Evolvodynamics - The Mathematical Theory of Economic by Len H. Wallast

By Len H. Wallast

Dissatisfied with the issues of orthodox economics, the writer proposes to base monetary conception at the 3 ideas of Darwinian evolution (variation, inheritance, selection). Pursuing a tenet of E.T. Jaynes of 1991, the innovation is in treating financial habit as likelihood occasions of choice. This includes leaving behind the tools of mainstream economics and to use as a substitute the equipment in which Claude E. Shannon analyzed info delivery over a desk bound channel. As financial approaches are non-stationary, the writer clarifies first how the Shannon-system has to be reshaped in a procedure able to explain financial evolution mathematically. As financial strategies are non-stationary, the writer first clarifies how the Shannon method needs to be reshaped into one in a position to describing monetary evolutions mathematically. Deriving the common kin among enter, output, the commercial development cost, inflation and cash movement includes utilizing differential units of choice, Venn diagrams, bitpulses as devices of choice and the chance distributions of  bitpulses. it is a thought-provocative and hugely informative ebook of which the explanatory energy is going a long way past that of conventional economics. it's going to be at the readers checklist of all people interested in the weal and woe of monetary theorizing.

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Extra info for Evolvodynamics - The Mathematical Theory of Economic Evolution: A Coherent Way of Interpreting Time, Scarceness, Value and Economic Growth (Lecture Notes in Economics and Mathematical Systems)

Example text

2 Note that the two samples—despite they are different samples—hold each the same content of entropy. 2). We will use the new notational convention interchangeably with the one with arguments X and/or Y closely resembling Shannon’s notational convention for entropy. Thus HðdSÀ i Þ ¼ HðXi Þ is þ per sample, HðdS Þ ¼ HðY Þ is the entropy content of dSþ the entropy content of dSÀ j j j i þ þ À per sample and HðdSÀ [ dS Þ ¼ HðX [ Y Þ is the entropy content of dS [ dS per 0 0 0 0 0 0 þ sample. The new convention with arguments dSÀ i and/or dSj is the more systematic one, the other one is closer to existing practice.

The total entropy “stocked” À þ \ dS is Zdt Á H X \ Y in dSÀ i j . 9)]. 2 Overall Selection, Transmission and Exchange, Conditional Entropy 37 M L C D + N K dS 0 P O dS 0− E J B F H A G Fig. 5 The Venn diagram of evolution of the three-sector economy S0 with N ¼ 3 sectors. The three non-differential sectors, S1, S2 and S3, have not been illustrated. The differential set dSþ 0 of 2 þ À outflow interacts with the differential set dSÀ 0 of inflow . Notice that there are 3 subsets dSi \ dSj of transmission.

The probability of the joint occurrence of the event that a sample is used up in state i on (t,t + dt) and the event that it has been called in existence after time instant t but prior to its moment of annihilation on (t,t þ dt) is negligible relative to its singular chance of being used up in state i on (t,t þ dt). Therefore we may also conclude here that—to first order of accuracy in dt—all the inflow that is used up on (t,t þ dt) already existed in Si at time instant t. This implies that the selected inflow H ðXi Þ reassembles entropy in state i on (t,t þ dt) that was already in that same state i at time t.

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