The hexagonal wheel

 

 

        In the Medieval Age, there was once an attempt by the priests, who were among the powerful ruling classes, to designate the round figure 3 as the gospel value for the newly invented term π.  The idea was to settle the seemingly endless argument of what the value of π should be.  Luckily, this attempt had never been materialized otherwise the craftsmen would have to take instruction from the Church and made all wheels hexagonal.

 

2.      The above story is not made up by me but was read from a book written by the famous scientific novelist, Issac Asmov.  While I would not bother to verify the truth of this story, I found it amusing and quite educational.  If you think that the Medieval priests inclined to be dictatorate and could not imagine that the craftsmen would follow rigidly the figure 3 as gospel, I can show you that similar mentality did prevail even today and in Hong Kong.

 

3.      By this, I am referring to the land matters in the New Territories that some people still stick to the registered areas of the old scheduled lots as gospel.  As is a matter of fact, we inherited the District Demarcation (DD) Sheets a century ago together with the areas schedule.  The latter was derived data from graphical measurements of the DD sheet and recorded to the nearest 0.01 acre as the smallest unit.  Apart from the measurement and the rounding off errors, the registered area might also contain copying and clerical errors as well.

 

4.      Numerous examples of these kind of errors could be found from the land registery and proofs are not lacking.  For example, there was a land lot of area 0.01acre but was divided into two sections of 0.01 acre each.  Another more extreme example was a land lot of area 0.02 acre divided into 5 sections each of which the area was still recorded as 0.01 acre.  There was a case that the land lot was clearly shown graphically as a square of 25 feet by 25 feet and the area was stated, correctly, as 625 square feet. However, alongside this figure a remark “or 0.02 acre” was also printed.  When only 0.02 acre was conveyed in subsequent land dealings, a false area would dominate the records instead of the original and correct one.

 

5.      I have chosen a group of house lots inside a walled village for demonstrating the area problem.  I reasoned that the wall we now survey must be the same as that existed at the time of the DD survey.  The total area of all the lots bounded by this wall could not have changed.  However the number of lots was 45 including 43 lots of 0.01 acre each and 2 lots of 0.02 acres each thus giving a total area of 0.47 acre.  By survey, the whole walled village including certain lane areas as Government Land measured only 0.27 acre.  The registered area was therefore nearly double the actual area and the effect of the rounding up error must be apparent.

 

6.      All these examples are the tip of an iceberg but sufficiently reveal the derivative nature of the registered area.  As far as the area information is concerned, the DD sheet must take precidence over the registered area.  Better still, the physical boundary monument, if still available on ground, should be the best evidence for area determination.

 

7.      Unfortunately, not everybody are accepting this reasoning. Some people still take the registered area as gospel.  Their argument seems to be that since the registered area is part of a legal document it must be regarded as binding.  There was further argument that as the landowner had been paying the corresponding rent, say $0.01 for 0.01acre of land, he must be entitled for the exact registered area.

 

8.      To the first argument, I maintain that the above story of theπvalue may provide the answer.  A physical quantity such as the numberπmust surely be a matter of fact.  It is of a definite value irrespective of whether it can be nicely expressed in terms of our numbering system or not.  Nor indeed it would not change to suit the liking of a ruler or a dictator otherwise we will have to live up with hexagonal wheels.  Similarly, the area of a land lot is a physical quantity which could only be obtained by realistic measurements. If it had been incorrectly recorded, the blessing with a legal status will not make it right again.

 

9.      To the second argument, I suggest that this is a fallacious one.  While it is true that an area of 0.01 acre is to attract $0.01 as the rent, it should no longer be true to reverse the statement.  Just consider that the fee for parking a car for an hour is, say $20, but the paying of $20 does not sufficiently prove that the car had stayed one full hour in the carpark.

 

10.     In short, I must advocate that the registered area should not be regarded as gospel but must be viewed from the correct perspective.  And we surveyors should not be timid in advising others, including landowners, solicitors, administrators and even judges of the true nature of the registered area.

 

 

LEUNG Shou-chun

12-5-03

 

 

 

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