I think some clarification might be required concerning the nature and implications of Novelty Theory and the Timewave as currently formulated and mathematically constructed. First of all, there are neither embedded ‘infinities’ nor singularities intrinsic to the formulation of Novelty Theory or to the mathematical construction of the current Timewave; i.e. the mathematics contains no features that include a division by zero. In fact, the Timewave fractal features are produced by an infinite series expansion, or fractal transformation, a mathematical operation that generates waveform data that decay to zero magnitude based on time remaining to the zero date/time - established as 6 a.m. on 12/21/2012. Although the rationale for aligning this fractal transformed waveform zero value to this zero date is somewhat vague, it was apparently done with some thought given to the ‘novelty fit’ of the Timewave time axis to other sections of the waveform. So it appears as though both the established waveform zero value, and its zero date temporal alignment we’re at the very least somewhat arbitrary, and certainly much more theoretical than empirical in nature. Nonetheless, it might be useful to fit the TW decaying fractal function with a decaying exponential function in order to explore an alternative plausible interpretation of the Timewave in the vicinity of the zero date.
It is important to note that the operative feature of an exponential decay function is its convergence to a zero-valued asymptote, meaning that the ‘zero point’ is actually not a point but an asymptote that is approached only as elapsed time approaches an extremely large value, or as t - something not achieved in the real world. The common analogy posits the question: ‘ how many steps would it take for one to cross a room if one were able to travel ¼ of the distance from one side to the other with each step.’ The proposed curve-fitting candidate for the aggregate Timewave graph would be the decaying exponential function expressed as
y = b*exp (-t/) ( 1 )Where: y = 0 is the zero entropy asymptote (zero entropy implies infinite novelty or information gain) that is approached as Timewave elapsed time approaches infinity, i.e. as t; b is the initial entropy (inverse novelty) state at time t0 = y (0); and is the system time constant or e-folding time (i.e. how long it takes for a selected novelty state (information state, or inverse entropy state) to change in magnitude by a factor of 2.71828 from its original value at a time, t1, to its’ value at a later time, t2. For an initial time, t0 = 0 (Timewave start date/time) this expression yields b * exp (0) = b*1, or simply b which is a novelty, information, or inverse entropy initial condition or state. Considering an elapsed time approaching infinity, t , we get the quantity y (b/∞) = (0), the zero entropy y-asymptote for this exponential function.
So let's examine the consequential results from our proposed exponential fit to the fractal Timewave graph. The information that interests us is how fast an established set of events changes with time. The mathematical operation for expressing this change rate is the time derivative of the decaying exponential fitting function – i.e. the time rate of change of the set of events for individual and collective processes at any given time, t – an operation that is clearly defined mathematically by the following differential expression,
dy/dt = -(b/)* exp(-t/) ( 2 )Where: the derivative, dy/dt, expresses the time rate at which a set of unspecified events unfolds, changes, or advances. This time rate of change of an individual or collective set of events (or process) could plausibly be correlated with one’s felt sense of an occurring time dilation (compression). Such time dilations would compress established time intervals for the set of events routinely occurring in our daily, weekly, or monthly lives. A temporal (time) compression would produce an experience in which an expanding set of individual or collective events occur in a given fixed time interval, ∆t, or it could produce an experience in which a set of fixed events occur in a an increasingly dilated (contracting or expanding) time interval; each creating the experienced perception of temporal contraction or expansion. This would mean that the normal sequence of daily events, chores, activities, etc. in one’s life would appear to be occurring over shorter and shorter time intervals; and the derivative dy/dt would define the process for such an event set mathematically.
A central issue here would naturally be how we actually determine or measure the time intervals that we perceive as progressively compressing or expanding (dilating). Can our ordinary house clocks be an absolute time standard, or can we use Earth’s rotation or stellar constellation cycles? Note that with whatever standard that we choose to use as a measure of time interval, it becomes relative to our perceived passage of time. All motion in space-time turns out to be relative, even the movement of our ‘internal’ perception of time. There are no preferred ‘inertial frames’, which means that we could perceive time interval ‘compression’, or time interval ‘expansion’ and we would have no way to verify our experience unless our reference frames remained fixed absolutes – which is precluded by fundamental principles of relativity. If we experience an expanded time interval between events, as measured by our external clock standards we cannot know if those standard clocks are also undergoing similar time dilations. Similarly, if we experience a compressed time interval between events, as measured by our external clock standards, we cannot know if those standards are also undergoing similar time dilations. Finally, if we experience a compressed time interval between events as measured by our ‘internal clocks,’ we still cannot know with confidence if our external standards are also undergoing compression or a similar dilation. The fact is that there is no absolute time standard that can be referred to, as there is no preferred reference frame in the cosmos. Consequently, the perceptions based on the local frame of our ‘internal clocks’ can arguably be taken as primary.
An examination of the result of this derivative operation as shown in equation (2) reveals the time rate at which the series of individual and collective entropy or novelty related events appear to pass as a function of elapsed time (y in this equation are the entropy/novelty values associated with the Timewave y-axis), at any given date and time. So as time, t, elapses (∆t) and increases to extremely large values from the t (0) = 0 initial state of the system, the time rate of change of novel or entropy associated events (perception of time passage), expressed by (2),
[dy/dt = -(b/)* exp(-/) = -(b/) * 0 = 0, for t]Which becomes vanishingly small as the Timewave approaches its zero entropy asymptote with t. Such a result suggests that events and time are interrelated by one of two processes: (1) an established fixed set of events is unfolding over continuously contracting time intervals; or (2) an increasingly smaller set of events is unfolding over an established fixed time interval, ∆t. In either case, to the observer, time appears to be accelerating in the sense that established time intervals are becoming increasingly shorter. Consequently, the time rate of change of process or unfolding set of events (ever fewer events occurring over a given time-span) would slow to a virtual stop for extreme elapsed times, approaching the actual entropy ‘zero asymptote’ as t. Interestingly, this does imply a temporal singularity of sorts, and there are similarities to general relativity and black hole event horizon physics; as the condition imposed on this process is that elapsed time approaches infinity, t. Fewer and fewer events experienced over the course of an established time period, ∆t, would very likely be perceived as a time compression or temporal acceleration.
In order to examine the effect of novelty changes (inverse entropy) on a given time span, ∆t), one can perform an inverse differentiation on equation (1). If the inverse derivative operation is performed, time dilation per unit of entropy (inverse novelty) change can be quantified as well. The result of this inverse derivative operation is expressed simply,
dt/dy = -/y, or alternately, dt = (-) dy/yWhich reveals an interesting result showing that the perceived time span, dt, for a given change in entropy, dy is compressed by a factor of (- * y-1), where y-1 is inverse entropy or novelty (novelty = 1/y or 1/entropy). So a perceived time span, ∆t, is being compressed by a factor of (- *novelty), or (- * information gain)
It turns out not to be necessary for one to invoke relativity or the Timewave resonance phenomenon to qualify (if not quantify) a felt sense of temporal acceleration (time dilation – compression or expansion). One’s sense of time is determined by the number of events or tasks that can be experienced over an established period of time, ∆t, under normal conditions. So if fewer events are experienced over an established fixed time frame, then the elapsed time, ∆t, is said to be compressed, dilated, or accelerated. Conversely, if a greater number of events or tasks can be experienced over a fixed time frame under normal conditions then the elapsed time, ∆t, is perceived as expanded, dilated (dilations work both ways), or decelerated. If the expression of the Timewave as established by Novelty Theory is truly a fractal temporal waveform that is converging to an asymptotic zero entropy state during any given evolutionary epoch (for a specified star system), then a plausible argument can be made that some type of phase transition rather than ‘end date’ is occurring. Such a phase transition could include a chaotic phase leading to an unknowable emergent state or paradigm that is inherent to complex systems. Such an emergent state, paradigm, or trajectory could conceivably include two or more 'bifurcations', or multiple distinctly separate emergent states, paradigmatic structures, or trajectories.
In order to tie all of this to the original query about how one could associate novelty/entropy concepts to the upcoming 'fiscal cliff,' I’ll apply principles derived from information theory. The so-called ‘fiscal cliff’ is a somewhat misleading concept foisted on the American populace by an increasing corrupt and unstable political system. As this system becomes more unstable and chaotic, information is lost and entropy increases. Additionally if such a system is becoming ever more calcified, very little additional information is gained, and its state of entropy moves ever closer to a chaotic collapse, disorder, and higher entropy. If a chaotic state does transition to some type of system collapse, then additional information (novelty) is lost and entropy again increases along with a corresponding increase in the number of possible emergent states – a probability distribution that is determined by the nature of a given collapse or disintegration. Information (novelty) is again gained when one or more of the ‘probable states’ emerges and becomes manifest. Emergence is a phenomenon, which is by definition, nearly impossible to predict (probability distribution of potential emergent states is very broad, and the emergent state is one with a low probability of occurrence) - so when 'emergence' does occur, there is a huge drop in entropy and a correspondingly large increase in Information or Novelty. Such a 'fiscal cliff' is only one feature of a complex reality that is undergoing a type of 'evolutionary metamorphosis.' Such a transformational process is highly unlikely to occur at a specific time on a specific date, although there may be some events (as I think there already are) that one could reasonably associate with such a 'phase transition'.
In summary, Novelty theory and its Timewave expression should be seen as both immature and incomplete. Additionally, the termination of the Timewave on a somewhat arbitrary ‘zero date’ must be seen as speculative at best. Moreover, Novelty Theory as proposed by McKenna contains no features that imply or state an historical ‘termination date.’ In view of these facts, I would argue that the Timewave is an incomplete expression of an immature theory of Novelty or Information. I would also argue that this particular type of ‘phase transition’ is most likely limited to our local star system in general, and perhaps even ‘collective subsets’ of our planetary system specifically. After all, any ‘evolutionary metamorphosis’ can only take place when the caterpillar ceases its environmental rampage, and falls into a pupation process of enzymatic dissolution. There is nothing in Novelty Theory that suggest or implies a termination singularity. In fact, Novelty Theory actually suggests otherwise, and that we may very well live in a cosmos where the creation and conservation of increasingly higher ordered states of complex form proceeds indefinitely through a expanding series of phase transitions. Here’s hoping.
