The New Orientation PDF

As far as I have been able to determine, there is no precedent for what Geocentric Design Code presents. Its connection to the tree of human thought, experience, and artifice is so tenuous that I have yet to find an easy way to say “it is like this, except . . . “ without folks responding with blank faces and eager to shift topics.

Because of this difficulty, I feel its formal detailed expression has to be just about perfect, as even the tiniest errors can distract from what is evidently a delicate logical path. And I can see this whenever I come back to a satisfyingly completed revision after an elapsed time and view what I have done more like what others would be presented with. In so doing, I inevitably find, along with nettlesome errors, a better way to portray the code, and as long as I do, the burden is on me to do so if it isn’t going anywhere.

So it is with the full 92-page PDF completed last November, with one tiny error like an “a” where there should have been an “an”, I set out for another revision and overhaul. As I proceeded to make the minor corrections, better ways of wording concepts came to mind that made them clearer and flow better with what came before and after.

With the first 9 of 13-pages of Part I (Orientation) just completed, that was all there was to it. But the last 4 pages dealing with attributes of the code’s geometric foundation (the cuboctahedron) were so piecemeal, ad hoc, strained, and convoluted, major reconstruction was called for and (I think) I have now succeeded in getting the most economic sequence of concepts possible, so that they build without sharp turns or backtracking.

The biggest change comes with bode wave generation at the end of the page (12) on geometric interplay. After much exploration described in the last post, I found I could expand the previous nominal and highly inadequate allusion to a 4 or 5 step climb to waves from the idea of intrinsic dynamism of spun cones.

Portrayed thus, the concept of wave generation melds with the essence of alternating bode pattern repetition on the final page of an indefinite accretion of spheres. And with that exploration, the idea of biasing the pattern with lines of spheres to give the quality of unending omnidirectional generation an order that eventually condenses to the geocentric cuboda.

As such, the sequence naturally concludes with the essences of pattern superimpositions to earth, an apt preparation for Part II cube-based abode architectural conceptualizations. All in all, the elegance of the code’s foundational geometry comes out more powerful than ever, and hopefully you find this so also.

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A Bode Wave Surprise

This post continues the effort described in a prior one which explored ways to abstract waveforms from bode geometry. The possibility of doing so was much encouraged by the ease with which the conic sections were derived from the interplay between bode manifestations – structural, planar, and spherical.

Octahedral gapWhat initially motivated my search was to find an elegant way of connecting opposing points of the octahedron. Because this form’s neighboring points are connected by spheres in material contact, so a more ethereal connection between those separated, something akin to the invisibly transmitted energy of electromagnetic waves, would seem possible. To find them, a fundamental relationship between two of the oldest known “irrational” numbers – √2 and π – would seem necessary.

Relative circular rotation of sphere/square relational pointsThe main ideas pertaining to waves in bode geometry noted in the prior post were: circular rotation of relational points (of contact) between intrinsically sectioned circles inscribed in equally intrinsic squares, where the circle is specified to have unit radius and angles subtending the point’s position equated to lengths of arc from a reference line – with graphs of the position projected onto either of the 2 rectilinear grid’s axes intrinsic to bode geometry characterized by waveforms.

The concept of the dynamically rotating square/circle relational point moving within a fixed square follows from the bodal shell rotation relative to the central sphere (earth), which relies on axes spanning midpoints of opposing innate bode elements.

Circular rotation in rectilinear context

By such abstraction, the arc length/angle finds ready correspondence to the natural world by ascribing it to the duration of time, a parameter inherent rotation. Aside from that, a better code expression of relative rotation between 2 squares lay in those common to the celestial co-cubes that guide the code’s salt-of-the-earth architectural style.

Beyond the correspondence to time, the prior post offered a much more speculative connection with regard to matter and electromagnetic waves derived from bode geometry and its inherent dynamisms. Whether or not the connections were made correctly, I do believe there is a relationship. However that may be, practical realization of the abstraction between bode circle-square dynamism and waves is found in the output of a circularly rotating element of opposing poles in the fixed stator of opposing alternator coils.

Wave friendly cuboctahedron

Otherwise, even if the wave is not intrinsic to bode geometry, a space-time fabric so characterized plausibly represents the medium through which waves spherically propagate; and furthermore poses a mechanism for shoaling when such waves come upon the slopes of bode planes (or lines in 2D portrayals).

Spherically sectioned ellipse projectionFinally, the prior post ends on the topic of ellipses and it is from this form that I report something new, at least for me. Ellipses are more fundamentally inherent to bode geometry than the other conic sections in that they don’t require rotation of a cone to be sectioned from. They can be made by planes slicing through the bode’s intrinsically omnipresent spheres, or from circles rotated about their diameters.

To explore ellipses in a possible wave context, also noted is a perhaps too obvious fundamental characteristic shared by bode and wave geometries: both repeat regularly and without limit, with the common element between their specific kinds of repetitiveness being the circle representative of the bode’s building unit and that which undergoes repeated regular rotation to form waves – the most elegant, economic transition between 2 parallel levels (also common to both geometries).

intrinsic cuboctahedron wave attributes

Looking more closely at spheres in the bode pattern, the fact of contact or relational points between a line of them is again noted. But in focusing upon one such sphere, the two diametric points that now define it can also be regarded as a bifurcated radius – or foci of an ellipse. So conceptualized, the ratio of horizontal to vertical axes (with the latter keyed to the original radius) is √2:1 – the one single number most characteristic of the square.

At this juncture, I mused about a relationship between the perimeter of such an ellipse and a wave of corresponding (slope) ratio but soon learned that arc length determinations for these curves are very difficult and impossible with the perfect precision of a neat expression. The surprise of this revelation also helped me to see why, in all my advanced math courses, the concept of curvature – which would seem to be both simple and very important – was not broached until a General Relativity – Cosmology elective, with the quickie explanation (w/o rigorous derivation) very unsatisfactory.

Before finding curvature formulas online, my approach was to toy with a combination of eyeballing computer graphic making and quasi-logical intuition (as I previously and dangerously did with waveforms) to make best (outside and in) guesses for the √2:1 ellipse with the hope of using them to find a simple perimeter expression.

Twin Ellipse curvatures

While doing this, however, I stumbled upon the (tentative) discovery that when the largest circles I could fit into the tighter curve of the horizontal axis extremes, they met at the mid point of the larger.

As I marveled at this development, there seemed something vaguely familiar about the relationship. The √2 squared = 2 was precisely what I found in the curvature of a waveform in which the maximum slope was also √2: 1. (Then I was seeking suitable cross-section placements for utility conduits in wave-formed berms).

Ellipse/wave curvature equivalence

To check to see if this was not a fluke, I applied the same method to a √3:1 ellipse (which I found uses the major √2:1 ellipse axis as the foci and signifies the number most associated with the triangle) and sure enough 3 (= √3 squared) seemed to fit perfectly and correspond to a wave of the same max slope.

Alas, verifying radius of curvatures with formulas found online meant the wave and the ellipse can both be scaled and shaped by the same specifications, and in alternative ways to those of the conventional wavelength/amplitude and major/minor axes used:

Alternative ellipse and wave specifications

For the wave, the (radius of) curvature and number of spheres or radius and maximum slope (ratio); and for the ellipse, radius of (tight) curvature sphere and number of spheres, or radii of tight curvature and reference sphere (or circumscribing radius of curvature sphere). So specified, the most obvious difference between the curves is that the ellipse is closed and the wave open.

As much as I like these results, the wave seems to merely be hinted at by these correlations but does not follow from them. Aside from the ratio/curvature relationship, I could find no deeper connection between the wave and the ellipse. No π. So I returned to the octahedral gap problem noted previously, and aligned the relational points of one cluster sphere toward the opposing sphere.

So oriented, the (radius of curvature) spheres of the generated ellipse reach to form’s midpoint, and since the same could be done from the opposing side, there was now a continuum of contacting spheres to bridge the gap (doing same for the hexagonal gap interestingly pegged centers of both originating and curvature spheres).

Joining opposing octahedral points

The whole notion that this spanning is effected is reinforced by joining the two spheres meeting at the midline with an identical ellipse to form a kind of chain. End to end it also posed a facsimile of a standing wave.

elliptical waves

When I treated the overlapping ellipses as a wave interference pattern, I determined with a little algebra that the peak constructive interference (amplitude) was √3. Although this interestingly evoked triangle geometry, a plot of key points and a lack of π in either height, length, or maximum slope told me this could not be a simple natural (sine) wave.

Cycloid ellipse comparisonI also tried working with cycloid geometry which is bounded identically to the simple wave ( π : 2 ) and which very much resembles (half of) an ellipse. As I failed to find the slope of its axis contact points online, I assumed 90º then proceeded to apply the cycloid’s proportion to the axes of an ellipse but found the focal point for the half latus rectum did not coincide with what the cycloid’s X-axis position for that y value. Alas, I said “uncle” and received consolation that the fact that what I was trying to do was essentially a variation of squaring the circle – a challenge that has vexed mathematicians for millennia.

Instead I found myself returning to a lone wave statement that concluded a brief sketch of bode intrinsic conic sections in the PDF and that cited spheric sections and cone slopes as sufficient elements for wave formation. The more I looked at it, the more I found the statement offering a good start and end to the matter – but greatly lacking in detail. Alas, I could now fill that in with all the recents efforts. The conic section of the circle is particularly relevant to wave generation because rotation is necessary for the cone’s rotation as opposed to the circle sectioned from a sphere which can undergo rotation independently of its surroundings but isn’t required to.

Rotating conic circle wave generation

Equally important are the relational points of contact between spheres, only one of which must necessarily situate on the rotating conic circle for tracking – with the relationship between its arc length (angle) and the shortest distance to an equally innate reference line passing through the circles center being a wave. Again, if this seems too much of an abstract reach between a circle and a wave, one only has to look at the relative rotation of bipolar magnet(s) to produce a wave-formed current in an alternator. For every contact point on the rotating contact circle there is an inherently opposing one.

Another reason for focusing on the rotating conic circle: the cone provides a slope that can be keyed to the wave’s maximum slope by focusing on the (tangent) ratio. After playing with the curvatures of waves and ellipses I had a problem with this because I thought the wave should be in their plane. But then I deemed this to be more of a picturing convenience, especially in light of how the angle is usually attributed to the practical matter of time.

Conic circle wave and ellipse generation

Directing the wave along the cone axis attunes to the pseudo axial vector, and if viewed as an EM wave, real electric and magnetic field vectors properly direct in the plane of the circle. So conceptualized, the cone slope ratios can be transposed to the concentric circles method of making ellipses where one circle is of unit radius. If the other is larger, the ellipse created is defined by the smaller of its 2 curvature circles; if the concentric circle is smaller, then it is defined by its larger curvature circle.

Either way these ellipses coincide with relational point ellipse generations, with both situating in the plane of the circle. Upon returning the circle to its spherical origin, the wave generated fits the curvature of the ellipses perfectly, which both being orthogonal, well signify the ocular mirror of the soul.

Elliptical Eyeball

 

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Doctoring of the Trinity

 

“The Trinity is either the most farcical doctrine invented by the early disciples or the most profound and thrilling mystery revealed by the Creator Himself” – CS Lewis

Over the last year or so, I have been wrestling with the doctrine of the Trinity, much because my skepticism precludes me from becoming a bona fide Christian. I want to believe because the denominations toward whom I have respect are believers, and because I feel at least some disdain for the anti-Trinity religion and most sects.

Another motivation pertains to the code at least tangentially, which is the reason I am posting this piece here, but this won’t come until later when addressing specific problems I have with the doctrine. Before proceeding I should clarify that one problem isn’t regarding the 3 entities in question as being holy.

IMG_1402The first problem arises from the doctrine’s traditional symbol. In artifice and nature, the triangle poses the simplest structure of stability. But when used to represent the Name of Love – God – it immediately comes off as being both divisive and restrictive. But believers who look to the symbol readily concede it doesn’t express all key aspects of the Trinity, and my “restrictive” first impression is easily dissolved by simply observing the “is not” labels to infer that the restricting lines do not really exist.

The main problem I have with the symbol speaks to the doctrine’s prime scriptural justification – that found in the “The Great Commission” of the Resurrected Jesus Christ at the end of Matthew: “in the name of the Father, the Son, and the Holy Spirit”. In my view the order and direction of these most powerful words are of upmost importance, but left out of the symbol make it more target than an aid.

The sequence (of the 3 principals) could easily be included in a line (Holy Spirit) extending from a point of origin (Father) and through a humbly situated middle (the Son) to potentially be the third and last experienced by those to whom the statement is addressed. In the distinctiveness of the 3 geometric entities’ correspondence to the distinctiveness of the 3 Entities they signify, note that no single one is describable without invoking the other(s). For a bonus, the symbol oriented vertically corresponds with the all but universal glyph for the number one.

IMG_1403

Notwithstanding the above elaboration, the line symbol obviously lacks the visual impact of the triangle. But upon reflection some of the former’s limitations speak to other key realities. If one is contemplating the symbol, one is not partaking of what it represents and to do so one must get in line. This one is straight and narrow, an attribute specified by Christ for those who follow Him; and if the delineating points scale to the line’s narrowness, such can aptly signify the eye of the needle a soul of rich self regard must eventually pass through to avoid eternal separation from God.

As the Holy Spirit paradoxically poses both a nebulous and an impossibly narrow entity in the proverbial haystack of infinite paths, to partake of it necessarily requires one to first meet the Son heart to heart, a prospect entirely within the reach of anyone. As promised, He does live and awaits your acceptance to share that life of boundless capacity throughout eternity.

This brings me to the matter of “persons”. The only “Person” I see in the Trinity is The Son, with application of the word’s origin to Christ literally making Him the Face of God. He certainly won the title in choosing to suffer red hot iron agony and humiliation in utter black interstellar cold alone – for others. As a flat plane, the triangle tends to lose the face by the relative indistinguishability of its 3 points, a factor that may have influenced the 3 persons idea. I cannot grasp a 3 person Trinity without a mother being one of them. In that light, it would seem the doctrinal concept of 3 Who’s in one What should be reversed with God being the general and Christ the specific Who, with the Father metaphorically so by His creative power.

Much of this may be semantics, but if my skepticism of the doctrine arises from valid grounds, the object of such might very well be yet another example of the time proven pitfall of symbols tending to replace that which they serve, which brings me to the third reason I want to believe the doctrine of the Trinity to be true.

IMG_1401

In conjunction with the 12-around-1 and omnipresent cross geometry of the code’s geometric foundation, the traditional symbol of the Trinity would lend a more sublime meaning to the form’s triangles. As tempting as this is however, I have to say no. Even if not a misfit, the 3-dimensionality of it would pose an even more powerful usurping tendency as described in a this previous post.

Finally, there is the pro-doctrine argument that God is Love (no dispute) and because love is relational, He must have an attribute of eternal plurality which scripture suggests by the use of Us. But in reading these passages over and over, I am inclined to tentatively conclude that the plurality refers to the angels of God, the spiritual beings of every possible good quality, who knew pride (and his allies) before their ejection, and who bowed to the essence of Love ruling supreme.

In a debate between christian Nabeel Qureshi and muslim Shakir Ally, the latter slices up the doctrine pretty well with his arguments until it comes to the love argument. Although I believe Dr Qureshi misapplies love to the doctrine to prove it, the passion of his assertion that God is LOVE draws a telling response from Dr Ally in which he (perhaps disingenuously) concedes love as a quality – just enough for him to avoid losing the battle on the matter of the Trinity, but far short of what would be required to win the war on what God is really like.

My views on all the above have been evolving and await a sound argument against them (perhaps from reading more CS Lewis). So at this juncture I cannot say with absolute certainty who doctors the Holy Trinity – early church thinkers, or me. However that may be, by their insistence I credit them for my having come to this point: That for us mortal human beings these 3 entities or aspects of the One God are the minimal essentials for our understanding of, and how we are to have a relationship with, Him.

As the 4th of July is upon us, I would like to take this opportunity to express my appreciation for being able to express views that would have got me totally ostracized, tortured or killed in past societies. In expressing my appreciation by using the freedom afforded me responsibly, the worst that can happen is to be labeled a cult (of one) by those I otherwise look up to – and I can live with that.

 

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Signs of the Times

In my recent travels I came across scenes and signs that are indicative of developing culture while pertaining to the biking and solar realms that provided key impetus behind the code’s initial development.

Perhaps you are familiar with the trend in paved recreation paths intended for walkers, joggers, and bikers amid urban green spaces. For the most part, I have observed civility between and among these users. I personally don’t care for the rare encounter I have with skaters who come at you like snakes ready to strike. However, a more frequent and disturbing encounter involves a subset of fellow bikers who seem to regard these paths as their own race tracks.

Tucson Recreation Path Warning

The near miss collisions of these wannabes around blind curves and user congestions, together with claims from elders who are frightened out of getting the benefits they need from these paths, and the above sign I came across along a dry river path in the Tucson, Arizona area tell me the problem is a growing one. This adds to the danger of ready rattlers during certain temperature ranges.

In a different locale, on a path snaking over the sand of a broad southern California beach, I came across a biker more like myself. His bike, parked just out of the picture below, was heavily loaded down, even without his solar array and sun shield. A number of questions came to my mind, but after asking permission to take the photo, I sensed he did not want to be taken further from his work, and so after sharing my opinion that more homeowners should follow his example, I left him to mouse away with his laptop in the shade.

SoCal Beach Solar

Although he was obviously homeless, I felt respect for how he was making the best of it and not demanding sympathy waiting for someone to give him something with or without a sign as many do. I don’t know why he needed that much area for his flexible panels or why he plopped them atop sparse vegetation. Although an eyesore, his set-up was not that much worse than many rooftop set-ups one sees these days. Finally, note how he compensates (intentionally or not, I don’t know) for the albedo degradation and global warming increase that the blackness of his panels causes with the white covering over his canopy.

Such concerns are lacking in the Paris Climate Agreement which President Trump announced he was pulling out of, and which will actually cause the  planet to heat up faster owing to its obsession with carbon while ignoring the kinetic aspect of it contribution, and the contributions of other energy sources.

Feynman Lecture Auditorium Entrance

If only the debate could receive input from Richard Feynman with his ability to get back to basic physics and the essence of the problem. The debate would be cover. Alas he is gone and his classroom empty* and the debate rages on with politics and big money driving it, instead of truth.

Feynman Lecture Auditorium

*thanks to the very gracious Cal Tech staff lady for offering me a peek at the room

 

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GDC by Field of Interest

The purpose of this post is to bring attention to a new “by field” link situated on this site’s navigation bar. What it leads to is a pathway by which architects and builders, or engineers and makers can get to the specific parts of the code that is most relevant to their particular interests.

Up till now, about the only way for one to get to those areas was to start at the beginning and slog one’s way through the code’s subject matter until arrival. In this age of instant gratification, such a prospect can be off-putting because code development entails a lot of abstract reasoning, and because there is a good chance some of that reasoning will first be applied to a construct or artifact far afield of what is sought to be given shape to.

The reason I put off the code-by-field approach is that in steering a designer directly to the relevant application, important context will then be missing. But I have come to think that that does not pose so much of a problem as one can always get that logical underpinning by simply going to the beginning. Hopefully, going directly to the application and its example first will spark enough interest to do so.

My next biggest concern about going straight to the relevant application is that the examples of such are necessarily the most simplified possible, and coming upon one a designer may conclude thats all there is to it. About all I can do in that case is to cross my fingers and assert once again that that is not the case as I did in the snowflake post, and by repeating that the built world’s seeming endless variety of 3D rectilinearity are but variations of the most simple cube.

The architectural functions listed in this new approach of accessing the code are residential; commercial; civic; institutional; industrial; agricultural; religious; and landscape. Engineering fields are civil; mechanical; aerospace; naval architecture; electrical; agricultural; and solar. Professions dealing with earth’s surface are urban planning; farm planting; and landscaping. Of course some overlap and a bit of redundancy is inevitable.

Finally, another page offers specific links to those who might, with no thought to application, be interested in the code’s abstract reasoning and its relevance to nature in the realms of math (geometry) and physics, respectively.

No specific links are provided for philosophers or artists because these can hypothetically start anywhere and appreciate the code’s simple underlying essence, its interplay of absolute and relative concepts, or how it poses a 3 (or 4) dimensional picture frame for the natural and manmade worlds – or not.

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