asymptotes are impossible too

[mellowtigger]

Suppose a function reaches a point where the input can continue to grow, but the output ceases to actually exist. In my thoughts, that's the entire concept of "asymptote".  The function simply "can't go there". Mathematically, though, it has a different and more precise definition. Thanks tosnousle for pointing out my error! It's led me to another interesting theory already out there.

I asked foeclan if he had a biology book that would discuss the practical limits on growth curves. Like a colony that grows too large to absorb nutrients through its surface area so it dies. He mentioned the classic giant ant of sci-fi B-movie fame, the insect that grows enormously large... too large to actually exist because its chitin skeleton couldn't possibly support the weight of all that chitin. He pointed me to the square-cube problem. That's apparently the appropriate name for my sample problem with colony collapse. Yes, yes, that's what I'm getting at!

The growth curve has a boundary on its maximum possible output value. The nature of the curve contributes to the evaluation of its maximum value. In my mind, that's why the exponential economic growth curve has an asymptote. There exists a maximum value which cannot under any circumstances be surpassed. (The value of the maximum can be increased thanks to technological advances resulting from prior economic activity, but that's a feature of the growth curve. It merely moves the maximum, it doesn't eliminate the existence of a maximum.)

Sure enough, that led me to something new called Constructal theory. It's meant to be a thermodynamic evaluation of flow systems, figuring out what forms the flow will take to minimize resistance. The nature of the flow determines the kinds of resistance it faces, therefore the shape it will take. Yes, yes, again this is what I'm getting at! *excitement* "Flow" is the same concept either way: money or electrons or oxygen molecules.  edit: Hey, someone is applying the concept to economies too.  Now if they'd just apply it to the underlying financial system.

Consider this video of Adrian Bejan, Professor of Mechanical Engineering at Duke University:

The Constructal law states that for a finite size flow system to persist in time, which means to survive, it must evolve in such a way that it provides greater and greater access to the currents that flow.

Socialism! It's a freaking mathematical way to prove that socialism (equal individual access to common resources) is where we need to go next. "Share the wealth!" Let's hope that Obama is the traitor socialist that Republicans claimed him to be. *un-serious laugh*

These patterns occur naturally in living systems such as society (...?) but also in the simpler systems such as the lung. And they also occur in inanimate, that is geophysical, flow systems such as the river basin and lightning. Lightning is a river basin of electricity flowing from the entire cloud to one point.

So economies, as complex systems trying to persistently keep money flowing among citizens, could be modeled the same way. (Or so I claim.) The nature of the system will determine the boundaries of its possible shapes.  On the surface, it sounds like "trickle-down economics" which has been a huge failure, as I see it.  Maybe because Constructal theory needs to define the nature of the "resistance" to the flow.  Rich people don't just hand out their money to lots and lots of poor people.  The money bottles up.  Constructal theory could provide an analysis of how to improve flow.  Like a tree, from diverse root system to central body back out to diverse leaf system?

I still insist that growth needs to be linear (preferably flat) and the individual agents (consumers, in a capitalist model) kept in near-equal flows of money. How utopian would that be? Could this new Constructal theory prove it mathematically as a stable possibility? And could it expose exponential growth systems as inherently unstable because they collapse under the necessities of the physical world and its bothersome limitations?

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[mellowtigger]

p.s. "Carrying capacity" is the term from the world of biology for the unreasonable/impossible y-value upper limit that I have in mind. Biology concedes that y-value is supposed to go flat eventually. Financing does not (yet) concede any such constraint.