šŸ“ Home ā€ŗ About: Meet the Team ā€ŗ Family Formulary

The Family Formulary: A Quirky Calculus of Connection

Welcome to our playful laboratory! Here, we've donned our metaphorical lab coats and assigned scientific formulas to capture the unique essence of each family member (pets included!). Think of it as our own special brand of "Quirky Calculus" ā€“ a fun way to explore the beautiful, complex 'chemistry' that makes us us. Hover over each block and discover the formulas that define our delightful dynamics!

Why Formulas? šŸ ā¤ļø
Just like scientific formulas capture the essence of natural phenomena, they can also beautifully express personality traits! Our family's unique "chemical elements" combine to create a wonderful compound called home.
Formula Selection šŸ”
Each family member's formula was chosen to match their core traits. From physics to psychology, we searched across scientific fields to find the perfect match for each personality!
Not Just Humans! šŸ¾
Even our beloved pets have their own "fur-mulas"! Samba follows the Matching Law with predictable reward-seeking, while Kola embraces the entropy of exploration and curiosity!

Grandma Kay

Ribot's Law

$M(t) \approx M_{initial} e^{-kt} + C(1 - e^{-\lambda t})$

Wisdom and perspective are like consolidated memories, resistant to disruption and valuing long-term experience.

Peek Behind the Science:

Ribot's Law describes memory loss patterns where recent memories fade before older ones.

Fun Fact Flash:

Shares her evening cracker ritual with her beloved dog, Kola.

Toni

Lorenz Attractor (Chaos Theory)

$$ \frac{dx}{dt} = \sigma (y - x) \\ \frac{dy}{dt} = x (\rho - z) - y \\ \frac{dz}{dt} = x y - \beta z $$
(Typical: $\sigma=10$, $\rho=28$, $\beta=8/3$)

Toni is the family's beautiful chaos: unpredictable, creative, but always finding her own unique orderā€”just like the Lorenz attractor's butterfly shape emerging from the whirlwind.

Peek Behind the Science:

The Lorenz attractor is a classic example from chaos theory. Even though its motion never exactly repeats, it always settles into a stunning, structured patternā€”a "butterfly" shapeā€”revealing order within apparent randomness.

  • Deterministic, Not Random: Follows exact rules, but tiny changes have huge effects.
  • The Butterfly Effect: Small changes in starting conditions lead to wildly different outcomes.
  • Self-Organization: Despite the chaos, the system always "comes home" to the attractor shape.

Fun Fact Flash:

Toni's creative energy is like a swirling attractorā€”her art, music, and ideas never repeat, but always form something beautiful and surprising!

Ken

Hooke's Law

$F = -kx$

Flexible and resilient; bends under pressure but possesses an internal restoring force to return to equilibrium.

Peek Behind the Science:

Hooke's Law states the force needed to extend or compress a spring is proportional to the distance.

Fun Fact Flash:

An INTP who built the 'TK LOVE BOT' and enjoys playing Spanish guitar.

Katie

Signal Detection Theory - Sensitivity (d')

$d' = Z(\text{Hit Rate}) - Z(\text{False Alarm Rate})$

Highly perceptive; possesses strong ability to discriminate subtle signals from noise, independent of response bias.

Peek Behind the Science:

Signal Detection Theory's d' (d-prime) measures sensitivity or the ability to distinguish signal from noise.

Fun Fact Flash:

Recently graduated and started her first full-time job, living with boyfriend Steven.

Steven

Newton's Second Law of Motion

$F = ma$

Driven and goal-oriented; applies force (effort) to create acceleration (progress) towards achievements.

Peek Behind the Science:

Newton's Second Law relates the force applied to an object, its mass, and the resulting acceleration.

Fun Fact Flash:

Loves to fish and is very supportive of Katie.

Tony

Shannon Entropy

$H(X) = - \sum p(x_i) \log_b p(x_i)$

Cautious and security-focused; seeks to minimize uncertainty and unpredictability (entropy) through analysis.

Peek Behind the Science:

Shannon Entropy measures the uncertainty or 'information content' in a message or system.

Fun Fact Flash:

Ken's father, lives in Palm Springs, and has built a strong, communicative relationship with Ken.

Gloria

Newton's Law of Universal Gravitation

$F = G \frac{m_1 m_2}{r^2}$

Values connection; relationship strength (force) depends on mutual importance (mass) and proximity (distance).

Peek Behind the Science:

Newton's Law of Universal Gravitation describes the attractive force between two objects with mass.

Fun Fact Flash:

Ken's mother, talks with him almost daily, and lives in Palm Springs with Tony.

Laura

Flow Theory - Optimal Experience Conditions

$\text{Challenge} \approx \text{Skill}$

Seeks deep immersion and enjoyment by balancing high challenges with commensurate skills.

Peek Behind the Science:

Flow Theory describes the mental state of being fully immersed ('in the zone') when skill level matches the challenge.

Fun Fact Flash:

Ken's sister, a world-class graphics artist with her own business.

Joe

Fourier Transform

$X(f) = \int_{-\infty}^{\infty} x(t) e^{-j2\pi ft} dt$

Analytical; decomposes complex situations (signals) into fundamental components (frequencies) to understand them.

Peek Behind the Science:

The Fourier Transform breaks down a signal (like sound or image) into its constituent sine wave frequencies.

Fun Fact Flash:

Laura's partner of 30+ years, a sound engineer with his own business.

Irene

Logistic Growth Curve

$P(t) = \frac{K}{1 + Ae^{-kt}}$

Learns effectively through observation; skill acquisition follows an S-curve of rapid initial growth then saturation.

Peek Behind the Science:

The Logistic Growth Curve models growth that starts exponentially but slows as it reaches a carrying capacity (K).

Fun Fact Flash:

Toni's mother, recently retired, navigating several mental health complexities.

Archie

Arrhenius Equation

$k = Ae^{-E_a / (RT)}$

Exhibits dual thinking; fast/intuitive (low activation energy) vs. slow/deliberate (high activation energy).

Peek Behind the Science:

The Arrhenius Equation relates the rate of a chemical reaction to temperature and activation energy (Ea).

Fun Fact Flash:

Toni's father, works long hours despite kidney disease, known for his patience.

Jenni

Ideal Gas Law

$PV = nRT$

Socially adaptable; adjusts interaction style (P, V) based on context (n, T) like gas adapting to conditions.

Peek Behind the Science:

The Ideal Gas Law relates the pressure (P), volume (V), amount (n), and temperature (T) of an ideal gas.

Fun Fact Flash:

Toni's sister, lives in Libya with husband Abdu and their daughters Sabria and Amina.

Abdu

Signal Detection Theory - Response Criterion

$c = -0.5 [Z(H) + Z(FA)] \quad \text{or} \quad \beta = \frac{\text{pdf}(Z(H))}{\text{pdf}(Z(FA))}$

Interpretation is biased by appraisal; criterion (c/Ī²) determines threshold for perceiving threat (signal).

Peek Behind the Science:

Signal Detection Theory's Response Criterion (c or beta) measures an observer's bias or tendency to say 'signal present'.

Fun Fact Flash:

Jenni's husband, helped Toni navigate the visa process to visit Libya.

Sabria

Hysteresis Loop

$\text{Graphical (Output vs. Input shows loop)}$

Emotionally sensitive/intense; state depends on history, slow return to baseline after trigger (lag).

Peek Behind the Science:

Hysteresis is the dependence of a system's state on its history (e.g., magnetism lagging behind the magnetic field).

Fun Fact Flash:

Jenni and Abdu's 17-year-old daughter, formed a close bond with Toni during a US visit.

Amina

Le Chatelier's Principle

$\text{System shifts to relieve stress}$

Relies on social support; support helps psychological system shift to counteract stressors and restore equilibrium.

Peek Behind the Science:

Le Chatelier's Principle states that if a system at equilibrium is stressed, it shifts to counteract the stress.

Fun Fact Flash:

Jenni and Abdu's 14-year-old daughter, also visited the US last year.

Samba

Herrnstein's Matching Law

$\frac{B_1}{B_1 + B_2} = \frac{R_1}{R_1 + R_2}$

Behavior shaped by rewards; allocates effort (B) proportionally to reinforcement rates (R) from choices.

Peek Behind the Science:

Herrnstein's Matching Law describes how animals distribute their behavior between choices based on reinforcement rates.

Fun Fact Flash:

Ken and Toni's 15-year-old 'chatty' cat, master of shoulder perching and keyboard interference.

Kola

Second Law of Thermodynamics (Entropy)

$\Delta S_{universe} \ge 0$

Independent; behavior shows inherent randomness/exploration (entropy increase), less tied to external shaping.

Peek Behind the Science:

The Second Law of Thermodynamics states that the total entropy (disorder) of the universe always increases or stays the same.

Fun Fact Flash:

Grandma Kay's beloved American Eskimo dog, obsessed with treats and physics (in his own way!).