{22}
The ten simulations produced the results shown in Table8. These figures demonstrate the awesome power of chance alinement, though we must bear in mind that the scores are somewhat artificially boosted by two factors.
447 sites, maximum width 50m.
| Sim. | Number of sites in line | Total | ||||
|---|---|---|---|---|---|---|
| 7 | 8 | 9 | 10 | 11 | ||
| 1 | 91 | 13 | 0 | 0 | 0 | 104 |
| 2 | 77 | 10 | 1 | 0 | 0 | 88 |
| 3 | 94 | 7 | 1 | 0 | 0 | 102 |
| 4 | 82 | 18 | 1 | 0 | 0 | 101 |
| 5 | 123 | 12 | 3 | 0 | 0 | 138 |
| 6 | 66 | 11 | 0 | 0 | 0 | 77 |
| 7 | 76 | 16 | 5 | 0 | 0 | 97 |
| 8 | 150 | 27 | 5 | 7 | 1 | 190 |
| 9 | 82 | 7 | 0 | 0 | 0 | 89 |
| 10 | 100 | 8 | 2 | 0 | 0 | 110 |
(i) Point-sharing. With a large number of sites (447) and a relatively large ley width such as we have here (50 m) we can find that some of the alinements are not independent of each other, but share common subalinements. In the printout for Coldrum2 (Appendix 6b) for example, lines 1 and 6, both 8-pointers, share 7 of their sites; lines 8, 9 and 10, again all 8-pointers, share 6 sites. Examination of the printout for Coldrum2 will show similar examples among the many 7-pointers. What point-sharing means is simply illustrated by Fig.7a. By shifting the line slightly the points 1, 2 and 3 can be made to aline on either point 4 or point 5. That is, we have two 4-pointers which share 3 points.
{23} Very often it is only the computer’s exactitude that distinguishes two point-sharing lines, and often the situation is as in Fig.7b: the computer still sees 1–2–3–4 and 1–2–3–5 as distinct, but to the practical eye they merge to form a single 5-pointer of slightly greater ley width than the two 4-pointers.
Point-sharing appears to be more common in a clustered site-distribution than in a uniform distribution. We ran 10 simulations with 447 sites uniformly distributed over the whole map (see Manual), and point-sharing was much less marked there than in the simulations which preserved the clustered distribution of Sheet 188.
(ii) Close sites. With so many sites on the map, and especially within site clusters, it occasionally happens in simulation that two sites turn out, after random nudging, to have their centres closer than the allowable ley width of 50m. This would be equivalent to allowing the 1mm disks that represent the sites to overlap. This is an artificial situation, and frankly we should have ensured that it didn’t happen at all. But we didn’t, so we must mention its effect, which is a tendency to boost the number of good alinements. If one member of a pair of close sites happens to fall on a good line, the chances are in favour of the other one doing so too, and if this happens in a point-sharing situation as well, then the statistics can go a bit haywire, as in fact they do in Simulation8. Simulation8 is so atypical that when compiling the summary above we played down its influence: the average of “about 10” 8-pointers per simulation is based on simulations 1 to 7 plus 9 and 10, and we made no mention of Simulation8’s seven 10-pointers and one 11-pointer, the details of which we give in Table9.
| Length (m) | Space (m) | Width (m) | Sites |
|---|---|---|---|
| 43328 | 154 | 46 | 3– 30– 42–283–284–296–333–355–356–445 |
| 28282 | 36 | 49 | 27– 45– 48– 49– 82–102–297–313–330–335 |
| 28282 | 36 | 42 | 27– 45– 48– 49– 82–102–313–330–331–335 |
| 38101 | 36 | 48 | 45– 47– 48– 49– 82–102–297–313–332–422 |
| 25884 | 36 | 48 | 45– 47– 48– 49– 82–102–313–330–331–335 |
| 21480 | 129 | 44 | 93– 94–204–283–284–296–331–334–336–355 |
| 21480 | 129 | 48 | 93– 94–204–283–284–296–331–333–334–355 |
| 38101 | 36 | 49 | 45– 47– 48– 49– 82–102–297–313–330–335–422 |
The effects of point-sharing and close sites are plain enough. Note the last two 10-pointers listed. They are close to forming an 11-pointer after the manner of Fig. 7b: a chance alinement worthy of mention, since no two sites are less than 129m apart, a figure well above the ley width. In fact this line probably should have been mentioned in the summary above.
In Coldrum2 (Fig. 3) there is only one pair of close {24} sites (numbers 166 and 167), which feature in line 7. They do not cause any statistical havoc, however! The two 7-pointers shorter than the Coldrum line, plus the six other 7-pointers longer than Coldrum but under 10km in length, were as shown in Table 10. Note that one of the 7-pointers shorter than Coldrum (simulation5) involves a pair of sites 31m apart, and shares 6 points with another short 7-pointer. The two 7-pointers in Simulation8 likewise share 5 points.
447 sites, maximum width 50m, maximum length 10km.
| Sim. | Length (m) | Space (m) | Width (m) | Sites |
|---|---|---|---|---|
| 2 | 8067 | 409 | 38 | 48–50–75–119–142–143–146 |
| 3 | 9799 | 294 | 40 | 37–38–107–147–149–151–176 |
| 5 | 5005 | 31 | 35 | 107–120–148–149–152–178–179 |
| 5 | 8635 | 31 | 33 | 120–148–149–152–178–179–216 |
| 7 | 9277 | 182 | 43 | 244–245–255–315–331–337–355 |
| 8 | 9913 | 75 | 42 | 235–314–316–330–332–335–354 |
| 8 | 8891 | 75 | 49 | 234–254–314–316–330–332–335 |
| 9 | 9084 | 803 | 45 | 61–76–106–120–148–178–189 |
