There is a connection between engineering and music. For the sake of simplicity, I will shorten “math, physics, computer science, mechanical & electrical engineering” to “engineering.”
Let’s start with the general question: Are engineering and music the same?
My immediate thought was that these fields constitute a gradient of knowledge and defining boxes that constitute each field is limiting to the solving of problems and the mastering of skills. I then realized that my immediate thought was an oversimplification and the question was too general to answer meaningfully, thus I refined the question slightly:
Are engineering and music two ways to look at the same thing?
I answer with a vague hypothesis: these fields are connected by general principles applied in different contexts.
As we know, one can’t prove that something is true purely by example; however, finding examples of these connections is exciting and interesting to think about. An example of evidence that supports this hypothesis is number theory. Number theory is deeply connected to the theory of harmonics. Using mathematics to prove that there exists a deep connection between the structures of engineering and music is almost cheating. Modern math becomes increasingly abstract. Each major concept works with many diverse objects, all sharing some common property. An abstract theory is born from the consequences of this property, which may then be applied to any of the diverse objects.
This led me to think about the connection of general thoughts and actions between the fields, rather than the underlying principles themselves. For example: the connection between completing projects in engineering and playing a musical instrument. Both activities are never-ending fountains of entertainment and learning; there is always room to improve yourself in your understanding and implementation of your knowledge in both cases.
The application of these knowledge bases involve a similar level of 3D spatial reasoning and abstract thinking. These subjects are built on modules and components. The understanding of each piece of the puzzle and how said piece connects and interweaves with the whole picture (which itself is another puzzle piece) is integral to both completing a project on time and understanding a piece of sheet music (especially if it is in an orchestral context).
I will attempt to demonstrate this connection with two specific examples: learning a complex piece <= learning an instrument learning to code <= learning a programming language.
(1) Before one learns and reliably performs a piece, they understand the language of music, whether that understanding is purely by ear or complemented by reading sheet music. They learn to play an instrument (in my case, the trombone). This learning forms a dictionary of muscle memory that consists of sheet music/sounds as keys and embouchure/hand position as corresponding entries. After practicing consistently over a long period of time, I began to feel the instrument as an extension of myself, as a voice to communicate with. To learn a complex piece, I practice each measure, and then practice weaving the measures together.
(2) Before one becomes a good programmer, they understand the basics of computer science (what it means to compile/interpret a program, how to create efficient programs, how to write general instead of hardcoded source, how to use existing libraries in your project, the practices of writing readable source/how to document code). They learn the basics of coding: variables and data types, strong vs weak typed languages, assignment vs. equality. They learn the syntax and lexicon of a programming language, and they learn to create code to execute their ideas. This new lexicon leads to a new way of thought, it includes the structures and semantics at a level of abstraction above the basic syntax of the language, this includes the concepts such as instantiation, monads, and verification. Enough practice leads to thinking in code, and intuitively recognizing how to compose an elegant and efficient solution to a computationally intensive problem.
Similarly, I find that composing orchestral music and creating/working on original research use similar structural thought and insight. Enough examples, I think you’ve got the point!
Although I am not a master of engineering nor music, I consider myself an engineer/scientist and an amateur trombonist. I enjoy learning and developing myself in both areas. I personally think of both music and engineering (especially mathematics, programming, and robotics) as collections of 3D structures to play with and put together whilst keeping in mind various properties and limitations.