Designing Your Personal Symbolic–Mathematical System

Step 1 – Framing Your System: Scope and Intent

Step 2 – Choose Your Tree: Graph Skeleton

Now you will pick the graph that underlies your system.

Mentally or on paper, answer these questions:

1. How many nodes (sefirot) will you use?

• 10 classical sefirot?
• 11 including Daʿat as a distinct node?
• A reduced or expanded set (e.g., 7 emotional sefirot only)?

1. How are they connected?

• Standard 3-column Tree of Life (like most Hermetic diagrams)?
• A variant (e.g., different placement of paths, or a circular arrangement)?
• A custom graph (e.g., hypercube, grid, or cycle) that you reinterpret as a Tree?

1. What is the orientation?

• Top-to-bottom (Keter to Malkhut)?
• Inside-to-outside (center to periphery)?

Activity (5 minutes):

• Sketch your Tree as a graph:
• Draw circles for nodes.
• Draw lines for edges.
• Label each node with a sefirah name (or your chosen node-label system).
• Then write 3 bullet points describing your design choices, for example:
• "I use 10 sefirot in a 3-column layout."
• "Edges follow the Kircher Tree except I add an extra path between Netzach and Hod."
• "Orientation is vertical: top = abstract, bottom = concrete."

Keep this sketch nearby: all later steps will build on this exact graph.

Step 3 – Example Tree Specification

Step 4 – Map Letters to Your Tree

Next, you will decide how letters attach to your graph.

Typical historical choices (for comparison):

• 22 Hebrew letters mapped to 22 paths between 10 sefirot.
• Sometimes letters also carry numerical values (gematria) and phonetic features.

You can adapt or depart from this, but you must be explicit.

Activity (5–7 minutes):

1. Choose your alphabet

• Option A: Classical Hebrew 22-letter set.
• Option B: Another alphabet (e.g., Latin A–Z, but you might still use 22 of them).
• Option C: A custom symbolic alphabet (e.g., 16 runes, 10 digits, etc.).

1. Decide the mapping rule

• Path-based: 1 letter per edge.
• Node-based: 1 letter per node.
• Mixed: vowels on nodes, consonants on edges, etc.

1. Implement it

• Make a table with columns like:
• Index (1, 2, 3, ...)
• Symbol (e.g., Alef, Bet, Gimel)
• Location (e.g., edge Keter–Chokhmah)
• Value (e.g., 1, 2, 3)

1. Constraint check

• Does every letter have a unique place?
• Are there any edges or nodes unlabeled on purpose? If so, why?

Write 3–4 sentences explaining why you chose this mapping (e.g., symmetry, ease of visualization, historical resonance).

Step 5 – Formalizing Your Model in Pseudocode

To make your system feel like an actual formal model, it helps to describe it in simple pseudocode or a real programming language (Python is common in 2026, but use any you know).

Below is a Python-flavored example showing how to encode:

• Sefirot as nodes
• Paths as edges
• Letters attached to edges

You do not need to run this code; it is a template for clear thinking.

```python

Example: minimal formal specification

1. Nodes (sefirot)

sefirot = [

"Keter", "Chokhmah", "Binah",

"Chesed", "Gevurah", "Tiferet",

"Netzach", "Hod", "Yesod", "Malkhut"

]

2. Edges (gates) as pairs of node names

edges = [

("Keter", "Chokhmah"), ("Keter", "Binah"),

("Chokhmah", "Tiferet"), ("Binah", "Tiferet"),

("Chesed", "Tiferet"), ("Gevurah", "Tiferet"),

("Chesed", "Netzach"), ("Gevurah", "Hod"),

("Netzach", "Yesod"), ("Hod", "Yesod"),

("Tiferet", "Yesod"), ("Yesod", "Malkhut"),

...add remaining edges to reach 22 total

]

3. Letters mapped to edges

letters = [

"Alef", "Bet", "Gimel", "Dalet", "He", "Vav",

"Zayin", "Chet", "Tet", "Yod", "Kaf", "Lamed",

"Mem", "Nun", "Samekh", "Ayin", "Pe", "Tsadi",

"Qof", "Resh", "Shin", "Tav"

]

Simple mapping: index letters onto edges

letteronedge = {

edge: letters[i] for i, edge in enumerate(edges)

}

4. A basic rule for a "walk" of awareness

import random

current_node = "Keter"

for step in range(10):

find edges that start or end at current_node

available = [e for e in edges if current_node in e]

chosen_edge = random.choice(available)

letter = letteronedge[chosen_edge]

move to the other end of the edge

a, b = chosen_edge

currentnode = b if currentnode == a else a

print(f"Step {step}: traverse {chosenedge} via {letter} -> now at {currentnode}")

```

Your task:

• Adapt this template to your own system:
• Replace `sefirot`, `edges`, and `letters` with your data.
• Optionally change the "walk" rule (e.g., bias toward downward moves, or forbid revisiting nodes).
• Even if you do not code, write a plain-language version of this logic: "From any node, awareness chooses a connected edge labeled by a letter and moves to the adjacent node."

Step 6 – Define Gates and Names as Operations

Now you will decide what gates and Names actually do in your system.

From earlier modules, you can treat:

• A gate as: an edge + its letter + a rule (e.g., transform state when you cross).
• A Name as: a sequence of letters that corresponds to a path or operation on the graph.

Activity (5 minutes):

1. Gate definition

• Choose a simple internal "state" for a traveler on the Tree (e.g., an integer energy level, or a 3-component vector [intellect, emotion, action]).
• For each gate (edge + letter), define a rule like:
• "Crossing Alef-gates increases intellect by 1."
• "Crossing Mem-gates flips the sign of emotion."

1. Name definition

• Pick 1–3 Names (they can be traditional, like a 3-letter Divine Name, or invented).
• For each Name, specify:
• The sequence of letters.
• The path it traces on your graph (if any).
• The net effect on state after traversing all its letters.

1. Consistency check

• Does every letter have a clear, reusable rule?
• If two different gates share the same letter, do they behave similarly? If not, why?

Write a short paragraph (4–6 sentences) summarizing how gates and Names function in your system.

Step 7 – Quick Consistency Check

Use this quiz to check your understanding of internal consistency in your model.

Step 8 – Symmetry, Redundancy, and Refinement

Now you will refine your system by looking for symmetry, redundancy, and possible simplifications.

1. Symmetry scan

Look at your graph and letter mappings:

• Are left and right sides balanced (e.g., same number of edges, similar letter types)?
• Do certain letters always appear on similar kinds of paths (e.g., vertical vs diagonal)?

If you see asymmetries, decide:

• Are they intentional (e.g., to express imbalance)?
• Or are they accidental and better removed?

2. Redundancy scan

Check for elements that do nothing new:

• Letters whose rules are identical to other letters.
• Gates that never appear in any important Name or path.

For each redundant element, choose to:

• Merge it with another element.
• Give it a distinct role.
• Or remove it.

3. Short refinement exercise (5 minutes)

Write answers to these prompts:

• One asymmetry I am keeping on purpose is: ... because ...
• One redundancy I am removing or merging is: ... because ...
• After this pass, my system is simpler / clearer in this specific way: ...

Step 9 – Key Terms Review

Flip these cards mentally to review core concepts you just used.

Step 10 – Assemble Your Formal Specification