The Beauty of Engineering

Recently, a Chinese mathematician, Hong Wang, was awarded the prestigious Fields Medal. Since then, an article entitled "The Beauty of Mathematics," which is said to have been written by her when she was sixteen, has become popular on the internet. This has driven me to write this article to express the beauty of engineering.

Engineering is how we solve practical problems, and thus engineers have to consider everything for the solution to be applied in the real world. It is strongly influenced by the developments of mathematics and natural science, but it has its own characteristics too. Any breakthrough in natural science can trigger significant changes in engineering, driving engineers to learn for life.  A typical example is that since the invention of optical fibre, theories and techniques in telecommunications engineering have been reshaped. 

Many engineering problems are complicated in scale. Engineers typically have to gain a broad knowledge to understand the whole system and its components. Since a lot of problems require repeatedly solving the same issue, reusability must be considered. In software engineering, this means separating functionalities into different functions, classes, or software components. Reusability is sometimes implemented by allowing configurations on a large component template. For example, C-YAWL, a component that I developed at QUT for the open-source YAWL project, provides a way to create simpler business process models through configurations of a large one.

Different from mathematics, where everything can be rigorously proved, an engineering problem can't be proved thoroughly, even though mathematics is often used as an approach to analyse it. 

Compressive sensing is a topic in signal processing which has strong mathematical foundations. Renowned mathematicians such as Terence Tao have made significant contributions. Theories have been proved that, under some conditions, an algorithm can be used to recover signals in a probability close to one, through random sensing. However, in practice it is still impossible to examine how closely the real signal sources fit the assumptions, while these assumptions will never be fully met. The result will be better if the input signals have characteristics closer to satisfying the conditions.

The approach to an engineering problem is very different from rigorous mathematical proofs. Sometimes we have to observe carefully and even use some imagination. I still remember that in a lecture on electronic circuits, the teacher presented his proof. In one step, the math function looked too complicated. Then he said, "It is impossible to solve this nonlinear function. But let me draw it." 

He then drew a curve on the blackboard, and said, "Just look at the curve of the function. If we only focus on this little region, the curve is smooth and we can approximate this part as a straight line. Thus, we can approximate it as a linear function like this, and then..." 

I am sure this type of approximation would never be allowed in pure maths but it is popular in every domain of engineering.

A engineering solution has to consider human behaviours too. For example, a software engineer has to keep in mind that there is some hacker wanting to break into the system they are developing.

Since not everything can be proved with maths or natural science laws, experimental evaluation is the only way to evaluate the performance of a method in engineering. 

I remember that one day I met a professor who was the director of a research group for speech, audio, image and video technologies. I told him that I had encountered a problem when training the Gaussian Mixture model. 

"The covariance matrix becomes singular after some iterations," I said. “Yes. This is a known issue for GMMs," he said. "Do you have an idea to solve it?"

I then explained what I wanted to do. "Do you think my method will work?" I asked. He smiled and said, "You can try and experiment. If it works, then you know it works. Otherwise, you will know it doesn’t.”