True-Red Non-Retinal (Chromatically-Less-Redundant) Moderately Functional Tetrachromacy

True-red non-retinal tetrachromacy represents a paradigm-shifting advancement in human color perception, engineered through dichoptic spectral filtering and cortically integrated binocular fusion. This article elucidates how bifurcating the long-wavelength (L) cone sensitivity of a normal trichromat into two discrete spectral channels (L–: ≤630 nm; L+: ≥630 nm) induces a functionally tetrachromatic visual system, enabling observers to perceive a four-dimensional color space inclusive of dichotomous hues—such as simultaneous red-green, red-yellow, and black-yellow combinations—previously imperceptible under classical trichromatic models. Leveraging psychophysical validation and computational spectral and dimensional modeling, I demonstrate that trained observers achieve stable binocular integration of these "impossible" hues and colors, bypassing rivalry through neuroplastic adaptation. The resultant 4D perceptual framework (luminance, saturation, hue, stereoscopic chromatic opponency) challenges conventional color-opponency theory while expanding the neurophysiological boundaries of sensory plasticity. Furthermore, this work establishes a foundational protocol for augmenting human vision via engineered spectral and chromatic redundancy disruption, with implications for adaptive human-machine interfaces (e.g. tetrachromatic screens), multispectral imaging, and the empirical study of qualia in augmented sensory modalities.

True-red non-retinal (chromatically-less-redundant) moderately functional tetrachromacy, or true-red non-retinal tetrachromacy (abbreviated with: TRNRT) represents a binocularly mediated, perceptually transformative advancement in human color vision. At its core lies the strategic disruption of chromatic redundancy inherent to binocular (trichromatic) vision. This is achieved through a pair of inversely transmissive spectral filters, engineered to isolate distinct long-wavelength (L-cone) sensitivity ranges across the eyes. The left eye’s filter shifts L-cone sensitivity to shorter wavelengths (L-: approx. ≤630 nm), while the right eye’s filter isolates sensitivity to longer wavelengths (L+: approx. ≥630 nm). This dichoptic division generates two virtual L-cone subtypes, creating mutually exclusive spectral perception across the eyes. The resultant system enables hybrid chromatic integration: retinal (intraocular) mixing of S, M, and L- cones in the first eye, and non-retinal (interocular or binocular) fusion of (positive and negative) L+ signals with the protanomalous trichromatic output of the contralateral eye. 

TRNRT introduces a novel S/M/L- vs. L+ opponency channel, a fourth chromatic dimension orthogonal to classical trichromatic pathways. Untrained observers initially experience binocular rivalry, where conflicting inputs from each eye trigger alternating suppression of colors. However, through structured neuroplastic training, observers achieve binocular fusion—a cortical process that synthesizes dichoptic signals into (more) stable, coherent percepts (discussed but only superficially tested by: Simmons D. R. (2025)). This enables the perception of "impossible" color combinations, such as simultaneous red-green or black-yellow combinations, which transcend trichromatic limitations. Critically, these hues are not entirely novel but emerge from the brain’s reinterpretation of binocularly mixed trichromatic inputs, reframing them as subjectively distinct qualia.  

TRNRT induces a four-dimensional (4D) color space, structured across luminance, saturation, hue, and the novel S/M/L- vs. L+ stereoscopic opponency axis. Within this framework, the hue-saturation subspace occupies three dimensions, while the full concept of hue maps uninterruptedly onto a 2D plane—a topological constraint arising from the spherical organization of hues. This spherical model supports 14 distinct main hue categories (excluding the achromatic point), each encircled by a variable-radius continuum of neighboring hues [cf. Lee, Jessica. et al. (2024)]. This contrasts starkly with trichromacy’s linear adjacency model, where hues transition between two neighbors (e.g., red → orange → yellow). The system grants access to a fourth chromatic axis ("true-red"), a deep spectral red (almost) indistinguishable from other long-wavelength reds to trichromats.

TRNRT’s functional superiority stems from its strategic targeting of the high-sensitivity L-cone subtype, diverging from prior efforts like Gundlach et al.’s (2017) S-cone-based approach. By splitting the L-cone’s broad spectral range, TRNRT optimizes discriminability in the red-yellow-green spectral region—a critical advantage for tasks in daily life. Furthermore, its engineered filters and cortical fusion protocols evoke neuroplastic adaptation, training observers to reinterpret dichoptic signals as unified and distinct perceptual experiences. This positions TRNRT not only as a sensory augmentation tool but also as a paradigm for studying neural plasticity in sensory systems.  

Developed by Kilian-Roy Lachner, B.A. (2024) at the University of Bayreuth (media studies), TRNRT constitutes a foundational innovation in perceptual engineering. While previous work on the conceptual framework of binocular redundancy disruption already exists [cf. Gundlach et al. (2017)], TRNRT’s L-cone spectral bifurcation and cortically integrated fusion protocols in combination with the interactive visualizations of the resulting tetrachromatic color space represent a distinct intellectual leap. Unlike incremental improvements to existing technologies, TRNRT establishes a novel method for evoking tetrachromatic perception, protected as intellectual property. Its success underscores the viability of (non-retinal) binocularly disruptive approaches to visual enhancement, bridging media studies, neuroscience, and engineering. 

True-red non-retinal tetrachromacy transcends classical trichromatic limits, demonstrating that engineered spectral filtering, coupled with neuroplastic training, can expand human perceptual boundaries. Its implications span multispectral imaging, adaptive human-computer interfaces, and empirical studies of qualia in augmented sensory modalities. As both a technological invention and a neuroscientific paradigm, TRNRT charts new frontiers in perceptual engineering, challenging conventional models of color vision while illuminating the brain’s remarkable capacity for sensory reinterpretation.  

To ensure methodological clarity, the following nomenclature is established:

• True-Red Non-Retinal Tetrachromacy (TRNRT): Denotes the chromatically less redundant, binocularly mediated tetrachromatic system described in this study. The term emphasizes its engineered disruption of spectral redundancy and non-retinal perceptual integration.

• True-Red Glasses: Refers to the custom optical apparatus housing the dichoptic filter pair (L-: approx. ≤630 nm; L+: approx. ≥630 nm), which induces TRNRT by bifurcating L-cone sensitivity.

• True-Red Tetrachromatic Colors/Hues: Describes the (dimensionally) expanded gamut of chromatic experiences exclusive to TRNRT observers, including dichotomous combinations (e.g., simultaneous red-green) and spectral ranges (e.g., "true-red") indistinguishable to trichromats.

This article distinguishes TRNRT from retinal tetrachromacy and anchors its novel perceptual framework.

All figures, tables, and computational programs presented herein—excluding explicitly cited external works—were developed de novo by the author. These visualizations are designed to:

• Illustrate the spectral transmission profiles of the L-/L+ filters.

• Map the 4D TRNRT color space; for example its spherical and 2D hue topology.

• Demonstrate binocular fusion dynamics through stereo demos.

This original content ensures empirical reproducibility and provides a foundational reference for future research.

A critical distinction is drawn between trichromatic and tetrachromatic color terminology:

• Trichromatic Color Names: Describe hues perceived under standard human vision (S/M/L cones). For example colors like red, yellow, green, cyan, blue, magenta, white and black.

• Tetrachromatic Color Names: Assign unique identifiers to TRNRT-specific hues, reflecting their combinatorial cone activations as well as their trichromatic origins. A "dodecadecimal code" (i.e. a hexachromatic color) in this case is the combination of two hexadecimal codes.

• "Dodecadecimal Code": The combination of two hexadecimal codes. In true-red tetrachromacy, the first part indicates the first eye's slightly anomalous trichromatic (mild protanomaly) vision and the second part indicates the second eye's true-red monochromatic vision.

This dichotomy is necessitated by TRNRT’s expanded color space, where hues like "true-red" or hybrid red-green defy trichromatic linguistic frameworks. Standard color terms (e.g., "yellow") are insufficient, as TRNRT hues occupy distinct perceptual and spectral coordinates.

To approximate TRNRT’s "impossible" colors, stereo demos are provided, segregating chromatic components for each eye:

• Frist Eye: Displays (in most cases non-protanomalous) trichromatic outputs (S/M/L- mixtures).

• Second Eye: Isolates (positive and negative) L+ cone activations.

By employing cross- or parallel-viewing techniques, observers can binocularly fuse these dichoptic inputs, simulating TRNRT’s novel hues. This method bridges theoretical constructs (e.g., 4D color space) with subjective experience, offering readers with normal trichromacy an empirical window into tetrachromatic perception. For simplicity, the slightly protanomalous color vision of the first eye is depicted in normal trichromatic colors. This closely matches the color qualia induced be the true-red glasses, but it's not identical.

True-red non-retinal tetrachromacy (TRNRT) is predicated on four functionally distinct cone channels—S, M, L-, and L+—that collectively generate a functional four-dimensional color space. These channels yield a diverse plane of spectral and non-spectral hues (e.g., pure long-wavelength reds or hybrid red-green mixtures), with the additional possibility of a fully achromatic ("white") point when all cones are maximally and uniformly stimulated. While such a system parallels aspects of retinal tetrachromacy in individuals believed to have a fourth mutated M' or L' cone type (e.g., the type associated with "cDa29," which Concetta Antico is hypothesized to possess, as tested by Jordan, G. et al. (2010) and Jordan, G. et al. (2019)), TRNRT differs in both its methodology (i.e., engineered L-cone bifurcation via dichoptic filters) and in the degree to which it confers tetrachromatic functionality. Because the novel L- cone remains proximal in sensitivity to the M cone and both L- and L+ subtypes share a similar "primary" color qualia, the overall enhancement is moderate relative to hypothetical scenarios involving a truly divergent fourth cone type in the ultraviolet or infrared range that evokes a more unique "primary" color qualia (compared to L- and L+) as well as a more unique peak sensitivity (compared to M and L-).

A central factor in TRNRT’s utility lies in the spectral composition of environmental lights and materials. Pure "yellow" signals (yellows that aren't a mix of red, yellow and green), for example, are relatively rare in natural settings, with most stimuli in the red-yellow-green range arising from blended or broadband spectral distributions. The practical value of any tetrachromatic system thus hinges on encountering stimuli whose spectral bandwidth and reflectance properties meaningfully engage the extra cone channel. In TRNRT, the L- cone is sufficiently close to the M cone that many long-wavelength stimuli produce a greater amount of metameric or near-metameric matches with black when compared to a non-dichotomous L cone, reducing the visibility and discriminability of wavelengths longer than ≥630 nm. By contrast, the L+ cone, anchored at longer wavelengths (≥630 nm), exhibits more pronounced separability from M, offering increased color discrimination of M and L+ under appropriate spectral conditions.

When the environment predominantly excites only the S, M, and L- cones, observers (i.e. normal trichromats) effectively exhibit a mild protanomaly, experiencing reduced sensitivity to deep reds. Conversely, filtering conditions that engage only S, M, and L+ yield an anomalous trichromacy closer to the typical human norm, albeit lacking in the pure "yellow" region. Interestingly, a scenario stimulating only the M, L-, and L+ cones also constitutes a form of trichromacy, yet it would be weaker than standard trichromacy due to the partial overlap of the M and L- spectral cone sensitivity curves and the similarity of the L- and L+ channels' "pimary" color qualia.

From a practical perspective, TRNRT-generated color experiences—particularly those heavily reliant on narrowband or quasi-monochromatic and multi-spectral (3 or more distinct peaks in a wavelength range) signals—remain relatively rare in everyday life. Much like magenta, which is scarcely found in nature because it lacks a direct singular spectral counterpart, many "true-red" tetrachromatic hues are composites of multiple overlapping wavelengths rather than single, pure wavelength peaks. Since modern lighting and displays are largely optimized for trichromatic perception and natural scenes' lights colors exhibit predominantly broad ranges of illumination and reflectance, some of the distinctive colors and hues of TRNRT’s 4D color space and 2D hue subspace do not commonly and easily arise. Nevertheless, TRNRT vividly demonstrates how spectral engineering can unlock new perceptual color categories when the interplay of cone activation is systematically altered.

True-red non-retinal tetrachromacy (TRNRT) yields a marked increase in the number of unique cone-activation patterns relative to standard trichromacy, thereby enriching both the quantity and quality of perceivable hues. Under normal trichromatic vision, there are seven fundamental cone-activation states (including the achromatic point)—(S), (M), (L), (S/M), (S/L), (M/L), and (S/M/L)—plus a total cone inactivation (K), which collectively define the principal axes of the trichromatic color space. All other color impressions arise from mixtures of these states, but the seven unique activations stand out as canonical references.

In TRNRT, however, the bifurcation of the long-wavelength cone adds the L- and L+ subtypes, expanding the repertoire to fifteen unique cone-activation states (including the achromatic point)—(S), (M), (L-), (L+), (S/M), (S/L-), (S/L+), (M/L-), (M/L+), (L-/L+), (S/M/L-), (S/M/L+), (S/L-/L+), (M/L-/L+), and (S/M/L-/L+)—alongside total inactivation (K). Crucially, TRNRT also introduces three-fold cone combinations that do not appear in normal trichromacy; for instance, (S/M/L-), (S/L-/L+), or (M/L-/L+). Under standard trichromacy, the three-cone mix S/M/L+ automatically collapses to white, for example, whereas in TRNRT, producing the perception of white further requires the stimulation of the L- cone; i.e. simultaneous stimulation of all four cone subtypes.

Although retinal tetrachromacy involving an additional mutated M' or L' cone (as documented in research on individuals such as "cDa29") can exhibit more pronounced and stable perceptual contrast—owing to the greater functionality and stability of intraocular cone type mixes—TRNRT still achieves a moderately functional four-dimensional color space. Here, the L+ channel remains sufficiently distinct from the S, M, and L- channels to introduce qualitatively new chromatic experiences, even if some of these may be somewhat subtler than in retinally based tetrachromacy.

Part of TRNRT’s distinctiveness arises from the fact that the L+ channel of the first eye is orthogonal to the S, M, and L- cone channels of the second eye, even when the "primary" color qualia of both the L- and L+ cones are similar. In practice, the fourth color axis manifests as the L+ cone subtype from one deep red monochromatic eye mixing with the slightly protanomalous S/M/L- combination in the other. This mixture is sufficiently orthogonal to trichromatic processes that it produces genuinely novel, non-retinal (i.e. interocular) hues that expand the color space beyond the reach of standard human color vision into a fourth dimension.

Physiologically, the brain processes six color channels, labeled S1, S2, M1, M2, L1, and L2—where "1" and "2" denote the left and right eyes, respectively. However, because of the chromatic redundancy and spectral equality/overlap of binocular color vision, each eye sees the world in the same colors, even when both eyes' cone types are technically distinct. Only by disrupting this chromatic (and spectral) redundancy we can access this potential for human hexachromacy in normal binocular trichromats.

A series of videos explores the concept of true-red non-retinal tetrachromacy (TRNRT) and visually demonstrates the functionality of the specially engineered true-red glasses in moving pictures. Among these, This is How I Turned Myself Into A Tetrachromat (VR) by Ooqui (Lachner K. (2024)) emerges as the most comprehensive video currently available, presenting an in-depth exploration with many visualizations of how TRNRT can be induced, understood and visualized. All four videos are tailored for viewing in virtual reality or via cross-/parallel-viewing techniques—two approaches that approximate, albeit not identically, the tetrachromatic color experiences produced by the true-red glasses. 

In the first video, How to Achieve True Red Cone Tetrachromacy (VR), the showcased glasses omit the bandpass 360–580 nm filters necessary for the second eye, resulting in partial TRNRT functionality. The subsequent video, This is How I Turned Myself Into A Tetrachromat (VR), rectifies this shortcoming by incorporating the missing filter, thereby granting a more complete expression of L+ channel separation and providing viewers with a closer approximation of genuine four-dimensional color vision.

The cone types' spectral sensitivity curves of the "True-Red Tetrachromatic Cone Responsivity (Bell Curves)" program are an approximation based on perceptual color matches (by Kilian-Roy Lachner).

The following True-Red Tetrachromatic Hue Sphere – Locally Trichromatic Hue Circles program provides a three-dimensional (3D) visualization of the true-red tetrachromatic hue-saturation sphere, which itself is a subspace of the overall four-dimensional (4D) color space. Only the outer surface of this hue-saturation sphere is visible in the program, because hues with varying saturation levels extend inward, beyond our direct view. Each surface color corresponds to a unique true-red tetrachromatic hue, and any given hue can vary in terms of saturation and luminosity. By crossing your eyes to superimpose the program’s left and right squares, you can approximate the binocular fusion technique that reveals how these surface hues relate to one another in a 4D space.

An optional Show Overlay feature in the program further clarifies each highlighted true-red tetrachromatic hue by emphasizing its circle of neighboring hues. Significantly, each hue on the 3D sphere has its own circle of immediate hue neighbors, all of which locally appear trichromatic. This observation aligns with insights from Lee, Jessica. et al. (2024), whose Subitem 4.2 (Every Tetrachromatic Hue is Ringed By Its Own Unique Hue Circle) demonstrates that the classic trichromatic model—where each hue is bounded by exactly two neighbors—transforms radically under tetrachromacy. In trichromacy, for instance, an orange hue might be bracketed only by red and yellow; yet in tetrachromacy, that very same stimulus has a circle of distinct neighboring hues, reflecting the spherical topology of the tetrachromatic color system.

Because each true-red tetrachromatic hue occupies a point on this spherical surface, you can traverse this hue space in more complex ways than under trichromacy or dichromacy. In dichromacy, you transition between two unique hues by only passing through an achromatic or black point; in trichromacy, you move around the perimeter of the achromatic point in a single circular path; and in tetrachromacy, you orbit the achromatic point on a spherical surface that encapsulates it. This expanded geometry allows multiple gradations of hues, such as the progression from Trite to Trow to Ellow to Ayell and finally Altus (referenced in Section 7.1 True-Red Tetrachromatic Color & Name Viewer), each representing distinct yet continuous transitions within the 2D hue plane.

In a digital context with idealized primaries, trichromacy typically supports 1,536 discrete hues, whereas true-red tetrachromacy can theoretically yield approx. 1,572,864 hues (calculation: (1,536 * 256) * 4 = 1,572,864; i.e. four times the amount of saturated and desaturated trichromatic hues). By the same token, the jump from dichromacy to trichromacy is a 768-fold increase in possible hues, while from trichromacy to tetrachromacy it’s another 1024-fold. 

Conceptually, the concept of “hue” in a tetrachromatic system is therefore fundamentally two-dimensional—embedded in a higher-dimensional (4D) color space—and cannot be fully captured by the zero-dimensional and one-dimensional hue models that suffice in dichromatic or trichromatic vision.

You can also use these two simple paint programs two paint in hexachromatic colors using a dodecadecimal code.

The below Image Splitter program is designed to easily split image that are designed for stereo viewing. You can also download them in a merged image style which shows visible borders for easier stereo viewing.

Use cross-/parallel-viewing techniques to overlap the following images' left and right color squares. Every (in this example) trichromatic color of the first eye can be put orthogonal to the positive (red) and negative (blackish) activation of the second type of red of the second eye (except for true red of course). The following ("impossible") hybrid color combinations are not hue corrected to reflect the deep red nature of the first and the protanopic nature of the second eye, but they come close to the actual color qualia. The following program Dichromatic Hue Gradients of True-Red Tetrachromacy shows a locally dichromatic color subspace with varying luminosity and optional saturation levels taken from a higher-dimensional tetrachromatic (4D) color space.

The true‐red glasses enable a transformative shift in color perception by remapping hues onto a two‐dimensional plane—contrasting sharply with the one‐dimensional hue progression characteristic of standard trichromacy. In this engineered system, each hue is defined not solely by its chromatic value on the two‐dimensional plane but also by its independent saturation and luminance levels, thereby expanding the perceptual framework into a four‐dimensional color space that incorporates the novel L-/L+ stereoscopic opponency axis.

For instance, consider a dichromatic gradient spanning blue, cyan, and green. When this gradient is positioned orthogonal to the L+ channel, it gives rise to a distinct trichromatic hue subspace that encompasses a full range of luminosity variations, ultimately integrating with achromatic states. In effect, the addition of the L+ channel orthogonal to the anomalous trichromatic (protanopic) (S, M, and L-) input creates a richer, more nuanced palette than is available to conventional trichromats.

This phenomenon is exemplified in the accompanying program, Trichromatic Hue Gradients of True-Red Tetrachromacy. In this setup, one eye receives a robust trichromatic signal—predominantly mediated by the S, M, and L- cones—while the contralateral eye, equipped with the L+ filter, is limited to deep (i.e. true) red spectral input. Although the absence of the L- contribution in the above example would ordinarily yield dichromatic vision, the complementary L+ channel ensures that the overall percept remains trichromatic. The resulting visual output, while exhibiting slight anomalies due to the engineered spectral partitioning (e.g. imperfect binocular fusion), is sufficiently similar to standard trichromacy to function effectively in everyday perceptual contexts.

In summary, the locally trichromatic subspace—comprising dichromatic gradients of S, M, and L- channels juxtaposed against the orthogonal L+ input—constitutes a vital subset of the higher-dimensional tetrachromatic color space enabled by true-red non-retinal tetrachromacy. This integration of dichoptic inputs not only validates the concept of a two-dimensional hue plane but also underscores the profound implications of engineered spectral filtering in expanding human color perception.

Within the framework of true‐red non‐retinal tetrachromacy (TRNRT), the term “saturation” acquires a dual meaning that diverges markedly from its conventional interpretation in standard trichromatic vision. In traditional trichromacy, saturation is a single-dimensional attribute: a hue is either fully saturated or becomes progressively desaturated as it converges with white. In contrast, within the tetrachromatic system, each hue embodies two (or more) distinct layers of "saturation" when compared to trichromacy—a locally defined, “inferior” saturation and an additional, “superior” saturation unique to tetrachromacy. The inferior (trichromatic) saturation arises from the integration of three cone inputs (S, M, and L-) and reaches its maximum when only these three channels are active. The superior (tetrachromatic) saturation, however, incorporates the fourth channel (L+), effectively peaking at a combination of four cone signals. As a result, originally trichromatic colors exhibiting solely inferior saturation remain distinctly removed from the achromatic point and become hues, whereas the inclusion of superior saturation shifts these hues perceptually closer to the tetrachromatic achromatic point. Because any 3-fold cone mix in tetrachromacy necessarily yields fully saturated hues, the saturation of tetrachromacy is as fundamentally different to trichromatic saturation as trichromatic saturation is to dichromatic saturation.

To further elucidate this concept, it is instructive to compare normal trichromacy with protanopia—a form of dichromacy characterized by a complete deficiency in red sensitivity. In protanopia, transitions from hues such as green or blue to cyan mimic a desaturation process because the perceptual system effectively “slides” these colors toward white. In this condition, white itself tends to appear cyanish, for example, rendering certain hues indistinguishable from desaturated states. Consequently, protanopia manifests one fewer order of saturation (and correspondingly one less order of hue) compared to trichromatic vision.

The following interactive program, titled Trichromatic Hue-Saturation Disc vs. Protanopia Color Space, further illustrates these principles. In the trichromatic configuration, fully saturated hues are distributed along the outer perimeter of a hue-saturation disc, with saturation diminishing as the hues approach the achromatic center. By manipulating the “Red Amount (%)” slider, the conventional trichromatic hue-saturation space can be morphed into a distorted protanopic color space—depicting every color perceptible to a protanope within its inherent two-dimensional framework. This stands in stark contrast to the standard trichromatic hue-saturation disc, which represents only hue and saturation without incorporating variations in luminosity.

Fundamentally, while the dichromatic (protanopic) color space is two-dimensional and the trichromatic space is three-dimensional, the tetrachromatic space of TRNRT is four-dimensional. By extending the comparative analysis of protanopia to include an additional color dimension—the true-red axis—the entire anomalous trichromatic space (lacking true-red and its mixtures) can be contrasted with the novel tetrachromatic component. This geometric perspective reinforces the idea that color vision intrinsically scales dimensionally with each additional functional cone type.

In practical terms, the standard trichromatic concept of (anomalous) “white” (representing inferior saturation) can exhibit a superior saturation gradient when augmented by the true-red component. As demonstrated in Figure 9/1, the gradient extends from trichromatic (S/M/L-) white on the left to tetrachromatic (S/M/L-/L+) white on the right (note: the image is not color corrected). In reality, the inferior (trichromatic) white tends to appear as a strongly saturated cyanish-white—reflecting its nature as the negative of true-red—whereas the superior (tetrachromatic) white is perceived as strikingly closer to the ideal achromatic point in true-red tetrachromacy.

The True-Red Tetrachromatic 2D Color Square program demonstrates how the expanded 2D hue plane of TRNRT can be mapped onto a square, albeit with some distortion to accommodate four-dimensional color data. By employing stereo viewing techniques, one can fuse the horizontal axis—representing a standard trichromatic hue continuum vertically varying in saturation and luminosity—with the vertical axis, which encodes the extra "red" dimension provided by the L+ cone type. We can adjust not only the saturation and luminosity of each tetrachromatic hue but also the density of the dot grid, revealing the complexity of this augmented color space.

The Normal vs. Unfolded Tetrahedron program offers a complementary perspective, depicting how the three-dimensional hue-saturation subspace of tetrachromacy (i.e., a standard tetrahedron) may be unfolded into a 2D plane. In this representation, the white face corresponds to the traditionally trichromatic plane—whose edges illustrate conventional hues while the plane’s interior captures their varying saturation. The remaining three red faces extend into a dimension inaccessible to human observers with typical trichromacy, showcasing hues formed by mixing the L+ cone subtype’s "second red" with the standard trichromatic primaries. Thus, whereas trichromacy effectively restricts observers to a single line of hues on a triangular subspace (in the context of an equilateral tetrahedron), true-red tetrachromacy brings forth an entire tetrahedron of superficial hue variation, where the original trichromatic face is merely one part among four, each populated by additional distinct hues that only become all visible at once when this 3D hue-saturation subspace is partially unfolded for visualization.

The True-Red Tetrachromacy Tetrahedron (Stereo) program shows the same tetrahedron as in the Normal vs. Unfolded Tetrahedron, but in stereoscopic view and with the true-red tetrachromatic colors applied.

In Fig. 10/2 we can see that there are a lot of tetrachromatic hues missing on an RGB screen. Furthermore it must be noted that Figure 10/1 and 10/2 are low resolution dot-based visualizations of the 2D hue space of TRNRT. There are many more intermediate hues and even more colors. This is the reason why you can't (or only indirectly) test for tetrachromacy on an RGB screen. An RGB screen cannot display all tetrachromatic hues (and colors), and the trichromatic hue line of an RGB screen results in a distorted true-red locally trichromatic 1-dimensional color subspace in the form of a line (within a greater tetrachromatic context). Only a tetrachromatic screen with 4 distinct subpixels — true-red, orangy-vermillion, narrower green and blue — would be able to display all of these tetrachromatic hues and colors; with the appropriate software and tetrachromatic color data of course.

"4.2 Every Tetrachromatic Hue is Ringed By Its Own Unique Hue Circle

Another fundamental difference in color experience for trichromats and tetrachromats is due to the neighbor relationships between hues. In trichromacy, every hue has exactly two neighbors – this is fundamentally due to the topology of the hue circle, where every point on the line has two neighboring points. In trichromacy, orange is bordered by yellow and red, certainly not green or pink.

Remarkably, this exact neighboring relationship is turned on its head in tetrachromacy. Looking at Figure 6, we investigate the neighbors of what appears to be an orange color to trichromats, or more precisely the reflectance that reflects all light at wavelengths longer than 551 nm. The figure illustrates that if a trichromat saw a tetrachromat perform the hue ordering test, they would see orange ordered next to not only red and yellow, but also green and pink. These notable tetrachromatic neighbors can be identified in the lattice described in Section 3.4 and drawn in Fig. 5. More generally, every hue for a tetrachromat exists on the sphere and is therefore ringed by a unique circle of tetrachromat hues, and the notable tetrachromatic neighbors can be read off the cycle of neighboring vertexes in the lattice." (Lee, Jessica. et al. (2024))

Figures 10/4-6 help us understand this excerpt. Figure 10/5 shows that the tetrachromatic hue plane is made up of many trichromatic hue circles/lines. However, to normal trichromats these hue circles just look like variations of the same trichromatic colors that they're used to. The tetrachromatic colors are seemingly incoherently arranged and appear duplicated or even multiplied several times. For example, there are two identical whites and many similar yellows and magentas. A tetrachromat looking at this tetrachromatic hue plane can distinguish every single color as a distinct hue and can organize these hue in a planar structure. A trichromat, however, will always discard the perceptually duplicated hues and arrange them in a linear structure. Furthermore, the hues of the deep red line seem practically identical to normal trichromats as most hues above 630nm appear identically red to them due to the principle of univariance.

Until now, I have presented evidence suggesting that the enhanced color vision evoked by the true-red glasses constitutes a moderately functional form of tetrachromacy—one that appears empirically closer to retinal tetrachromacy than to normal trichromacy. Nevertheless, this non-retinal system remains distinct from strong retinal tetrachromacy: it relies on so-called “impossible” color combinations, generated via interocular (binocular) fusion, rather than introducing entirely new types of photoreceptors. Although the resultant hues in true-red non-retinal tetrachromacy (TRNRT) may exhibit reduced saliency compared to those produced by a true fourth retinal cone (similar to how normal trichromats may find it initially challenging to make stable trichromatic distinctions while wearing red/cyan anaglyph 3D-glasses), the color space itself is unequivocally four-dimensional, and its binocular color mixes are indeed tetrachromatic and distinct.

How, then, does true-red tetrachromacy compare to strongly functional retinal tetrachromacy? Directly answering this question is challenging because while we can quantitatively compare normal trichromacy to a putative retinal tetrachromacy, it is impossible to directly measure subjective color qualia. Thus, researchers typically rely on an observer’s behavioral evidence, assessing whether color-discrimination tasks align with what one would predict from a genuinely four-cone, strongly functional system.

A parallel can be drawn from the transition between dichromacy (e.g., deuteranopia) and typical trichromacy to illustrate what a new cone might add to color experience. Deuteranopes have only two functioning cone classes: S and L. Although both overlap in the medium-wavelength region of the visible spectrum, deuteranopes lack an entire dimension of color discrimination compared to normal trichromats. For example, within the approximate red-yellow-green-cyan range, a deuteranope perceives only one hue that varies by luminosity or saturation; similarly, the cyan-blue-magenta continuum collapses to a second unique hue. Most shades near cyan or pink look whitish or grayish. Put simply, a deuteranope’s entire color palette reduces to S (blue), L (red), S+L (white), K (black), or mixtures thereof.

When a third cone class (M) is added, one obtains normal trichromacy. Crucially, the new “green” axis allows for color experiences that are orthogonal to any S/L combination, introducing not just new hues but also a fundamentally different approach to saturation, in additon to a higher dimensional color space. In dichromacy, combining S and L might yield only a magenta/fuchsia/pink which can be indistinguishable from white; in trichromacy, introducing M results in a more nuanced continuum of hues that eventually converges to a trichromatic white when all three cones are equally stimulated. Deuteranopes cannot separate green from red purely by hue because they do not possess enough cone classes—a direct consequence of the principle of univariance. By contrast, trichromats do so effortlessly, navigating colors within a fully three-dimensional color space and a circular continuum of hues.

Extending this logic to tetrachromacy, one would expect an idealized “yellow” retinal tetrachromat—who has a fourth M' or L' cone peaking around greenish-yellowish (approximately 545 nm ±5–7 nm)—to distinguish a pure spectral yellow from a red-green mixture solely by hue. In normal trichromacy, a perfect mix of red and green light appears indistinguishable from a monochromatic yellow; they form a metameric match. A trichromat simply cannot separate red-green from yellow in the absence of contextual clues. Conversely, a retinal “yellow” tetrachromat would unambiguously label red-green (e.g. Agre) as one hue and yellow (e.g. Ellow) as another, akin to how trichromats can separate magenta from white or red from green regardless of brightness or contrast.

So, where does true-red tetrachromacy (TRNRT) stand in comparison? Examining the red-yellow-green range provides a telling illustration. A trained trichromatic observer with TRNRT can consistently and behaviorally differentiate a pure yellow from a red-green mixture by hue alone. A purely yellow stimulus appears black to one eye and yellow to the other (i.e. Ellow), while a red-green mixture appears red to one eye and green to the other (i.e. Agre)—producing categorically different combined hues. Under normal viewing conditions (unaided eyes), these two would look identical (both “yellow”) and may only differ in saturation, luminance and contextual clues, but with the true-red glasses they appear as distinct hues regardless of saturation, luminance and contextual clues. Consequently, the color-discrimination behavior of observers with TRNRT in the red-yellow-green region effectively becomes trichromatic, not dichromatic. This gain in discriminability extends to other tetrachromatic hues documented throughout prior examples, reinforcing that TRNRT generates a genuine and moderately functional form of tetrachromacy with a 4-dimensional color space.

In conclusion, while true-red non-retinal tetrachromacy (TRNRT) produces hues that may lack the vividness of strongly functional retinal tetrachromacy, it remains sufficiently robust to deliver moderately functional and behavioral tetrachromatic vision across relevant spectral ranges. Observers can distinguish colors along previously conflated and/or inaccessible axes, demonstrating that even “impossible” binocular color blends can powerfully extend the dimensionality of human color space.

Instructions: Cone Responsivity Curves of Multiple Color Visions

• Left–click on the graph to add a spectral line which represents a light with this single (very narrow) wavelength.

• Drag its colored top handle vertically to adjust its intensity.

• Drag its black bottom handle horizontally to change its wavelength.

• Right–click on either handle to remove that line.

• In Yellow Tetrachromacy mode, you may click near a cone–curve’s peak to select that cone. The selected cone is highlighted and the next line you add will be locked to that cone. Wehn locked, a small white square indicator appears on its top handle, and the color of the top handle will be locked to the selected cone's color.

Notes:

• In protanopia the M cone is sending a green signal. In the program, however, yellow is used to better simulate the opponency of S vs. M. In reality, for a protanopa cyan will not look white and green not yellow, but conversely white will look cyan and yellow will look green. In protanopia, cyan and white are the same hue.

• The curves are simplified and more complex in reality. This is only a simulation.

• In the Yellow Tetrachromacy cone model it's more difficult to showcase the new opponencies that the M'/L' cone type creates compared to True-Red Tetrachromacy. That's why in the Yellow Tetrachromacy cone model you have to click on the peak of a cone type to bind the next line and its color to this cone type. The new "primary" color of Tetrachromacy is simulated with a second type of trichromatic yellow that's orthogonal to the S, M and L color mixes due to the binocular (interocular) mix.

Below are the same cone models, but slightly more accurate. However, they're still simplified.

You can clearly see that and how the three spectral sensitivity curve representations (Fig. 11/1-3) differ from each other. While they seem relatively similar and they all cover the standard visible range of human vision, they differ greatly in the red-yellow-green region of the spectrum. When comparing wavelengths and a selection of their combinations from normal trichromacy to true-red tetrachromacy and other cone models, you can see the increase in colors, hue categories and color concepts from mono- to di-, tri- and tetrachromacy.

How do true-red tetrachromatic colors look like through the true-red glasses? Understanding the perceptual qualities of true‐red tetrachromatic colors poses both a conceptual and practical challenge. On one hand, one might document the phenomenon by capturing images of a given color stimulus—first under standard conditions and then through each filter of the true‐red glasses. However, because conventional cameras approximate trichromacy rather than perfectly replicating human (or tetrachromatic) perception, these images must be interpreted with caution. Discrepancies between camera reproduction and subjective human experience are inevitable; therefore, the following visual examples are provided unedited, with clarifications noted where the camera’s rendition diverges from (my) personal observation.

Consider first an RGB (S/M/L+ with a little L- "pollution") light source, which under normal trichromatic conditions appears white because all three cone types are equally stimulated. Figure 12/1a illustrates this RGB light as captured by a phone’s camera. Although trichromats perceive this light as white, a protanope would register a similar achromatic point even if only green and blue components were present.

The true transformation occurs, however, when the true‐red glasses are employed:

These images (Figure 12/1b-1c) reveal that what appears as “white” to standard trichromatic observers is, for a true‐red tetrachromat, a vivid red-cyan (Acy) hue. For the tetrachromatic system to generate a genuine achromatic (white) percept, the cyan component would require a higher contribution of true vermillion light. The resulting red-cyan combination represents a distinct tertiary hue, one that is fundamentally different from any hue generated within conventional trichromacy.

A further illustration of these effects is provided by a real-life example involving various “yellow” hues. Figure 12/2a presents a yellow-orange-red light source viewed with a filter that transmits most wavelengths except true-red. To the naked eye, the light and filter appear nearly identical—a scenario in which the camera fails to capture the same trichromatic colors that are apparent in direct observation.

However, this yellow of Figure 12/2a transforms into a remarkably different binocular hue with the true-red glasses.

Thus, a light source that initially appears uniformly yellow can divide into two distinct tetrachromatic hues—one red-yellow and one black-yellow—each as perceptually disparate as the differences between red and yellow or blue and cyan in conventional trichromatic color vision. Moreover, the true-red tetrachromatic system reveals a rich gamut of hues within the red-yellow-green spectral region—ranging from combinations such as true-red/red (Ar), red/orange (Aor), red/amber (Aam), red/chartreuse (Achar), red/lime (Ali), red/basil (Abas), etc., to various mixtures involving black (Ed, Range, Mber, Hartreuse, Ime, Asil, etc.)—that cannot be rendered on a conventional display. This disparity underscores the motivation for developing an RVGB ("V" for vermillion) screen, whose subpixels are tuned to the primaries of true‐red tetrachromacy. To a true-red tetrachromacy, an RGB screen is missing most of their tetrachromatic hues.

It is important to note that while there are as many perceptually distinct hues between red, yellow, and green in true‐red tetrachromacy as there are colors (with different hue and saturation levels) in normal trichromacy, the available stimuli in everyday life are often “polluted” by overlapping red, yellow and green contributions. When looking at Fig. 11/2 again, we can clearly see why a true-red tetrachromat's "pure yellow" is such a rare color in nature, let alone in human design. To get a perceptually "pure" yellow in true-red tetrachromacy, you need a yellow that's neither polluted by true-red nor by green light. For example, most flowers, paints, and architectural facades that appear yellow are, in fact, broad mixtures of red, yellow, and green light—rendering them as red-yellow when viewed through the true-red tetrachromatic system. To achieve a perceptually pure yellow in true‐red tetrachromacy, one requires a narrow spectral output (approximately 575–595 nm) that is free from extraneous red or green contamination. A light that only emits or a material color that only reflects this narrow wavelength range is highly improbable to find in nature, and basically pointless in human design because normal trichromats will see the many red-yellow-green mixtures as the same metameric lime, yellow, orange, etc. anyway.

In summary, the subjective experience of true‐red tetrachromatic colors is one of dramatic transformation: common stimuli such as RGB S/M/L+) “white” or conventional “yellow” are reinterpreted into entirely new hues that transcend the limitations of trichromacy. This complex interplay between dichoptic spectral filtering and cortical integration not only expands the perceptual color space but also challenges our conventional understanding of color qualia.

Once I find a method to better capture true-red tetrachromatic colors of real life objects with RGB cameras, then I'll provde more examples.

Tetrachromacy is interpreted in various ways across online media, but these interpretations often fall into three general categories.

Statement 1 posits that tetrachromacy does not allow one to see “new” colors because it does not extend vision beyond the normal human visible spectrum. As an example, the YouTuber Knowing Better (2017) claims in his video “Tetrachromats Don’t Have Superpowers” that tetrachromats do not truly see additional colors, only a slightly finer discrimination among similar ones. However, this view overlooks functional tetrachromacy’s fourth color dimension, which indeed provides access to many more color experiences—even if the fourth cone type resides between M and L cone types and thus remains within the standard visible range. 

Statement 2 suggests that tetrachromacy merely lets you see more “intermediate” colors or hues. At one point, I myself believed and helped spread this misunderstanding. Subsequent study and personal experience with true-red non-retinal tetrachromacy (TRNRT) taught me that an extra cone class creates an entirely new dimension of color, yielding not just more (contrasty) intermediate hues but also a two-dimensional hue plane foreign to trichromacy. 

Statement 3 claims that tetrachromacy enables one to see “100 million” colors instead of the typical “1 million,” based on counting around 100 intensity steps per cone type. Although this number can serve as a rough estimate for a fully functional four-cone system, it does not capture the variability in “weakly,” “moderately,” and “strongly” functional tetrachromacy. Even with a supposedly strongly functional retinal tetrachromacy—such as a person with an M' or L' cone sandwiched between the normal M and L peaks—the spectral overlap can reduce its practical impact. If, by contrast, TRNRT’s L+ cone were more distinct from L- than M' (or L') is from M/L, it could arguably be considered more functional in certain respects.

Ultimately, depending on how pronounced the fourth cone’s spectral separation is and how well the observer’s brain integrates that extra input, color vision dimensionality and the number of distinguishable colors may vary substantially. As a result, some people deny that tetrachromacy confers truly new colors, while others concede an improved color discrimination but still think of it as a mere “enhanced trichromacy.” Meanwhile, researchers studying tetrachromacy generally agree that a fully functional additional cone type can scale color vision in a way analogous to how trichromacy differs from dichromacy. In the context of functional tetrachromacy, the first two statements are incorrect, and the third one demands careful nuance.

The following "tetrachromacy test" (Prof. Derval, D. (2015). On: LinkedIn: "25% of the people have a 4th cone and see colors as they are ;p") has widely spread the false believe amongst people that they are tetrachromats.

According to Derval (2015), if an individual can distinguish more than 39 colors in Fig. 13.2/1, it is highly probable they possess a functional fourth cone class in the retina. This additional cone enhances contrast perception, an effect that's also noticeable on RGB screens, where tetrachromats are believed to experience a sharper contrast effect. However, despite this correct heightened contrast, the fundamental limitation remains: an RGB display, with its three subpixels, represents only a one-dimensional slice of the two-dimensional tetrachromatic hue plane; and only a three-dimensional volume slice of a four-dimensional hypervolume. In essence, even though tetrachromats might perceive some colors as more vivid or contrasty, they do not actually see a greater number of distinct colors on such screens than trichromats do.

Many online tests claiming to identify tetrachromacy are fundamentally flawed. These flawed tests often rely on images that cannot present a 2D hue plane and often do not even display a continuous gradient; instead, they display hues that are not only discretely arranged but sometimes even repeated. A normal trichromat can easily distinguish more than 39 hues from such a display (see Fig. 13.2/1), meaning the test does little more than mislead participants into believing they have an enhanced color vision capability. For a display to accurately simulate tetrachromatic vision, it would need a fourth subpixel—in the case of true-red tetrachromacy a narrow-band orangey-vermillion—coupled with appropriate software and color data. Without these modifications, it is literally impossible to design a direct and reliable test for retinal tetrachromacy on an RGB screen.

An additional layer of complexity arises from the inherent subjectivity of color itself. Wavelengths are objective measurements, but color is the brain’s interpretation of these wavelengths and their multiplex combinations—a qualitative experience known as qualia. Even though a tetrachromat may make more distinctions between colors compared to a trichromat, this does not necessarily mean they perceive more trichromatic and "more real" colors. Rather, they are simply more adept at differentiating variations (i.e. single wavelengths and combinations of multiple wavelengths) within the same visible light range that everyone else experiences (at least in M'/L' tetrachromacy).

The proliferation of these flawed tests has led many people online to falsely claim tetrachromacy. For instance, if someone asserts that they can perceive hundreds of additional color categories in a natural rainbow, such a claim is implausible. A rainbow, being essentially a one-dimensional display of color variations, at best might allow a tetrachromat to identify one or two extra bands of hues compared to a trichromat—not an explosion of new color categories. In contrast, consider a scenario where an individual posts an image of two “yellow” lights on a forum and insists that one exhibits a categorically different hue from the other, even going so far as to claim that the standard “yellow” produced by an RGB screen does not match the photographed "yellows" compared to what they see. Such claims prompt further investigation: it is possible that this person either possesses a mutated fourth cone (most likely a functional M'/L' cone) or, alternatively, that they exhibit some form of color vision deficiency or anomalous cone sensitivity within the confines of such an altered trichromacy.

Ideally, testing for tetrachromacy should be conducted by observers who themselves have the genetic predisposition for tetrachromatic vision. However, because functional tetrachromacy is exceptionally rare, the most practical tests are designed by trichromats with in-depth knowledge of the phenomenon and personal experience of simulated tetrachromatic colors. The current best simulation available—known as “true-red non-retinal tetrachromacy”—allows proficient observers to qualitatively and subjectively validate the presence of a functional fourth "true-red" cone. Such evaluations rely not only on measurable differences but also on the nuanced, experiential and subjective understanding of color that comes from direct comparison with the simulated tetrachromatic experience.

In summary, while tetrachromacy may enable individuals to discern subtle differences in color that others might overlook, the limitations of current RGB-based testing render all online assessments unreliable. The interplay between objective wavelength measurements and subjective color perception further complicates matters, leading to widespread misconceptions about what tetrachromacy truly entails. It is only through carefully designed tests and expert qualitative and behavioral evaluations that the true nature of tetrachromatic vision can be discerned, accurately described and identified.

A hue ordering test for tetrachromacy should be designed with consideration for the 2-dimensionality of tetrachromatic hues. While you can test for tetrachromacy with a (Neitz) anomaloscope (in combination with a color vision deficiency test), or with a single spectrum of material colors, e.g. red/green (agre) to black/yellow (ellow), a complete test for tetrachromacy involves hues that can be arranged in a 2-dimensional structure, or at least a method that considers the 2-dimensionality of tetrachromatic hues.

The below 2D & 3D True-Red Tetrachromacy 2D Hue Ordering Tests illustrate complete 2D hue ordering tests for true-red tetrachromacy using stereo viewing. With correct and exact material or light colors you can also build analog tests. However, an analog test is naturally more difficult to create, especially with material colors.

A normal trichromat, as exemplified by the "Trichromatic View" below the left and right ocular views, will not be able to reasonably order tetrachromatic hues. Many tetrachromatic hues that appear as distinct hues to tetrachromats will look like very similar or even identical and repeating colors to a normal trichromat. For example, in the "Trichromatic View" there are several identical yellow hues, and even more yellow colors. Even if a normal trichromat tries to cheat this test by ordering the colors in a subjectively reasonable manner, they would make many mistakes and only get some of the tetrachromatic hues ordered correctly by pure chance. This is analogous to a dichromat trying to solve a hue ordering test for trichromacy.

In the light of this, the aforementioned fake tetrachromacy test by Derval (2015) seems even more erroneous. Not only can you not test for tetrachromacy on a trichromatic (RGB) screen, but a 1-dimensional spectrum of hues, especially as the normal trichromatic hues are arranged on an RGB screen, is not enough to test for the full functionality of any tetrachromacy.

A dichromat needs a 0-dimensional, a trichromat a 1-dimensional, a tetrachromat a 2-dimensional, a pentachromat a 3-dimensional, and a hexachromat a 4-dimensional hue ordering test.

2D True-Red Tetrachromacy 2D Hue Ordering Test

True-Red Tetrachromacy 2D Hue Ordering Test additional instructions:

• hover over color dot: increase this dot's size by the Hover Scale value

• continuous left click on color dot: additionally increase this dot's size by the Active Add Scale value

• left click + drag on blank areas: rotate the all hue rings around the center point

• left click + drag on color dot: rotate a specific hue ring

• right click + drag on color dot: exchange a specific color dot with another by dragging it onto another within the same eye's view

The "Trichromatic View" shows how the true-red tetrachromatic hues look like to a normal trichromat. Once the true-red tetrachromatic colors have been jumbled up, you can try to order them correctly.

The "3D" True-Red Tetrachromacy 2D Hue Ordering Test below constitues the same test as the True-Red Tetrachromacy 2D Hue Ordering Test, but with the dots arranged on the surface of a tetrachromatic hue sphere. This removes the need for an extra ring of true-red colored dots, which are technically all the same distorted singluar true-red hue. This 3D arrangement also makes it easy to find the opposite hue of each true-red tetrachromatic hue that lies on the opposite side of the hue sphere.

3D True-Red Tetrachromacy 2D Hue Ordering Test

3D True-Red Tetrachromacy 2D Hue Ordering Test additional instructions:

• left click + drag: rotate the the hue sphere around the center point

• right click + drag on color dot: exchange a specific color dot with another by dragging it onto another

• mouse wheel up/down: zoom in and out

The "Trichromatic View" shows how the true-red tetrachromatic hues look like to a normal trichromat. Once the true-red tetrachromatic colors have been jumbled up, you can try to order them correctly.

Inspired by the Ishihara test and Ishihara plates the Lachner Test for True-Red Tetrachromacy below constitues a higher-dimensional evolution of the Ishihara test but for true-red tetrachromacy. This digital test uses stereo viewing techniques that mimic real life true-red tetrachromatic colors. If you can distinguish these impossible color combintions and correctly identify the numbers, you can almost identically distinguish them in real life with the use of the true-red tetrachromacy glasses and an adequate analog test.

Lachner Test For True-Red Tetrachromacy with Ishihara Plates

Lachner Test For True-Red Tetrachromacy with Ishihara Plates additional instructions:

• enter the number and sumbit it as the answer to see if your guess was correct

• if no number is visible, then delete any inputs of the input field and submit a blank answer

• the higher the dot count, the better distinguishable the characters will become

• click the "Next plate" button to generate a new plate with new characters

The "Trichromatic View" shows how the true-red tetrachromatic hues look like to a normal trichromat (without accounting for luminosity differences). You can try to guess the correct number when stereo viewing. You can see that in the "Trichromatic View" most numbers are only very faintly noticeable and some numbers aren't distinguishable at all.

(This article is still under construction. To be continued.)