Tag: abstraction

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Engineering Curriculum

Benefits of an abstract engineering education

My prior post was critical of the abstraction-based, mathematics-heavy, and computation-focused eduction served up to today’s engineering students. It has been my experience has been that the most successful engineers in industrial practice are very hands-on, with years of practical experience, and insights that have little to do with academic equations. That’s not to say that the academic abstractions are unimportant, for they provide the language of discussion. An intelligent conversation about, say, a motor drive system, requires participants to understand that additional motor horsepower is not necessarily needed to produce greater output torque. (An engineer friend recently shared with me his attempt to explain this to a non-engineer boss. In the end, the boss said, “This doesn’t make any sense to me, but if you say it’s so, it must be.”)

Despite possible shortcomings in the current methods of engineering education, today’s graduates continue to be hired, and paid well-above average salaries—so employers obviously benefit from bringing on students who survive the current curriculum. Whatever modifications I might advocate for improving engineering pedagogy, I would certainly hope not to abandon these beneficial characteristics of today’s engineering programs. So what does an engineer learn from dealing with high levels of abstraction?

  • Perseverance — It often takes hours, maybe even days, to work through a single homework assignment. One has to look at each problem statement and begin trying to match the available information with potential methods of solution. Often times, roadblocks in understanding are encountered. The instructional material needs to be re-read, and re-evaluated to build a more comprehensive understanding of the solution technique. If the solution is not already known (from prior semester homework files, or found online), then a student has to at least convince themself that their path of deduction and computation is logical and rational. Shortcuts in this process are rarely rewarded in the long run, and engineering students rarely make it past their sophomore year if they haven’t acquired a healthy dose of perseverance.
  • Emotional suppression — Solving math problems is not a matter of nuance, or persuasion. It doesn’t matter how mad you get, or how optimistic you may be. Either your solution works, or it doesn’t. A successful student learns to keep cranking away at a problem until the correct solution is found, regardless of their emotional state.
  • Delayed gratification — Not withstanding the time spent working individual problems, engineers have to spend several years working on fundamentals before they can begin to solve higher-order engineering problems. Want to study photography? Grab a camera and go take some pictures. Want to be a writer? Start a blog. Want to be a civil engineer? Then expect to take four semesters of prerequisite courses to get to the point where you can begin seriously talking about bridge construction. In fact, your four years in engineering school are just a warm-up for going into industry, where you have to learn how engineering is carried out in the real world.
  • Humility — Solving complex math problems leads one to be wary of false optimism. A dropped sign, a transposed notation, a forgotten property, a misunderstood application—all can lead to an incorrect solution, even though the methodology seems correct. This aspect of the engineering education has been well-stated by Vivek Haldar:

    To be a successful software engineer (or indeed, any engineer), one first needs to be utterly and completely broken by failure. One must be so humiliated by a complex system that they give up and realize that the only chance of moving forward comes from being a supplicant to the complexity, by approaching it with humility and caution, not with hubris. You have to listen to the system, coax it into behaving. Commanding it does not work.

  • Sub-problem identification — Getting the hang of breaking complex problems into solvable sub-problems is an important engineering skill. My understanding of how this could be accomplished came in the second half of my sophomore year. No longer did I have to look for an equation or method that solved an entire problem at once; I could break the problem into smaller parts and solve the sub-problems individually. This was my first inkling that I might actually be able to “think” like an engineer.

Any other benefits to a traditional engineering education that I’ve missed?

Categories
Engineering Revision

Bait and switch in engineering education

It seems that many children have never considered the possibility of an engineering career. Well-meaning programs therefore attempt to nudge students toward engineering through exposure to engineering-like projects. These activities most often involve the manipulation of physical objects, such as constructing toothpick bridges, building LEGO models, preparing for an egg drop, or working with robots. Youngsters may alternatively be presented with a simulation of working with physical objects. As I’ve stated before, the role of an engineer is to implement new methods, devices, or systems. For an engineer working in the physical realm (a physineer), this means constructing something novel in the material world. So I have no problem with these introductory programs attempting to capture the imagination of students with physical-realm activities. My concern is the abrupt switch to purely abstract thinking that we impose on those who have expressed a desire to pursue an engineering career.

When students are sent off to college, they are immediately thrown into a series of math and physics courses that can seem wholly irrelevant to the activities that enticed them to enter the engineering curriculum. Although my undergrad experience took place more than thirty years ago, I remember struggling to rationalize how my knowledge of integration techniques was going to help me design production machinery. I had seen industrial equipment being built in a local machine shop, and I was fascinated with the banks of electrical relays that automated mechanical movement. (This was prior to the time that PLCs came into wide usage.) I wanted to learn how to design such machinery, and so I enrolled in my state’s largest engineering school, taking both mechanical and electrical engineering courses. Although I’m not sorry that I learned calculus along the way, I can safely state that knowing how to integrate by parts was never of benefit in my industrial career. In fact, over the two decades I spent in industry as a design engineer, I never found myself needing to solve an integral equation.

Given that several decades passed before I returned to my alma mater for a PhD, I presumed that the situation had improved. But my conversations with students currently in the middle of their undergraduate studies suggest that things are marginally better, at best. They are learning techniques of solution, but have little engineering insight. Children of my college buddies are now enrolled in various engineering schools around the country. When I talk with them I hear similar stories of being led blindly through math-heavy courses that appear to have little relevance to what they’ve heard at home about real-world engineering duties.

Is it any surprise that students are dropping out of this type of curriculum? Some claim the subject material is simply too hard. However, I think that Robert Talbert correctly identifies the problem:

Students aren’t put off by hard work. They are merely put off by any kind of work that doesn’t appear to be worth the effort.

I’d go further and say that engineering students can’t see the connection between the abstract and physical realms. This confusion is reflected in the following illustration, which has been floating around the internet. (Click on the image to see full size graphic.)

[The upper graphic seems to be from Valve’s Team Fortress 2. If someone knows which textbook the lower derivation is from, I’d be happy to give appropriate credit.]

The sad part is that this graphic is wrong. While research engineers may work in high-level abstractions, a great many engineering activities do not need such advanced mathematical acumen. In fact, many engineering problems are solved with spatial or experiential skills that require little mathematical prowess. So while I see nothing wrong in teaching abstract thinking, I think that engineering studies should advance from the physical realm toward the abstract realm, rather than the other way around. Otherwise, we’re promising to teach students one set of skills (to entice their enrollment), and delivering something else entirely. It strikes me that we’re teaching them how to be graduate students, rather than employable engineers. I suspect that this misalignment has real costs for students, employers, and the nation.

Categories
Engineering Roles

Engineering spectrum differences

In my prior post, I proposed that each engineering position requires a different level of abstraction. To a research engineer, almost everything is model-based, while the production engineer may be primarily focused on issues that are object-based. Although freshman and sophomore engineering students receive guidance as to the sub-discipline they should enter (electrical, mechanical, chemical, etc.), I’ve never seen any discussion about specializing in a particular level of abstraction. So I want to illustrate how skill sets vary according to one’s position along the engineering spectrum. The following abbreviations are used below: high abstraction (HA), moderate abstraction (MA), and low abstraction (LA).

Solution focus

HA: Primary focus is finding an optimal solution within a tightly controlled problem domain. Journal referees don’t want to read about yet another mediocre solution; they want to see mathematical, statistical, or experimental evidence that the proposed solution is in some manner better than previously discovered approaches. Only a single solution can be considered best.

MA: Central effort is placed in discovering a bounded solution. For instance, a bridge doesn’t have to be optimal in every respect, but it had better withstand the specified traffic loads. A bridge with too much strength is of far less concern than one with too little carrying capability. Any solution that meets the project constraints is potentially useable.

LA: Making sure that each component/batch/output is operating correctly often requires a rapid solution. If a manufacturing process is going out of tolerance, the first concern is getting product back within tolerance. Causes of the deviation can be examined later, or passed on for further study, but the key focus is on quickly finding a solution that works. For outputs of sufficient financial worth, almost any workable solution will be considered acceptable, at least on a temporary basis.

Solution domain

HA: Solutions are developed in the symbolic domain, where analytic tools of mathematics are most effective.

MA: Problems are solved in the spatial or schematic domains, where computer-aided-design (CAD) tools allow the consideration of multiple solution possibilities.

LA: Troubleshooting success is highly dependent upon prior exposure to similar problems, and thus the requisite skills are experiential in nature.

Social influence

HA: Symbolic solutions stand on their own, and require minimal social interaction to be presented and accepted.

MA: Gathering problem specifications, managing organizational expectations, and presenting solution proposals requires a moderate level of social interaction.

LA: Talents in motivating and managing others are quite valuable in bringing the right technical skills to bear on a problem, and in coordinating troubleshooting activities, especially in a high-pressure manufacturing environment.

Temporal effects

HA: Symbolic solutions do not care when a system is set into motion, as nature’s laws are assumed not to vary with the passage of time. Thus, problems of high abstraction accommodate everlasting solutions.

MA: Schematic solutions can remain valid over long periods of time. However, as types of components or methodologies change with time, moderate abstraction problems may need to be updated and improved.

LA: Corrective solutions may be specific to particular outputs, or a specific set of events acting on an output. Thus, actions associated with low abstraction problems are highly time dependent.

Summary

Individual engineers may have to move up and down the engineering spectrum over the course of a career, or a year, or even a single day. This post has attempted to point out that the skills needed to be a successful engineer necessarily vary with the abstraction level being utilized. In my next post, I’ll discuss why most engineering students are only exposed to high abstraction skills during their time in college.

Categories
Engineering Curriculum

Along the engineering spectrum

My prior series of posts (part 1, part 2, and part 3) proposed that a common characteristic of all engineering activity was the use of abstract models to search a solution space before implementing a new method, device, or system. Engineers fill the gap between science, which seeks to generate accurate models, and manufacturing, which aims to accurately replicate a given embodiment. Some engineers are more “hands-on” than others, so we have a spectrum of engineering activities that range from mostly abstract to mostly physical. It is this spectrum of engineering skills that I want to discuss. (Since the traditional engineering fields focus on the physical realm, I’m addressing that particular domain. However, the same spectrum issues will exist for engineers operating in alternate realms. See my prior posts for a discussion of engineering realms.)

There are many different kinds of engineers, but I’m going to constrain the conversation by dealing with just three types of engineering professionals: research, design, and production engineers.

High Abstraction

Research engineers operate at a high level of abstraction. This necessitates that they be part scientist, and part applied mathematician, as well as an engineer with knowledge of the physical world. When striving to create models that more accurately represent physical world behavior, they take on the role of scientist. In creating such models, they tend to look for general behaviors that apply to all systems, or sets of systems, rather than the idiosyncratic behavior of individual implementations.

Researcher engineers do not normally need to extend the bounds of mathematics (although some do), but must have very strong mathematical skills to create and manipulate abstract models of physical behavior. A researcher in chemical engineering might, for instance, develop a new means for causing to plastics to decay in a ecological manner. The primary focus would likely be on a model that explains the decay mechanism, rather than how the method might someday be introduced into production.

Moderate Abstraction

Design engineers bridge the gap between high and low levels of abstraction. While they are free to consider a broad range of implementation methods, they must eventually deliver a design that will produce a desired result. They use existing models to examine possible solutions, rather than launching new experimental studies.

Rather than seeking a theoretically optimal result, as the researcher might, the design engineer must settle for a practical compromise between competing interests. Experience plays heavily into knowing how much weight to give to each design constraint. A thorough knowledge of manufacturing methods is also crucial to the design engineer, as the end design must allow for robust performance, whether for a single prototype, or for a product that will be reproduced millions of times.

Low Abstraction

A production engineer worries about keeping the manufacturing line operating in a smooth fashion. There is no need to worry about the theory of how the end product operates, or what it is going to look like–those decisions have been made upstream by the research and design engineers. Instead, the production engineer is mostly a troubleshooter, waiting for a production snag to arise, then resolving the issue in a manner that keep the problem from reoccurring.

While the research and design engineers can worry about more global issues, the production engineer has to be concerned about individual elements. Specific batches, machines, and output units each give indications as to the state of the manufacturing process. Coordination of corrective efforts, mixed in with the natural stress of high-volume manufacturing, requires that the production engineer be a strong communicator.

Summary

Just as there are differences between the various realms of engineering, each engineering job requires its own level of abstraction. In my next post, I’ll write more about the skill sets needed along the engineering spectrum, and their impact on engineering education.