Diese Präsentation wurde erfolgreich gemeldet.
Wir verwenden Ihre LinkedIn Profilangaben und Informationen zu Ihren Aktivitäten, um Anzeigen zu personalisieren und Ihnen relevantere Inhalte anzuzeigen. Sie können Ihre Anzeigeneinstellungen jederzeit ändern.
Mathematical Models of Love & Happiness
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  ...
Some “Romantic Styles” <ul><li>dR/dt = aR + bJ </li></ul><ul><li>a =0 (out of touch with own feelings) </li></ul><ul><li>b...
What about Juliet? dJ/dt = cR + dJ She has her own style 4 parameters with 3 choices for each gives 81 different  romantic...
Both out of touch with their own feelings <ul><li>dR/dt = aR + bJ </li></ul><ul><li>dJ/dt = cR + dJ </li></ul><ul><li>Four...
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 ...
With Self-Awareness and  bc  < 0 (nerd + lover) a  +  d  < -2| bc | 1/2 a  +  d  < 0 a  +  d  > 0 Extremely cautious Rapid...
Fire and Water (Do opposites attract?) <ul><li>Take  c  = - b  and  d  = - a </li></ul><ul><li>Result depends on  a, c,  a...
Peas in a Pod (Are clones bored or blissful?) <ul><li>Take  c  =  b  and  d  =  a </li></ul><ul><li>Result depends on  a, ...
Romeo the Robot (How does Juliet react?) <ul><li>Take  a  =  b  = 0  ( dR/dt =  0) </li></ul><ul><li>dJ/dt = cR + dJ </li>...
A Love Triangle <ul><li>Romeo has a mistress, Guinevere </li></ul><ul><li>Guinevere and Juliet don’t know about one anothe...
Love Triangle Examples
Romeo’s Fate <ul><li>Averaged over all romantic styles (64 combinations of parameters) and 64 initial conditions: </li></u...
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 <ul><li>What happens if Guinevere and Juliet know about one another?  </li></ul><ul><li>What happ...
Summary <ul><li>Love and happiness are wonderful </li></ul><ul><li>So is mathematics </li></ul>
References <ul><li>http://sprott.physics.wisc.edu/ lectures/love&hap/   (expanded version of this talk) </li></ul><ul><li>...
Nächste SlideShare
Wird geladen in …5
×

love

712 Aufrufe

Veröffentlicht am

Veröffentlicht in: Bildung, Unterhaltung & Humor
  • Als Erste(r) kommentieren

  • Gehören Sie zu den Ersten, denen das gefällt!

love

  1. 1. Mathematical Models of Love & Happiness
  2. 2. Disclaimers It’s Strogatz’ fault This is not serious sociology I won’t get to the happiness part
  3. 3. 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”
  4. 4. Some “Romantic Styles” <ul><li>dR/dt = aR + bJ </li></ul><ul><li>a =0 (out of touch with own feelings) </li></ul><ul><li>b =0 (oblivious to other’s feelings) </li></ul><ul><li>a >0, b >0 (eager beaver) </li></ul><ul><li>a >0, b <0 (narcissistic nerd) </li></ul><ul><li>a <0, b >0 (cautious lover) </li></ul><ul><li>a <0, b <0 (hermit) </li></ul>
  5. 5. What about Juliet? dJ/dt = cR + dJ She has her own style 4 parameters with 3 choices for each gives 81 different romantic pairings
  6. 6. Both out of touch with their own feelings <ul><li>dR/dt = aR + bJ </li></ul><ul><li>dJ/dt = cR + dJ </li></ul><ul><li>Four subclasses: </li></ul><ul><ul><li>b > 0, c > 0 (mutual love fest or war) </li></ul></ul><ul><ul><li>b > 0, c < 0 (never-ending cycle) </li></ul></ul><ul><ul><li>b < 0, c > 0 (never-ending cycle) </li></ul></ul><ul><ul><li>b < 0, c < 0 (unrequited love) </li></ul></ul>0 0
  7. 7. 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
  8. 8. 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)
  9. 9. Fire and Water (Do opposites attract?) <ul><li>Take c = - b and d = - a </li></ul><ul><li>Result depends on a, c, and the initial conditions </li></ul><ul><li>Can end up in any quadrant </li></ul><ul><li>Or with a steady oscillation </li></ul><ul><li>But never apathy </li></ul>
  10. 10. Peas in a Pod (Are clones bored or blissful?) <ul><li>Take c = b and d = a </li></ul><ul><li>Result depends on a, b, and the initial conditions </li></ul><ul><li>Can end up in any quadrant </li></ul><ul><li>Or at the origin (boredom) </li></ul><ul><li>But no oscillations </li></ul>
  11. 11. Romeo the Robot (How does Juliet react?) <ul><li>Take a = b = 0 ( dR/dt = 0) </li></ul><ul><li>dJ/dt = cR + dJ </li></ul><ul><li>There is an equilibrium at J = -cR/d </li></ul><ul><li>Can be either love or hate depending on signs of R, c, and d </li></ul><ul><li>Stable if d < 0, unstable if d > 0 </li></ul><ul><li>Her feelings never die </li></ul><ul><li>No oscillations are possible </li></ul>
  12. 12. A Love Triangle <ul><li>Romeo has a mistress, Guinevere </li></ul><ul><li>Guinevere and Juliet don’t know about one another </li></ul><ul><li>Romeo responds to each with the same romantic style (same a and b ) </li></ul><ul><li>Guinevere’s hate has the same effect on his feelings for Juliet as does Juliet’s love, and vice versa </li></ul>
  13. 13. Love Triangle Examples
  14. 14. Romeo’s Fate <ul><li>Averaged over all romantic styles (64 combinations of parameters) and 64 initial conditions: </li></ul><ul><ul><li>37% loves Juliet & hates Guinevere </li></ul></ul><ul><ul><li>37% loves Guinevere & hates Juliet </li></ul></ul><ul><ul><li>6% loves both (2% everyone in love) </li></ul></ul><ul><ul><li>6% hates both (2% everyone in hate) </li></ul></ul><ul><ul><li>14% apathy (10% everyone apathetic) </li></ul></ul><ul><li>Anything can happen! </li></ul>
  15. 15. Effect of Nonlinearities Replace ax with ax (1-| x |), etc. (logistic function) x ax ax (1 - | x |)
  16. 16. One Chaotic Solution of Nonlinear Love Triangle “ Strange attractor of love”
  17. 17. Possible Further Studies <ul><li>What happens if Guinevere and Juliet know about one another? </li></ul><ul><li>What happens if only Guinevere knows about Juliet? </li></ul><ul><li>What happens if Juliet and/or Guinevere has another lover? </li></ul><ul><li>What are the dynamics of a free-love commune? </li></ul><ul><li>Is there an optimum pairing of romantic styles that encourages success or portends failure? </li></ul>If such problems interest you, let’s collaborate!
  18. 18. Summary <ul><li>Love and happiness are wonderful </li></ul><ul><li>So is mathematics </li></ul>
  19. 19. References <ul><li>http://sprott.physics.wisc.edu/ lectures/love&hap/ (expanded version of this talk) </li></ul><ul><li>Steven H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, 1994) </li></ul><ul><li>[email_address] </li></ul>

×