The Markovian Mind

In many ways, human engagement with information happens in such a manner that, with the accumulation of information over time, the dataset constructed out of the latest volume of information has the strongest relationship of any kind with the consecutively next dataset – a Markovian trait.

At any point of time, the future state of the dataset is determined solely by its present one. In other words, with a discrete understanding, its nth state is dependant solely on its (n – i)th state, where ‘i’ is a cardinal index. Upon a failure to quantify its (n + i)th state, there is no certain state that we know the dataset will intend to assume.

At the same time, given its limited historic dependency, the past’s bearing on the state of the dataset is continuous but constantly depreciating (asymptotically tending to zero): the correlation index between the (n + i)th state for increasing i with the (n – k)th decreases for increasing k (for all k = i).*

Over time, if the information-dataset could be quantized through a set of state variables, S, then there will be a characteristic function, φ(n), which would describe the slope of the correlation index’s curve at (i, k). Essentially, the evolution of S will be as a Markov chain whereas φ(n) will be continuous, rendering (i, k) random and memoryless.

(*For k = i, (n – k) = (n – i). However, for a given set of state variables S, which evolve as a Markov chain, the devolution that k tracks and the evolution that i tracks will be asymmetric, necessitating two different indices to describe the two degrees of freedom.)

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