Finding HMAS Sydney Chapter 5 - Kormoran Database & the Mathematics of Reliability


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Finding HMAS Sydney Chapter 5 - Kormoran Database & the Mathematics of Reliability

  1. 1. HMAS Sydney II: X turret. Note sighting ports open for gun layer. Copyright: Australian War Memorial. The Kormoran Database and The Mathematics of Reliability 5
  2. 2. <ul><li>What is the contents of the Kormoran Database? </li></ul><ul><li>The Database included the reports based on interrogations with survivors conducted between November 26th and December 10th 1941 </li></ul><ul><li>Eighteen reports referred to 26° S 111° E. Ten further reports referred to either 26° S or 111° E </li></ul><ul><li>Six reports referred to a distance from land, the values given being 60 nm (1), 120 nm (3) and 150 nm (2). 120 nm was the most frequent report </li></ul><ul><li>Two reports stated that one lifeboat sailed 150 - 153 nm NE from the point of disembarkation from Kormoran to the coast </li></ul><ul><li>One report stated that the battle occurred 160 nm SW of NW Cape. NW Cape and Cape Cuvier provide an obvious point of confusion, and Cape Cuvier was probably the target for all five lifeboats </li></ul><ul><li>Four reports referred to 130 nm SW of Shark Bay </li></ul><ul><li>Fourteen reports referred to 26°34’, 26° 32’, 26° 31’ or 26° 30’ S 111° E </li></ul><ul><li>Reports involving singletons and outliers were discarded. The geographical depictions in the Selection of Source Arguments includes constraints derived from other sources </li></ul>
  3. 3. HMAS Sydney II: X turret. Note sighting ports open for gun layer Why did the 1941 interviews and interrogations constitute the primary source? First, because they were reported in November and December 1941, months or possibly years prior to the preparation of the coded dictionaries, it is appropriate to assume that they were more reliable Second, as survival was critical following disembarkation from Kormoran , it may be assumed that critical information was distributed among the lifeboat crews, and not the ‘property’ of Detmers alone. Third, where key personnel are concerned, information about location and distance from the coast constituted ‘expert knowledge’ as distinct from ‘memory’ in the traditional sense Fourth, unless the reports associated with Detmers’ coded dictionary involve different dot patterns with the same information – and there is no suggestion that this is the case - it may be assumed that their reliability reflects only the dot copying skills of Detmers or Detmers’ secretary
  4. 4. <ul><li>Total number of reports ≈ 62 </li></ul><ul><li>Number of reports from people in position to know ≈ 48 </li></ul><ul><li>Number of unique reports ≈ 24 </li></ul><ul><li>Number of reports involving 26°South and / or 111°East ≈ 30 </li></ul>Concentration of reports involving 26° South 111° East [From Kirsner, Norman & Dunn, 2003] The table on the slide illustrates the extent to which the reports in the Kormoran Database were concentrated aound 26° South 111° East . With seventeen out of c 60 reports on the same location, and numerous other reports pointing to the same general area, the case for a search near the Abrolhos Islands was difficult to grasp.
  5. 5. The Mathematics of Reliability Clark Little: George Zipf  (1902 – 1950)
  6. 6. Zipf's Law Do the reports reflect one carefully rehearsed ‘story’, as many critics claimed, or do they reflect ignorance, as if no-one had any idea at all, or do they reflect expert knowledge, about location, accompanied by random error? Zipf's law states that given some corpus of natural language utterances (or memory reports), the frequency of any word is inversely proportional to its rank in the frequency table. The most frequent word will occur approximately twice as often as the second most frequent word, which occurs twice as often as the fourth most frequent word, etc. Similar relationships occur in many other rankings, including memory reports . In the memory case, it is assumed that the spread of the reports reflects random error. The rankings are consistent with the assumption that the database is reliable evidence. The pattern does not “prove” that the results are reliable.
  7. 7. The is the distribution shown in ‘The Kormoran Database’ turned on its side, so that it provides a platform for the following figure. The frequency distribution is consistent with the assumption that the Kormoran database consists of random errors around a single position [From Kirsner, Norman & Dunn, 2003, Finding Sydney Foundation , 2005]
  8. 8. Log Rank Log Frequency Use of Zipf’s Law to assess reliability? Grey circles are from a simulation based on Kormoran survivors’ reports The black triangles are the reports from The Kormoran Database in log-log coordinates Red triangles are reports from The “War of the ghosts’, a memory study by Bartlett (1932)
  9. 9. Conclusion The data conform to Zipf's law to the extent that the plot is linear (a straight line) in Log-Log coordinates. The functions shown in the previous figure are approximately linear, and the results are consistent with the assumption that the survivors were telling the truth, to ‘the best of their ability’ Further support for the validity of the reports is present in the fact that Bunjes, an anti-Nazi, provided three different types of information that produced approximately the same solution.