In the last post on channel theory we went from the thermostat paradox to the forced interpretation that agents agree, apriori, on inventory variance relative to plan. I give full credit for that step to Nick, and suggest we call it the Canadian Interpretation. How does that get to quantum flows and why the two sigma rule?
Consider the simple one stage model where the firm seeks to keep inventory variance as insurance from deviations from mean. The firm also seeks to minimize transactions, it would like to make the minimum number of shipments to market. When is there surplus inventory to generate a single product load? When the the variance from mean is exactly two sigma from agreement. Then the firm can take one sigma from inventory, generate products, leaving one sigma in inventory and guaranteeing only one shipment.
In the hydraulic model, that point is noticed with the double ended statistical test when inventory level is at the 15% probability level. Seems like a trick. But later when we construct proofs that define multi-stage networks we will see this rule converge with the Nyquist rule upon which Shannon Channels are built. It really is fundamental to nature, like the Euler paths.
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