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The scientist seeks to understand nature at its core, to get to the fundamental essence. To do this, the scientist typically strips away extraneous effects and dives deeply into a very narrow element of nature. And from this look comes what is known as the laws of nature: energy and mass are the same thing, for every action there is an equal and opposite reaction, and so on. There are lots of laws of nature, and they apply everywhere all the time.
Engineers live with the laws of nature. We have no choice. Our goal is to design things that work within what nature allows us. To do this, we have to be able to predict the behavior of systems. So a big question for engineers is, how do we understand and predict the behavior of systems in which all the laws of nature apply everywhere all the time. This is an issue of integration, and it is every bit as difficult as finding the laws in the first place. To account for all the laws of nature everywhere all the time is an impossible task. So the engineer must find ways of determining which laws are important and which can be neglected, and how to approximate those laws that are important over space and time.
Engineers do more than merely predict the future. We make decisions based in part on their predictions in the knowledge that their predictions cannot be both precise and certain. Understanding and applying the mathematics of this is also important. This includes the application of probability theory, decision theory, game theory, optimization, control theory, and other such mathematics in the engineering decision making context. This also is a legitimate area of research for engineering.
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