Seldon Plan - Mathematical Modelling

Mathematical Modelling

The Seldon Plan is statistical in nature. Future events are described as being probabilities. The variables, as discussed (see above) require a very large number of human beings, literally the population of the Galaxy, in order to reduce the ordinarily random events concerning human affairs to become amenable to statistical modelling.

Seldon's original address at the Decennial Convention on Trantor in 11,178 G.E. was his proof, using the irreducibility theorem (or First Seldon Theorem) that the population of the people of the galaxy fell just short of being a dynamic system which would be impossible to model adequately mathematically, the definition of 'just' most likely being one order of magnitude, though this is not discussed within the novels. At the time of this discovery, Seldon was not yet sure of either the scope or time constraints required to develop this discovery further.

Initially, Seldon was unable to make any headway on developing the model, as he was attempting to bring knowledge of all Galactic History, as well as considering all of the Galactic Population into modelling. Inadequate history and news reporting in the 12th millennium G.E. hindered his progress during his first year on Trantor, particularly during the period known as 'The Flight'.

After some consideration, at the end of the period of 'The Flight', Seldon realised that Trantor and its attendant worlds constituted an 'Empire In Miniature' on which he might model the past and future course of the Empire. Events in the rest of the Empire could be effectively modelled as second-order effects. Seldon often described this breakthrough as being 'the result of a turn of phrase' he encountered during The Flight.

During Seldon's lifetime, congruent points in the Plan were developed and modeled with enough accuracy to determine the critical points of inflexure that would set the Galaxy on the path of Foundation, and the Second Empire. In order to ensure that the First Foundation would be created, Seldon and the Psychohistorians of Trantor placed the Commissioner Linge Chen (then actual if not crowned Emperor) under intense scrutiny, as well as Mentalic influence in order to achieve their aims. This was a clear but vital breach in the limits of psychohistorical theory, as psychostatistics is meaningful only with planetary numbers, and not with individuals.

Thereafter, refinement in mathematical modelling saw the development of specialists with Seldon's group of Psychohistorians, now the nascent Second Foundation. Specialisations mentioned include:

• Psychohistorian
• Psychostatistical Technician
• Observer
• Proctor
• Librarian

The Foundation also developed an Assembly, which was not a feature of its early days.

The Seldon Plan was never, even from its start, kept stored in any form of paper, as the mathematics was expressed not as simple equations, but of necessity as a dynamic process model. Computer technology allowed the development of the Prime Radiant, which permits not only observation of mathematics, associated papers, and related data in multi-dimensional dynamic displays, but also permits inclusion of changes, improvements, and modifications of the Plan. The Prime Radiant has had offshoot technologies to improve mathematical modelling, including the mini-radiant, which allows Speakers access to the Plan in private, for the purposes of refinement. Mini-radiants are able to access the Prime Radiants containing the Plan in real-time across radio data-networks.