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Elemental Sight (エレメンタル・サイト) otherwise known as the Eyes of the Spirits (精霊の眼) is a Perception Type ability/ Superpower that allows users to connect to the Information Dimension at the highest possible level.
In theory, If a magician improves their ability to perceive information, they can gain Elemental Sight. But at present, only Tatsuya and Minoru are known to achieve this ability.
It's user can specify the Eidos of their surroundings individually, regardless of distance, physical obstacles with greater details about Eidos Information. They can easily identify the Eidos of targets, allowing for precision aiming at long distances.
In short, The "Eyes of the Spirits" — "Elemental Sight" refers the ability to identify the "landscape (color)" of the information dimension.
Tatsuya's "eyes" aren't a kind of clairvoyance nor a clairvoyant ability to automatically sort out what he wants to know in the unconscious realm and project everything into his consciousness. It's an intelligence that can't reach the information he needs unless he chooses it. 
If Tatsuya pours in all his resources, it becomes possible for him to find specific individuals with special structural information from within the country, to which not even a hundred percent is needed. Applying seventy percent of his resources to Elemental Sight is sufficient. He usually assigns half of the resources of Elemental Sight to Miyuki. 
By further applying Gram Demolition and by creating a durable large mass of Psion's into a signal bullet, he can trace it through Elemental Sight for several days. This process of injecting Psion is called as "Psion Marker". Once marking is done, even the formidable Ghost Walker will become useless. 
Originally only able to follow in a three-dimensional vision, Tatsuya obtained the ability to see through a bird's-eye view from the repetitive searching and investigating for the mastermind (Jiedo Heigu) behind the Hakone Terror Incident. 
Each of the Four Major Systems and Eight Major Types of magic projects Magic Sequences onto the Eidos through the information dimension. Thus, Magicians who wield modern magic have the ability to link to the information dimension. By connecting to the information dimension and verifying its "existence" — Tatsuya's senses could be said to expand the field. And this "expansion" has dire consequences. Anything with a physical body in this world has their Eidos imprinted in the information dimension. Also, this isn't done through the five senses, or as if he could "see through" this expanded information dimension and the subsystem's signals to pull out the targets he needed. Rather, he is able to identify each and every Eidos and target them separately. In other words, no one can escape from his Elemental Sight. Also, by using Elemental Sight, users have a 360˚ field of "vision," regardless of physical obstacles, making it excellent for protection.
It also allows Tatsuya to see the 'past' of any magic - what magic had been used and the nature of the magic. By analyzing the Eidos, users can see how it was affected by any magics. Tatsuya can see up to 24 hours into the past, allowing him to use his skill Regrowth, returning an object to whatever state it was in at any point in those 24 hours. However, if a person had already died, the magic cannot restore the person to life, despite the body being perfectly fine.
What Tatsuya sees is not images but information. Structural information of corporeal bodies are converted by the unconscious mind into signals the conscious mind can easily comprehend.
Shiba Tatsuya, the one of the two mentioned users of this magic, does not use this magic openly because it may raise a warning flag for him if people saw what should not be seen. He has used it in front of Erika due to her being unable to realize precisely what it is he is doing, yet he is more careful around powerful, more knowledgeable Magicians like Katsuto and Mayumi.
It can be expanded by connecting to "Link Space", that connects to the relationship of cause and effect. Although this usually operates in the background, by linking to Link Space, Tatsuya is able to fully place his vision into the Information Dimension.
Theoretically, this could also allow him to see the future, but at the moment he is unable to do that.
Elemental Sight cannot be detected by Psion sensors, but may be detected by some ESP users.
|“|| He was not focusing his mind, but diffusing it. Wider and wider, with Miyuki and himself as the two focal points, he laid his perceptions over every nook and cranny in the area. This was not looking down from a bird’s eye view, but looking at things from the point of view of the information dimension. It was not an elliptical sphere around the double focal points, as it had nothing to do with physical distance; Tatsuya fixedly concentrated his 'eye,' intensifying his contact with the law of cause and effect within Link space. Suddenly invoking his vision of the relationship of cause and effect left him open to 'accidents;' namely leaving his body behind in the physical dimension by incessantly using it; when he was in link space, any wound he suffered wouldn't heal. Becoming engrossed in 'observation' was a situation that could indeed make him switch his mind to that side. Even if he called it Link space, the dimension did not really have that kind of meaning. The ways you were able to see something formed part of a framework of recognition.
Also, even if he called it Links, it did not mean he saw red strings or black chains connecting people; he could read no more than the information related to cause and effect. Perhaps someone else would be able to see red strings or black chains if they used those symbols; the images Tatsuya used pointed out the existence of what he realized were focal points jutting out behind the scene indicating the existence of cause and effect and events, etc.
In theory, the way he did things could be used to predict events; however, Tatsuya still could only read information on the 'present' and twenty four hours of the 'past.' As a result, it was extraordinarily effective at searching for enemies. It was probably equal to having an innate skill at remote viewing, though it was better than that because it had the potential to distinguish enemies with precision and range.
Elemental Sight was a rare ability, but Tatsuya wasn’t the only user. Magic was fundamentally recognizing and temporarily recognizing the Eidos of a phenomena. Magicians can perceive this information to varying degrees depending on the users skill, so Elemental Sight – the highest possible ability to perceive information, the ability to completely perceive the information dimension – was available to every magician. If a magician improves their ability to perceive information, they can gain Elemental Sight.
The nature of people’s Elemental sight could differ greatly. It varied for each magician
For example, Minoru was very skilled in passive perception. When he was in Ikoma, Minoru detected the clash between Tatsuya and Bezobrazoff occurring in Izu, despite the locations being nearly 400 km apart. On the other hand, Tatsuya must consciously focus to detect magic, but when he focused, he could gain far more detail - even to the point of going against the passage of time and viewing a log of Eidos changes.
Minoru was fairly skilled at sensory magic. Parade worked by substituting information about a target to fool an opponent’s senses. Because of this, Minoru’s Elemental Sight manifested as a passive detection skill.
Similarly, Tatsuya’s restoration worked by reverting Eidos changes to a point, going against the flow of time. As a result, Tatsuya’s Elemental Sight allowed him to read Eidos changes.
In other words, Elemental Sight manifested differently based on the skill sets of the magician using it.
- Shiba Tatsuya – one of the notable uses of Elemental Sight by Tatsuya is analyzing activation sequences through the idea and then using Gram Dispersion, the strongest counter magic whose use is considered impossible due to it needing the use of Decomposition and Elemental Sight. It can be implied that Elemental Sight is a pillar supporting both of his innate abilities due to their nature of targeting the Eidos.
- Kudou Minoru -- Different from Tatsuya, due to this Minoru is able to sense powerful magic from a distance of over 400 kilometers passively without needing direction and without needing to intentionally watch it.