"Would it be possible for me, or any one person, to learn the color of the eyes of every other person on the planet?"
In principle? Yes.
An algorithm based on a general theory of biological inheritance can predict from sufficient data the distribution of past and future eye color by population domains, and correct for anomalous variables when these domains interact. Sure, I knew that you're involved in breeding horses, which is the reason I thought this a good example.
Thoreau said that some circumstantial evidence is compelling, " ... as when one finds a trout in the milk." Suppose one of your mares gave birth to some spotted foal unknown in the genetic line of horses that you are raising. Will you jump to the conclusion that someone tampered with the semen tube? Maybe. More likely, you'll want to do some forensic investigation (and certainly the breeder's attorney will demand it) that establishes some nonvanishing probability for this birth from data of a sufficient number of generations back.
In foundational physics, though, the appearance of anomalous data *never* has a sufficient past to make a closed judgment on whether the anomaly is organic to a general theory of origins or a genuine anomalous and unexplained discovery. The best we can do is compare a comprehensive theory (a mathematical structure) to an experimental result.
I get aggravated in these discussions (probably more than I should, but my left brain dominance gets away from me) when so many -- not just you -- claim they have found a trout in the milk when it's easy to show that they really haven't.
"If you were to try to remember the colors of the eyes of just every person you ever met, it is safe to say this information would start to blur and run together."
No it isn't safe to say that! If the object is to remember discrete colors of eyes, it's ridiculous to conclude that everyone you ever met has the same blurry eye color!
I'm familiar with the ant intelligence complex systems model (have actually had the pleasure of listening to E.O. Wilson lecture on it) -- complex systems is my primary research interest.
"I would argue we operate in the same fashion ..." and you would be wrong.
The author quotes Herbert Simon (who did groundbreaking research in this area) " ... the ant's path is irregular, complex, and hard to describe. But its complexity is really a complexity in the surface of the beach ..." and then tries to obviate Simon's argument by saying, "We now know that the path produced by a navigating ant is based on sophisticated mechanisms.
"Ants use a variety of cues to navigate, such as sun position, polarized light patterns, visual panoramas, gradient of odors, wind direction, slope, ground texture, step-counting ... and more."
You bet. However, that only *extends* Simon's argument to a more complex "beach" of added dimensions and more complicated topology.
"Indeed," says the author, "the list of cues ants can utilise for navigation is probably greater than for humans."
Doubtful. As made apparent in the subhead of the article, "Unlike humans, ants don't build a unified map of the world." Yaneer Bar-Yam's theory of multi-scale variety* answers the author's claims, using the principle of self similarity at multiple scales; human complex neural networks allow us to choose the scale at which we make decisions, while ants apparently cannot. (Bar-Yam also solved Herbert Simon's problem of bounded rationality, showing how laterally-distributed information in a complex network is more robust than the conventional hierarchical model).
* Bar-Yam, Y. . "Multiscale Variety in Complex Systems." Complexity vol 9, no 4
Bar-Yam, Y.,  *Making Things Work.* NECSI, Knowledge Press.