Too many, too much, too fast
The question of scaling is essentially one of how well something works as its size increases. In computer science we are often faced with the question of how well an algorithm fares in solving a specific kind of problem as the size of the problem, say the number of items being processed, increases, usually linearly. But the concept of scaling is far more general than problem solving in CS.
In an ideal case the performance of a process remains constant or even might improve somewhat as the process grows in size. Indeed economists long ago recognized what is called 'economies of scale' in which the fixed costs of operating do not increase at the same rate that the size of a production organization increases. Variable costs increase with each unit, but total costs (variable plus fixed costs at some point in time) actually increase more slowly than the incremental growth of the process. Of course, over the long haul, at some discrete points there must be an increase in the infrastructure that underlies the fixed costs (a step function) so that even fixed costs go up proportionally with the growth of the process. Nevertheless, economies of scale have often been used as a major argument for organizational growth. When a process is 'large enough' its per unit costs are minimized and it can compete more effectively with other producers.
At the same time, economists have also known that there is a tendency for systems to show a diminishing return on investment as a constraint on unlimited growth. They just sometimes fail to remember it. But this is the essence of a scaling problem. In every dynamic system, as the system gets bigger or processes faster (or both) there comes a point at which each new increment of increase produces less in terms of accomplishment. In situations where this decline is actively monitored, the growth function can be restrained and the system enters a more or less steady-state. For those mathematically astute, you may recognize this as described by the logistic function — the 'S' curve.
Unfortunately, there are cases in which the growth is not monitored and the growth continues beyond its marginal positive return. These systems then go into decline. That is, there is negative return on each new increment of growth. The mathematical curve that is fitted to this type of system behavior is some version of the Gaussian function — the normal curve. On the up side (left-hand side of the peak) things look a bit like an S curve, so it isn't until after the peak that you realize something is wrong! Fundamentally, this model is telling us that the bigger we get or faster we go the worse off we are. But it is more of an idealization rather than a predictor of smooth decline. The real curve for real systems undergoing over-growth generally follows a much steeper decline on the right side. It is called a crash and is more typical of dynamic systems.
We are currently witnessing several examples of scaling problems in human affairs. I get a kick out of the rhetoric about banks or companies being too big to fail. Of course they have already failed, they are moribund, but the government comes along and gives a transfusion of money (sucked out of nothingness, i.e., debt) to keep the organization on life-support in hopes it will recover. But who is going to give the government a transfusion?
Our globalized institutions, from governments, to education, to corporations, even to non-profit NGOs, have all gotten too big to function well. They have become the dinosaurs of our time. And we know what happened to the dinosaurs. Size matters. With it comes increased complexity, longer communications channels with increased opportunity for noise and time delays that lead to dysfunction. Watching many of the bank and auto CEOs testifying, seeing the stumbling attempts by Obama's economic team to stanch the bleeding, it is clear that no one really grasps what is going on, even within their own organization. And either they are too afraid to admit that they don't know (for fear of being perceived as 'weak') or they really don't know that they don't know. If the latter you would think they would get tired of always being surprised at how badly things are going.
In the long run there will be more detrimental scaling issues to deal with than whether GM or AIG survive. The production of greenhouse gases, the depletion of soils, water, fossil fuels, and the dumping of garbage and toxic chemicals into the environment — all of these are the results of there being too many of us, using too many resources, and doing it all too fast. Human 1.xx has long since passed the point of diminishing returns on each new mouth to feed. Without a monitor on the population or its per capita consumption and an effective check on growth, we have entered the downward phase of the asymmetric Gaussian. The question remains as to how steep the fall off will be.
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