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Table 1, Figures 1, 1(a), 1(b), 2, 3, 4, 5, 6, 7, 8, Endnotes.

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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.

The above terms are respectively analogous to "distance", "velocity", and "acceleration".  

DISTANCE                  S 



VELOCITY             V=dS/dt

°EMOTION °E=dP/dt   =
C:Fig. 2, I:Table 2, James

C:Fig.1(a), Figs. 2, 3, 4, 5, 6.


°FAITH      °F=d²P/dt²   =
I:Table 3


Table 1- The Key to Understanding °EMOTION & °FAITH
Expressed in Calculus.
Mull carefullyChapters of Spinoza's insights are embedded.

Table 1 Notes:  
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:  "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.



I:Table 2

°Bad, Evil

<-----Subjective terms----->
E1:Bk.VII:609, Bk.III:21027

==------ --------------- ------------ ----------I-----------
   D:1.11a, D:1.17, C:4.3c.
----------- ------------- ------==
loss of
in surgery
major loss
of eyesight
minor loss
of eyesight
no change
in eyesight
minor gain
of eyesight
major gain
of eyesight
in surgery

Fig. 1(a) - Spectrum of °EMOTION
 D:1.14e, D:1.17.

I:1.4b, I:1.5.

C:1(a), I:Table 2
I:Table 3



==------- --------------- ----------- ---------I----------
D:1.11a, D:1.17, D:1.36f.
----------- ------------- --------==
same eye doctor throughout

Fig.1(b) - Spectrum of °FAITH
 D:1.30a, D:1.38.

Figure 1 -  Spectrums of °EMOTION & °FAITH
                                                               C:Fig.1(a)                          C:Fig.1(b)

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 thingG-D, they are irrelevant. See Notes 4.6, 7, & 8.

E-mail for Figure 1 clarification request, suggestion, or disagreement.


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}
: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 callE3: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 - Constantly changing EMOTION
                                            Life's Roller Coaster
                                          Its amelioration
                                By analogy, similar to constantly changing °VELOCITY (°V)
       when the Y-axis is re-titled  °DISTANCE (S).

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.

2.2   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.

       E-mail for Figure 2 clarification request, suggestion, or disagreement.


Figure 3 - Reality Curve
        The curve considers only one thing at any one instant.
 JOY (gain) going up the curve; SORROW (loss) going down the curve.
  For a Mode of G-DThought or Extension
                    EL:[43]xxiv                                         idea, knowledge       ^        eyesight, size, wealth.
                                                                       Mind - Body

The curve with the two ends asymptotic, as shown, is an hypothesis designed
to help understand °EMOTION; it stands or falls by the deductions made from it.
 For the concavity of the curve see C:Endnote Temperament.

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

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  totala  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.

      E-mail for Figure 3 clarification request, suggestion, or disagreement.


Figure 4 - Reality Curves
Note Well - See Delta B & C in Fig. 3. and Note 3.3.

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.}

4.2.   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 extinctdestroyed                     LeDoux96:129


                  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

                 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:xxvImpersonality 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.

        E-mail for Figure 4 clarification request, suggestion, or disagreement.


Figure 5 - Negative Half of Fig. 4
Note Well - See Delta B & C in Fig. 3 
JOY (gain) going up the curve; SORROW (loss) going down the curve.

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. }

     E-mail for Figure 5 clarification request, suggestion, or disagreement.


Figure 6 - Positive Half of Fig. 4
Note Well - See Delta B & C in Fig. 3.
JOY (gain) going up the curve; SORROW (loss) going down the curve.

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. }

       6.2c. Another example.

Self-preservation - Rational (above x-axis)
                         Self-destructive - Irrational (below x-axis, see Note 7.1)

Self-destructive - Irrational  (below x-axis, see Note 7.1)
Represents a person at any given irrational instant.

Figure 7- Rational-Irrational Reality Curves
Study well, Figure 3 and Note 3.3 and see
why Delta Sub B & C are of different length.

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.

7.2.  See Figure 4 Notes and Figure 3 Notes.

7.3.  See Notes 4.1a to 4.1c.


Self-preservation - Rational (above x-axis)
                      Self-preservation - Rational (below x-axis, see Note 8.1)

Self-preservation - Rational (below x-axis, see Note 8.1)
Represents a person with problems (debts, bad health) at any given rational instant.

Figure 8 - Rational-Rational Reality Curves
Study well, Figure 3 and Note 3.3 and see
why Delta Sub B & C are of different length.

Figure 8 Notes:

8.1  Figure 8 flips Figure 4 about the X-axis. The curves both above and below the X-axis,
       represent a rational person. Above the X-axis, a solvent rational person; below the        X-axis, a rational person in debt, in ill health, or in infamy.

Continue  with  SPINOZISTIC  INSIGHTS  Table 1.


C:Endnote Mull - Mull—think about carefully.

C:Endnote TemperamentTemperament.

The concavity of the Reality Curve depends on the person's temperament.     Mark Twain
For  a  phlegmatic, unexcitable, unemotional person, the curve would tend    Hampshire:138
to  a  straight  line between the two asymptotes. For a temperamental, excit-
able,  emotional  person  the curve would be more concave; hugging more
the x-axis and y-axis.

If you flip the curve about the line connecting the two asymptotes, the con-
cavity  of  the curve  now  faces  downward.  The curve now represents a
person who is suicidal. (The effect is the same as flipping Fig. 4 about the
x-axis, see Figure 7.)

C: William James' Fear - From LeDoux96:129—Extinction of the Human Species.

C:Endnote Common Good

Understanding 'dS/dt = V' in Table 1.—For those not familiar with Calculus.

Since November 6, 1997  Calculus hits. 


Revised: August 28, 2006 

"A Dedication to Spinoza's Insights"