Hunebedden (Dutch dolmens) in proportion

About orientation patterns with hunebedden (in European context)

Accounts

Statistical accounts

The study of orientation patterns with hunebedden touches a few specialities: the archeology, the geometry and the astronomy. This combination of disciplines is generally called astro-archeology. Because of some sweeping claims, which could be verified hardly, the astro-archeology became discredited a lot. Alexander Thom proved the existance of geometrical patterns in stone circles for example, but he linked them up with an implausible rigorous definition of the megalithic yard. Some authors report of alignments without spending a word on the possibility of chance. Often the restoration history is neglected, so that a statement is open for sharp criticism. A study in the field of astro-archeology may expect a certain degree of distrust therefore and should aim for the highest degree of meticulousness and transparency.

Within the astro-archeology two mainstreams exist in the approach of the orientations of Neolithic monuments. The first starts off with the inner structure of a site (e.g. the work of Thom) and the other tries to discover trends in large amounts of orientations (like Hoskin). Both approaches have their advantages and disadvantages. The first method offers the possibility of exact and verifiable statements about alignments and geometrical shapes, but gets easily wrecked by lack of the proof, that chance or trial-and-error can be excluded (Heggie [4.1]). The second method can rely on statiscal correctness, but isn’t able to come forth with more than indications of alignments on sun, moon or some stars. In addition, one should reckon with the fact, that it isn’t possible to find the axis of a dolmen closer then 2° or 3° most of the time (Hoskin [4.2]).

As said, outside of the astro-archeology scepticism is the rule. To separate wheat from the chaff Heggie formulates a few guidelines. First of all one should establish that an orientation or pattern can be intended to create an alignment or geometrical shape. He describes two demands [4.3]:
1. The alignment or shape should be feasible with the means of the time, the Neolithic Age.
2. There should exist properties of the site, which would be strange without the alignment or shape.
When both demands are satisfied, it should be made plausible, that the pattern was in use indeed and is not the result of chance or trial-and-error. Heggie comes up with two arguments for support:
3. The alignment or shape should be found in geographicle spread places [4.4].
4. Statistical support by means of a calculation of probability. (However, Heggie drops this argument from practical point of view towards the geometrical shapes) [4.5].

In addition to Heggie’s first point a fifth demand can be raised:
5. The accuracy of the geometrical pattern should stand in proportion to the technical possibilities of the time.
Heggie criticizes the exactness of Thom’s megalithic yard for example with this argument, but fails to mention it as a criterion.

The fact, that the statistical proof of geometrical patterns stumbles upon practical problems, should not be enough reason to leave it out of scope. There is another way to meet this demand as much as possible. Unlike direct astronomical alignments, with geometrical shapes it’s possible to put the goodness of fit in proportion to the minimal number of occurences in a domain.

Having a freedom of ± 1° (as used in this website) we need to work with a class width of 2°. In a geometrical shape it doesn’t mather which side of a line is directed to the measured azimut (e.g. 90° or 270°). Therefore as the domain we choose 0-180°. For a random placement on a beforehand determined orientation one gets a chance of P = 2/180 = 0,011. Drawing additional lines should be seen as a series of mutually inclusive events. With a pattern consisting of three lines, which has a predefined orientation, we get a chance of P = 0,011 × 0,011 × 0,011. With a random orientation the chance becomes P = 0,011 × 0,011. The next table shows the number of monuments needed with a sudden number of lines in order to expect a matching pattern (= 1/P).

The number of monuments in the Funnel Beaker area doesn't surpass the 700000 for sure. Therefore in this study the demand is put forward, that a pattern found in more then one megalithic building should exist of minimal three (when they have the same orientation) or four (with different orientations) lines in order to be accepted as a cultural expression.

Furthermore an important point is missing in the argumention of Heggie. In some way the structures should have been identifiable to the Neolithic ’user’ - being a deceased or any visitor. This argument changes the third demand of the geographical spread of locations. The geometric shape itself doesn’t need to be wide spread, when the mechanisms which make it identifiable already are. Therefore this demand is applied to what on this website are called the markings in stones and the orientation patterns. They form the guiding principle for discussing the geometric figures.

Finally it’s usefull to formulate a demand for the geometric figure as it is. Some authors (e.g. Seidenberg and van der Waerden) compared the earliest sources of mathematics with each other. Those sources consist of mainly ritual and land surveying problems, which should be solved using integral right angled triangles. A common origin is suspected and it is looked for in the preceeding times, the Neolithic Age [4.6]. This limits the geometrical mechanisms to be applied to the shapes. Patterns should be kept quite simple, because in the earliest sources they are derived from integral right angled triangles.

Measurement accounts

NB. The measurement phases between parenthesis refer to the page The instruments used.

How precise an orientation will be measured, depends on four aspects:

  • The maximum of exactness people in the Neolithic Age could gain.
  • The exactness that is needed to distinguish between the alignments.
  • The effect of thousands of years on the building materials.
  • The exactness of modern measurement instruments.
  • By simple means it’s possible to setup an alignment with an exactness of 0.1° towards the sun or moon a little above the horizon. One can use the shadow of any object. An alignment direct above the horizon is far less precise because the atmosphere fades away the lines. The rising and setting of celestial bodies is best measured by the means of two steady objects on some distance from each other. This counts for the orientation on stars as well. After some practise it’s possible to reach an exactness of about 0.5°.

    What kind of exactness people needed in the Neolithic Age? In the literature there are speculations about dolmens as a kind of signposts towards each other. For the navigation over small distances a few degrees more or less don’t matter. When pointing 3° in the wrong direction, still the goal of a journey over 100 km lies in a radius of 5 km and can be seen at the horizon. More obviously is the use of orientations in order to determine the time of the year. Then a small fault of 0.1° is too much for appointing the winter solstitium within a period of five days. With a fault of 0.5° this mounts up to 20 and with 1° to 30 days. Also people could have had ritual motives to setup an orientation. As far as such an orientation didn’t intend to point out the path of the soul or wasn’t meant to be a calendar for the deceased, we aren’t able to say much about it by lack of tradition.

    Furthermore the next remark of Schuldt deserves some attention: "Die technische Ausführung dieser Arbeiten in den verschiedenen Grabtypen ermöglichte die Feststellung, dass die Errichtung der Monumente unter Anleitung eines Spezialisten oder von Spezialistengruppen durchgeführt wurde." [4.7] On one hand we may expect the work of specialists, on the other hand the conscientious attitude of the manpower will have determined the result. In a time, that every now and then within an area of 50 km2 a few dolmens a year were erected, it will not have been specialists only who carried out the task. An orientation meant by a specialist can have been constructed less carefully by a figurehead. This we may not overlook.

    Suppose people were able to place a stone with its flat side on a line with a 0.1° preciseness, then still we wouldn’t get it nowadays. Weathering of it with 1 mm gives a fault of the same amount on a distance of 50 cm already. Merely over long distances (Thom presumes that people used the skyline) the desired exactness can be reached. On the other hand, this doesn’t count for orientation patterns. A tolerance of 1° in the calculation of probability above allows an corrosion of 8 mm on a distance of 50 cm. Therefore weathering does not endanger the tracking of patterns. When stones are replaced or setup right again, we should take bigger faults into account.

    While van Giffen complained about the lack of a suitable device for measuring the exact orientation, nowadays everyone is able to dermine an orientation with an accuracy of 1/3° using a sounding compass. In order to get the orientation of a flat surface on a stone, one should measure horziontally along that surface. Using a normal spirit level (measuring phase I and II - see the page The instruments used) or a self leveling sounding compass (measuring phase III) this is accomplished rather hard. Generally the side stones slope and the grounds in and around a chamber slants a little. With a normal slope the deviation (II in the figure beside) remains less then 1°, in spite of the fact that one holds the compass a little slant (I in the figure beside). With a rather big slope the deviation can be restrained by recurrent measuring and then taking the average.

    Since the usage of laser technology (measuring phase IV) the problems to restrain the deviation belong to the past. A horizontal cross-section of the chamber is obtained using an automatic laser level. Along the leveled line, distances and angles are measured and combined into a precise vector map. In principle the azimut deviation during calibration is restricted to the fault of the sounding compass (1/3°). In practice the calibration can be difficult due to the field conditions, so that the error for a measured point can run up over one centimeter. This means, that the deviation of the orientations in the map are kept under the 1° for distances longer then 1½ meter. As the width of a hunebed or dolmen generally amounts to 1½ meter or more and the orientation pattern always takes up the complete breadth, the measurement fault is not a threat for the search of patterns.

    In summary, because of the condition of the megalith buildings in combination with the measuring method, a maximum deviation of 1° is feasible for distances over 1½ meter. On the other hand, considering the possibilities of the Neolithic Age, an exactness of 0.5° should be prefered. We may ask ourselves, if Neolithic manpower always made enough effort for an optimal exactness. A tolerance of 1° seems to be a good equilibrium.

    The usage of ground plans

    In addition to the self-made ground plans, this website shows existing ground plans too. When they are excavation plans, we may assume sufficient preciseness. These plans are drawn via horizontal layers using a field grid. With field plans this is not the case. The grounds in and around a chamber varies in height, so there is a rather height chance on distortion. Field plans are employed only, when an existing pattern can be applied to it - never to find a new pattern.

    Finally, with the field plans as well as the excavation plans there is the problem of true north. Authors almost never mention the amount of magnetic declination they used. Running the risk of wrong conclusions, this website still assumes the correct determination of true norh on the plans.