After 25 vision therapy appointments, I thought I had mastered the art of “opening my peripheral vision.” With every exercise given by my optometrist, I have been directed to open my peripheral. What I didn’t realize was that I was missing the most important part, the z-axis.

So what does the z-axis have to do with peripheral vision, and how will it 10X your results in vision therapy? ** Peripheral vision doesn’t just include what is seen on the x and y -axes (left and right, up and down), it includes all the beautiful depth in front of you that the z-axis offers. As you open your vision to see the world with depth, imagining the z-axis can train your brain to see the space between every object in view. Once this skill is mastered, vision therapy will become much more effective. **

When I learned this concept for the first time, it was the epiphany of all epiphanies. I was reading a research article by Dr. David Cook and read, “The words, “be peripheral” can be used, but only if the patient understands that “being peripheral” includes awareness of space, not just on the x-axis, but on all three axes: x,y, and z.”

The words hit me like a ton of bricks. Suddenly, everything seemed clear and I realized what I had been missing. As a math teacher, I have so much experience with graphing and the x,y, and z axes that I finally had something concrete to help me understand the concept of depth.

I’ve had strabismus and no depth perception my entire life so visualizing real depth is very challenging for me. When I pay attention and look for the z-axis, the whole world transforms. Let me help you understand the z-axis and transform your world as well.

## What is the Z-Axis?

I’m assuming that if you are reading this, you’ve most likely completed an Algebra class at some point in your life, but just in case, I’ll start with the basics.

You’ve probably seen a coordinate graph before. Usually, we see 2D graphs with a horizontal x-axis and a vertical y-axis, like in the following picture.

The fun part is adding points to the graph. Points come in an ordered pair which basically just means two numbers separated by a comma, like so, (2,7). If I wanted to graph the point (2, 7) on my graph. I would remember that the first number always moves in the x direction and the second number moves in the y direction. So we would go to the right 2 and up 7, see the pink dot in on the graph?

If you superimposed this grid onto a 2D image, you could describe the position of different objects in the picture using coordinates.

Take this lovely photo of Island Park, Idaho during the winter, for instance. If I wanted, I could use a coordinate graph to explain where the tip of the mountain, clouds, or the trees are.

We could estimate that the mountain tip is at about (7.5, 3), there is a nice fluffy cloud at (-2, 2) and trees can be found all over, but my favorite is at about (-6, 0).

You may be wondering why in the world any of this matters or how it has any connection to strabismus or vision therapy, but hear me out, I promise.

If we add a third axis to the graph, the z-axis, we are suddenly able to represent depth. Instead of just identifying how high, low, left or right an object is, we can suddenly figure out how far in or out it is.

To graph a point on the x, y, z axis a coordinate with 3 numbers is used, such as (7, -3, 2). The numbers are alphabetical, (x, y, z) so to graph you’ll go to right 7 on the x axis, down 3 on the y axis and out 2 on the z-axis.

If you have strabismus like me, visualizing this is probably really challenging! I have struggled my whole career in math with visualizing 3D graphs and scenarios. Many many hours were spent in my Multivariable Calculus teacher’s office trying to understand the 3 dimensional math world. All those hours feel well spent now because they’ve helped me bridge the gap from 2D to 3D in the real world.

If this is really challenging for you to grasp visually, go down to the last section on helping children understand and try doing the activity that I suggest. It can really help with the concept of 3D. There are also a ton of free online 3D graphing calculators that you can mess around with to help your brain start getting the concept.

## How Can I Use the Z-Axis to See the World in 3D?

Real life situations are rarely only two dimensional which is why math teachers have struggled since the dawn of time to answer the question, “when am I ever going to use this?” Because honestly, most of the math being taught in high school is two dimensional and will never be used in the real world. Why? Because the real world is not two dimensional.

Of course, it’s necessary to learn those basic building block skills, but they are preparatory. They prepare for the real world, for the real applications. Once the third dimension is added into math, the applications are limitless. It becomes an actual tool for innovation, problem solving and real life everything.

Peripheral vision is the same way! It is great to be able to see straight to the sides or straight up and down. But true peripheral vision extends infinitely in all directions. It encompasses the limitless, unseen air that fills the space between objects.

When you learn to see that volume of space at a glance, it is so much easier for your eyes to work together. That part, I’m still working to understand, but for now, I know that when I try to visualize the world in 3D, my brain can suddenly see it that way. Instead of feeling like I’m inside of a tunnel, I can see everything and the world stretches higher, lower, and further.

Hopefully, you understand what the z-axis is now so let me give you some tips for applying it to the world that you live in.

Take a step back from whatever screen you are viewing and try to see the room you are in with an x,y, z graph inside of it. Sometimes I will look at the back wall of the room I’m in and imagine that it is the x and y axis and then picture the z axis coming straight out towards me.

Once you have that visual, pick an object in the room, maybe it’s a vase, water bottle, desk or pencil. Using your imagined 3D grid, estimate the coordinates of that item.

I’m sure 90% of the people reading this have had a mini math heart attack and have run far far away, but if you like math and your brain gets it, geek out with me for a minute longer.

As you see the vase and imagine it’s coordinates, **try to see all the empty coordinates around it that are occupied by space**. What about behind the vase? When I start doing this, I can feel my eyes lock in together and try to look around the object.

Visualizing where the objects stand on the grid is great, but visualizing the space, especially behind the object is even more valuable.

Usually, my brain ignores the space between and behind objects. They just look like they are right on top of each other. I know that they aren’t because there are other cues that I use, but those cues don’t allow me to see space behind them. Seeing the world as an enormous, infinite, 3D grid, gives my brain permission to see in this new way.

The brain doesn’t want to change. It is so practiced at doing things the way they have always been done, it won’t allow you to see in a new way. My brain needs concrete concepts and proof to believe in the space. Believing it is there is the first step towards actually seeing it.

### How Can I help a Child Understand the Z-Axis?

For those of us who have never experienced depth in the real world, the concept of a 3D grid can be extremely abstract and overwhelming. It is such a helpful concept in improving peripheral vision for strabismics and is worth dedicating time to teaching children and adults how it works. Learning about the x, y, z coordinate plane in the real world will take an abstract concept and transform it into a concrete tool for changing and training the brain.

**What you will need:**

- Sharpie
- Painter’s Tape
- Marsden Ball, ie Ball on String (I say this because most of us in vision therapy have one of these for exercises already so it’s easy to access. If you don’t, you could also use a yardstick or post)

**How to Set Up Your Own 3D Coordinate System**

- Hang your Marsden Ball from the ceiling wherever you normally do your exercises and let the string down so that it is just touching the ground/table. This will be your “y” axis.
- Put tape on the ground in a large “t” with one piece representing the x-axis, the other will be the z axis. They should cross right where the ball touches the ground.
- Number your tape, I would leave 6-8 inches between each mark. For super little kids you could use letters on one and numbers on the other like in battleship.
- Make markings on the string to represent units. You could use tape and just write a number on it. With little kids having to use 3 numbers for the x, y and z axis and keep track of which is which is pretty overwhelming so you could use colors going up. This could be done with colored post it notes stuck to the string, or just color the string with a sharpie.
- Put several objects “within” your grid. Keep it simple, a chair, water bottle, person, etc. Legos are great because you can build different heights, and depths and use color.

**Sample Questions:**

- Can you find the place, (C, -2, red)? Answer: the top of the wine glass. Try several different combinations to get them acquainted with the numbers/letters/colors.
- Where is the Whale on the Alphabet Axis? On the Number? What color?
- What colors does the ladder span? Numbers? Letters?
- How many numbers does the popcorn tub take up?
- Name a point where there is empty space. Practice identifying “empty” zones.
- How much space is between the dump truck and Lego tower? Can you visualize the space? If it were a swimming pool, how much water would be between the different objects?
- Where is the largest space? Look for space in each direction first, then for whole volumes of space.

Having the child actually point to specific areas of space and feeling the air can be so powerful in helping them understand that space is just as much an “object” as the items that they can hold or touch.

If you have the space, you can make a larger grid and have them jump or point to specific places on the graph.

I remember the first time I taught this concept to high school students. I had a similar set up and was ready to help them visualize a 3D graph because I was sure that this would be an extremely difficult and abstract concept for them to understand. It wasn’t.

I was majorly disappointed to realize that the majority of my students understood the concept pretty easily and all the time that went into my elaborate explanation and hands on graphing experience was uneccesary, they just “got it.”

I haven’t thought about that experience as a student teacher until recently, and now I realize that for some, the concept of 3D is second nature, or maybe first nature. The same is not true for those of us with 2D vision. It takes some work and concrete, hands on experiences to quantify the 3D world.

### How do I Apply this Idea to Vision Therapy?

With this concrete understanding of depth, apply these concepts into your vision therapy exercises. Every time you are working on the Gem, Brock String, tracking, red/green glasses activities or any other wild activity your vision therapist gives you open your peripheral vision.

That doesn’t mean look to the sides, it means to take in the whole world at once. Let your peripheral vision not only see and notice objects throughout the room, but also see the volumes of space between the different objects.

Relax and as you feel and see the space, your brain will go into hyperdrive and do the exercises with more precision and accuracy. Believing and seeing the space allows your brain to see magical things like rings floating in air.

When you take these concepts and apply them to explore the world around you, you will be amazed at the magnitude and limitless depth of the glorious planet we live on.