What Is Engineering, After All?
Engineering and Mathematics
Just like mathematics, engineering is a technical discipline. By that, we mean that abstract techniques—such as algebra, calculus, statistics, and probability—are used to manipulate ideas or data.
One of the recurring problems engineers are called on to solve is resource allocation. Say you want to build a house or another type of structure.
It is a given that resources such as money and time are not infinite. It is plainly wasteful to spend twice what is needed to build a single house when two houses could have been built to the desired level of quality.
Engineers are thus asked to estimate: “How much material is needed to meet safety parameters?”, “How long will construction take?”, “How should we lay the foundation if we aim to have this many floors?”, and so on.
Depending on the estimates and available resources, the plan may need to change or adapt. Engineers add value to the project by bringing in a “view into the future” in the form of predictions or estimations.
Some of the central tools for predicting and estimating are provided by mathematics. Say I can measure how large a load a block of concrete can bear before it shears. If a model can estimate how much load is on each block of concrete in the edifice, the materials needed for the project can be safely planned, budgeted, and acquired.
Linear algebra, calculus, probability, and statistics provide the mathematical tools needed to implement this model, allowing conceptual iteration and refinement while it is still relatively cheap to make changes—say, compared to having to build “test buildings” to try out ideas.
Engineering and the Sciences
The natural sciences are concerned with arriving at true knowledge about the world. That knowledge is usually universal and stems wholly from nature.
Furthermore, science is built on iterative refinement. Maybe a classical Newtonian conception of time is enough for almost all earthly applications, and one could go through life without concern for relativity. But for satellite navigation systems such as GPS, we need to incorporate Einstein's conception of time dilation to achieve the required accuracy.
Engineering, thus, is concerned with solutions to real-world problems. If the problem is “How do we put a satellite into space?”, engineers will reach for the best tools available—often drawn from the sciences—to solve the problem most effectively. “Most effectively” meaning solving the problem well enough, for some definition of “well enough”, within budgetary and time constraints.
All in all, engineers are asked to reach into abstract areas of knowledge, such as mathematics and the sciences, and come up with proposed solutions that, when applied to the problems at hand, will yield the best results within existing constraints.
Science and mathematics, in the theoretical sense, are not concerned with resource constraints, since their goal is universally true knowledge. (Well, unless the goal is to come up with a technique to estimate or optimize a given set of constraints, but that is beside the point.)