Michael Hurben, PhD

When I was much younger and had normal eyesight, I worked as a line cook. I enjoyed the mental and physical challenge of handling dozens of orders at once. You had to constantly think about your next actions, and your hands, eyes, and feet were obliged to move quickly. Mistakes and inefficiency were cumulative; if you couldn’t keep pace, an angry wait staff (and even angrier customers) would be your reward.

Those days are past, but I do all the cooking at home, as it helps me pretend that I am still a teenager. There is usually no need to hurry, nor to juggle more than a few “orders” at once, but my habit of moving with alacrity in the kitchen is deeply ingrained. I have to fight the instinct to hurry.

Having tunnel vision due to retinits pigmentosa (RP) along with this proclivity to hustle about the kitchen does not a good combo platter make; it is not uncommon that food items get knocked off counters and onto the floor. When this occurs, I have a ritual: I don’t stand there and look around for the cherry tomato, or whatever, that fell. Instead I walk out of the kitchen and view the situation from afar. The reason for doing this is geometrical.

Visual range, or field of view, can be quantified in terms of an angular width. My window to the world is about fifteen degrees from side to side, and the same from top to bottom. It roughly corresponds to the size of your fist held at arms’ length. With normal vison, you can see just over 180 degrees from side to side, but less from top to bottom, due to parts of your face being in the way. I know my range thanks to the visual field test that opthamologists use: with one eye covered, you stare into a large hemispherical bowl where pinpoints of light occasionally appear at different places and with varying intensities. You push a button every time you see a flash. The machine then contructs a map of your vision. The figure below shows how my right eye performed, when measured back in 1997. If your better eye has no more than twenty degrees of width, you are considered legally blind in the USA.

You might be wondering what might stop someone from trying to fake legal blindness, for whatever reason. After all, one could simply not press the button for anything but flashes in the center of the field. It would not suffice to get you an RP diagnosis: a physician will determine that you have it by dilating your pupils and inspecting your eyes: this will clearly indicate the disease; pigmentosa refers to a dark, splotchy discoloration of the retina.

Back to the geometry lesson in the kitchen. Fifteen degrees is equivalent to 0.26 radians. If that term means nothing to you, know that radians are simply an alternative way to measure angles. Degrees and radians are a bit like miles and kilometers, if you will, with one radian equaling about 57.3 degrees. Radians are more practical: they provide an easy way to relate actual size of some perceived object, its apparent angular size (how much of the field of view it occupies), and how far away it is. The actual size corresponds to the angular size in radians, multiplied by the distance.

As an example, my eyes are about 60 inches away from the floor when I am standing. With my field of view, I can see a spot on the floor with a width of about fifteen inches (15 = 60 x 0.26). That is not very large. Imagine looking for the tomato in a dark kitchen with a flashlight that cast a circle of light fifteen inches wide. You’d have to systematically scan around the floor. It might take a while.

It is much faster to instead walk away and have a look back. By standing twenty feet from the center of the kitchen floor, the total distance to my eyes is about 250 inches, and my field of view lets me see a spot just over five feet wide (250 inches x 0.26). This window of visibility harvests a much larger portion of the floor. The tomato pops into view and I can go get it.

So when I am birding and hear a song or call from a tree that is neither distant nor at hand, the natural inclination is to get closer. I fight this instinct, for the closer I get to the tree, the smaller my window becomes. It would take more time to search for the bird from up close. What’s more, if while I am scanning a middle branch on the left side, say, and the bird hops between low branches on the right side, I won’t see it. But had I been looking at the tree from a distance, so that the entire tree fit into my field, I’d have picked up the movement, locked-on to the position, and put my bins on the spot. Yes, I’d get a much smaller image than someone standing closer would. But had I been closer, I’d have gotten no image at all.

Birding guides, even after I have explained my vison problems to them, will usually still react to a singing bird by getting close, closer, too close to the tree (for me). Years of training draws them there, I suppose just like years of training keeps me flying about the kitchen. It’s fine; depending on the situation, I can just hang back and take it all in from a distance. It’s yet another way that a disability can give rise to a behavior that may seem counter-intuitive.

Something else that doesn’t accord with intuition: a visual field of twenty degrees is a lot smaller than you might think, as quantifying visual field in terms of a width is somewhat misleading. Each eye takes in a two-dimensional scene to form an image, so we should be thinking in terms of something like area, not width, if we want to really understand how the legal blindness criterion compares to normal vision.

With two healthy eyes, the full range of vision will be about 190 degrees from side-to-side, and 135 degrees from top to bottom (source). Upwards, we lose the top 30 degrees, blocked by brows and eyelids, while downwards, the lower 15 degrees are obscured. Each eye has a blind spot due to the optic nerve, but these are not coincident; the left eye can see where the right cannot, and vice-versa. Similarly, your nose gets in the way of lateral vision for a single eye, but having a pair makes up for that.

You can imagine the total area that can be percieved at once by picturing yourself at the center of a large sphere, with your gaze directed at a point straight ahead. If you were to paint every bit of that surface that you could see at that instant, without moving your eyes, you would need to cover about 40% of the total area. Obviously, the half the sphere behind you is impossible to see, and the other 10% are those up and down extremes that are off-limits.

For the legal blindness limit of twenty degrees (and assuming a circular field), that area drops from 40% to just under 0.8% of the total spherical surface. This means that a legally blind person (due to tunnel vision) will see at most 2% (0.8 divided by 40) of what those with normal vision do.

What about the other alternate criteria for legal blindness, that accounts for poor visual acuity? Here your better eye, with the best possible corrective lenses, would have no better than 20/200 vision. That means, to see the detail that normal eyes resolve on an object at 200 feet, then, you would need to stand 20 feet from it. The geometry of this situation allows us to put this factor of ten to use in another way: with 20/200 vision, if you were looking a metric ruler placed at a distance such that you could just make out the centimeter marks, a person with normal vision could stand next to you and see the millimeters. Now imagine a square full of dots, each at millimeter spacings, with a total height and width of a centimeter. You’d just be able to discern that the entire square, while our friend would make out the 100 dots in the grid. You’d be seeing effectively 1% of what they can.

Finally, a useful way to think about either of these conditions and the connection of width and area: consider a chessboard. Along any one side, there are eight equal divisions, so in terms of width, a single square takes up 12.5% (1/8) of the total. But in terms of area, a single square takes up only about 1.6% (1/64) of the total. That is essentially what low vision, or legal blindness, entails as a best-case scenario; the chessboard must be scanned a square at time, while most of the world takes in the entire game all at once.