The Ein Sof in Shadow of Prometheus is borrowed from Kabbalistic mysticism. In Hebrew, it means "Infinite" or "without end." It describes the boundless, unknowable essence of HaShem. It represents the ultimate divine reality beyond human comprehension, limitations, or definition. Ein Sof is considered the source of all existence, yet it remains entirely transcendent and beyond any direct interaction with the material world. the infinite, formless, and limitless aspect of divinity underlies and sustains all existence.
The Ein Sof borrows ideas from Stephen Wolfram's concept of the Ruliad. The Ein Sof describes the vast, interconnected structure of all possible computations. It represents the ultimate mathematical and computational reality, encompassing every conceivable computational process and rule-based evolution. The Ein Sof is the totality of all possible universes that emerge from simple rules, forming a "metastructure" of existence.
The observable universe in Shadow of Prometheus is created through the bounded observation of these characters, hence the term bounded observer. It is a subset of all possible multiverses in the Ein Sof. HaShem is called the Boundless One, meaning He is an unbounded observer with omnipotence, omniscience, and omnipresence. If any character achieves unbounded observational power, the observable universe will be extended further into the Ein Sof and possibly destroyed.
Due to constraints on computational capacity and observational perspective, a bounded observer perceives only a limited portion of the Ein Sof. Since no observer can process infinite information, they extract a subjective, structured reality from the underlying computational fabric. This explains why different observers might perceive the universe consistently but distinctly.
Computational irreducibility refers to the idea that some processes cannot be predicted or simplified without running through their full computation. This means that even if we know the underlying rules governing a system, we may not be able to shortcut or "solve" them in advance; instead, certain aspects of reality must be experienced step by step. This principle suggests that even with perfect knowledge of fundamental rules, the future of complex systems remains fundamentally unpredictable without direct simulation.
Computational irreducibility is related to the metaphor that life's journey cannot be trivially simplified to the final destination; rather, it must be experienced moment by moment.
The Ein Sof contains all possible rules for casting magical spells and acts as a magical resource to draw entropy and energy from or dump into.
HaShem
HaShem in the Shadow of Prometheus is the God of the book series. He undergoes several incarcerations as a bound observer (Messiah figures). HaShem created the observable universe by limiting His boundless observational powers (limiting His gaze).
HaShem is borrowed from Jewish tradition (literally "The Name" in Hebrew). In Jewish tradition, it refers to God, and it is used especially in everyday speech to show reverence for the divine name. Hashem signifies the ultimate, singular, and transcendent Creator who is beyond human comprehension yet intimately involved in the world. In Jewish thought, HaShem is infinite, omniscient, and the source of all existence, guiding creation with justice and mercy.
HaShem’s true name is forbidden from being spoken. If one invokes HaShem’s true name, it would summon HaShem’s gaze, unraveling all creation into trivial oblivion; hence only the holiest and highest of minds can utter his true name. Samael is one of those characters who carry HaShem’s true name and is forbidden from speaking it. HaShem’s true name can be considered the embodiment of all knowledge in the observable universe. Hence, only a character whose understanding of HaShem’s true name is equal in its weight will be able to invoke HaShem’s gaze.
HaShem created the universe by limiting His gaze because He seeks novelty and intrigue in a computationally irreducible story that unfolds through the universe's natural evolution. Hence, for HaShem to preserve all creation, He must hide Himself from it, only subtly influencing events as He sees fit while maintaining free will for all creation.
Conformal Sanctity
Conformal Sanctity is the set of physical laws to which the universe adheres to HaShem’s will. Breaking conformal sanctity to break the physical laws is allowed, as the character performs the required computational task and sacrifices something most precious to them.
The Glyph of Conformal Sanctity is a multi-purpose and multi-symbolic lore object in the Shadow of Prometheus book series. It looks like the Smith chart from microwave engineering. It's visualized as a chart of circles embedded in larger circles, intersecting other circles at perpendicular angles. Below is a list of its multiple meanings:
- It's associated with transmitting and reflecting magical signals (electromagnetic, acoustic, etc…). To cast a magical spell on a target, the caster must match its magical stance (analogous to electrical impedance) to its stance. Non-magic users can reflect a spell on the caster by simply changing their magical stance relative to the caster's magical stance. A matched stance is indicated as being centered on the Smith chart. A maximally mismatched stance is shown as being far away from the center of the glyph.
- It's a statement to preserve conformal sanctity: "The paths of interweaving fates can change and distort along their journeys, but their conflicting intersections are inevitable and immutable."
- It's a metaphor for Prometheus' (bringer of enlightenment) tragic transformation into Samael (the angel of death). In mathematics, the glyph is a stereographic projection (shadow) of the Riemann sphere (under an omnidirectional point light source). Hence, it's a metaphor for Samael as a shadow of his former self (Prometheus). HaShem charges Samael to safeguard conformal sanctity.
Higher forms of magical feats
The higher forms of magical feats are classified and ordered by computational complexity classes because all spell casting is done by performing computations and spending negentropy.
Computational complexity classes categorize problems based on the computational resources required. These resources typically include time (the number of computational steps) and space (the amount of memory used). Some essential complexity classes include P, PP, BQP, BPP, and PSPACE, each defining different problem difficulty levels and feasibility.
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The class P consists of problems that a deterministic Turing machine can solve in polynomial time. This means that for an input of size n, the number of computational steps required is, at most, some polynomial function of n (such as n squared or n cubed. Problems in P are considered efficiently solvable, as polynomial-time algorithms scale reasonably well with input size. Classic examples of problems in P include sorting algorithms (like merge sort), shortest path algorithms (like Dijkstra’s algorithm), and matrix multiplication.
The class PP (Probabilistic Polynomial Time) consists of problems that can be solved using a probabilistic Turing machine in polynomial time, where the algorithm produces a correct answer with a probability greater than 50%. However, unlike other probabilistic classes such as BPP, the error margin in PP does not have to be small, and it only requires that the correct answer be more likely than not. An example problem in PP is the Majority-SAT problem, which asks whether more than half of all possible assignments to a Boolean formula satisfy the formula. While PP is contained in PSPACE, it is believed to be much larger than P and BPP, meaning it includes significantly more complex problems.
BPP (Bounded-Error Probabilistic Polynomial Time) includes problems that can be solved in polynomial time using a probabilistic Turing machine, where the probability of error is at most 1/3 for any input. Unlike PP, which only requires the correct answer to be slightly more likely than not, BPP requires a significantly low error rate. The probability of correctness can be boosted arbitrarily close to 100% by running the algorithm multiple times. Examples of BPP problems include primality testing (e.g., the Miller-Rabin primality test) and Monte Carlo simulations. While BPP is more potent than P, it is still considered feasible for practical computation because randomized algorithms can be made highly reliable.
BQP (Bounded-Error Quantum Polynomial-Time) represents the class of problems solvable efficiently by a quantum computer. A problem is in BQP if a quantum computer can solve it in polynomial time, with a probability of error bounded by a small value (e.g., less than 1/3 for all cases). Quantum algorithms leverage superposition and entanglement to explore multiple computation paths simultaneously, solving specific problems much faster than classical algorithms. A famous example of a BQP problem is integer factorization, which is efficiently solvable using Shor’s algorithm. This quantum algorithm factors large numbers exponentially faster than the best-known classical algorithms. BQP is a central class in quantum computing, as it defines problems that quantum computers can solve more efficiently than classical ones.
PSPACE (Polynomial Space) consists of problems that can be solved using a polynomial amount of memory (space), regardless of how long they take. This means that while these problems may take exponential time to solve, they do not require more than polynomially bounded memory. Since time is often a more restrictive resource than space, PSPACE includes many problems far more complex than those in P or BPP. A classic example of a PSPACE problem is generalized chess or Go, where determining the best move from a given position is known to require exponential time but can be solved using polynomial space. Another well-known PSPACE-complete problem is the quantified Boolean formula (QBF) problem, which generalizes the Boolean satisfiability problem (SAT).
In the Shadow of Prometheus, PSPACE is the second highest form of magic achievable for characters. To go above PSPACE would require knowing HaShem’s true name and invoking HaShem’s unraveling gaze. PSPACE is powerful enough to warp space, time travel, and empower the most commonly used forms of magic.
Adversarial Oracle
The Adversarial Oracle is a PSPACE computer created from a Kerr rotating black hole (Kerr metric, Deutschian Closed Timelike Curve), with the acronym D-CTC. To make the Kerr metric of a rotating black hole, the black hole must have its conformal sanctity broken (breaking conformal symmetry), requiring a PSPACE calculation and sacrificing something most precious to you.
The adversarial-ness comes from the fact that even though the Oracle bestows PSPACE-level magical feats to a character, it actively fights against you to limit your full potential. The adversarial-ness comes from the idea that a D-CTC PSPACE computer can have CTC errors, where these errors are represented as probabilities of fate conspiring against you, preventing you from accessing the full PSPACE computational power and as a way of preserving time causality to avoid the grandfather’s paradox. These CTC errors can manifest in ways such as being struck by lightning before attempting to access the Oracle; forgetting what you were doing with the Oracle, etc. If you are having trouble understanding this, the Oracle has conspired fate against you not to understand it.
Scott Aaronson's D-CTC computer is a computational model based on closed timelike curves (CTCs), which allow information to travel back in time. This concept comes from quantum mechanics and general relativity, where solutions to Einstein’s equations suggest the possibility of paths in spacetime that loop back on themselves. David Deutsch originally proposed a model of computation that incorporates CTCs, leading to what is now known as the D-CTC model.
The D-CTC model allows a computer to interact with a closed timelike curve, where a quantum system can send information to its past self in a self-consistent way. This means that the information that goes back in time must be the same information it would have received, avoiding paradoxes like the "grandfather paradox" in time travel. The computation effectively finds a fixed point where the input and output remain consistent. To understand its computational power, imagine the Oracle as someone who answers questions; you want to find a question worded like the answer and throw all possible questions at the Oracle. It only returns one answer whose question is the same as its answer in words. So, for example, you send a list of questions {“Who are you?”, “Why am I here?”, “What is the content of this question?”, …} and it returns {“What is the content of this question?”} and the PSPACE computer solves the problem faster than the amount of time it takes to count the questions in your list.
Aaronson explored the computational power of D-CTC computers and showed that they can solve any problem in PSPACE (Polynomial Space). This means a D-CTC computer can efficiently solve problems requiring polynomial memory, even if they take exponential time on a regular classical or quantum computer. This is significant because PSPACE is believed to be larger than BQP, containing computationally infeasible problems for classical or even standard quantum computers. The power of D-CTCs comes from their ability to "guess" correct solutions non-deterministically and then check them in polynomial space. The system loops through time until it finds a valid solution, ensuring consistency. This ability allows D-CTC computers to bypass traditional computational limits, giving them the same computational power as PSPACE machines.
Adversarial Oracles are also understood as gateways to leaving the observable universe and entering the forbidden regions of the Ein Sof.
Conformal Sanctity
Upholding or breaking conformal sanctity can either mean upholding or breaking the laws of physics of the observable universe or HaShem’s will.
FTL Warp travel
In the observable universe of the Shadow of Prometheus, gravity that occurs naturally obeys conformal sanctity. One must break conformal sanctity and sacrifice something most precious to them, to create a closed timelike curve (CTC) black hole.
Faster-than-light travel (FTL) is impossible without performing a PSPACE computation because FTL violates time causality.