From Chaos to Synthesis: At the gateway of new Civilisation, Culture and Ideals of the Aquarian Age

 We continue describing some examples of categories from the last post. This will be a very small list of examples and many books on the subject list long tables of categories.  I am attaching two slides to quote examples of some common categories in mathematics and physics. Unless you already have a mathematics background it will be OK to not understand what these categories are.   But if you have at least some mathematics background then you might understand that the first slide describes what structure we are considering on objects. All the objects in these categories are constructed from plain sets along with additional well-defined axioms on their elements.   Using above objects we can form corresponding categories as shown below. Don't worry if you are not able to understand these examples since they need some mathematical background. However I will try to give some visual intuition regarding what these structures are and how an arrow preserves these structures thereby settin

If your perspective on nature has evolved up-to the point where you observe that life cannot be just a collection of random events but is structured and therefore naturally intelligent then category theory is a very interesting mathematical language that takes interest in structures and their inter-relationships. We shall look at some basic examples of categories today.  Before trying to understand the examples, a word on the notion of object and arrow is due. An object carries a structure while an arrow or morphism refers to a correspondence between two objects carrying that common structure. Through the notion of correspondence we intuit that given an unknown object we can study it by setting up various possible correspondences with a known object. This is one of the most fundamental philosophy underlying the notion of arrows and their composition and therefore category theory itself. Here the mathematicians treat arrows and their composition more fundamentally than objects themselve

 In this post we will complete the definition of a category partially done in the last post.  The third axiom says that for every object in a category there exists an identity arrow of the object. This intuitively says that for every object we can always do nothing and leave the object as it is or in other words transform the object in such a way that it leaves the object exactly in the same state from which we originally started. This translates to no rotation of the propeller (which is same as rotation by 0 degrees or rotation by 360 degrees). This rotation (or effectively no rotation) is the identity arrow of the propeller. Similarly in the case of second object, no permutation (which is same as the permutation in which we send every element to itself) is the identity arrow. Take a visual look to make sure you understand that identity arrow will always exists given an object because we have nothing in effect to do to the given object.  Now if we ponder on the clockwise rotation by 1

In this post, the goal is to intuitively understand the definition of a category through two very simple practical and concrete examples.   1.The first example is a four blade propeller, whose blades we shall label as 1,2,3 and 4.   2. Another example is a four element set A = {1,2,3,4}.  Let us form two categories containing these objects. The first example of a propeller will give rise to a category we shall call PROP (the label reflects that its object is a propeller). The second example of a finite set will lead to a second category which we will call SET. Notation wise the categories are denoted using capital bold letters.  The above figure is a visual depiction of the first axiom of a category. The first axiom says that every category consists of a collection of objects. In both categories that we have formed there is just a single object. But in general a category can have finitely or even infinitely many (collection of) objects. In fact mathematicians have also discovered categ

On the first blog of the post, I wrote about the fact of around four theosophists in Grothendieck's list of mutants. Grothendieck is considered to be the greatest mathematicians of the last century informally by some of the eminent mathematicians. Although Samuel Eilenberg and Saunders Maclane gave the first definition of category, functor and natural transformations in their 1945 paper, the recognition and development of a separate mathematical discipline of category theory has been generally attributed to Grothendieck's influence by the mathematical community. The following parallels between theosophy (as an occult philosophy) and category theory in contrast to current set-theoretic approach to science might give us a clue to the deeper thought patterns of this mathematician:  1. The study of theosophy like that of geometry proceeds from the universal to particulars. This is also the approach of category theory which can be thought of universal mathematics. It is in distinct

The opposition between intuitionism and empiricism in psychology and between intuitionism and analysis persists to the present day. In psychology, intuition had been concerned with the means by which that which is known comes to be known as opposed to questions of ultimate reality in philosophy. In kantian philosophy, there were innate categories of mind which forced particular categories of perceptual judgement. Also it held a priori knowings of truth - intuitions of such truths as the basic axioms of Euclidean geometry. The implicit metaphysical differences remain among pyschologists as they remain among philosophers: is there a reality to be discovered or are there multiple realities to be constructed ? Those who take successful probabilistic prediction as equivalent to knowledge would maintain that they never do know anything with certainity and indeed that one cannot know anything with certainty. On the other hand, harmonious certainty has been the hallmark of intuitionism for cen

Some of the seeds of synthesis I have discovered (experiments are ongoing to give fair consideration and enlighten ourselves) so far between sciences, religions, philosophies are listed below for the lovers of truth and wisdom - Synthesis of mathematics - Category theory (Grothendieck, Saunders Maclane) Synthesis of religions - Theosophy (Helena Blavatsky) (A mathematical expression of the law of Karma or cause and effect is in my thesis) Synthesis of philosophies and Human Knowledge itself - A treatise on seven rays (24 Books of Djwal Khul and Alice Bailey) Synthesis of pyschology - Psychosynthesis (Roberto Assagioli), Humanistic astrology and soul-centred psychology (Dane Rudhyar, Alan Oken) Synthesis of ancient systems of Yoga - Synthesis of Yoga (Sri Aurobindo),Auroville (Experiment of synthesising city), Agni Yoga (Nicholas and Helena Roerich) Synthesis of agriculture - Permaculture (Masanobu Fukuoka) Synthesis of signal representation - Functorial Signal Representation Synthesi

If one does research on the sayings of almost all great minds they have indirectly pointed out that all ideas came to them through intuition. Then in this post, let us see what a mathematician or a scientist has to say about intuition in the sense how he/she interprets the word. Mathematicians have been concerned about induction, inference, and intuition in their own field, not only because they bring in invention, innovation, and discovery just as all other groups of scholars do, but because certain aspects of the field of mathematics are very closely related to pure logic and the link with philosophy is extremely close. Blaise Pascal famous for the Pascal's law and the unit of pressure in physics which is termed after him had to say the following which clearly shows that he is emphasising the fact that intuition lies beyond reason. "The heart has its reasons which reason knows nothing of... We know the truth not only by the reason, but by the heart."  Polya (1954) finds

What is this blog about ? This blog is an outward expression of my inner experiences on a journey upon a path onto which I had consciously decided to walk starting sometime in 2005. After earning a bachelors degree from a local university in engineering I had frustration of not having learnt anything substantial or rather having learnt only superficially. So  I made a decision to go into the very depths of everything (today after many years it can be termed as examining the causes underlying the situations rather than just addressing them at the effects level). It was a decision not to accept any body of so called knowledge (therefore I used to keep it only as a working hypotheses) from any source without understanding it (today I consciously recognize that the very faculty that made it possible is termed as intuition and the Knowledge obtained through it is what Sri Aurobindo says as "The Knowledge by Identity") and being convinced after a thorough consideration. The feeling

 The purpose of this post is to put forth theosophy (or Brahma Vidya in ancient India) as a branch of metaphysical and moral philosophy: not as fairy tales or conjectures of exceptional individuals popularly known as initiates in theosophical circles, but as purely divine universal ethics, the exercise of which in daily living unfolds the latent divine powers in man. In its practical bearing, it inculcates certain great moral truths upon its followers, and all those who are true to their own conscience or lovers of the truth.   Following some arguments of Bertrand Russell a modern philosopher, the way in which he proposes and defends analytic philosophy, I shall attempt to briefly exhibit theosophy a.k.a ageless wisdom as the perennial source of modern academic philosophy. Humanity ever since the dawn of civilised races has been challenged with problems of two major types: The first problem has everything to do with the nature especially mastering of natural phenomena and forces govern