobby".

"Do not look at these illustrations of the profound scientific meaning, explains Chris. Just watch and enjoy the complexity and beauty of those data we encounter in everyday life, but usually can not perceive. My visualization give this data a voice, form. It's like painting, but instead of brush strokes, I use computer algorithms, but instead of paint — digital data. Do my ‘painting' people? Many believe that these paintings cannot be considered art because they are too analytical. But there are those who see these charts and austere beauty, and hidden from the naked eye the connection between familiar concepts."

Annual rings

If you cut down a tree, then the rings to determine how old it is, how it grew, whether these dry years, or Vice versa. By analogy with this model Chris reviewed the process of publication and discussion of thematic materials on the website where members of the community themselves placed notes. Various themes are marked with different colors, thickness of each ring is proportional to the popularity (number of views). Top row: the distribution of rings months, lower by day of week (averaged data over a year 24.05.2007 on 23.05.2008).

Card bookstore Amazon

The owner of the site Aaron Swartz has compiled a list of 735 323 books available for purchase in one of the largest online retailers- Amazon. Moreover, he tried to combine them using 10 316 775 links. Chris built according to this "world map", using the program, trying to place the "associated" books as close as possible to each other. After 140 hours of operation of the program, the average distance between the "associated" books dropped from 350 to 9. Colors denote subjects, and if you use a very high resolution, you can even consider book covers.

Ancient hypertext

This is one of the most simple and clear visualizations based on data provided by Chris Lutheran pastor Christoph Remhelda. The pastor considered the Bible as hypertext, that is, the set of texts containing navigation nodes (links) from one text to another. Just had to track and process more than 63 000 hyperlinks contained in the text of the Bible. However, the goal was not to build your model book to study (there is a number of much more functional programs). Instead, Chris decided to focus on another aspect — not functional, and aesthetic.

This diagram gives an opportunity to understand how complex this ancient book. The columns below indicate the chapters of the Bible, the length of each bar is proportional to the number of verses in this Chapter. Each alternating grey and white stripes denoting a book of the Bible.

The upper part of the chart is given for the connection between the texts of the Bible. Each of the 63 779 links connects two of text. For greater clarity, the arc made color — the color denotes the "length" of a hyperlink, resulting in a kind of "rainbow".

The Bible as a social network

Another very nice example of visualization of disparate data is to build a kind of biblical social network. Chris analyzed the text of the book (had used the king James Bible), paying attention to people's names and geographical names (in total, 2619), which are found in one verse — in this case it was considered that there is a connection. Then he built this distributed social structure in which size is proportional to number of contacts (over 10 000). Names with more than 40 connections are written horizontally and the others at an angle.

Third dimension Wikipedia

Studying relationships between different topics, Chris could not ignore such a data source, like Wikipedia (Wikipedia). This encyclopedia covers various areas of knowledge, and anyone can add, Supplement or correct any article. In the result the English version now contains over 2.5 million articles (for comparison, the famous encyclopedia Britannica has 120 thousand articles), and this number is constantly growing.

In the center of each graph is the top (thematic category), from which depart the connections to the tops of the "child" categories, which, in turn, connected with themes of on the level below. Ties are marked with different colors depending on the nesting of topics. The graph is constructed in such a way that the length of the ribs was minimal. In this algorithm the vertices of the third level form a kind of "Islands" on the surface of the spheres, the center of which is any thematic category.

Dmitry Mamontov

The article was published in the magazine "Popular mechanics" (№11, November 2008).

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