When humans dream of Algebra, nature crafts our Geometry!

A Collection of thoughts on Mathematical Languages:

Natural Reflections on Algebra & Geometry

This post is inspired by an intriguing thought that disturbs me often when I try to relate the beauty of algebraic notions and their syntactical complexities with the physical dimensions and measures of geometric nature. Geometrical shapes of vivid complexity is all over us. Algebraic knowledge becomes richer and deeper day by day. 

At the outset, algebra appears to me as the attempts of human mind to find an order within the physical and its own humane cognitive nature. Hence at times algebra becomes associative and at times abstract. Geometry is mostly occupied with unique physical operators for measuring nature and natural objects. As human mind and its boundless imagination works in both the streams of knowledge, they always explore anew territories and often produce complex functions and abstractions. Humankind crafts nature in their own reflection. 

As we know, our innate tendency to imitate nature has been one of the fundamental driving force in all our scientific, artistic and engineering initiatives. This tendency gets transformed into further advanced forms of knowledge as we apply our reflections of nature into our labor process. This tendency can be seen in the mathematical languages as well. Our mathematical observations about geometry has helped our investigations to find patterns in the field of numbers and algebraic symbols. Is there a difference in the nature of measurement in Algebra and Geometry? Though the approach remains the same the challenges differ widely.

Some metric level contradictions in the nature of Algebra and Geometry

I was always perplexed about the physical differences between various elementary mathematical operators like addition, subtraction, multiplication and division. When I add entities of different properties, the sum never accumulates in nature. It occupies a physical space less than or equal to the nature of individual entities. 

Taking an example, if we add one mango and an orange in a physical box they take space as equal to their physical dimensions. In the representational mathematical space also they occupy distinct locations. When we take two mangoes here they occupy same space in the physical box whereas they add on to the same quantity in the representational space. 

The question is whether the mathematical symbolic space is as accurate as the physical geometrical space. For convenience we may denote this representational space as algebraic. The algebraic space is often limited by the limits of our abstractions and the capacity to associate them whereas the geometric space is challenged by the scope of observation and the limits on the minutest quantum that we can reach. 

Numbers are the base constructs of the symbolic space. They become complex when the physical world in the scope becomes wider and deeper. We think of complex numbers and complex plane when we reach a limit to measuring the diagonal of a triangle made of single unit edges. Then the new symbol enters our mathematical vocabulary. This is just an example. Similarly when we think of trigonometric measurements, we find new sinusoidal and cosine patterns emerging in symbolic space. It is a new synthesis of physical and symbolic space.

Next question is can symbolic space travel ahead of the physical space. In other words, can we dream a physical entity before experiencing its real physical nature. I must say that at times yes. It is not magic or miracle. It is because of the intellectual capacities of human cognition and the power of knowledge to expand the horizons of our recognition. Each strides in the cognitive skills of human mind and our social experiences enrich our mathematical languages, whether they reflect our knowledge about symbolic space or physical space. 

Nature of Evolution : A Note on the boundaries of Darwinism

Self Similarity of Cognition

Self Similarity of Cognition

Do we perceive the grand nature as a reflection of our innate self? This question may sound philosophical at large. To make it clear, let me frame the question as: how do I conclude that the society is evolving? Are we comparing the history of life with our present achievements? When we examine the organs, bones, muscles, movement patterns, anatomy, cell structures in context of evolution, we tend to compare them with human specific configurations. Is this model quite subjective? May be it is true that this reflexive element is an inevitable aspect of experiments. My point of view is not towards attributing subjectivity to the methodology of observation-ism in scientific experiments. 

Rather, I see an aspect and a drive for self-similarity in many of the human cognitive activities. Going further, this self-similarity seems to be driven from an innate instinct of nature itself. Our cognitive mind is essentially seeking self-similarity in all the material objects of life. Even its cognitive processes are affected / influenced by this instinct. Our art works, aesthetics, and our artistic creations are many at times influenced by nature. We see mimicking nature a prelude to many original creations. Even highly original engineering and aesthetic works are inspired and driven by nature. This all suggest an inclination towards self similarity in our cognitive mind. This self similarity at times makes measurement of our experiences highly subjective. Thus a metric for self similarity is worth a mathematical pursuit.

+Gokul Alex 

De-Cognition: Social Media and the Information Architecture

Demystifying the Internet Pragmatism: A Cognitive Approach

Any media ecosystem evolves around the currents of communication. How different is Social Media from the mainstream media and the traditional formats of a communicative medium? The levels and depth of commoditization has liquidated the reach of communicative rationality in the media formats such as Television, Film, etc. Social Media has evolved around the concept of social networking and the inherent non-linear and decentralized nature of Internet. Social Networking as a concept has roots in Sociology and demands a wider narrative. To analyze Internet as a Public Sphere, we need to demystify various abstractions to reach the political economy of the worlds largest producer and consumer of information.

Can Social Media, with its base in Social Networking topology has always offered a potential for becoming the next generation cognitive network. It has even been visualized as the axis for a semantic web where information becomes a self organizing network. Is this technological pragmatism anywhere near real life possibilities? If not, why so? This is the vantage point of this critique. Why do we need this much of information in Social Media. What is the driving force behind the information architecture and the accumulation of information in the social media space. Big Data and the information overloading has becomes the prime movers for the Social Business. Social Business has been predicted as the game changer in the information technology landscape. Thus it is a big business now. 

The question is has the cost of business sacrificed the potentials for developing cognitive networks around Social Media. When it comes to the information architecture, we need to know the basics. Who is the producer of information. It is each of us. How is the Search Engine giants generating wealth of information and the uniform resource locators (URL). The URLs act as the nodes in the information graphs. It is each of us, consumers, who creates various paths around these nodes and make them alive. This is largely forgotten. Thus the real value of information is generated by the end users like us. Information machines are thriving on the cognitive networks created by our information production, consumption, circulation and re-production. Search Engines are only one side of the coin. The present generation content aggregators are also only dynamic nodes of information. 

Cognitive networks created by us becomes commodity in the split of each second. This commodity again circulates among the networks of us. In each turn and twist of this information nodes and network, it generates money, the real money ! Thus we are working for a global system of finance capital virtually not knowing the sweet sweat that we shed in front of the the dumb terminals of computers. It is indeed a great state of hibernation or a glorified state of social pathology. 

+Gokul Alex 

Some Pathological Trends in the Social Media

On the Ideological Apparatus behind the Social Media Measurements

Social Self? This supposed to be 'oxymoron' has been with us for quite some time now. Now we believe that the more we are social in social media, the more we become identity conscious and identity empowered. May be a small leap of faith for the humanity and a giant step for the technology. What is happening in this flurry of affairs? 

Now we have conceded that the Social Media spread across the nation states has generated a huge volume of data about the humanity. May be this is the data store about the people with the access to internet and the world market forces believe that they are going to the the drivers of growth for the decades to come. Hope their predictions and reasons stand the test of time. 

Looking at the state of Social Media, now we can see that every other social media preaches to measure our online presence and to rationalize it. In other words, formalize our social self. But a moment please, what is that we are doing? Are we becoming more social and empathetic towards each other? Are we becoming more conversant in real life. If not, we need to look beyond the social media metrics that projects our presence in scores and dashboards. 

The Social Media is making us more and more eloquent about our thoughts, our connections, the number of friends in our network, the number of different profiles we have, so on and so forth. In other words, this semiotic framework is centered around each of us. Thus each of us becomes the target for different market segments. It is a really intricate mathematics where an end node is being referred by different graphs and each graph generates a different visualization out of the same node based on its diverse semantic potentials. Hence each of us becomes the perpetual sources of information for various networks and they generate insight out of our primary, secondary, tertiary and virtually an infinite set of semantic connections. As my interest is least on this mathematical modelling let me go beyond this abstraction.

I have just stated a problem provoked by my endless nights wandering in different social media systems to create an inflated ego. Now I am working on resolving this illusion and beyond the semiotics of this media ecosystem. Rather than being inflated about the semiotics of this ecosystem  we need to make it as conversant and communicative as possible. Here comes relevant the study of communicative rationality devised by Habermas. Rationality and reason can only decipher the signs and lead us to the real world of affairs. This post by no means is a call to boycott social media instead to understand the ways not to get paranormal by its illusory apparatus. 

Work of Art and Inspirations : A Late Night Argument

Night past 12, I was indulged in a water color, quite unknowing what is next going to happen in my canvas. Colors were shading and fading in my palette and the picture alike. Initially my intention was to use my brushes only in vertical strokes. I succeeded to a greater extent up to the middle. But as the colors began to dominate my senses, I gave my self to the freedom of the stokes. Vertical strokes became rectilinear  curves became horizontal sweeps, horizontals become horizons. And it went on to become a collection of a lot of lines, colors, shapes and shades.

My interest is not on the end product called an art work, but on the process of creating a painting  How are the lines leading the work of art to some specific direction? Is there a sense of beauty that leads and directs lines to take certain shapes or position. Is beauty an end in itself. Why should an art form be so much obsessed with beauty and its nuances. I feel that beauty is just an immediate realization of an artistic process. 

Art and artist transcends the demands of beauty by a necessity and urge to create a logical formation of lines, shades, edges, curves, depths and so on. This in a way leads lines to take more complex forms. When I had a lot of places in paper, lines had a different grammar and syntax. When the colors dominated the canvas, colors were more subtle and nimble. Thus I believe an art and artist is inspired by the totality of the conception than the urge of a pleasing experience of beauty.

+Gokul Alex 

New Languages of Mind : Beyond Philosophy and Fiction

Philosophy and fiction, it began with an attempt to negate the existence of philosophy. 
Is it a dead cat? Will it come up again and again with nine lives ? How will we posit philosophy in the quest for knowledge. Is it always congruent with the inquisitiveness to find what is truth? For sure, this question can never be philosophical in life. It can be ideological but I will have to rational in that attempt. 

Coining an allegory of a dead cat with philosophy, one of my psycho-analytic encounter is described as below. 

A corridor of myself
A window where I hug and hung my shadows
I am there again
With cats dead and with nine lives

Cat in his selfish tone said ...
I am born again to die
She smiled and murmured
A dead cat is just born again

She saw those words in a dream. Voices that speak themselves. Words into voices, thoughts bleeding themselves. Words into shells and snails of mind. As if they are leaving their ocean and hunting her down.

A dead cat, neither black nor white; it is having a mesh of letters all around its body. Those words look engraved in its body. It smiled her through eyes and cried aloud through its lovely small cheeks.

Again and again, she is seeing dead cats in her dream. She saw them while standing in the long queues, sitting in lone gardens, walking up and down irritating stairs and so on. Dreams that she see awakened. She is not sure what is real and what is not. I would like to omit the expression surreal because it has some tint of real in it. Now she begins to ask how can she see a dead cat and a stream of words together in a dream. She ask herself  is dreaming an act or an act of denying truth or not at all an act in itself? She took a pen and started hunting down the dead cats and paper tigers.

In the nakedness of truth
A lie is born
In the weakness of my genes
My death cells are born
In the hatred of my body
My mind begins to bleed
In the cavities of my heart
My flowers begins to bloom
In the boundaries of my lies

She laughed aloud and smiled at those shadows. She tore those papers into pieces. She wed the thickness of her summer blanket and started her cat race. In the dilating moments of her eyelids, those cats vanished in dream planes. Into their own space times ...