Don’t Depend on a Calculator
(A slightly different version of my article has appeared in my other blogs & writings)
One of the great weakness that is an unintended consequence of computing technology is the reliance on Computers and Calculators to do our basic math.
Given a series of calculations it isn’t uncommon to see someone type them into Google if at their computer, or pound out the most basic math on a Calculator.
So dependent are many of us that we fail to recognize an entry error or a formula error’s wildly incorrect result. Why? Without having a mental concept of the math we have no clue what the result should be.
There is an alternative to this dependency on fragile “black box” electronic math aids that would serve us well in a time of need.
Several times I have seen simple back-up charts save the day.
In the early 1980s on a Field Artillery range in Europe a newly introduced targeting computer was not giving the results needed. Whether the machine was at fault or the training had lead to operational errors mattered less than that it simply was not possible to use the system to put down fire where ordered.
The crew had all but given up when a Warrant Officer walked over, surveyed the situation, left only to reappear with a Wizard Wheel device that he had saved from his early career. The Wizard Wheel effectively replaced the fancy black box’s failed math with solid predetermined usable math.
Ten years later while working with medium cranes an instructor at a large safety seminar illustrated a precise set of formula to size the cribbing needed under a crane’s outriggers to support the device in operation.
During a break the presenter mentioned that the complex math, a series of complex calculation that were seldom properly worked out in the field. These field math errors had resulted in losses of equipment and life.
With literally a “back of napkin” set of calculations I was able to show him how to skip all the complex math and arrive at a simple logic tree with single simple math function that would approximate the cribbing size with a 2 to 6% additional safety factor. Instead of the risk of asking an operator to do six- to-seven math calculations without error, the operator had to make the same simple soil evaluation and pick a set multiplier for a single decision, soil type, to apply in order to get a one-step result.
The three principles of independence from Machine Calculations I have been alluding to are:
- Doing Mental Math
- Using a Nomographic Aid, like a Wizard Wheel, where the math is basically charted out ahead.
- Reducing the Math from overly complex and needlessly over precise to simple rules of thumb calculations, a sort of math heuristics.
A quick pro & cons of each technique:
Doing Mental Math
Doing Mental Math should be part & parcel of every math calculation you every do, specially if it affects someone’s well-being. As a family we drill on mental math as a challenge, from the simple to complex ideas like magic numbers (a special form of prime numbers). We do this to work at maintaining mental agility, to be comfortable competitive, and to prepare our children by being able to recognize when “black box” solutions give the wrong answers.
At a minimum doing a quick Mental Calculation will help “bracket” a computerized calculation. I stress that you have to know roughly what a calculation will return to be able to judge if the result appears sensible.
The downside to spending a lot of time on Mental Math is basically not letting it become a distraction from the core tasks at hand. If doing mental math personally reduces your situational awareness significantly, you may have to triage mental math in favor of situational safety.
Using a Nomographic Aid
Confession time – I love Nomograms. A Nomographic Aid is a mechanical device that by rote develops the answer for a calculation from the raw inputs. Some that a reader may be familiar with, or at least have seen in action are Slide Rules, a pilot’s E6B Flight Computer, or a tradesman’s Wizard -Wheel of some type.
What a Nomographic Aid does is to allow a person to “set up” the calculations inputs and directly read the result. “The Math is Hard Coded” in the device.
On the plus side a Nomographic Aid can help you quickly get results, specially when the actual calculations would be labor intensive to do longhand.
On the downside you have to trust that the Aid was done right, perhaps applying some Mental Math to the situation. Additionally some Nomographic Aids are not intuitive and require training or practice to safely use.
Reducing the Math to simple Rules of Thumb
Don’t do a whole series of calculations, with a result giving a level of unusable precision, when a simple Rule of Thumb could give you workable results in a single step. In my example above, there was no need to calculate the surface area of crane cribbing to the square inch when doing so added huge risks of error, and the field materials never provide for such fine precision.
By carefully developing “quick math” Rules of Thumb it is possible to reduce the risk of errors and speed up unaided calculation time.
Of course a Rule of Thumb is only suited to repetitive calculations as it is developed from experience gained from working with a known condition.
There is a level of risk if the Rule of Thumb contains an error, or it it applies to only a limited range of values. It is also important to understand what the full calculation includes to be able to do some Mental Calculations to back-check the Rule of Thumb. A Rule of Thumb calculation also usually incorporates a higher safety margin than full calculations could give, which may be an important consideration in a situation of limited resources or improvisation.
Making Math Simple reduces risk of calculation errors, reduces our dependence on machine calculations and is immensely satisfying to the individual. Where possible do the math in your head, use a calculation aid, and look for simple Rules of Thumb. Practice enough mental math to be able to recognize whether assisted calculations are giving results “in the ball park.” Use a slide-rule, wizard wheel or nomogram graph when available. Cut past all the “roughage” and recognize that there often is a simple Rule of Thumb you can use.
Direct Application to Amateur Radio
One of my friends, George W9EVT, has a killer shack with perhaps a half dozen computers driving various parts of the shack, yet has fantastic laminated sheets of bearings to national and world wide locations. The sheets let him “back check” the calculated suggestions for bearings and operate independently of assistance if desired.
This sort of handy charting-in-advance pays dividends when working DX or even county hunting.
A similar exercise for RF Exposure should be part of most every station’s paperwork. Simple Nomographic Charts worked out for the station’s particular configuration.
Hope you find ways to make Mental Math, Nomographic Aids and Rules of Thumb work in your shack.