Y Combinator, the fixed-point combinator function


4 years ago

The bond between technology and math is undeniable, but is most evident in the application of advanced mathematics to the field of Computer Science. High-level mathematical theory is at the heart of Computer Science, and recursion specifically often presents the first major challenge of a formal computer science education. James video emphasis on the importance of the Y Combinator function was very apt, and I can speak from personal experience as a software engineer in saying that understanding this process is the key to utilizing the full capabilities of the high-level language you are working in.

This summer, I developed a full-stack video transcoding system for Platzi on demand and livestreaming needs. In building this system, I decided to write a server in NodeJS to handle queries to the transcoding service in the form of POST requests. These queries would serve to check whether the current transcoding job had been completed. The problem of repeatedly making these queries confounded me until I decided to try a recursive approach to the problem. I wrote a function in Javascript to check for an affirmative response from the server. If the response was as desired (the transcoding job was finished), my server’s process would continue. If not, the function would call itself, sending the same query again until the desired response was received.

I was thrilled to discover such an effective application of recursion in working to streamline my server. The Y Combinator, a function that computes fixed points for use in a recursive algorithm is a fascinating mathematical concept, and its practical relevance to everyday engineering makes it all the more exciting. Computer Science gives us the unique opportunity to see abstract concepts like the Y Combinator in action, which is the best learning opportunity any student could ask for.

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