I always get vexed when a lot of textbooks and lectures introduce concepts for the first time so formally they end up misunderstood by the listener, (maybe an attempt to make the science appear like a convoluted subject matter or just a blind following of tradition), to the point the gist or underlying meaning of the concept is lost. Take for example a lecture in industrial electronics. Students become familiar with SCRs, UJTs, thyristors, diacs, triacs - learning their function as regulators of power delivery and how they're applied in triggering circuits and resistors (like for the misleadingly named Programmable Unijunction Transistor or PUT). Fast forward a couple years where these students are now working in the industry. Say, there is a series of loads supplied by a low power supply. The client wants all loads to continue operation even after breakdown. From the student's schema on basic circuit analysis, he will offer to place loads in parallel. Unfortunately, the client needs a stable supply of current on each load, and driving loads in parallel risks current instability, because it is impossible for 2 loads to have the exact same resistance to have a stable current flowing through each by Kirchoffs laws (not to mention varied impedances).

     What solution do you think will the student implement? What book or lecture spoon-fed instructions on how to deal with fixing a load in series that has failed? When the load in series fails, a potential occurs at its terminals. This potential must serve as a trigger to activate a short circuit over the two points. But what field of low power electronics could implement this kind of logic? Could it be a logic circuit? Why not design a logic circuit with a Zener diode at its feed point (to regulate towards threshold voltages) that will short the 2 terminals when a voltage is sensed? What if the student doesn't know that the logic circuit above can be replaced by a low rating SCR and a few resistors (which will compose the trigger circuit)? A big difference in cost, since the number of components needed is significantly reduced. When a potential is exerted at the terminals, current will travel through the resistors towards the gate terminal of the SCR. If the resistors have been chosen appropriately so that the threshold voltage is reached at the gate, the SCR will fire and create a short circuit. SCRs also happen to be the perfect candidate for this kind of switching since it dissipates minimal power. But going back to our student, how could he/she realize that an SCR could do a better job if his/her mind has filtered it out as a component for control of power delivery? (okay, this may not be the best example out there, but it's the easiest I can think of... naturally sound critical thinking will lead to this solution). A student can't just rely on textbook definitions and lecture. A deep understanding of the concept is needed to apply it effectively outside intended use, where the student has no margin to be pedantic. Eventually, the student may learn that possibilities for application can be boundless.

                I'm not saying this is always the case and is unavoidable in the academe. Even I am not adept at thinking this way yet, but there's a lot that can be done to practice this mindset. Maybe a paradigm shift is necessary to realize most demarcations that separate the sciences are not rigidly fixed, but meant to be overlooked to reach novel solutions.