Mathematical models of love happiness
Download
1 / 19

mathematical models of love happiness - PowerPoint PPT Presentation


  • 214 Views
  • Updated On :

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.

Related searches for mathematical models of love happiness

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'mathematical models of love happiness' - libitha


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Mathematical models of love happiness l.jpg

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 l.jpg
Disclaimers

It’s Strogatz’ fault

This is not serious sociology

I won’t get to the happiness part


The mathematics l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
Both out of touch with their own feelings

0

  • 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


Out of touch with their own feelings continued l.jpg
Out of touch with their own feelings (continued)

b > 0, c > 0

b < 0, c < 0

b > 0, c < 0

War

Two lovers

Love fest (or war)

Two nerds

Unrequited love

Nerd + lover

Never-ending cycle


With self awareness and bc 0 nerd lover l.jpg
With Self-Awarenessand 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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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



Romeo s fate l.jpg
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 l.jpg
Effect of Nonlinearities

Replace ax with ax(1-|x|), etc. (logistic function)

ax(1 - |x|)

ax

x


One chaotic solution of nonlinear love triangle l.jpg
One Chaotic Solution of Nonlinear Love Triangle

“Strange attractor of love”


Possible further studies l.jpg
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 l.jpg
Summary

  • Love and happiness are wonderful

  • So is mathematics


References l.jpg

http://sprott.physics.wisc.edu/ lectures/love&hap/ (expanded version of this talk)

Steven H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, 1994)

[email protected]

References


ad