Testing: From Aristotelian to Galilean, Part 1

Any discipline can focus along a spectrum of thinking. That’s no less true of testing, of course. The spectrum I want to introduce from history is that of moving from an Aristotelian to a Galilean way of thinking and “doing science” which, in many ways, is synonymous with “doing testing.”

I would argue that becoming, and being, a test specialist means understanding types of thinking. The path from Aristotle to Galileo actually takes you through a series of types of thinking: Aristotelian, Ptolemaic, Copernican, Keplerian, and finally Galilean. Technically I could extend this even further from Newtonian to Einsteinian but I’ll spare everyone that.

Testing Around Competing Models

There was a time where a geocentric view of the universe was the accepted way to look at things:

This was a view championed by Eudoxus, refined by Aristotle and even further refined by Ptolemy.

Essentially this was the idea that the Earth was the center of everything. This was a requirement for how everything must work and it was “tested” by reason: we see the Sun move and we don’t feel the Earth move.

And, if you think about it, that kind of reasoning is not entirely ridiculous. It’s essentially the idea of trusting what your senses, via observation, seem to be indicating to you.

Then along comes Nicholas Copernicus who, in 1543, published De revolutionibus orbium coelestium (“On the Revolutions of the Heavenly Spheres”). Copernicus told us that we might want to shift our thinking to a heliocentric view:

Copernicus wasn’t the first one to come up with this, incidentally, but he is the first one that people seemed to listen to or at least take seriously.

This was the idea that the Sun was at the center of everything and that the Earth and other planets moved around it. This was effectively a new requirement and, obviously, one that was incompatible with the previous.

This is all pretty well understood, historically speaking, but there’s a few critical points to this that sometimes gets overlooked.

  • Copernicus was not trying to explain how everything worked in any sense that we would now call “scientific.”
  • There was no actual “physics” that Copernicus was dealing with in his model.
  • Copernicus was not necessarily telling us how it all really worked.

All Copernicus wanted to do was use his heliocentric model to provide a way to calculate planetary positions via a geometrical system that reproduced the motion of the Sun and the planets. But this is pretty much exactly what the geocentric model was already doing, wasn’t it?

This is a position that testing, as it eventually became more established, found itself in: dealing with potentially conflicting requirements, often with competing notions of value.

So why did Copernicus bother with all this? Well, it turns out that putting the Sun at the center made the geometry a whole lot easier.

Thus that geometrical system was, in effect, Copernicus’ testing method. “Made geometry a whole lot easier” could be said to be a particular quality that was being tested for. The value of that quality was that this system could be used for practical things, like navigation and for the creation of calendars that stood a chance of putting holidays at the right time of the year.

So a key point there: a testing method — albeit a nascent testing method — was tied to reasoning about observations and the ultimate aim was to demonstrate value. Yet it’s worth noting that Copernicus’s viewpoint did seem to go against what we actually saw and felt. So this quality was one of viewpoint and rooted in value.

This was something testing had to struggle with early on: that what we saw and felt, and thus assumed, may not in fact be accurate. Thus our notions of quality could lead to disagreements between what people were valuing differently.

The Orbital Tug of Testing

You’ll likely note here that Copernicus, as was mentioned of Galileo in a previous post, challenged one philosophical bit of orthodoxy. Copernicus said the Earth could move while the orthodoxy said that this wasn’t the case.

Yet Copernicus also said that all the orbits in his new system had to be perfect circles. Why did he say that? Well, he inherited a way of thinking or a particular philosophy.

There was a core philosophical argument operative at the time which was that motion in a circle — constant and unending — was perfect, essentially being a shape and path worthy of a divine Creator.

Any other form of motion was, well, not so perfect. Any deviation from circular motion, and thus unvarying speed, was seen as a system that required fine-tuning. Fine-tuning was not seen as being in line with perfection. Keep in mind that this is another quality that some people put emphasis on thus fine-tuning was seen as a degradation of quality.

Here was another area that testing had to grow up in: the idea that anything less than “perfect” could not be the way the world actually worked. There was a “perfect” quality and we just had to find it.

Also worth noting here is that that Copernicus had an interesting lack of faith in one idea (Earth unmoving at the center) while maintaining another element of faith (orbits must be circles). Then, as now, we sometimes simply choose the bits of philosophy / orthodoxy we happen to agree with or that we find most easy to work with.

Thus were cognitive biases inherent in the basis of how science, and thus testing, formed. To overcome this required the eventual idea of evidence but that was also complicated by conflicting interpretations of evidence.

Quality Was … Tricky

The problem that people like Copernicus faced was that constructing a system of circles that precisely reproduced the paths of the planets was really not that easy.

Yet Copernicus, like others, was very much stuck on that idea that circles had to be the thing.

That idea came by way of Aristotelian natural philosophy, part of which was added to by the later Ptolemaic astronomical system.

Yet consider that we’re dealing with quite similar models here.

Similar models for sure and yet one was based on providing a certain quality (fidelity with navigation and calendrical uses) and another was based on providing another quality (fidelity with what we seem to actually experience).

Using Testing to Understand Ontogeny

Ontogeny, broadly speaking, is the way things change and how, and to what extent, they retain their identity as they do change. In this case, we can use testing as a way to frame how the ontogenic change in these ideas led to the varying notions of quality.

So let’s keep in mind the basic, or perhaps underlying, quality we’re talking about here: people wanted models that described the motions of the objects seen in the sky.

One of the core ideas of the geocentric models was that the celestial bodies are attached to multiple nested spheres, all rotating about different axes at different rates. This nested, concentric sphere approach is pretty much the one Aristotle touted, hence the inherited philosophy bit.

Even to general observation, the apparent motion of the stars across the sky isn’t all that complicated. As one of my images above shows, the stars appear to be fixed and at rest on some spherical surface that surrounds us. Those stars appear to rotate around the north-south axis once per day.

We can model this just like Aristotle, and eventually Ptolemy, did:

This is a geocentric model, remember, so the Earth is located right at the center. The little dot you see there is just used to make it easier to see when one complete rotation has occurred.

In this model, the Sun rotates around the north-south axis once per day, just like the stars do. In addition, however, the Sun gradually drifts from west to east, taking one year to go all the way around. Aristotle/Ptolemy had to account for that and they did so by using two spheres.

The outer red sphere (fixed stars) rotates once per day. The inner blue sphere (Sun) is attached to the red sphere. So you have to imagine that the blue sphere’s daily motion “picks up” the motion of the red sphere. In addition to this, the blue sphere turns slowly in the opposite direction, moving around a tilted axis, which the black lines in the above visual are meant to show.

In this picture, the Sun is the dot on the blue sphere. It might be hard to see; it’s a light blue dot. Note how, during each cycle of the red sphere — that is, each day — the Sun goes around the sky once, but comes back slightly shifted.

I want to stress here: as these images — these models — were being built up, you have to imagine that a form of testing was being built up with them. This was leading us to the scientific method.

So our model so far handles the fixed stars and the Sun. What about the planets?

Well, the apparent motion of the planets is more complicated than the Sun. The planets move across the sky with respect to the Sun at varying speeds. The planets even seem to “turn around” — undergo retrograde motion — at somewhat regular intervals.

Of course, we now know that this is caused by the fact that we are observing the planets from the Earth, which is itself moving. But Aristotle and Ptolemy didn’t have that insight. So, for them, this planetary motion was accounted for by giving the planets complicated combinations of motions of their own. You probably guessed it: yet more spheres were needed to explain the motion of the planets.

This is the mode that testing was in: simply add more spheres and see if things started to make sense. It was essentially a testing portfolio that relied on only one technique.

So, to model this, suppose that we have just two spheres, which rotate at the same rate, but do so around two different axes:

The outer green sphere is just turning at a steady rate. It carries the inner sphere around with it, while the inner sphere itself rotates in the opposite direction about its own axis, represented by the black lines.

Now suppose that a particular planet, say Venus, is located on the inner sphere at the location of the light blue dot. If you observed this planet from the Earth — located, remember, at the center of the spheres — you would see it wobble back and forth. That’s the motion you see in the image.

In fact, though, that’s not what the planets do!

They mostly move around one way — from west to east — but only occasionally turn around and go backwards. So how did Aristotle/Ptolemy deal with that? They found they could match the actual observation by nesting the above pair of spheres inside a third sphere, which slowly carries the other two around:

If you were to stand at the center of all these spheres and watch the light blue dot, you’d see it move in pretty much the way the planets actually do move: gradual drifts from west to east, punctuated by some periods of retrograde motion.

Pretty cool, huh? We can essentially see how an observational testing method led to a certain model.

Now I’ll make the outermost sphere invisible, to make it easier to see the inner ones.

Finally, I’ll make the second sphere invisible.

Here you can see the complicated motion of that inner sphere, caused by the combination of the motions of all three spheres.

See what we did? We figured out, by a form of testing, what that innermost sphere must be doing. We did that by adding bits to our model. Then we removed those bits but retained the thing we wanted to observe.

What we see here is a very, very early way that testing had to shift between the reductionist and the ecological viewpoints. This is something I talked about in my Testing is Like… post.

Testability Makes Its Appearance

These spheres rotating within spheres are beautiful and all but we have to wonder how much of this is actually real. Are we truly describing something real here or are we just theorizing about a possible way to conceptualize how something real works?

Make sure you see the distinction!

This is definitely what people began to wonder at a certain point. And this very much focuses on the idea of testability. How testable are the ideas we come up with? And how much does that testability allow us to match our concepts to real world observations?

This gets back into the idea of evidence that I mentioned earlier.

Keep in mind, the geocentric view matched observations very well yet was out of sync in other ways. Let’s also keep in mind that Copernicus was only really considering certain testing: that which allowed for navigation and calendrical concerns but not that which necessarily matched our perceived experience.

This gets back into the idea of shifting ideas of what quality actually matters in a given context.

As contexts became more complicated, there were more possible viewpoints of quality to consider and thus more evidence that could be gathered and interpreted.

Testing, as it was beginning to be formed, had to learn how to deal with more complexity as more and better information came to light. How testable something was thus became a shifting spectrum.

This seems like a good place to end this post. The second part will pick up on this idea of how testing, or at least test thinking, had to evolve as systems became more complicated and as competing views of quality had to be potentially be accommodated.


This article was written by Jeff Nyman

Anything I put here is an approximation of the truth. You're getting a particular view of myself ... and it's the view I'm choosing to present to you. If you've never met me before in person, please realize I'm not the same in person as I am in writing. That's because I can only put part of myself down into words. If you have met me before in person then I'd ask you to consider that the view you've formed that way and the view you come to by reading what I say here may, in fact, both be true. I'd advise that you not automatically discard either viewpoint when they conflict or accept either as truth when they agree.

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