The “Fourth” Information Dimension – Constructing the First Domain
Douglas Paul Rose
The purpose of this research is to propose the initial stages of development of a construct of an actual information domain. Despite robust considerations on the value of information and efforts to institute it as a subset of other systems, there currently is no mechanism for information to stand on its own (i.e., to be specified as “the information domain”). Utilizing select portions of fourth-dimensional (4-D) constructs and several theories representing various facets of complex adaptive systems theory should expose the base value of this new theory of information and illustrate the significant differences between what is now frequently referred to as the phenomena of observation and the irrelevancy of perception. Upon examination of this new structure, employing the distinctions that this theory makes regarding the unique distinctions between perception and observation in the existing policy and practice should allow for examination that is more efficient and for the handling of large quantities of information for almost any end user.
A significant amount of discussion and misunderstanding surrounding the use of information – even beyond its “weaponization” by the military – means that our global use of information may be falling short of an exponentially expanding opportunity to develop a hegemonic role in the evolution of commerce, defense, policy, and overall control of the information environment. What follows is a discussion of the initial stages of a proposed information domain from first principles
Outside of substantive queries regarding the source of information-based threats, an understanding of what the information domain is – and is not – requires from the beginning that the reader accept the boundless nature of information, an abstraction (though nonetheless real for being abstract). In order to support the subsequent establishment of a well-defined information domain, strong comparisons will be made to the concept of four-dimensional (4-D) space. The multiple levels of observation that lie at the core of the basic 4-D premise will be employed to show how the basis of a physical information construct can be observed from multiple points without the need for perception – which represents a key distinction in representing a construct. In previous thought (i.e., “Newtonian” studies of physical systems), there was a universal space (e.g., “the ether”) and objects that moved within it according to mechanical laws (often of great complexity, as in the case of celestial mechanics). Einstein demonstrated that the space itself was dependent on the objects moving within it and that measurements previously thought to be universal and independent were, in fact, relative to the observer and his or her frame of reference.
The need for definitions in this context of the endogenous generation of variables gives rise to an apparent paradox of self-categorization. In fact, it is not a contradiction, simply a recursive definitional mechanism. For our purposes, information shall be “that construct by which decisions are derived; sometimes in the absence of perception, but always inclusive of observation.” The information domain will be considered as the place “…where information represented by thoughts, ideas, and decisions can be observed.”
Any domain is a system; the information domain discussed within these pages is no exception. In order to demonstrate structure, constructing or proposing a specific system involves deriving the connections that make such a nomenclature possible and even viable. This goes beyond the physical perception of a space, to acceptance of the shape of said system or even the ability to observe it. This observation, while vital, may transpire without conscious knowledge of it or even the perception typically associated with the ability to distinguish the presence of information.
Discussions regarding information or data must involve a framework for addressing the sheer size of any modern engagement in the information domain. “Big data”…a term oft-used in any number of contexts presents its own challenges but does not effectively quantify information within a domain, nor does it offer any starting point for doing so. The National Academy of Sciences recently released an analysis that highlights the need for this definition of the bounds of data and how to organize it despite its sheer size:
“The research and development necessary for the analysis of massive data goes well beyond the province of a single discipline, and one of the main conclusions of this report is the need for a thoroughgoing interdisciplinary in approaching problems of massive data. Computer scientists involved in building big-data systems must develop a deeper awareness of inferential issues, while statisticians must concern themselves with scalability, algorithmic issues, and real-time decision making. Mathematicians also have important roles to play, because areas such as applied linear algebra and optimization theory (already contributing to large-scale data analysis) are likely to continue to grow in importance.[i]”
Accepting a premise sans limits is one hurdle, however to concede the existence of another dimension, there must be discussions on size and boundary, as limitations of a construct must be identifiable. Here it is primarily appropriate to consider Edwin Abbott Abbott’s Flatland: A Romance of Many Dimensions illustrations on this issue. Abbott transcends discussion of shape by saying “...all beings…animate and inanimate, present to our view, the same, or nearly the same, appearance…that of a straight line.”[ii] The rest of Abbott’s book develops from recognition of “flat” shapes and the consequences that result in failure of perception regarding shape. [iii] While traditional interpretation of a 2-D model does not immediately integrate itself into the premises surrounding a 4-D structure, the value lies in the inferences of shape only.
The 4-D premise overall has been debated for hundreds of years. While Aristotle himself did not subscribe to such a possibility, in his work On the Heavens, he writes:
“Now a continuum is that which is divisible into parts always capable of subdivision, and a body is that which is every way divisible. A magnitude if divisible one way is a line, if two ways a surface, and if three a body. Beyond these there is no other magnitude, because the three dimensions are all that there are, and that which is divisible in three directions is divisible in all.[iv]”
While Aristotle’s theory may have been based on religion and belief at the time regarding the number three and the triad,[v] he only addresses construct, and not perception: a key theme that throughout this study will be revisited because the basis of shape itself, even as offered by a proponent of the limits of a 3-D realm, lends to the credence of an extension of a construct if the value of an enhanced shape can be demonstrated. Abbott’s examples of shape and explanations on edges and observation bear this out.[vi] Although Abbott’s discussions are not necessarily adaptive from a systemic aspect, the suggested consequences for failing to observe efficiently integrate themselves into the forthcoming discussions regarding use, boundaries, and ramifications. The selective application of these meanings in conjunction with particular theorems aims to justify the formal construction of this information domain.
Where this thesis considers itself emergent is the proposition of how perception spreads across a 4-D environment without asserting radical change of the perception of the world in which we inhabit. This is not a proposition to redefine the concepts of 3- or 4-D space; this work does not challenge the dimensions in which we live, as Abbott clearly outlines but relies wholly on the observation of information as defined here across multiple spectra that specifically defines the information domain.
The issue at hand is the conceptualization of high-dimensional data in a lower-dimensional output form.[vii] While this is a loose interpretation of dimensionality reduction, making use of the associated, attributable data points will initially outline the structure of a data set[viii] and provide the baseline for selected theories to which they attach themselves. This model will provide both the required distinction of construction and advance the requirement for recognition of structure outside the previous confines of an information environment.[ix]
Similarly, this construction is not a commentary on the use of mathematical or scientific models in intelligence-related theory, as those uses are well documented, and, indeed, they serve to validate a portion of this effort. This initiation then may be achieved by postulating how cognitively based pieces of an information domain tie into a construct that may not contain physical properties but would be constructed as some sort of complex system, and how that system can involve perception across multiple levels of information without regard to time, but specifically considering that parallel conception. This work argues that borrowing portions of the construct of the fourth dimension accomplishes these purposes.
Therefore, the assembly of a model in this fashion necessarily relies on appropriate theories as both the structure and boundaries of the domain. These theories shall be oriented across a 4-D construct, referred to as “pillars”, and anchored from the standpoint of (a). Relying on them to produce a construct also has to consider the fleeting “physical” nature of said information.
In the interest of not overwhelming doctrinal decisions or deterring the average user of information from considering this model, the outline of the structure is implied without the need of an explanation on how this 4-D construct filters information, as it is not intended to store or transform[x] what passes through the model. This is more along the lines of pattern recognition,[xi] which fits into other intelligence-related heuristics.
While largely conceptual and abstract, this approach aligns with scientifically aligned criteria for dealing with patterns[xii] even if they are not specific to information. Again, this reliance on attributes and theory that represent lynchpins of other scientifically developed theorems validates the presence of a construct that exists solely within information; a precept that is no longer questioned in domains that exist in the current doctrine. In identifying patterns, this model serves not to call out the subsets of information but to demonstrate the value of explicit formation of the pillars in order to produce predictive, calculable, and naturally stochastic values.[xiii]
Where this construction starts to touch the fourth dimension is when these theories take the shape of a Boolean hypercube[xiv] and the linear points between each peak in data are the theories selected in an analysis problem. This “contraction and dilation”[xv] that Cajori notes allows for this without diminishing the validity of the chosen construct. Utilization of this method had the added benefit if not being as limiting as some conventional analytical techniques – those that can restrict analysis – because this construct is subject agnostic. It could also scale indefinitely in order to piece together large data sets – those having passed through some sort of analytic filter – in order to break out the overlying portions of the dimension into manageable pieces. The following illustration demonstrates the construct of this theory with the peaks and the potential emphasis with the pillars, and this ability to integrate smaller constructs into complex intelligence problems. The lighter shaded lines represent the pillars of the information domain with the darker, overlapping spaces allowing for the corners of subsequent cubes to establish said connections.
Figure 1. – Base Theory Construct of the Information Domain
The challenges of working with a construct without physical topography include the inability to predict collisions or undesired interactions, although these instances are oftentimes what intelligence seeks. Leveraging select portions of the 4-D premise without including complex calculations on time and velocity is a purposeful attribute of this study. Taking the Boolean cube design to infer the multidimensional complexities of an intelligence problem encompasses the same traits of the information domain, but allows this theory to illustrate the irrelevance of perception.
State spaces, typically used for motion planning and the identification of a series of combinations resulting from motion,[xvii] do not apply to this construct, as the information selected for analysis is not in and of itself dynamic. Selection of pieces to include in analysis are themselves forced through rigid theory that is the pillar of this model, hence the motion is likely controlled and limited. Likewise, the “level of abstraction”[xviii] here resulting from individual selection of theory will eliminate the need for definition of configuration space because of the lack of motion; the motion involved here resides within the resultant decisions and is wholly existent within the cognitive environment. This construct is less about degrees of movement[xix] and more about the flexibility of the application of this system, and the borders of an information domain that enables perception across a fixed structure. Further, discussions on topology will necessitate the distinction of the intervals between points within the information being analyzed in order to show relationships, not movement. With the boundaries formed by the theories themselves, and, given the nature of the intelligence problem, most of these intervals between points will be open and their sets (relationships)[xx] mapped hence:
If distinctions A, B, C, and D are the boundaries of the construct, then subsets and so on are their subsets showing relationships to those boundaries.
Figure 2. – Distinctions within the Information Environment
Each boundary consists of the span of A-B, B-H, etc., with an exponential resultant subset limited less by the content or availability of the information than by the perception applied. These subsets would exist within the spans of this model.
Surely, the Boolean hypercube model has some visual, physical traits. There are lines, spaces, and connections, but, as stated throughout this study, anyone considering this domain for their purposes needs to be able to look past their flat aspects. The progressive consideration of perception through the increasing numerical designations of dimensions (2-D through 4-D) requires recognition of similarly applied attributes. Taking each visual representation of a line reveals the 3-D trait of height, and combinations of multiple lines and heights involve representations of planes.[xxi] The innate ability to disregard perception across these planes concedes that any one piece of information may occupy multiple subsets, and this is where the 4-D concept reveals itself. The other fourth-dimensional tie-ins referenced throughout this work certainly do not follow basic definitions or progressions; however, they also do not lend themselves to the necessary inclusions of their base form given their already advanced natures. Progression beyond crude discussions of the mass of a system of systems are implied and should represent the logical scale vice acreage or weight of the output[xxii] – since this model is intended to be leveraged against specific instances or in conjunction with other related applications.
This study is not about detailed discussions and validation of the physics and mathematically based theories it touches; it is designed more for the end user of an intelligence construct or process. There is slightly more granularity presented than a user of this magnitude requires since the information domain construct is an emergent model that serves to avoid the pitfalls of some structured analytical techniques that have fallen victim to their own historical successes in their applications of situations that do not fit their original intent or shape. Obviously, portions of these theories have been extracted to construct this baseline; however, this mirrors the selective use of situational-specific methods to build the boundaries but serves as the principal bridge to continue this work. Evaluations of space and time along with the supporting mathematics are necessary in order to establish the impact of the velocity of information through a fixed model and the potential resulting impact on perception, if any. These computations very well may be already developed, but it is precisely the state of both cyberspace and the information domain that precludes them currently. This work prefaces any strategic decision on the clear delineation of either of these. Even past the need for emergent policy positions for the broader information community, the primary need to recognize what we conceptually lack remains.
[ii] Abbott, Edwin. 1884. Flatland: A Romance of Many Dimensions. New York: Cosimo Classics.
[iv] Massachusetts Institute of Technology. 1957. “On the Heavens by Aristotle” Translated by J.L. Stocks. Accessed October 7, 2014. http://classics.mit.edu/Aristotle/heavens.1.i.html.
[vi] Abbott, Edwin. 1884. Flatland: A Romance of Many Dimensions. New York: Cosimo Classics.
[viii] The Committee on the Analysis of Massive Data. 2013. Frontiers in Massive Data Analysis. Washington D.C.: The National Academies Press. Accessed October 7. http://www.nap.edu/catalog.php?record_id=18374.
[ix] DTIC Online. “Joint Publication 3-13: Information Operations.” http://www.dtic.mil/doctrine/new_pubs/jointpub_operations.htm (accessed October 7, 2014).
[x] Shalizi, Cosma and James Crutchfield. “Pattern Discovery and Computational Mechanics.” Paper presented to the Proceedings of the 17th International Conference on Machine Learning, Santa Fe, New Mexico January 29, 2008.
[xv] Florian Cajori. 1926. “Origins of Fourth Dimension Concepts.” The American Mathematical Monthly 33, no. 8 (October): 397-406. Accessed October 7, 2014. http://www.jstor.org/stable/2298325.
[xvi] The University of Wisconsin Madison. 1999. “Direct Interconnection Networks I + II: Topics in Parallel Computing.” Computer Science Home Page. Last modified 2007. Accessed October 7, 2014. http://pages.cs.wisc.edu/~tvrdik/5/html/Section5.html.
[xvii] LaValle, Steven. 2006. Planning Algorithms. Cambridge: Cambridge University Press.
[xxi] Abbott, Edwin. 1884. Flatland: A Romance of Many Dimensions. New York: Cosimo Classics.
[xxii] IEEE Control Systems Society. 2011. “Systems of Systems.” Overview, Success Stories, and Research Challenges. Accessed October 7, 2014. http://ieeecss.org/sites/ieeecss.org/files/documents/IoCT-Part3-04SystemsOfSystems.pdf.