One of the first things I noticed when I conducted my Deterministic Bass experiment using three time periods of data was a boundary condition:

This condition becomes more obvious when we scan out:

And even more obvious when we scan further out:

But what does it mean? Where does it come from? Is it a theoretical or a practical limitation? What mathematical form might it take, and why?

I soon determined the mathematical form:

The “theory” is in fact a mathematical formula with no theoretical justification other than it seemed to fit the data. But the mathematical fit was less than perfect, and the theoretical justification remained nonexistent, or emergent, to give it a finer sounding moniker.

For the last decade, this situation has remained basically unchanged. There is an observed limit, with nothing else known about it.

Until now.

We talked about free will mostly in our last post. That’s because sensible people prefer to exercise free will rather than allow themselves to be exposed to the terrible indignity of predestination. Sadly, predestination does occur in the lives of everyone at some point in time, specifically to include the end of existence as we know it in this world, otherwise known as death itself. Predestination mathematically takes the form of a dichotomous discrete choice variable suspended in time between before and after.

As the above graph illustrates, when a step function is separated in time from one time period to the next, there is one step up in time period 1, and no change thereafter. This type of decision is the product of an overwhelming external influence that always explains 100% of the variation in the dependent variable, leaving nothing more than 0% for the internal influence to explain.

This graph and the relationship it explains is unaffected by the internal influence, which can take any value from negative infinity to positive infinity and still fail to explain even the smallest portion of the variance. A rather odd situation, you must agree. This dichotomous discrete choice time variable occupies a single point in Decision Space {1,0}, and thus has a rather limited dimensionality of 0 dimensions.

Where do we go from here?

Who among us is capable of exercising free will in decision making based on their very own needs, wants, desires, and goal orientations? Conversely, which of us may be subject to predestination, and are therefore doomed by fate even before they are born, no matter what they may choose to think, say, or do? The correct answer is both, of course.

Free will and predestination are both built directly into the structure of the universe we live in. Free will and predestination are both explicit functions of time, and nothing else. Free will occurs when you have all of the time in the world. Predestination occurs when you have no time left at all. With rare exceptions.

The moment of death, which takes less than an instant, is the only time in any decision maker’s life when it can truly be said that predestination is fully in control, for time itself has run out for that particular decision maker. No decision maker is ever capable of exercising free will in its purest form unless they literally have all of the time in the world, all of the time in the universe, an infinity of time in other words. For the rest of us mere mortals, decision making is by its very definition a mixed bag, in which free will and predestination both appear as internal and external influences on the necessarily discrete process of decision making.

The above graph is a little rough, and might be improved, but clearly demonstrates the effect of time on free will. The more time one has, the greater the range of possibilities in terms of goal-oriented behavior, otherwise known as free will.

How simple life can be, when you really think about it.

But where does predestination live?

The Butterfly Effect is real. Not just in the physical universe we so much love and respect, but in the mental universe of Decision Space as well. Let’s see if we can figure out how this is possible just for fun.

I would say that the Butterfly Effect in the physical universe is a function of uncertainty in the first instance. Uncertainty emerges as a fundamental property of the fabric of which the physical universe is composed from little things like chaos theory and complex systems analysis. In a sense, the Butterfly Effect is the form that uncertainty takes in relation to our inability to sense the presence of the physical universe or to obtain measurable data regarding the physical universe in any or all of its manifold forms. The modeling implications are rather trivial by comparison, since all you need to model the universe is a perfect copy of the universe itself.

The Butterfly Effect in the mental universe of Decision Space operates on somewhat different terms. Unlike the physical universe, where the Butterfly Effect emerges from chaos as a fundamental limitation on knowing or describing or predicting future changes in the state of the physical universe as a system, in the mental universe of Decision Space the Butterfly Effect represents a wildly different kind of limitation or uncertainty. The Butterfly Effect in Decision Space has more of a dreamlike quality to it, a goal that can never be achieved, but which like all the colors of the rainbow appears to be quite near, and can be captured if one only takes the one more step necessary for its realization in both form and substance. A chimera which is both the only real goal in life, and one that can never be obtained. A paradox, a contradiction in terms, and the fundamental meaning of life itself. No one ever said the universe had to be fair.

The Butterfly Effect in Decision Space is intimately tied to McFadden decisions. McFadden decisions provide the most basic and fundamental goal of civilization in mathematical form. McFadden decisions mark the boundary between two distinct dimensional domains, those occupied by Normal Bass decisions and Strange Bass decisions. There are an infinite number of permutations that can produce McFadden decisions in theory, yet examples of pure McFadden decisions are very difficult to find in decision making practice.

One simple example of a practical McFadden decision is this:

Practical McFadden decisions are interesting in and of themselves, but in general have have little or nothing to do with the Butterfly Effect. Another paradox of traffic flow, ye gods!