Because of the recursive nature of ξ, ξ is able to be represented within itself. Many life forms have learned to leverage this property for communication purposes, but humans have developed further methods for devising symbols of ξ. Mathematics as a field developed, shaping a series of rules, effectively forming a math graph that could process sets, and data within them, from ξ, and output symbols representing states that could be used for actionable planning.
So then, if mathematics can be used to represent symbols in ξ, what if it were used to generate new ones? Under normal pretenses, mathematics does not necessarily introduce significant changes to ξ since it operates on symbolic restrictions of numbers, and by design ensures that its outcome is restricted to numbers. However, if we were to use mathematical concepts to map out the structure of ξ, then our changes to that structure would reflect a change in the shape of available symbols in ξ.
Introducing a symbol into ξ, however, does not make it manifest in the universe. Compared to ξ, the universe is much more resistant to change. However, by creating a state for it in ξ, it is at least able to exist in the universe. From there, additional methodology can be applied to improve the statistical likelihood of the desired state in ξ being achieved. The methods of influencing the universe are numerous, and can be as simple as carrying out a plan to enact the desired outcome. From a reality hacker's methodology, one of the simplest ways of creating this influence is the use of some sort of encoding of the desired state of the universe in order to solidfy the symbolic outcomes in ξ. One such method for doing so can be found here.
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