A theory’s most significant application is often established through an interpretation of how its physical counterpart might be destroyed. SFEcon portrays the catastrophic collapse of a capitalist system as an implosion of the savings loop caused by the investment term T’s uncontrolled fall to zero. Computation of an economy K’s investment term T proceeds from transcendental and an algebraic specifications of net present value NPV:

These equations reference K’s interest rate -i and its (single) intermediary’s contra-accounts to investment k and savings g. The investment term T is computed by a eliminating NPV from these equations. Regrettably, simultaneous solution to this system is only possible through application of some technique such as Newton-Raphson approximation; and this is not conducive to meaningful visualization. Separate solutions of these equations for the investment term T do, however, suffice to exhibit the particulars of a financial collapse in terms of SFEcon’s variables:

The equations above reveal that trivial simultaneous solutions are always available at {T=0 and NPV=1}, and at {T= and NPV=0}. Note that levels of investment k and savings g become meaningless in these situations, and that the hazard of encountering such solutions approaches certainty as the interest rate -i approaches zero.

An investment term trying to be both zero and infinity at one moment constitutes the singularity in SFEcon’s analog to the catastrophic collapse of a capitalistic system. Obviously the only physical counterpart to these abstractions is for savings g to be null so as to allow this ‘nothing’ to move with infinite speed. A capitalist epoch ends when every intermediary’s interest rate has vanished: savings positions might endure as bookkeeping entries under such circumstances, but their reality in terms of convertibility to objective commodities is no more. As the realization of this fact dawns, the contradictions implicit in T’s computation will be manifested.

A visualization of the transcendental expression for net present value NPV shows that the field of financial rationality is bounded by 0<NPV<1 and -i>0, and that it inclines toward the fatal singularity:

This portrait of allowable financial activity can be used to interpret the policies by which the destruction of savings has been historically forestalled (and is being forestalled as this is written in early 2010). The United States during the 1930’s and Japan during the 1990’s both effected massive infusions of fiat money into the capital accounts represented in Model 0 by the variables k_IK. And both experienced essentially limitless extensions of their investment terms T: if one were fully invested in US stocks during 1929, one’s principal would not be fully returned until approximately 1954; those fully invested in Japan since 1989 have not yet dared to test their principal’s represented worth.

Model 0 replicates the prospective causality in these observations by its response to an arbitrary factoring-up of all an economy K’s capital accounts k_IK. Any such stimuli are entirely absorbed in an expanded term T_K and higher prices — with absolutely no other transients being induced. These experiments produce the same result for any interest rate, however puny or robust.

As a practical matter, governments have historically effected such policies by injecting fiat money into their own capital account, while making their currency into ‘carry tender’ by restricting its interest rate -i_K to essentially zero. Government is thus oblivious to its indebtedness because it pays no interest upon it, while wealthy elites are nonetheless anxious to underwrite sovereign debt as a refuge from alternate financial positions that are in danger of complete collapse. Recent swaps of ‘troubled assets’ for long-term Treasury obligations at 100¢ to the dollar instantiate such operations.

Our interpretation of these circumstances has the financial state artificially tethered to the origin of our financial playing field, keeping the investment term infinite so as to prevent material realities from careening beyond the calculable limits of financial order. Unfortunately, enforcement of this policy suite removes all limits to an ultimately meaningless (because motionless) accumulation of fiat money. Once elite money placements have been effected, further monetary flow requires the attraction of a point at which investments are remunerated. Absent a return rate, there are no such points — only welfare recipients, indifferently distinguished among rich and poor, corporate and private.

If analogies to physical singularities are appropriate for the investment term, then they have at least three things to tell us:

1) Causal theories are of no help in predicting what might lie beyond the singularity. It is, however, obvious that spontaneous regeneration of a collapsed capitalist economy requires a positive interest rate. And we might further speculate that a new capitalistic epoch would logically proceed from  k=g and T=1 year, i.e.: the neoclassical norm in which no industry can invest a dollar until a household has saved a dollar.

2) We know that it is possible for systems to persist at their singularity for an indefinite period. For example: a structural column can, in theory as well as in practice, be loaded to an extent that one point on its length becomes entirely plastic and can be pushed about with minimal lateral force. Absent any disturbance, this critical situation might be maintained indefinitely, as are Japan’s ‘zombie banks’ and the many more banks worldwide that are now following upon their example.

3) Creating money when at a point of economic singularity only increases its denominations and lengthens the investment term T. As for effecting actual changes to an economy’s physical state, it is only an attempt at homeopathic magic that, unlike the prototypical rain dance, has absolutely no chance of success.