(Impossible) Temporal Colors 

Another Way to Think About Colors

Previously we've discussed the concept of impossible color combinations. A fascinating topic which — when done right — can lead to about 140 trillion new and distinct color experiences. Looking at this enormous number, which means that you can literally see 8 million times more colors than normally, it is challenging to determine where to go next for an even greater color vision enhancement.

Now you might ask:

• Aren't 140 trillion colors already enough?

• How would you add more colors? Isn't an impossible combination of two colors already the limit? (Because we only have 2 eyes.)

To which I say:

'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 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 see three or more colors simultaneously in an impossible combination, similar to impossible color combinations that exploit binocular redundancy (i.e. binocular impossible color combinations).

Previous Dimensions & Binocular Vision

Our second eye allows us to see colors two-dimensionally. With only one eye colors would still look normal, but we wouldn't be able to see impossible color combinations; at least the way they've been discussed here in previous articles on impossible color combinations. 

However, looking at how binocular impossible color combinations are created we can discern a pattern:
The step from 16 million to 140 trillion colors was achieved by adding another dimension, whatever this new dimension might be. 

Consequently, we can follow up with a thought experiment:

If we had three eyes instead of two we would be able to see impossible color combinations of three different colors. Colors such as a red-green-blue, which would not be basic white, would become possible. We would have the potential for nonachromacy, a color vision with nine distinct cone types. The amount of new threefold impossible color combinations would be roughly 4.5 sextillion 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 these numbers would increase equally exponentially.

But we're still far away from such a 'third-eye' implement, let alone one for four or more eyes. And even if such an operation was possible it would be accompanied by many short- and long-term risks. This means that adding new dimensions via the implementation of additional eyes is not an option.

The Dimension of Time

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 binocular impossible color combinations by crossing our eyes (or using a VR headset with Color in Color, for instance). The qualia of these time-based impossible colors [hereafter called: (twofold, threefold, etc.) temporal or time colors] would not be the same as binocular impossible color combinations, but they would behave similarly enough to functionally be the same.

Time-based Alternation Methods

The dimension of time, however, is vast. 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 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 seem to be hard flickering and soft (vertical line) transitions.

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 like such a singular color experience.

Soft Transitions

Soft transitions also make use of time as an additional dimension but without the hard flickering, which can lead to little headaches if you're not used to it. There's still a flickering, but much softer and easier on the eyes. However, the downside of this method is that there will be in-between colors during the transitions of the two (or more) colors. This can lead to unwanted identification problems of the original 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.

After several experiments both of these methods seem equally adequate.

The Combination of Temporal Colors and Binocular Impossible Color Combinations

Now to the even more fascinating realization:

Because binocular impossible color combinations and temporal colors operate in entirely different dimensions these two methods can be combined. Consequently, we can alternate between two binocular impossible color combinations. Let's call this new kind of color experience an impossible temporal color, or a fourfold (impossible) color.

Exponential Numbers

It's 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. Colors which can't even be mapped on the usual depictions of human color vision; like the color spectrum, color circle, and/or HSV color space. We achieve the potential for dodecachromacy, a color vision with twelve distinct cone types. The amount of new (twofold) impossible temporal colors would be roughly 75 octillion colors. That's a 75 followed by 27 zeros. This is about 4.5 sextillion times more colors than you can normally see; a number higher than the amount of atoms inside of your body. That's the power of exponential growth!

Because the brain takes a little bit longer to perceive and discern binocular impossible color combinations than basic colors the alternation rate of these impossible temporalcolors 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 state of mind). Unless we lower the rate we won't be able to properly indentify each individual of the four colors in the fourfold impossible temporal color mix; though naturally there are exceptions.

The Implication of Impossible Temporal Colors

The increased amount of details we can perceive with the implementation of binocular impossible color combinations into our vision is already incredible to look at. Compared to an alphabet, letters and words the addition of binocular impossible 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 application Color in Color, which makes use of these impossible colors, normal images and videos transform into spectacles of color with a previously unthinkable amount of visual details; if the settings are adjusted properly. But this astounding canvas of enhanced visual details pales in comparison to the enhanced color vision made possible by the implementation of impossible temporal colors into our vision.

Examples of Impossible Temporal Colors

Let's take impossible temporal  red (you can also call it impossible temporal red) as an example. The next few examples will be static at first.

Temporal Colors in Action

But all of the previous templates were just one-dimensional representations of four-dimensional (or higher-dimensional) colors. While I can't show you bincoluar impossible color combinations without you crossing (or being able 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 a little application that let's us see (impossible) temporal colors with a customizable set of colors (up to four), 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 the two points together into one when they're smaller. If you don't want to customize the two sets of colors by hand you can just randomize them via the randomization buttons.

Play around with the settings to get a feel for how (impossible) temporal colors function and are perceived. You can put the colors from the previous static examples of impossible temporal colors into this application, for example.

No Time Limits But Human Limits

Words can't describe how these impossible temporal colors feel, especially the more colors you throw into this mix, and when you get the settings just right. In context (i.e. in my application Color in Color) when these higher-dimensional colors actually have meanings assigned to them our vision transforms remarkably. 

However, there's a limit to the amount of temporal colors you can loop between. That's because the more colors you add to the mix the faster the alternation rate has to be in order to account for the additional time of the added color. At one point — let's say for example when you're looping between ten colors — the alternation speed would have to be so high that the colors wouldn't really combine well, and it would just look like a really fast slide show of colors. In my experience, the optimum is two- to fourfold 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.

Closing Words

The potential for enhancing human color vision is incredible. While temporal colors aren't as simultaneous as binocular impossible color combinations, which are literally perceived at the same time, they operate so similiarly that their qualia is virtually the same. Being able to encode 4 distinct tristimulus values into a single pixel, thereby giving this pixel the ability to display about 75 octillion different color experiences instead of just about 16 million, results in a color vision that I haven't even been able to dream about a few years ago. The amount of details I can see with a color vision which uses such x-fold impossible temporal colors is beyond superhuman vision. 

The color visions of functional human tetrachromats (these women can distinguish between up to 100 million colors) and mantis shrimps (they have 16 cones, but in spite of that their color vision isn't as detailed as human color vision; they can also distinguish the polarization of light) are nothing compared to such a x-fold impossible temporal color vision.

I'm still searching for yet another dimension into which I can once again cram additional colors, thereby creating even more impossible color combinations. But for now, let's leave it at the unique visual dimension created by the duality of our two eyes and the temporal dimension of time. However, the future is uncertain and there may be even more dimensions out there that are just waiting to be discovered and exploited to create more impossible color combinations.

So, stay tuned in order to fetch new ways to experience life.

I am Ooqui, and I will show you how to reshape and enhance your sensory experiences, because it is nothing but our senses that connect us to this world.

Thanks for reading!