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EVOLUTION OF COMPLEX SYSTEMS BY AGGREGATION: SIMON's Hora and Tempus Parable 1)2)

H. SIMON explains through his famous Hora and Tempus Parable how complexity may have evolved:

"Let me introduce the topic of evolution with a parable. There once were two watchmakers, named Hora and Tempus, who manufactured very fine watches. Both of them were highly regarded, and the phones in their workshops rang frequently – new customers were constantly calling them. However, Hora prospered, while Tempus became poorer and poorer and finally lost his shop. What was the reason?

"The watches the men made consisted of about 1.000 parts each. Tempus had so constructed his that if he had one partly assembled and had to put it down – to answer the phone say – it immediately fell to pieces and had to be reassembled from the elements. The better the customers liked his watches, the more they phoned him, the more difficult it became for him to find enough uninterrupted time to finish a watch.

"The watches that Hora made were no less complex than those of Tempus. But he had designed them so that he could put together subassemblies of about ten elements each. Ten of these subassemblies, again, could be put together into a larger subassembly; and a system of ten of the latter subassemblies constituted the whole watch. Hence, when Hora had to put down a partly assembled watch in order to answer the phone, he lost only a small part of his work, and he assembled his watches in only a fraction of the manhours it took Tempus.

"It is rather easy to make a quantitative analysis of the relative difficulty of the tasks of Tempus and Hora: Suppose the probability that an interruption will occur while a part is being added to an incomplete assembly is p. Then the probability that Tempus can complete a watch he has started without interruption is (1- p)1 000 – a very small number unless p is.001 or less. Each interruption will cost, on the average, the time to assemble 1/p parts (the expected number assembled before interruption). On the other hand, Hora has to complete one hundred eleven subassemblies of ten parts each. The probability that he will not be interrupted while completing anyone of these is (1- p)10, and each interruption will cost only about the time required to assemble five parts.

"Now if P is about.01 – that is, there is one chance in a hundred that either watchmaker will be interrupted while adding anyone part to an assembly – then a straightforward calculation shows that it will take Tempus, on the average, about four thousand times as long to assemble a watch as Hora.

"We arrive at the estimate as follows:

1. Hora must make 111 times as many complete assemblies per watch as Tempus; but

2. Tempus will lose on the average 20 times as much work for each interrupted assembly as Hora [100 parts, on the average, as against 5]; and

3. Tempus will complete an assembly only 44 times per million attempts (.991000 = 44 x 10 -6), while Hora will complete nine out of ten(.9910 =9x10 -1)/(44x10 -6) = 2x104. Multipying these three ratios, we get:

1/111 x 100/5 x.9910/.991000 = 1/111 x 20 x 20 x 20,000~ 4,000 " (1965, p.65-66).

Two conclusions are obvious:

a) complexity results from ordered aggregation of elements.

b) complexity is more easily obtained by fractioned aggregation, from level to level.

And a third conclusion is tentative:

c) evolution very probably proceeds by fractioned level of aggregation to produce complexity.

Another interesting comment by SIMON: "…we may be sure that the watchmaker's metaphor gives an exceedingly conservative estimate of the savings due to hierarchization" (Ibid).

Of course, fractioned aggregation is related to hierarchy, as a result from competition between systems, destined to become subordinated and to undergo processes of internal reorganization of their structures and functions to adequate them to their new settings.

1) general information

2) methodology or model

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