5. Transcendental Logic

(Structural Logic)

 

The human brain, as nature, is a pattern making device. It has arisen by the laws of nature and in adaptation to nature. It produces patterns by abstracting elements from experience. The most effective patterns which allow it to understand and adjust to the world must be those which conform to the patterns of nature.

We have seen in previous chapters that the notion of a triad is constantly occurring in religious and philosophical literature. One form of logic consists of three propositions, each consisting of three terms, in which the third, the conclusion, is derived from the other two, the premises. The philosopher Kant studied the structure of Aristotle's logic and came to the conclusion that certain ideas were inherent in the human mind. They were not learnt from experience, but existed before any sense could be made of the observed world. We interpret our experiences by them. He called these Categories of Thought. He divided them into four classes, each having three forms as follows:-

Quantity - Unity, Plurality, Totality

Quality - Affirmation, Negation, Limitation

Relation - Causation, Substance, Interaction

Modality - Necessity, Possibility, Existence

The distinction between the Categories of the mind and experience changed the nature of Western Philosophy thereafter. Philosophers began to explain the phenomena of the Universe by means of a vital force such as the Will to Life (Schopenhauer) and the Will to Power (Nietzche) The Philosopher Hegel noticed that the the three Categories in each set were related. The first was positive, the second its opposite, and the third was a combination of the two, a synthesis. If you impose Unity on Plurality you get Totality, for instance. Thus the categories are reduced to three. He, therefore, invented a method of thinking known as Dialectical Idealism. According to this the evolution of the Universe and all things in it, including human history, could be explained thus:-

There is first a Thesis (created by God or a Universal Mind). This gives rise to an Anti-thesis. And it is the combination of these which formed the Synthesis. The Synthesis could then be regarded as another Thesis which gave rise to an Anti-thesis, and the two combined to form another Synthesis. And so on. The material world would arise because of a Synthesis.

Karl Marx, however, turned this up side down and regarded the material world as the Thesis, human desires etc as the antithesis and Ideas and other human products arising as a synthesis. Thus the material or economic conditions would produce new ideas which would result in new technologies, changing the social conditions. Human history could also be explained by the arising of a dominant class which by the need of interaction with the lower class would produce a middle class. In the Feudal system dominated by an aristocracy, a middle class arose and this became the dominant Capitalist class, creating a new social system. This method of thinking is called Dialectical Materialism. It is, however, easy to see that Dialectical Materialism is itself the anti-thesis to Dialectical Idealism which was the original thesis. There ought, therefore, to be a Synthesis. And there are certainly indications that this happening. Capitalism is getting modified by increasing state power. It is being socialised. Communism progressively introduces personal incentives and becomes more like capitalism.

The point remains that we still have a triad. There are reason to criticise these ideas in the way they were formulated, mainly on the grounds that the three factors coexist. Christianity and Hinduism have Trinities. In Indian religions we have the notion of the three 'Gunas', an active, a passive and a mediating, principle which are the basis of all phenomena. Apart from this all the colours can be created by a mixture of red, green and blue, the Universe can be described by mass, energy and order, and even space has three dimensions. There appears to be something fundamental about the triad in thought and nature.

It is possible, using Islamic guidelines, to reconstruct these ideas. This will now be attempted without claiming absolute truth for them.

We read in the Quran:-

"Glory be to Him Who created all the pairs, of that which the earth grows, and of themselves, and of that which they know not." 36:35

"He hath made for you pairs of yourselves and of the cattle also pairs whereby He multiplies you. Naught is as His likeness." 42:11

"And all things have We created by pairs that haply ye may reflect, therefore, flee unto Allah." 51:49-50

"Unto Allah belongs the East and the West, and whithersoever ye turn, there is Allah's countenance. Lo! Allah is All-embracing, All-knowing." 2:115

"The foolish of the people will say: What has turned them from the Qibla which they formerly observed? Say : Unto Allah belongs the East and the West. He guideth whom He wills unto a straight path. Thus We have appointed you a middle (or balanced) nation, that ye may be witnesses against mankind..." 2:142-143

Three remarks can be made here:-

Firstly, the pair of forces, positive and negative, active or passive, appear to be fundamental ones in the Universe. It is recognized in Science and also in Chinese Philosophy where they are called Ying and Yang. Everything arises from their interaction. The verse above, however, tells us to flee unto Allah, to take the Straight Path, to be a Middle or balanced nation. Allah is unity and the creator of the pair. The Will of Allah may be thought of as the third factor which separates them and later combines them. The pair in turn by interaction creates something else, a third factor, and there are interactions between the three. Male and female create a child, and three interact.

Secondly, thought itself has the same structure. We cannot know anything which is not relative. It must have two relata. If we isolate something for examination we immediately create a dichotomy. We see good as opposed to evil, pleasure as opposed to pain, black as opposed to white and so on. But the relata are connected by a relating factor.

Thirdly, in the beginning there is nothing. When a child is first born, or a person is unconscious then there is nothing for him. The development of consciousness implies the arising of a distinction between 'self' and 'not-self', between the observer and the object. To say that something is created is the same as saying that it has come into knowledge or vice versa. However, there is an interaction between self and not-self.

If we represent a positive factor by P, a negative factor by N and the result of the interaction by R, then it is possible for the factor R to act as a positive or negative force with respect to some other factor. It can react with both P and N of its source, and these can act on R. We have the format in Fig-1.

Suppose P1 acts on N1 to produce R1; R1 becomes the active force P2, relative to some negative force N2, and this interaction produces R2. And so on. We have several levels as in Fig-2.

The dotted lines in Fig-2 show that R can also act as a negative force, N with respect to some other positive factor P. Thus R2 can become either P3 or N1; and R3 can become P4 or N2 and so on. We have an involution by the steps downwards and evolution by the steps upwards. If R3 is active (P4) so that it acts on a relatively passive force, N4 it creates an intermediate state R4. If, however, it is passive, (N2) and is acted on by a higher force P2, it creates an intermediate state R2. Note that a catalytic process is also defined here since R2 acting as P3 creates N2 which recreates R2.

The Solar energy, P, falling on earth, N, produces organic life, R. But organic life acting on the earth causes material changes in it, while if it is acted on by Solar energy, it evolves to a higher level. The food we eat is acted on by digestive juices producing certain products required by the organism. These are further acted on by the air we breath and the energy we absorb, and the products will then be the very digestive juices we required in the first place. It will also produce the kind of energies we require for thinking, for instance. It is not, too difficult to see that if we regard our mental faculties to be equivalent to N1, then if we are receptive to higher forces, P1, we may have the kind of spiritual experiences and capabilities, R1. These acting as P2 on our brains, N2, will create the mental faculties R2. The diagram may represent a whole ecological system rather an individual, or a complete industry, or the Universe itself.

We have a self-maintaining system, except for a force P1 entering the system and a product N4 being produced at the end. The diagram could represent an organism with multiple inner processes which receives an input from outside and produces an output. On the other hand, it could represent the Command of Allah (P1) entering the Universe which transforms these forces and produces an output (N4), the various created objects.

If we start from nothing or an originally stable state and some new factor arises in it, then its equal and opposite must also come into existence. This is also recognized in Newton's Law of Motion. We can represent this by saying that 0 = +1,-1. or by the letters A and C. However, since these two factors were originally combined and have now separated and will combine, there must be a cause for this. This leads us to the notion of a third or reconciling factor which we can represent by *1, or by the letter B. We now have a Triad.

This third factor can behave in three ways:- (a) It can separate the pair of opposites. (b) It can act on the side of one of the pair of opposites so that that factor can dominate or repress its opposite or produce some kind of compromise. This creates three conditions (in which either A or C dominate or some kind of rule dominates their relationship. (c) It can reconcile or combine them. These three functions of the third factor correspond to the three factors themselves.

Creation in actuality or thought has three stages:-

1. We have the original unity which is an Absolute.

2. It gives rise to a pair of opposites. This pair is sometimes regarded as the origin of the Universe in some systems of thought. But here, from the Islamic point of view, it is not the origin, but itself a creation.

3. The pair of opposites by their interaction give rise to a third factor. This obviously represents the third factor which kept the pair of opposites united in the first place. Here we have a Trinity and it is this which is responsible for the Universe. The Trinity appears in several religions, but it is then, from the Islamic point of view, a fundamental description of the Universe and not the cause of it. It cannot be identical with Allah, the Absolute.

If we use analytical thinking then taking any object as a unity which is as yet unknown, we can analyze it exhaustively into three factors. Each of these taken as Unity can again be analyzed exhaustively into a similar triad. On the other hand we can think synthetically. If we see some unity then we can postulate the presence of its opposite as well as a third reconciling factor. The combination of the three creates a concept at a higher level.

Pythagoras and others described creation as being the result of four factors. The original unity X, plus the pair of opposites and their resultant can be represent as a diamond having three levels, where X creates A and B which create C. Thus C represents X at a lower level.

X

A B

C

This is also called the Tetragrammaton. The four letters in the Hebrew word for God, Jehovah, spelt in JHVH are also regarded as referring to this. The Trinity could then be understood in five ways:- As the three levels (X, AB and C), as XAB, as ABC, as XAC, as XBC . There are two pairs of opposites XAB - ABC and XAC - XBC. Trinities of all these types occur in various teachings.

The three dimensions of space can also be regarded in the same way. They arise progressively from a single factor, Time from the point called the Big Bang. These directions are not the same. Each of the three dimensions may be regarded as extending from a point where the observer stands, into a positive and negative direction. This gives us six directions plus the 7th centre = 7 factors. These are not alike. There is certainly a difference between up and down owing to gravity, and there is left and right handedness, and there is forward and backward direction. The two directions form a pair of opposites and the balance is in the centre. All kinds of growths on earth, of minerals, plants and animals and man depend on these asymmetries. The human embryo and later the brain also develops differently in these directions. There appears to be a compensation for the downwards pull of gravity in the formation of a negative image in the mind. These dimensions have a psychological correspondence. In fact, we can divide man into a spiritual, a mental and physical aspect. The spiritual aspect is itself divisible into consciousness, conscience and will. These correspond at the mental level to perception, motivation and action (or intellect, emotion and action). These correspond to the physical faculties for sensation, processing and reaction. Other corresponding triads are faith, love and hope, the absence or opposite of which causes psychological and social diseases. Corresponding to these, we have Divine Attributes or categories of Truth, Goodness and Power, which give rise to the value systems called science, ethics and economics, aesthetics being the overall harmony between them. The main Ethical principles are Truth, Compassion and Justice.

If the original unity, X is divided into A,B,C and if each of these is divided similarly into a,b,c, then we have nine factors which we may represent thus:- a1,b1,c1 a2,b2,c2 a3,b3,c3.

Certain rules apply to these sets.

1. X > ABC i.e.. X implies, produces, divides into or is equivalent to A ,B and C . We may substitute for X any factor, including A, B or C, and the formula will still apply, though we may denote the elements differently. e.g..

A > a1,a2,a3 B > b1,b2,b3 C > c1,c2,c3

 

2. A,B,C > a1,b1,c1 i.e.. There is a correspondence between the relationship which exists between A, B and C and that which exists between a, b and c

A,B,C > a2,b2,c2

A,B,C > a3,b3,c3

We may combine these in a single formula,

A,B,C > a1,b1,c1 > a2,b2,c2 > a3,b3,c3

(Caution: It is not stated that a1 is like A, b1 is like B etc, but that the relationships between ABC are like the relationships a1,b1,c1 etc just as 1/2 is like 3/6 and 5/10 etc)

 

3. A,B,C > a1,a2,a3 > b1,b2,b3 > c1,c2,c3

 

4. It follows that since A,B,C correspond to two different sets, then there is a correspondence between these sets. We have

(a1,a2,a3 > b1,b2,b3 > c1,c2,c3) > (a1,b1,c1 > a2,b2,c2 > a3,b3,c3)

These sets may be called X(o) and X(r), where (o) stands for original and (r) stands for resultant. The elements of X(o) are of course, A,B,C. The elements of X(r) may be named A(r),B(r),C(r). Or we may distinguish between the two sets by A1,B1,C1 and A2,B2,C2

5. We could also remove the brackets from the sets and see that

a1,a2,a3 > a1,b1,c1 > b1,b2,b3 > a2,b2,c2 > c1,c2,c3 > a3,b3,c3

 

6. There is also a correspondence between

A,B,C > a1,b2,c3

 

Since every unit must be a combination of these three factors, it is not difficult to see that combinations can take place in 7 ways. We have already seen that the original unity where the three factors are blended has been named X. But each of the factors can take up either a dominant position, or an intermediate position or a passive position with respect to the others. These positions also correspond to the qualitative relationship between the three factors. We will indicate these by their position, the first position (left most) is Active, Positive or dominating; the middle position is mediating, reconciling or catalytic; the last position (right most) is negative, passive or inert. We have

X, ABC, ACB, BAC, BCA, CAB, CBA We call this a Septet.

But we have also seen how X(o) turns into X(r). We may, therefore, write:-

X(o), ABC, ACB, BAC, BCA, CAB, CBA, X(r) We call this an Octave. Here X(r) is a recombination of the three factors in a balanced manner, but it refers to one of many entities. It s like the many reflections of an object in mirrors.

Certain laws apply to these.

1. Since A is an active force and dominant in ABC, while it is passive or inert in CBA, then we have a series of diminishing power as we go towards the right, and increasing power as we go towards the left. We call these an evolving or developing series, and an involving or degenerating series. This allows us to arrange our concepts in order.

2. The first half of the series forms a mirror image in the second half, except that the fifth and sixth triads are exchanged. That is, ABC is the inverse of CBA, ACB is the inverse of BCA, and BAC is the inverse of CAB, but the position of BCA and CBA are exchanged. Or we could say that the position of the third and fourth triads are exchanged.

3 The triads can also be considered as three pairs, another triad.

(ABC, ACB), (BAC, BCA), (CAB, CBA) > A,B,C where the dominant factor in each pair is the same. We could also find pairs where the intermediate or passive factors are the same, but this is less significant.

4. The six triads can be regarded collectively as a single item where all the factors occupy each of the positions and, therefore, form a perfect blend. We can call this X(t) where t stands for transition. We now have a triad

X(o), X(t), X(r) > A,B,C

5. All these new triads can generate further septets, and the law of correspondence will continue to apply to all triads and therefore, also to the septets.

.

One way of applying the system is as follows:-

1. There is originally a unified self-existing undifferentiated absolute Reality we call Allah. Since nothing else exists it is unmanifest and unknown. We call it X

2. Since there is no external cause for any change, the creation of the Universe must come from an Impulse, Desire, Purpose, Intention or Will in the Absolute. This must be integral to the Absolute. This manifests as the Word or Command of Allah and can be regarded as a fundamental vibration. We denote by W. According to a Hadith, Allah created the Universe because He wished to be known.

3. Creation according to the Quran is from Nothing. This appears to imply that it takes place within Allah, in the Mind of Allah. Coming into existence is the same thing as coming into Consciousness of Allah. For something to come out of nothing requires the simultaneous creation of a pair of opposites e.g. 0 = +1 -1. The further implication is that it is state of unbalance - something has been taken from one place in the homogeneity, leaving a negative hole and put into another place causing a positive state. There is, therefore, a constant flow from the positive to the negative, a third condition of activity. Indeed, we must suppose that before the separation of the pair of opposites, this third factor must have existed to keep them in unity and it now tries to reunite them. This accounts for all processes in the Universe, including Life. To put it in another way:- If we define an opposition as a problem and reconciliation as a solution, then the function of Life is problem solving and restoring the Unity from which all things began. There is a creative or Involutional process leading from Unity to multiplicity and an opposite Evolutionary process leading from multiplicity to Unity, These are taking place simultaneously as well as cyclically.

4. The creative act begins with the separation of these three forces which we may call the active, the inertial, and the ordering. We denote them by A, M and P. These act on each other and create resultants. These could be represented by Gravity, Electro-magnetism and the Strong force. One could say that the Self-contemplation of the Absolute creates a distinction between observer and object. The interaction between them produces the third factor, observation or experience. Thus a distinction occurs between the Knower, the Knowledge and the Known, though the three interact and are inter-dependent. We have an Active, a mediating and a passive principle. Kinetic energy could be converted into order or information or congealed into matter particles. The realm of activity of these three could be called the Universal Mind. It has three layers - Universal Consciousness or Being, Universal Will (e.g. creativity etc), Universal Memory (the Records in Heaven).

5. The achievement of Unity is development towards Allah, the Absolute Unity and results in Peace, Self-fulfilment, Happiness, Perfection, Joy, Bliss, (89:27-30). Disintegration is a motion away from Allah, the Absolute Unity and produces conflict and suffering and is known as Hell.

6. The Knower gives rise to the notions of something unitary, integrated, sentient, creative, internal, active and controlling. The known object gives rise to notions of something inert, passive, receptive, external, separate, containing multiplicity, of space like a blank piece of paper, something which can accommodate or memories which are fixed. Knowledge gives us the notion of, experience, relating, something mediating, interactive. Corresponding to these we have the following notions:- Spirit, matter, life or mind; will, consciousness, conscience; Order, mass, energy; Truth, Justice, Love; Synthesis, interaction, analysis; Creativity, Modification, Memory. In some systems a distinction is made between Universal Mind, Universal Life, and Universal Memory (e.g. the Preserved Tablet). If we look at the Universe as a system, then there is a process of disintegration or increasing multiplicity the more we place our attention on the parts, and process of integration or unity the more we place our attention on the whole. In between we have several levels where there is a balance between these opposites.

7. It is possible for the Knower to be dominant, that is, to be active and creative; or to be a passive observer, or to mediate, relate, adjust. This can be done in thought as well as in action. We do change the world by what we do and by how we think about it. Science is not merely a passive observation but also consists of the invention of concepts and techniques of thinking, apart from physical instruments. If we allocate the first position from the left to Activeness, the second or middle to Mediation and third or right most to Passivity then we get the following combinations:-

X1, X2 (= AMP, APM, MAP, MPA, PAM, PMA), X3

Here X1 denotes the original synthesis of the three, the Absolute, the six intermediate stages are represented by X2, and X3 denotes the last synthesis or Image. The two are not necessarily the same. The Sun (X1), for instance, produces rays (X2) which form many images (X3), e.g. in mirrors or other objects. We have a Logical Octave here.

Suppose we think of X1 as Allah, the Real Self or the Higher faculties associated with it; X3 denotes the world around us or to the physical body. The three letters may be regarded as referring to a person's psychological, social and physical life. The six middle triads represent living man. In so far as he is required to act he ought to work through the first triad AMP. But in so far as he is acquiring knowledge he ought to be represented by the last triad, PMA where he is completely passive and receptive. If he is not then he will be actively inventing ideas and these do not constitute knowledge. Some activity is automatic and some thinking is imaginative, and these are represented by APM and PAM. The central triads represent different combinations of these activities. His social relationships should be represented by MPA and MAP in which he is a mediator with active or passive ingredients. 'Surrender', Islam, has three meanings here. It is to act positively in association with World, to be passive with respect to Allah in so far knowledge is concerned and to be a good social mediator.

One consequence of these ideas is that if we define the original unity as truth, then the existence of an opposition between the two factors constitutes a 'problem'. To solve it requires a third reconciling factor. The problem cannot be solved by suppressing either of these factors since this creates another opposition, another problem. If we use B to suppress A in order to allow C freedom, then we have created an opposition between A and B. There is, moreover, an opposition between the free factor C and the state of conflict between the others. If we use B to neutralise C in order to allow freedom to A, then we have created an opposition between B and C. When both these conditions are obtained then we have created two separate entities. The number 1 becomes two. Multiplicity arises from unity. This happens whether the problem is an internal, psychological one, an interactive one (that is, between an inner condition or desire and an outer state), or a purely external one. It happens whether the problem is an intellectual, social or material one. It is not difficult to see that many political and other conflicts arise precisely because each side has suppressed opposite considerations within themselves. Inner conflicts produce outer ones.

This method of thinking has several advantages:-

1. It allows us to analyse any phenomena exhaustively into three interdependent factors and their combinations. Analysis conducted in any other way is not exhaustive. There is, otherwise, always a chance that something has been overlooked.

2. Other forms of analysis treat each item as something separate as if they could exist by themselves. In fact, however, the parts have meaning and function only with respect to each other and the whole in which they belong and where they have arisen.

3. We also overcome the problem posed by the fact that the whole, owing to its organization, is always more than the sum of its parts. We do not destroy the object by analyzing it. It is an Absolute, an X in its own right, an image of the Absolute, a Unity.

4. This mode of thinking conforms to nature itself and does not require the intellect to form its own formal independent rules according to which all things must be seen.

5. In so far as all analysis follows the same rules it is possible to discover more universal relationships and patterns. This allows a much greater synthesis of knowledge.

6. It allows the individual to study nature by interaction. Objectivity no longer means non-involvement. The individual should engage his mind, feelings and actions. They are legitimate instruments. Objectivity means detaching the observing consciousness from these faculties.

7. It allows factual, meaningful as well as ethical thinking.

8. It promotes awareness and understanding rather than mere information.

However, this mode of thinking may be inapplicable to Science.

 

We can call this system of thinking the Logic of Correspondence.

This structure has, in fact been applied at times throughout this book. But the reader should remain aware of what is being done. The structure is being used as a TEMPLATE to describe phenomena in order to facilitate one kind of understanding. It is used to ensure, where it is used, that nothing is left out.

It may be represented diagrammatically. The outer circle contains the three circles which combine to form the 7 shapes, the central one is a reflection of the outer circle.

 

Another way of looking at this is as follows:-

Six points are placed to form a hexagon, a seventh point is placed at the centre. This hexagon represents the created world. The central point represents the observer as the 7th point and an eighth hidden point beyond it, represents the Absolute. There is a line parallel to the hexagon connecting the Observer to the Absolute through the centre O.

This figure can also be seen as a cube with 6 sides and 8 points or corners (The eighth corner is hidden and represented by O. If we choose a corner on this cube (any corner) and regard it as the Absolute, then we also see that there 7 lines or rays connecting it to the other 7 corners. But each of the surfaces has 3 rays. (e.g.. on the surface 6-1-7-5, we have rays 6>1, 6>5, 6>0. On surface 6-5-4-0, we have rays 6>5, 6>4, 6>0).

The cube has equal sides, but the relationship between the side and diagonal on the surface is given by the square root of 2 and that between the side and the opposite corner of the cube is given by the root of 3. These are approximately: Ö2 = 1.414 and Ö3 = 1.732.

The 3 surfaces each with 3 rays gives us 9 rays. Though two are shared they have a different function in relation to the other rays on the surface. We can only see 3 surfaces. The other 3 are hidden. We could change our position or rotate the figure to see the other surfaces. But still we would not see a cube in the centre.

The cube described above is one of unit side. So that we have 1 x 1 x1 = 1. The number 1 represents the Absolute while the 3 represents the created world of Relativity. It is generated by 1. We could describe a cube of two. So we have 2 x 2 x 2 = 8. And a cube of three = 3 x 3 x 3 = 27 and one of four = 4 x 4 x 4. = 64. These 64 can be represented as points on the cube. If this cube represents the whole Truth, then it is also represented by the number 64. Which by theosophical addition gives us 6 + 4 = 10 = 1. If we look at this cube, then the three surfaces we see have 37 points representing the manifest truth, and there are 19 hidden points on the other 3 surfaces, which could represent truth when revealed. 37 by T-addition gives us 10 = 1, and 19 also gives us 1. 37+19 = 56 which by t-addition = 11 = 2. This represents the total number of points on the surface. But there still remains a cube of 8 points in the centre of the figure which remains unknown, a Hidden Mystery. Add 8 + 2 from the surface and we have 10 = 1 again. Note that 8 - 1 = 7 rays, so also 27 - 8 = 19 rays and 64 - 27 = 37 rays. There is a relationship between these four cubes. If the Cube of 4 is all Truth, the cube of 1 is the Absolute, the cube of 2 is the Hidden Mystery. There are 8 possible cubes of 3 in the cube of 4.

The whole of Existence can probably be described in 8 dimensions. The series of real numbers is regarded as describing one dimension:- ….-3, -2, -1, 0, 1, 2, 3……. Then if we multiply by tthe imaginary number e, which is the square root of -1, this describes a second dimension at right angles to the first. We can have up to 8 dimensions (7 described by imaginary numbers) after which algebra ceases to work. We can represent these dimensions by the figure below. As we see the 7 from the first, the 8th can be regarded as hidden behind or in front of the 7th,. These 7 are connected by 6 lines, each having 3.

The 8 steps from X1, through X2 to X3 can be demoted by the letters A B C D E F G H which can be called one cycle. The sequence ABCD is the reverse or mirror image of EFGH. We can call one the Ascending branch and the other the Descending branch. The Cycle itself is Stationary and unchanging. It has no direction. It may be regarded as being composed of two cycles - an upward moving and a downward moving one, represented by the two directions e.g.. ABCDEFGH and HGFEDCBA. The difference between them is caused if we transfer one step from one branch to the other, thereby causing asymmetry. We then have two sections on of 5 parts and of 3. The upward cycle has 5 ascending parts and 3 descending parts while the Downward cycle has 5 descending parts and 3 ascending parts. These are known as Elliott Cycles. Together these cycles cancel each other out.

This displacement is the cause of the differentiation and hence of recognition and knowledge because these require a contrast. It constitutes a stimulus or problem which creates awareness and action. The cause of the displacement is unknown and is attributed to Allah. In other words it is something fundamental and integral to Creation.

These cycles contain sub-cycles, which contain further sub-cycles as in fractals. The relationship between them follows the Fibonacci Sequence. This is a series of numbers where each number is the sum of the previous two numbers:- 1 1 2 3 5 13 21….etc. It describes growth and can be found throughout nature from the spirals in sea shells to cells in the brain and the behaviour of the stock market.

----------<O>----------

 

There is another way of describing the relationship between the whole and the part which appears to have been first described by Pythagoras:-

If we have a whole A, and divide this into two unequal parts B and C such that the ratio between

A/B = B/C then we have what has been called the Golden Rule which creates the most aesthetically pleasing proportions. This ratio has also been found to be important in Science and occurs in nature in many places. It is denoted by Phi and equals (1+ root of 5)/2 = 1.6180339887….. This is an endless number. Phi + 1 = Phi^2 and Phi - 1 = 1/Phi

If A/B = B/C then A = B^2/C and B = AC/B and C = B^2/A

and AC = B^2 and B = rootAC and B^2/AC = 1 and B^2 - AC = 0

We can draw a rectangle with sides B and C where A= B + C. And if we draw an inner square on the smaller side as base, then the remainder is also a rectangle of the same proportions. We can draw another square within this, leaving another rectangle of the same proportion and so on. Clearly the original rectangle is also a part of a similar rectangle. If all these rectangles are drawn then if we join the diagonal points we get a spiral like the ones the Galaxies make. Spirals also appear on sea shells, in the way the leaves on the stem of a plant are arranged, in certain crystals that have a five fold symmetry, and in the behaviour of Black Holes.

---------<O>----------

 

Numbers

 

There are three tools we use in thinking - words, numbers and notations. They correspond loosely to qualities, quantities and relationships, not on a one to one basis, but the relation between the one triad corresponds to the relationship between the other. Notations refer to such things as music and dance movements etc, and can be extended to many other things. There is also a fourth tool which has an overall use - the diagram or graph.

Numbers are connected with something fundamental about nature, that it is divisible into separate objects. It is the ultimate abstraction. 10 apples and 10 men and 10 tables, if all qualities that distinguish them are stripped, leave that which is common to them, namely 10. Numbers, unlike words, are more closely connected with reality. Everyone agrees that 2+3 makes 5, and all will disbelieve anyone who makes them other than 5. We have complete precision here. This is not the case with words. This is why it is possible for people to cooperate in mathematics and to check each other's results. It is not, therefore, surprising that science should use mathematics to achieve precision and agreement and that philosophers and politicians who use words cannot agree.

The Greeks divided knowledge into three levels, namely Metaphysics, Mathematics and Physics. Aristotle thought that Mathematical objects were obtained by abstraction from physical objects, and metaphysical by abstraction from mathematical. Each of these should be studied by its own principles. Plato, however, reversed this. He thought Metaphysical objects created Mathematical ones and these created the physical ones. Thus a dichotomy arose between two opposite views. In Newton's time mathematics was thought of as a means of describing the world as it is, but it could not tell us anything new about reality. Leibnitz, who held that mind and matter were distinct, proposed a "pre-established harmony" between the two. Minkowski showed that there was a close correspondence between the results of independent mathematical thinking and the observed behaviour of the physical world. However, it was found that experiments were required to establish certain constants and to choose between different equations. Thus, a third factor, namely interaction was required. We now had a trinity. It is true to this day in the West that mathematical models have to be created first in order to explain observational results and these then have to be tested. It was true about Newton's Laws, Einstein's Relativity theories and the newest String Theory, the development of which is held up by absence of appropriate mathematical models.

In modern times in the West, there are several views:-

(1) That mathematics is a set of deductions from self-consistent axioms. It was part of logic. It is a type of game played by certain rules. Gödel, however, proved that there must always be statements whose truth or falsity cannot be proved from these axioms.

(2) That mathematics is a human creation which may sometimes prove useful in explaining some features of nature if we select the right kinds of concepts and data. In particular we must avoid infinities.

(3) That mathematically described objects really exist, so that any object so described will exist. Computers and the results of their programming on the screen are also realities indistinguishable from other kinds of reality.

The Islamic view is:-

"Lo, We have created everything by measure, and Our Commandment is but one, as the twinkling of an eye." 54:49-50

"The beneficent Hath made known the Quran. he hath created man. He hath taught him utterance. The sun and moon are made punctual. The stars and trees adore. And the sky He hath uplifted; and He hath set the measure, that ye exceed not the measure, but observe the measure strictly, nor fall short thereof. And the earth He hath appointed for His creatures." 55:1- 10

Numbers and mathematics are inherent both in nature and the human mind, because man is part of nature and has responsibility towards it as vicegerent. Man is made of the same laws and forces which exist in the world and he has developed in interaction and adjustment to it. He will see the world correctly if he is psychologically adjusted correctly. Bacon, in the 12th century, who had studied in Arab universities in Spain, regarded mathematics to be inherent in the human mind as well as in nature. There was no dichotomy or trinity. He was the first to use mathematics to describe features of the Universe. Newton and others followed his lead. It is necessary to realize , also, that the modern mathematics uses Arabic numerals.

 

Numbers have been used in several ways:-

1. To count things because experience shows discrete or separate objects. Here the laws of arithmetic apply. 2 apples plus 3 apples makes 5 apples, for instance.

2. To measure things in weight, space and time for comparison. Here we use units invented by man. e.g. inches, metres, grams, pounds, seconds etc. When something is measured as 2 cm and something else as 3 cm, then we cannot say that adding them together makes something 5 cm long. Two planks of wood, 2 and 3 cm long do not do the same job as a 5 cm plank. It is a common mistake to confuse these two ways of using numbers. It gets one into difficulties because the objects in nature do not conform to the units we have invented. Exact measurement becomes impossible and we get infinities such as those in measuring Pi, the relationship between the circumference and radius of a circle. It is probably impossible that the Universe can ever be described fully by means of arithmetic alone. In particular the rules discovered by a study of the parts can never be used to describe the whole. Each number is a wholeness in itself.

3. They have also been used to denote positions in a series or the order of occurrences. The 5th position is different from the 2nd and 3rd position. Adding the 2nd to the 3rd will not give us the 5th position. This can be seen if we examine students and give them marks 90, 75, 73, 66, 30 and so on according to performance. This mistake is also made in mathematics.

4. They could also be used to study qualities. If we arrange things according to a gradual change of characteristics, e.g. from black to white, then we form a series so that the numbers will stand for the position on this artificially constructed series.

5. It may have been noticed in the discussion above that there is still another use for numbers. They can be used to denote interactions and structures.

6. They can be used to distinguish between levels and categories of reality.

The number 1 stands for the Absolute, the fundamental Unity. It has no parts and is indivisible. There are three aspects to this:- It may refer to the wholeness of something or it may refer to any indivisible part of the whole, or it may refer to the fact that all other numbers arise by the reproduction of 1. i.e. 1+1, 1+1+1 etc. This first category may be regarded as a 7th use of numbers, but not by man. The three aspects of it refer to ;- (a) The unit particle denoted by 1. (b) The series of numbers and their uses (1 to 6 above). (c) The Wholeness denoted by 0 because there is nothing outside it, and we cannot, therefore, count. Zero is denoted by a circle because of this fact. This gives us the 8th or 0 use of numbers, also not by man. The fact is that man can only accept that there is a wholeness above (the large) and below (the small) and that multiplicity exists between them and he can only deal with this multiplicity. His function may be defined as:- to reconcile these two extremes.

The number 2 stands for the pair of opposites which arises when something is created or distinguished from the Absolute. It stands for the creative forces. The distinction between good and evil, positive and negative, active and passive arises here. We are aware of nothing which is uniform. Awareness requires an opposition. It constitutes a stimulus. This number can also be seen as the reproduction of the first number. A separate unitary world has been created.

The number 3 stands for the world of phenomena and relativity. We cannot be aware of anything unless there is some connection between things. All thought or action is an attempt to reconcile the opposition. The pair of opposites interact, thereby creating three conditions. A mediating or reconciling factor has to be recognised. This number can be seen as the combination of the first two numbers, 1+2, which themselves form a pair of opposites, odd and even.

The number 4 stands for stability, permanence or recognisable things since the fourth factor keeps the other three in combination. It imposes duration, hence time is regarded as a fourth dimension. It is a combination of three and one. It could, however, also be seen as two twos, an opposition to an opposition. It could be seen as 1 with an inner life, an inner triad.

The number 5 stands for potentialities since there is now an opposition as well as a triad. Something new can come out of it. Unity has also been imposed on two pairs of opposites which are in opposition to one another.

The number 6 stands for recurrence or repetition since there are two triads, one reflecting the other. Knowledge is generally only possible because phenomena are repeated. Classification depends on it and so does the notion of variation which requires some kind of similarity.

The number 7 stands for a structure or pattern by which a unification is imposed on repeated items. There is an inner opposition between two triads. A triad is formed by the one and the two triads, 1+3+3

The number 8 stands for an inner unitary existence or integration within the structure. Individuality.

The number 9 is a triad of triads. It reflects number 3 at a higher point. . It represents a pattern.

The number 10 would represent a unity imposed on the higher triad. It represents 1, 4 and 7 where similar unities are found. It contains a triad of unities. This number is, therefore, the same as 1 in that it represents all the potentialities of 1. The addition of zero, 0, nothing, denotes this fact. However, zero is another digit representing the fact that a second cycle begins here.

Normally, we need go no further than 8 since the number 8 takes us back to 1 at another level. An individual who is fully integrated could be represented by it. Essentially, it is the first number which produces all the others by simple reproduction, and first three numbers reproduce all the others. The mystery lies in this that 1 is able to replicate itself. This power must be regarded as a property integral to the number.

It should be remembered that this discussion is not about words. It is a fact of nature that things do occur in numbers as the Quran repeatedly points out. It is perfectly possible to think in these categories rather than the usual ones. Categories, as the Philosopher Kant and others have pointed out are the forms thought takes prior to logical thinking.

The series of numbers can be progressively added up as follows:-

0, 0+1=1, 1+2=3, 3+3=6, 6+4=10, 10+5=15, 15+6=21, 21+7=28, 28+8=36, 36+9=45…..

Ao we get the series 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66…..

We can add the digits in each number to give us 0, 1, 3, 6, 1, 6, 3, 1, 9, 9, 1, 3

These are all multiples of 3.

The numbers 0 to 9 have only one digit and can be regarded as a cycle at level 1.

The second cycle begins with 10. The two digits give us a cycle at level 2.

This second level has 9 cycles 10-19, 20-29, 30-39, 40-49, 50-59, 60-69, 70-79, 80-89, 90-99. This forms one great cycle.

The third level has 3 digits and goes from 100-999. It has 9 great cycles each consisting of 10 cycles.

 

One of the numbers of particular interest for Islam is given by the following verse:-

"And what will make you understand what the burning (Hell-fire) is? It leaves naught, it spares naught. It scorches and shrivels the mortal. Over it are nineteen." 74:27-30

If all things are measured then, it is argued, the Quran is also mathematically constructed. Investigation by Rashad Khalifa and others show that much of the Quran, when the number of chapters, verses and letters is taken into consideration then these turn out to be multiples of 19. For instance, there are 114 chapters in the Quran which is 19x6. The words "In the name of Allah, the Beneficent the Merciful" in Arabic has 19 letters and head every chapter of the Quran but one. But it occurs twice in chapter 27. So the number of times this invocation occurs is also 114 = 19x6. The Word "Quran" occurs 57 = 19x3 times in the Quran. The total number of verses in the Quran is 6346 which is 19 x 334. This it is claimed, is the reason why the Quran has been preserved in its original condition. However, as this is only a recent discovery this cannot be so. But it can be regarded as proof that it has, indeed, been preserved unchanged.

The number 19 is the 9th prime number. It is formed from 1 which is the first in the series of basic numbers and 9 which is the last in the series. As such it can be regarded as representing Allah who is the first and the last (57:3). By digital addition (DA) 19 becomes 10, which by another DA becomes 1. 19 is the end of the third cycle. 19 may be regarded as representing outer manifestations below which are two hidden levels.

The multiples of 19 are also significant. We have

19x1=19, 19x2=38, 19x3=57, 19x4=76, 19x5=95, 19x6=114, 19x7=133, 19x8=152, 19x9=171

Digital addition of each number gives us the series:- 1, 2, 3, 4, 5, 6, 7, 8, 9. That is, any number multiplied by 19 reproduces that number. This is, of course, because DA of 19=1.

 

Before the present scientific and material age all phenomena on earth were explained in terms of just four elements, namely:- fire, air, water and earth. These terms refer to the essence, states or inherent qualities of things, taking into consideration physical as well as vital and psychological properties. They may be regarded loosely as referring to the radiant, gaseous, liquid and solid states. The above categories of thought are given objectivity. Using these concepts thinking takes place in terms of states not materials. The purpose of such systems is different from science. It is not technology.

However, three other elements were also recognised, namely:- ether, light and sound. This set of three can be distinguished from the previous set of four by the terms Heavenly or Celestial elements and Mundane elements respectively, making a total of 7. The three create the four. Spirit, light and sound (the Word or Logos) are regarded in most religions as emanating from the Absolute.

There are several ways of looking at these. We have an upper triad and a lower quartet separated by a barrier. The fourth mundane element, fire, can also be regarded as a bridge between the upper triad and the lower triad, thus creating 3 sets or levels. Taken three at a time, the middle can be regarded as the result of the combination of the other two, e.g. air and earth give rise to water, and fire and water give rise to air. All these relationships have different meanings.

The point of this discussion is to show that it is possible to think in completely different categories, and to explain, organise and systematise experiences in ways which differ from the way science does. These different systems are not more or less true, but are useful for different purposes, and some may have a much greater significance for man than others.

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