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*Published: 9 June 2017*

**Abstract:**

**Introduction**

In a widely cited poststructuralist / anti-humanist critique of European humanism^{[1]}, Badmington [1] argues that “there is nothing more terrifying than a posthumanism that claims to be terminating ‘Man’ while actually extending ‘his’ term in office.” (p.16) In this prescient statement, attention is drawn to the very real possibility of a posthumanist orientation that, while claiming to be ‘critical’, ends up re-inscribing precisely that very humanism – focused on the figure of ‘Man’ as white, male, European and anthropocentric – that it sets out to challenge (‘post-’ *as* dialectical-engagement) and overcome (‘post-’ *as* temporal / historical transcendence to a new ontological condition). In this paper, I want to explore Badmington’s statement in terms of a possible ‘entangled’ relationship between Transhumanism and posthumanism, with the latter considered in *both* its ‘critical’ *and* ‘techno-scientific’ or ‘popular’ manifestations, against the background of what is, ostensibly, a contemporary resurfacing – or *re*-iteration – of the historical phenomenon of ‘White Crisis’ with the aim of mounting a decolonial critique^{[2]} of the Transhumanist / posthumanist project.

Badmington argues that “apocalyptic accounts of the end of ‘Man,’ it seems to me, ignore humanism’s capacity for regeneration and, quite literally, recapitulation.” (p.11) Against this, I want to suggest that it is the very ‘apocalyptic’^{[3]} nature of the phenomenon of ‘White Crisis’ – that is, perceived threat to white supremacy under mounting contestation from the non-white ‘other’ – that contributes to^{[4]} engendering what I refer to as the ‘algorithmic’ transformation of humanism into posthumanism via Transhumanism as an ‘iterative shift’ within the historically-sedimented onto-logic of Eurocentric racialization. My point of departure turns on the ‘between-ness’ of the Transhuman^{[5]} vis-à-vis the posthuman, such that the former is engaged against the background provided by the latter as *telos*, irrespective of how this is ultimately realized in techno-scientific form, viz. augmented biological form, uploaded mind or synthetic, artificial intelligence – that is, ‘Mind Children’. Engaging Transhumanism as an ‘iteration’ within the ‘algorithmic logic(s)’ of race / racism / racialization^{[6]} associated with colonial modernity, I explore how ‘critical’ posthumanism lends itself to co-option into techno-scientific posthumanism, and the implications of this in terms of its contributing to deferral of the ‘decolonial moment’ – that is, decolonization of the world system. Crucially, I maintain that the emergence of the techno-scientific posthuman points to a transformation in the nature of humanism that maintains structurally-asymmetric power relations between ‘the (formerly) human’ (as white, Western, male etc.) and the subaltern ‘other’ even as the latter contests the Eurocentric terrain of ‘the human’^{[7]}.

**Methodological Precedents**

In the context of exploring race ‘and/as’ technology, Chun [16] maintains that race *as* technology “shifts the focus from the *what* of race to the *how* of race, from *knowing* race to *doing* race by emphasizing the similarities between race and technology”; further, that “*race as technology* is a simile that posits a comparative equality or substitutability – but not identity – between the two terms.” (p.8) I am interested in exploring the implications of positing a similar ‘comparative equality or substitutability’ between two terms, however, one in which the ordering of terms is inverted somewhat in relation to that presented by Chun, viz. Transhumanism and/as whiteness^{[8]}, thereby engaging the issue of how Transhumanism might be thought about in relation to processes of racialization – specifically, those associated with the largely tacit ‘background’ phenomenon of a hegemonic whiteness^{[9]}. Chun maintains that “by framing questions of race *and* technology, as well as by reframing race *as* technology, in relation to modes of media naturalization [we can] theoretically and historically better understand the force of race and technology and their relation to racism.” (p.8) Similarly, I want to argue that framing questions of Transhumanism *and* whiteness, as well as reframing Transhumanism *as* whiteness, in relation to historical processes of re-articulation of the latter (i.e. whiteness) enables us to theoretically and better understand how Transhumanism can – and arguably *does* – function as a techno-scientific articulation of whiteness during a period arguably marked by increasing contestation of other forms of this racial phenomenon^{[10]}.

Drawing inspiration from Chun’s engagement with race and/as technology, and building on earlier work reflexively exploring other related ‘as/and’ configurations such as race and/as information [20] and Orientalism and/as information [21], informed by a critical race theory of information [22] and decolonial computing perspective [23][24] – that is, in terms of consideration of the ‘entanglement’ of race, religion, information, computing and related ICT phenomena with the body-politics and geo-politics (and theo-politics) of knowing and being – I critically interrogate Transhumanism as a techno-scientific response to the phenomenon of ‘White Crisis’ at least partly prompted by ‘critical’ posthumanist contestation of Eurocentrically-universal humanism.

**Summary of Argument**

I begin by briefly sketching the relationship of Transhumanism to Renaissance and Enlightenment humanism, and to ‘critical’ and techno-scientific posthumanism, drawing on arguments presented by Jotterand [25], Hughes [7], Ranisch [26] and Sombetzi [27] among others.

In framing my argument for Transhumanism and/as Whiteness, I draw upon the sociological exploration of the latter due to Garner [28][29] – in particular, (1) his ‘processual’ understanding of whiteness in dynamic relational-tension to other racialized identifies, (2) the function of whiteness as a tacit invisible ‘background’ standard, and (3) the socio-political structural manifestation of whiteness as continued, yet contested, globally-systemic white supremacy – a position he derives from Mills [30]. Concerns about the future of whiteness [31] are engaged against the backdrop of a purported shift to a ‘post-racial’ reality, the latter of which is subjected to decolonial critique by Sayyid [32][33]. Anxieties about the future (or otherwise) of whiteness can be shown to be related to the late 19^{th} and early 20^{th} century phenomenon of ‘White Crisis’ explored by Füredi [34] and Bonnett [35][36][37], the latter of whom refers to a ‘decline’ of overt discourses of whiteness and the concomitant ‘rise’ of a discourse about ‘the West’^{[11]}. It is suggested that the recent election of Donald Trump at President of the united States, the Brexit phenomenon in the UK, and the continued rise of Far / Alt-Right politics in the US and Europe can – and *should* – be seen as *one* response to the re-emergence of the phenomenon of ‘White Crisis’, almost fifty years on from the anti-racist struggles of the 1960s, and almost a century on from when ‘White Crisis’ was first being discussed in ‘the West’ (specifically, Britain and America); as Bonnett [37] states, “whiteness and the West ... are both projects with an in-built tendency to crisis. From the early years of the last century ... through the mid-century ... and into the present day ... we have been told that the West is doomed.” (p.25)

In terms of thinking more specifically about *Transhumanism* and/as Whiteness, I want to argue that Transhumanism / posthumanism should be viewed as a somewhat *different* response to the phenomenon of ‘White Crisis’, one that is techno-scientific and occurs in parallel with, albeit somewhat obscured by, the more overt phenomenon of conservative ‘White Backlash’ vis-à-vis socio-political phenomena associated with the response described earlier^{[12]}. In particular I want to argue that the shift described by Füredi and Bonnett from ‘white’ to ‘West’ is usefully framed in terms of the re-inscription^{[13]} – or rather, ‘algorithmic’ *re-iteration* – of whiteness under different signifiers including the techno-scientific signifier of Transhumanism associated with the convergence of GRIN/NBICS technologies; furthermore, that this shift in ‘whiteness’ needs to be situated within a longer historical frame than that going back to the late 19^{th} century, arguably one that commences with the Columbian voyages in 1492 CE and results in the emergence of a racialized world system [38]^{[14]}; moreover, a history involving *other* ‘paradigmatic’ shifts including those from ‘religious’ to ‘philosophical’ to ‘scientific’ and latterly ‘cultural’ expressions of race / racism / racialization, such transformations constituting re-articulations – or rather, ‘re-iterations’ – of the difference between the human (European) and the sub-human (non-European)^{[15]}. Insofar as such iterations might be seen as different manifestations of the same phenomenon – thereby pointing to a certain continuity through change – I want to suggest that they are usefully understood in terms of what has been described elsewhere as ‘algorithmic racism’ [41]^{[16]}. However, I argue that the contemporary moment is marked by a shift from the distinction between sub-human (non-European, non-white) and human (European, white) to that between human (non-European, non-white) and Transhuman (European, white)^{[17]}, such shift being prompted, at least partly, by certain kinds of ‘critical’ posthumanist contestation of Eurocentric conceptions of the human against the much broader background or ‘horizon’ of a resurfacing of the phenomenon of ‘White Crisis’.

Against more optimistic – and, I would aver, somewhat naïve – postmodern, post-structuralist, postcolonial and feminist readings of the cyborg as an emancipatory figure championing the destruction of borders, boundaries and binaries, and the embrace of hybridity, multiplicity and socio-political ‘levelling’ under a ‘critical’ posthumanism, I want to argue instead for viewing Cyborgism / Transhumanism as a techno-scientific response *by whiteness* to the perceived phenomenon of ‘White Crisis’ and mobilized *by whiteness* for purposes of maintaining Eurocentrism via refinement / adaptation and expansion under subaltern contestation. Drawing on recent mounting criticism^{[18]} of the so-called ‘ontological turn’ towards a non-anthropocentric, post-dualistic ‘materialism’, yet conceding that such a turn was at least partly motivated by a concern to address legacy political and ecological injustices associated with modern/colonial projects by engaging with postcolonial and other forms of critique, I maintain that ‘critical’ posthumanism ultimately proves to be rather ‘brittle’ and ‘unstable’ vis-à-vis its commitment to emancipation of, and reparations towards, the ‘other’ and that this is due to a tendency to conflate different conceptions of the posthuman, including those that upon close inspection can be shown to be Eurocentrically rationalist. Going further, I argue that the hegemony of such Eurocentrically-rationalist conceptions of the posthuman, masked (or occluded) via their conflation with alternative variants of ‘critical’ posthumanism, enables the co-option and transformation of the latter into techno-scientific posthumanism, and that one means by which such transformation is facilitated is via their shared commitment to rather nebulous notions such as ‘information’ as ontologically basic^{[19]}. On my more pessimistic reading, the ‘entanglement’ of the ‘cybernetic’ – latterly, ‘computational’, ‘informational’, ‘algorithmic’ – ‘turn’ with the ‘ontological turn’ to the posthuman acts to facilitate Transhumanism as a means by which to retrench Western hegemony, especially under conditions of ‘White Crisis’ resulting from increasing subaltern contestation of Eurocentrism, and that ‘critical’ posthumanist endorsement of ‘flat’ ontologies functions discursively to occlude the continued existence of asymmetric hierarchies, and their algorithmic (re)production.

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© 2017 by the author; licensee MDPI and ISIS. This abstract is distributed under the terms and conditions of the Creative Commons Attribution license.

^{[1]} Badmington’s argument is informed by various ‘critical’ currents within contemporary European thought including postcolonial theory and a commitment to the post-discursive, ‘new materialist’ embrace of boundary-disrupting ontological-affinity with the non-human (animal, machine etc.) associated with the ‘ontological turn’. It is also motivated by a concern to address the political and ecological implications of the anthropocentrism and subject-object dualism associated with dominant strands of Enlightenment thought.

^{[2]} By a ‘decolonial’ critique, I mean one that foregrounds considerations of the body-politics (who) and geo-politics (where) of knowing and being, and is preferentially disposed towards thinking through conceptual frameworks emerging from the margins / borders / periphery of the modern/colonial world system.

^{[3]} There is a secular Enlightenment rationalist tendency to dismiss ‘apocalyptic’ narratives as an irrational hangover from the ‘age of religion’; however, as Gray [2] convincingly argues, apocalyptic and utopian thinking derived from the Christian tradition informs secular frameworks, both those on the conservative ‘right’ and on the critical ‘left’. In addition, there is the need to consider Noble’s [3] and Davis’ [4] exploration of the long durée ‘entanglement’ of apocalyptic religious and occultist thinking with scientific and technological development in the European / ‘Western’ tradition.

^{[4]} By framing the issue in terms of ‘contribution’ rather than ‘causation’, I recognise that the Transhumanist / posthumanist project is over-determined in terms of its historical motivations and causes. Noble [3], Davis [4], Gray [2], Zimmerman [5, 6] and Hughes [7] trace some of these motivations to technological manifestations of Gnostic, millenarian / millenialist and apocalyptic currents within medieval Western Christianity, and drawing on recent scholarship at the intersection of critical race theory and critical theory of religion [8][9][10][11], I want to suggest that such ‘techno-millenialist’ currents feed into the emerging ‘technology’ of ‘race’ at the onset of colonial modernity which commenced with the Columbian voyages in 1492 CE. In short, insofar as ideas of leveraging technology to achieve utopian and/or apocalyptic purposes have a long history, I am *not* suggesting that the Transhumanist project is driven solely by a post-racial ‘crisis of whiteness’; rather, I argue that under contemporary conditions of ‘White Crisis’, the Transhumanist project gains a sense of urgency as a techno-scientific resolution – or ‘fix’ –to such an anxiety-ridden state of affairs.

^{[5]} According to Bostrom [12], “in its contemporary usage, ‘transhuman’ refers to an intermediary form between the human and the posthuman.” (p.4) Transhumanism is generally framed in terms of the application of GRIN (Genetics, Robotics, Information Technology and Nanotechnology) in the service of self-directed evolution – that is, enhancement of the human – towards a technocratic future. A related acronym is NBICS which refers to the combined resources of nanotechnology, biotechnology, information technology, cognitive science and synthetic biology.

^{[6]} Bostrom [13] maintains that “transhumanists [consider that] murder and enslavement, whether of humans by posthumans or the other way around, would be a moral atrocity and a crime”, and points to their condemnation of “the racist and coercive stateāsponsored eugenics programs of the 20^{th} century” (pp.19-20). It is interesting to note, however, that a recent survey of the beliefs held by so-called ‘technoprogressives’ conducted by Hughes [14] revealed that only 35% self-identified as anti-racist. In addition to what this figure might indicate vis-à-vis relative lack of engagement with the issue of ‘race’ among Transhumanists, it is not at all clear how racism and anti-racism were understood in Hughes’ survey, by questioners and respondents alike: for example, was racism framed in tacitly liberal terms – that is, as something personal, irrational, transient and exceptional – or was it understood along critical race theoretical terms as a systemic, rational, persistent and pervasive structural phenomenon [15]?

^{[7]} As Badmington [1] states, “the seemingly posthumanist desire to download consciousness into a gleaming digital environment is itself downloaded from the distinctly humanist matrix of Cartesian dualism. Humanism survives the apparent apocalypse and, more worryingly, fools many into thinking that it has perished. Rumours of its death are greatly exaggerated” (p.11); in short, “the new *now* secretes the old *then*. Humanism remains.” (p.14)

^{[8]} In the context of the argument presented herein, ‘whiteness’ should be understood as referring to people of European descent. That said, it is important to appreciate that there are ‘shades of white’ among Europeans, the ‘intensity’ of whiteness tending to increase as one moves closer to its ‘core’ located in ‘the West’ – that is, Northern Europe, the United States, Canada and Australia. For a useful discussion of how whiteness came to be exclusive to Europeans, see [17].

^{[9]} In this connection, it is interesting to note that Bostrom [18] and other Transhumanists regularly invoke the notion of ‘technology races’, 20^{th} century examples of which includes races to build the first fission or fusion bombs, achieve satellite and human launch capability, build an artificial intelligence etc. While Chun [16] invites us to consider race *as* technology, I am interested in exploring technology *as* race, in both the metonymic / ontic sense of technology as a *specific* means by which to instantiate race, as well the metaphorical / ontological sense of technology as a *general* means by which to think about the series of iterative shifts in how race is articulated at different periods within colonial modernity.

^{[10]} Somewhat optimistically, Coleman [19] has argued that “technology’s embedded function of self-extension may be exploited to liberate race from an inherited position of abjection toward a greater expression of agency” (p.177); on her view, by “extending the function of *techné* to race, I create a collision of value systems. In this formulation, race exists as if it were on par with a hammer or a mechanical instrument; *denaturing it from its historical roots, race can then be freely engaged as a productive tool*. For the moment, let us call ‘race as technology’ a disruptive technology that changes the terms of engagement with an all-too-familiar system of representation and power [emphasis added].” (p.178) I would suggest that such assertions, alleged resistant rhetorical potential aside, are problematic on account of an ostensibly tacit assumption that technology stands separate from, rather than ‘entangled’ with, race. What appears to be missing from Coleman’s (and Chun’s) formulation is reflexive consideration of technology and/as race – that is, recognition of the *racialized* ontology of technology under colonial modernity, and I suggest that this follows directly from the ‘bracketing’ of the historical that Coleman is committed to embracing in her ‘technological turn’. Yet my critique of their position should not be understood as entailing support for the view that technology is *necessarily*, in the sense of *trans*-historically, racialized; on the contrary, a commitment to the *contingency* of technology’s racialization is maintained, yet one that requires us to consider more seriously how the field of technology / ‘technique’ is racially-inflected, such racial inflection contributing to a *historical* essence that in colonial modernity has a racialized underside, and which thereby constraints / limits scope for resistant action vis-à-vis affording non-abject possibilities for racial agency.

^{[11]} It is important to note that this ‘crisis’ literature appears at a time when proclamations of ‘white racial supremacy’ are made openly by various commentators belonging to the dominant Euro-American powers of the1920s and 1930s. Less than fifty years on, and whiteness under the signifier of ‘the West’ is plunged into further crisis as a result of the Civil Rights movement in the US and the increasing linkage of this struggle to global anti-colonial struggles. Formal independence from European colonial powers is achieved in the late 1960s, and the Civil Rights struggle achieves certain limited victories; however, structures of colonial domination persist in the ‘operating logics’ of the newly independent post-colonial states, decolonization as a project arguably being aborted under the transition from a liberal to a neo-liberal world order in the 1980s onwards. As neo-liberalism morphs into neo-conservativism, the ‘apocalyptic’ project of a ‘war on terror’ surfaces [2] and the historically-sedimented figure of the Muslim ‘other’ as threat / enemy *re*-emerges [38]. Yet concurrent with and at least partly due to this centring of the specifically *Muslim* ‘other’ as enemy and the actualization of war against it, ‘breathing room’ is provided in South America, South Asia and latterly South Africa for the gestation and development of a *decolonial* project – that is, *re*-engagement with the unfinished project of decolonization (to be contrasted with Habermas’ unfinished project of modernity). During the 2000s, the ‘decolonial option’ begins to be embraced by some members of ‘minority’ non-white groups located in the West, this tendency escalating in the ‘post-racial’ era under Obama, with increasing contestation of whiteness and Eurocentrism in the academy, activist mobilizations against anti-blackness and white supremacy in movements such as Black Lives Matter, and various contemporary ‘anti-racist’ responses to the rise of the Far / Alt-Right in the US and Europe against the backdrop of the continued rise of Islamophobia.

^{[12]} Such phenomena include the resurgence of strident and protectionist ‘strong-man’ nation-statism, racialized articulation and foregrounding of ‘concerns’ about border controls, immigration, citizenship and notions of ‘belonging’, along with the rise of cruder and more overt forms of white supremacy in comparison with what was arguably the more subtle, more refined and more covert operation of the socio-political logics of ‘racial liberalism’ [30] in Western nation state formations.

^{[13]} Bonnett [37] appears to concede the ‘iterativity’ of whiteness in referring to its ‘re-invention’, “well into the twenty-first century”, pointing out that “the history of whiteness is one of transitions and changes.” (p.17)

^{[14]} Hayles [39] argues that “we do not leave our history behind but rather, like snails, carry it around with us in the sedimented and enculturated instantiations of our pasts we call our bodies.” (p.137) Apart from the need to decolonially interrogate *whose* history needs to be considered (body-politics of knowledge) and from where (geo-politics of knowledge), it is crucial to note that it is not *just* bodies that are sites for sedimentation and enculturation, but rather regimes of governmentality which include but transcend the body to include institutions, land, discursive practices etc. [40].

^{[15]} What tends to be obscured, if engaged at all, in discussions of the relationship between the human and the Transhuman is the prior relationship between the human and the sub-human (which should not to be conflated with the broader category of the *non*-human), the latter providing the ‘ontological ground’ against which the former is constituted through a process of hierarchical negative dialectical opposition, viz. the human (superior) as the negation of the sub-human (inferior).

^{[16]} According to Coleman [19], “race as we know it is an ‘algorithm’ inherited from the age of Enlightenment.” (p.184) I want to suggest that not only is race an algorithm, *metaphorically-speaking*, but that following the ‘cybernetic turn’ of the 1950s, the continued rise of informational, computational and algorithmic logics (technical, social, cultural, economic, political etc.) has resulted in a *metonymic* situation wherein the racial algorithm has engendered algorithmic formations of race.

^{[17]} Notwithstanding the international nature of Transhumanist, Extropian and related techno-scientific movements, and granted the need to take seriously the ‘hybrid’ nature of these endeavours involving the contributions of various ethnicities, genders and nationalities, it is empirically demonstrable on demographic grounds, both quantitative and qualitative, that Transhumanism is hegemonically white, male and ‘Western’ (Euro-American); furthermore, it is a project whose trajectory is traceable, genealogically, to a specific historical and geographical experience, viz. the European Enlightenment – although arguments have been made that Transhumanism has much earlier antecedents within the European tradition going back to the twelfth, if not the ninth century CE [3][4]. On this basis, and in terms of its ‘entanglement’ with ‘race’, I want to suggest that Transhumanism is readily identified as a Eurocentric phenomenon.

^{[18]} Criticism of the so-called ‘ontological turn’ associated with ‘critical’ posthumanism pointing to its tendency to re-inscribe Eurocentric rationalism despite the emancipatory rhetoric allegedly associated with ‘flat’ actor-network schemes, speculative realism, procedural metaphysics and object-oriented ontology etc., has been mounted from various perspectives including indigenous cosmology [42][43], black thought [44][45] and postcolonial critiques of Orientalism [46][47].

^{[19]} I would suggest that such co-option occurs through a two-fold process of (1) ‘epithet transfer’ [48] – that is, simultaneous projection of subjective (mental) traits onto the objective (material) and vice versa, or a ‘double movement’ of anthropomorphization of the mechanistic and mechano-morphization of the anthropic – and (2) recourse to a de-materialized abstraction, viz. disembodied information, and its application to human and non-human (specifically, animal and artefactual) phenomena alike [49]. Ferrando [50] maintains that ‘critical’ posthumanism “does not turn technology into its main focus, which would reduce its own theoretical attempt to a form of essentialism and techno-reductionism” (p.28), however, I would suggest that framing ‘critical’ posthumanism against the background of what might be described, following Heidegger, as an *onto-theology* of ‘information’ (both totalizing and reductive), and the process of epithet transfer whereby objects-become-subjects (and subjects-become-objects), engenders precisely such a techno-reductionism; in short, ‘critical’ posthumanism, at least as framed against the Eurocentric backdrop of the ‘ontological turn’ towards objects, networks and informational flow, readily lends itself to such ‘techno-reductionism’. In this connection, and in the context of exploring the implications of the ‘ontological turn’ to objects within anthropology, Fowles [47] points to the emergence of “a kind of quasi-posthumanist anthropology *in which objects freely assume the position of subjects* [emphasis added]” (p.20); crucially, he goes on to assert that in such a shift “there is some sort of transference at work. Critiques of the Western colonial project and of the human sciences' contribution to this project have been deflected onto the world of things. Eurocentrism has been discursively reconfigured as anthropocentrism” (p.23) such that “anthropological philosophers now find themselves empowered not just to make *claims about the basic entities of the world itself* (or, as some would insist, of ‘the worlds themselves’) but also to develop schemes for ‘how things could be’ ... all by ‘thinking through things’ and without bothering much about the active political struggles of anthropology’s traditional human subjects, subjects who now quietly retreat into the blurred backdrop [emphasis added].” (p.24)

*Published: 9 June 2017*

**Abstract:**

A combination of directed homotopy topological and Morse theoretic methods can significantly extend control and information theories, permitting deeper understanding of ‘developmental' pathologies afflicting a broad spectrum of biological, psychological, socioeconomic, machine, and hybrid processes across different time scales and levels of organization. Such pathologies emerge as phase transitions driven by synergistic forms of environmental insult under stochastic circumstances, causing `comorbid condensations' through groupoid symmetry breaking. The resulting statistical models should be useful for the analysis of experimental and observational data in many fields.

More explicitly, developmental process -- ontology -- is ubiquitous across vast biological, social, economic, and machine realms. Rosen (2012) characterizes this as ‘...anticipatory behavior at all levels of... organization'. Maturana and Varela (1980) see cognition permeating biology. Atlan and Cohen (1998) invoke a ‘cognitive paradigm' for the immune system that generalizes to wound healing, blood pressure regulation, neural dynamics, and so on (Wallace 2012). West-Eberhard (2003; 2005) sees ontology as a matter of ‘choice' at developmental branch points. Traffic flow involves repeated ‘ontological' choices by atomistic vehicles at road junctions, as well as during ordinary passage in heavy traffic (Wallace 2016a Ch.9). Indeed, machine cognition quite generally requires repeated choice of response to environmental cues (Wallace 2016a). A firm responding to market pressures must, at least annually, reconfigure product lines and marketing strategies, also a cognitive process (e.g., Wallace 2015 and references therein). Democratic state actors confronted by changing patterns of threat and affordance must, at least during elections, repeatedly choose among the different patterns of response made available by the contending parties and candidates. Active warfare involves constantly repeated choice at all levels of organization leading up to, and during, combat operations.

All developmental phenomena are, however, subject to patterns of failure and dysfunction. These range from neurodevelopmental disorders such as autism and schizophrenia (Wallace 2016b) to collapse of vehicle flow in traffic jams (Kerner and Klenov 2009), and catastrophes of governance like Brexit, or the US occupation of Iraq. Here, we attempt to extend results from information and control theories to statistical tools useful in understanding developmental failure.

The underlying model of development is that a system begins at some initial ‘phenotype' So confronting a branch point Co leading to two (or more) possible subsequent ‘phenotypes' S1 and S2, where new branch points C1 and C2 will be confronted, and at which choices must again be made, and so on.

Two of the three essential components of this model are intrinsically linked.

The first component is that of directed homotopy, in the sense of Grandis (2009) and Fajstrup et al. (2016). That is, there are equivalence classes of paths leading from ‘phenotype' S_{n} to S_{n+1}, as defined by the branch conditions C_{n}. A group structure -- the so-called ‘fundamental group' -- is imposed on a geometric object by convolution of loops within it that can be reduced without crossing a hole (e.g., Hatcher 2001). An algebraic topology of directed homotopy can be constructed from the composition of paths that constitutes a groupoid (Weinstein 1996), an object in which a product need not be defined between every possible object, here the equivalence classes of possible linear paths. As Weinstein (1996) emphasizes, almost every interesting equivalence relation on a space B arises in a natural way as the orbit equivalence relation of some groupoid G over that space. Instead of dealing directly with the orbit quotient space B/G$as an object in the category of sets and mappings, one should consider instead the groupoid G itself as an object in the category of groupoids and homotopy classes of morphisms. An exactly similar perspective involves use of the homotopy and homology groups of algebraic topology to characterize complicated geometric objects (Hatcher 2001).

The second component is recognition that choice at developmental branch points involves active selection of one possible subsequent path from a larger number that may be available. This is often done, in the sense of Atlan and Cohen (1998), by comparison of ‘sensory' data with an internalized -- learned or inherited -- picture of the world, and upon that comparison, an active choice of response is made from a larger number of those possible. Rosen (2012) invokes `anticipatory models' for such processes. Following the Atlan/Cohen model, choice involves reduction in uncertainty, and reduction in uncertainty implies the existence of an information source that we will call `dual' to the underlying cognitive process. Wallace (2012) provides a somewhat more formal treatment.

What is clear is that the dual information source or sources associated with developmental process must be deeply coupled with the underlying groupoid symmetries characterizing development. As development proceeds, the groupoid symmetry becomes systematically richer.

As Feynman (1996) argues, information is not ‘entropy', rather it can be viewed as a form of free energy. Indeed, Feynman (1996), following Bennett, constructs an idealized machine that turns the information within a message into useful work.

Second, groupoids are almost groups, and it becomes possible to apply Landau's symmetry breaking/making arguments to the dual information sources characterizing developmental process (Pettini 2007). In that theory, phase transitions are recognized in terms of sudden shifts in the underlying group symmetries available to the system at different temperatures. High temperatures, with the greatest available energies, have the greatest possible symmetries. Symmetry breaking occurs in terms of the sudden nonzero value of some `order parameter' like magnetization at a sufficiently low critical temperature.

For a road network, for example, the `order parameter' would be the number of road turnoffs blocked by a traffic jam. The temperature analog is an inverse function of the linear vehicle density (Kerner and Klenov 2009; Wallace 2016a).

The third component of the model looks in detail at the embedding regulatory apparatus that must operate at each branch point to actively choose a path to the desired ‘phenotype'. This requires exploration of the intimate connection between control and information theories represented by the Data Rate Theorem (Nair et al. 2007).

In a sense, the underlying argument is by abduction from recent advances in evolutionary theory: West-Eberhard (2003, 2005) sees development as a key, but often poorly appreciated, element of evolutionary process, in that a new input, whether it comes from a genome, like a mutation or from the external environment, like a temperature change, a pathogen, or a parental opinion, has a developmental effect only if the preexisting phenotype can respond. A novel input causes a reorganization of the phenotype, a `developmental recombination' in which phenotypic traits are expressed in new or distinctive combinations during ontogeny, or undergo correlated quantitative changes in dimensions. Developmental recombination can result in evolutionary divergence at all levels of organization.

Most importantly, perhaps, West-Eberhard characterizes individual development as a series of branching pathways. Each branch point is a developmental decision, a switch point, governed by some regulatory apparatus, and each switch point defines a modular trait. Developmental recombination implies the origin or deletion of a branch and a new or lost modular trait. The novel regulatory response and the novel trait originate simultaneously, and their origins are inseparable events: there cannot be a change in the phenotype without an altered developmental pathway.

Thus, there are strong arguments for the great evolutionary potential of environmentally induced novelties. An environmental factor can affect numerous individuals, whereas a mutation initially can affect only one, a perspective having implications, not only for evolutionary economics, but across a full spectrum of ubiquitous `developmental' phenomena: even traffic streams `evolve' under changing selection pressures, and, indeed, such pressures act at every level of biological, social, or economic organization, as well as across rapidly expanding realms of machine cognition.

That is, just as the Atlan/Cohen ‘cognitive paradigm' for the immune system generalizes across many different systems (Wallace 2012), so too does the West-Eberhard model of development: repeated branching under the control of an embedding regulatory apparatus responding to environmental cues is widely observed. Here, we apply a control theory formalism via the Data Rate Theorem, and using information theory, invoke the dual information source necessarily associated with regulatory cognition. The intent is to examine developmental disorders, in a large sense, over a spectrum that ranges from cellular to socioeconomic and emerging machine levels of organization, and across time scales from those of biological evolution to extremely rapid machine response.

The main focus is on exploring the influence of environmental insult on developmental dysfunction, where insult itself is measured by a projected scalar `tangent space' defined in terms of the invariants of a complicated `fog-of-war matrix' representing interacting environmental factors. The synergism between control and information theories via the Data Rate Theorem, and the extensions using topological and `free energy' Morse Theory methods, provide a new theoretical window into the dynamics of many developmental processes, via the construction of statistical models that, like more familiar regression procedures, can be applied to a broad range of experimental and observational data.

References

Atlan, H., I. Cohen, 1998, Immune information, self-organization and meaning, International Immunology, 10:711-717.

Fajstrup, L., E. Goubault, A. Mourgues, S. Mimram, M. Raussen, 2016, Directed Algebraic Topology and Concurrency, Springer, New York.

Feynman, R., 1996, Feynman Lectures on Computation, Addison-Wesley, Reading, MA.

Grandis, M., 2009, Directed Algebraic Topology: Models of Non-Reversible Worlds, Cambridge University Press, New York.

Hatcher, A., 2001, Algebraic Topology, Cambridge University Press, New York.

Kerner, B., S. Klenov, 2009, Phase transitions in traffic flow on multilane roads, Physics Reviews E, 80:056101.

Maturana, H., F. Varela, 1980, Autopoiesis and Cognition, Reidel, Netherlands.

Nair, G. et al., 2007, Feedback control under data rate constraints: an overview, Proceedings of the IEEE, 95:108-137.

Pettini, M., 2007, Geometry and Topology in Hamiltonian Dynamics, Springer, New York.

Rosen, R., 2012, Anticipatory Systems: Philosophical, Mathematical, and Methodological Foundations, Second Edition, Springer, New York.

Wallace, R., 2012, Consciousness, crosstalk, and the mereological fallacy: an evolutionary perspective, Physics of Life Reviews, 9:426-453.

Wallace, R., 2015, An Ecosystem Approach to Economic Stabilization: Escaping the neoliberal wilderness, Routledge Advances in Heterodox Economics, New York.

Wallace, R., 2016a, Information Theory Models of Instabilities in Critical Systems, Vol. 7 of the World Scientific Series in Information Studies, Singapore.

Wallace, R., 2016b, Environmental induction of neurodevelopmental disorders, Bulletin of Mathematical Biology, doi 10.1007/s11538-016-0226-5.

Wallace, R., 2016c, Subtle noise structures as control signals in high-order biocognition, Physics Letters A, 380:726-729.

Weinstein, A., 1996, Groupoids: unifying internal and external symmetry, Notices of the American Mathematical Association, 43:744-752.

West-Eberhard, M., 2003, Developmental Plasticity and Evolution, Oxford University Press, New York.

West-Eberhard, M., 2005, Developmental plasticity and the origin of species differences, PNAS, 102:6543-6549.

*Published: 9 June 2017*

**Abstract:**

The communication of health knowledge in social media plays an important role in public health literacy and health behavior promotion. But with the accumulation of user-generated health knowledge in social media, more and more misleading health information, health gossip and health rumors are inhibiting the communication of health knowledge and the development of information ecology in social media. This study focuses on the information ecology in social media and contributes to the communication of health knowledge in social media ecology, highlighting the characteristics of health knowledge and the special Chinese culture. Based on the definition of three effective communication forms embedded in the communication of health knowledge—the fear communication, the trust communication and the face communication, an explanatory framework is constructed to examine their interactions and impacts on the communication of health knowledge in social media. Data collected from 329 respondents was tested using a partial-least-squares (PLS) approach. The results indicate that fear communication and trust communication both act as effective communication forms contributing to the communication of health knowledge; face communication acts as a barrier constraining the trust communication while no effect on fear communication. Theoretical and practical contributions are discussed in this paper.

**Information Taxonomy**

*Published: 9 June 2017*

**Abstract:**

There is a diversity of different types and kinds of information. To organize this huge collection into a system, it is necessary to classify information with respect to various criteria developing a *Multiscale information taxonomy*, in which each dimension is an *aspect information taxonomy*. We construct such a multiscale information taxonomy based on the general theory of information (Burgin, 2003; 2004; 2010) and making use of its principles and technical tools.

It is important to understand that taxonomies are not auxiliary edifices in science but they are also laws of science when scientifically grounded and validated. For instance, the biological taxonomy of Carolous Linnaeus is a law of biology in the same way as Newton’s laws are laws of physics.

Here we follow taxonomic traditions of Linnaeus Carolous Linnaeus and Charles Saunders Peirce in the direction of information science. On the one hand, the results of our research connect new information science and technology with classical science demonstrating intrinsic links between information theory and profound results of Linnaeus. On the other hand, these results show unity in achievements of scientists working in different countries and on different continents such as biological classification of Linnaeus, chemical classification of Mendeleev, semiotic classifications of Peirce, classifications of subatomic particles in contemporary physics and classifications in information science developed here. We begin with a brief exposition of methodological principles of taxonomy construction and then apply these principles to the development of basic information taxonomies. Here we describe only some of them due to the space restrictions.

**Principles of taxonomy construction**

Having a multiplicity of objects, it is necessary to induce organization because it can help to study, understand and utilize this multiplicity. Organization is achieved by structuration of the multiplicity. An efficient technique of structuration is construction of taxonomies, classifications, typologies and categorizations. Let us consider the process and basic principles of taxonomy construction.

Taking a multiplicity of objects *M*, a researcher explicates objects’ properties molding aspects or amalgamated features of *M*. Then the researcher elucidates a criterion for each aspect. This allows us to form a scale for measuring/evaluating each aspect. Such a scale together with the corresponding criterion allows the researcher to build an aspect taxonomy. Combining together all aspect taxonomies, the researcher obtains a multiscale taxonomy of the multiplicity *M*.

It is important to understand that according to the contemporary methodology of science, there are three types of scientific laws: classificational, equational and implicational laws. Scientists traditionally consider only two latter types as laws of nature although the first type also reflects important regularities in nature and society.

An *equational law* has the form of an equation, for example, of a differential equation as many laws in physics, e.g., *E*^{ }=* mc*^{2}, chemistry or economics.

An *implicational law* has the form of an implication “If *A*, then *B*”. For instance, if āABC is a right triangle, then its sides satisfy the equation *c*^{2 }=* a*^{2} + *b*^{2}. It is a mathematical law called the Pythagorean theorem.

A *classificational law* has the form of a classification, typology or taxonomy. The biological taxonomy of the great biologist Linnaeus Carolous Linnaeus (1707-1778) and triadic typologies of the great logician Charles Saunders Peirce (1839-1914) are examples of classificational laws.

In addition, scientific laws can be qualitative and quantitative.

A *quantitative law* describes relations between quantitative characteristics of definite phenomena. For instance, Newton’s law of motion *ma* = *F* is a quantitative law of physics.

A *qualitative law* describes relations between qualitative characteristics of definite phenomena. For instance, Galilean law of motion “Every body continues its state of rest or of uniform motion in a straight line unless it is compelled to change that state by forces impressed upon it” is a qualitative law of physics. Classificational laws are usually also qualitative laws.

These methodological findings determine a higher scientific status and importance of the groundbreaking Linnaeus’ classification, as well as of the taxonomies constructed in this paper. Namely, this new understanding of scientific laws shows these taxonomies are qualitative laws of information science.

Note that while equational and implicational laws have been acknowledge in science from its very origin, classificational laws acquired their nomological status only recently in the structure-nominative direction of methodology of science.

**Three basic taxonomies of information**

We begin with the uppermost level of the taxonomic arrangement, which includes a huge diversity of types, kinds, sorts, categories and classes of information. On this level, we build the existential taxonomy

As information is an omnipresent phenomenon (Burgin and Dodig-Crnkovic, 2011), it is crucial to start its classification on the global level of the whole world. This thesis implies the conjecture that the structure of the world affects existence of forms of information, which correspond to this structure. The large-scale structure of the world is represented by the* Existential Triad* *of the World* (Burgin, 2012):

- Physical World
- Mental World
- World of Structures

In the Existential Triad, the Physical (material) World is conceived as the physical reality studied by natural sciences, the Mental World encompasses different levels of mentality, and the World of Structures consists of various forms and types of structures.

The existential stratification of the World continues the tradition of Plato with his World of Ideas (Plato, 1961) and the tradition of Charles Sanders Peirce with his extensive triadic classifications (Peirce, 1931-1935).

This stratification brings us to the phenomenon studied by the general theory of information and called *information in a broad sense *(Burgin, 2010). According to this approach, information in a broad sense is represented in each of the three worlds. In the Physical (material) World, it is called energy supporting in such a way the conjecture of von Weizsäcker that *energy might in the end turn out to be information* (Weizsäcker, 1974). Situated at the first level of the Mental World, individual mental energy includes psychic energy studied by such psychologists as Ernst Wilhelm von Brücke (1819-1892), Sigmund Freud (1856-1939) and Carl Gustav Jung (1875-1961). Information in a broad sense, which is situated in the World of Structures, is called information in a strict sense.

As a result, we have three types of information in the **global existential** **taxonomy**:

*Physical*-*world information*or*energy**Mental*-*world information*and its particular case,*mental energy**Structural*-*world information*or information*per se*defined as*information in a strict sense*

We will not analyze here the first two kinds of information in a broad sense as the first of them belongs to the scope of physics, while the second one is in the domain of psychology. Our concern is information in a strict sense or simply information.

The **developmental taxonomy** is brought on by the temporal aspect of information:

*Potential information**Actualized*information*Emerging*information

Let us consider some examples.

**Example 1.** Information in a book before somebody reads it is potential.

It is possible to measure potential information by its potential to make changes in the corresponding infological system. For instance, measuring potential epistemic information, we estimate (measure) potential changes in the knowledge system (Burgin, 2011).

**Example 2.** Information that already gave knowledge about something, e.g., information about observation of a positron obtained by Carl Anderson in 1932, is actualized.

It is possible to measure actual information by changes it made in the corresponding infological system. For instance, measuring actualized epistemic information, we determine (measure) changes in the knowledge system made by reception of this information (Burgin, 2011).

**Example 3.** Information in a computer, which processes this information or in the head of a person who thinks about it, is emerging.

It is possible to estimate emerging information by its potential to make changes, by transformations it made in the corresponding infological system and by the rate of ongoing transformations. For instance, measuring emerging epistemic information, we estimate (measure) what changes in the knowledge system have already been made and reckon the rate of ongoing changes.

Based on the extended triune model of the brain developed in (Burgin, 2010), we have the following bifocal **formation/action taxonomy/typology**, in which the first facet reflects the form nature of information existence while the second facet mirrors action category of information existence:

*Epistemic*(form) or*cognitive*(action)*information**Instructional*(form) or*effective*(action)*information**Emotional*(form) or*affective*(action)*information*

In this taxonomy, the first term/name of each class represents the form of the corresponding infological system, while the second term/name represents action of information. It means that the first nominal attribute of the taxonomic classes characterizes formation aspects of information while the second operational attribute of the taxonomic classes characterizes procedural aspects of information.

**Taxonomies suggested by other authors**

Banathy (1995) consider three important types of information. With respect to a system *R*, it is possible to consider referential, non-referential, and state-referential information.

*Referential information*has meaning in the system*R*.*Non-referential information*has meaning outside the system*R*, e.g., information that reflects mere observation of*R*.*State-referential information*reflects an external model of the system*R*, e.g., information that represents*R*as a state transition system.

Braman (1989) classifies roles of information:

1) *information as a resource*, coming in pieces unrelated to knowledge or information flows into which it might be organized;

2) *information as a commodity* is obtained using information production chains, which create and add economic value to information;

3) *information as a perception* of patterns has past and future, is affected by motive and other environmental factors, and itself has its effects;

4) *information as a constitutive force* in society, essentially affecting its environment.

All constructed taxonomies together form a hierarchical multiscale information taxonomy, which gives a systematic picture of information.

**References**

Banathy, B.A. (1995) The 21^{st} century Janus: The three faces of information, *Systems Research*, v. 12, No. 4, pp. 319-320

Braman, S. (1989) Defining information: An approach for policymakers, *Telecommunications Policty, *v. 13, No. 1, pp. 233-242

Burgin, M. *Theory of Information*: *Fundamentality*,* Diversity and Unification*, World Scientific, New York/London/Singapore, 2010

Burgin, M. (2011) Epistemic Information in Stratified M-Spaces, *Information*, v. 2, No.2, pp. 697 - 726

Burgin, M. *Structural Reality*, Nova Science Publishers, New York, 2012

Burgin, M. and Dodig-Crnkovic, G. (2011) Information and Computation – Omnipresent and Pervasive, in *Information* *and Computation*, World Scientific, New York/London/Singapore, pp. vii – xxxii

Linnaeus, C.* Systema naturae, sive regna tria naturae systematice proposita per classes, ordines, genera, & species*, Johann Wilhelm de Groot for Theodor Haak, Leiden, 1735

Peirce C. S. (1931-1935) *Collected papers*, v. 1-6, Cambridge University Press, Cambridge, England

von Weizsäcker, C.F. *Die Einheit der Natur*, Deutscher Taschenbuch Verlag, Munich, Germany, 1974

*Published: 9 June 2017*

**Abstract:**

In his search for the ‘essence’ of continuity, Richard Dedekind (1872) discovered the notion of *cut*. Epistemologically speaking, a cut produces a separation of a simply infinite system into two parts (*Stücke*) such that all the elements of one part are screened off all the elements of the other. The distinct continuity of a two-state quantum system is encapsulated in the notion of *qubit*, the basic ‘unit’ of quantum information. A qubit secures an infinite amount of information, which, however, appears to be only penetrable through ‘sections’ of classical bits. Whereas Dedekind’s cuts dwell on the discrete of number theory, the theory of nature is primarily concerned with continuous transformations. In contrast with Dedekind’s line of thought, could the notion of information be derived from a ‘principle’ of continuity?

**1. The ‘Phenomenon’ of the Cut**

Dedekind’s main concern was to clean the science of numbers from foreign notions, such as measurable quantities or geometrical evidence. Hence, the real challenge was to extract a purely arithmetic and perfectly rigorous definition of the essence of continuity from the discrete of rational numbers.

The *vexata quaestio *of “continuity and irrational numbers” originated with the Pythagorean discovery of *incommensurable *ratios. In the eyes of Pythagoreans, however, it was the divergence between the harmony of geometrical forms and the “atomism” of numbers to be disturbing. The early Pythagoreans “did not really distinguish numbers from geometrical dots. Geometrically, then, a number was an extended point or a very small sphere” (Kline 1972: 29). By contrast, in Dedekind’s view, “numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things” (1888: 791).

Amazingly, Dedekind extracted the essence of continuity from *cuts*. Considering that every point produces a separation of the straight line into two parts such that every point of one part lies to the left of every point of the other, Dedekind recognized the special character of continuity in the converse, *i.e. *in the following principle:

- If all points of the straight line fall into two classes such that every point of the first class (
*Klasse*) [*A*_{1}] lies to the left of every point of the second class [*A*_{2}], then there exists one and only one point which produces this division of all points into two classes, this severing of the straight line into two portions. (Dedekind 1872: 771)

What is precisely determined is primarily the *division *itself [1]. Hence, whenever we have a cut (*A*_{1}*, A*_{2}) produced by no rational number, we can create a new number, an *irrational *number, which we regard as completely defined by this cut (Dedekind 1872: 773). So the system of real numbers is obtained by filling up the gaps in the domain of rational numbers and making it continuous; “*taking the object that fills each gap to be essentially the gap itself*” (Stillwell 2010).

Dedekind’s notion of ‘cut’ raises distinguishability on to a higher level – from (integer) numbers to classes, from elements to properties – taking into account not solely the relations of one individual number to another, but also the relations between (infinite) sets of elements. As Dedekind emphasized, if “one regards the irrational number as the ratio of two measurable quantities,” then this manner of determining it is already set forth in the clearest possible way by Euclid. But a presentation “in which *the phenomenon of the cut in its logical purity *is not even mentioned, has no similarity whatever to mine, inasmuch as it resorts at once to the existence of a measurable quantity, a notion which (...) I wholly reject” (Dedekind 1888: 794).

**2. F****rom Atoms to Qubits**

While Dedekind’s axiom of continuity guarantees the logical purity of real numbers, physics needs measurable quantities to unravel the continuity of nature into elements. It is noteworthy that the Pythagorean arithmetical atomism as well as the Democritean physical atomism were stuck on ‘continuity.’ Since the harmony of (natural) forms ought to be expressed by (whole) numbers, there was no way to fill the gap between the finite and the infinite. If the discovery of incommensurable ratios meant the departure of geometric constructions from arithmetic operations, Zeno’s paradoxes made it clear that *motion *is not attainable by summing up an infinite series of discrete *states*.

It is a great achievement of quantum theory to have read the divide between measurable quantities and continuous transformations as a dialectic contrast and to have made it the source of physical meaning.

2.1. *Ghost **fi**elds*

Interestingly, a ‘*quantum *Zeno effect’ was first noticed by John von Neumann (1932): a sequence of measurements frequently performed on a quantum system can slow down or even halt the evolution of the state. As a consequence of the quantum Zeno effect, in a classical interference experiment [2], when a photon emerging from a Mach-Zehder interferometer informs that a ‘which-path’ measurement was set on its way, the probability that no measurement was actually performed (*i.e.*, no photon-observer *interaction *took place) could be stretched to the limit of 1.

The debate on the impact of ‘null-result’ measurements on the behaviour of quantum systems or, more generally, on the nature of *quantum interference *urged the search for a more ‘sensible’ description of physical reality. It is well known that Einstein, Podolsky, Rosen’s celebrated essay (1936) was supposed to highlight the conflict between the completeness of the quantum physical description of physical reality and Heisenberg’s *uncertainty relations*, but in fact it drew attention to a form of ‘non-locality’ underlying quantum physics. When measurements are performed on certain *pairs *of particles, the values of the same physical quantity for the two separated particles appear *instantly correlated*. Seemingly, the failing attempts to find a reasonably ‘realistic’ (*via *experiment) explanation of quantum interference effects led Einstein to coin the term ‘ghost fields’ (*Gespensterfelder *) for quantum waves.

2.2.* Perspectives **on distinguishability*

Rather than questioning non-locality, quantum correlations enlighten a notion of *non-separability*, called ‘entanglement.’ As Schrödinger (1935) observed, two quantum systems interact in a way such that only the properties of the pair are defined. Consider for instance the spin components. Although any individual particle holds a set of well-defined values, once two particles get entangled in a pair, the spin of one particle and that of the other go in the *same *direction or in *opposite *directions; ‘being the same’ or ‘being opposed’ are clearly properties concerning two objects. Accordingly, quantum theory forges pure *relational *properties, which do not work for individual systems.

As for a measurement on a single particle, it also involves a correlation be- tween two ‘subjects’: the system and the observer. Any physical system numbers a set of characteristic ‘potential’ features. To become ‘temporarily real’ (*observable *), any of these features is bound to a feasible system-observer interaction. In this perspective, any measurement brings about a special ‘relational property’ of the pair (cf. Rovelli 1996). To the extent that measurement can be viewed as an interaction where a certain perspective on one observable determines the distinct value to be ascribed to the observable, it requires to refine the very notion of ‘distinguishability.’ In order to satisfy this requirement, quantum theory introduces *complex probability amplitudes*, which size the angular separation between alternative possibilities and must be *squared *to generate probabilities.

Thus, the classical tenet that measurement unveils a property *of *the system must be revised. It is wrong to attribute a feature to a quantum system until a measurement has brought it to a close by an act of irreversible amplification (cf. Wheeler 1982).

2.3.* The*

**“**Elementary Quantum Phenomenon”“One who comes from an older time and is accustomed to the picture of the universe as a machine built out of ‘atoms’ is not only baffled but put off when he reads [...] Leibniz’s conception of the ultimate building unit, the monad” (Wheeler 1982: 560). What Leibniz wrote about the “monad”, Wheeler observed, is more relevant to what he called “quantum phenomenon” than to any- thing one has ever called an ‘atom’. The very word ‘phenomenon’, according to Wheeler, is the result of a long lasting debate between Bohr and Einstein about the logical self-consistency of quantum theory and its implications for *reality *: “No elementary phenomenon is a phenomenon until it is a registered (observed) phenomenon.” But Leibniz’s monad has neither extension, nor shape, hence it is *not *observable.

A monad is a *simple substance and a unity of perceptions*. As a unity of perceptions, it contains the whole universe. As a simple substance, it is not a ‘tangible’ thing, but rather the ‘perceiving faculty’ itself. Indeed perception performs the inner constant change, and also, as a function of correlation, enables monads to *express *each other:

- This
*interconnection*or accommodation of all created things to each other, and each to all the others, brings it about that each simple substance has relations that express all the others, and consequently, that each simple substance is a perpetual*living mirror*of the universe. (*Monadology*56; Leibniz 1989)

How to draw ‘meaningful’ perceptions – *i.e.*, natural phenomena – from an impenetrable faculty of perceiving, from the infinite unity of each monad? More than to the ‘quantum phenomenon’, the characteristic features of the monad apply to the *qubit*.

Like a monad, a qubit, which is the basic unit of quantum information theory, involves an infinite multitude. As a two-state quantum system, it can be prepared in a coherent superposition of two distinguishable states. It follows that there is no way to extract information from qubits other than by measuring them with ‘yes-no’ questions.

**3. The Essence of Information**

In the ‘artificial’ construction of a theoretical model – be it the Euclidean geometry or the universal computer – one starts with distinct elements and ponders how to achieve the connecting structure. In the attempt to figure out the intelligence of nature, one starts with the structure and tries to analyze it into elements. At its heart, stands the ultimate inner principle of ‘existence’: a principle of *metamorphosis*.

Reversing the Euclidean perspective, in his search for a general *geometric characteristic*, Leibniz pursued the ‘inner principle’ of geometry:

- Imagine taking two points in space, hence conceiving the indeterminate straight line through them; one thing is that each point is regarded individually as single, another thing is that both are regarded as simultaneously existing; besides the two points, something else is needed for seeing them as co-existent in their respective positions. When we consider one of the two points as if we took its position and looked at the other (point), what the mind determines is called
*direction*. (Leibniz 1995: 278)

Time enters geometry and generates the concept of space: “Space is the continuity in the ‘order of co-existence’ according to which, given the co-existence relation in the present and the law of changes (*lege mutationis *), the co-existence relation in any given time can be defined.”

For Leibniz, the whole universe is encapsulated in every monad from the very beginning, and the simple substance of monad coincides with the continuity principle of the disclosure of itself. Therefore, every monad must be also endowed with an original faculty of *representing*, which makes it able to match the variety of phenomena. To deliver ‘information’ about the universe, perceptions must become *observable *in the guise of phenomena.

Now, like a straight line, each perception needs two *co-existent elements *to be determined by an external observer. Thus, all measurable quantities (*i.e.*, the basic constituents of physics) must come into existence as *pairs*. This imposes one constraint on natural phenomena: given the infinity of perceptions, the number of natural elements must be the logarithm to the base two of that infinity. In this sense, Pythagoras correctly drew the geometry of nature from whole numbers. On the other hand, Leibniz insightfully saw the infinite multitude of natural forms as *related to *the different points of view of each monad.

In Leibniz’s world, however, there is no conflict between the continuity of the simple substance and the distinguishability of perceptions, because each monad is a “*living mirror *of the universe.” By contrast, in the (quantum) physical world, distinct points of view influence the spectral decomposition itself. The ‘substance’ of nature is captured by a unitary transformation, but physical *knowledge *rests upon *cross-ratios *between distinct perceptions. Thus, the essence of information springs from *correlations*.

**References**

- R. Dedekind (1872), Continuity and Irrational Numbers, (Ewald 1996: 765-779)
- R. Dedekind (1888), Was sind und was sollen die Zahlen, (Ewald 1996: 790-833)
- A. Einstein, B. Podolski, N. Rosen (1935), Can Quantum Mechanical Description of Physical Reality Be Considered Complete?,
*Physical Review*, 47: 777-780. - W. Ewald (ed.) (1996)
*From Kant to Hilbert: A source book in the foundations of mathematics*. Vol. 2 (Oxford Univ. Press, Oxford) - M. Kline (1972)
*Mathematical Thought from Ancient to Modern Times*. Vol. 1 (Oxford University Press, Oxford) - W. Leibniz (1989)
*Philosophical Essays*, eds. Ariew, R. and Garber, D. (Hackett Publishing Company, Indianapolis & Cambridge) - W. Leibniz (1995)
*La caractétistique géométrique*, eds. Echeverría, J. and Parmentier, M. (Librairie philosophique J. Vrin, Paris) - C. Rovelli (1996), Relational Quantum Mechanics,
*Int. J. Theor. Phys.*,**35**: 1637-1678 - E. Schördinger (1935), Die gegenwrtige Situation in der Quantenmechanik,
*Naturwissenschaften*,**23**: 807-812. - J. Stillwell (2010)
*Roads to Infinity*. (A. K. Peters, Natick, MA) - J. von Neumann (1932)
*Mathematische Grundlagen der Quantenmechanik*. (Springer, Berlin) - J. A. Wheeler (1982), The Computer and the Universe,
*Int. J. Theor. Phys.*, 21: 557-572

**Notes**

[1] Any separation of the domain of rational numbers into two classes, *A*_{1} and *A*_{2} , such that every number of one class is less than every number of the other, defines a *real *number.

[2] Think of photons set going through a Mach-Zehnder interferometer. After encountering the first beam-splitter each photon can choose between two mutually exclusive paths to reach the second beam-splitter.

*Published: 9 June 2017*

**Abstract:**

*Type of the Paper: Proceeding*

**The Difference That Makes a Difference for the Conceptualization of Information**^{†}

**Marcin J. Schroeder **^{1,}*****

^{1} Akita International University, Akita, Japan; mjs@aiu.ac.jp

***** Correspondence: mjs@aiu.ac.jp; Tel.: +81-18-886-5984

† Presented at the Symposium on **Theoretical Information Studies** of is4si Summit at Gothenburg, June 12-16, 2017.

Published: date

**Abstract: **Information is a subject of multiple efforts of conceptualization leading to controversies. Not frequently sufficient effort is made to formulate the concept of information in a way leading to its formal mathematical theory. Discussions of conceptualizations of information usually are focusing on the articulation of definitions, but not on their consequences for theoretical studies. This paper compares two conceptualizations of information exploring their mathematical theories. One of these concepts and its mathematical theory were introduced in earlier publications of the author. Information was defined in terms of the opposition of one and many and its theory was formulated in terms of closure spaces. The other concept of information was formulated in a rather open-ended way by Bateson as “any difference that makes a difference”. There are some similarities between Bateson’s concept of information and that of MacKay. In this paper a mathematical theory is formulated for this alternative approach to information founded on the concept of a difference in terms of generalized orthogonality relation. Finally, the mathematical formalisms for both approaches are compared and related. In conclusion of that comparison the approach to information founded on the concept of difference is a special case for the approach based on one-and-many opposition..

**Keywords: **Information concept; Information definition; Information theory; Generalized orthogonality; Closure spaces.

**Introduction**

The concept of information is a subject of never ending discussions. The fact that these discussions do not lead to consensus generates a lot of anxiety among those who are engaged in the study of information, while this should be considered best evidence for the non-trivial character of this concept and as such be a source of joy. The actual problem is not in the variety of different definitions, but in the fact that many of them are deficient in logical rigor and that their mutual comparisons rarely go beyond the surface of verbal articulation. It seems that more attention is payed to the normative question what “should” be called information than to the issue of the explanatory power of the concept in the contexts of its use. There is nothing necessitating the choice of the particular definition of any concept and of course this applies to the concept of information too. Therefore, criteria for evaluation and comparisons of definitions can be found only in their consequences for the development of the theory of information understood as a complex of assertions regarding its characteristics, structure, properties and relations to other concepts.

This is exactly why so called information theory developed by Shannon is not a theory of information at all, but a theory of communication. Shannon never defined the concept of information in his great study of communication, which does not tell us anything about the structural characteristics or properties of information and even its quantitative characteristic in the form of entropy is problematic [1]. Actually, the word “information” in his famous article appears only few times and its only important occurrence (and probably last in entire text) is in the context of quantities that have form of entropy known from “statistical mechanics” and that “play a central role in information theory as measures of information, choice and uncertainty” [2]. Probably Shannon’s unfortunate reference to “information theory” as if such theory existed already contributed to persisting confusion regarding what information theory is in spite of the continuing strong objections to its identification with Shannon’s theory of communication [3].

Shannon’s goal was to develop a mathematical theory of communication and therefore he cannot be blamed for not paying enough attention to the concept of information and its characterization. It is more problematic that frequently contributions to the discussion of information are equally vague regarding what exactly information is, how its concept can be described in a formal way and what we can assert about it. Competing voices about information are usually so incompatible (information as representation, information conceived through conduit metaphor, information in linguistic context, information as data in computation, etc.) that no comparison of the concepts involved is possible. Even more controversial are very strong claims, for which their authors do not provide any justification (e.g. “no information without representation” used as a slogan by followers of MacKay’s approach to information as “that which adds to a representation” [4]).

Not always, or even not frequently sufficient effort is made to formulate the concept of information in a way leading to its formal mathematical theory. Mathematical formulation is important, because mathematical theories of concepts can be easily compared through analysis of their theorems. This paper is exploring such comparison between mathematical theories of information for two conceptualizations of information. One of these concepts and the theory derived from it were introduced in earlier publications of the author. Information was defined by him in terms of the categorial opposition of one and many, as that which makes one out of many either by the selection or by structuralization [1,5]. Thus, this many can be made one by a selection of an element of the variety constituting the many, or by a structure which unify the many into one. Mathematical theory of such concept was presented and analyzed in many earlier publications of the author [6,7].

The other concept of information considered here is probably the most popular of all attempts in conceptualization of information was formulated in a rather open-ended way by Gregory Bateson in several of his publications from the 1970’s [8]. But it was the glossary appended to his last book that made it a famous, commonly invoked slogan “information is any difference that makes a difference” [9]. This description of information is not a precise definition, but not just a game of words either. Of course, its popularity owes a lot to its polysemic, proverbial form and vernacular language. The lack of precision may increase its attractiveness, as everyone can find it consistent with own views. In particular, the use of the idiomatic expression “makes a difference” opens it to a variety of interpretations. It can indicate effectiveness, for instance in the sense of causation, or it can have a normative interpretation as an indication of importance. Actually Bateson apparently appreciated this ambiguity, as he dropped the ending “in some later event” suggesting the former interpretation from his “definition” as formulated in earlier papers (“information is any difference that makes a difference in some later event” [8]).

To be fair, we can find similar idiomatic expression in MacKay’s study of information in the context of what he considered “operational” definition of information: “We shall find it profitable to ask: ‘To what does information make a difference? What are its effects?’ This will lead us to an ‘operational’ definition covering all senses of the term, which we can then examine in detail for measurable properties” [10]. He tries to answer the question about the effects of information, but not how information makes a difference. So his use of the idiomatic expression has the same intention as that of Bateson to avoid being bound by any commitment to a specific interpretation.

Bateson’s way to information as “any difference that makes a difference” began already in 1951 in the spirit much closer to MacKay’s representational view of information: “Every piece of information has the characteristic that it makes a positive assertion and at the same time makes a denial of the opposite of that assertion” [11]. But already at that time he recognized the role of differences: “In this sense, our initial sensory data are always ‘first derivatives’, statements about *differences* which exist among external objects or statements about changes which occur either in them or in our relationship to them. [...] What we perceive easily is difference and change – and difference is a relationship” [12]. In the following years we can see that his view of information became increasingly general, but instead of lifting the level of abstraction and looking for more abstract conceptual framework, Bateson remained at the level of common sense concepts, but tried to formulate his description increasingly open-ended.

Why are Bateson’s and MacKay’s studies of information distinct among so many other attempts? They both are motivated by the interest in structural aspects of information, but try not to severe the connection to Shannonian theory of communication. Neither includes actual structural analysis of information or goes beyond purely declarative interest in structures, but both recognize the importance of structural characteristics of information. MacKay explicitly refers to the concept of a structure, for instance when he writes: “By representation is meant any structure (pattern, picture, model) whether abstract or concrete, of which the features purport to symbolize or correspond in some sense with those of some other structure” [13]. Also, he writes about Structural Information-Content as “The number of *distinguishable groups or clusters* in a representation [...] Thus structural information is not concerned with the *number* of elements in a pattern, but with the possibility of *distinguishing between *them” [14]. There is nothing here about what actually structure is, except some scattered common sense examples of “pattern, picture, model” and a vague statement that structure’s presence is manifested by some grouping or clustering of elements and that this introduces possibility of making distinctions, i.e. to recognize differences.

Since neither Bateson, nor MacKay clarified the qualifying expression of “making difference” and the former intentionally leaves this qualification open-ended, in this paper the second, alternative to that of the present author approach to information is understood as founded on the concept of a difference without its qualification. It will be shown in the next section of the paper that this concept has a surprisingly rich philosophical consequences and interesting mathematical theory. Finally, in the third section the mathematical formalisms for both approaches are compared and related. The surprising conclusion of that comparison is that the approach to information founded on the concept of difference is a special case for the approach based on one-and-many opposition and its formalism in closure spaces.

**Difference and Structure**

The concept of difference (Latin *differentia*, Greek *diaphora*) assumed very early prominent position in philosophy along with those of a genus and species due to its role in Aristotelian logic (*Prior Analytics 24 ^{a}16 - 25^{a}13*) [15]. Differentia between species became a fundamental tool in defining universals. Aristotle gave it also an important role in the study of substance (

*Metaphysics 1037*) [15]. However after the decline of the interest in Scholastic philosophy in the advent of the Scientific Revolution of the 17

^{b}8-1039^{a}8^{th}century it was relegated to the secondary role of the negation of the equality or equivalence relations. There was more interest in what makes things similar than different.

One notable exception was the recognition by John Wilkins of the importance of difference in cognition and especially in matters related to cryptography in his 1642 book on the subject of cryptography *Mercury or the Secret and Swift Messenger*: “For in the general we must note, that whatever is capable of a competent Difference, perceptible to any Sense, may be a Sufficient Means whereby to express the Cogitations. It is more convenient, indeed, that these Differences should be of as great Variety as the Letters of the Alphabet; but it is sufficient if they be but twofold, because Two alone may, with somewhat more Labour and Time, be well enough contrived to express all the rest” [16].

Bateson’s description of information as “a difference that makes a difference” and MacKay’s references to structural content of information clearly associated with differences are always considered as independent, original and unprecedented contributions to the study of information. Sometimes there are voices that at least chronological priority should be given to MacKay in the setting foundations for information in the concept of difference, which is disputable. However, they both must have been influenced by the dominating at the time philosophical and methodological structuralism. It is extremely unlikely that they both were unaware of the works of Herman Weyl [17], Jean Piaget [18], Claude Levi-Strauss [19] and stayed insulated from the philosophical discourse on the fundamental role of structures across all domains of human inquiry.

Furthermore, it is very unlikely that they were not familiar with the original source of the structuralistic methodology in the works of Ferdinand de Saussure, specifically in his 1916 book *Course in General Linguistics*. His general study of the language (after all the primary example of information system) was based on the idea of the transition from the traditional diachronic approach focusing on the derivations of linguistic forms from historically earlier ones to the synchronic methodology analyzing structural characteristics. But the structure of the language according to de Saussure is manifested in differences: “Everything that has been said up to this point boils down to this: in language there are only differences. [...] Language has neither ideas nor sounds that existed before the linguistic system, but only conceptual or phonic differences that have issued from the system. [...] Any nascent difference will tend invariably to become significant but without always succeeding or being successful on the first trial. Conversely, any conceptual difference perceived by the mind seeks to find expression through a distinct signifier, and two ideas that are no longer distinct in the mind tend to merge into the same signifier [20].

**Mathematical Formalisms**

We can proceed to mathematical formalisms of the two approaches to information. Thus, the author of this paper defined information as a resolution of the one-many opposition, or in other words as that, which makes one out of many. There are two ways in which many can be made one, either by the selection of one out of many, or by binding the many into a whole by some structure. The former is a selective manifestation of information and the latter is a structural manifestation. They are different manifestations of the same concept of information, not different types, as one is always accompanied by the other, although the multiplicity (many) can be different in each case.

Now we can interpret this definition within mathematical theory of closure spaces [21]. The concept of information requires a variety (many), which can be understood as an arbitrary set S (called a carrier of information). Information system is this set S equipped with the family of subsets** **F satisfying conditions: entire S is in F, and together with every subfamily of F, its intersection belongs to F, i.e. F is a Moore family. Of course, this means that we have a closure operator defined on S (i.e. a function f on the power set 2^{S} of a set S such that:

(1) For every subset A of S, A is a subset of f(A);

(2) For all subsets A, B of S, if A is a subset B, then f(A) is a subset f(B);

(3) For every subset A of S, f(f(A)) = f(A)).

The Moore family F of subsets is simply the family f-Cl of all closed subsets, i.e. subsets A of S such that A= f(A). The family of closed subsets F = f-Cl is equipped with the structure of a complete lattice L_{f} by the set theoretical inclusion. L_{f} can play a role of the generalization of logic for not necessarily linguistic information systems, although it does not have to be a Boolean algebra. In many cases it maintains all fundamental characteristics of a logical system [22].

Information itself is a distinction of a subset F_{0} of F, such that it is closed with respect to (pair-wise) intersection and is dually-hereditary, i.e. with each subset belonging to F_{0}, all subsets of S including it belong to F_{0} (i.e. F_{0 }is a filter in L_{f}).

The Moore family F can represent a variety of structures of a particular type (e.g. geometric, topological, algebraic, logical, etc.) defined on the subsets of S. This corresponds to the structural manifestation of information and gives the expression “structural” explicit meaning. Filter F_{0} in turn, in many mathematical theories associated with localization, can be used as a tool for identification, i.e. selection of an element within the family F, and under some conditions in the set S. For instance, in the context of Shannon’s selective information based on a probability distribution of the choice of an element in S, F_{0} consists of elements in S which have probability measure 1, while F is simply the set of all subsets of S. Thus, this approach combines both manifestations of information, the selective and the structural.

Now we can consider the formalism for the general concept of difference. In mathematics this concept is usually called generalized orthogonality (with possible qualifications indicating its variations as “strong”, “weak”, etc.). The reason is that orthogonality in vector spaces equipped with scalar product is a good model of the relationship in a very general case.

The abstract orthogonality relation is defined on a set S by the conditions [23,24]:

- Relation # is symmetric,
- For every x in S, if x#x, then x#y for all y in S.

Of course, the second condition may seem strange. How anything can be different from, or orthogonal to itself. However zero vector in vector spaces with a scalar product is orthogonal to itself. Also, if we assume that the relation is irreflexive (no element is orthogonal to itself) the second condition is satisfied. Therefore there is no reason to object such generalization when it merges several different mathematical concepts analogous to the common sense word “difference”.

If the set S has an additional structure of a partial order, then we can enrich the theory of orthogonality in the following way.

We can consider more general structure of a poset <P, << > with the so called strong orthogonality relation ^ defined as <P, <<, #> by the conditions:

- The relation # is symmetric, i.e. if x#y, then y#x,
- For every x in P, if x#x, then x#y for all y in P.
- For all x,y in P, x << y
*iff*#(y) is a subset of #(y), where #(x) = { z in P: z#x}

For instance Aristotelian syllogistics can be considered an example of such structure [22].

**Conclusions**

In the extended version of this paper a theorem is provided that shows in what way every orthogonality space is associated with a unique closure space. On the other hand we have specific properties for closure spaces to be derived from a generalized orthogonality relation. It turns out that only very narrow class of closure spaces can be associated with orthogonality relations. This shows that information formalized with the concept of difference understood as a very general orthogonality relation is a special case of information described in terms of closure spaces.

**Conflicts of Interest:** The author declares no conflict of interest.

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*Entropy***2004**,*6*, 388-412. - Shannon, E.C. A mathematical theory of communication. In
*The Mathematical Theory of Communication;*Shannon, E. C.; Weaver, W., Eds.; University of Illinois Press: Urbana, IL., 1949; p. 20. - Bar-Hillel Y., Carnap R. An outline of a theory of semantic information, Technical Report No. 247, Research Laboratory of Electronics, MIT (1952); In Bar-Hillel, Y. (ed.),
*Language and Information: Selected Essays on Their Theory and Application*, Reading, MA, Addison-Wesley, 1964; pp. 221–274. - MacKay, D.M.
*Information, Mechanism and Meaning.*MIT Press: Cambridge, MA, 1969; p. 163. - Schroeder, M.J. Philosophical Foundations for the Concept of Information: Selective and Structural Information. In
*Proceedings of the Third International Conference on the Foundations of Information Science, Paris, July 2005*; Available at http://www.mdpi.org/fis2005/proceedings. html - Schroeder, M.J. From Philosophy to Theory of Information.
*International Journal Information Theories and Applications***2011**,*18 (1)*, 56-68. - Schroeder, M.J. Towards Autonomous Computation: Geometric Methods of Computing.
*Philosophy and Computers (Newsletter of the American Philosophical Association)*,**2015**, 15 (1), 9-27. http://c.ymcdn.com/sites/www.apaonline.org/resource/collection/ EADE8D52-8D02-4136-9A2A-729368501E43/ComputersV15n1.pdf - Bateson, G. A Re-examination of ‘Bateson’s Rule’. Journal of Genetics,
**1971**, 60 (3), 230-240. - Bateson, G.
*Mind and Nature: A Necessary Unity.*E.P. Dutton: New York, 1979. - MacKay, D.M.
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*Communication: The Social Matrix of Psychiatry,*Ruesch, J, Bateson, G., Eds.; Norton: New York, 1951; p. 175. *ibid.*p.173.- MacKay, D.M.
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*Selections.*Ross, W.D. Ed.; Charles Scribner’s Sons: New York, 1955. - Gleick, J.
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© 2017 by the authors. Submitted for possible open access publication under the

terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)

*Published: 9 June 2017*

**Abstract:**

The significant breakthrough and innovation obtained by modern information science and technology enable the “information” gradually become the internal driving force of economy development and social progress, causing a great advance of the productivity of modern society, and the information technology quickly transform into the actual productivity-informational productivity. From the perspective of dual-evolution of material world and informational world presented by information philosophy, and through using the information thinking mode and treating the “information” as a way of existence, this article will discuss the evolution of informational productivity and its role for sustainable development society.

First, this article will summarize the development process of productivity theories, and will analyze the formation conditions and the evolution process of informational productivity; second, it will expound that the informational productivity is a brand-new productivity form that is different from material productivity and spiritual productivity; third, it will make a dialectical analysis on the systematic, static and dynamic characters, properties and the inherent operation laws of the elements in the structure of informational productivity. At last, this paper will advocate that the realization of informational productivity will depends on the actual conditions, including economy, politics and cultural environments and so on, and will conclude that developing the information productivity is an inevitable road to realize the sustainable development society.

*Published: 9 June 2017*

**Abstract:**

A combination of directed homotopy topological and Morse theoretic methods can significantly extend control and information theories, permitting deeper understanding of ‘developmental' pathologies afflicting a broad spectrum of biological, psychological, socioeconomic, machine, and hybrid processes across different time scales and levels of organization. Such pathologies emerge as phase transitions driven by synergistic forms of environmental insult under stochastic circumstances, causing `comorbid condensations' through groupoid symmetry breaking. The resulting statistical models should be useful for the analysis of experimental and observational data in many fields.

More explicitly, developmental process -- ontology -- is ubiquitous across vast biological, social, economic, and machine realms. Rosen (2012) characterizes this as ‘...anticipatory behavior at all levels of... organization'. Maturana and Varela (1980) see cognition permeating biology. Atlan and Cohen (1998) invoke a ‘cognitive paradigm' for the immune system that generalizes to wound healing, blood pressure regulation, neural dynamics, and so on (Wallace 2012). West-Eberhard (2003; 2005) sees ontology as a matter of ‘choice' at developmental branch points. Traffic flow involves repeated ‘ontological' choices by atomistic vehicles at road junctions, as well as during ordinary passage in heavy traffic (Wallace 2016a Ch.9). Indeed, machine cognition quite generally requires repeated choice of response to environmental cues (Wallace 2016a). A firm responding to market pressures must, at least annually, reconfigure product lines and marketing strategies, also a cognitive process (e.g., Wallace 2015 and references therein). Democratic state actors confronted by changing patterns of threat and affordance must, at least during elections, repeatedly choose among the different patterns of response made available by the contending parties and candidates. Active warfare involves constantly repeated choice at all levels of organization leading up to, and during, combat operations.

All developmental phenomena are, however, subject to patterns of failure and dysfunction. These range from neurodevelopmental disorders such as autism and schizophrenia (Wallace 2016b) to collapse of vehicle flow in traffic jams (Kerner and Klenov 2009), and catastrophes of governance like Brexit, or the US occupation of Iraq. Here, we attempt to extend results from information and control theories to statistical tools useful in understanding developmental failure.

The underlying model of development is that a system begins at some initial ‘phenotype' So confronting a branch point Co leading to two (or more) possible subsequent ‘phenotypes' S1 and S2, where new branch points C1 and C2 will be confronted, and at which choices must again be made, and so on.

Two of the three essential components of this model are intrinsically linked.

The first component is that of directed homotopy, in the sense of Grandis (2009) and Fajstrup et al. (2016). That is, there are equivalence classes of paths leading from ‘phenotype' S_{n} to S_{n+1}, as defined by the branch conditions C_{n}. A group structure -- the so-called ‘fundamental group' -- is imposed on a geometric object by convolution of loops within it that can be reduced without crossing a hole (e.g., Hatcher 2001). An algebraic topology of directed homotopy can be constructed from the composition of paths that constitutes a groupoid (Weinstein 1996), an object in which a product need not be defined between every possible object, here the equivalence classes of possible linear paths. As Weinstein (1996) emphasizes, almost every interesting equivalence relation on a space B arises in a natural way as the orbit equivalence relation of some groupoid G over that space. Instead of dealing directly with the orbit quotient space B/G$as an object in the category of sets and mappings, one should consider instead the groupoid G itself as an object in the category of groupoids and homotopy classes of morphisms. An exactly similar perspective involves use of the homotopy and homology groups of algebraic topology to characterize complicated geometric objects (Hatcher 2001).

The second component is recognition that choice at developmental branch points involves active selection of one possible subsequent path from a larger number that may be available. This is often done, in the sense of Atlan and Cohen (1998), by comparison of ‘sensory' data with an internalized -- learned or inherited -- picture of the world, and upon that comparison, an active choice of response is made from a larger number of those possible. Rosen (2012) invokes `anticipatory models' for such processes. Following the Atlan/Cohen model, choice involves reduction in uncertainty, and reduction in uncertainty implies the existence of an information source that we will call `dual' to the underlying cognitive process. Wallace (2012) provides a somewhat more formal treatment.

What is clear is that the dual information source or sources associated with developmental process must be deeply coupled with the underlying groupoid symmetries characterizing development. As development proceeds, the groupoid symmetry becomes systematically richer.

As Feynman (1996) argues, information is not ‘entropy', rather it can be viewed as a form of free energy. Indeed, Feynman (1996), following Bennett, constructs an idealized machine that turns the information within a message into useful work.

Second, groupoids are almost groups, and it becomes possible to apply Landau's symmetry breaking/making arguments to the dual information sources characterizing developmental process (Pettini 2007). In that theory, phase transitions are recognized in terms of sudden shifts in the underlying group symmetries available to the system at different temperatures. High temperatures, with the greatest available energies, have the greatest possible symmetries. Symmetry breaking occurs in terms of the sudden nonzero value of some `order parameter' like magnetization at a sufficiently low critical temperature.

For a road network, for example, the `order parameter' would be the number of road turnoffs blocked by a traffic jam. The temperature analog is an inverse function of the linear vehicle density (Kerner and Klenov 2009; Wallace 2016a).

The third component of the model looks in detail at the embedding regulatory apparatus that must operate at each branch point to actively choose a path to the desired ‘phenotype'. This requires exploration of the intimate connection between control and information theories represented by the Data Rate Theorem (Nair et al. 2007).

In a sense, the underlying argument is by abduction from recent advances in evolutionary theory: West-Eberhard (2003, 2005) sees development as a key, but often poorly appreciated, element of evolutionary process, in that a new input, whether it comes from a genome, like a mutation or from the external environment, like a temperature change, a pathogen, or a parental opinion, has a developmental effect only if the preexisting phenotype can respond. A novel input causes a reorganization of the phenotype, a `developmental recombination' in which phenotypic traits are expressed in new or distinctive combinations during ontogeny, or undergo correlated quantitative changes in dimensions. Developmental recombination can result in evolutionary divergence at all levels of organization.

Most importantly, perhaps, West-Eberhard characterizes individual development as a series of branching pathways. Each branch point is a developmental decision, a switch point, governed by some regulatory apparatus, and each switch point defines a modular trait. Developmental recombination implies the origin or deletion of a branch and a new or lost modular trait. The novel regulatory response and the novel trait originate simultaneously, and their origins are inseparable events: there cannot be a change in the phenotype without an altered developmental pathway.

Thus, there are strong arguments for the great evolutionary potential of environmentally induced novelties. An environmental factor can affect numerous individuals, whereas a mutation initially can affect only one, a perspective having implications, not only for evolutionary economics, but across a full spectrum of ubiquitous `developmental' phenomena: even traffic streams `evolve' under changing selection pressures, and, indeed, such pressures act at every level of biological, social, or economic organization, as well as across rapidly expanding realms of machine cognition.

That is, just as the Atlan/Cohen ‘cognitive paradigm' for the immune system generalizes across many different systems (Wallace 2012), so too does the West-Eberhard model of development: repeated branching under the control of an embedding regulatory apparatus responding to environmental cues is widely observed. Here, we apply a control theory formalism via the Data Rate Theorem, and using information theory, invoke the dual information source necessarily associated with regulatory cognition. The intent is to examine developmental disorders, in a large sense, over a spectrum that ranges from cellular to socioeconomic and emerging machine levels of organization, and across time scales from those of biological evolution to extremely rapid machine response.

The main focus is on exploring the influence of environmental insult on developmental dysfunction, where insult itself is measured by a projected scalar `tangent space' defined in terms of the invariants of a complicated `fog-of-war matrix' representing interacting environmental factors. The synergism between control and information theories via the Data Rate Theorem, and the extensions using topological and `free energy' Morse Theory methods, provide a new theoretical window into the dynamics of many developmental processes, via the construction of statistical models that, like more familiar regression procedures, can be applied to a broad range of experimental and observational data.

References

Atlan, H., I. Cohen, 1998, Immune information, self-organization and meaning, International Immunology, 10:711-717.

Fajstrup, L., E. Goubault, A. Mourgues, S. Mimram, M. Raussen, 2016, Directed Algebraic Topology and Concurrency, Springer, New York.

Feynman, R., 1996, Feynman Lectures on Computation, Addison-Wesley, Reading, MA.

Grandis, M., 2009, Directed Algebraic Topology: Models of Non-Reversible Worlds, Cambridge University Press, New York.

Hatcher, A., 2001, Algebraic Topology, Cambridge University Press, New York.

Kerner, B., S. Klenov, 2009, Phase transitions in traffic flow on multilane roads, Physics Reviews E, 80:056101.

Maturana, H., F. Varela, 1980, Autopoiesis and Cognition, Reidel, Netherlands.

Nair, G. et al., 2007, Feedback control under data rate constraints: an overview, Proceedings of the IEEE, 95:108-137.

Pettini, M., 2007, Geometry and Topology in Hamiltonian Dynamics, Springer, New York.

Rosen, R., 2012, Anticipatory Systems: Philosophical, Mathematical, and Methodological Foundations, Second Edition, Springer, New York.

Wallace, R., 2012, Consciousness, crosstalk, and the mereological fallacy: an evolutionary perspective, Physics of Life Reviews, 9:426-453.

Wallace, R., 2015, An Ecosystem Approach to Economic Stabilization: Escaping the neoliberal wilderness, Routledge Advances in Heterodox Economics, New York.

Wallace, R., 2016a, Information Theory Models of Instabilities in Critical Systems, Vol. 7 of the World Scientific Series in Information Studies, Singapore.

Wallace, R., 2016b, Environmental induction of neurodevelopmental disorders, Bulletin of Mathematical Biology, doi 10.1007/s11538-016-0226-5.

Wallace, R., 2016c, Subtle noise structures as control signals in high-order biocognition, Physics Letters A, 380:726-729.

Weinstein, A., 1996, Groupoids: unifying internal and external symmetry, Notices of the American Mathematical Association, 43:744-752.

West-Eberhard, M., 2003, Developmental Plasticity and Evolution, Oxford University Press, New York.

West-Eberhard, M., 2005, Developmental plasticity and the origin of species differences, PNAS, 102:6543-6549.

*Published: 9 June 2017*

**Abstract:**

**Abstract.** Information is a subject of multiple efforts of conceptualization leading to controversies. Not frequently sufficient effort is made to formulate the concept of information in a way leading to its formal mathematical theory. Discussions of conceptualizations of information usually are focusing on the articulation of definitions, but not on their consequences for theoretical studies. This paper compares two conceptualizations of information exploring their mathematical theories. One of these concepts and its mathematical theory were introduced in earlier publications of the author. Information was defined in terms of the opposition of one and many and its theory was formulated in terms of closure spaces. The other concept of information was formulated in a rather open-ended way by Bateson as “any difference that makes a difference”. There are some similarities between Bateson’s concept of information and that of MacKay. In this paper a mathematical theory is formulated for this alternative approach to information founded on the concept of a difference in terms of generalized orthogonality relation. Finally, the mathematical formalisms for both approaches are compared and related. In conclusion of that comparison the approach to information founded on the concept of difference is a special case for the approach based on one-and-many opposition.

**Introduction **

The concept of information is a subject of never ending discussions. The fact that these discussions do not lead to consensus generates a lot of anxiety among those who are engaged in the study of information, while this should be considered best evidence for the non-trivial character of this concept and as such be a source of joy. The actual problem is not in the variety of different definitions, but in the fact that many of them are deficient in logical rigor and that their mutual comparisons rarely go beyond the surface of verbal articulation. It seems that more attention is paid to the normative question what “should” be called information than to the issue of the explanatory power of the concept in the contexts of its use. There is nothing necessitating the choice of the particular definition of any concept and of course this applies to the concept of information too. Therefore, criteria for evaluation and comparisons of definitions can be found only in their consequences for the development of the theory of information understood as a complex of assertions regarding its characteristics, structure, properties and relations to other concepts.

This is exactly why so called information theory developed by Shannon is not a theory of information at all, but a theory of communication. Shannon never defined the concept of information in his great study of communication, which does not tell us anything about the structural characteristics or properties of information and even its quantitative characteristic in the form of entropy is problematic [1]. Actually, the word “information” in his famous article appears only few times and its only important occurrence (and probably last in entire text) is in the context of quantities that have form of entropy known from “statistical mechanics” and that “play a central role in information theory as measures of information, choice and uncertainty” [2]. Probably Shannon’s unfortunate reference to “information theory” as if such theory existed already contributed to persisting confusion regarding what information theory is in spite of the continuing strong objections to its identification with Shannon’s theory of communication [3].

Shannon’s goal was to develop a mathematical theory of communication and therefore he cannot be blamed for not paying enough attention to the concept of information and its characterization. It is more problematic that frequently contributions to the discussion of information are equally vague regarding what exactly information is, how its concept can be described in a formal way and what we can assert about it. Competing voices about information are usually so incompatible (information as representation, information conceived through conduit metaphor, information in linguistic context, information as data in computation, etc.) that no comparison of the concepts involved is possible. Even more controversial are very strong claims, for which their authors do not provide any justification (e.g. “no information without representation” used as a slogan by followers of MacKay’s approach to information as “that which adds to a representation” [4]).

Not always, or even not frequently sufficient effort is made to formulate the concept of information in a way leading to its formal mathematical theory. Mathematical formulation is important, because mathematical theories of concepts can be easily compared through analysis of their theorems. This paper is exploring such comparison between mathematical theories of information for two conceptualizations of information. One of these concepts and the theory derived from it were introduced in earlier publications of the author. Information was defined by him in terms of the categorial opposition of one and many, as that which makes one out of many either by the selection or by structuralization [1,5]. Thus, this many can be made one by a selection of an element of the variety constituting the many, or by a structure which unify the many into one. Mathematical theory of such concept was presented and analyzed in many earlier publications of the author [6,7].

The other concept of information considered here is probably the most popular of all attempts in conceptualization of information was formulated in a rather open-ended way by Gregory Bateson in several of his publications from the 1970’s [8]. But it was the glossary appended to his last book that made it a famous, commonly invoked slogan “information is any difference that makes a difference” [9]. This description of information is not a precise definition, but not just a game of words either. Of course, its popularity owes a lot to its polysemic, proverbial form and vernacular language. The lack of precision may increase its attractiveness, as everyone can find it consistent with own views. In particular, the use of the idiomatic expression “makes a difference” opens it to a variety of interpretations. It can indicate effectiveness, for instance in the sense of causation, or it can have a normative interpretation as an indication of importance. Actually Bateson apparently appreciated this ambiguity, as he dropped the ending “in some later event” suggesting the former interpretation from his “definition” as formulated in earlier papers (“information is any difference that makes a difference in some later event” [8]).

To be fair, we can find similar idiomatic expression in MacKay’s study of information in the context of what he considered “operational” definition of information: “We shall find it profitable to ask: ‘To what does information make a difference? What are its effects?’ This will lead us to an ‘operational’ definition covering all senses of the term, which we can then examine in detail for measurable properties” [10]. He tries to answer the question about the effects of information, but not how information makes a difference. So his use of the idiomatic expression has the same intention as that of Bateson to avoid being bound by any commitment to a specific interpretation.

Bateson’s way to information as “any difference that makes a difference” began already in 1951 in the spirit much closer to MacKay’s representational view of information: “Every piece of information has the characteristic that it makes a positive assertion and at the same time makes a denial of the opposite of that assertion” [11]. But already at that time he recognized the role of differences: “In this sense, our initial sensory data are always ‘first derivatives’, statements about *differences* which exist among external objects or statements about changes which occur either in them or in our relationship to them. [...] What we perceive easily is difference and change – and difference is a relationship” [12]. In the following years we can see that his view of information became increasingly general, but instead of lifting the level of abstraction and looking for more abstract conceptual framework, Bateson remained at the level of common sense concepts, but tried to formulate his description increasingly open-ended.

Why are Bateson’s and MacKay’s studies of information distinct among so many other attempts? They both are motivated by the interest in structural aspects of information, but try not to severe the connection to Shannonian theory of communication. Neither includes actual structural analysis of information or goes beyond purely declarative interest in structures, but both recognize the importance of structural characteristics of information. MacKay explicitly refers to the concept of a structure, for instance when he writes: “By representation is meant any structure (pattern, picture, model) whether abstract or concrete, of which the features purport to symbolize or correspond in some sense with those of some other structure” [13]. Also, he writes about Structural Information-Content as “The number of *distinguishable groups or clusters* in a representation [...] Thus structural information is not concerned with the *number* of elements in a pattern, but with the possibility of *distinguishing between *them” [14]. There is nothing here about what actually structure is, except some scattered common sense examples of “pattern, picture, model” and a vague statement that structure’s presence is manifested by some grouping or clustering of elements and that this introduces possibility of making distinctions, i.e. to recognize differences.

Since neither Bateson, nor MacKay clarified the qualifying expression of “making difference” and the former intentionally leaves this qualification open-ended, in this paper the second, alternative to that of the present author approach to information is understood as founded on the concept of a difference without its qualification. It will be shown in the next section of the paper that this concept has a surprisingly rich philosophical consequences and interesting mathematical theory. Finally, in the third section the mathematical formalisms for both approaches are compared and related. The surprising conclusion of that comparison is that the approach to information founded on the concept of difference is a special case for the approach based on one-and-many opposition and its formalism in closure spaces.

**Difference and Structure**

The concept of difference (Latin *differentia*, Greek *diaphora*) assumed very early prominent position in philosophy along with those of a genus and species due to its role in Aristotelian logic (*Prior Analytics 24 ^{a}16 - 25^{a}13*) [15]. Differentia between species became a fundamental tool in defining universals. Aristotle gave it also an important role in the study of substance (

*Metaphysics 1037*) [15]. However after the decline of the interest in Scholastic philosophy in the advent of the Scientific Revolution of the 17

^{b}8-1039^{a}8^{th}century it was relegated to the secondary role of the negation of the equality or equivalence relations. There was more interest in what makes things similar than different.

One notable exception was the recognition by John Wilkins of the importance of difference in cognition and especially in matters related to cryptography in his 1642 book on the subject of cryptography *Mercury or the Secret and Swift Messenger*: “For in the general we must note, that whatever is capable of a competent Difference, perceptible to any Sense, may be a Sufficient Means whereby to express the Cogitations. It is more convenient, indeed, that these Differences should be of as great Variety as the Letters of the Alphabet; but it is sufficient if they be but twofold, because Two alone may, with somewhat more Labour and Time, be well enough contrived to express all the rest” [16].

Bateson’s description of information as “a difference that makes a difference” and MacKay’s references to structural content of information clearly associated with differences are always considered as independent, original and unprecedented contributions to the study of information. Sometimes there are voices that at least chronological priority should be given to MacKay in the setting foundations for information in the concept of difference, which is disputable. However, they both must have been influenced by the dominating at the time philosophical and methodological structuralism. It is extremely unlikely that they both were unaware of the works of Herman Weyl [17], Jean Piaget [18], Claude Levi-Strauss [19] and stayed insulated from the philosophical discourse on the fundamental role of structures across all domains of human inquiry.

Furthermore, it is very unlikely that they were not familiar with the original source of the structuralistic methodology in the works of Ferdinand de Saussure, specifically in his 1916 book *Course in General Linguistics*. His general study of the language (after all the primary example of information system) was based on the idea of the transition from the traditional diachronic approach focusing on the derivations of linguistic forms from historically earlier ones to the synchronic methodology analyzing structural characteristics. But the structure of the language according to de Saussure is manifested in differences: “Everything that has been said up to this point boils down to this: in language there are only differences. [...] Language has neither ideas nor sounds that existed before the linguistic system, but only conceptual or phonic differences that have issued from the system. [...] Any nascent difference will tend invariably to become significant but without always succeeding or being successful on the first trial. Conversely, any conceptual difference perceived by the mind seeks to find expression through a distinct signifier, and two ideas that are no longer distinct in the mind tend to merge into the same signifier [20].

**Mathematical Formalisms**

We can proceed to mathematical formalisms of the two approaches to information. Thus, the author of this paper defined information as a resolution of the one-many opposition, or in other words as that, which makes one out of many. There are two ways in which many can be made one, either by the selection of one out of many, or by binding the many into a whole by some structure. The former is a selective manifestation of information and the latter is a structural manifestation. They are different manifestations of the same concept of information, not different types, as one is always accompanied by the other, although the multiplicity (many) can be different in each case.

Now we can interpret this definition within mathematical theory of closure spaces [21]. The concept of information requires a variety (many), which can be understood as an arbitrary set S (called a carrier of information). Information system is this set S equipped with the family of subsets **M** satisfying conditions: entire S is in M, and together with every subfamily of **M**, its intersection belongs to **M**, i.e. **M** is a Moore family. Of course, this means that we have a closure operator defined on S (i.e. a function f on the power set 2^{S} of a set S such that:

(1) For every subset A of S, A is a subset of f(A);

(2) For all subsets A, B of S, if A is a subset of B, then f(A) is a subset of f(B);

(3) For every subset A of S, f(f(A)) = f(A)).

The Moore family **M** of subsets is simply the family f-Cl of all closed subsets, i.e. subsets A of S such that A= f(A). The family of closed subsets **M** = f-Cl is equipped with the structure of a complete lattice L_{f} by the set theoretical inclusion. L_{f} can play a role of the generalization of logic for not necessarily linguistic information systems, although it does not have to be a Boolean algebra. In many cases it maintains all fundamental characteristics of a logical system [22].

Information itself is a distinction of a subset **M**_{0} of **M**, such that it is closed with respect to (pair-wise) intersection and is dually-hereditary, i.e. with each subset A belonging to **M _{0}**, all subsets of S including A belong to

**M**

_{0}(i.e.

**M**

_{0}_{ }is a filter in L

_{f}).

The Moore family **M** can represent a variety of structures of a particular type (e.g. geometric, topological, algebraic, logical, etc.) defined on the subsets of S. This corresponds to the structural manifestation of information and gives the expression “structural” explicit meaning. Filter **M _{0}** in turn, in many mathematical theories associated with localization, can be used as a tool for identification, i.e. selection of an element within the family

**M**, and under some conditions in the set S. For instance, in the context of Shannon type selective information based on a probability distribution of the choice of an element in S,

**M**consists of elements in S which have probability measure 1, while

_{0}**M**is simply the set of all subsets of S. Thus, this approach combines both manifestations of information, the selective and the structural.

Now we can consider the formalism for the general concept of difference. In mathematics this concept is usually called generalized orthogonality (with possible qualifications indicating its variations as “strong”, “weak”, etc.). The reason is that orthogonality in vector spaces equipped with scalar product is a good model of the relationship in a very general case.

The abstract orthogonality relation T is defined on a set S by the conditions [23,24]:

- The relation T is symmetric,
- For eery x in S: If xTx, then xTy for all y in S,

Of course, the second condition may seem strange. How anything can be different from, or orthogonal to itself. However zero vector in vector spaces with a scalar product is orthogonal to itself. Also, if we assume that the relation is irreflexive (no element is orthogonal to itself) the second condition is satisfied. Therefore there is no reason to object such generalization when it merges several different mathematical concepts analogous to the common sense word “difference”.

If the set S has an additional structure of a partial order, then we can enrich the theory of orthogonality in the following way.

We can consider more general structure of a partially ordered set (poset) P, with partial order < (inclusive!) with the so called strong orthogonality relation T defined by conditions:

- The relation T is symmetric, i.e. For all x,y in P: If xTy , then yTx,
- For every x in P: If xTx , then xTy for all y in P,
- For all x,y in P: x<y
*iff*T(y) is a subset of T(x), where T(x) = {z in P: zTx}

For instance Aristotelian syllogistics can be considered an example of such structure [22].

**Conclusions**

In the extended version of this paper a theorem is provided that shows in what way every orthogonality space is associated with a unique closure space. On the other hand we have specific properties for closure spaces to be derived from a generalized orthogonality relation. It turns out that only very narrow class of closure spaces can be associated with orthogonality relations. This shows that information formalized with the concept of difference understood as a very general orthogonality relation is a special case of information described in terms of closure spaces.

**References and Notes**

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*Entropy***2004**,*6*, 388-412. - Shannon, E.C. A mathematical theory of communication. In
*The Mathematical Theory of Communication;*Shannon, E. C.; Weaver, W., Eds.; University of Illinois Press: Urbana, IL., 1949; p. 20. - Bar-Hillel Y., Carnap R. An outline of a theory of semantic information, Technical Report No. 247, Research Laboratory of Electronics, MIT (1952); In Bar-Hillel, Y. (ed.),
*Language and Information: Selected Essays on Their Theory and Application*, Reading, MA, Addison-Wesley, 1964; pp. 221–274. - MacKay, D.M.
*Information, Mechanism and Meaning.*MIT Press: Cambridge, MA, 1969; p. 163. - Schroeder, M.J. Philosophical Foundations for the Concept of Information: Selective and Structural Information. In
*Proceedings of the Third International Conference on the Foundations of Information Science, Paris, July 2005*; Available at http://www.mdpi.org/fis2005/proceedings. html - Schroeder, M.J. From Philosophy to Theory of Information.
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**1971**, 60 (3), 230-240. - Bateson, G.
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*Information, Mechanism and Meaning.*MIT Press: Cambridge, MA, 1969; p. 157. - Bateson, G. Information and Codification: A Philosophical Approach. In
*Communication: The Social Matrix of Psychiatry,*Ruesch, J, Bateson, G., Eds.; Norton: New York, 1951; p. 175. *ibid.*p.173.- MacKay, D.M.
*Information, Mechanism and Meaning.*MIT Press: Cambridge, MA, 1969; p. 161. *ibid.*p. 165.- Aristotle.
*Selections.*Ross, W.D. Ed.; Charles Scribner’s Sons: New York, 1955. - Gleick, J.
*The Information: A History, A Theory, A Flood.*Pantheon Books: New York, 2011; p.161. - Weyl, H.
*Symmetry*. Princeton Univ. Press: Princeton, 1952. *Piaget, J.**Structuralism (Le Structuralisme).*Harper & Row: New York, 1971.*Structural Anthropology*. Transl. Claire Jacobson and Brooke Grundfest Schoepf. Doubleday Anchor Books: New York, 1967.- de Saussure, F.
*Course in General Linguistics*. Transl. Wade Baskin. Columbia Univ. Press.: New York, 2011; pp. 120-121. *Lattice Theory, 3*American Mathematical Society Colloquium Publications: Providence, R.I. Vol XXV, 1967.^{rd}. ed.- Schroeder, M.J. Search for Syllogistic Structure of Semantic Information.
*J. Appl.Non-Classical Logic,***2012**, 22, 83-103. - Schroeder, M.J., Wright, M.H. Tolerance and weak tolerance relations,
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© 2015 by the authors; licensee MDPI and ISIS. This abstract is distributed under the terms and conditions of the Creative Commons Attribution license.

*Published: 8 June 2017*

**Abstract:**

Since algorithmic recommendation has been widely adopted in information distribution, as a new concept of "network neutrality", "algorithmic neutrality" has come into the public view. Thus, from an initial requirement only to Internet Service Providers providing wire or wireless services, restricting their controlling of the application and content providers, "network neutrality" requirement has extended to contain content providers, service providers and terminal equipment manufacturers, until covers all the upstream and downstream industries’ technologies around fixed or mobile networks. Nowadays, it has further become a requirement of platishers represented by social media to recommend information to users by algorithm.