In Acton Conservation Land there is a collection of rock stacks covering approximately an acre of flat ground, and lying above a natural spring. The stacks are well built and appear to be aligned in a grid pattern. For some time I have been trying to draw a correct plan of this site to see if the apparent alignments are real, and have been considering how to calculate the probability of an alignment, in order to see whether this arrangement is non-random. Click on the following to see the final version of the site plan.

In this article I will describe the site, explain how the plan was drawn, and apply a formula from probability theory to calculate the likelihood that this arrangement is random. It turns out that the site is non-random, and so it is probably deliberately constructed. Since such a site cannot be put into the context of colonial New England history, it follows that the site may be pre-historic.

Description of the Site
This site is in the eastern part of the Nashoba Brook watershed in Acton Massachusetts. To the northwest lies the Nashoba Praying Indian Village in Littleton; to the east lies the Great Brook Farm in Carlisle; to the southeast lies the Estabrook Woods in Concord. The general area contains many lithic structures, hidden in the woods. Two or so miles to the north lies the "Potato Cave", an underground stone chamber whose "light box" and winter solstice alignments were described in a talk by Mark Stromeyer at the 1997 NEARA meeting in Falmouth Mass. In Carlisle a stone turtle, also found by Stromeyer, is recognized by the Native Americans as part of a summer solstice view. Stromeyer, as well as Jim Mavor and Byron Dix, were the first people to explore these woods with an eye for pre-historic stonework and what they call "sacred landscape".

You get to the site of the rock stacks by walking up a trail in the Acton Conservation Land. To the left is a natural spring and to the right is a small triangular standing stone. As you come to the top of a short rise, to the right, roughly thirty rock stacks sit in the woods, framed by a corner of a stone wall. Later, where the trail passes through the stone wall, the ends of the wall are squared-off, rather than broken down, which shows that the trail was there before the wall was built. One suspects this trail is part of an old north-south trail.

There are several subtle features of the site that should be noticed. Just as the trail passes the spring on the left, there is a small arrangement of three rocks leaning against each other. Lying next to the trail, this arrangement marks the place where you need to leave the trail to go down to the spring. At this point, on the right of the trail is a U-shaped enclosure perhaps eight feet across, open to the trail and facing west, and made of small rocks poking up through the dead leaves. There are two other "U" shaped enclosures like this. The next is on the left of the trail, slightly larger, facing east; and the next is immediately after the break where the trail passes through the wall. This last enclosure is to the right of the trail and faces westward. These enclosures open directly on the trail. [The second two enclosures are illustrated in the figure above.] Where the trail passes through the stone wall the trail forks and in the bit of woods between the two forks, about twenty feet from the wall, there is a small corn grinding stone covered with leaves and pine needles. It is a slightly hollowed rock, the characteristic shape for a corn grinding stone. Finally, it is worth looking at the back of the large stones in the wall near the opening. They appear to have been dressed to provide a flat vertical surface. One rock has uneven vertical channels, or flutes, that raise the question of what tool was used to dress the stone.

Walking north on the trail, before coming to the break in the stone wall, one sees several rock stacks to the right, or east, of the trail. A single stack lies to the left of the trail and it is a fine example. It is well built, from approximately 15 rocks of a uniform size, in the range 1.5 - 2 feet across. One side of the stack is nearly vertical and the other slopes down towards the ground. From above, the rock stack is tear shaped with the point at the lower end, which in this case is the northern end of the stack. Several other stacks in the array have a similar structure. They are built on a support boulder, with one vertical side higher than the others, and with a teardrop shape. It is not clear if this structure is part of the original design, or whether the piles have been damaged. Others are flat on top and more circular in outline, others are little more than a bumps in the soil with a few rocks poking through. For the most part, the stacks are of the same general size, made from rocks of the same general size. Linda McElroy pointed out that many of the piles have this single steep side. Some of them look something like this:

How the Plan was Drawn
When I first explored this site I saw several alignments of three or more stacks and came away with a strong impression that they were arranged in a grid. Going back with tape measure and compass, I tried to make measurements and a sketch. I found myself confused by variable compass readings, by the difficulty in attaching one end of the tape measure while leading out the other and, most of all, by not being able to keep track of which stack I was standing at. They look so much alike that you quickly loose track. Clearly this was not how to survey the site and my first effort was a failure. When I got home I could not reconcile the measurements into a coherent diagram.

I tried again with no tape measure or compass. This time I walked over the site for about three quarters of an hour, gettting the overall plan in my head, before trying to do a sketch. Again I got confused and started making mistakes about which pile I was plotting; but when I got home I created a reasonable plan - that at least illustrated what I thought was a grid. The result was, of course, a fantasy.

Finally I was lucky in that I mentioned my "surveying" problem to Lisa Grashow, a fellow NEARA member, and she offered to bring down a surveyor's transit and do the job right. On a clear Saturday afternoon in January, Lisa came with Ann Banks and Bob Morton, and in less than two hours made measurements of position and distance of all the rock stack from one central surveying point. Lisa worked the transit from this central point while Bob held the surveyor's rod. Ann and I tried to be helpful. The problem of seeing stacks from a distance is simplified when someone stands at the far stack holding a highly visible surveyor's rod. A couple of weeks later, Lisa sent me a very nicely drawn map of the site, which finally showed the overall plan in its correct proportions.

Unfortunately when I got a copy of the plan I did not see the alignments that I expected. I was sure that there were some alignments that did not appear on the plan. So I went back out to check it one more time. When we did the survey, Lisa wanted to get accurate elevations. This required placing the bottom end of the surveyor's rod on the ground rather than on top of the individual rock stacks. So we had to stand on the far side of the stack from Lisa's point of view, and hold the rod so it was centered on the stack from that view. The result was an error on the order of the stack's radius. When I went back out again, I was able to use the plan and check it against the actual array, and was able to keep track of which stack was which, and was able to confirm several of the alignments that I had suspected, but that were not shown in the survey. The above plan is derived from the survey by correcting a total of nine stacks by an amount on the order of the stack radius. In particular, I did this only where I had confirmed an alignment by eye. In one case I deleted an alignment that appeared in the survey, in another I deleted a pile that was shown in the survey but that I could not locate. Also I added one pile that had been missed. The result is accurate to the best of my ability, and it does show a surprising number of confirmed alignments.

The arrangement is not so much a grid as a collection of superposed families of parallel lines. Since several stacks sit on lines in more than one family, this gives the impression of a grid. I cannot be sure that the lines are parallel, and cannot be sure about their relation to the alignment of the adjacent stone wall. In the plan above, alignments drawn with solid black lines are confirmed. This means I stood at one end of the line and could see three of more stacks in a direct line. Sometimes I was able to move along the line to another of the stacks and see still further stacks from there - allowing the confirmed alignment to extend beyond three stacks. Alignments drawn with a dashed line are suggested by the plan, but could not be comnfirmed by a direct line of sight. If the observation is correct that several of the alignments are parallel, then it is worth asking: what equipment would be needed to construct such parallels?

Without confirmation, I observe that there are basically two families of parallel lines. One family of lines are all directed along magnetic north-south. The others are (at least roughly) parallel to the stone wall that lies on the left side of the figure. This suggests that these two directions are important. It is not surprising that north-south is considered an important direction, but why was the direction parallel to the stone wall interesting? There is a possible third family of lines, less clearly parallel, with lines lying in directions near to the direction of the other wall, at the top of the figure. The reader may find it interesting to look at the plan again to see if there are any other alignments that are suggested.

Calculating the Probability of an Alignment
How likely is it that three objects, placed at random, are aligned in a given direction? The reader will forgive me if I spend a moment deriving a formula for this. The answer comes from the field of geometric probability and there are several versions which might apply.

Consider the simplest: with objects of radius r, lying in a rectangular area of width L; and suppose that we wish to know the probability that three objects line up vertically. We project the positions of the objects vertically and several are "aligned" in the vertical direction when the projections overlap enough - say when the centers are less than r/2 apart. This is illustrated with the projections of the objects represented as black dots on the lower edge of the rectangle in the figure. In this figure, two white dots that project onto slightly overlapped black dots probably would not be seen as an alignment in the vertical direction.

Now, if you have M objects, there are [M*(M-1)*(M-2)] / [3*2*1] triples. For randomly placed objects, you expect the same fraction of these to be aligned in the vertical direction as is represented by the ratio (r/L)².

Let us apply this to our rock stack array using actual numbers. To start off, the "rectangluar region" is well enough approximated by the area inside the corner of the stone wall. I estimate that the horizontal distance of this area is about 380 feet. So L = 380. I estimate that the average radius of one of the stacks is 2.5 feet. So the probability of three aligned rock stacks (where alignment is defined up to one half a radius) is

Rather than applying this to the vertical direction, apply it to the direction parallel to the wall on the left of the figure. So this is the probability that three stacks will be aligned in the direction parallel to the stone wall.

I estimate that there are 29 stacks (or large rocks) in the figure, so how many triples are there? The answer is

How many alignments should we expect? The answer is N alignements are expected when N satisfies

Multiplying both sides by 3654 gives N = 0.159. So in this situation we do not expect even a single alignment (0.159 is less than 1). But take for example just a single confirmed alignment - say the leftmost one parallel to the stone wall on the left of the figure above. There are five stacks (or large rocks) along just this one line. This makes for 10 different three-fold alignments. This alone is more than an order of magnitude greater than the 0.159 expected from a random collection. This is without even taking into account other alignments that appear to be in the same direction. We can arrive at the conclusion a different way, using the probability of five simultaneously aligned objects, with probability (2.5/380)⁴. This is something like 0.0000000019 and again, this means the occurance is not likely to happen at random. Most of these probabilities could be estimated more conservatively, but the conclusion is the same.

We do not need mathematics to tell us that there is no way that five aligned objects out of thirty could be random. But it is worth satisfying ourselves about this point. For reference, the expected number of n-fold alignments in a fixed direction out of a collection of M objects of radius r, in an area of width L (perpendicular to the fixed direction) is:

N =   (r/L)^n-1 *  {  M*(M-1)*(M-2)*...(M-(n-1))   /   n*(n-1)*(n-2)*...(3)*(2)*(1) }
 

Conclusion
So this array of rock stacks in Acton is not random. There are many other ways to show the same fact. For example, the spacing between the stacks is close to uniform, and this cannot happen at random either. It follows that the array is a deliberate construction. It follows that these alignments (and spacings) meant something to the person who built the stacks. There is no record of colonial farmers making constructions of this sort. Making a construction like this for field clearing is out of the question. There is not enough room to turn a plow between these stacks, the stacks fill the field, they are too well built, and they are made from uniformly sized rocks - not random glacial till. So there is no basis for assigning this construction to colonial farmers. nor to anyone since that time. The construction would have required rather careful surveying and a substantial amount of work.

On the other hand, there are many examples of structures like this in pre-historic contexts. For example: Malcolm Pearson's site report in 1959 to the Early Sites Research Society entitled "Stone Mound Site, Sutton Massachsetts"; or [more grandly] the famous fan of megaliths at Grand Menec in Brittany - which Alexandre Thom calls :"megalithic graph paper"; or "The Stone Alignments of Southern Hyderabad" by F.R. Allchin; in Man, 56:133-136, 1956., or many others which are compiled in the "Ancient Man: A Handbook of Puzzling Artifacts" by William R. Corliss as part of the Sourcebook Project. What these examples show is that pre-historic alignments, designed and built into the landscape, are found in many parts of the world.

Given the deliberate structure of the array of rock stacks, and given  the several other features, such as the corn grinding stone, the marking of the spring, the enclosures opening onto the trail; given these things it seems likely that this rock stack array is pre-historic. Although Acton has been highly developed in recent times, some pre-historic traces may have been preserved.