Negentropy indicative of Consciousness: a Law of Nature; Link between Consciousness, Randomness and Sparse Distributed Networks

Maharishi Mahesh Yogi posited the concept of ‘The Source of Thought’. In Vedic science (Shiksha), the concept may be equated with Para when describing the four levels of thought. Para is transcendental to the space of ideas. It is the state of mind in "transcendence" (deep meditation) i.e. empty of ideas. Yet the word Para also means supreme, which refers to that state also being the source of all possible ideas. From a Mathematical and Computer Science perspective, the only equivalent candidate for such a source is a true Pseudo-Random Number Generator, with the caveat that it should have a seed of infinite-length and no periodicity. Maharishi also stated that "new ideas" in knowledge must be "discovered" simultaneously, citing Legendre's theorem "A subgroup subdivides a group", a statement which directly implies that knowledge forms the overall set. Indirect implications are that: Conscious beings form a set, and that ‘God’ is the largest member. However, it is not immediately obvious how Legendre's theorem applies to knowledge, until Sparse Distributed Memory emerges from Consciousness, and Hankey's Complexity Biology critical instability theory is considered, as satisfying the properties of a Banach space. This paper also explores the difference between time-distributed and domain-distributed randomness as a source of creativity and thought, and their implications for simplified efficient Particle Swarm Optimisation. Randomness is seen to be just as important a part of the Definitions of Consciousness (McKenzie's Memory, Perception, Imagination and Looping). It is then sufficient to postulate as a Law of Nature: non-zero Negentropy indicates the presence of Consciousness. Finally, we highlight the insight that properties of Sparse Distributed Memory, aka a Banach space, inherently lead to Analogy. Its use by any Consciousness entity should result in self-directed learning. Tononi et al were right, with the caveat that Integrated Information Theory's properties may be inherent and emergent rather than exclusively explicit.