The document discusses quantifying and modeling aspects of love. It begins by listing attributes of love that were brainstormed, including care, sharing, passion, and trust. Examples are then given of how some attributes could be quantified, such as setting goals to reduce lies in a relationship each year to measure trust. A paper on quantifying love with mathematical models is referenced, including a simple linear model to represent how Romeo and Juliet's love for each other changes over time based on constants. However, there are limitations to quantifying and modeling something as complex as love.

1. Love
Quantification
a
4.5
minute
lightening
Talk
at
ACCU
Conference,
Oxford
April
15
2010
tom@gilb.com
www.gilb.com
Subset
April
15
2010

2. 8. Quantify
Exercise:
Aspects
of
Love,
or
Love
is
a
many
splendored
thing!
• Make
inventory
of
love’s
many
aspects
• QuanOfy
one
requirements
for
love
• DuraOon:
6
minutes
See note for Sutra
www.Gilb.com
Slide
2

3. Love
ATributes:
Brainstormed
By
Dutch
Engineers
• Kissed-­‐ness
• Care
• Support
• Sharing
• Attention
• Respect
• Passion
• Comfort
• Satisfaction
• Friendship
• ...
• Sex
• ...
• Understanding
• ...
• Trust
www.Gilb.com
Slide
3

4. Trust
[Caroline]
• Love.Trust.Truthfulness • Other
aspects
of
Trust:
Ambition: No lies. • 1.
‘Truthfulness’
Scale: 2.
Broken
Agreements
Average Black lies/month from 3.
Late
Appointments
[defined sources]. 4.
Late
delivery
Meter: 5.
Gossiping
to
Others
independent confidential log from
sample of the defined sources.
Past Lie Level:
Past [My Old Mate, 2004] 42 <-
Bart
Goal
[My Current Mate, Year = 2005]
Past Lie Level/2
Black: Defined: Non White Lies
www.Gilb.com
Slide
4

5. Camaraderie
(Real
Case
UK)
Ambi@on:
to
maintain
an
excep,onally
high
sense
of
good
personal
feelings
and
co-­‐opera,on
amongst
all
staff:
family
atmosphere,
corporate
patrio,sm.
In
spite
of
business
change
and
pressures.
Scale:
probability
that
individuals
enjoy
the
working
atmosphere
so
much
that
they
would
not
move
to
another
company
for
less
than
50%
pay
rise.
Meter:
Apparently
real
offer
via
CD-­‐S
Past
[September
2001]
60+
%
<-­‐
R
&
CD
Goal
[Mid
2002]
10%,
[End
2002]
<1%
<-­‐
R
&
CD
Ra@onale:
maintain
staff
number,
and
morale
as
core
of
business
and
business
predictability
for
customers.
www.Gilb.com
Slide
5

6. My
‘ChrisOan’
Friend
• Lawrence
Day.
SeaTle
Washington
• “Love
is
not
quanOfiable”
– Not
in
Bible
– LiTle
guidance
from
God
and
Jesus

7. Love:
Biblical
Dimensions
<-­‐
Lawrence
Day,
Boeing
A
person
who
loves
acts
the
following
way
toward
the
person
being
loved:
The
biblical
cita@on
(Book
of
First
1.
suffereth
long
Corinthians,
Chapter
2.
is
kind
13)
I
included
gives
the
3.
envieth
not
quan@fica@on
of
the
4.
vaunteth
not
itself,
vaunteth...:
term
"love"
(agape
in
or,
is
not
rash
(Vaunt
=
extravagant
self
praise)
Greek).
The
5.
is
not
puffed
up
‘quan@fica@on’
for
love
6.
Doth
not
behave
itself
unseemly
would
be
as
follows:
7.
seeketh
not
her
own
8.
is
not
easily
provoked
-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐>
9.
thinketh
no
evil
10.
Rejoiceth
not
in
iniquity
(=an
unjust
act)
11.
rejoiceth
in
the
truth
12.
Beareth
all
things
13.
believeth
all
things
14.
hopeth
all
things
15.
endureth
all
things
16.
never
faileth
www.Gilb.com
Slide
7

8. A
Paper
on
‘Love
QuanOfied’
hTp://www.gilb.com/Oki-­‐download_file.php?fileId=335
-­‐download_file.php?
fileId=335
•

9. MathemaOcal
Models
of
Love
&
Happiness
J.
C.
Sproe
Department
of
Physics
University
of
Wisconsin
-­‐
Madison
Presented
to
the
Chaos
and
Complex
Systems
Seminar
in
Madison,
Wisconsin
on
February
6,
2001

10. Outline
• Love
model
-­‐
Inspired
by
Steve
Strogatz
(Cornell
University)
• Happiness
model
-­‐
In
collaboraOon
with
Keith
Warren
(Ohio
State
Univ)

11. Simple
Linear
Model
• dR/dt
=
aR
+
bJ
• dJ/dt
=
cR
+
dJ
• where
– R
is
Romeo’s
love
for
Juliet
– J
is
Juliet’s
love
for
Romeo
– (or
hate
if
negaOve)
– a,
b,
c,
d
are
constants
that
determine
the
“RomanOc
styles”

12. LimitaOons
of
Model
• It’s
difficult
to
quanOfy
and
measure
love
and
hate.
• Love
is
not
a
scalar
(different
types).
• Parameters
change
in
Ome
and
with
the
situaOon.
• Parameters
may
be
different
for
love
and
hate.

13. Some
“RomanOc
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
(narcissisOc
nerd)
• a<0,
b>0
(cauOous
lover)
• a<0,
b<0
(hermit)

14. Number
of
Pairings
• 6
styles
for
Romeo
X
6
styles
for
Juliet
=
36
different
pairings.
• Only
21
give
unique
dynamics
(because
of
R/J
symmetry)
but…
It’s
actually
worse
than
that:
• 4
parameters
with
3
choices
(-­‐,0,+)
for
each
gives
34
=
81
combinaOons
of
which
45
are
unique
• And
there
are
subclasses
depending
on
values
and
iniOal
condiOons.

15. Both
out
of
touch
with
their
own
feelings
0
• dR/dt
=
aR
+
bJ
• dJ/dt
=
cR
+
dJ
0
• 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)

16. Out
of
touch
with
their
own
feelings
(conOnued)
b > 0, c > 0 b < 0, c < 0 b > 0, c < 0
War
Two lovers Two nerds Nerd + lover
Love fest (or war) Unrequited love Never-ending cycle

17. With
Self-­‐Awareness
and
bc
<
0
(nerd
+
lover)
a + d < -2|bc|1/2 a+d<0 a+d>0
Extremely cautious Somewhat cautious Overly eager
Rapid apathy Eventual apathy Growing volatility
(The only equilibrium is apathy)

18. Fire
and
Water
(Do
opposites
aTract?)
• Take
c
=
-­‐b
and
d
=
-­‐a
• Result
depends
on
a,
c,
and
the
iniOal
condiOons
• Can
end
up
in
any
quadrant
• Or
with
a
steady
oscillaOon
• But
never
apathy

19. Peas
in
a
Pod
(Are
clones
bored
or
blissful?)
• Take
c
=
b
and
d
=
a
• Result
depends
on
a,
b,
and
the
iniOal
condiOons
• Can
end
up
in
any
quadrant
• Or
at
the
origin
(boredom)
• But
no
oscillaOons

20. 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
oscillaOons
are
possible

21. Effect
of
NonlineariOes
Replace ax with ax(1-|x|), etc.
(logistic function)
ax(1 - |x|) ax
a tanh x
x

22. New
kinds
of
Dynamics
New equilibrium points Limit cycles
(but no chaos in 2D)

23. A
Love
Triangle
• Romeo
has
a
mistress,
Guinevere
• Guinevere
and
Juliet
don’t
know
about
one
another
• Romeo
responds
to
each
with
the
same
romanOc
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

24. Love
Triangle
EquaOons
• dRJ/dt
=
aRJ
+
b(J
-­‐
G)
• dJ/dt
=
cRJ
+
dJ
• dRG/dt
=
aRG
+
b(G
-­‐
J)
• dG/dt
=
eRG
+
fG
• System
is
4D
(4
variables)
• There
are
6
parameters
• System
is
linear
(no
chaos)

25. Linear
Love
Triangle
Examples

26. Romeo’s
Fate
• Averaged
over
all
romanOc
styles
(combinaOons
of
parameters)
and
iniOal
condiOons:
– 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
apatheOc)
• Anything
can
happen!

27. One
ChaoOc
SoluOon
of
Nonlinear
Love
Triangle
“Strange attractor of love”
a,b,c,f > 0; d,e < 0
(Romeo is an “eager beaver”)

28. Possible
Further
Studies
• What
happens
if
Guinevere
and
Juliet
know
about
one
another?
(6D
system)
• What
happens
if
only
Guinevere
knows
about
Juliet?
(5D
system,
asymmetric)
• What
happens
if
Juliet
and/or
Guinevere
has
another
lover?
(6D
or
8D
system)
• What
are
the
dynamics
of
a
free-­‐love
commune?
(large-­‐D
system)
• Is
there
an
opOmum
pairing
of
romanOc
styles
that
encourages
success
or
portends
failure?
If such problems interest you, let’s collaborate!

29. Simple
2D
Linear
Model
• dR/dt
=
aR
+
bJ
• dJ/dt
=
cR
+
dJ
• d2R/dt2
+
βdR/dt
+
ω2R
=
0
– β =
-­‐a
-­‐
d
(damping)
– ω2 =
ad
-­‐
bc
(frequency)

30. SoluOons
of
2-­‐D
Linear
System

31. Happiness
Model
• d2x/dt2
+
βdx/dt
+
ω2x
=
F(t)
Damping Oscillation External forces
• Happiness:
H
=
dx/dt
– HabituaOon
– AcclimaOon
– AdaptaOon
• Only
changes
are
perceived

32. What
is
x?
• x
=
integral
of
H
• x
is
what
others
perceive
• H
(your
happiness)
must
average
to
zero
(with
posiOve
damping)
• x
does
not
average
to
zero

33. Winning
the
LoTery

34. Drug
or
Other
AddicOon

35. IntermiTent
Reinforcement

36. Random
Events

37. Real
Life

38. Parameter
Space
β
2
ω

39. Some
ImplicaOons
• Constant
happiness
is
an
unrealisOc
goal.
• Others
see
less
volaOlity
in
you
and
oxen
wrongly
conclude
how
you
feel.
• Individuals
can
be
categorized
by
their
values
of
β
and
ω.
• Manic
depression
may
correspond
to
β
~
0.
• Long
prison
terms
may
be
ineffecOve.

40. A
few
other
happiness
studies
• Brickman,
Coates
&
Janoff-­‐Bulman
(1978)
report
only
small
differences
in
life
saOsfacOon
between
paraplegics,
control
subjects,
and
loTery
winners.
• Lykken
(1981)
reports
that
religious
people
are
not
noOceably
happier
than
freethinkers.
• Diener
&
Diener
(1996)
review
studies
indicaOng
that
all
American
socioeconomic
groups
score
above
neutral
in
life
saOsfacOon,
as
do
people
with
severe
disabiliOes.

41. What
disabiliOes,
you
ask?
• Hellmich
(1995)
reports
that
84%
of
individuals
with
extreme
quadriplegia
say
that
their
life
is
average
or
above
average.
• Delespaul
&
DeVries
(1987)
report
that
people
with
chronic
mental
problems
claim
posiOve
well-­‐being.

42. As
for
the
dynamics
• Silver
(1982)
reports
that
individuals
with
spinal
cord
injuries
are
very
unhappy
immediately
following
their
injury,
but
that
58%
state
that
happiness
is
their
strongest
emoOon
by
the
third
week
axer
their
injuries.
• Suh,
Diener,
&
Fujita
(1996)
report
that
good
and
bad
events
have
almost
no
effect
on
happiness
axer
6
months.

43. In
Summary
...
(Lykken
1999)
• There
seem
to
be
no
permanent
ups
and
downs;
natural
selecOon
has
made
us
this
way,
because,
by
accommodaOng
to
both
adversity
and
to
good
fortune
in
this
fashion,
we
remain
more
producOve,
more
adaptable
to
changing
circumstances,
and
more
likely
to
have
viable
offspring.

44. Other
Similar
QualiOes
• Sense
of
wealth
• Health
• Intelligence
• Skills
• Senses
– hot/cold
– smell
– vision
– hearing
...

45. Summary
• Love
and
happiness
are
wonderful
• So
is
mathemaOcs

46. References
• hTp://sproT.physics.wisc.edu/
lectures/
love&hap/
(This
talk)
• Steven
H.
Strogatz,
Nonlinear
Dynamics
and
Chaos
(Addison-­‐Wesley,
1994)
• sproT@juno.physics.wisc.edu