There's a grey area, but I find your example (or the way you posed it) a bad one. Creating a mental model is science, even if it was done to be applied in a eng

There's a grey area, but I find your example (or the way you posed it) a bad one. Creating a mental model is science, even if it was done to be applied in a engineering context. First, even the math and science behind the structural harmonic response was made by an engineer, it was a science advance after all. They allowed people to better understand the world, creating models of phenomena that are observable. Of course, engineers can do science, as anybody else can, and that does not transform science endeavours into engineering endeavours. However, it must be noted that there is a lot of science in engineering: people can approach engineering problems and subjects with a science mindset so they can advance engineering. A new DSP algorithm is basically math, even if it is math with some constraints set by engineering realities, and may be analysed as such - more often than not, by people with engineering degrees, who are doing science. Both engineering and science are less about fields of knowledge and more about process: if you are trying to understand something, and to observe things that exist in a methodical way, aiming to create a model that can reproduce and predict events, you are doing science. If you are trying to design something that help you efficiently achieve some practical goal, you are doing engineering.