Friday, 18 March 2016

Complex numbers and algebra of human life

Those who have studied Mathematics at college level must have studied Complex numbers and most of the engineers would have used them to solve many problems. A complex number is expressed in the form a + ib where both 'a' and 'b' are real numbers and 'i' is the imaginary unit, equal to square root of −1. In this expression 'a' is the real part and 'ib' is the imaginary part of the complex number. The real and imaginary parts are as different as apples and onions. They cannot be mixed up by direct addition or subtraction and there are special rules for their multiplication and division. What these complex numbers have to do with human life?

It is generally believed that every living person has a body and a soul. The soul or आत्मा leaves the body at the end of its life and goes to heaven, hell, स्वर्ग, नरक, जन्नत, जहन्नुम etc. or gets into another new body taking birth or just rests in peace or may become a spirit and keep haunting. These are some divergent common beliefs. However, what is the role of the soul or आत्मा  when the person is alive?

Scientists mainly influenced by Physics have not found any practical method of detecting the soul or आत्मा or measuring its properties. So they do not have any scientific evidence of its presence. As per the present medical knowledge, all organs of the body function or do their कर्म  as instructed by their brain, another part of their body. The brain has a rational part intelect (बुद्धी) and an irrational part mind (मन). However, we are also told during our upbringing that consience, जमीर, विवेक , nature (स्वभाव) of the person nurtured by conditioning during upbringing (संस्कार) play a dominating role in deciding his actions. These are mostly associated with his soul or आत्मा. Rather that is the main driving force in many situations.

This combination is described in a complex number theory by a brilliant mechanical engineer, Shri Raghuveer Rustagiji, who is also a philosopher and योगी .  He had once suggested that nothing in nature is simply scaler but a vector quantity, A+iB. Which leads us to a combination of a real no and a virtual or illusionary quantity. To see it in part would be misleading the self.

This was further discussed in quite interesting as well as intriguing manner as given below.

Mohan Rao :
 I consider that the totality we all live in has plenty of our sensual perception on the one hand, and whatever is beyond perception which we may call the ‘Absolute’ or ‘what makes up the total’ on the other. To use math symbolism we may note the totality as I + iF where I stands for the Infinite (i.e. Infinite or what lies beyond our perception; I is also the subjective pronoun one uses for identifying one’s own Self is an interesting co-incidence) and F the finite part of the ‘totality’ which of course is our perceptual illusive reality, hence iF.

There are two ways of seeing ‘totality’ of our existence. As a worldview, one can live inside the finite world, the one we have put together by our sensual and analytical knowledge and ignore the ‘Infinite’ or the ‘Absolute’ which would then be an atheistic worldview and one can be perfectly happy in it, although people like Buddha have said that such a world is the cause of our sorrow. On the other hand, one can have a worldview centric to the Infinite and try to achieve self-realization by a process of meditation and thereby claim that they have the truer world devoid of the virtual or the illusive sensual world in it. If one doesn’t compartmentalize one’s worldview into either of these ways, by default, we live in an I + iF world and be either perfectly happy with it or lament about it pointing to the sources of misery in the finite world.
Ashok Malhotra:
  Frankly, I have not devoted much time on this "discovery of truth" perhaps because, like all others, winning the daily bread took all the energies.
  There is no doubt that at any given time n space, there are multiple realities and platforms. Long back I had read that it is impossible for the human mind to comprehend God, Universe, Life, Nature, Reality, call what you may, because the unit of our mind is much bigger than theirs. It's like measuring a cm with an inch scale. That's why Krishna had to "reveal" to Arjuna its virat roop, or the rishis talk of attaining higher levels of consciousness for salvation n truth, kundalini जागृति etc.
   So Sir I don't even try to understand these truths n realities from our finite angles, as we know them, though mathematically I would have preferred the equation to be F+iI than I+iF since the finite or reality part can not be in the virtual zone, as we, being finite, may all vanish in the virtual zone without a trace.
      By the way, I am curios to trace the path Einstein went on for his  "Theory of Relativity", if you have any references.
Anand Ghare :
We may call our being as I+iF or F+iI, but 'I' is said to be 'infinite nothingness,' whatever it means. So it cannot have any finite value. F has certainly some sensible value and we keep trying optimising it.
Ashok Malhotra :
Another thought on F+iI 's existence, perhaps a postulate:
       In nature, every thing, living, nonliving, micro or macro cosmos exists in duality as mutually dependent/supportive. Nothing exists in isolation, even the speed of light, time, matter, many other constants, space, gravity  etc long thought as unique values exist & vary relative to something else. So we may be on a right path of thinking about F+iI..

Mohan Rao :
Re your question regarding Einstein: What Einstein has taught us is that whatever we hold today as incontrovertible proof of something may be foolishly outdated as time moves on, in the same manner that Newtonian mechanics became to be known as a very limited worldview of the clockwork of nature when Einstein started developing his theories on relativity. In the I + iF formulation of totality as we discussed earlier, alas, we have already seeing holes such as in Swiss cheese.

Our first exposure to Einstein’s work : Among his views: Motion through space is a meaningless concept; only motion relative to material bodies has significance; physical laws are independent of the frames of reference, etc. etc. The wellknown findings he came up with relating to relativistic effects moved us from Newtonian worldview to the larger universe as they saw it at the time (i.e. space-time continuum, gravitational effects, relativity etc.). Peeling this layer of the totality by Einstein changed our view to a great extent. I remember, at the turn of the millennium, he was branded as the Person of the Century by a noted newsmagazine (interestingly followed by Mahatma Gandhi in the second position).

At a personal level, it seems to me that Einstein was deterministic and his statement that God plays no dice is wellknown although this view came back to haunt him as the Quantum Mechanics grew later on and randomness in nature at the quantum mechanical level and uncertainties came into the evolving view of the universe.

 With this background, it is an interesting topic to figure out what these developments do to our I + iF formulation of totality. If we ignore for the moment the universe prior to the big bang and the fabric of space outside of the space-time cocoon we live in since the big bang, pretty much the entire universe seems to be trending to be deterministic and hence finite. The only unknown pertains to the question what else is there in the universe and what might have happened before the big bang. This is the grey zone left where scientists continue to speculate about (already there are tons of work and postulations in scientific literature such as multiple universes, dark energy, further knowledge about the space etc etc.).

On the whole, it is like peeling an onion as I mentioned elsewhere. In the first stage we learnt about the Newtonian mechanics, which served our purpose for a while. When we peeled further, outward from our “terrestrial” reference we found the relativistic effects, which explained the larger universe since the big bang. There may be more peels to pare. Either we may reach a stage in the future where ‘whatever is’ is all pared and we find as the Upanishads suggest, nothing particular to write home about, or we may be into an endless bonanza from an exercise of peeling layer by layer, finding more layers to worry about, more patterns of existence and newer rules of the game to explore etc. The I + iF formulation may finally be unsolvable at which point the I(nfinite) may be meaningless to pursue any further. As Nietzsche discussed denial of God in his works we may be able to say: The Infinite is dead because what is left of it to explore may be so remote, so intractable and most of all may be of little interest.

What the rishis wondered in the opening of the Rig-Veda however would still ring true:
“There was not then what is, nor what is not. Who knows the truth? Who can tell whence arose this universe? Who knows when came this creation? Only that Infinite who sees the highest heaven. He only knows whence comes this creation and whether it was made or uncreated. He only knows, perhaps he knows not” (adapted from translation by Juan Mascaro).

Karen Strong, Author of “A History of God” concludes not surprisingly that a state of “un-knowing” is built into the human condition.

S Dayal :
Einstein statement that God plays no dice ... was re stated by Stephan Hawking.
God, not only plays dice with the World, sometimes he throws the dice, from where they are not retrievable.
Obviously, Hawking is referring to Black Holes.

Ashok Malhotra :
    There are times to integrate n times to differentiate to enhance our understanding. But here we are in the  "nowhere" zone. From holes in cheese-space_time continuum-quantum mechanics-dice throwing-what else. Yes the state of unknowing is built into our nature, as I said the same in different words "measuring cms with an inch scale. The symbol of zero also contains some space.
   So where are we? Lost in all this maze or Godly web. Thanks any way for some  flash lights.

Mohan Rao :
Totality is all there is in the cosmos and beyond.  Totality can be considered either as Infinite, or as Finite. In the Infinite, we consider all that is God-centred, timeless, beginning-less and endless and other abstract notions (scientific as well as theosophical) that we may notice to exist in the cosmos. In the Finite, we consider all that exists in the physical cosmos, including our own place it, the solar system, the planet and physical existence that fill our everyday life. For some, Infinite may be an illusive or imaginary notion, not grounded in their perception of reality while perceived reality is all there is. For some others, Infinite may be the only reality (rather than faith) and the Finite an illusory part created by our sensory perception, limited and impermanent. For some others, totality may be a combo of both Finite and Infinite to various other degrees.

As human beings we are individuals in this totality and each may have differing views. There are some who are hard-wired to lead a God-centric life  for whom God is all there is and there are some to hold an atheistic view and focus only on the anthropic part of the equation. Then there may be some who see themselves as a hybrid of the two and holding either the Infinite as reality and Finite as illusory or vice versa.

To find meaning in life, we need to search our souls to see what line of thinking we believe in or if we find alternate expressions for our being and our place in the cosmos. We need to reflect to ourselves our interpretation of the Totality and find out where we lie in the spectrum of  these  expressions. Like in vector analysis, one can contemplate and quantify the relativity of the Infinite and the Finite in various ways and orient one’s spiritual compass for navigating our lives in different waters. Knowing where one’s spiritual compass is directed to is, from my life’s experiences, helpful for dealing with one’s trials and tribulations. On the other hand, some may feel that they are already aware of their spiritual position and re-thinking all these matters again is a waste of time.

Ashok Malhotra :
Current Sub Subject: Conception and Stretch of "Totality" in the Finite n Infinite Zones, its Connect with Individual Life, or in a nutshell, me n my universe:
           Now, if Philae-Rosetta can land on the comet 67P, New Horizons can fly past the Pluto after a 11 yrs journey and a Russian tycoon can plan to upload his brain to a computer, hoping to "live a virtual life for ever", we might as well be permitted to pHyLoSoPhIsE a bit into these unknown zones, where our peers n  scriptures have also played lead roles.
    As known till now, these zones can be experienced in 3 known ways, though Christianity also recognises service to the invalid as well; 1. Scientific Principles 2. Faith Trust n belief. 3. Bhakti Tap n Revelation.
    As a trained mind in Sciences, only the  mathematics has concepts of infinity, space, time, n penetrated the micro cosmos to a fair degree, rest are only postulates, even the quantum mechanics, theory of every thing etc are not exact sciences. Lets hope the Russian succeeds in his effort on mental replication and we may better understand "consciousness n virtual life".
   The other two means are propped by the Religions of the world in various degrees n forms, quite disconnected from the  "Scientific Principles".
Raghavan Varadhan :
When iF becomes a Blackhole, Totality is nothing but Infinite Nothingness as Anandji would like to call it. Upanishad calls it "Purnam". Raghavan.

Mohan Rao :
Right now, I see at least five ways of conceptualizing totality as under:
Simply we can express totality [T] (i.e. whatever ‘is’) in five ways to start with:

A.  [T] = [I]
B.   [T] = [I] + i[F]
C.   [T] = [F]
D.  [T] = [F] + i[I]
E.   [T ]= [I] + [F]


A: God is all there is. I stands for Infinite, implying he encompasses whatever is, is infinite, limitless, transcendent, supreme, absolute and is non-objective consciousness that shines on us. Totality is all God-centred and that is all there is, [T] = [I].

B: This is a God-centric anthropic view of who we are and how we co-exist with the supreme. Here we recognize that there is an additional component we consider to be a manifestation of [I], the Finite, consisting of all of our sensory knowledge. The finite is sense-driven, subjective, limited  and cannot be considered as either absolute or supreme.  It is an illusory or imaginary quantity, hence [T] = [I] + i[F].

C: This is an atheistic view that does not recognize the God-related components in totality and considers only what are anthropic views that consist of physicalities all of which are considered real and not illusory, [T] = [F].

D. This is a gnostic view that nonetheless recognizes that there things besides [F] that are not human-driven and are spiritual matters as those discussed in the Infinite but intuitive and pervasive, unknown and unknowable and beyond our intervention or capitulation. The latter are illusory or imaginary, hence [T] = [F] + i[I].

E. Lastly, E is the agnostic view, both God-centric [I] and anthropo-centric [F] views are considered real and considered a part of our totality [I] + [F].

If a computer like HAL comes into life in Russia, it may beat us all and find out the meaning of totality and we may have a computer-generated sense of it. One of the postulated ideas in current cosmology consists of countless universes that are more multi-dimensional than the one we have fantasized about. There may be a neo-Einsteinian view of the Totality, the Infinite, virtual lives, 11-dimensional math, travel between universes and simultaneous upswings and downswings in various corners of the new cosmos, etc etc  one day. Knock on wood they say.

I have made myself a toy for this topic to play with. I have two sealed but empty cartons with a slot on the top (like ballot boxes) and have marked it [I] and [F]. As time passes by and as I get new “revelations” I jot them on a note and drop in the right box. I plan to go back to these boxes, collect all the bits and pieces and see if ideas change over time or get outdated because of the Russians (in lighter vein).

I think we should close out this topic at least for the moment.

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