Lesson 1.8: The Spell of Mathematics

Glossary

Pythagorean Philosophy & Beliefs

• Pythagoreanism – A mystical and philosophical tradition centered on mathematics, harmony, and ascetic living.

  • Pythagoras founded communities with strict ethical and intellectual rules.

  • Emphasized numerology, the belief that numbers govern reality.

• Metempsychosis (Μετεμψύχωσις) – The belief in the reincarnation of the soul.

  • Ethical implications: Killing animals may be wrong because they might contain reincarnated human souls.

  • Connected to Indian traditions and Empedocles’ view of the soul.

• The Acusmata (Ἀκούσματα) – A collection of Pythagorean sayings that guided daily life.

  • Three types:

    • Definitions – "What is x?"

    • Superlative Identifications – "What is the most x?"

    • Precepts – "What should (or should not) be done?"

  • Example: "Avoid beans," which may have originally meant not to eat beans but later symbolized avoiding politics (since early voting was done with beans).

• The Harmony of the Spheres (Μουσική τῶν Σφαιρῶν) – The idea that the cosmos is structured according to mathematical harmony.

  • Numbers underlie reality—everything from music to planetary motion follows precise numerical ratios.

  • Implication: Moral and political life should also be harmonized according to proportion and balance.

Mathematics & Science in Pythagoreanism

• Symbolic Speculation (Arithmology) – The belief that numbers have mystical properties.

  • Example: The number 10 was sacred, leading to the idea of a “counter-earth” to make the celestial count reach 10.

• Numerology & Ethics – Pythagoreans believed numbers not only described the physical world but also defined moral and ethical truths.

  • Example: Odd numbers were considered masculine, even numbers were feminine.

• Mathematikoi (Μαθηματικοί) vs. Akousmatikoi (Ἀκουσματικοί) – Two branches of Pythagorean followers:

  • Mathematikoi – Philosophers and scientists who engaged in mathematical reasoning.

  • Akousmatikoi – Those who followed the precepts without questioning them.

• Archytas on Mathematics & Political Science – Archytas (a Pythagorean philosopher and statesman) believed mathematics should guide political decisions.

  • Example: Justice should be based on what is proportionate and fair, just like equations balance proportions in nature.

• Calculative Justice – Archytas proposed that fairness could be mathematically determined.

  • "Once calculation was discovered, it stopped discord and increased concord.”

  • Implication: Social harmony is achievable if resources and obligations are distributed proportionally.

  • Modern Parallel: Economic theories that attempt to measure social benefits and costs (e.g., studies on which professions contribute most to society).

Ethical & Political Ideas

• Virtue as Harmony – To be virtuous is to be in harmony with oneself and the world.

  • Ethical implications: Disharmony (e.g., excess desire, injustice) leads to social and personal imbalance.

• Asceticism in Pythagorean Communities –

  • Life was highly regimented—what you ate, said, and did was strictly controlled.

  • Pythagorean Discipline:

    • Pleasure is bad—self-denial cultivates wisdom.

    • Endurance is good—suffering strengthens the soul.

    • Daily rituals were meticulously followed to develop self-discipline.

• Freedom as Self-Mastery (Archytas) –

  • Archytas identified three types of freedom:

    1. Not being a slave (legal freedom).

    2. A self-sufficient state (political freedom).

    3. Freedom from excessive desires (personal self-mastery).

  • The highest form of freedom is internal discipline—ruling one’s own impulses rather than being ruled by them.

• The Role of Law (Archytas) –

  • "The law should not be written on temples but in the character of the citizens."

  • Implication: The best legal system is one that trains people to act justly without needing external enforcement.

  • Contrast with Aristotle: Aristotle believed fear of punishment is necessary for most people. Archytas suggests social shame and ethical training are better enforcers.

• Pythagorean Democracy vs. Anti-Democracy –

  • Some later Pythagoreans became anti-democratic, but Archytas was pro-democracy, arguing for rational governance based on proportion and fairness.

Social & Psychological Insights

• The Power of Habit & Routine –

  • Pythagoreans ritualized daily life because they believed rigorous planning ensures long-term success.

  • Modern Parallel: Psychological studies show that good habits reduce decision fatigue and help people avoid temptation.

  • "Good habits, not self-control, are what keep disciplined people from making bad choices."

• Social Pressure as a Tool for Ethical Living –

  • Pythagorean communities used social reinforcement to encourage ethical behavior.

  • Modern Parallel: Today, peer pressure can be both negative (toxic social media culture) and positive (accountability groups, support networks).

• Pleasure as a Danger –

  • Archytas, like Plato, warned against bodily pleasures, believing they weaken self-control and rationality.

  • Cicero quotes Archytas:

    • "No more deadly gift has been given to men by nature than bodily pleasure, for our lusts spur themselves on blindly and without restraint."

  • Examples of being controlled by desire:

    • Social media addiction → Dopamine-driven engagement loops.

    • Junk food addiction → Processed food designed to be hyper-palatable.

    • Video game addiction → Companies use behavioral psychology to maximize screen time.

Words You Might Not Know

• Metempsychosis (Μετεμψύχωσις) – The transmigration of souls, i.e., reincarnation.

• Acusmata (Ἀκούσματα) – The Pythagorean precepts that dictated ethical and practical living.

• Mathematikoi (Μαθηματικοί) – The Pythagoreans who engaged in mathematical reasoning.

• Akousmatikoi (Ἀκουσματικοί) – The Pythagoreans who followed the teachings without questioning them.

• Arithmology – A system of symbolic numerology that assigns mystical significance to numbers.

• Calculative Justice – The idea that fairness can be mathematically determined.

• Harmony of the Spheres – The belief that the universe operates according to mathematical harmony.

• Asceticism (Ἀσκητισμός) – The practice of self-denial and discipline to achieve wisdom and virtue.

• Self-Mastery (Ἐγκράτεια) – The ability to govern one’s desires and impulses rationally.

• Pythagorean Democracy – The idea that governance should follow mathematical principles of proportion and fairness.