Once you get to know what something looks like you can see design intent where people, who are not used to looking at that sort of thing, might just see a random object. Sometimes the difference between intentional design and randomness is so dramatic, so extreme, that you think: "not being able to see this is absurd!".
For example, here is one of my favorite rock pile pictures (from JimP's article "The Queen's Cairns" [see here for the article and some other fine examples of rock piles])
And here, by contrast, is what I believe is a field clearing pile:
How could anyone maintain that these are the same sort of phenomenon as the Queen's Cairns above? Further, why would you ever want to argue with somebody about it? To exaggerate and emphasize this idea: it would be like trying to argue with someone who was convinced that the Cathedral of Notre Dame in Paris just happens to be a large peculiar cliff and rock formation that happens to spring, conveniently, from the Island of the City in the middle of the Seine river.
It seems absurd to talk about but, unfortunately, the subject of archeology is routinely providing examples of man-made objects that shade off from the obviously man-made into the barely recognizable - even for the expert. Most would not questions that a well-made arrowhead is the work of man (although I have shown some perfect arrowheads to people from -say- Mumbai, India, who ask: how do I know that is not just a rock?) but, for example, when a gentleman named Boucher de Perche first found primitive flint tools [see here] along the banks of another french river, he was ridiculed by people thinking he was just making up stories about rocks.
An intuitive judgement depends on the person's level of experience. Plainly put: if you have not encountered something before, you might think it is random because you do not know how to recognize the elements of design, or the elements of manufacture that are a clue to an item being man-made. Sometimes I want to make this point with some examples: a broken shredded piece of tree branch I pick up off the ground versus the whittled point of a stick. Most of us used jack-knives when we were kids and made pointed sticks; so we recognize them - there is no confusing between the smooth knife cuts versus shredded ends of a naturally broken stick.
But you do not want to have to rely on intuition, especially when communicating to people who do not have the needed background. So you wonder: how can you prove there is design intent and signs of manufacture? How can you demonstrate design? Usually the question does not come up; no one questions that Notre Dame is man-made and proving it doesn't seem necessary. Similarly with beautifully crafted arrowheads: No one thinks about proving they are man made. Some academic archeologists (and I can tell you that Steven Williams of the Peabody museum at Harvard is a perfect arm-chair example, because we had this conversation) are so used to seeing the beautiful items of the past, the fancy Wyoming arrowheads and freshly dug up ceremonial items, that they also have little experience recognizing the non-obvious; and certainly never pose the question: How is design recognized, outside of a reliance on intuition?
I spent years looking at rocks under foot in the fields of Concord. I thought I was finding stone tools at least a year before I found something that was obviously an arrowhead. I filled drawers and closets with old stone tools [I believe] and only stopped collecting them when I learned where to find the good stuff. Also I realized no one was interested in those junky old tools. But before I moved on to being an amateur archeologist and arrowhead collector, I did spend a good deal of time showing people those old things and trying to explain the, to me, clear signs of manufacture and design that were present. Poor George Carter had a much worse time of it [see here].
After moving on from old stone tools, I found a different subject matter with the same problems: rock piles. Almost no one has any experience comparing the structured intent of a well made rock pile and the loose scatter of a edge-of-field rock pile dump. Just to make the intuitive point again, take a quick look again at these magnificent rock piles from Norman Muller [click here]. Also a destroyed, smeared-out rock pile is not too different from field clearing pile and, sure, there are some tough cases that may be too far gone to have any visible design.
In any case, the question of demonstrating design remains. Is there a way to quantify the amount of design? Any way to measure the amount of design? Any way to make the point without relying on the experience level of the listener? I had a few thought about this. For example here is an old stone tool (something like a spoke-shave) from Silicon Valley.
The lower edge is worked. Not only are the removed flakes concave - indicating percussive force, but also there are about 8 removed flakes, done in a sequence of decreasing size across a very small portion of the lower edge. You could get into a discussion of the impossibility of random forces producing such an object but there is something much more quantitative here to use in discussion: you can count and size the removed flakes, compare their number and location to the overall perimeter dimension of the rock, and you can start defining a kind of "entropy" number to reflect the degree of non-randomness of these attributes you have selected for measurement. I thought, for sure, someone must have already discussed this sort of thing and went looking online to see what I could find. Maybe I did not get all there was to get, using Google, but the only place I saw a discussion of similar topics was in the original papers on "Intelligent Design" - way back before the religious politicians disgraced that discussion. I do not want to alienate any readers with a discussion of life forms or mechanisms for how changes to the forms occur through time. But I do want to mention that the topic of quantifying non-randomness does have a genuine history. I am just not enough of a scholar to know a lot about it. For example, there were efforts made to quantify the degree of bi-lateral symmetry of an object. I think it was Weyl? [Update: yes it was].
I have, however, worked professionally on software that was intended to perform pattern recognition. A sad truth learned from that effort is that effective pattern recognition was only possible when the pattern was previously defined. You could not expect a piece of software to discover new kinds of patterns. Take the notion of a straight line. That can be defined and you can write software to detect sequences of dots that line up in a straight line and even a curve (for fun, mention that when semiconductor wafer defects show up in a line this means the wafer was scratched, permitting diagnostic support for manufacturing). In our subject of New England stone work, we see stones in a line, and accept that these are man-made, a stone wall, built for one of several well-known (and also not so well known) reasons.
If you wanted to, you could quantify "linearity" of a stone wall [I tried here]. If there was doubt, you could haul out this measurement and settle a question or, at least, have something objective to fall back on during a discussion. If you wanted to, you could do something similar for rock piles. And what kinds of "patterns" would we need to have in advance, like "linearity"? I am not going get to that in this discussion here.
In general there is a question: where do the designs come from? I am not going to discuss that philosophically but there are certain concepts of quantifying existing patterns that I do want to mention. One kind of pattern, like the flake sequence in the stone tool above, is inherently non-random. There is a reasonable proceedure for measuring (counting, sizing, locating) the flakes and a reasonable quantification of the overall randomness of the item. This approach uses the statistical likelihood of such things - in themselves. Another kind of pattern comes about by comparing an item to other similar items found in proximity. The pattern comes from noticing traits in common. Once identified, the traits can be detected on a number of proximate items (like the different rock piles in Jim P's photo above). Once a collection of traits is determined, that can be used to quantify whether or not a new item has those same traits. That is a different way of quantifying design. Besides that, for multiple rock piles, the site itself is non-random in a measureable way that can be used to compare different collections of rock piles.
I always wanted to show this example. I found these two within a few feet of each other in a pile of rubble at the Concord Waste Water Treatement Facility.
The right hand one has some slightly more evident man-made flakes in it. But it is the striking parallel between these two item, and the fact that they were found so close together, that convinces me that this is design. It must be possible to quantify this (for example using chi-squared on the flake positions).
This last example brings up a final point: Not all the flakes match between these two rocks. If they were used as tools, their function did not require them to be identical and what the variations are gives a clue as to the function. Similarly, the rock piles at a site that seem structured are still not identical with each other - they might vary in height or in the number of rocks, or etc. In that context, the "pattern" that is to be quantified needs to leave out those attributes that vary and, at the same time, address the question of the proposed function of the objects. In this superficial overview, lets leave it at that: you have to come up with the pattern that you wish to demonstrate and you need to identify which elements of an object are included and which are expluded in a way that is consistent with a proposed function.