PES Tiles, v0.04.20170121
(20170210 note: This is the latest most complete start version for PES_Tiles. Near the end of this draft is the updated link where PES_Tiles continues. When an official destination will be the latest and most complete version, a link right here will point to it. This draft and its variants will remain here, because core values of the Fictioniverse based on #BAUniC)
Premises:
* Every exponential, even the lowliest exponential, will overtake every parabola, even the highest power parabola short of infinity, based on the same grid orientation.
* A parabola cannot touch the exponential from up. The exponential touching the parabola will always be over the parabola at the point of their meeting.
Part1: PES Tiny
We take the lowliest of exponentials (eg. 1.00000....00001^x; it should look like a flat line of value almost 1), and an even powered parabola (eg. x^2).
We displace the exponential to the parabola origin.
From this displacement we see the positive part of the exponential going over the x axis, and the negative part going under (fig001).
fig001
We rotate the exponential so that the x axis is tangential to the exponential (fig002). We see the exponential with both its 'up' side (the part with the knee of the curve) and 'down' side (the part that approaches x) pointing up in comparison to the grid of the parabola.
fig002
The rotation is finitesimaly small.
Zooming in to the junction point we are going to see a point where the parabola, being flatter than the exponential, goes under it (fig003, and exaggerated in fig004).
fig003
fig004
The junction in fig004 has 3 points of touching between the exponential and the parabola, 2 crossing and 1 touching (with the exponential up)
If we displace the exponential down, we see the middle touch splitting into 2 crossings, for a total of 4 (fig005).
fig005
Further displacement has the crossings on either side come closer to 'annihilate' each other. At their most touch-like point we are met with a similar situation to the one we started with: a parabola trying to touch the exponential from up.
At the 4 point crossing (fig005) we take the liberty to change the parameters (vertical/horizontal stretch+displacement, and a bit of rotation adjustment) so that we end up with 'segments' of the desired size. We start with segments of size 1, 1 and 2 (fig006).
fig006
Here we can overlay a sinusoid of desired specifications to match this gap (fig007).
fig007
This structure we call PES Tiny (para-expo-sin at the finitesimaly small)
Part2: PES Tunnel
The 'flat' exponential at fig001 will grow bigger than the parabola (fig008, fig009 and fig010).
fig008
fig009
fig010
Within the confines of the PES Tiny and the adjustments we allow with a sufficiently finitesimally small gap, we can fit the quality of exponentials overtaking parabolas.
Here we can fine tune the PES Tiny parameters to achieve a few resonating combinations of parabolas, exponentials and sinusoids at the point where the exponential overtakes the parabola. For example a spiral-like form.
We can craft an exponential to pass through any finite gap in between 2 displaced parabolas, matching the PES Tiny parameters.
This combination we call PES Tunnel.
While all parabolas will be overtaken by the exponential on the same grid rotation, any rotation, even the tiny ones, will void that. For the chosen rotation, we get fig011 & fig012. We could get a rotation of no tunnel for the same rotation, or the exponential crossing the other arm of the parabola (along with the grid oriented for the parabola) for a rotation on the other side (fig013, fig014 & fig015).
fig011
fig012
fig013
fig014
fig015
These rotations and displacements will be important in the combination of various PES Tiles, displacements, and parabola powers. Especially the x^odd and x^even for powers of +-1 and +-2, and their +- infinity along the x axis of the base grid.
Part3: PES Tiles
For a quasi-identical PES Tiny segment, we can rotate the parabola/expo to each other so that the corresponding PES Tunnels are adjacent based on the sinusoid and tempo in PES Tiny, with minor horizontal or vertical displacements (base grid horizontal and base grid vertical displacements, since displacements could be relative to the parts, eg. up/down the PES Tunnel following the parabola or the exponential). fig016, fig017, fig018 and fig019.
fig016
fig017
fig018
fig019
For ease of communication we will assume the exponential y growing on the positive x axis, clockwise rotated parabolas (CRP?) having 1 crossing with the exponential on the PES Tunnel with no further interceptions on that arm up (their 6th point of interception would be on the other arm; 4 points on the PES Tiny + 1 point on the PES Tile + 1 point on the other arm), and anticlockwise rotated parabola (ARP?) having its 6th point further up on the same arm as the 5th crossing on the PES Tunnel (fig020 to fig030).
fig020
fig021
fig022
fig023
fig024
fig025
fig026
fig027
fig028
fig029
fig030
To aid representation, understanding, and mental models, the parabolas and exponentials in fig030 will be represented using symbols as in fig031.
fig031
The rate with which these functions grow makes it hard to imagine, therefore the need to use symbols, and even to include the text in the photos to imagine the zoom-out, considering a form of exponential representation is the zoom-out itself.
To help visualization, the exponential zoom-out for fig032 is pressed vertically at twice the rate of horizontal. The elements are also artistically exaggerated, preparing the ground for a higher power parabola to be shown in relation to the existing components.
A zoom out like that is represented in fig033 to fig085.
We start to differentiate the rotation on x^3 at fig040.
Despite growing to almost base grid in relation to higher parabolas, lower power parabolas have well defined and appreciated effects on the PES structure (fig041 to fig049).
We start to zoom-out at same-rate again at fig047, since the exponential zoom-out horizontally has spread out the parabolas to what does not resemble their natural ratio of growth by comparison, and the differential zoom-out rate was meant to help imagination, not confuse it. This is the effect of exponential growth for you (and us).
At fig072 we resume zooming out with 'pressing' vertically at twice the rate of horizontal, preparing for a x^4 representative of positive parabola powers.
A PES Tile is a parabola of the same power, displaced along the exponential, on the same step as the sinusoid connecting their PES Tiny with their PES Tunnel (fig086).
This allows the tiles to be connected in a coherent way on a displacement and rotation, with effects of overlay of their sinusoids and the addition/multiplication consequences of getting the values from PES and assigning constructive/destructive interference as extra meaning upon those values.
PES_Tiles v.04.20170121 notes
fig110: They are called 'Tunnels' because they are a unique exception in between 6p_para and 5p+1p_para
fig125: the point where parabola crosses inversely rotated parabola is close to the grid's vertical axis, therefore represented in perspective
fig127: If we align phases of a sinusoid of size PES_Tiny to the parabolas, and amplitudes to the exponential (or vice versa), we can see emergent phenomena of the type 'bubble conditions', 'expand conditions' and 'edge conditions'. In bubble conditions we can see "quasi 1/(x^(D-1))" pendence. In expand conditions we can see "quasi 1/(x^(D+1))" pendence. They are in relation to each other as the electron field is in relation to the quark field, or as branes are to each other at the "bang" (not short of 'Big Bang', but meaning something similar to the classical Big Bang of e=mc2 physics.)
5p+1_para crossing 5p_+1power_para
whether this comes before or after the crossing of the expo needs to be reasoned through, in the search for familiar territories such as lightspeed or assumed unfamiliar territories such as 'Uber Time'
All the 1D sinusoids based on PES_Tiny and grid, can be represented in Fourier overlays of infinite sinusoids with the desired amplitude and phase, with amplitude being itself an overlay based on rate of occurrence (not frequency) probability of occurrence to bring it to classical terms.
This goes hand in hand with the concept of the "Wave Function Never Collapses" (WFNC or wfnc) of Hugh Everett III. We have 'no problems' adding horizontally PES_Tiles synchronized on PES_Tiny scale. ('no problems' as in a way of saying, close to 'nothing stopping us', conceptual type,, since we do have problems of the practical difficulty type reaching this point of understanding to begin with, and to find the proper equations to address it and then represent it in code).
Zoom-to scale are part of the coordinates, otherwise they would all look like vertical lines compared to our classical understanding. 1D wfnc also has to be represented in variable coordinates, else the lower parabola intriguing points would be represented as a bunch of clustered points compared to extremely far points of interest of higher power parabolas.
fig147: If we stop chasing the fold points, they still fold, off the render window, and their effects are observable.
fig160: Food for thought: Parabolic zoom? When the rate of zoom change is not an equal or constant?
fig164: The gradient of parabolas is eternally approaching the PES_Tunnel, never quite reaching it, except at the edge conditions right adjacent to the unique 5p. The adjacent +-1 PES_Tiny_Step are the tunnel walls, while the 5p represents a form of perfect/impossible equilibrium.
fig170: Displacement of odd-pow-para has a different tune than displacement of even-pow-para. The sin-like of their power when not at zero, almost as if the sin that wraps around the full sinusoid between parallel lines.
Between PES_Tunnels we can craft an exponential that passes between any 2 displaced parabolas.
Continues here:
baunic-movie.blogspot.com/2017/02/pestiles-v00720170228.html
-Work in progress.-
Expectation: Between the PES Tunnel and the infinity upward, there are vibrational resonances that can be representative of electron field, photon (omniphoton), space/distance (black hole), branes (as in membranes in M theory), Sheppard tones representing eternal fall, a self-emergent grid of 3+1 dimensions of the micro-macro collapse-expansion of a form similar to "1.2.3:4.8.12:16.32.48:64.128.192:256.512.:..:..". The size of these graphs is enough to contain all Feynman diagrams for not only our cosmos folded at spacetime quants, but a multiverse of such cosmoses in familiar and unfamiliar physics.
Taking inspiration from nature, looking to find patterns we are familiar with (eg. t or -t, force, distance, lightspeed, etc.) within the vibrations of PES Tunnels in bigger grids composed of PES Tiles, filled with what could be seen as paradoxes from the point of view of the regular grid, but perfectly consistent within the limitations we are choosing.
Part4: The physics dimensional structure;
Part5: The physics multiverse crystal;
Part6: The physics universe, the emergence of time;
Part3: PES Tiles
For a quasi-identical PES Tiny segment, we can rotate the parabola/expo to each other so that the corresponding PES Tunnels are adjacent based on the sinusoid and tempo in PES Tiny, with minor horizontal or vertical displacements (base grid horizontal and base grid vertical displacements, since displacements could be relative to the parts, eg. up/down the PES Tunnel following the parabola or the exponential). fig016, fig017, fig018 and fig019.
fig016
fig017
fig018
fig019For ease of communication we will assume the exponential y growing on the positive x axis, clockwise rotated parabolas (CRP?) having 1 crossing with the exponential on the PES Tunnel with no further interceptions on that arm up (their 6th point of interception would be on the other arm; 4 points on the PES Tiny + 1 point on the PES Tile + 1 point on the other arm), and anticlockwise rotated parabola (ARP?) having its 6th point further up on the same arm as the 5th crossing on the PES Tunnel (fig020 to fig030).
fig020
fig021
fig022
fig023
fig024
fig025
fig026
fig027
fig028
fig029
fig030To aid representation, understanding, and mental models, the parabolas and exponentials in fig030 will be represented using symbols as in fig031.
fig031
A zoom out like that is represented in fig033 to fig085.
We start to differentiate the rotation on x^3 at fig040.
Despite growing to almost base grid in relation to higher parabolas, lower power parabolas have well defined and appreciated effects on the PES structure (fig041 to fig049).
We start to zoom-out at same-rate again at fig047, since the exponential zoom-out horizontally has spread out the parabolas to what does not resemble their natural ratio of growth by comparison, and the differential zoom-out rate was meant to help imagination, not confuse it. This is the effect of exponential growth for you (and us).
At fig072 we resume zooming out with 'pressing' vertically at twice the rate of horizontal, preparing for a x^4 representative of positive parabola powers.
A PES Tile is a parabola of the same power, displaced along the exponential, on the same step as the sinusoid connecting their PES Tiny with their PES Tunnel (fig086).
This allows the tiles to be connected in a coherent way on a displacement and rotation, with effects of overlay of their sinusoids and the addition/multiplication consequences of getting the values from PES and assigning constructive/destructive interference as extra meaning upon those values.
PES_Tiles v.04.20170121 notes
fig110: They are called 'Tunnels' because they are a unique exception in between 6p_para and 5p+1p_para
fig125: the point where parabola crosses inversely rotated parabola is close to the grid's vertical axis, therefore represented in perspective
fig127: If we align phases of a sinusoid of size PES_Tiny to the parabolas, and amplitudes to the exponential (or vice versa), we can see emergent phenomena of the type 'bubble conditions', 'expand conditions' and 'edge conditions'. In bubble conditions we can see "quasi 1/(x^(D-1))" pendence. In expand conditions we can see "quasi 1/(x^(D+1))" pendence. They are in relation to each other as the electron field is in relation to the quark field, or as branes are to each other at the "bang" (not short of 'Big Bang', but meaning something similar to the classical Big Bang of e=mc2 physics.)
5p+1_para crossing 5p_+1power_para
whether this comes before or after the crossing of the expo needs to be reasoned through, in the search for familiar territories such as lightspeed or assumed unfamiliar territories such as 'Uber Time'
All the 1D sinusoids based on PES_Tiny and grid, can be represented in Fourier overlays of infinite sinusoids with the desired amplitude and phase, with amplitude being itself an overlay based on rate of occurrence (not frequency) probability of occurrence to bring it to classical terms.
This goes hand in hand with the concept of the "Wave Function Never Collapses" (WFNC or wfnc) of Hugh Everett III. We have 'no problems' adding horizontally PES_Tiles synchronized on PES_Tiny scale. ('no problems' as in a way of saying, close to 'nothing stopping us', conceptual type,, since we do have problems of the practical difficulty type reaching this point of understanding to begin with, and to find the proper equations to address it and then represent it in code).
Zoom-to scale are part of the coordinates, otherwise they would all look like vertical lines compared to our classical understanding. 1D wfnc also has to be represented in variable coordinates, else the lower parabola intriguing points would be represented as a bunch of clustered points compared to extremely far points of interest of higher power parabolas.
fig147: If we stop chasing the fold points, they still fold, off the render window, and their effects are observable.
fig160: Food for thought: Parabolic zoom? When the rate of zoom change is not an equal or constant?
fig164: The gradient of parabolas is eternally approaching the PES_Tunnel, never quite reaching it, except at the edge conditions right adjacent to the unique 5p. The adjacent +-1 PES_Tiny_Step are the tunnel walls, while the 5p represents a form of perfect/impossible equilibrium.
fig170: Displacement of odd-pow-para has a different tune than displacement of even-pow-para. The sin-like of their power when not at zero, almost as if the sin that wraps around the full sinusoid between parallel lines.
Between PES_Tunnels we can craft an exponential that passes between any 2 displaced parabolas.
Continues here:
baunic-movie.blogspot.com/2017/02/pestiles-v00720170228.html
-Work in progress.-
Expectation: Between the PES Tunnel and the infinity upward, there are vibrational resonances that can be representative of electron field, photon (omniphoton), space/distance (black hole), branes (as in membranes in M theory), Sheppard tones representing eternal fall, a self-emergent grid of 3+1 dimensions of the micro-macro collapse-expansion of a form similar to "1.2.3:4.8.12:16.32.48:64.128.192:256.512.:..:..". The size of these graphs is enough to contain all Feynman diagrams for not only our cosmos folded at spacetime quants, but a multiverse of such cosmoses in familiar and unfamiliar physics.
Taking inspiration from nature, looking to find patterns we are familiar with (eg. t or -t, force, distance, lightspeed, etc.) within the vibrations of PES Tunnels in bigger grids composed of PES Tiles, filled with what could be seen as paradoxes from the point of view of the regular grid, but perfectly consistent within the limitations we are choosing.
Part4: The physics dimensional structure;
Part5: The physics multiverse crystal;
Part6: The physics universe, the emergence of time;
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