Iterations of Oneself

Six degrees of inclusion

Recently, I started studying network science. Network science is the analysis of complex systems that can be represented as networks of nodes linked by edges. I am currently taking the Social Network Analysis class on Coursera; and I’m finding it really interesting, and very well worth my time. (I want to take this space to give a special mention to professor Lada Adamic from the University of Michigan for her enthusiasm and excellent class).

There is an enormous number of phenomenons that can be represented using networks. Social networks are just one of them, but other networks such as flavor networks, product exports by country are just some of the many possibilities.

As part of my project for this class, I decided to analyze the networks formed by file inclusions in software projects coded in the C programming language; and I had some interesting findings.

As part of this project I analyzed the code bases of three different software projects: xv6, git and MySQL.

The following image shows the network representation of Git.

Initially, I coded a simple shell script to extract the graph formed by the file inclusions, and generate a simple file of the Pajek .NET format. Once the graph file was generated, I was ready to import that into either Gephi or R, and start analyzing some data.

One of the most interesting and most expected outcomes of looking at the data is that there seems to be a definite division between files that are included by many other files (and don’t include many other files), and files that include many other files (and are not very much included by others).

This is understandable, and even expected; but it is still useful and interesting to see it being confirmed. This can be explained because there usually are files in software projects that define basic functionality that is utilized by many others. In the research paper, I called these files “service files”, as they define functions and services that can be accessed by other files.

On the other hand, there are few files that tend to include a bunch of other files. These files are generally files that drive the execution of the applications. Particularly for the xv6 project, the file that includes the most other files is that which implements the command console of the xv6 system; and thus it is the one that drives the execution of the application.

On the following image, it is plotted in blue the number of times a file was included, vs the number of times it included any other files. As it can be noted, although not all files adjust perfectly to the idea of service and execution files, there is a general trend to do so.

Other interesting findings of the analysis were that although the file count of large projects, such as git and MySQL was actually very high, the distance between two files was generally quite short. For MySQL, although it has about 2900 nodes, the distance between files averaged under 5 hops, and over 95% of the paths were of 7 hops or less.

One of the possible explanations of this small world where any file can be quickly reached from any other file is that these projects are coded in the C language, and the simplicity of C allows projects to gravitate towards a monolithic architecture. An interesting trend to look at is whether or not this small world effect manifests in projects written in languages that encourage encapsulation, such as Java or C++.

The graph generated by file inclusions is still rather coarse grained. A more fine-grained analysis of the networks generated in software is the graph of function calls. This promises to be an even better way of identifying the relationships that take place in software.

I uploaded the whole paper I wrote, along with the scripts and network structure for the three projects. All of them can be downloaded as part of the following repository:

https://github.com/pabloem/code_networks

Of old ladies and alien languages

On September 20 of 2012 I had a pretty strange encounter. This encounter gave me a really strong impression, and I intend to write about it and about a little bit of research I did on the topic.

For reasons of little relevance; that evening my roommates and I found ourselves knocking on the door of the janitor of our apartment building. He was not home; and instead it was his mother the one to open the door to attend our call. I told her naturally what the issue was, to which she responded with a single word that I could not understand.

“Pardon me?” - I said.

The same word again; and a load of things that I could not understand.

It took me a few moments before realizing that this lady was speaking to us in an indigenous language; and that she could not speak Spanish. I was speechless. How could I not have the slightest idea of what she was saying? She and I were born in the same country. We lived in the same building; and yet, I could not figure out a way to communicate with her. Holy shit.

In the year of 2005, it was estimated that the number of people who could speak an indigenous language in Mexico was almost 6 million. Of these, about 5.1 million are also able to speak Spanish, and the rest can only speak their mother tongue. Also, almost 10 million people identified themselves as indigenous. These are some interesting numbers to think about. Keep them in mind!

Mexico, in the second article of its constitution, is defined as a ‘pluricultural’ nation; in recognition of the several ethnic and cultural groups that integrate the country. The constitution is careful to give different cultural groups the right of self-determination. This allows all the indigenous groups to freely determine their political, social and religious form of organization, as long as human rights and gender equality are respected. There are 68 indigenous Amerindian languages recognized as national languages.

However, although Mexico does well to recognize its cultural diversity in paper; how well does Mexico do in fostering and empowering all the different peoples that share the country?

There exist several programs offering scholarships and financial support to indigenous students, to be able to attain higher education. Also, there is a strong rhetoric of trying to improve living conditions and services for indigenous communities. Unfortunately, this rhetoric does not materialize in much development for these communities; which usually lack a strong capital flow that could make investment more attractive.

So what would be the right steps to take in order to empower the indigenous people of Mexico to develop their cultures and their potential? Consolidating, and making Spanish education compulsory? Making sure that they get education in their mother language, to make it relevant again? Not acting, and continuing the slow cultural assimilation into the mainstream Spanish-speaking Mexican culture?

I honestly don’t know the answer. I’m just throwing my thoughts out there. It surprises me deeply that not only could we not communicate, but it was also impossible for us to find an interpreter to allow even the smallest amount of communication. How could I expect her to know my language if I didn’t have a single clue about hers?

Sources:

[1] Los Pueblos Indígenas de México - http://www.cdi.gob.mx/index2.php?option=com_docman&task=doc_view&gid=62&Itemid=24

[2] Indigenous Peoples of Mexico - http://en.wikipedia.org/wiki/Indigenous_peoples_of_Mexico