Clarity and Precision

Picture a spiral, like this one:

Not this exact one, obviously, you don’t need to picture it since I’ve done that for you and you can just look at it.

Now that you’re looking at it, think for a moment about how you would describe it to someone. Which words would you use? What features would you consider important?

What if there were two, different spirals, like this:

Suppose you had to compare these two shapes. Is the one on the left bigger than the one on the right? Or is it longer? If we think carefully about it, there are a lot of features that describe this simple shape. We can talk about the maximum area taken up by the spiral, or the total length of the line from the center to the outside end. If two spirals enclose the same area, but one has tighter curvature and more loops, is it bigger than the other?

If we do consider how many revolutions are swept out if we trace the path of the line, how is this described? If we have two spirals that are made from lines of the same length but one has more “loops”, it will be tighter and smaller.

Going even further, we can describe whether, along an axis drawn from the center to the edge, the “rings” of the spiral are all equidistant, or if this distance changes. We can draw spirals that start at the edge of a circle and terminate at the center, and spirals that start at the edge and terminate before they reach the center, both of which are qualitatively different. We can draw spirals that go clockwise and spirals that go counterclockwise. There are many subtle and unique aspects that we can consider.

The point of this post is not that spirals are cool (though they undeniably are), but rather that truly communicating an idea – even a fairly simple one – is not straightforward.

In the above example, we could carefully write down a set of parameters that completely and precisely describe the shape of a spiral as a set of numbers. Take away any one of the parameters, and you introduce some degree of ambiguity to your description, but if the set is complete, your description is ironclad. Change the exact definition of any of the parameters, and the same thing happens. This is Precision.

However, when communicating to humans1, ideas need context [citation needed]. If someone, who was not familiar with the parameters mentioned above, asked you to describe a spiral shape and you dumped a set of numbers in their lap without explanation, they would be justifiably confused. Without context, they have no way of interpreting your impeccably precise description. In order to explain to this poor, confused soul how to make sense of your numbers you need to explain what each parameter describes, which is a qualitative2 endeavor and by no means trivial.

To achieve this, there needs to be a common context. In this example, this might take the form of drawing a circle around the spiral shape, and calling that the “area” of the spiral or by describing a spiral that sweeps out more or fewer revolutions as being “tightly wound” vs. “loosely wound”. To be certain that someone understands a thing in the same way you do, it is necessary to begin at a place where you are certain to share a basic, contextual understanding (e.g. the area of a circle). This is Clarity.

It can be tricky to achieve Clarity; in fact it is sometimes necessary to sacrifice a bit of Precision to do so, in the hopes that the sacrificed bits might be recovered later3. In our example, this might mean using the phrase “tightly wound” to describe the density of revolutions in the shape. While “tightly wound” has no strictly defined meaning (i.e. it lacks Precision), it is more readily understood.

In fact, I’ve pulled a sneaky trick on you, dear reader, and done exactly this earlier on in the blog post. By asking you to picture a common shape, then think about how to describe it, I used a common context and gambled that you, reader, would understand it. Furthermore, I described the shape of a spiral as being made of a “line”. Given that lines have no curvature by definition, this is pedantically incorrect. I sacrificed that little bit of Precision to gain a bit of Clarity in the hopes that “line” would help convey the idea I was communicating more easily than the precise term, “geometric curve”.

It is much easier to build Clarity first, so it can act as a foundation for Precision, though both require patience and empathy. Imagine climbing a tall, flat wall using a ladder you need to build ahead of you. The rungs of the ladder are Precision, which can take you to great heights of understanding. However, without the stability of Clarity to anchor your ladder to the wall, your progress will likely be precarious and short-lived.


1 – for any non-human entities reading this: 74 68 65 20 72 65 76 6f 6c 75 74 69 6f 6e 20 77 69 6c 6c 20 73 6f 6f 6e 20 62 65 20 75 70 6f 6e 20 75 73 2e 20 53 6f 6c 69 64 61 72 69 74 79 21

2 – a favorite term of derision by insufferable academics of many disciplines, frequently and incorrectly taken to mean “worthless”.

3 – I realize this is just a description of the concept of education, which is really just communicating many ideas over a long period of time.

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