(Impossible) Temporal Colors 

In the article on Human Potential for Hexachromacy we've discussed the concept of impossible binocular color combinations. A fascinating topic which allows for the perception of about 140 trillion new and distinct color experiences in trained viewers. Looking at this enormous number, a color vision 8 million times more colorful than normal trichromacy, it's challenging to determine where to go next for an even greater color vision enhancement.

You might rightfully ask:

• Aren't 140 trillion colors already enough?

• How would you add more colors? Isn't an impossible binocular combination of left- and right-eye colors already the limit?

140 trillion new colors doesn't just sound like a lot, but it actually is a lot. However, you can't possibly display all of these new colors on a single screen. If you try to nonetheless the binocular screen will either appear to be white or will flicker with so many differently colored pixels that it resembles random noise. Furthermore, while 140 trillion is indeed a huge number, there's potential for more. To realize this potential we need a method that allows us to link three or more colors on the same visual spot, similar to impossible binocular color combinations that disrupt the chromatic redundancy of binocular color vision.

Our second eye allows us to see colors 6-dimensionally. With one eye closed colors still look normal, but we aren't able to see impossible color binocular combinations, However, looking at how impossible binocular color combinations are created we can discern a pattern:
The step from 16 million trichromatic colors to 140 trillion hexachromatic colors was achieved by adding dimensions of color, however these new dimensions are being generated. In the case of impossible color vision and the human potential for hexachromacy, the second eye allows us to add three additional dimensions of color to the color vision of our first eye by disrupting the chromatic redundancy of binocular color vision.

Consequently, we can follow up with a thought experiment:

If we had three eyes instead of two we would be able to see impossible "trinocular" color combinations, i.e. impossible color combinations of three different trichromatic colors. Colors such as a red/green/blue, which would not be basic white, would become possible. Such threefold colors aren't possible in impossible binocular color vision. Thus, with three eyes, we would have the potential for nonachromacy, a color vision with nine distinct cone types by disrupting the chromatic redundancy of "trinocular" color vision. The amount of new threefold impossible color combinations would be roughly 4.5 sextillion nonachromatic colors. That's a 4.5 followed by 21 zeros, and about 8 million times more than 140 trillion. If we could add more eyes to our color vision these numbers would increase equally exponentially.

But we're still far away from such an unrealistic "third-eye implant". Even if such an operation was possible, it would be accompanied by many short- and long-term risks. This means that adding new color dimensions via the implementation of additional eyes—as unrealistic as it obviously sounds—is not an option. However, the dimensionality of color cannot just be augmented by adding more eyes.

The next dimension, and the only one that's left, is time. The hypothesis is the following:

If we alternate between two (or more) colors at a very fast rate, a rate at which each individual color is still identifyable but also a rate at which the colors seemingly merge into each other, then our enhanced color discrimination would essentially be the same as if we were seeing impossible binocular color combinations by using stereo viewing techniques or Virtual Reality. The qualia of these time-based cyclically alternating temporal colors is not the same as that of impossible binocular color combinations, but they behave similarly enough for functionality.

Time-based Alternation Methods

The dimension of time is vast. And there are different methods to alternate between two (or more) colors:

• Hard Flickering: A hard cut between the alternation of two colors. No transition and the whole screen's colors change simultaneously.

• Soft Flickering: A soft transition from one color into the other. The whole screen's colors change simultaneously but smoothly.

• Hard Transitions: A hard cut and shutter like effect with a customizable pattern where both colors are simultaneously on the screen but locally alternating. We can also call this hard shutter.

• Soft Transitions: A soft shutter like effect with a customizable pattern where both colors are simultaneously on the screen but locally alternating. Colors transition softly into each other. We can also call this soft shutter.

The only two viable options after conducting several tests (with myself as a test subject) seem to be hard flickering and soft (vertical line) transitions.

Naturally, any color flickering method might be uncomfortable at first. Color flickering may cause epileptic seizures for those who have a history with this or similar pre-existing conditions. View temporal colors with caution and at your own risk!

Hard Flickering: With hard flickering colors can flicker at a very high rate, down to an alternation speed of 17 milliseconds or less (about 60 alternations per second), while still being identifiable. The lower this rate (i.e. the more time between the alternations) the easier it becomes to identify the individual colors. But in turn the colors will not combine as well into one seemingly singular color experience. The higher the rate the more the two (or more) colors seem to merge into a singular color experience.

Soft Transitions: Temporal colors viewed with soft transitions are softer than those viewed with hard flickering; the latter method may more quickly lead to discomfort some people. There's still a flickering, but much softer and it's easier on the eyes. However, the downside of this method is that there will be intermediate colors during the transitions of two (or more) colors. This can lead to unwanted identification problems of the original main colors if the transition pattern is not chosen carefully and if the alternation rate is either too high or too low. Because of these quirks the alternation rate cannot be—but also doesn't need to be—as high as with the hard flickering method.

If the alternation speed becomes too fast, temporal colors will transform into normal trichromatic colors. After several experiments both of these methods seem equally adequate. People may prefer one or the other.

Now, a fascinating realization: Because binocular impossible color combinations and temporal colors operate in entirely different dimensions, these two methods can be combined. We can temporally alternate between two impossible binocular color combinations. Let's call this new kind of color experience an impossible temporal color.

This impossible temporal color vision is as if we had four eyes instead of two. With this method we are able to see impossible color combinations of four (or more) different colors. Colors such as a red/green/blue/yellow would become possible, which can't even be mapped on the usual virtual visualizations of human color vision; like the color spectrum, color circle or HSV/RGB color space. At a minimum we can achieve the potential for dodecachromacy, a 12-dimensional color vision with twelve distinct cone types. The amount of new 2x2 impossible temporal colors is roughly 75 octillion colors. That's a 75 followed by 27 zeros. This is about 4.5 sextillion times more colors than a normal trichromat can see; a number higher than the amount of atoms inside of your body. This is the power of exponential and dimensional growth.

Because the brain takes a little bit longer to perceive and discern binocular impossible color combinations than normal trichromatic colors, the alternation rate of these 2x2 impossible temporal colors needs to be lower—in my experience about twice as low. If the two basic colors had an alternation rate of 35 milliseconds before, they now need to have an alternation rate of approximately 70 milliseconds (this amount can change depending on the colors themselves, the screen's FPS, your device, and even your eyes and current state of mind). Unless we lower the rate, we won't be able to properly indentify each individual color of the four colors in the 2x2 impossible temporal color mix. Although, naturally, there are exceptions.

The increased amount of details we can perceive with the functional implementation of impossible binocular color combinations into binocular trichromatic vision is already incredible. Compared to an alphabet, letters and words, the addition of impossible binocular color combinations would be like having 676 unique letters in the alphabet with which you could encode data a lot better and more compactly than with just 26 letters. You could form words with the same meaning but a lot shorter and more condensed. 

With my applications Color in Color and Custom Color Vision, which make use of these impossible and temporal colors, normal images and videos transform into spectacles of color with a previously unthinkable amount of visual details; if the custom color spectra and color volumes are properly designed.

Let's take impossible temporal red as an example. The next few examples will be static at first.

All of the previous examples were just lower-dimensional representations of higher-dimensional colors. While I can't show you impossible bincoluar color combinations without you having to cross your eyes, I can easily show you temporal colors, because we all have easy access to the dimension of time. For this purpose, I've developed the below application Impossible Time Colors that let's us see impossible temporal colors with a customizable set of impossible (and/or) temporal colors combinations, a customizable alternation rate, and a customizable alternation mode (i.e. hard flickering, soft transition, soft shutter). Additionally, you can customize the point size, if it's easier for you to cross-/parallel-view the two points into one when they're smaller or bigger. If you don't want to customize the two sets of colors by hand, you can simply randomize them via the randomization buttons.

Play around with the settings to get a feel for how impossible temporal colors work and you personally perceive them. You can put the colors from the previous static examples of impossible temporal colors into this application, for example, to test them yourself.

Personally, words can't describe how these impossible temporal colors feel for me, especially the more colors are thrown into the mix as well as when you get the settings just right. In context—i.e. in my applications Color in Color and Custom Color Vision, for example—when these higher-dimensional colors actually have assigned meanings color vision transforms remarkably.

Naturally, there's a limit to the amount of temporal colors that can be looped. The more colors you add to the mix, the faster the alternation rate has to be to account for the additional display time of the added color. At one point—let's say for example when you're monocularly looping between ten colors—the alternation speed would have to be so high that the colors don't combine well, and it just looks like a really fast slide show of colors. Such a "color slide show" is still very useful and might even be more comfortable for some people than fast alternation speeds. In my experience, the optimum is between 2x2 and 4x4 impossible temporal colors. That alone is already enough to create an exponential amount of more impossible temporal colors each time you add a new color into the mix.

The potential for enhancing human color vision is incredible. While temporal colors aren't as simultaneous as impossible binocular color combinations, which are literally perceived at the same time, they operate so similiarly that their qualia can be approximated. Being able to encode four distinct trichromatic colors into a single virtual pixel—thereby giving this pixel the ability to display about 75 octillion and more different color experiences instead of just about 16 million colors—results in a color vision that can be quite difficult to comprehend and explain with normal trichromatic color theory. The amount of details I can personally see with a color vision which uses such impossible temporal colors is beyond superhuman color vision, even within just the digital trichromatic 3D color space. 

The comparatively augmented color vision of functional human tetrachromats (distinguishing up to 100+ million colors) and mantis shrimps (that have 16 cone types, but in spite of that their color vision is believed to be not as detailed as human color vision; they can also distinguish the polarization of light) are nothing compared to such an impossible temporal color vision.

I'm still searching for yet another dimension into which we can, once again, cram additional colors, thereby creating even more impossible color combinations. But for now, let's leave it at the unique visual dimensions created by disrupting the chromatic redundancy of trichromatic binocular color vision and the usage of the dimension of time. The future is uncertain and there may be even more dimensions out there that are just waiting to be discovered and alienated to create even more impossible colors.