Home Science Page Data Stream Momentum Directionals Root Beings The Experiment
The Graph below illustrates the potential impact of different Data points upon Unravelings, Q = 2->4, and upon the Directionals, P= 0->2. (For illustration we let the Decay Factor, D, =12 in this graph). {See derivation in the Appendix.}
Note that the sum of the area underneath each of the lines in the above graph equals one, because one is the total impact upon the measure, be it directional or unraveling. So the graph can be read two ways. It can be read that each successive point's potential impact upon the measure is represented by the vertical axis or it can be read that as the potential impact of the Data Event over time. It represents the whole potential impact upon the measure of all the data. Or it represents the potential impact of the one piece of data over all time. One Data over all Time. Or All the Data at one moment in Time. It is the same, in this case. So we can say, from the green line, that a piece of data has its greatest impact on the 3rd unraveling after 12 moments of time, after it has decayed 12 times. Or we could say that the 12th data point after the present has the greatest impact upon the 3rd Unraveling. One Point over all time or all points at one moment.
More explication: each graph can be looked at in two ways. First they can be viewed as the concentration of past data influence upon the present, the Now. This is the makeup, the structure, of the derivatives of XN, the Now. They chart the potential impact of each piece of Data. We see the accumulation of all the data. We'll see that each piece of Data is scaled down with each separation from the Present. This is Decay from the Past. This is a vision from Now into the Past. Second the graphs can be looked at as potential impact of Now upon the Future. The energy comes in on a certain dimension and then is scaled down with each step into the future. Decay into the Future. They can be looked at as the Past's influence upon the Present or as the Present's influence on the Future. They are one and the same. The Now is the dividing line between Past and Future. Each Data Point back to beginning of non-existence has decayed to this point of Now. This point and all that led up to it begin Decaying at the same rate into the Future.
The 2nd unraveling, the zeroth Directional and the Decaying Average are the same. The red line represents the potential impact of successive Data bits upon the Decaying Average. This is a nice logarithmic curve, scaled, successively down. See the following graph for the logarithmic representation. Our Decaying Average is logarithmic in nature. The potential impact of the Data maximizes immediately and then falls logarithmically with the slope of the line equal to -K, which equals the scaling factor, (D-1)/D; D being the Decay Factor. This is not surprising because Decay tends to be logarithmic, shrinking that which is proportionally, rather than which went before.
The green line represents the third unraveling. The bell shape at the beginning shows that the most recent data doesn't have the greatest potential impact upon the second unraveling, but that instead its potential impact grows rapidly after its occurrence, N=0, until it peaks when N=12. Then its impact gradually falls after this point. This is quite different from the green Decaying Average line, whose impact hits and then decays. It is like a hit, which is immediate, and whose impact wears off over time. This influence is like coming into contact with poison oak or getting bitten by a mosquito. The initial impact is nothing, but then the influence of the poison in the plant or bite grows over time, and then gradually fades away.
The blue line represents the potential impact upon the first directional, the Change Vector. (The 1st Deviational is the Change Scalar.) It is the difference between the present unraveled twice and the previous unraveled thrice, three times. Thus the blue line is a combination of the red and green line. The blue line is a much flatter line than is the red line, which is the zeroth directional. The impact is immediate and begins decaying, but much more slowly due to the influence of the green line, the 3rd unraveling
The yellow line represents the potential impact of the data upon the 4th Unraveling. It is very similar to the green line, the third unraveling, except that its rise is even slower, it doesn't reach as high, and it falls more slowly. This is another Poison Oak type influence, where the immediate impact is delayed.
The Pink Line represents the potential impact of the data upon the 2nd Directional, the Acceleration Vector. It equals the sum of the 2nd & 4th Unraveling subtracted from twice the 3rd Unraveling. Thus the impact is spread equally between these four measures. Hence the pink line is a combination of the blue, green and yellow lines. It starts higher, than the Unraveling lines, rises a little bit and then falls. From a casual inspection of the line, it looks like the potential impact of the first 24 data points is between 2% and 3% each. The residual impact of the Data Points comes from the higher unravelings as seen in the above lines. It is as if the energy from the immediate impact is stored and then released over time.
The X-Axis represents the first five Directionals: the zeroth Directional on the left, the fourth Directional on the right. The Y-Axis represents the cumulative potential impact of successive pieces of Data upon the Directionals, the most recent at the bottom, the least recent at the top. In this example D, the Decay Factor, equals 12. We used the first 100 Data Points. Note that the first 100 Data points doesn't quite approximate 100% for the 4th Directional.
It is clear from this graph that as the number of the Directional, P, increases that the impact of each piece of Data becomes more equally distributed. On the zeroth Directional the black density at the top absorbs the 30th Data Point; the first 29 Data Points contribute over 90% of the potential Impact. By the 4th Directional, P=4, following the white line down, the first 30 data points have barely contributed 50% of the potential impact. Also the impact of the most recent data is minimized, with greater impact being given to the preceding Data.
Remember that the Directionals are made up of different combinations of Raveled Data. Below is a graph of the potential impact of the 100 most recent Data Points on 5 different levels of Raveling. The parameters are similar to graph above except that the X-axis represents 5 levels of raveling instead of Directionals. Note that the zeroth Directional is the 2nd level of Raveling, is the Decaying Average, is the Fractal Root Equation. Such an interconnected system.
Here the decline in impact is even more dramatic as the level of raveling increases. The data that contributes over 90% potential impact to the 2nd level of raveling barely contributes 10% to the 6th level of raveling. All the major contributors have been reduced to the black density at the bottom right of the graph. The broad middle assumes most of the impact by the 6th level of Raveling. Note also that by the 4th level of raveling that 100 Data points are not enough to approximate 100% of the impact.
Below is a graph that shows the potential impact of each individual data point upon the Directionals. The Y-Axis represents the % potential impact of the individual Data Points. The X-Axis represents the Data Points from 0 to 100, with 0 being the most recent, N, and 100 being the least recent, N-100. The lines are the different Directionals
Note that for the zeroth and 1st Directional that the greatest impact comes from the most recent Data and that it falls from there. The impact is immediate and then fades over time. In the subsequent Directionals the impact of the most recent Data is lower and then rises over time. The impact is delayed immediately and then comes on stronger later. This is the Energy absorption cycle that we will mention soon.
Below is the same graph as above except that the Y-axis has a logarithmic scale. Note that the zeroth Directional is a straight line, revealing that the zeroth Directional, or the Decaying Average, or the Fractal Root Equation, is a logarithmic Decay Function. It is scaled discontinuously rather than diminished continuously. The rest of the measures, after playing around for the first few points, also fall into a logarithmic decay.
Below is a graph that shows the potential impact of each individual data point upon the Unravelings. The Y-Axis represents the % potential impact of the individual Data Points. The X-Axis represents the Data Points from 0 to 100, with 0 being the most recent, N, and 100 being the least recent, N-100. The lines represent the potential impact on the different Unravelings.
It is easy to see that from the third level of unraveling on down that the impact of the various data points is delayed more and more. For the 6th level of Unraveling the data's impact doesn't reach its peak until 50 time sequences past its occurrence. Only with the 2nd level of unraveling does the impact hit and then decay logarithmically. The rest hit softly and then grow in influence.
This is the same graph as above except that the Y-Axis is logarithmic. Once again the different measures play around a little before hitting their logarithmic decay. Each of the successive unravelings begins lower than the one before, doesn't rise as high, and then decays much more slowly. The higher the Unraveling level, i.e., the greater the Q, the more spread out is the impact of individual pieces of Data.
All these Unravelings are successively combined in different proportions to make the Directionals. Hence the Directionals are not quite as extreme in their manifestations as the Ravelings. The Directionals don't start as low. Their peak is a little gentler and they decline a little more quickly than their corresponding level of Unraveling. This gives the most recent Data a greater Impact on the Directionals than it has on the Ravelings. {See graph above.}
Below is a practical graph, designed to help choose an appropriate decay factor, D. The X-Axis represents different decay factors, chosen for illustration. The Y-axis represents the cumulative percent potential impact of the 100 most recent Data Points upon the various measures.
It is easy to see that as D, the Decay Factor, gets larger
it takes more and more Data Points to approximate 100% of the potential impact.
Also it is plain to see that the Raveled numbers are more severely affected by
this phenomenon than are the Directionals. When D=50 and Q=6 not even 10% of
the potential impact is included in the first 100 Datazs? e5qw5x=F1|/~8n? ]> e @v-fuuKP,MީNwl_-P*h=;e0s
qXWxlQ^u V|&@OB-vQRDbgmP!C~+G4?=,8繞GY%MGAG $qV!nb<)W٩l^!sDZ҇7o.p#V8 IDATw\fH!*͑7mΈP~<BĄ7S