REPLY Meaning of Stock/Level (SD6895)

[SDMAIL Tom Fiddaman]

Posted by  Tom Fiddaman <tom at ventanasystems.com>


At 05:59 AM 4/9/2008, SDMAIL Alan McLucas wrote:
> Stocks in system dynamics models represent quantities of material.  The
> stock-and-flow representation has precise and unambiguous meaning:
> stocks accumulate or integrate their flows; the net flow into the stock
> is the rate of change of the stock (Sterman, 2000: 195).
>
> If this is true, ...

I think the problem here is that the premise is false, i.e. that the 
restriction to material is overly stringent (except as I'll argue below 
that soft variables are material). Another synonym for stock or level is 
"state". The state of a system often implies a quantity of material with 
conserved flows, but not exclusively.

> Unfortunately, the possibility that we can have stocks of materials
> that are not physical in nature is sometimes interpreted as meaning that
> it is quite legitimate to build models where the stocks are soft
> variables or intangibles.

If this were true, how would we include soft variables in models? Would 
the world even have soft variables?

> ...  In the case of intangibles, inflows
> and outflows CANNOT produce accumulations that are calculated by
> numerical integration: a model having a stock "Trust" with an inflow
> "Change in Trust" will fail the essential mass-balance test.

I agree that inflows and outflows of intangibles couldn't lead to an 
accumulation of a physical quantity, but I don't see why that precludes 
calculating an intangible state as the integral of the rate of change of 
that state.

> The only way that such a model could be correct is if initial stock of
> "Trust", measured as a*1<<trust units> > had a further amount of trust
> added at the rate of x*1<<trust units / units of time> > and an amount of
> trust deducted at a rate of y*1<<trust units / unit of time> >, with the
> current stock being calculated as Trust = INTEGRAL (Inflows - Outflows,
> Initial Trust)

This seems reasonable, except for the dimensionless constant 1 buried in 
the equation, for which I do not understand the purpose. There's nothing 
about a stock/level/state that requires a separate inflow and outflow.

> "Trust" is an intangible which
> cannot be represented by this integral equation.  Therefore, we cannot
> build system dynamics models that contain stocks of intangibles such as
> "trust".

Again, this seems to hinge on the premise that stocks must be material, 
which strikes me as overly limiting. Certainly there are intangible 
variables in Industrial Dynamics.

> I appreciate the desire to build models which incorporate soft
> variables and intangibles, because ignoring such variables leads to
> erroneous models (Forrester), but building models that purport to
> represent soft variables and intangibles as stocks is not the answer.

This begs the question, what is the proper representation of soft 
variables?

Let me suggest a counterargument:

Suppose that beneath every soft variable is a system of material states 
that obey conservation laws. Thus for "trust" one could imagine a 
conserved accounting of neurons in a particular electrochemical state. 
Neurons would arrive in or depart from that state, comprising an inflow 
and outflow or net rate of change. Then one could in principle construct 
a mapping between the neuron accounting and the state and rate of the 
soft variable, and be confident that the soft representation did in fact 
imply material conservation. In fact, I don't see how it could be 
otherwise, unless the universe permits persistent states to exist 
without a material substrate.

Also, a thought experiment, borrowing from an old observation about 
averages:

Suppose that I'm sitting in a bar. Looking around, I notice that most of 
the clientele are grad students, so I mentally calculate that the 
average income is about 14,000 $/person/year. So, I have an intangible 
state representing my expectation, denominated in $/person/year. Later, 
I look up and notice that Bill Gates has walked in. It takes me a minute 
to update my expectation of the average income to 120,000,000 
$/person/year, at a rate of 119,986,000 $/person/year/minute. Now, would 
it matter where that 119,986,000 came from? I don't think so. Going back 
to the neural analogy, the representation of my expectation might be a 
bit like a binary string, where a change of large or small magnitude 
could be accomplished with equal material implication by flipping more 
or less significant bits.

You could argue that this is a poor example, because it's too discrete. 
But that problem applies to material stock/flow systems as well. If the 
expectations of 100s of barflies were averaged, the aggregate movement 
of the system would be well-represented by continuous integration.

( http://edstrong.blog-city.com/paul_krugman_inequality_in_the_usa_1.htm )

Tom
Posted by  Tom Fiddaman <tom at ventanasystems.com>
posting date  Wed, 09 Apr 2008 20:42:39 -0600