Prepared in the light of the Joint Hearing of the US Commerce, Science and Transportation Committee
with the Senate Judiciary Committee
entitled "Facebook, Social Media Privacy, and the Use and Abuse of Data" (Washington DC, 10 April 2018).
followed by a hearing before the House Energy and Commerce Committee
The following questions can be considered in the light of widely disseminated video coverage of the hearings, a transcript, and the extensive range of commentaries made about the process (see References). It is noteworthy, for example, that many of those represented at the hearings admitted to being Facebook users and had received campaign funds from Facebook (as well as other tech companies). The hearings had been primarily triggered by controversy aroused by alleged Russian interference in the US presidential elections of 2016 and by the role of Cambridge Analytica in the misuse of Facebook data on 87 million people. Concerns were also expressed regarding unforeseen misuse of Facebook by the campaigns of US presidential candidates (Barack Obama on social media; Donald Trump on social media).
Requisite variety of questions? The many hours of hearings over two days will give rise to hundreds of pages of transcribed official records. It is necessarily difficult to isolate points of focus, although the references indicated below are attempts by many commentators to do so. The exercise above endeavours to provide a focus through a set of questions -- a number of which feature variously in those references. Why 30? This is necessarily an arbitrary number, as with the much smaller numbers of questions which feature in some of those references. The selection of questions is also necessarily arbitrary and open to challenge.
The assumption here is however that a larger number of focal questions is consistent with the quest for the requisite variety to encompass the systemic complexity and preoccupations evoked during the hearings. By comparison, it is appropriate to note that the Universal Declaration of Human Rights consists of 30 articles affirming an individual's rights -- not 5 or 10. Rather than the closure implied by such "articles" in legalese, use is made here of "questions" as a means of evoking further reflection. This approach was previously applied to the terrorism which is such a preoccupation of security services and Facebook (30 Questions for the Counter-terrorism Experts of the World: raising the question as to why they are not effectively addressed, 2017).
Confusing multiplicity of "faces"? Lengthy checklists, whether "bullet-points", articles or questions, are increasingly alienating. This is most notable with respect to comprehension of any systemic whole, whose elusive nature they may be optimistically assumed to imply. Ironically it can be argued that Facebook has many "faces", which would then call for their more integrative representation. These can be variously understood in terms of:
Curiously the hearings made almost no use of illustrations to enhance comprehension of those "facets" of the underlying nature of Facebook as a whole. More curiously, given the vast range of animations which are so characteristic of content on Facebook, no such animations were employed in the hearings.
How indeed are people to be expected to "get their head around Facebook"?
Animation -- and Facebook dynamics? There is therefore a strange sense in which the final comment to the Roman Catholic Inquisition of Galileo Galilei regarding movement calls for speculative consideration with respect to the absence of a new understanding of movement during the hearings. This is a new form of movement which Facebook enables. Paradoxically there is however a sense in which Facebook is itself complicit in a static representation of its various faces -- a "frozen" face, or "veiled" -- to the point of reinforcing any sense of its "superficiality".
Exploiting the play on words, there is a case for recognizing that the "soul" or "spirit" of Facebook -- anima in Latin -- would be understood to a greater degree through "animation", one which it is so central to enabling. In contast with the stasis characteristic of the conventional hearings, Mark Zuckerberg might well have framed his confrontation there from the contrasting perspective of E pur si Muove -- or so it might be seen by the future.
Mapping the whole in movement: This argument justifies the following experimental mapping of the 30 questions above onto the 30 faces of a polyhedron -- a rhombic triacontahedron, for example -- with spherically symmetrical properties suggesting its integrative nature. Such a form can best be understood through rotational movement.
The mapping is necessarily arbitrary, for purposes of illustration, but suggests the possibility of refinement (with the aid of AI) to augment its integrative systemic significance -- and its comprehensibility through symmetry and other effects.
Use of a spherically symmetrical polyhedron for such a mapping has previously been made with respect to the articles of various charters of human rights (Dynamic Exploration of Value Configurations: polyhedral animation of conventional value frameworks, 2008). In that case use was made of a rhombicuboctahedron and a rhombicosidodecahedron to indicate -- through the gometry -- a degree of complementarity between the identified values of the 30 articles of the Univeral Declaration of Human Rights, the 18 articles of the European Convention on Human Rights, and the 53 articles of the Arab Charter on Human Rights.
|Animation of mappings of Facebook questions onto a polyhedron and its dual|
|Mapping of questions onto 30 faces
of rhombic triacontahedron
|Mapping of questions onto 30 vertices
of icosidodecahedron (faces transparent)
|Animations prepared using Stella Polyhedron Navigator|
Curiously the global representation (above left) clarifies the extent to which any such configuration of faces necessarily has a "hidden" hemisphere from any given perspective -- a set of faces only revealed by rotation. The image on the right suggests a form of transparency in this regard -- however this may be interpreted.
Another approach to visualization can be taken through unfolding the polyhedron into a flat presentation as shown below. For purposes of illustration and education, the 2D variant can then be cut out and folded back to form the 3D version -- as might be done for future hearings.
|Screen shots of stages in unfolding the mapping of 30 Facebook questions onto a rhombic triacontahedron -- from 3D to 2D|
|Animated version. Tabbed 2D version (cut-out and fold).
Prepared using Stella Polyhedron Navigator.
Implicit face framing in discourse by explicit points and lines: The Q and A process of the hearings and testimony could be understood as one which lends itself to discourse analysis in its own right, and this may well be done, given the significance of the event. Although a live transcription of the hearings was evidently made, it is unclear to whom the resulting text might have been made immediately available -- as has been a practice in web dissemination of plenary meetings of ICANN. This clearly meets a need for the hearing-challenged as well as enabling online (automatic) translation to other languages. It is a service that might have been offered by Google, if not Facebook. [Somewhat ironically, ICANN has a key contract for Internet governance with the government agency for which the bodies holding the Facebook hearings provide oversight -- namely the US Department of Commerce]
Missing however was any process whereby the points made, together with the lines of inquiry, could be immediately incorporated into some form of map for general display, for the personal screens of those present, and for wider dissemination -- as has long been technically possible (Complementary Knowledge Analysis / Mapping Process, 2006). The absence of any such mapping of the content of many hours of hearings undermined -- for all concerned -- any overall comprehension of the pattern of issues implied by the long sequence of questions and answers.
Such a transcript would have lent itself to immediate processing by content analysis software applications such as Leximancer. This operates under th slogan "text in -- insight out" -- one from which the hearings could well have benefitted. This (AI) machine learning technique determines the main concepts in a text and how they relate to each other. It conducts a thematic analysis and a relational (or semantic) analysis of the discourse. It provides a method for transforming lexical co-occurrence information from natural language into semantic patterns or maps in an unsupervised manner. The algorithms used are statistical, but they employ nonlinear dynamics.
By contrast it can be argued that the hearings constituted an exercise in "skating" over the surface of concern, temporally highlighting points of preoccupation, briefly pursuing lines of argument, readily forgotten. Whilst the points and lines might variously converge, most obvious was the level of repetition in repeatedly traversing the same terrain -- in the absence of any map accumulating the points of focus and fields of concern.
In thereby exemplifying the superficial, it was consistent with questionable metaphors noted above with respect to Facebook -- notably the need for all concerned to "look good" for the audience, to "keep up appearances", and to "avoid losing face". Any sense of an accumulating overview -- a configuration of viewpoints and lines of argument -- was lost as the hearings progressed. To the extent that networks of points and lines define areas of concern -- potentially to be framed as "facets", if not "faces" -- these too were lost.
Metaphorical uses of points and lines: Of considerable potential interest is the metaphorical role of points and lines in discourse, also discussed under the following headings in relation to other means of framing and holding insight (Point and line considerations in discourse mapping, 2015; Experience of Cognitive Implication in Fundamental Geometry: unexamined metaphoric framing of strategic discourse, 2012; Cognitive Realignment: making points and aligning a target, 2009):
|Comprehension framed by "Point"
Comprehension framed by "Line"
Comprehension framed by polygons: "Triangle", "Square", etc
Comprehension framed by "Circle"
|Comprehension framed by "Cylinder"
Comprehension framed by polyhedra: "Tetrahedron", "Cube", etc
Comprehension framed by "Sphere"
Comprehension framed by "Torus"
Point is extensively used with regard to making a point and clarification of a viewpoint, for example. It is a common feature of presentations as "bullet points". It is typically expected that points are configured in terms of a line of argument which can be followed, with several such lines framing a more general field of concern -- a "face". In psychosocial settings, notably in the language of electronically enabled discourse, use may be made of node rather than point, and of link rather than line. The sense of non sequitur (of fundamental concern to the coherence of an argument) may then be partially understood in terms of "following" (or not), as in social media.
Of further relevance is the transformation of points and lines into legal and strategic discourse, as with the points in a declaration or plan, and adaptation of lines into "pillars", as is typical of the language of the European Union with regard to strategic principles (Coherent Value Frameworks: pillar-ization, polarization and polyhedral frames of reference, 2008; Symbolic stars vs Strategic pillars; Polyhedra vs Helices; Logic vs Comprehension? 2017).
The strategic potential of this array of metaphorical possibilities is evident from current international preoccupation with the The Triple Helix concept with respect to the Triple Helix model of innovation, as notably promoted by the Triple Helix Association.
How might Facebook's declaration of principles be rendered more comprehensible in such a light? How might the use of AI facilitate the process of using such conceptual geometry in future -- in many arenas -- and enabling transformation between geometrical and topological configurations?
"Facebook"? As an extremely sophisticated information system, Facebook necessarily has a fundamental commitment to the organization of data. A contrast can therefore be made with any static checklist of points as typically favoured in the presentation of government documents and media declarations. In a sense the linear sequence of hearings -- and the viewpoints successively articulated -- constituted an antithesis of the coherence of the systemic operation of Facebook with its multiplicity of viewpoints expressed simultaneously in realtime..
To enable Facebook to "work", the data has to be ordered to a far higher degree. Arguably, to comprehend its operations, information about Facebook also calls for a higher degree of organization -- or run the risk of falling victim to "subunderstanding" (Magoroh Maruyama, Polyocular Vision or Subunderstanding, Organization Studies, 25, 2004, 3, pp. 467-480). Hence the argument above for moving beyond checklists, however hierarchically nested, to polyhedral mappings as presented above.
There is a sense in which the term "facebook" necessarily reinforces an oversimplisitic comprehension of what is involved in Facebook as an information system -- however much the term has appeal for public relations purposes, however other dimensions of significance may be disguised. Subtler insight is offered by the following (playful) "expansion" of its implications
|Shifting metaphors -- beyond "face" and "book"?|
|point / vertex||data points (nodes)||Pointbook||Pointmap||Pointform||Pointframe|
|line / edge||links / likes / (axes)||Linkbook||Linkmap||Linkform||Linkframe|
|face||areas / frames / categories||Facemap||Faceform||Faceframe|
The transition across the four right-most columns helps to highlight the sense in which the many data points collected, together with the complex network of relationships (and "likes"), combine to "frame" a "face". This is essential to enabling the "face-time" valued by users in their interaction preferences, and by advertisers in attracting, capturing and holding their attention -- achieving "buy-in". Facebook can then be understood as a "framing" process, however that is to be appreciated or deprecated. As the quantity of data points and relationships increases in (geometrical or topological) complexity, so does the subtlety of the frame, and potentially the quality of the attention with which it is associated. Especially intriguing is the sense in which the framing process enables ithe possibiity of "facing" an issue strategically -- "facing up" to a challenge.
Given the interplay of optical metaphors associated with face and frame, and the mirroring function of Facebook content (selfies, etc), of further interest is the extent to which transparency enables passage "through the mirror" (Stepping into, or through, the Mirror: embodying alternative scenario patterns, 2008). Given the preoccupation with optics, it is curious to recognize that association between image, face, mirror, frame, and window as favoured metaphors for use of web technology.
Nesting polyhedra: Whether in terms of government oversight, strategic management, or user understanding, there is a need for a form of "cognitive hegemony", as separately argued (Embodying Global Hegemony through a Sustaining Pattern of Discourse: cognitive challenge of dominion over all one surveys, 2015). However deprecated globally, "hegemony" suggests the nature of the engagement with a worldview that an individual seeks to develop and sustain. That argument discusses, and illustrates, the further possibility of nesting polyhedra to hold multiple levels of understanding and enable transformation between them (Nesting polyhedra to enable comparison of patterns of discourse, 2015; Dynamic patterning of discourse by nested polyhedra?. 2015).
A useful metaphor to clarify this need is that of gearbox -- a "conceptual gearbox" -- enabling a transmission system between modalities of knowledge of different degrees of order (The Future of Comprehension: conceptual birdcages and functional basket-weaving, 1980). The operation of such a gearbox is now best illustrated using virtual reality technology, as featured in animations reproduced below.
Use of "gearbox" is necessarily a distortion in its own right, since future face-framing may need to be dynamic to a greater degree -- already implied by user "following" and the manner in which advertisers must track shifting trends. There is the further implication that this will in all probability call for higher dimensionality of which polychora, the 4D analogues of polyhedra, are one indication, as previously discussed (Four-dimensional requisite for a time-bound global civilization?, Comprehending the shapes of time through four-dimensional uniform polychora, Five-fold ordering of strategic engagement with time, 2015).
Ordering the nesting of polyhedra: The Kepler image (below) offers a classic suggestion of how the polyhedra might be ordered -- as a means of articulating "universal" insight through his cosmological model (George W. Hart, Johannes Kepler's Polyhedra, Virtual Polyhedra, 1988). Because of their contrasting symmetries, the Platonic polyhedra do not in themselves however offer a coherent pattern whereby they might be ordered and nested -- whatever this might imply in cognitive terms in relation to discourse.
A far more coherent approach to the nesting is offered by the rhombic triacontahedron (used above) -- with its 30 rhombic faces 60 edges and 32 vertices of two types. It is the dual of the icosidodecahedron, one of the Archimedean polyhedra, and is also a zonohedron, namely a convex polyhedron where every face is a polygon with point symmetry (or, equivalently, symmetry under rotations through 180 degrees). There is extensive commentary on the geometry of this polyhedron (Rhombic Triacontahedron, Wolfram Mathworld; Robert W. Gray, Rhombic Triacontahedron, Encyclopedia of Polyhedra, 2007; Paul Bourke, Rhombic Triacontahedron, 2002) As indicated by Stefan Schwarz, it consists of 30 uniform rhombi and shows the Golden Ratio in its diagonals (Wooden Polyhedron: rhombic triacontahedron, VisMath). The center of each rhombic face is the intersection point of the edges of a dodecahedron and icosahedron; the edges of the dodecahedron and icosahedron form the diagonals of the rhombic faces.
With respect to the nesting of the Platonic polyhedra, the most extensive study would appear to be that of Kenneth J. M. MacLean (The Rhombic Triacontahedron) -- namely an extract from his more general study (A Geometric Analysis of the Platonic Solids and Other Semi-Regular Polyhedra, 2007) in which reference tables are included for its construction. Unique amonst those authors with an interest in the geometry, MacLean also explores a theme of relevance to the discourse focus above (Dialogues: Conversations with My Higher Self, 2003).
For Kenneth MacLean (2007), the rhombic triacontahedron elegantly describes the nesting of the five Platonic solids in the following order: icosahedron, dodecahedron, cube, tetrahedron, octahedron, as remarkably illustrated (presumably extracts from his study), most notably with an animated gif. As the dual of the icosidodecahedron, the rhombic triacontahedron is usefully understood as a combination of the icosahedron and the dodecahedron, demonstratings the proper relationship between the 5 nested Platonic solids. He notes that the nested solids may not only grow and contract to infinity, but do so in a perfectly harmonious way.
Of particular interest is the manner in which the rhombic faces (diamonds) of the rhombic triacontahedron assure a form of "reconciliation" between discourse patterned in icosahedral or dodecahedral form -- between 20-fold and 12-fold patterns. This is illustrated below in relation to the outer pattern of edges in the image on the left which follows:
The cross-over midpoint could be understood as the intermediate position in any value polarity -- a form of "middle way", centered on each of the 30 faces of the rhombic triacontahedron. It is not a vertex on any of the three defining polyhedra indicated above. It corresponds to a vertex of the dual of the rhombic triacontahedron, namely the icosidodecahedron. Of further interest is the cybernetic work of Stafford Beer with respect to the icosahedron in its relation to discourse (Beyond Dispute: the invention of team syntegrity, 1994) leading to development of the process of Syntegration®. The schematic above raises the valuable question of how a polarized discourse can be "crossed" by another -- whether to neturalize it or to recognize and give credibility to such an intermediary position.
Clarification of the nesting of polyhedra then offers a sense of the fruitful connectivity between levels of discourse -- whatever this may imply.
|Dodecahedron (blue) and Icosahedron (red)
nested within Rhombic Triacontahedron (green)
|Tetrahedron (cyan) and Tetrahedron (magenta),
with Octahedron (yellow) nested within Cube (grey)
|Accessible via virtual reality viewers/browser plugins
-- VRML97 version or X3D version>
|Accessible in virtual reality viewers/browser plugins
-- VRML97 version or X3D version
By combining the two structures above, the complete nesting configuration becomes evident -- a more consistently ordered version of Kepler's original image (below). The virtual reality viewers (including browser plugins) enable rotation and zooming into the structures. Of particular interest is the view from within the image on the left above or within that below. This recalls the work of Keith Critchlow both with respect to patterns in architecture and those in flowers, following his work on polyhedra (The Hidden Geometry of Flowers: living rhythms, form and number, 2011; Islamic Patterns: an analytical and cosmological approach, 1999; Order in Space: a design source book, 2000). It is of some interest that the flower metaphor -- in relation to polyhedra -- can be fruitfully associated with communication processes in the rise and fall of civilizations (Flowering of Civilization -- Deflowering of Culture: flow as a necessarily complex experiential dynamic, 2014)
|Comparative animations in which the icosahedron and dodecahedron are variously implicit
(great circles partially distinghished by colour)
|Rotation of rhombic triacontahedron||Rotation of icosidodecahedron|
|Animations prepared using Stella Polyhedron Navigator|
Virtual reality representation: Given the technological commitment of Facebook to the revolution in augmented reality and virtual reality, experiments have been undertaken separately with polyhedral representation using virtual reality software. Given the commitment of Facebook to the development of AI applications, a wide variety of experiments of this nature is to be expected in the years to come in order to enable content to be more meaningful and exciting to explore. Just as computer screens have finally come to be used by govenment representatives in committee and plenary sessions, it is to be expected that at some stage use will be made in such contexts of virtual reality and augmented reality technology.
The image on the right is a virtual reality exercise in pulling together in an animation the arguments above relating to the ordering and nesting of fundamental categories of organization. It is usefully contrasted with the famous image on the left, given its significance in 1596 -- immediately prior to the Galileo affair in 1633 (cited above). For many, in terms of its global significance, Facebook functions as a form of solar system in their daily lives. The question is whether Facebook is currently mistakenly understood by many in ways comparable to the misunderstanding by Kepler of the solar system at the time.
In addition to astronomical cycles and climate cycles, there is considerable recognition of social cycles, and especially business cycles (see List of cycles). Recognition of how a system "works" is also understood in terms of thermosynamic cycles. These involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other variables within the system -- eventually returning the system to its initial state. In considering how Facebook "works", there is a case for exploring such categories as metaphors. One unique online experiment in enabling understanding of how structures worked was Soda Constructor (now disabled) -- which attracted millions of users at all levels of society (Animating the Representation of Europe: visualizing the coherence of international institutions using dynamic animal-like structures, 2004). In that spirit, the animation on the right can be explored as a source of clues as to how Facebook works in cycling through configurations of categories of more or less fundamental nature. The nested cycles potentially recall the dynamics of a pumping heart -- raising the provocative question as to whether Facebook can be considered to have a "heart".
|Nested polyhedral model of solar system
of Johannes Kepler (1596)
|Rhombic Triacontahedron (green)
as a nesting framework (combining the images above)
with Dodecahedron (blue), Icosahedron (red), Cube (grey),
Octahedron (yellow), with Tetrahedron (cyan) and Tetrahedron (magenta)
|Reproduced from Wikipedia entry on
Mysterium Cosmographicum (1596)
|Virtual reality variants: static: vrml or x3d;
mutual rotation: vrml or x3d; "pumping": vrml or x3d;
videos: "pumping" mp4; "rotation" mp4
How Facebook "works" systemically? Several commentators highlighted the mystery of how Facebook "works" (Amy Goodman, "Facebook Doesn.t Sell Your Data. It Sells You": Zeynep Tufekci on how company's profit really works, Democracy Now, 11 April 2018; Shira Ovide, Mark Zuckerberg refuses to admit how Facebook works, MoneyWeb, 14 April 2018). This mystery mirrors that of how global society "works" -- highlighted to some degree by the mysterious nature of the "international community" to which so many appeals are made (International Community as God or Sorcerer's Apprentice? Strategic chaos in the absence of an interlocking temporal pattern of longer-term cyclic processes, 2015).
Fundamental to how it "works" is the underlying implication that a face can be "booked" -- however questionably this process may be framed. It can be partly understood as an extension of the operation of the computer-enhanced match-making facilities of its origins, notably as enhanced subsequently by online dating and escort agencies. However it is the manner in which its business model is effectively based on "booking" "face-time" that is more difficult to comprehend -- in the sense of reserving exclusive "attention time" for advertising.
Facebook now plays a primary, if not essential, role in the attention economy (Investing Attention Essential to Viable Growth, 2014; T. H. Davenport and J. C. Beck, The Attention Economy: understanding the new currency of business, 2001; Michael H. Goldhaber, The Attention Economy and the Net. Telepolis, 27 November 1997).
For Davenport: Understanding and managing attention is now the single most important determinant of business success. For Goldhaber: The currency of the New Economy won't be money, but attention. As described by Wikipedia: attention economics is an approach to the management of information that treats human attention as a scarce commodity, and applies economic theory to solve various information management problems. In the extensive review of issues relating to the Attention economy by the P2P Foundation, it is recognized as an economy driven by the exchange of attention with the implicit goal of tightly intertwining everyone at the level of mind.
Potentially more intriguing is the sense in which attention will come to be entangled with tokens of confidence ("likes"?) as has traditionally been the case with monetary tokens.
Oppositional logic? The fundamentally questionable bias of the workings of the Facebook ecosystem -- with respect to "likes" -- has been highlighted above. As noted, this implies that "dislikes" are only implicit. On a spherically symmetrical polyhedral representation, as above, this would tend to imply that whatever is "disliked" is somehow associated with the opposite side of that form -- at some distance, and thereby "hidden", if not unconcious and "lost".
It could be argued that there is a strong case for Facebook AI to incorporate the subtle insights of so-called "oppositional logic" into its systems (Guoping Du, Hongguang Wang and Jie Shen, Oppositional Logic, Logic, Rationality, and Interaction, Springer, 2009, pp 319-319). As noted by the authors:
In intuitionistic logic system, constructive negation operator complies with the law of contradiction but not the law of excluded middle in intuitionistic logic system.... Oppositional logic is an extended system of classical propositional logic.
As noted separately, in the use of the more complex dynamic framings beyond that of the afore-mentioned Triple Helix Model, oppositional logic draws heavily on polyhedral representation (Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity: Eppur si muove: Biomimetic embedding of N-tuple helices in spherical polyhedra, 2017). With respect to Neglected recognition of logical patterns -- especially of opposition, it is there noted that:
...there is continuing interest in polyhedral patterns as a means of clarifying distinctions in logic. What could be considered amazing at this time is the manner in which this focus is restricted to an extremely limited range of polyhedra. No questions seem to be asked as to why related polyhedra are not of significance -- even when extensively studied by other disciplines, This is especially striking in the case of the rhombic dodecahedron, favoured as a pattern in the study of logical connectivity. This polyhedron is a geometric dual of the cuboctahedron whose particular characteristics with respect to transformation between polyhedral forms have been highlighted by Buckminster Fuller and notably proved fundamental to enabling him to design geodesic domes.
Of related significance is the sense in which the opposition implied by "dislike" is of fundamental importance to the security services in terms of their secretive assessments of threat. This follows from the frequently articulated US policy noted above: You're either with us, or against us. The formal extension beyond simplistic oppositional logic enables consideration to be given to the potential triangular, quadrangular, pentangular, hexangular, heptangular, octangular, enneagram, decagonal, hendecagram and dodecagram patterns of group and thematic bonding (Dynamic bonding patterns in n-tuple helices engendering n-fold rotating symbols, 2017). Engendering groups on Facebook in this way would then be analogous to the current investment in design of molecules with new properties. From genetic engineering to memetic engineering?.
Such possibilities could be detected and enabled by Facebook AI and rendered widely comprehensible through its virtual reality adaptations (Lisa Eadicicco, Inside Facebook.s Plan to Take Virtual Reality Mainstream, Time, 2 August 2017; Alice Morby, Facebook launches virtual-reality headset that can be used without other devices, De Zeen, 13 October 2017; Ben Popper, Facebook.s head of social VR talks about the future, The Verge, 15 October 2017).
|Selection of 2D orthographic projections of hypercubes to be comprehended in virtual reality
(Discussed in Neglected recognition of logical patterns -- especially of opposition, 2017)
|Reproduced from Wikipedia entry on hypercubes|
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