Before we descend into the mesopelagic abyss, let's ask a basic optical engineering question: What is the F-number of the human eye?

This is not something you'll find in most biology textbooks. Optical engineers think in F-numbers. So let's think like one.

The human eye is not a camera—it's a variable optical system. The pupil expands and contracts, so the effective F-number changes throughout the day. But we can estimate a typical midpoint.

Key anatomical parameters:

Focal length:         ~17 mm (measured from cornea to retina)
Pupil diameter (daylight, typical): ~3-4 mm
Pupil diameter (dark-adapted, max): ~7-8 mm

At typical daylight conditions (pupil ~3.5 mm):

F-number = focal_length / pupil_diameter
F = 17 mm / 3.5 mm
F ≈ 4.9 → ~F/5

At dark-adapted conditions (pupil ~7 mm):

F = 17 mm / 7 mm
F ≈ 2.4 → ~F/2.5

Average working F-number across normal conditions:

F_typical ≈ F/6 to F/8

So the human eye operates in the F/5 to F/8 range under most circumstances. This is the result of 400 million years of vertebrate optical engineering.

Here's where it gets interesting. We could have evolved larger pupils—frog eyes do exactly that. A human eye with a 10mm pupil (F/1.7) would gather 8 times more light than our current design.

But we didn't. And there's a reason.

Depth of field at F/2.0:    ~1-2 mm (at 50 cm focus distance)
Depth of field at F/6:      ~10-20 mm (at 50 cm focus distance)

A shallow depth of field means the focusing mechanism must be perfect.

If your eye is F/2.0, even a 100-micrometer error in lens position pushes the image out of focus. At F/6, you have 5x more tolerance. This tolerance—this optical redundancy—is what allows the human eye to remain functional across a 60+ year lifespan.

This is the central tension: gather more photons, or maintain focus reliability as you age?

Before asking why so many humans are nearsighted, it may be worth stepping far back in evolutionary time—far earlier than Homo sapiens, earlier than the rise of mammals, and into the era when the vertebrate eye was still shaped by the optical constraints of life in water. In those ancient environments, the strongest selective pressure was not fine spatial resolution, but sheer brightness. Any organism that could capture more light from the dim underwater world immediately gained an advantage, even at the cost of accepting optical trade-offs.

This raises an intriguing possibility: perhaps the roots of modern myopia are not a uniquely human defect, but an inherited architectural compromise—an ancient bargain struck in a world where gathering photons mattered more than maintaining a wide depth of field.

It is from this angle that the Splendid Alfonsino (Kinmedai), a deep-sea fish with an astonishingly fast F/2.0 optical system, becomes more than a biological curiosity. It becomes a window into the original constraints that vertebrate eyes have carried forward for hundreds of millions of years.

Deep in the mesopelagic zone, the magnificent Kinmedai swims in perpetual twilight. To capture the few stray photons that filter down from the surface, this fish has evolved one of the most remarkable optical systems in the animal kingdom: an enormous eye with a monstrously large pupil.

Our analysis of the Kinmedai's known morphology reveals an F-number of approximately F/2.0 or faster:

F = focal_length / pupil_diameter ≈ F/2.0

Compare this to the human eye at F/6: the Kinmedai gathers roughly 9 times more light.

In photography, F/2.0 signifies incredible brightness, but it comes with a steep price: an extremely shallow depth of field (DoF). For the Kinmedai, the world is divided into a razor-thin plane in perfect focus and everything else blurred. This makes precise accommodation—the act of focusing—not just important, but essential for survival.

The depth of field for a given circle of confusion c is:

DoF = (2 * N * c * s²) / f²

Where:

• N = F-number

• c = circle of confusion (acceptable blur)

• s = object distance

• f = focal length

At F/2.0 vs. F/6, with typical parameters:

Kinmedai (F/2.0, 50cm focus):    DoF ≈ 2-3 mm
Human (F/6, 50cm focus):         DoF ≈ 10-15 mm

The Kinmedai has 5-7 times shallower depth of field than a human eye focusing at the same distance. At F/2.0, even micron-scale errors in lens positioning cause catastrophic blur.

Humans experience presbyopia when their lenses harden with age, losing the ability to change shape. Fish, however, use a different mechanism: they shift a hard spherical lens back and forth using the retractor lentis muscle.

For the Kinmedai, age-related focusing issues arise from two compounding factors:

Physical Crowding: The lens grows continuously throughout its life. As it expands, it restricts the available stroke of the focusing muscle, reducing the range of accommodation.

Muscle Entropy: The precision of the retractor lentis declines with age, turning a once-deterministic movement into a noisy, uncertain process influenced by neuromuscular fatigue and thermal fluctuations.

This is where statistical mechanics becomes the ideal analytical tool.

We can model the aging focusing system as a spring-loaded muscle operating in a noisy environment. A young muscle maintains a low-entropy state—stable and precise focus. As noise increases with age, the system drifts toward a high-entropy state, where the position of the lens is no longer a single value but a probability distribution.

The fundamental model follows the Boltzmann distribution:

P(x) ∝ exp( -E_pot / (k_B * T_eff) )

Where:

• E_pot = potential energy of lens position (related to muscle stiffness and accommodation effort)

• k_B = Boltzmann constant

• T_eff = effective temperature representing neuromuscular noise

As the fish ages, T_eff rises. The probability distribution widens, and the focal plane becomes uncertain. Instead of a sharp peak at the correct focal distance, the lens position becomes a blurred cloud of possibilities.

Now consider the contrast:

Human eye (F/6, DoF ≈ 15mm):

• Muscle jitter of ±100 micrometers is invisible to the visual system

• Even with doubled age-related noise, the image remains acceptable

• The large DoF provides a buffer against aging

Kinmedai (F/2.0, DoF ≈ 3mm):

• The same ±100 micrometer jitter is catastrophic

• At F/2.0, the tolerance is 5-7x smaller

• Age-related noise that a human tolerates easily becomes vision-destroying

Muscle jitter tolerance at F/2.0:   ~20-50 micrometers
Muscle jitter tolerance at F/6:     ~100-200 micrometers
Safety margin loss per decade:      ~15-20%

By age 15, the Kinmedai's muscle tremors exceed its optical tolerance. By age 20, focus is probabilistic rather than deterministic.

Define the focal entropy as:

S(t) = -∫ P(x,t) log P(x,t) dx

For a Gaussian distribution with variance σ(t)²:

S(t) = (1/2) * log(2πe * σ(t)²)

As age increases, σ(t) grows due to accumulated muscle noise and physical constraints. For Kinmedai, we observe:

σ(t) = σ₀ + α(t - t₀)

Where α ≈ 0.01 mm/year. The entropy increases monotonically:

S(t) = S₀ + (1/2) * log( 1 + (α(t - t₀) / σ₀) )

By age 15, entropy has roughly doubled compared to age 5. The system has transitioned from an ordered, low-entropy focusing apparatus to a high-entropy, probabilistic blur generator.

To illustrate this concept, we built an OpenGL-based stochastic ray tracer in CHICKEN Scheme. The simulation models:

1. Age-dependent lens jitter following a Gaussian distribution centered at age 5–20 years

2. Stratified Monte Carlo sampling to reduce variance in ray tracing

3. Thin-lens optics with accommodation via focal length variation

4. Distance-dependent color absorption (red light scatters over deep-sea distances; blue penetrates further)

Rays from a nearby prey item converge sharply on the retina. The probability curve is narrow. The visual image is crisp and predation succeeds.

Age: 5.0 years
Lens jitter: σ ≈ 0.07 mm
Focal tolerance: SATISFIED
Status: Sharp & Ready

Focal rays form a probability cloud. The lens jitters, and light spreads across the retina instead of striking a precise point. The resulting image is statistically blurred beyond recognition.

Age: 18.0 years
Lens jitter: σ ≈ 0.13 mm
Focal tolerance: EXCEEDED
Status: PRESBYOPIA (High Entropy)

The Kinmedai's tragedy reveals a fundamental principle of optical systems: you cannot simultaneously maximize light-gathering and maintain robust focus across a long lifespan.

The human eye's choice of F/6-F/8 reflects a different environment and a different timescale:

• Environment: Mostly daylit, with sufficient ambient light even at F/6

• Timescale: Must remain functional from birth to age 80+

• Solution: Accept less light gathering in exchange for deep depth of field and aging-resistant design

The Kinmedai, operating at the extreme end of the aperture spectrum, sacrificed longevity for photon capture. It is an eye optimized for now—for the immediate hunt in perpetual darkness—not for decades of reliable vision.

The myopia we see in modern humans—driven by near work and indoor environments—is not a new disease. It is the manifestation of a design constraint forged 400 million years ago, when vertebrate eyes were carved by the trade-offs of dim-light vision.

In the eternal darkness of the mesopelagic zone, a Kinmedai loses its edge not because evolution failed, but because it succeeded too well at gathering light. That success, frozen in the aperture equation, creates an inevitable fate: as neurons jitter with age and muscle entropy rises, even the most exquisite optical system becomes blind.

Perhaps the real question is not why presbyopia happens. It's how anything sees at all in a universe governed by entropy, and why we chose the optical path we did.

The simulation implements:

Thin lens equation:

1/f = 1/s + 1/s'

Magnification:

m = -s' / s

Age-dependent focal jitter:

σ(t) = 0.02 + 0.01 * max(0, t - 5)  [mm]

Retinal image position: Calculated via stochastic ray tracing with stratified sampling:

n_strata = 10
n_samples_per_stratum = 8
total_samples = 80

Color attenuation: Distance-dependent with wavelength-specific absorption coefficients:

Red channel:   k_r = 0.0008 mm⁻¹
Blue channel:  k_b = 0.00025 mm⁻¹

The visualization renders rays from object space through the pupil to the retinal plane, coloring each ray by its contribution and age-induced uncertainty.

The code to simulate when "Kinmedai" will develop presbyopia is below:
https://github.com/Yoshyhyrro/how_to_create_-/blob/kinme/kinmedai-eye-sim.scm