It is well accepted Physics that a mass at absolute temperature will emit energy proportional to the square of its surface area and the fouth power of the temperature. Under all but experimental conditions, these emissions are very small - too small to detect against a background of ambient temperatures. Nonetheless, statistics (Stefan-Boltzmann Distribution) can be computed for small groups.
This computation is an experimental observation in the scientific sense. Humans are a competitive bunch, and like to think that any system can be gamed by the assumption of sufficient risk. There may be some theoretical problems (c.f. The Darwin Awards).
An efficient allocation of resources, based on presumptive needs of group members, can be calculated easily, the "heavy lifting" (maths) transparent in functions.
Countries and political subdivisions, Court Systems, and many other virtual groups follow these power sharing statistics.
... because they have in common a complete set of jurisdictions - the sum of the surface areas of the individual jurisdictions equals the total.
... because the entities can be numerically quartered or cut into four pieces. This is a non-negotiable limit, in the absense of scientific (rational, explained) observations to the contrary. Any metric can be cut in two and those pieces cut in two - but that is the limit of measurement on observation - Zeno's Paradox in reverse - one can be imagined as two, two can be computed as four, five must be seen, validated by observation, or the system will, without "volume", collapse. The square units are no longer well defined.
... because the entities cannot be dime'ed (0.1), nickel'ed (0.05), or penny'ed (0.01) either, relentlessly, as is the custom in the Commercial World. These fractions, if based upon a computation of "quarters" have no independent identity and will not add or comute with any naturality conserved. As above, the system will collapse, this time because the units will stop meaning anything.
As a necessary first step, the Countries of the World are listed with their area in sq km. The ISO 3166-1 Code Set is listed as a Code Page with 676 Members (CodePageID). This defines an RDF List with <rdf:first> as Antarctica (AQ) and <rdf:rest> as all the other Governments and Organizations. Commercial Entities do not "qualify" for this set. Other additions to the table have a TableID (integer). The double identifier is useful for consolidations of smaller sets.
A data base with this information has been created.
The CIA World Factbook contains estimates of surface area, by Country. The Table below indicates the initial partitions.
|
Entity |
Sq km |
id |
Synonyms | |||
|
Earth |
|
|
|
5.10072000e+08 |
009 |
|
|
|
Water |
|
|
3.61132000e+08 |
025 |
|
|
|
|
Arctic Ocean |
|
1.40560000e+07 |
002 |
|
|
|
|
Atlantic Ocean |
|
7.67620000e+07 |
005 |
|
|
|
|
Indian Ocean |
|
6.85560000e+07 |
012 |
|
|
|
|
Pacific Ocean |
|
1.55557000e+08 |
018 |
|
|
|
|
Southern Ocean |
|
2.03270000e+07 |
021 |
|
|
|
|
High Seas NOC |
|
2.58740000e+07 |
011 |
|
|
|
|
|
|
|
|
|
|
|
Land |
|
|
1.48940000e+08 |
015 |
|
|
|
|
Antarctica (Ice Covered) |
|
1.22207140e+07 |
003 |
|
|
|
|
Governance Bodies |
|
1.36719286e+08
|
|
Land (excl. Antarctica Ice Covered) Countries (R001-R676) |
|
|
|
|
rdf:first |
2.80000000e+05 |
019 |
AQ (R017) |
|
|
|
|
rdf:rest |
1.36439286e+08 |
020 |
Countries (R001-R676) |
|
|
|
|
|
|
|
|
In the grand scheme, very rough approximations are sufficient. Since the area of a sphere is 4πR2, and π is an irrational number (without end), it should be obvious that no amount of precision will provide a correct answer. As a practical computational matter, any Country or group will always be a small part of the whole. Moreover, the model used is of emissive power, and obeys Lambert's Cosine Law - the power starts at a maximum (cos(0)=1). This has the effect of conveying a contribution identity to the parts, since only partial sums of those parts have an objective value (adding subjective weights is different issue).
The entry above for "Governance Bodies" is the habitable portion of the planet. Every rdf:List of territory must account for all territory. It need not contain references to all territory.
<?xml version="1.0" encoding="UTF-8"?>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:dcam="http://purl.org/dc/dcam/"
xmlns:dct="http://purl.org/dc/terms/"
xmlns:xsd="http://www.w3.org/2001/XMLSchema#">
<rdf:Description rdf:about="http://www.rustprivacy.org/2011/phase/">
<dct:Jurisdiction>
<rdf:Description rdf:about="#Governance Bodies">
<dcam:memberOf rdf:resource="http://www.rustprivacy.org/2011/phase/www-cbp-12.xml"/>
<dct:title>WWW and CBP Territorial Domains</dct:title>
<dct:issued>2011-01-13</dct:issued>
<rdf:value rdf:datatype="xsd:float">1.36719286000000e+14</rdf:value>
<dct:coverage rdf:parseType="Collection">
<rdf:List>
<rdf:li rdf:parseType="Literal">
<!--<rdf:first> -->
<dct:description>The first member of the List is always Antarctica</dct:description>
<dct:coverage>
<rdf:value rdf:datatype="xsd:float">2.80000000000000e+11</rdf:value>
</dct:coverage>
<!-- </rdf:first> -->
</rdf:li>
<rdf:li rdf:parseType="Literal">
<dct:description>Other List Members</dct:description>
<dct:coverage>
<rdf:value rdf:datatype="xsd:float">0.0e+00</rdf:value>
</dct:coverage>
</rdf:li>
<rdf:li rdf:parseType="Literal">
<!-- <rdf:rest> -->
<dct:description>The List is filled in the middle, with the rest as the balance.</dct:description>
<dct:coverage>
<rdf:value rdf:datatype="xsd:float">1.36439286000000e+14</rdf:value>
</dct:coverage>
<!-- </rdf:rest> -->
</rdf:li>
<rdf:li><rdf:nil /></rdf:li>
</rdf:List>
</dct:coverage>
</rdf:Description>
</dct:Jurisdiction>
</rdf:Description>
</rdf:RDF>
Note also that the "issued" field is a date, not a date-time. This is not a trivial point. The issue date should be the date of the last Midnight UTC. The Earth, unlike many celestial bodies has no "dark side", for example, the Moon. For computation, that sort of body is considered to have two dark sides and two visible sides which are complementary. Just as one might decant a bottle of wine, that is not the same as saying the bottle is being consumed from the bottom up. Many Time dependent resources have this property, but it is common elsewhere: it arises from a race condition where two outputs must be reconsilled which are not continuously available. In this case, a watch and a sundial both measure time. The sundial also counts days. If you were to say the watch is always more accurate, you would be incorrect. In fact every watch is a bit under four minutes fast - it measures Mean Solar Time. The sundial measures Sidereal (Star) Time and is always correct, except of course at night when the measurement is unavailable.