An Asemics of a Permutation Principle for Deleuze - AI / EZE, 2026

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The permutation principle is a mathematical concept focusing on the specific ordering or arrangement of a set of objects where the order matters. It calculates the total number of ways to arrange items, distinguishing it from combinations, where order is irrelevant. [1, 2, 3, 4]

Key Principles of Permutations

• Order Matters: A-B-C is considered a different permutation than C-B-A.
• Factorial Notation: The number of ways to arrange \(n\) distinct objects is \(n!\) (n factorial), calculated as \(n \times (n-1) \times \dots \times 1\).
• Permutation Formula: When selecting \(r\) items from a total of \(n\) items, the formula is \(P(n,r)=\frac{n!}{(n-r)!}\). [1, 2, 3, 4, 5]

Common Examples & Types

• Linear Ordering: Arranging people for a photograph or booking letters to form words.
• Slot Filling: Filling positions, such as assigning 1st, 2nd, and 3rd place in a race (e.g., \(P(10,3)\) for 10 runners).
• PIN/Code Creation: Determining how many 4-digit codes can be made from 10 digits (0-9). [1, 2, 3]

Permutations help determine how many ways to arrange items, whereas the related multiplication principle calculates the total number of steps in a sequence. [1, 2]

Deleuze’s concepts—particularly in Difference and Repetition and A Thousand Plateaus—correspond to a permutation principle by replacing fixed, identical structures (like a set deck of cards) with a dynamic, generative system where elements are constantly rearranged, exchanged, and transformed. [1, 2]

In a permutation (reordering elements), the focus is on the rearrangement between elements rather than the identity of the elements themselves. Similarly, Deleuze prioritizes "difference in itself" and "complex repetition" over the "same" or "identity". [1, 2, 3, 4]

Here is how specific Deleuzian concepts correspond to this principle:

1. Rhizome: Non-Linear Permutation [1]

• The Principle: A rhizome connects any point to any other point, operating with \(n-1\) dimensions.
• Correspondence: Unlike a tree structure (fixed hierarchy), a rhizome functions like a topological mapping that allows constant re-pairing of connections. If you change one connection, the entire structure ("multiplicity") changes, similar to how a permutation of a sequence creates a new arrangement.
• **"The book is a rhizome... a map... a mapping that can be entered at any point, and rearranged". [1, 2, 3, 4]

2. Nomad Distribution: Shifting Locations

• The Principle: Deleuze contrasts "sedentary" (fixed) distribution with "nomadic" distribution.
• Correspondence: Nomadic distribution is a space without fixed boundaries or pre-existing ownership. Elements (people, ideas, intensities) distribute themselves freely, with the pattern changing based on "who is there" and "who is not". It is a system where the "territory" is continually permuted by the presence or absence of "intensities". [1, 2]

3. Difference and Repetition: Rearranging Difference [1]

• The Principle: Repetition is not the recurrence of the same thing; it is "difference without a concept".
• Correspondence: Deleuze uses the Borges story of Pierre Menard, who rewrites Don Quixote. The text is the same (general equivalent), but the repetition creates a profound difference due to its re-contextualization in time. It is a "repetition of pure differences" rather than a repetition of the same.
• The "Eternal Return" does not bring back the same, but rather returns the same through an infinite variety of different permutations. [1, 2, 3, 4, 5]

4. Assemblage (Agencement): Varying Components

• The Principle: An assemblage is a contingent gathering of heterogeneous elements (machines, bodies, ideas) that form a temporary whole.
• Correspondence: Assemblages are constantly "deterritorializing" and "reterritorializing". They are not static structures but are subject to a constant permutation of their components (lines of flight, intensities), changing their nature when connections break or new ones are made. [1, 2, 3, 4, 5]

5. Intensive Multiplicities: The Generator of Forms

• The Principle: Intensive properties (like density or potential) are incommensurable and cannot be divided without changing their nature, unlike extensive quantities.
• Correspondence: Deleuze argues that differences in intensity are what drive the creation of new forms. It is the shifting of potential difference—like "difference of electrical potential"—that produces the "lightning" of a new phenomenon, rearranging the elements of the "actual" world. [1, 2, 3]

Summary Table

Deleuzian Concept [1, 2, 3, 4]	Correspondence to Permutation Principle
Rhizome	Constant rearrangement of connections (\(n-1\) dimensions).
Nomadic Distribution	Free shifting of elements across an open, boundary-less space.
Repetition	Difference without a concept; re-contextualizing the same element.
Assemblage	Dynamic, temporary groupings of elements with varying roles.
Intensity	The generative force of differences that rearranges identities.

In short, Deleuze's philosophy is a system of "heterogenesis," which is a "system of differential relations between reciprocally determined genetic elements" that are always in flux, forming, remaking, and unmaking themselves. [1, 2]