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Mathematical Model Of Love & Happiness
 

Mathematical Model Of Love & Happiness

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    Mathematical Model Of Love & Happiness Mathematical Model Of Love & Happiness Presentation Transcript

    • Mathematical Models of Love & Happiness J. C. Sprott Department of Physics University of Wisconsin - Madison Presented to the Kiwanis Club of Downtown Madison in Madison, Wisconsin on June 3, 2002
    • Disclaimers It’s Strogatz’ fault This is not serious sociology I won’t get to the happiness part
    • The Mathematics R is Romeo’s love for Juliet (or hate if negative)‏ J is Juliet’s love for Romeo dR/dt = aR + bJ a and b describe Romeo’s “Romantic Style”
    • Some “Romantic Styles”
      • dR/dt = aR + bJ
      • a =0 (out of touch with own feelings)‏
      • b =0 (oblivious to other’s feelings)‏
      • a >0, b >0 (eager beaver)‏
      • a >0, b <0 (narcissistic nerd)‏
      • a <0, b >0 (cautious lover)‏
      • a <0, b <0 (hermit)‏
    • What about Juliet? dJ/dt = cR + dJ She has her own style 4 parameters with 3 choices for each gives 81 different romantic pairings
    • Both out of touch with their own feelings
      • dR/dt = aR + bJ
      • dJ/dt = cR + dJ
      • Four subclasses:
        • b > 0, c > 0 (mutual love fest or war)‏
        • b > 0, c < 0 (never-ending cycle)‏
        • b < 0, c > 0 (never-ending cycle)‏
        • b < 0, c < 0 (unrequited love)‏
      0 0
    • Out of touch with their own feelings (continued)‏ b > 0, c > 0 b < 0, c < 0 b > 0, c < 0 Two lovers Love fest (or war)‏ Two nerds Unrequited love Nerd + lover Never-ending cycle War
    • With Self-Awareness and bc < 0 (nerd + lover)‏ a + d < -2| bc | 1/2 a + d < 0 a + d > 0 Extremely cautious Rapid apathy Somewhat cautious Eventual apathy Overly eager Growing volatility (The only equilibrium is apathy)‏
    • Fire and Water (Do opposites attract?)‏
      • Take c = - b and d = - a
      • Result depends on a, c, and the initial conditions
      • Can end up in any quadrant
      • Or with a steady oscillation
      • But never apathy
    • Peas in a Pod (Are clones bored or blissful?)‏
      • Take c = b and d = a
      • Result depends on a, b, and the initial conditions
      • Can end up in any quadrant
      • Or at the origin (boredom)‏
      • But no oscillations
    • Romeo the Robot (How does Juliet react?)‏
      • Take a = b = 0 ( dR/dt = 0)‏
      • dJ/dt = cR + dJ
      • There is an equilibrium at J = -cR/d
      • Can be either love or hate depending on signs of R, c, and d
      • Stable if d < 0, unstable if d > 0
      • Her feelings never die
      • No oscillations are possible
    • A Love Triangle
      • Romeo has a mistress, Guinevere
      • Guinevere and Juliet don’t know about one another
      • Romeo responds to each with the same romantic style (same a and b )‏
      • Guinevere’s hate has the same effect on his feelings for Juliet as does Juliet’s love, and vice versa
    • Love Triangle Examples
    • Romeo’s Fate
      • Averaged over all romantic styles (64 combinations of parameters) and 64 initial conditions:
        • 37% loves Juliet & hates Guinevere
        • 37% loves Guinevere & hates Juliet
        • 6% loves both (2% everyone in love)‏
        • 6% hates both (2% everyone in hate)‏
        • 14% apathy (10% everyone apathetic)‏
      • Anything can happen!
    • Effect of Nonlinearities Replace ax with ax (1-| x |), etc. (logistic function)‏ x ax ax (1 - | x |)‏
    • One Chaotic Solution of Nonlinear Love Triangle “ Strange attractor of love”
    • Possible Further Studies
      • What happens if Guinevere and Juliet know about one another?
      • What happens if only Guinevere knows about Juliet?
      • What happens if Juliet and/or Guinevere has another lover?
      • What are the dynamics of a free-love commune?
      • Is there an optimum pairing of romantic styles that encourages success or portends failure?
      If such problems interest you, let’s collaborate!
    • Summary
      • Love and happiness are wonderful
      • So is mathematics
    • References
      • http://sprott.physics.wisc.edu/ lectures/love&hap/ (expanded version of this talk)‏
      • Steven H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, 1994)‏
      • sprott @physics. wisc . edu