MATHEMATICAL BUDDHISM

PREFACE

          A personal interpretation of Buddhism is presented in a concise form in which basic terms are introduced, defined (whenever possible), and then used in a systematic development leading to applications in daily living.  This should be considered as work in progress that will probably be in a slow pace at a non-constant rate.  Furthermore, what has already been written will likely be edited from time to time for consistency and increased lucidity.

          My intention is simply to share what I have found useful in my life personally.  Since we all have different background, what one finds useful may not be so for others, or if it is, it is unlikely to be so to the same extent.

CONTENTS

(Point and click.)

Chapter 1.  The Nature of Things

Chapter 2.  Human Nature

Chapter 3.  The Worlds of Senses

Chapter 4.  Wisdom and Ignorance

Chapter 5.  Heaven and Hell

Chapter 6.  Mindfulness

Chapter 7.  The Buddhist MBA

THE BUDDHIST MBA

Continuing from . . . 

MINDFULNESS

Chapter 7.  The Buddhist MBA

          Buddhism is not merely a philosophy; it is a religion that consists of a philosophy together with a system of practice leading to its religious goal, i.e. attaining wisdom to see everything the way it is in each breath of life.  Its system of practice shall be coined the “Buddhist MBA”.  Here, MBA is an abbreviation for Mental Business Administration.  Attainment of such wisdom will follow from culmination of one’s skills in one’s administration of one’s own mental business.  The tools of administration are IM and EM.

          Since one’s  I  (the Internal World of Senses) is complex and intricate, starting out as the CEO overseeing the whole  I  may be overwhelming.  One may need to start out as a trainee, practicing simple tasks to develop skills and gain experiences before one takes on the entire enterprise.
         
          Simple exercises of training for development of one’s skills in applying IM and EM can be invented by restricting IM and EM to subsets of  I .  For example, consider a subset of  N₁₅ X N₂₅ X N₃₃, which is itself a subset of  I , consisting of ordered triples of breath consciousness, breath perception, and neutral sensation.  As one breathes in, focus one’s attention to the breath in the nostrils and count 1.  As one breathes out, focus one’s attention to the breath in the nostrils and count 1.  Represent these first two counts by (1,1).  Continue in the same manner and count (2,2).  Then continue and count (3,3), (4,4), and (5,5).  Consider these five pairs of counting as the first round with five inhalations and five exhalations.  Repeat the first round and append it with another pair of count (6,6).  This is the second round with six inhalations and six exhalations.  The third round will consist of seven inhalations and seven exhalations.  Continue until reaching the sixth round with counts up to (10,10).  This completes the first exercise that can be represented as follows:

   (1,1)  (2,2)  (3,3)  (4,4)  (5,5)
   (1,1)  (2,2)  (3,3)  (4,4)  (5,5)  (6,6)
   (1,1)  (2,2)  (3,3)  (4,4)  (5,5)  (6,6)  (7,7)
   (1,1)  (2,2)  (3,3)  (4,4)  (5,5)  (6,6)  (7,7)  (8,8)
   (1,1)  (2,2)  (3,3)  (4,4)  (5,5)  (6,6)  (7,7)  (8,8)  (9,9)
   (1,1)  (2,2)  (3,3)  (4,4)  (5,5)  (6,6)  (7,7)  (8,8)  (9,9)  (10,10)

To complete the above exercise, one must be both intensively and extensively mindful with one’s counting as one breathes in and out.  Should one lose track of one’s counting at any time, recollect and start all over until one completes the exercise.  Then immediately proceed to the second exercise by repeating the first exercise and so on.  All these exercises can be performed anywhere at any time in any posture one may wish.  Bed time before one goes to sleep is perhaps a convenient time.  One may set one’s own goal as to how many such exercises one wants to perform each time.  As one starts seeing the benefits of these exercises, one will want to do more and more.  Such an exercise may sound rather simple, but those who have not tried it before will quickly find out concerning their concentration ability.

To be continued . . . 

Back to the beginning . . . 

MATHEMATICAL BUDDHISM

PREFACE AND CONTENTS

For discussion, go to . . . 

MATHEMATICAL BUDDHISM DIALOGUE

MINDFULNESS

Continuing from . . . 

HEAVEN AND HELL

Chapter 6.  Mindfulness

          In N₄, there exist two transformations of particular interest and practical use.  They are transformations from  I  into  P , which shall be called “Intensive-Mindfulness (Pāli: sati) transformation” and “Extensive-Mindfulness (Pāli: sampajaññā) transformation”, and denoted by IM and EM, respectively.

          Buddhist mindfulness is conscious attentiveness.  Let (a,b,c) ∈  I .  Then IM(a,b,c) is the knowledge acquired from conscious attention to the occurrence of (a,b,c) by watching the phenomenon locally and EM(a,b,c) is the knowledge acquired from conscious attention to the occurrence of (a,b,c) that is being watched by IM over an extended period of time.  For example, suppose that  a ∈ N₁₅  such that  a = r₅(x)  where x is an inhale breath, b ∈ N₂₅, and c ∈ N₃₃.  That is, a is the touch consciousness arising from the inhale breath passing through the nostrils, b the corresponding touch perception, and c a neutral sensation.  In this example, IM(a,b,c) is indifferent awareness (a kind of knowledge) at the nostrils of the entering breath and EM(a,b,c) is indifferent awareness of the entering breath through the nostrils over an extended period of time.


Continuing to . . . 

THE BUDDIST MBA

Back to the beginning . . . 

MATHEMATICAL BUDDHISM

PREFACE AND CONTENTS

For discussion, go to . . . 

MATHEMATICAL BUDDHISM DIALOGUE

HEAVEN AND HELL

Continuing from . . . 

WISDOM AND IGNORANCE

Chapter 5.  Heaven and Hell

          When a sensory receptor and a sensory object meet, an element of the Internal World of Senses occurs.  At this juncture, if we think wisely, peace and happiness naturally take their course.  However, if we think ignorantly, misery and suffering will inevitably follow.  When we are happy, we say that we are in “heaven” and when we feel miserable, we say that we are in “hell”.  That is, heaven and hell are states of mind and are momentary depending on our thoughts.  If we think wisely, we are on our way to heaven and if we think ignorantly, we pave our way to hell.

          Mathematically, think of  N₄  as a set of transformations with various domains and ranges.  Some are from  I  (the Internal World of Senses) into  P  (the World of Wisdom) and many are from  I  into  T X U  (the World of Ignorance).  Still, some are real functionals on  P  and  T X U  measuring amounts of happiness (in heaven) and misery (in hell), respectively.  Others will be introduced at appropriate time.

Continuing to . . . 

MINDFULNESS

Back to the beginning . . . 

MATHEMATICAL BUDDHISM

PREFACE AND CONTENTS

For discussion, go to . . . 

MATHEMATICAL BUDDHISM DIALOGUE

WISDOM AND IGNORANCE

Continuing from . . . 

THE WORLDS OF SENSES

Chapter 4.  Wisdom and Ignorance

          “Wisdom” (Pāli: paññā) is knowledge of the three universal states of things (anattatā, aniccatā, dukkhatā).  Lack thereof is “ignorance” (Pāli: avijja).  To be wise is therefore to be constantly aware of these universal laws.  At the very moment of forgetfulness of the laws, one becomes ignorant.  That is, wisdom and ignorance are moments to moments, i.e. they are functions of time.  Craving (Pāli: taṇhā) and attachment (Pāli: upādāna) are two common manifestations of human ignorance.  To crave for or attach to something (saṅkhatadhamma) at any moment of time is evidence of not recognizing at that moment that the very thing one craves for or attaches to is impermanent (aniccā), unstable (dukkhā), and has no fundamental identity (anattā).  Heed therefore Buddha’s advice:

“Sabbe dhamma nalam abhinivesaya.”

That is, "nothing whatsoever should be clung to".

          Since we were born ignorant and have by and large lived among the ignorant, we have not normally been educated or trained to be wise.  On the contrary, we have been systematically educated and trained to crave and attach.  In all, our craving is of three types and attachment four kinds.  We crave sensual pleasures (Pāli: kāma-taṇhā), crave to become (Pāli: bhava-taṇhā), and crave not to be (Pāli: vibhava-taṇhā).  Our attachments are sensual (Pāli: kamupadana), habitual (Pāli: silabbatupadana), theoretic (Pāli: ditthupadana), and egoistic (Pāli: attavadupadana) in nature.  Having been led to walk such a normal well-trodden path, it becomes extremely difficult to see, think, and behave wisely.  We must unlearn and learn anew to see, to think, to speak, and to act wisely.

          Let  T  be the set of all human cravings and  U  be the set of all human attachments.  The set  T X U  will be called the “World of Ignorance”, while  P  will be used to denote the “World of Wisdom”, the set of all knowledge based on “Wisdom” (Pāli: paññā) defined above.


Continuing to . . . 

HEAVEN AND HELL

Back to the beginning . . . 

MATHEMATICAL BUDDHISM

PREFACE AND CONTENTS

For discussion, go to . . . 

MATHEMATICAL BUDDHISM DIALOGUE

THE WORLDS OF SENSES

Continuing from . . . 

HUMAN NATURE

Chapter 3.  The Worlds of Senses

          H contains six sense receptors:

r₁, eyes to see;  r₂, ears to hear;  r₃, nose to smell;
r₄, tongue to taste;  r₅, body to touch;
r₆, mind to recall and imagine.

Let E₁, E₂, E₃, E₄, E₅, and E₆ be the sets of the corresponding sense objects of r₁, r₂, r₃, r₄, r₅, and r₆, respectively.  Each r_i (where i = 1,2,3,4,5,6) can be thought of as a mapping (possibly multivalued) from the set E_i into the set N_1i X N_2i X N_3j (where j = 1,2,3).  That is, if x ∈ E_i, then r_i(x) = (y, z, w) where y ∈ N_1i, z ∈ N_2i, and w ∈ N_3j.  For example, when the eyes (r₁) see something (x ∈ E₁), eye-consciousness (y ∈ N₁₁), perception pertaining to the eyes (z ∈ N₂₁), and eye-related sensation/feeling (w ∈ N_3j) arise and the sensation/feeling is pleasant for the case j = 1.
             
          Define the set  I  (“Internal World of Senses”) and the set  E  (“External World of Senses”) as follows:

       I  =  (N₁₁ X N₂₁ X N₃₁) U (N₁₂ X N₂₂ X N₃₁) U (N₁₃ X N₂₃ X N₃₁)

     U (N₁₄ X N₂₄ X N₃₁) U (N₁₅ X N₂₅ X N₃₁) U (N₁₆ X N₂₆ X N₃₁)

     U (N₁₁ X N₂₁ X N₃₂) U (N₁₂ X N₂₂ X N₃₂) U (N₁₃ X N₂₃ X N₃₂)

     U (N₁₄ X N₂₄ X N₃₂) U (N₁₅ X N₂₅ X N₃₂) U (N₁₆ X N₂₆ X N₃₂)

     U (N₁₁ X N₂₁ X N₃₃) U (N₁₂ X N₂₂ X N₃₃) U (N₁₃ X N₂₃ X N₃₃)

     U (N₁₄ X N₂₄ X N₃₃) U (N₁₅ X N₂₅ X N₃₃) U (N₁₆ X N₂₆ X N₃₃)

and

E   =   E₁  U  E₂  U  E₃  U  E₄  U  E₅  U  E₆.

If we set

X   =   D  –  I  –  E

and solve for D, we obtain

D   =   I  U  E  U  X.

Now, if we stipulate that X = Ø, we have an “anthropocentric partition” for D:

D   =   I  U  E.

An argument that can be given for X to be empty is that any dhamma not detectable by the physical five senses is certainly comprehensible by the sixth sense.  Our approach is to not make the assumption and leave the issue to future proof and/or discovery.


Continuing to . . . 

WISDOM AND IGNORANCE

Back to the beginning . . . 

MATHEMATICAL BUDDHISM

PREFACE AND CONTENTS

For discussion, go to . . . 

MATHEMATICAL BUDDHISM DIALOGUE

HUMAN NATURE

Continuing from . . . 

THE NATURE OF THINGS

Chapter 2.  Human Nature

          Dhamma can aggregate to form more dhamma and the aggregates can combine to form bigger and more complicated dhamma, and so on. There are five aggregates that are of particular interest. They are referred to as the "Five Aggregates" (Pāli: Panca Khandha) and will collectively be denoted by H .  The set H consists of two subsets, R (Pāli: Rūpa) containing one aggregate and N  (Pāli: Nāma) containing four aggregates, which will be denoted by N₁, N₂, N₃, and N₄.   H  is identifiable to a human individual with R and N  being what commonly referred to as the human body and the human mind, respectively.  More precisely,

R contains (or includes) all body parts, external and internal organs including all the sense organs, nerves, blood, fluid, as well as all the physical, chemical, and physiological processes.

N₁ contains six kinds of sense-consciousness, i.e. eye-consciousness, ear-consciousness, nose-consciousness, taste-consciousness, touch-consciousness, and mental consciousness.  The Pāli term for N₁ is "viññāna".

N₂ is perception and sixfold with respect to the five senses and the ideas perceived by the mind.  The Pāli term for N₂ is "saññā".
  
N₃ contains three kinds of sensation and feeling, i.e. positive or pleasant, negative or unpleasant, and neutral or neither pleasant nor unpleasant.  The Pāli term for N₃ is "vedanā".

N₄ is thinking and all kinds of mental formation.  The Pāli term for N₄ is "saṅkhāra".
            
          In sum,  H  ∈  D  and  H  ⊂  D such that
                       

H  =  R U N     where     N   =  N₁ U N₂ U N₃ U N₄.

Furthermore,

N₁  =  N₁₁ U N₁₂ U N₁₃ U N₁₄ U N₁₅ U N₁₆

where N₁₁, N₁₂, N₁₃, N₁₄, N₁₅, and N₁₆ are eye-consciousness, ear-consciousness, nose-consciousness, taste-consciousness, touch-consciousness, and mental consciousness, respectively.  Similarly,

N₂  =  N₂₁ U N₂₂ U N₂₃ U N₂₄ U N₂₅ U N₂₆

where N₂₁, N₂₂, N₂₃, N₂₄, N₂₅, and N₂₆ are perceptions pertaining to the eye, ear, nose, taste, touch, and mind, respectively.   In addition,

N₃  =  N₃₁ U N₃₂ U N₃₃

where N₃₁, N₃₂, and N₃₃ are positive, negative, and neutral sensation and feeling, respectively.


Continuing to . . . 

THE WORLDS OF SENSES

Back to the beginning . . . 

MATHEMATICAL BUDDHISM

PREFACE AND CONTENTS

For discussion, go to . . . 

MATHEMATICAL BUDDHISM DIALOGUE