|Spoiler Alert: This page contains spoilers. Read at your own risk.|
Eidos (個別情報体, literally "individual information body") refers to the Psion information body of a phenomenon. The usage of Modern Magic refers to the modification of a target's phenomena by modifying its Eidos, hence producing the results. The Magic Sequence targets the Eidos, overwriting the information of the target. Information is associated with events, and when the information associated with it is overwritten, the event will also be overwritten. This leads to physical changes in the real world itself. Magicians use Modern Magic to create false signals to manipulate and rewrite the Eidos of a target and not because they can exert their will to control the Eidos itself.
Eidos refer to the event where information associated with a target is temporarily overwritten. Since information is associated with events, any revisions to it will lead to the rewriting of an event associated with it. As the nature of phenomena is written in Psions, modifications to these will lead to real world events undergoing temporary modifications to their state as well. 
Magic Cast Simultaneously by Multiple Users
Only one Magic Sequence, the one with the strongest Interference Strength, can work on a select Eidos at a time. All other magic sequences are overwritten, and although they still remain with the Eidos, their effects do not appear at all. However the more Magic Sequences affecting an Eidos, the stronger the Interference Strength required to make it work. This was the main reason, although for a single caster only, why Flying-Type Magic didn't work, as the interference required to overwrite the previous Magic Sequences that haven't faded would compound exponentially.
Analyzing Magic Sequences
All of the 4 Great Systems and 8 Major Types of magics, project Magic Sequences onto the Eidos through the Information Dimension. Therefore anyone who uses Modern Magic can connect to the Information Dimension. Anything with a physical body has their Eidos imprinted in the Information Dimension. Shiba Tatsuya is able "see" this
Information Dimension, and is therefore able to identify each and every Eidos and target them separately.
One can analyze Magic Sequences and figure out the way it will affect the Eidos, although the only one person known who can effectively do this is Shiba Tatsuya. Non Systematic-Type Magic directly affects the Eidos. Any Modern Magic will create unavoidable ripples through the Eidos, and a skilled Magician can identify the location of the caster, as well as the type of magic used.
The Activation Ritual is a large block of data for building a Magic Ritual. Mages can intuitively guess what kind of effect the ritual would have. By looking at how the Magic Ritual would interfere with the Eidos, and what parts wouldn't be affected, it's possible to read and attempt a guess at the effect the Magic Ritual would have. However the Activation Sequence alone is simply a chunk of data, representing a massive amount of information, and even the Magician deploying it can only dynamically interact with it in the subconscious. Therefore, the act of reading the Activation Sequence requires the enumeration of endless strings of image data, then reproducing an image from those in your head. Normally, such things cannot be done in the consciousness. 
Preventing Eidos Re-writing
Ways to prevent the overwriting of Eidos include Cast Jamming, Zone Interference and Data Fortification. Cast Jamming works by releasing random Psion waves that overwhelms the transfer of data from the Magician, usable with Antinite. Zone Interference works by affecting an area around a Magician so that other Magicians cannot affect it. Only works when the Interference Strength of the caster is stronger than the attacker. Data Fortification is similar in result to Zone Interference, as it defines a target and prevents it from being altered, however it works through a completely different concept. It does it by reading the original Eidos of the target, and then projecting it back on to the target to protect it from being altered further. It is more efficient than the wide area Zone Interference as it only worries about a single target. However it does not prevent the physical affects of magic. For example, magic may not be able to set a piece of ice on fire, but lighting a fire beside it will still melt it.