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Mental Modeling

Experiencing the Flow

One way to understand a dynamic system is to get into it and to experience it fully, like the scientist above is demonstrating.  Another way is to think about it and to model it as a structure of levels, rates and policies - and to simulate its behavior.

 

Later, we can go to program the system structure in a simulation language (Excel works fine.) and simulate the system behavior, one moment of now at a time.  For now, we take the first step and build a mental model.

 

The model building process is an excellent way to define and refine assumptions and theories about how a system operates.

 

 

 

The Flow Rate Changes the Level

 

One way to understand a dynamic system is to model it as a structure of levels, rates and policies.

 

 

A System Structure Diagram

shows how the elements interact.

 

 

In this model, your milk glass filling policy determines the milk flow rate. The level informs this policy.

 

One policy (the proportional method) is to keep the flow rate proportional to the distance remaining to the target.

 

Another policy (slam-shut method) is to start the flow "at the max" and then to "slam the valve shut" when the level approaches the target. 

 

This policy may easily over-shoot, particularly if you have some reaction time in the policy.

 

Another policy (small pulses method) is to stop the flow when the level nears the target and then to zero-in on the target by adding small pulses of milk, allowing time to think between pulses.

 

Your "optimal" policy, depends upon your objective function (bliss function). For example, your view of optimal may depend on your relative valuation of (1) the speed of filling the glass and (2) the accuracy of filling.

 

In general, a policy that fills the glass quickly with high accuracy is optimal.

 

The model building process is an excellent way to define and refine assumptions and theories about how a system operates.

 

In the next section, we build an excel model of the proportional method.

 

the excel model

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Clips:

http://lh3.ggpht.com/_9_Am7NXTPzc/SgbxyC54NGI/

AAAAAAAADnw/jUZnayAPJwM/milk1%5B6%5D.jpg

 

http://heureuxpourtoujours.files.wordpress.com/

2008/08/milk_pouring1.jpg