Discovering Foundational Principles

The pursuit of a deeper understanding of vision likely traces back to the dawn of humanity, as it is essential for survival. Thus, it’s only natural to ponder the questions of what, why, and how we perceive our surroundings. To maintain focus, we will concentrate on the contributions of three pivotal figures: Young, Helmholtz, and Svaetichin.

Our first stop introduces the remarkable Thomas Young, a British polymath who delved into both the anatomy of the eye and the physics of light. His influential work, "On the Theory of Light and Colours," introduced two groundbreaking theories. He first proposed the wave theory of light and showcased how different colors correspond to various wavelengths using diffraction, setting the stage for his famed double-slit experiment. He also formulated the theory of trichromatic vision, explaining how our eyes perceive colors—a concept confirmed by the presence of three types of cones in the retina.

Fast forward to the 1860s, Hermann von Helmholtz built upon Young's findings. While Young suggested only three types of photoreceptors, Helmholtz demonstrated their existence and functionality. He theorized that these photoreceptors respond to varying wavelengths of light: short, medium, and long. While there was debate over which colors corresponded to these wavelengths, Helmholtz proved that all visible colors could be created by combining three primary colors.

Next, we encounter Gunnar Svaetichin, a physiologist who explored the sensitivity of fish retinas to different wavelengths of light, supporting the Young-Helmholtz trichromatic theory with biological evidence.

Our Contemporary Understanding

While entire textbooks could delve into the anatomy of the eye, we will focus on the retinal layers responsible for interpreting color and light. Within the retina, the innermost light-sensitive layer, reside millions of rods and cones. Rods dominate our peripheral and low-light vision, with approximately 120 million cells per retina, but they lack color sensitivity. Conversely, cones, numbering around 6 million per retina, are responsible for high-resolution color vision.

Each type of cone contains a unique photosensitive pigment, attuned to specific wavelengths of light. The three cones—L, M, and S—respond best to long (around 560 nm), medium (530 nm), and short (420 nm) wavelengths, respectively. Recent findings indicate that 64% of cones are red-sensitive, 32% are green-sensitive, and only 2% are blue-sensitive, with green and red cones concentrated in the fovea while blue cones are positioned elsewhere.

Armed with this historical context and modern insights, we are now ready to explore the mathematics behind the transition from biological to digital color representation, spanning decades of research and technological advancement. How did we progress from Maxwell's first color photograph in 1870 to the vivid LCD screens of today? Let's delve into the mathematics of this transformation.

The Mathematical Foundations of True Color (24-Bit)

Everyone knows what a pixel is—the basic unit of an image. When you zoom in on your screen, you see countless pixels, each formed by three closely spaced RGB light sources. From a standard viewing distance, these sources blend together, creating the illusion of solid color.

In the late 1990s, the competition among various pixel structuring methods led to the establishment of a universal standard: True Color (24-Bit) color depth. This standard is now integral to virtually all displays, including televisions, computers, and smartphones, and serves as the foundation for color representation in design software. To understand why True Color became the gold standard, we must first consider the limits of human color perception.

Psychologist Frank Geldard's 1972 study suggested that humans can distinguish around 7 million different color variations, while a 1996 study by Kurt Kleiner estimated this figure at approximately 2.3 million. Thus, to develop a universal color system, we must aim to represent at least 2.3 million colors.

Research indicates that the average human eye can differentiate around 150 hues within each RGB channel. This mathematical validation confirms that 150³ (approximately 3.4 million) falls within the range of our earlier estimates.

Now, let's shift our focus to the digital realm, starting with the fundamental unit of information: a bit. Due to the principles of circuit design, a bit can only represent one of two states—0 or 1. If each RGB value can represent up to 150 gradients, we must determine the minimum number of bits required to store these values. We need to find a value n such that 2ⁿ > 150. Solving for n shows that we need at least 8 bits per color channel in an RGB model to ensure all perceptible colors are displayed.

Interestingly, in computer science, 8 bits are known as a byte. Since three bytes (24 bits) can fully represent the RGB model, this system effortlessly accommodates non-binary color coding that is user-friendly. In design software, users can manually input values from 0 to 255 (256 total possibilities) for each RGB channel, confirming that this range stems from 2⁸.

You may also encounter hexadecimal color codes, such as #012f5b. In this system, each character represents one of sixteen possible values (0-9 and A-F), with pairs corresponding to the three RGB channels. Again, this checks out mathematically, as each pair of characters can represent 256 colors (2⁸).

In Conclusion

By unraveling the mathematics behind True Color (24-Bit), we uncover a fascinating coincidence: an RGB channel stored in a single byte encapsulates all perceptible shades for the average viewer. Any deviation in data storage, such as using seven or nine bits, would have led us astray. Thus, the rationale for True Color (24-Bit) as the universal digital standard becomes evident.

However, as we transition from mere replication to augmentation, how will our understanding of color continue to evolve? What new patterns and principles will emerge as we push the boundaries of our most vital sense?

This essay is part of a series on mathematical topics published in Cantor's Paradise, a weekly Medium publication. Thank you for reading!

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