would otherwise be a complicated beyond reach situation. One of the properties found around singularities, is the Joss of absoluteness in contextual characteristics such as the scale of the observation. We no longer can say that what we are studying happens in inches or miles, in seconds or days, now or in the past. In the place of a single unit of relevant measurement, we have a distribution of spatial and temporal feature sizes that stretch toward both the infinitely small and the infinitely large.
We can illustrate a dynamical transition involving the passage of the system through a singularity by using the metaphor of another kind of water experiment. If we pour a small amount of water through a filter full of coffee grounds, or watch our coffee maker do it, the first spurt of water makes an incomplete path of wet grounds in the bed of dry ones. The next bit of water soaks this path more thoroughly and may form additional and multiple, new and branching, incompletely penetrating paths. Eventually, on just one more of these pourings, a connection in the paths occur, such that the water snakes all the way through the coffee grounds and the first brown drop of coffee falls into the pot. At this flow singularity and opposite to the dynamic of a faucet water drop, a discontinuous system of pathways becomes continuous in finite time in a process called percolation,
Trying to set up a predictive model, we can count the number of water deliveries that occur before the first drop finds its way through. Repeating the experiment many times yields a span of the number of pours required to reach the singular point of percolation. If we do the experiment enough times, the distribution of the number of pours required to reach percolation will range from one toward infinite. In the neighborhood of the transition, time as recorded as the number of small pouring events may stretch.
In aa comparable system, as elegantly described by Detrich Stauffer in his Springer-Verlag book on percolation, multiple hot spots in the woods can suddenly fuse into a forest fire. Isaiah said, “...glorify the Lord in the growing fires of dawn...” Faith fires spreading through a faithless dense forest, its hot irregular front damped by the disbelief of water-filled leaves, or disillusionment gaps of already burned out
trees, can, under the right motivating conditions of dryness, wind velocity, tree
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