No better example of the metaphorical nature of scientific models can be found than in Membrane Theory or M-theory: the new so-called 'Mother of all Theories' that challenges the 'standard model' of cosmology, looks back beyond the Big Bang and promises the unification of General Relativity and Quantum Field Theory. M-theory had its roots - not surprising from the point of view of Fundamental Science - in a quasi-musical model of the universe called String Theory. In this model, elementary particles are conceived as different excitational modes or 'notes' of vibrating strings, rather like musical strings except with their own intrinsic tension. Strings could be closed loops or open. Stretched across the time dimension they would form tubes or planes respectively. In M-theory, strings can take many forms. A membrane is a two-dimensional string, called a 2-brane. But other types of brane are postulated too, including both 5-branes and 0-branes. In string theory, strings have the peculiar property of being able to 'curl' and 'wrap around space'. They vibrate in 11 dimensions that include three ordinary dimensions of extensional space, seven further spatial dimensions and one dimension of time. In M-theory, every point in extensional space can be described mathematically as a 'curled up' space of seven dimensions. We see in the language of string and membrane theory the most elaborate attempt so far to conceive and picture intensional or non-extensional reality in extensional terms - using both mathematics of higher-dimensional spaces and figurative spatial metaphors such as 'strings', 'membranes' or 'curled up' space.
M-theory is allowing physicists to once again speculate mathematically on the existence of multiple parallel universes, each constituted by a particular membrane shape 'floating' in the 5th dimension. Cosmologists now speculate that our own universe might be the result, not of a primordial Big Bang but of a 'Big Crunch' - the collision of two pre-existing branes in the fifth dimension which brings about a local collapse of that dimension. The uneven distribution of matter in the cosmos is thought of as resulting from the uneven and undulating surfaces of the colliding branes, which are visualized in three dimensions as having different shapes such as spheroid and doughnuts or toroids. The advantage of the theory for physics is that it gives gravity a central role as the fundamental medium coupling matter in different universes of branes. Gravity ceases to be merely an awkward and oddball force within the cosmos we know but the medium linking universes in the 5th dimension. String theory describes dimensions of microcosmic space. M-theory couples this microcosmic but multi-dimensional space with macrocosmic events and the process of cosmogenesis itself. For according to the principle of T-duality, physics in a space time dimension of radius R is equivalent to physics in a space-time dimension of 1/R.
The language of the new, non-standard model of cosmogenesis based on a mathematics of 11 dimensions is extraordinary in its naïve but duplicitous use of spatial metaphors derived from extensional, three-dimensional space as we know it. Thus we read of branes "colliding" like particles with one another, "bouncing" or "peeling" off one another, or "melding" with other branes. There is no better example than M-theory of a basic paradox of physical-science - the paradox being that the closer it comes to an adequate and comprehensive model of the extensional universe, the more it (a) relies on ever-more complex mathematics to avoid recognizing the fundamental nature of intensional reality, and (b) unwittingly comes with new and imaginative metaphors such as 'membranes' which are indeed far more adequate metaphors of intensional reality and the psychical universe than previous models of extensional reality and the physical universe.
Concepts such as '0-branes' or 'Calabi-Yau' spaces of seven dimensions 'wrapped' or 'curled up' in every point of three dimensional space are as mind-boggling for the physicist as for the layman. Why? Because whilst they clearly point to the nature of intensional reality and intensional space they do so only in an abstract mathematical way. Were we however, to attempt a fundamental psychoanalysis of the basic metaphors of string theory and M-theory, we might say that the concept of the 'string' is a direct metaphor of a basic dimension of intensional reality - namely thought itself.
The 'strings' of the physicists are a metaphor of their own thoughts, capable of taking different forms according to their excitation mode. Similarly, their 'membranes' are metaphors of their own intensional body or organism with its encapsulating envelope or membrane of awareness. Such an analysis of scientific concepts is of course heretical, for it points to a fundamental deficiency in the way the significance of these concepts is understood. As far as the physicist is concerned, a concept like 'wave', 'field', 'string' or 'brane' has one and only one vector of signification - its physical signification in denoting something 'out there' in extensional reality. The physicists cannot deny that their own imaginative scientific concepts arise from and within their own field of awareness. Yet they can and do continue to deny the psychical signification of these concepts - their meaning as figurative expressions of intensional or psychical reality. Fundamental Science understands the mathematician's figures, the figurative pictures of the physicists and the figures of speech they imply as figurations of awareness giving direct expression to inner fields, field-shapes and field-dynamics of awareness.
The current scientific understanding of M-theory in particular, however, is fundamentally deficient in another respect too. For it not only fails to recognize the psychical as well as physical signification of the concept of 'branes', it lacks any fundamental concept of what a membrane as such essentially is. The mathematical models of M-theory focus on various possible interactions between the boundary surfaces of different membranes. Such models treat membranes as things in themselves, like bodies in space which then happen to interact in a particular way. But the fundamental nature of any membrane is that it is not a 'thing in itself' which interacts with other things at its boundary. Rather the essence of a membrane, understood dialectically, lies in being a dynamic interface or boundary state of interaction. Fundamental concepts, as Hegel recognized, are intrinsically dialectical - they refer not to pre-given elements 'in' a certain relation to one another but to elements of a dynamic relation. Relationality itself inherently is not something static or unilateral but 'dialectical' - dynamic and reciprocal. Frontiers, for example, are not boundaries between separate territories. They are what define those territories in the first place, allowing a dynamic flow of goods and people between them.
In general, a determinate phenomenon such as a cell or any figure such as a circle only ever emerges or stands out (ex-ists) in relation to the background field that is its context of appearance. We cannot logically posit the phenomenon as an entity (+A) without reference to the co-defining field or context of appearance that constitutes all that it is not (-A). Text and context, phenomenon and field, are circularly self-related, defined in and through their relation to one another. (+A) and (-A) are mutually defined elements of their relation, of a singular boundary state (!A). Just as it is a line or frontier that defines the territories on either side of it, so does a circle or three-dimensional membrane of any shape define its own inside and outside. What appears as a figure such as a circle, sphere or surface membrane of any sort is just as much an inner surface and inner boundary of the area or field around it as the outer surface and boundary of the area of field within it. The fundamental concept of a surface membrane or envelope cannot be grasped by mathematics alone but only by its intrinsic dialectical logic.
Any two 'membranes', like the two circles in Diagram 1, are not just related externally through their possible contact or 'collision' with one another in the 'empty' space or field between them. To think so is to see each membrane only as a surface boundary of the space inside it. If instead we see both circles as internal surfaces or boundaries of the space around them (Diagram 2) the picture is quite different. For then logically, they are already intrinsically or internally related, simply by virtue of being internal boundaries of a common field or space.
Two 'membranes' seen as the external surface boundaries within a common space or field that separates them.
Two circular membranes seen as internal surface boundaries of a common field or space that unites them.
From M-Theory to SEM-Theory
Much attention is paid in our culture to what scientists think, very little to what doing science involves. We think only of physical laboratory instruments and experiments and not of the mental models and metaphors in which the scientist's awareness dwells and through which it finds expression. These constitute a singular and highly specific network of verbal signifiers which constitute the scientist's own mental universe or semiosphere. The information provided by physical instruments constitutes another semiosphere, shaped by the selective significance attached by the scientist to particular signs and signals. The physicists think they are studying and describing invisible and complex features of the outer universe, when in fact they are projecting features of the inner universe or mental semiosphere in which they dwell onto the outer universe.
The surface of a semiosphere is a semiotic membrane or 'sembrane'. Sembrane theory is the counterpart to string theory and M-theory in Fundamental Science. It allows us to understand science, scientists and their theories in a new way - as different universes of discourse or semiospheres. Each of these semiospheres or universes of discourse both in-forms and gives form to the inner universe of awareness that constitutes the scientist's own noosphere. But Sembrane Theory is not just a fundamental semiotics. It is the semiotic foundation of Fundamental Science as such. The notion of the semiosphere transcends the dichotomies of word and world, linguistic and extra-linguistic reality. We dwell within the world as we dwell within the word, both constituting distinct but inseparable semiospheres. There are as many worlds as there are semiospheres - each sphere constituting the surface of a distinct layer of meaning.
The basis of sembrance theory is the semiotics of the French linguist Saussure, for it was he who first introduced the idea of surface fields or 'planes' of signification, using the analogy of a sheet of paper:
"A language can be compared to a sheet of paper. Thought is one side of the sheet and sound the reverse side. Just as it is impossible to take a pair of scissors and cut one side of the paper without at the same time cutting the other, so it is impossible in a language to isolate sound from thought, or thought from sound. To separate the two for theoretical purposes takes us either into pure psychology or pure phonetics, not linguistics."
"Linguistics, then, operates along this margin, where sound and thought meet. The contact between them gives rise to a form, not a substance."
For Saussure a sign consists of two elements, a signifying sound and a signified thought or concept. Signifier and signified, or sound and thought are thus conceived as distinct but inseparable sides of a singular plane or surface boundary. Similarly, specific signifiers and their signifieds can be thought of as distinct but contiguous areas inscribed or cut into this plane, like interlocking pieces of a jigsaw puzzle. The meaning of any given sign is like the boundary contour of one of these areas or puzzle pieces, a contour which both defines and is defined by the contours of continuous pieces - other signs in the language or sign system.
Since Chomsky introduced the idea of language having both a surface and a deep structure, however, no one has thought to relate this to Saussure's model of language. This is unfortunate, for in parallel with M-theory, we can conceive not only of two-dimensional planes or membranes of signification - 'sembranes'. We can also conceive of three-dimensional ones. Indeed Saussure himself implies a notion of semiotic depth by introducing a picture of wavy regions or fields of amorphous thought and sound bounded by the signifying plane or sembrane.
"So we can envisage…language… as a series of adjoining subdivisions simultaneously imprinted both on the plane of vague amorphous thought (A) and on the equally featureless plane of sound (B)…what happens is neither a transformation of thought into matter, nor a transformation of sounds into ideas. What takes place, is a somewhat mysterious process by which 'thought-sound' evolves divisions, and a language takes shape with its linguistic units in between those two amorphous masses."
His analogy is a telling one: "One might think of it as being like air in contact with water: changes in atmospheric pressure break up the surface of the water into a series of divisions, ie waves. The correlation of thought and sound, and the union of the two, is like that." For what this picture also suggests is the possibility of a deep oceanic undercurrent of thought - a deep structure - more or less manifest in the surface waves or undulations of the sembrane.
Lacan adopted Saussure's ideas of chains of signification - analogous to the strings of physics - linking one signifier with another, but denied any fixed relation between signifier and signified. For him, planes of signification were composed of signifiers only. On the one hand the signified latter could 'slide' under the signifier, like undercurrents in a sea. On the other hand no signified could be identified as a thing in itself, but rather constituted a 'no-thing' that could manifest only as signifier - a wave or wave packet on the plane of signification.
Fundamental Semiotics, as a multi-dimensional field semiotics, understands planes of signification as sembranes surrounding or bounding an inner semiotic space with a depth dimension of meaning or sense, and consisting of intrinsically meaningful flows and streamings of awareness as such. From this point of view the very language of String Theory and M-Theory, like the languages of other sciences, are themselves semiospheres - sembranes of interrelated signifiers, surrounding a noosphere or semiotic space. The mathematical problems involved in describing the spatio-temporal dimensionality of strings and branes in physics is an expression of its failure to acknowledge the non-extension or intensional nature of semiotic space or meaning space - the noosphere enclosed or bounded by semiospheres and sembranes. What physics calls the fifth dimension is no dimension of extensional space-time but is the depth dimension of meaning or sense that constitutes the inwardness of any word or signifier - its intensional or semiotic space.
Viewed within our perceptual semiosphere, a book is a bounded three-dimensional body in extensional space. Each of its pages is a two-dimensional sembrane. As soon as we start reading the book however, our awareness flows into its interior semiotic space - its noosphere. Physically, the book remains the same size. But feeling our way into its concepts or characters, ideas or images, its internal space of meaning expands. As our own inner awareness flows into it, we experience an inward expansion of awareness within the book - not as a physical phenomenon but as the visible outer surface of a multi-dimensional world of meaning - a semiosphere with its own internal noosphere. We experience different layers of meaning within it, each of which constitutes a semiosphere of its own. The mental associations and images that flicker in our mind as we read a novel for example, represent one such semiosphere. The felt bodily sensations and emotions it evokes are another.
Dwelling within the intensional meaning space of the book we lose consciousness of the book as an object in extensional space. It is as if a singular noospheric space of awareness within our own bodies and minds merges with the internal noosphere of the book. Diagram 1 shows the relation of reader and book as two separate bodies in an extensional spatial field of awareness that constitutes the perceptual semiosphere of the former. What is missing in this picture however, is any acknowledgement of the internal noosphere of the book and its connection with the author.
Diagram 2 shows what happens when an author writes a book or a reader reads a book. The noosphere or inner awareness of the author/reader forms and flows into the membranes and spheres of signification that constitute the book, ensouling it with its own noosphere, uniting the noosphere of the reader and author within the semiosphere of the book.
According to Derrida, however the "presumed interiority of meaning is already worked upon by its exteriority". This is true, but then again there is no such thing as an exteriority without an interiority. The fact that any sembrane or semiosphere consists of a network of mutually related signifiers does not imply that there is no interior semantic depth dimension to these planes or spheres of signification. Fundamental Semiotics is not a semiotic reductionism which treats sense as a product of the signifiers and the symbolic. It recognizes however, that sounds and other signifiers not only articulate or express sense but attract and give form to sense. Fundamental 'sense' however, is not signified sense but felt sense - it consists of sensual field-qualities and field-patterns of awareness which are intrinsically meaningful, and that constitute the inner noospheric dimension of any semiosphere. The fundamental, felt sense of any verbal or perceptual signifier is reducible neither to its relation to other signifiers in a plane or sphere of signification, nor to its reference to a 'signified' - a pre-given meaning or thing.
© Peter Wilberg 2002