It was John Smith, who did the delivery of the monkey wrenches, according to the author of Database Design and Relational Theory, Chris Date. He wanted to show the formal anomaly (connection trap) that is accompanied by loss of information if n-ary relations are decomposed into multiple binary relations and rejoined again. What he omitted was to indicate why there is a need to use a n-ary relation instead of binaries – without any formal reason. The formal oriented database design does not give a clue on design, i.e. what form to use for what. This all has to be provided by domain knowledge, i.e. the semantics and pragmatics that provide the detailed structure of the objects to depict.
The SPJ-relation “Supplier-Parts-Project” contains the data of all actual deliveries of parts for any project. By decomposing SPJ into three binary relations (Supplier-Parts, Parts-Project and Supplier-Project) the relations are projected such that edges (pairs of nodes) only become available. Joining relations means to combine all tuples by identity. The join operation creates the set of all feasible tuple combinations, not just the subset of the real ones. The example above shows four deliveries instead of three.
The idea to use an uniform structure for all data has been proposed by J.R. Abrial (“The Semantic Binary Model, J.R. Abrial, “Data Semantics,” in J.W. Klimbie, K.L. Koffeman (eds.), Data Base Management. North Holland, 1974.”) Within Abrial’s framework the SPJ-relation would be redesigned as three binary relations with foreign keys to some new relation containing the keys of all delivery events. One could easily reconstruct the facts by joining along the delivery keys. From this point of view binary restrictions may effect the efficiency of the retrieval process but cannot restrict the information to be retrieved.
After aggregation there may be anomalies…
We know the relativistic point of view which is all around during high school, at university and nowadays in the public press as LIGO’s search for gravitational waves is featured. The relativistic point of view does not accept a predefined common frame of reference and insists to apply relative velocities only. This is a mystery! How did Einstein manage to add the velocities, e.g. the speed of A and the speed of C? If vAB is said to be the speed of A with respect to B then vBA is the speed of B with respect to A. If vBC is to be added to vAB the result would more than doubtful because vBC needs C to refer to some anchor and vAB refers to B which is moving independently from C. So we must state:
The addition of velocities without common reference is void.
To add vBC and vCB is void then. To add vBC and vAB we have to use B as common reference. But what is the semantics of this sum if we don’t know the angle ABC? We have to admit:
The addition of velocities without regarding the incident angle at the common reference is void.
How do we get the angle ABC, and how do we ensure that it does not change during the maneuver? There must be a measuring process in order to check the distance between A and C -or which does the same- to measure the speed vAC directly. So we have:
In order to add two relative velocities we must have more than two relative velocities, we must have all relative velocities.
If all points are lined up and the point in the middle hides the third from the first the angle could be checked easily. But all other cases show the same rule: If we want to aggregate the velocities of all particles within a given segment we have to know the complete graph which is the velocity of any node with respect to any other node. This is equivalent to be omniscient.
What did science wrong when dealing with Einstein and his followers? They never tackled the fundamental lack of inference which opens the gateway for paradoxical phenomenons that may not even concerned as antinomies.