SPINOZISTIC  CALCULUS         
The Calculus ot the Emotions           

Spinoza  defined  the  terms  "perfection";  "sorrow-boredom-joy"; "hate-indifference-love"
by  their  causes;  not  by  their  properties.  They  can  be  expressed  using  a  Calculus format—precise definition, rates-of-change at any one instant. Expressed in a Non-Calculus Format, Life's Roller Coaster, Biology of the Emotions, Biology and Human Behavoir, Neurotransmitters, William James.

From Tape 4 - "Einstein’s Relativity and the Quantum Revolution:
                         Modern Physics for Nonscientists"; Lecture 3, CG1; pg 7 

Newton's second law, F=ma, tells quantitatively how a given force (F)    
produces changes in motion (acceleration, a) in an object of mass m.      
            {By analogy: F=external Force, m=temperment, a=acceleration}     

Table 1 Notes:  
                                                                                                                                       EL:[43]  
1.  The  degree  sign (°)  indicates that the term is a mode and is a spectrum
    or a portion thereof.  For °P see G:includes.  

     Note well that all terms are values at any given instant for a rational person.
     If the person is irrational (bent on suicide) change all + signs to - signs.  

2.  The first derivative, °EMOTION, is a spectrum. °JOY is its positive portion,
     °SORROW the negative, and BOREDOM the transition.   C:Fig.1(a). 

3.  The second derivative, °FAITH, is a spectrum. °LOVE is its positive portion,
     °HATE the negative, and INDIFFERENCE the transition.   C:Fig.1(b).   
 
4.  The  third  derivative  is  a  constant—changes  no  longer  occur,
     finite  existence  ends.   I:1:7c.  

          a.  An indefinitely accelerating body eventually reaches
               the speed of light—a constant. The body is no more;
               it has become energy.  

          b.  A stream eventually falls into the abyss of the ocean
               and is no longer.  

          c.  A life falls into the abyss of death and is no longer.  

          d.  The world will come to an end when the sun's fuel
               is depleted—if not sooner.  I:1.7c.  

5.  Suggestion to Calculus Educators:—to widen your students' concept
     of  rates-of-change (and perhaps have an influence on their lives—it
     did on mine) teach Table 1, 1:4, and 2:4.  See also I.1:3d.
     A useful Web Page for Calculus Educators:
     http://www-cm.math.uiuc.edu/  "Instead  of  using  rote memorization,
     students   in   Calculus  &  Mathematica   use   experimentation  and
     real-time  visualization  to  learn  fundamental calculus concepts and
     ideas.   The   successful   calculus  course  produces  students  who
     recognize  a calculus situation  and who know what calculus tools to
     bring to bear on it".

From Marshall McLuhan, "Understanding Media",  ISDN: 0262631598; Page 117.

For  the  Renaissance,  it  was the infinitesimal calculus that enabled
arithmetic  to take over mechanics, physics, and geometry.  The idea
of  an  infinite  but  continuous  and  uniform  process, so basic to the
Gutenberg  technology  of  movable  types,  gave rise to the calculus.
Banish  the  infinite  process  and  mathematics,  pure and applied, is
reduced  to  the state known to the pre-Pythagoreans.  This is to say,
banish  the  new  medium  of  print  with its fragmented technology of
uniform,  lineal  repeatability,  and  modern  mathematics  disappears.
Apply,  however,  this infinite uniform process to finding the length of
an arc, and all that need be done is to inscribe in the arc a sequence
of rectilinear contours of an increasing number of sides.  When these
contours  approach  a limit, the length of the arc becomes the limit of
this  sequence.  The  older  method of determining volumes by liquid
displacement   is   thus   translated,   into   abstract  visual  terms  by
calculus.  The  principles  regarding the concept of length apply also
to  notions  of  areas, volumes, masses, moments, pressures, forces,
stresses and strains, velocities and accelerations (& °EMOTION & °FAITH).    C:Table 1 & Notes
 
 

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Figure 1(a) and 1(b) Notes:
 

1.1.  Fully capitalized words are precisely defined in Table 1 – much
        as letting X=Y.   G:Note 2.

1.2.  Non-fully capitalized words express the varying intensities of the
        capitalized words—dictionary definItions.   G:Note 1.

1.3.  The degree sign  (°)  stresses that the term varies in degree, but
        not in kind.  The dictionary definitions do not stress such distinct-
        tion.   G:Note 2.

1.4.  All  the  terms  in  Figures 1(a)  and  1(b)  are subjective terms but
        nevertheless they are useful with respect to the species 'man'. To
        an Eternal thing—G-D, they are irrelevant. See Notes 4.6, 7, & 8.
 

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EMOTIONS,  like  waves,  are always relentlessly flowing over you—at            Mark Twain
times like a storm; at times placidly. Nevertheless with understanding, it        Dictate of Reason
is possible to maintain a modicum of PcM.  {Ethics - Part V, Conatus, Games.}        PcM, Peace of Mind

To illustrate the constantly changing EMOTIONS consider the Figure 2           {Autonomic
curve;  which  curve  every  person constantly unconsciously generates.       Nervous System}
{E3:LIX(9):172, D:1.11a, G:Sin, C:Calculus, James' Emotion, James' Bear.} 





A-B. Your shoes are getting soiled,
B-C. You go to a shoeshine parlor.
C-D. Shoepaste being applied.
D-E. Buffing shoes to a shine.
E-F. Shoes are getting soiled.
F-G. You are about to be run over.
G-H. You may not get hit.
H-J. Close call. E3:Games
J-K. Elation. C:(a)
K-L. Negative°JOY (a °SORROW).
L-M. Finally settling down.
M-N. You start getting hungry.....
 
 
 
 

Figure 2 Notes:

2.1   The curve is generated for successive Reference Points (benchmarks)
        for a succession of different modes.  For A-F, your Reference Point is
        your shoes; for F-M, your life; for M-N, hunger.

2.1a.   Your evaluation (judging) of °P includes your thoughts;                  Mind - Body
           who do you  want to impress with the shoeshine.

2.2   At  Y1  you  feel a minor °JOY; at Y2, a major °SORROW; at Y3,
        a  major °JOY.  There is smaller increase Y1 over more time X1
        than  the  greater  changes  Y2  &  Y3  in  time  X.   At  Y1  your
        Reference  Point ( the  shine  on  your  shoes ) has a relatively
        small effect on your °P; but at Y2 and Y3, your Reference Point
        is your life!

2.3.  Y2 is greater than Y3 because the intensity of sorrow (Delta C) is
        greater than the intensity of joy (Delta B) for the same loss or gain
        (Delta A).     E3:XLVII(7):161.

2.4.  Tangents to the Figure 2 curve are °EMOTIONS.  Tangent 1 with
        positive  slope  indicates  °JOY;  negative slope, T4, °SORROW;
        horizontal tangents, T2 & T3, BOREDOM.   I:1.6b.

2.4a.   C, E, H, K  are  transitions  of  tangents from positive slope
          (°JOY) to negative slope (°SORROW) or vice versa.

2.4b.   B, D, G, J, & L  are  inflection  points—change of curvature
           from convex to concave or vice versa.   It signifies a change
           from increasing °EMOTIONS to decreasing °EMOTIONS or
           vice versa.  

2.4c.   Note that the curve can seldom be a straight line; you always
           change  your  benchmark  to  the  summation of the previous         C:Fig.4.3c
           increments.  A  straight  line  is  virtually  possible  if  the time
        involved is very short as for F-H & H-K.


2.5.  Your  Peace-of-Mind,  (°PcM),   also  varies  with  the Fig. 2  curve.
        You gain °PcM on the up-curve. You lose °PcM on the down-curve
        UNLESS  you  understand  the  reason  or  ultimately by  a leap-of-
        faith   accept   that   the   reason resides  in  your G-D—either  an
       immanent or transcendent  G-D;  both   hypotheses have the same
        useful, practical result—it's "cash-value" in Bk.X:xiv terms.  C:4.3d.

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For °P100;  x = 0 (asymptotic).
for °Py;      x = the emotion (joy) in increasing from y% °P to 100% °P.
for °Py;     (infinity - x) = the emotion (sorrow) in decreasing from y% °P to 0% °P.
for °P0;      x = infinity (asymptotic).

    The curve is analogous to plotting °Distance (Y axis) versus °Velocity (x axis):

For °S100 (speed of light);  x = 0  (no change of velocity is possible ).
for 100% > °S > 0%;  x = the increase in velocity from y% °S to °S100.
for 100% > °S > 0%;  (infinity - x) = the decrease in velocity from y% °S to °S0.
for °S0;  x = infinity; similar to °P0.

Figure 3 Notes:    All these Notes apply also to Figures 4, 5, 6, 7.

3.1.   The curve is asymptotic to the °P axis as 100% °P is approached
         and  asymptotic  to the °EMOTION  axis as 0% °P is approached.
         At 100% °P, no deterioration  is possible.                                                    C:Fig.4.4
         At  0% °P, no improvement is possible.                                                        I:1.5b.
 
         3.1a.  100% °P = G-D, infinity, G-D has no emotion.                                G-D at 100% °P
                       0% °P of any finite thing is inconceivable. Think of
                                  conservation of matter or energy—substance.

         3.1b.  100% > °P > 0%  are  finite  things, i.e. modes,  and are the            C:Fig.3
                    manifestations of G-d.   Skin, natura naturata.                                   G-d at <100% °P

3.1c.   While giving examples of modes, it is useful to note that the              SpinIdea:3.4
                    misuse  of any part ( mode ) to the detriment of the whole is             worm
                    idolatry and leads to chaos:        Organic  Interdependence

                                                   a mode
1.  The  misuse  of  the  automobile,  causing  accidents,        LeDoux96:129
     gridlock, and smog, is idolatry.
                              a mode
2.  The misuse of fertilizers,  causing pollution of rivers
     and  groundwater,  is  idolatry,  which  then causes
     ecological disaster.
                            a mode
3.  The misuse of wealth, causing slums, prejudice, and           Read and reread
     uneducated  masses, is idolatry, which then causes         "The  Affluent Society"
     crime, substance-abuse, disease, and terrorism.
         a mode
4.  Nationalism  which  impedes  One-world  is Idolatry.           Read "One World,
                                                                                                     Ready or Not"
5.  All  the above indicate people who think only of their
     own money and convenience. They do not consider
     the cancer (figurative and literally) they cause. That               I-It Relation
     lack  of  consideration  is  idolatry  and  is a sin. The
     Sins of the Parents  will  be  visited on their children.

6.  Economists who neglect the horrible effects  (to  the
     environment   or   human   values)   of  uncontrolled     "For the Common Good"
     capitalism are idolaters.        No praise, no blame.
 

3.2.   The  reason  for  the  shape of the Reality Curve is that 'x' decreases
         as  'y' increases, because each increment is a smaller percentage of
         the  increasing  total—a  new  Reference  Point higher on the 'y' axis.
         At higher and higher °P, less and less °EMOTION is possible.               {At 100% °P (G-D)
           TEI:[25:IV]:10, C:4.3c, C:4.4.                                                                            has no emotions}

3.3.   The same change (Delta A) in °P causes a greater intensity (Delta B)
         at a lower °P than (Delta C) at a higher °P.   C:4.3b.

              a.  A  $100  gift to a poor man causes him more °JOY than
                   the same $100 gift to a rich man.

              b.  Simultaneously the poor man will °LOVE the $100 more
                   than the rich man.

3.4.    This illustrates the concept in Economics of "Marginal Value" and
          and Diminishing Returns.  As products become more and more           (Read and re-read
          cheaper,  they become less urgent (economically)—example air.       "The Affluent Society")

3.5.   For additional explanation of curve see Figure 6 and Note 6.2.
 
 

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Figure 4 Notes:   (See also Fig. 3 Notes.)

4.1.  The same change (Delta A) in °P causes a greater intensity of sorrow
        (Delta C) than the intensity of joy (Delta B).  { C:4,3b.}

 4.1a  For a man with $200, the intensity of sorrow (Delta C) for a $100 loss
         is greater than the intensity of joy (Delta B) for a $100 gain. Because
         the loss is 100% of what he has; the gain, 50% of what he had.

4.1b  Emotion, subjectively, is judged with respect to what one has for sorrow,
         and with what one had for joy.

4.1c  The last dollar lost represents a larger percentage of the sum in hand;
         the last dollar gained represents a smaller percentage of the sum in hand.
         See Note 3.2.

4.2.   See Figure 3 Notes and C:Endnote Temperament for how Reality Curve
         was  constructed.  The  curve  is for a rational person at any one instant.

         Figure 7 flips the curves about the x-axis. The curves above the x-axis
         represent a rational person. The curves below the x-axis represent an
         irrational person (one bent on suicide). See Notes 7.1

4.3.   I  call  D-R-D'  an  "Actuality Curve".  If  R  is  moved up to 100%; D to the
         negative asymptote; and D' to the positive asymptote; the Actuality Curve
         is identical with the Reality Curve. Q.E.D., actual equals real.   G-D is      G-D at 100% °P
      manifest all along the °P axis as one of his finite modes and is subject
         to  subjectivity  and  °EMOTIONS.   All  things  are  in G-D.  Satan is          1P1ff, 1P26ff.
         a part  of  G-D   as  we  are  a  part; antagonistic parts of an organism     { G-d at <100% °P
         will  obliterate  each  other.  Explicitly,  if  we  don't destroy or learn to        JBY added }
         control these things, we will become extinct—destroyed.                      LeDoux96:129

         Disclaimer:

                  Talk of G-D as equal to or less than (<) 100% °P
                  is  for  analysis  only.   G-D is infinite and infinity  
                  cannot be divided.  The  tendency  to treat parts                   but viewed correctly
                  as separate entities leads to idolatry.

      4.3a.  The  R-D' (Actuality Curve) curves because °EMOTION (°JOY)  
                 is decreasingly intense as the °P increases.

       4.3b.  The   D-R   (Actuality Curve)   curves   because   °EMOTION
                 (°SORROW) is increasingly intense as the °P decreases.                   C:Fig. 3, C:3.3.

     4.3c.   The  intensities  change because you are constantly  changing
                  Reference Points (R).  During °JOY, you judge each increment             C:2.4c.
                  with the summation of the previous increments as a Reference
                  Point  and  the  new increment  is a smaller percentage of the
                  new  Reference  Point.   During  °SORROW,  you  judge  each
                  decrement with the summation of the previous decrements as a
                  Reference Point and the new decrement is a larger percentage
                  of the new Reference Point.

       4.3d.  1.  With  a  lot  of money, getting a little more is not all that
                      exciting; but with little money, losing a little soon brings
                      you to destitution.

                 2.  If  your  eyesight gets better,  it can get only so much
                      better;  but  if  your  eyesight deteriorates you can go
                      blind. 

                 3.  If  your  health  gets  better,  it  can get only so much
                      better;  but if your health completely deteriorates you
                      die—and  all  must  eventually  fall  into  the abyss of
                      death.  { Table 1, Note 4.}

4.4.   At  higher  and  higher  °P of Figs. 4, 3, 5, & 6 there is less and less
                                                         enlight-ened                             shook-up
         intensity of emotion. The more objective you are, the less emotional

         you are.   { C:3.2, C:6.1a. }

                                                    EL:[43]:xxiv            by hypothesis
         At 100% °P  are  the  attributes  of  SUBSTANCE, Natura Naturans.           includes

         Fig. 3 curve  is  useful  to  help  visualize  that  at 100% °P there can              5p17
          E5:XVII(1):255, E3:GN(2)n,                      Bk.XIV:1:xxv—Impersonality of G-D {at 100% P}.
         be  no  °EMOTION,  and  therefore  no  °HATE,  no  °LOVE.                      G-D at 100% °P

         E5:Endnote 18:1, E1:Endnote XXXI.

4.5    At complete enlightenment you are G-D like;  (the Actuality Curve
         slides into the Reality Curve) without discontinuity. Q.E.D.

4.6    The 100% °P of any mode implies the 100% °P of all modes—G-D;
         if not, the finiteness of any mode could destroy the others.  Say, if       C:3.1c, C:4.3, & E3:V.
         you  had  all  the  money in the world, bad health could destroy all
         your money—analogy.

4.7    At 100% °P; °EMOTION = 0.
        °EMOTION varies as 1/dt but at zero, °EMOTION is independent of        Einstein Time
         Time.  Therefore a thing at 100% °P, i.e. G-D, is Timeless, Eternal.       Hawking Time
         At   100% °P;   because  °EMOTION  =  0,   °FAITH  is  also  zero.           E5:XVII:255 
         Therefore a thing at 100% °P, i.e. G-D, does not °LOVE or °HATE .        E5:XVIIc:256
         anything. See 5P17.

4.8   G-D is neither BORED nor INDIFFERENT. See Note 1.4.
 

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Figure 5 Notes:  (See also Fig. 3 & Fig. 4 Notes.)
 

5.1.  The Actuality Curves illustrate the deterioration of a mode:

        a.   See C:4.3b.

5.2.  How the envelope is developed:

        a.   H represents a deterioration of a mode to the not the worst
              possible, J.   Eyesight that deteriorates, but not to worst
              possible.  All Points H fall under the maximum possible
              °Sorrow Reality Curve.

          b.   Example.

                If  G-J  represents  the  worst  deterioration a man's eyesight can
                undergo in a given condition, he would have had Delta B + Delta C
                °SORROW.  G-H is the amount it actually deteriorates, hence he      Reality, E3:GN2n
                has only Delta C  intensity of sorrow  and  DELTA  B  represents
                an intensity of joy.
           (The  arrows  indicate  direction:  J  to  H'  for  Delta B,  characteristic  of  an
                    optimist;  and  G'  to  H'  for  Delta C,  characteristic  of  a  pessimist.)

5.3.   Figure 5 Reality Curve drops to asymptote at P=0, showing
         great EMOTION unless there be resignation or acceptance;
         Actuality Curve, E-F at F—death is approaching.    { C:4.3d. }
 
 
 
 

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Figure 6 Notes:  (See also Fig. 3, Fig. 4, & Fig. 5 Notes.)
 

6.1.  Improvement of a mode:

        a.   Note that the intensity of emotion diminishes as the maximum
              possible is neared.  { C:3.2, C:4.4 }

        b.   A-B, A-J, and H-J represent an improvement to the best possible
              °P.  Eyeglasses  that  improve your eyesight to the best it can be.

        c.   F-G  represents  an  improvement  to the best possible °P from a
              low  °P.  Note that even though the improvement is small there is
              great °EMOTION (horizontal distance from F' on curve (not shown)
              to G on curve).

6.2.  How the envelope is developed:                                                            Concavity of Curve

   6.2a.   C-D   represents  an  improvement  of  a  mode  to  not the best
              possible °P (E).  Eyeglasses improved your eyesight, but not to
              the  best  that  you  subjectively  expected. All subjective Points,
              such as D, fall under the Reality Curve and should be projected
              across to D'.

    6.2b.   Examples.

                     It is only subjectively, with respect to our own species, that we          Ferguson
                 call things perfect or imperfect—good or bad.
                 { TEI:[12]:6, 1App25, Completion. }

                 passive, Garden of Eden
D  is  a subjective  judgment that, with new glasses, a man was
saddened  that  his eyesight was not improved to 20/20 (E), the
best normal eyesight) and hence he loses Delta C intensity of joy.
If  D  were  objectively  called  reality in the sense that it was the      G:In That Sense
result of given causes  (and therefore  in  G-D, 1P27), it would be         E3:GN2n
projected  to  D' and  he  would  have  Delta B  intensity  of joy.
(The  arrows  indicate  direction:  E  to  D'  for  Delta C, characteristic of a
 pessimist;  and  C'  to  D'  for  Delta B,  characteristic  of  an  optimist.)
If  he  had  gone  to  E,  his  intensity  of  joy  would  have been            C:Fig. 3
Delta C + Delta B.   When  subjective,   he  would  °HATE  the
Optometrist; when objective, he would  °LOVE  the  Optometrist.


Subjective  Points D  do  not  exist  in  nature,  they  are  false.        Inadequate Idea
They  should  be  projected  to  the  curve  at  D'—that is why
I call the curve "Reality Curve". Although there is no such thing           True Idea
as  good and bad,  an  individual  can  nevertheless  "think"  in
those  terms  from the point-of-view of his own species—hence
points D.  Delta C represents °SORROW, with resulting loss of
Peace-of-Mind,  and  it  is the purpose of Religion to alleviate it
by understanding or faith.                                                                    Leap-of-faith

       6.2c. Another example.

D is a subjective judgment that, in a contest, he was saddened
that he won only Third Prize,  and not First Prize, E, and hence
he loses Delta C  intensity of joy. If  D  were  objectively called
perfect  in the sense that it was the result of given causes (and
therefore  in  G-D),  it  would  be  projected  to D' and he would      Reality
have Delta B  intensity of joy.  If he had won, E, his intensity of
joy  would  have  been Delta C + Delta B.  When  subjective,
he   would  °HATE    the  "contest";  when  objective,  he  would
°LOVE  the "contest".


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Figure 7 Notes:

7.1.  Figure 7 flips Figure 4 about the X-axis. The curves above the X-axis represent a rational  person. The curves below the X-axis represent at any given instant an irrational person         (one who is not determined to preserve himself at that same instant) say, from excruciating pain from         cancer with no possibility of a cure, a mental illness, or for any reason (however possibly             justified). An irrational person changes the negative coordinates to positive coordinates on        the Y-axis below the X-axis, because what a rational person considers a bad thing (a -), an irrational person considers a good thing, (a +), and vice versa.

7.1a  Quadrants I & IV:  Delta sub A = $50; (fig. 7) 

        At the +X asymptote, the rational and the irrational are equal, both are                                 non-existent, as is evident from the diagram.

7.1b  Quadrants II & III:  Delta sub A = $50; (fig. 7) 

         At the -X asymptote, the rational and the irrational are equal, both are non-existent,             as is evident from the diagram.

7.1c  Quadrants I & II:

         At the rational +Y asymptote, there is no emotion as is evident from the diagram.

7.1d  Quadrants III & IV:

         1.  An irrational person changes the negative coordinates to positive coordinates on                 the Y-axis below the X-axis. See Note 7.1.
      2.  At the irrational +Y asymptote, there is no emotion as is evident from the diagram.

7.1e  Quadrant I - He gained $50; Fig.7, R to D' - Rationally called 'JOY':
 

7.1f   Quadrant II - He lost $50; Fig.7, R to D - Rationally called 'SORROW':
 

7.1g  Quadrant III - He lost $50; Fig.7, R to D1; Irrationally called 'JOY':

        1.  For a person (no matter his station in life) whose genes and nurture tend to make him              irrational at any given instant, a loss of his positive things (money, health, fame) will              reach a critical point where he will actually commit suicide.

        2.  It is irrationally called 'JOY' because he cannot live with the loss and his death              is its alleviation.

7.1h  Quadrant IV - He gained $50; Fig.7, R to D'1; Irrationally called 'SORROW':

         1.  No matter, if he still wants to die (he is suffering excruciating pain); or it helps make               him momentarily rational (he won a lottery and the pain is not that excruciating that he can give                  the gain of the money a moment's thought) and he jumps momentarily to the rational side               of the X-axis and can then rationally call it a 'JOY'.

7.1i  Figures 1 to 8 help understand human actions.

7.2.  See Figure 4 Notes and Figure 3 Notes.

7.3.  See Notes 4.1a to 4.1c.
 
 

 
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