The Origin of Writing

by John Barclay-Morton

Technical Considerations

A Penny For Your Thoughts

Dear Mr. Barclay-Motion,

NMAI staff referred me to your recent emails and your web-site regarding the origin of writing.  While I am certainly impressed with the great effort you have contributed to this line of research, I remain unconvinced.  The chief difficulty, from my perspective, is not so much whether the identifications of the figurations on stones are correct (the “pareidolia” argument) but the nature of the figurations themselves.  In all the instances illustrated on your site, the images look like natural inclusions or patterns of mineral crystallizations in the rock.  I see no evidence of human workmanship or technique, i.e. carving, inlay, engraving, etching or marking.  I found no discussion on your site about how you imagine these things were made.  Have you consulted a geologist?  I don’t believe we can help you much with your research.  Thank you.

David W. Penney
Associate Director for
Museum Research and Scholarship
Smithsonian National Museum
of the American Indian

03/15/17 at 11:34 AM

Lenape Woman, New York City Area

World Map

Trace Evidence of Non-Conscious Neural Processes

Artifact (left); with the image of a Lenape Woman (center); and an overlay (right) showing Fast Fourier Transform analysis of spatial frequencies, indicative of Grid Cell engagement during production of the images on this artifact.

Technical Considerations In Analyzing Image Writing


In seeking to find some commonality between writer and reader — such as would afford the same kind of continuity of interpretation and understanding found between individuals who share a linguistic heritage, through learning the same meanings from a form of phonetic writing held in common — it has become apparent that the preconscious neural processes which inform our conscious awareness of visual imagery can serve this function very well indeed.

Exploring how anametric image writing functions coherently means examining those neural processes which underpin vision. Many clinical studies have undertaken such research, using advances in imaging technologies which allow for the active monitoring of ongoing neural processes inside a subject’s brain, even while that individual is engaged in specific vision-related tasks. Research of this nature has returned significant information regarding which areas of the brain process different aspects of vision.

Very recently, such studies have led to an understanding of how facial recognition is processed, yielding results which were as unexpected as they were insightful. These insights allow us to make some very basic interpretive contextualizations regarding the pivotal position that personal identity plays in the functional nature of anametric image writing; but it also positions us to understand the nature of the complexities that interconnect individual image elements within grammatological compositions.

Starting from observations regarding the positional localization of differential image elements within facial composites, we find that: grouping patterns, defined in terms of temporal duration, determine states of immanence; which can serve to connect the diagrammatic features of anametric image writing as intensive ordinates; which can compositionally produce conceptual structures. In this, we can trace a transitional shift: from the point-of-view perspectivalism that defines an observer relative to the situation in which they are placed; to the productive nature of conceptual personae, which demarcate relationships with that world (through acts of deterritorialization and reterritorialization, undertaken relative to that part of this earth where they find themselves). This in turn provides us with the kind of geophilosophical context that can ground an interpretive methodology capable of extracting meaningful information from the interrelationships depicted within examples of anametric image writing.


Considering Neural Processes of Scale

Given that an understanding of the basic functionality of those neural processes which inform facial recognition has provided significant insights into the mechanisms through which anametric image writing conveys information, a more thorough investigating into the neural processes that inform vision is certainly in order.

Starting again from the positional localization of differential image elements, as defined by their placement within identifiable facial composites, we can note something worth further investigation: the differential nature of such image elements, defined positionally, is often characterized by a disparity in scale. This is not the natural relationship of a proportional ratio: the image outline of a person, appearing in the place of an eye, projects a large scalar differential; and the outline of a mammoth appearing in place of an eye does this all the more so.

Such observations can lead to a new area of inquiry, which allows for some very insightful investigations: that of scale, and how it arises as a conceptual determination within consciousness. At first glance, the concept of scale might not seem at all integral to any determinations directly related to linguistic considerations; but in point of fact, scale has been demonstrated to be a fundamental principle which appears to be implicit within all language constructs. As demonstrated by Nai Ding et al in Cortical Tracking of Hierarchical Linguistic Structures in Connected Speech, scalar relation as a fundamental principle of organization can be show to hold across all language groups tested, indicating that scale is an innate interpretive pattern which is somehow embedded in human consciousness:

“In speech, hierarchical linguistic structures do not have boundaries that are clearly defined by acoustic cues and must therefore be internally and incrementally constructed during comprehension. We found that, during listening to connected speech, cortical activity of different timescales concurrently tracked the time course of abstract linguistic structures at different hierarchical levels, such as words, phrases and sentences. Notably, the neural tracking of hierarchical linguistic structures was dissociated from the encoding of acoustic cues and from the predictability of incoming words. Our results indicate that a hierarchy of neural processing timescales underlies grammar-based internal construction of hierarchical linguistic structure [Nai Ding et al, Abstract; 2015].”

Note that these findings are of particular relevance to the grammatological aspects of language — which is precisely what we find ourselves dealing with when engaging with this form of anametric image writing. Also of interest, given that anametric image writing is characterized throughout by temporal distinctions, is the fact that the scalar differentiations discovered in this study — found to hold in common between such radically different languages as Chinese and English — are discerned through temporal determinations:

“It remains puzzling how the brain simultaneously handles the distinct timescales of the different linguistic structures, for example, from a few hundred milliseconds for syllables to a few seconds for sentences.” “We hypothesized that cortical dynamics emerge at all timescales required for the processing of different linguistic levels, including the timescales corresponding to larger linguistic structures such as phrases and sentences, and that the neural representation of each linguistic level corresponds to timescales matching the timescales of the respective linguistic level. “By manipulating the levels of linguistic abstraction, we found separable neural encoding of each different linguistic level.” “Although the construction of abstract structures is driven by syntactic analysis, when such structures are built, different aspects of the structure, including semantic information, can be integrated in the neural representation. Indeed, the wide distribution of cortical tracking of hierarchical linguistic structures suggests that it is a general neurophysiological mechanism for combinatorial operations involved in hierarchical linguistic structure building in multiple linguistic processing networks (for example, phonological, syntactic and semantic). Furthermore, coherent synchronization to the correlated linguistic structures in different representational networks, for example, syntactic, semantic and phonological, provides a way to integrate multi-dimensional linguistic representations into a coherent language percept, just as temporal synchronization between cortical networks provides a possible solution to the binding problem in sensory processing [Nai Ding et al, 2015].”

It would be fair to say, then, that scalar relationships form an integral aspect of linguistic structure; and that, further, temporal duration can function as a fundamental mechanism in imparting coherence between disparate scalar constructs.

Locating Scale: Grid Cells

The discovery of those neural processes which are responsible for imparting a sense of scale into our experience of the world is something which happened fairly recently, and that proceeded with much fanfare. Edvard and May-Britt Moser were awarded the 2014 Nobel Prize in Physiology or Medicine for their discovery of Grid Cells, an honor they shared with John O’Keefe for his discovery of Place Cells.

Grid cells are neural structures which allow animals to construct a mental a map of the space they inhabit; place cells identify and maintain the location of discrete features encountered within that space. Both of these considerations are of obvious concern when trying to determine the structural relationships holding within a form of image writing; and among the many insights that came out of these discoveries was the fact that grid cells form in modules that are responsive at different scales:

“But grid cells came in different varieties. There were at least three parameters of variation (Hafting et al., 2005). First, the cells differed in phase, or the x-y locations of the grid vertices. All possible grid phases were represented. Second, grid cells differed in scale, or spatial frequency, or the size of the fields and the spacing between them. In the grid cells with the smallest scale, the distance between the firing fields was only 30 cm. Other cells had field distances of more than a meter. Finally, grid cells sometimes had different orientations, i.e., the axes of the grid were tilted at different degrees from a reference axis such as a wall of the recording environment [E. Moser, Nobel Lecture, pgs. 409–410].”

This matrix of grid cells (which provides us with a metric for spatial orientation) has very distinct quantitative properties directly related to scale. Given that the organizational relationships that form of differential image elements, relative to the grouping patterns in which they occur as positional localizations, are often scalar in nature, it may well be that such relationships are in some way a product of the functional nature of grid cells. If this is the case, then the neural processes which grid cells are responsible for may be structurally apparent in the spatial organization that constitutes the grammatological framework of anametric image writing.

In addition: in that it has been demonstrated — within their shared neurological processes — that perceptions are differentiated in consciousness from memory through rotation, the fact that orientation appears as a fundamental characteristic of grid cells is another potentially useful insight for any possible interpretive methodology we might construct in attempting to discern the basic functional mechanics for anametric image writing.

Scale As Spatial Frequency

The functional nature of grid cells, and their contribution to consciousness through the neural processes they enable, strongly indicates that they may provide access to quantitative tools with which to define those relationships of scale observable through positional localizations occurring in the context of facial recognition; and, that such determinations would be quantifiable in the form of spatial frequencies. Such relationships could therefore provide a set of quantifiable parameters, as an (or several) aspect(s) of the différance that Derrida postulates would necessarily be integral to a scientific study of linguistics. This possibility is certainly worthy of further research, given that very precise measurements of the differences between grid cell scale modules have been defined:

“On average, grid spacing increased from dorsal to ventral, as we had observed before, but there were only four or five levels of spacing. We referred to each level as a module. As the electrodes were moved from dorsal to ventral, new modules were recruited in an additive manner, such that the most dorsal levels of medial entorhinal cortex had only the smallest module (M1), whereas more ventral levels had both M1 and M2, and even more ventral levels M1, M2 and M3. The number of cells in each module decreased substantially from M1 to M4 and M5. Thus, grid scale is organised topographically but the map consists of anatomically overlapping modules. The organisation is quite different from the strict anatomical separation of functionally similar cells in some primary sensory cortices.”
“What is the relationship between the grid scales of successive modules? To determine this we measured the ratio between values for grid spacing of each successive pair of modules. Despite considerable variation in the scale ratios, the mean ratio was almost constant, between 1.40 and 1.43. For each pair of modules, the scale of the larger module could be obtained by multiplying the scale of the smaller module by a constant factor, just like in a geometric progression. This way of organising grid scale might, according to theoretical analyses, be the optimal way to represent space at maximal resolution with a minimum number of cells (Mathis et al., 2012; Wei et al., 2013) [E. Moser, Nobel Lecture, pg. 413].”

Of more immediate interest, however, is the almost casual mention by Edvard Moser of the fact that those variances in scale which characterize grid cell modules can be conceptualized in terms of spatial frequency. This is of great importance for any study of image writing: spatial frequency is a tool often used to distinguish between different visual aspects, when clinical studies are being conducted to discern which specific areas of the brain process different visual components. As a result, there is in fact a wealth of data from clinical studies that defines ways in which scales of spatial frequency can be applied in assessing visual components — such as the paper, Usage of Spatial Scales for the Categorization of Faces, Objects, and Scenes:

“Studying scale usage for the categorization of complex visual images is important if we are to understand how visual perceptual and cognitive processes operate, thus enabling us to interact efficiently with our complex visual environment. “Luminance variability in the visual field, arguably a crucial source of information for recognition, is encoded by spatial filters. For example, the encoding of detailed edges portraying the contours of a nose, eyelashes, the precise shape of the mouth and eyes, and so forth can be traced to spatial filters operating at a fine spatial resolution (i.e., high spatial frequencies; HSFs). In contrast, spatial filters at a coarser resolution (i.e., low spatial frequencies; LSFs) could encode pigmentation and shape from shading from the face [D.J. Morrison and P.G.Schyns, pg. 454].”

It is more than a little interesting to find that the different components that inform facial recognition can be directly related to variations in spatial frequency. Given that we have found (on the one hand) a relationship between differential contrasts in facial recognition (Doris Tsao), and the grammatological complexities of interrelation found within anametric image writing (Jacques Derrida); and (on the other hand), a relationship between spatial frequencies, grid cells, and the semiological nature of differential image elements as they occur within image writing through positional localization: taken together, with the realization that scalar relationships are inherently an integral part of linguistic constructs, it would seem that further investigation of those non-conscious processes attributable to the neurology of grid cells is well warranted.

Applying Spatial Frequencies

Spatial frequencies in images are usually separated from each other using a computational technique called a Fast Fourier Transform (FFT), which converts pixel-based images into frequency space. There, specific frequencies can be selected by masking out unwanted spatial frequencies; whereupon the image is converted back to a pixel-based format — but, as an image which is only composed of the spatial frequencies that were selected for, in frequency space. This is a technique that is often employed for producing the specially-modified photographs that are used in clinical studies investigating how images are processed by visual neurology. This technique allows researchers to discern which neural processes are responsible for resolving different spatial aspects of images.

John Russ, in The Image Processing Handbook , explains quite well the process for working with the power spectrum produced using the FFT technique:

“The spacing of the features that produce the point in the power spectrum is simply the width of the image (e.g. 256 pixels in the example, times whatever calibration applies) divided by the distance in pixels from the origin to the center of the peak in the power spectrum [Russ, pg. 345].”

The simplicity of this approach makes working with specific spatial frequencies very easy; and, there is a large and growing body of clinical information regarding neural processes that has been compiled using research techniques based upon spatial frequencies. Since this technique can be applied to any image, it can also be utilized in assessing photographs of anametric image writing. Note that, in the following examples where I apply this technique, calibration is not an issue (as it would be for images obtained through, for instance, microscopy), since the artifacts I am working with are large enough to be directly measured should the need arise, without resorting to any imaging processes.

By way of a very simple demonstration, here is an example of image writing that was found (in a store display case for sunglasses, as ornamentation) in Freeport, Maine. That location would place this artifact in the territory of the Wabanaki (“People of the Dawn”) First Nations; and the artifact itself, displaying as it does the image of at least one mammoth, must date to 11,000 years ago or more:

The lower spatial frequency image on the bottom left definitely makes it much easier to discern the outlines of specific images, with the higher spatial frequency image on the right providing a better sense of the detailing used to refine those images during their production. Using software created by Chris Russ of Reindeer Graphics , I was able to easily separate these two broad ranges of spatial frequency using his plug-in Photoshop filter for FFT conversion; and as a result, was able to notice the characteristic “C” shape of the prehensile tip found on a mammoth’s trunk in this image (as indicated by green arrows). Knowing that there is at least one mammoth evident, it is then possible to recognize more than one. Of incidental interest is the fact it has recently been demonstrated that mammoths were resident in New England at the end of the last ice age:

“It has long been thought that megafauna and humans in New England did not overlap in time and space and that it was probably ultimately environmental change that led to the extinction of these animals in the region but our research provides some of the first evidence that they may have actually co-existed,” said Dartmouth College researchers Dr. Nathaniel Kitchel and Dr. Jeremy DeSilva. “The Mount Holly mammoth was one of the last known occurring mammoths in the Northeast,” Dr. DeSilva said. “The radiocarbon date for the fossil of 12,800 years old overlaps with the accepted age of when humans may have initially settled in the region, which is thought to have occurred during the start of the Younger Dryas.” Mammoths Co-Existed with Early Americans in New England, Study Suggests; Mar 4, 2021.

In the course of my research into anametric image writing, I have consistently seen the conclusions I have reached substantiated by scientific research that is entirely unexpected — which is exactly what one should see when working with something that is in fact real, using methodologies that are demonstrably true-to-form.

Spatial Frequencies And Linguistic Scales

At the moment, it is far too early to say if the distinction between the large spatial frequencies of image areas, and those of the finer LSF details that inform them, might in some way correspond to the hierarchical differentiation — between sounds, words, and sentences — demonstrated earlier as inherent within phonetic forms of language; but, that is a possibility which would definitely invite further investigation. Proceeding with image analyses utilizing techniques based upon the Fast Fourier Transform seems a promising path toward further insights regarding anametric image writing. The accuracy that can be achieved when using FFT for selectively masking specific spatial frequencies is quite spectacular. By way of example, here is an artifact sourced from the New York City harbor area, making it part of the Lenape First Nation’s cultural heritage. Note the rather amazingly detail image of a Lenape woman on this stone:

Utilizing FFT masking to selectively edit for specific spatial frequencies presented by this artifact, I took the image area of the Lenape woman’s face as my baseline. Selecting for that spatial frequency, I also then edited the image for spatial frequencies that would be associated with hypothetical grid cell modules both one above, and one below, a hypothetical module based upon the spatial frequency defined by the image area of the Lenape woman’s face. Nothing about this approach is anything more than idle speculation on my part, but it is interesting to see the kinds of results I achieved in applying this methodology:

In the top row of images, note first of all that it really does take a trained eye to discern the image patterns upon this artifact (fig. 1a). However, masking the artifact using the spatial frequencies assigned to the largest hypothetical grid module very much makes specific areas of the artifact’s image structure stand out. I would take this to mean that, these larger spatial frequencies imply the artifact’s maker engaged visually with the artifact’s surface through a larger grid cell module, when assessing the artifact to determine where (and what) images would be created upon its surface (fig. 1b). Note that the actual spatial frequencies most directly associated with the image area of the Lenape woman’s face are not noticeably implicated in the larger image areas previously made apparent (fig. 1c).

In the bottom row of images, the first example presents the result of a layer blending mode called division: the baseline output of FFT masking for spatial frequencies characteristic of the image area for the Lenape woman’s face, is divided by, the result yielded for the spatial frequencies that would characterize a hypothetical next-largest grid cell module. The math behind Photoshop’s “Divide” blend mode between layers is quite straightforward: the value for white (256) is divided by, the result of the top layer’s division by the bottom layer; such that a value of [256 / (Layer A / Layer B)] is generated for each pixel in the image. This means that only those values in the bottom layer which are darker (indicating the presence of some aspect for the spatial frequency selected) than the layer above will be rendered; and, any values that are equal in both layers will cancel out and be rendered as white in the final image. The image shown (fig. 1a) presents the result of that calculation, and displays in bright green only those areas associated with the hypothetical largest grid cell module for which spatial frequencies were selected. Excluding the areas around the edge of the stone (where the visual record is distorted by the extreme perspectival curvature of the artifact’s surface), it appears that a very pronounced pattern emerges: two very distinct hexagonal rings of six positional localizations are evident as co-joined, with the suggestion that other such hexagonal rings extend into the curvature of the artifact’s edges, where the resolution of their imaging is lost. This pattern strongly suggests that which is associated with grid cell modules, as imaged during clinical studies of their active arrangement:

The second image in the bottom row (fig. 2b) repeats the procedure utilized in the first (fig. 2a), but this time the original baseline FFT result is divided into the spatial frequencies yielded for the image areas of the hypothetical next-smallest grid cell module. This yields only those areas which are present in the bottom FFT result (the baseline image area for the Lenape woman’s face), excluding any areas held in common with the next-smallest hypothetical grid cell module. Predictably, this produces a greater number of areas of interest (shown in bright green). Again, the perspectival curvature of the artifact’s edge creates an area of distortion; and as would be expected, the width of this section for the baseline image areas selected (fig. 2b) is proportionately less than in the first example (fig. 2a), which presents image areas associated with a hypothetical next-largest grid cell module.

What is particularly interesting about this rendering of spatial frequencies associated with the image area of the Lenape woman’s face is that, although some trace of the hexagonal pattern which could be indicative of grid cell modules is still apparent, other influences also seem to be in evidence. Rather than appearing as distinct and separate, such selected image areas are now chaining together in ways that might suggest the influence of other neural processes, such as those associated with Border (or “Boundary”) Cells.

The final image in the bottom row (fig. 2c) combines the results of the two previous images, again through division. This time, I have not applied the result to the original image: at this point, it is the pattern formed by the combination of the selected spatial frequencies that is itself of interest. Looking at these interference patterns formed from hypothesized grid cell modules of different spatial frequency, it seems apparent to me that the lighter areas invoke the larger images areas of faces; but in contrast, the regular patterns of small black intrusions into those larger, lighter areas seem reminiscent of something entirely different: these seem to be more characteristic of the productive methodology employed in the manufacture of stone tools, where edges are imparted onto stone forms by flaking them until they present a sharp, usable edge.

I wish to stress at this point that the image editing techniques I’ve employed here are still very exploratory in nature, and do not yet rise to even the threshold for ‘proof of concept’; but the results achieved do appear promising enough to warrant their development into a fully documented methodology — a path I intend to pursue.

For the moment, I will say that with the third image in the bottom row above (fig. 2c), there does seem to be a pronounced, definitive shift documented — one that moves away from demonstrating strictly the influence of grid cell modules occurring at progressively finer spatial frequencies. Possibly, the effect of what are known as boundary cells might be in play, as motivated by the orientation of grid cell modules toward mapping motion and movement (perhaps during the deterritorializations and reterritorializations of substantiation that occur during production). It is too soon to say if path integration might be playing a role here, or if this would correspond to the structural effects noted of sentences in phonetic language; but it does seem apparent that the act of production is playing a key role here, in the form of those patterns which become evident as the spatial frequencies associated with different hypothetical grid modules are brought together — for, these seems strongly reminiscent of a basic technique for the production of stone tools: refining edges by systematically flaking along their course.

The Edge of Imaging

I will mention in passing that Leibniz described the functional nature of “minute perceptions” in terms of ‘differentials’; and if at first it seemed a stretch of the imagination to think that Leibniz’s contribution to the invention of differential calculus (as a way of dealing algebraically with infinitesimal quantities) could somehow inform a sense of personal identity, as perspectival point-of-view, it does appear that here we have a trace of the productive technology used for manufacturing stone tools — applied instead, through deterritorializations and reterritorializations, to create image assemblages of an articulation between direct perception and memory as experienced by the person who created this artifact — all of which has become evident through a directly mathematical calculation of differential values, taken as holding between spatial frequencies again selected for their differential values as spatial frequencies. Indeed, it would appear that differential values generated through grid cell activations may well be directly implicated in both event-based and language-based memory:

“The modular organization of grid cells may further influence how information is processed and stored downstream in the hippocampus. If hippocampal place cells are excited by convergent input from multiple grid modules, two types of effects can be envisaged. First, convergence of signals from multiple grid modules would prevent propagation of noise that is uncorrelated across modules, allowing the hippocampus to estimate location with a precision that exceeds that of the individual grid modules. Second, such convergence might facilitate the formation of new and unique representations for new environments. If converging modules respond independently to displacement or reconfiguration of the environment, the altered co-activity may activate a new subset of hippocampal neurons at each location in the changed environment. A similarly effective redistribution would not necessarily be seen if the entire grid map responded coherently. Computational simulations have shown that convergence of signals from only 2 to 4 independently aligned grid modules may be sufficient to obtain near-complete remapping in downstream place cells. Each change in relative phase and orientation among a set of grid modules might lead to a unique hippocampal activation pattern, suggesting that the number of distinct representations that can be formed is large. By combining input from a small number of independently operating grid modules, hippocampal cell populations may thus acquire the ability to generate discrete representations individualized to specific places and experiences, an ability that may lie at the heart of the contribution of the hippocampus to episodic and semantic memory formation [Stensola, pgs. 77–78].”

If grid cell modules function independently, to produce together accurate maps of unique environments, them it might be expected that differential values extracted across a range of spatial frequencies could provide information relevant to how an individual had related to that environment; or in this instance, how a person's visual experience of a mediating substrate might have informed their productive activity in creating images upon that surface.

Referencing another artifact — one of Algonquin origin, from the area of Ottawa, Ontario in Canada — we can see something relevant, and of further interest: rather than simply working with whatever variations the stone utilized as mediating substrate offered, someone actually applied a coating of what appears to be a calcium-rich crust; and then began to rework the images on the stone’s surface. We will always be left to wonder why this process was left unfinished, and what might have happened to the person who undertook it; but what we can see from this rare example is that the process of imparting images onto such an artifact appears to proceed from larger image areas, through a process of detailing, into the production of ever-smaller image areas. This is a process which would be entirely consistent with observations made in the context of the imaging results yielded by the example of the Lenape woman; and it would be entirely consistent the processes whereby stone tools are created, as noted earlier.

I will note in passing that the Lenape, the Wabanaki, and the Algonquin First Nations are all members of the same language group — without a doubt, there is historically a linguistic continuity between these peoples. Where there isn’t linguistic continuity, though, is with the phonetic forms of writing that arose from a point of origin in the Near East: note how the linguistic hierarchies of phonetic languages (which in turn inform phonetic forms of writing) extend from sounds, to words to sentences — which is to say, from smaller units to larger ones. By all indications, the form of image writing which arose in North America proceeds from larger contexts down to smaller, more refined image areas — an approach which is the opposite of what we see with the phonetic forms of writing we are more familiar with.

Conceptually, within a visual context, the process of moving from larger grid cell modules to more refined, smaller modules corresponds to the process of “Substantiation” encountered earlier through Félix Guattari; where initially one starts from a generalized concept of “Matter” that is then refined, through the assessment of specific characteristics, into the concept for a specific “Substance”. Guattari also noted that such an approach supports the formation of anasemantic and a-signifying semiologies, that are potentially quite distinct from phonetic forms of signification; and now, we are beginning to get somewhat of an insight into how such forms of non-phonetic writing might actually function.

What we are seeing here is quite different from an approach where sounds are composing words which make sentences. Instead, we are starting from a positional localization of the individual; and we are disambiguating their position through larger grid cell modules, then increasing the accuracy of that position through smaller grid cell modules. In Optimal configurations of spatial scale for grid cell firing under noise and uncertainty, researchers investigated how varying the scale of grid cell modules affected the accuracy of the positional relations these encoded for place cells. In this, it was noted that:

“. . . independent spatial noise across modules, which would occur if modules receive independent spatial inputs and might increase with spatial uncertainty, dramatically degrades the performance of the grid system. This effect of spatial uncertainty can be mitigated by uniform expansion of grid scales. Thus, in the realistic regimes simulated here, the optimal overall scale for a grid system represents a trade-off between minimizing spatial uncertainty (requiring large scales) and maximizing precision (requiring small scales). Within this view, the temporary expansion of grid scales observed in novel environments may be an optimal response to increased spatial uncertainty induced by the unfamiliarity of the available spatial cues.”
“To conclude, increasing spatial uncertainty reduces the fidelity and range of the grid system, and these effects can be mitigated by uniform expansion of grid scale. This provides a potential explanation for the transient expansion of grid scales observed when an animal is placed in a novel environment. We suggest that novel environments are characterized by increased spatial uncertainty, the animal being unfamiliar with the form and reliability of the available spatial cues. In such circumstances, to minimize degradation of the spatial encoding, the grid system expands. As the environment becomes more familiar and the animal learns about the available cues, spatial uncertainty reduces, and the grid scale returns to baseline levels [Towse BW et al, 2014].”

By every indication, it is an entirely consistent practice for areas of larger spatial frequency to be employed when orienting within a new environment, or when engaging with an otherwise unknown context. It seems apparent that this can be accepted as a basic principle defining the functional nature of anametric image writing, and as such can be incorporated into any interpretive methodology we might construct for gleaning information from this image writing form. Certainly, we can expect the functional nature of grid cells to inform any observations we make concerning the way in which image assemblages are realized within anametric image writing; for as Edvard Moser notes:

“The entorhinal-hippocampal space system is one of the first cognitive functions to be understood in some mechanistic detail at the cell and cell-assembly level. “Moreover, what is particularly fascinating about grid cells is that they may inform us about general principles of neural pattern formation. Grid cells may for example offer a window to understanding continuous attractor mechanisms in the cortex, mechanisms that may be applied in different forms across the entire brain [E. Moser, Nobel Lecture, pg. 432].”

As noted earlier, neural processes engaged through the entorhinal-hippocampal system are quite removed from those associated directly with sensory perception; and as such, it would seem that this system of grid, place, and other cells is well situated to contribute to the formation of conceptual structures within conscious awareness.