October 23, 1997

The art of guesstimating

Jack Ganssle

When we get burned by a hot resistor or when we've had a tantalum capacitor installed backward explode in our face, we develop our own rules of thumb that give us a new understanding of electronics.

Our need to compute, to routinely deal with numbers, led to the invention of dozens of clever tools, from the abacus to logarithm tables to the slide rule. All worked in concert with the user's brain in an iterative, back-and-forth process that only slowly produced answers.

Now, even grade-school children routinely use graphing calculators. The device assumes the entire job of computation and sometimes even data analysis. What a marvel of engineering!

Those of us who spend our working lives parked in front of a computer have even more powerful computational tools. The spreadsheet is a multidimensional version of the hand calculator, manipulating thousands of formulas and numbers with one keystroke. Microsoft Excel is one of my favorite engineering tools. It lets me model weird systems without writing a line of code and tune the model almost graphically. Computational tools have evolved to the point where we no longer struggle with numbers; instead, we ask complex what-if questions.

Network computing lets us share data. We pass spreadsheets and documents among co-workers with reckless abandon. In my experience, widely shared big spreadsheets are usually incorrect. Someone injects a row or column, forgetting to adjust a summation or other formula. The data at the end is so complex, based on so many intermediate steps, that it's hard to see if the data's right or wrong, so we assume that it's right. This is the dark side of a spreadsheet: No other tool can make so many incorrect calculations as fast.

Mechanical engineers now use finite-element analysis to predict the behavior of complex structures under various stresses. The computer models a spacecraft vibrating as it is boosted into orbit, giving the designers insight into its strength without running expensive tests on shakers. Yet, finite-element analysis is so complex, with millions of interrelated calculations. How do engineers convince themselves that a subtle error isn't lurking in the model? Like subtle errors hidden in large spreadsheets, the complexity of the calculations removes the element of "feel." Is that complex carbon-fiber structure strong enough when excited at 20 Hz? Only the computer knows for sure.

The modern history of engineering is one of increasing abstraction from the problem at hand. The C language insulates us from the tedium of assembly, which removes us from machine code. Digital ICs protect us from the real analog behavior of each of the millions of transistors encapsulated in the chip. When we embed an operating system into a product, we're given a wealth of services we can use without really understanding the how and why of their operation.

Increasing abstraction is both inevitable and necessary. An example is the move to object-oriented programming and, more important, software reuse, which will someday lead to software ICs whose operation is as mysterious as today's giant LSI devices yet that elegantly and cheaply solve some problem.

But, abstraction comes at a price. In too many cases, we're losing the feel of the problem. Engineering has always been about building things. Building, touching, and experiencing failure are the tactile lessons that burn themselves into the wiring of our brains. When we delve into how and why things work, when we get burned by a hot resistor, when we've had a tantalum capacitor installed backward explode in our face, or when a CMOS device fails from excessive undershoot on an input, we develop our own rules of thumb that give us a new understanding of electronics. Book learning tells us what we need to know; handling components and circuits builds a powerful subconscious knowledge of electronics.

A friend who earns his keep as a consultant sometimes has to admit that a proposed solution looks good on paper but just doesn't feel right. Somehow, we synthesize our experience into an emotional reaction as powerful and immediate as any other feeling. I've learned to trust that initial impression and to use that bit of nausea as a warning that something is not quite right. The ground plane on that pc board just doesn't look heavy enough. The capacitors seem a long way from the chips. That sure seems like a long cable for those fast signals. Gee, there's a lot of ringing on that node.

The flip side of a feel for a problem is an ability to combine that feeling with basic arithmetic skills to quickly guesstimate a first approximation into a solution.

The art of guesstimating was once we engineers' most basic tool. Old engineers love to point to the demise of the slide rule as the culprit. "Kids these days," we grumble. Slide rules forced us to estimate the solution to every problem. The slide rule also forced us to have an easy familiarity with numbers and with making coarse but rapid mental calculations.

We forget, though, just how hard we had to work to get anything done. Nothing beats modern technology for number crunching, and I'd never go back. Remember that the slide rule forced us to estimate all answers; the calculator merely allows us to accept any answer as gospel without doing a quick mental check.

Complexity

We're building astonishing new products, the simplest of which have hundreds of functions requiring millions of transistors. Without our amazing tools and components--those things that abstract us from the worries of biasing each individual transistor--we'd never be able to get our work done. Though the abstraction distances us from how things work, it enables us to make things work in new and wondrous ways.

The art of guesstimating fails when we can't or don't understand the system. Perhaps in the future we'll need computer-aided guesstimating tools, programs that are better than feeble humans at understanding vast interlocked systems. Perhaps that will be a good thing. Maybe, like double-entry bookkeeping, a computerized guesstimater will at least allow a cross-check of our designs.

When I was a nerdy kid in the '60s, various mentors steered me to vacuum tubes long before I ever understood semiconductors. A tube is wonderfully easy to understand. Sometimes, you can see the blue glow of electrons splashing off the plate onto the glass. The warm glow of the filaments and the visible mesh of the control grids always conjured a crystal-clear mental image of what was going on.

A 100,000-gate ASIC is neither warm nor clear. There's no emotional link between its operation and your understanding of it. It's a platonic relationship at best.

So, what's an embedded engineer to do? How can we re-establish this feel for our creations, this gut-level understanding of what works and what doesn't?

The first part of learning to guesstimate is to gain an intimate understanding of how things work. We should encourage kids to play with technology and science--help them get their hands greasy. It matters little if they work on cars, on electronics, or in the sciences. Nurture that odd human attribute that couples doing with learning.

The demise of Heathkit's kit business removed one of the most visible of the electronics playgrounds, but others still exist. Check out Nuts & Volts Magazine (1-800-783-4624), which is an amazing compendium of ads for parts, kits, and, unfortunately, what is probably illicit telephone-modification gear. It is fascinating and just like a virtual junk box.

The second part of guesstimation is a quick familiarity with math. Question engineers (and your kids) deeply about things. "Where did that number come from?" "Do you believe it and why?"

Work on your engineer's understanding of orders of magnitude. It's astonishing how hard some people work to convert frequency to period, yet that is the most common calculation we do in computer design. If you know that a microsecond is a megahertz and a millisecond is 1000 Hz, you'll never spend more than a second getting a first-approximation conversion.

The third ingredient of guesstimation is to constantly question everything. As one bumper sticker says, "Question authority." As soon as the local expert backs up his opinion with numbers, run a quick mental check. He's probably wrong.

| EDN Access | Feedback | Table of Contents |