**📅 Date:** ➤ ⌈ [[2025-03-30-Sun〚How Different Number Systems Shape Our Thinking〛]]⌋ **💭 Note:** ➤ The number system we default to shapes how we think. - Decimal makes us **social animals**: tolerant, cooperative, emotional. - Binary makes us **computational animals**: efficient, logical, modular. - Ternary and beyond: toward **wisdom animals** — accepting ambiguity, contradiction, and complexity. ➤Ternary (Base-3) - Enables design of more “human-centred” algorithms and models - Fosters **grey-area thinking** — not everything is black or white - Useful in AI and fuzzy logic systems ➤ related reading : Gödel's Incompleteness Theorem ⇩ 🅻🅸🅽🅺🆂 ⇩ **🏷️ Tags**: #👾/Dig **🗂 Menu**: ⌈[[₃ 🌟 ₃ Map Of Content/✢ M O C ➣ 03 ⌈M A R - 2 0 2 5⌉ ✢|2025-M A R-MOC]]⌋ ⌈[[✢L O G ➢ ⌈M A R - 2 0 2 5⌉ ✢|2025-M A R - LOG]]⌋ #👾/Private ➤ ⌈[[Leibniz-Computational Universe (计算宇宙）]]⌋ ➤ ⌈[[On Leibniz- Rational Utopias, and the Seduction of Total Knowledge]]⌋ --- ![[Screenshot 2025-03-30 at 22.36.29.png]]  ---   # 🧠 Number Systems & Mindsets ## 🔹 I. Abstract ### What Is a Number System? A number system (numeral system) is a way of representing quantity using a set of symbols (digits). #### Chart | Base System | Symbol Range | Example (Decimal 10) | Common Use Cases | |-------------|--------------------------|-----------------------|--------------------------------------------| | Binary (2) | 0, 1 | 1010 | Computers, digital logic | | Ternary (3) | 0, 1, 2 | 101 | Fuzzy logic, AI research | | Quaternary (4) | 0, 1, 2, 3 | 22 | Mayan number systems | | Quinary (5) | 0–4 | 20 | Math experiments, tribal systems | | Senary (6) | 0–5 | 14 | Educational games | | Decimal (10)| 0–9 | 10 | Daily life, human culture | | Hexadecimal (16) | 0–9, A–F | A | Programming, colors, memory addresses | | Sexagesimal (60) | 0–59 | : | Babylonian time system (60s, 60min, etc.) | --- ### 🧠 How Number Systems Affect Thought #### ➕ Decimal (Base-10): Intuition, Continuity - Based on ten fingers — natural to humans. - Encourages approximation, fluidity. - Fuzzy thinking, socially adaptive. >[!Abstract] >• We’re raised using base-10, mainly because we have 10 fingers — a natural counting tool. • It emphasizes **sense of quantity** and **continuity**. • Thinking style is often **linear** and **approximate** (e.g., “about 5”). #### **Impacts:** - Human communication, social coordination. - Tolerance for ambiguity ("roughly 5"). - Flexible, imprecise, good for emotional complexity. --- ## 🔹 II.Different Base ### 🟢 Binary (Base-2): Absolute Logic, Discrete World #### Overview - 0 and 1 represent off/on, false/true. - Forms the core of the **computable worldview** (everything as information). #### Impacts: - Precision, modularity, structured reasoning. - Basis of programming and logic circuits. - Encourages abstraction and control. #### 🧠Transformation in Thinking: - From estimation → computation/calculating - From sensory world → ==structured abstract== world - From experiential knowledge → algorithmic logic --- ### ⚖ Ternary (Base-3): Harmony and Nuance (Multivalent Thinking) #### Overview - #### Adds a middle state: **0 (false)**, **1 (neutral)**, **2 (true)** - Aligns with Chinese philosophy (I Ching / 易经): yin, yang, and the middle. #### Impacts: - Useful in AI and fuzzy logic systems - ==Enables design of more “human-centered” algorithms and models== - Fosters **gray-area thinking** — not everything is black or white --- ## 🔹 III. Number Systems as Operating Systems for Thinking Our worldview and logic are silently shaped by **the base system we use to perceive reality**. ### BASE • **Base-10** makes us **social animals**: intuitive, collaborative, tolerant of ambiguity • **Base-2** shapes us as **computational animals**: precise, programmable, efficiency-driven • **Base-3+** may bring us closer to **wise animals**: capable of handling paradoxes and complexities ### 🌌 Base Systems as Mental Operating Systems > The number system we default to shapes how we think. - Decimal makes us **social animals**: tolerant, cooperative, emotional. - Binary makes us **computational animals**: efficient, logical, modular. - Ternary and beyond: toward **wisdom animals** — accepting ambiguity, contradiction, and complexity. --- ### Why Binary is the Language of the Universe (Leibniz's View) > "God created everything out of nothing, using only 0 and 1." > — Gottfried Wilhelm Leibniz - Binary = **metaphysical language** (光明世界规律的语言) - Mirrors the yin (0) and yang (1) of the **I Ching** (易经) - Allows for **computational metaphysics** — a metaphysical model of reality that can be calculated. --- ## 🔹IV. Common vs. Rare Base Systems: Symbolic Meanings | Base | Cognitive Style | Symbolism / Application | |-----------|----------------------------------------|------------------------------------| | Binary | Black-white, precise, discrete | Programming, digital systems | | Ternary | Gray thinking, inclusive, non-binary | Fuzzy logic, Eastern philosophy | | Decimal | Approximate, continuous, social | Culture, daily economics | | Hexadecimal | Compressed, abstract, modular | Tech systems, color coding | | Sexagesimal | Modular, cyclical | Time, ancient cosmology | ### 📊 Common & Uncommon Number Systems — Comparison Table |**Base**|**Symbol Range**|**Decimal “10” in this base**|**Usage or Cultural Meaning**| |---|---|---|---| |Binary (2)|0, 1|1010|Computers, logic circuits| |Ternary (3)|0, 1, 2|101|Fuzzy logic, AI research| |Quaternary (4)|0–3|22|Ancient Maya numeral systems| |Quinary (5)|0–4|20|Tribal systems, theoretical math| |Senary (6)|0–5|14|Mathematical experiments, education| |Decimal (10)|0–9|10|Everyday human life and trade| |Hexadecimal(16)|0–9, A–F|A|Programming, colors (#FF00FF), machine code| |Sexagesimal(60)|0–59|:|Babylonian time system (60s/min, 60min/hr)| --- ### 🧠 How These Systems Shape Thinking Patterns |**Base**|**Thinking Style**| |---|---| |**Binary**|Rigid, digital, black-and-white thinking| |**Ternary**|Flexible, inclusive, tolerant of ambiguity| |**Decimal**|Intuitive, continuous, “fuzzy” judgment| |**Hexadecimal**|Efficient, compressed, abstract engineering| |**Sexagesimal**|Modular, cyclical, suited for measuring time| --- ## 📌 Side Notes - 🕰️ **Babylonians** - used base-60: 1 hour = 60 minutes, 1 minute = 60 seconds - 🧬 **DNA** - resembles quaternary (A, T, G, C = 4 symbols) - 🤖 **Future computing** - may explore ternary logic for faster, smarter AI systems --- ### 🧭 Thoughts #👾/Thoughts - Your **number system** isn’t just math — it’s how your brain organizes reality. - Learn new bases = expand cognitive frameworks.