Resplendence

The famous words by Morphius in Matrix : “What is Real?” I was thinking about that, (haven’t we all at one point in time?) when I was reading some topic in AI, I pondered it and when I gave it the thought I could spare at the moment, I changed my status message to “What is, is not what it is, what it is not, is also not what it is” some complemented me(my mom was first) but most others asked “what does it even mean?”, this

Imagine a point, now this point has no awareness of itself. Why? Because it does not even have an existence, now you’re wondering what I am even talking about, but remember a point does not have dimensions, and what does not have dimensions, does not exist as, at least not as  matter or any form of interaction ( the slightest disturbance by the hypothetical gravitational waves also causes a change in dimensions of object matter) , so a truly zero dimensional object is only an imagination (which it truly  is, because this paragraph began with the word “imagine..” ). So now imagine a Line, now I claim a line does not exist either, as geometrically speaking, a line is just a two dimensional a set of infinitely many points. Going further, nor does a plane exist (which contains infinite-squared number of points ;-P, read about cantor sets ) . But let’s take just one more step further, and make a 3-D space, is it hard to imagine it? I hope not, the world we perceive is three dimensional, of course. So something happened here that transformed the in-existence of two dimensions into existence by just adding a dimension (that which had not happened last two times) into, turning it into some easily perceivable “world” around us. I believe you will not find it difficult now to extrapolate to fourth dimension, let’s call it time.This addition of a fourth dimension added a temporal aspect to reality, a “life” if you will. ( Digressing a bit, have you wondered why we call it “animation”? ‘Animate’ is to ‘bring to life’ (as we use “an inanimate rock”), and some how the cartoon on the Sunday paper is not ‘animation’, but the one that runs on television is,  because it ‘moves’, changes in times, thus even linguistically speaking, adding the time dimension ‘brings life’ ). So far so good, from a point that did not exist to line which had one extra dimension and also did not exist to time, down to fourth dimension which adds “life”. Now add a dimension more, physicists have called it many things, including “probability”. A physicist, Gerard ‘t Hooft  called it the space-time fabric.

But that is beside the point, as the point is, if there exists an intelligence, a self aware entity in this 5th dimension, will it call the world we perceive, inanimate? Do we want to call it inanimate, or call it something that exists only as imagination ? Well some do, there has always been a school of philosophy (and physics and mathematics and theology and drug addiction) that claims that the world is not real but only exists in our imagination, read about Rene des Cartes’ philosophy(for the benefit of those who didn’t know: he claimed “I think, therefore I am”) ? He associated the existence to thought, though I think he did not mention what he meant by “think”, which is topic unto itself. It might be funny if we note that we call the system of dimensional measurement the “cartesian” system. A system of representation of an entity in n-dimensions with a vector with n values.

We have digressed enough, to re-iterate my question, is existence a perception in finite dimension? How about interpolation this time? The idea of watching things in dimensions that have value between 2 and 3 or 1 and 2? I can’t help but mention Cauchy’s Snowflake and other fractals here. Do they exist or is it a simple mathematical manipulation to represent something that cannot be explained otherwise? Let’s, for a moment think they are the latter. If they are only a mathematical convenience, then why are any of the dimensions not a just a mathematical convenience?

Hmm, our discussion till here has left far too many lose threads in the form of unanswered questions, the answers to which are both inconclusive and arguably unattainable. There is a very easy avenue out of this, I feel, and that is to decouple the idea of existence from idea of dimensions, and instead associate reality with conscious assimilation of the world . Here I chose these words that I have, for a reason: I want to steer clear of the “reality is perception, and perception is reality” ideology, but retain in essence the the decoupling of physical world as we see it, from what we call real. Let’s delve a bit further on what I meant by “conscious assimilation the world”.

You must have seen many 3D- movies, but you “know” they are not really in 3 dimensions, but an illusion that causes them to display an apparent “depth”. What gave you this knowledge is your understanding of the world that is not simply what your sensory percepts input (this lack of one-to-one correspondence motivates the decoupling). We know that our picture of reality is somehow more, a step further in what we understand, in my word: “assimilate” the world( In his book “On Intelligence” James Glieck gives a very elaborate and interesting view on this) So reality, in my opinion is that abstract representation, that gives meaning independent of percepts, and also at times independent of the subject matter in front of us. Also it is surely not “mind”: mind is more akin to an “algorithm” and possibly a meta algorithm, but it is not understanding in itself, we can go as far as to say the output of this meta- or meta-meta-algorithm, which traverses our various levels of consciousness, giving a “depth” to the small dimensional world fed to it by our percepts, and this is makes  the “it” around us that i refereed to in my status message that day. The system of thought, the ethereal flow of that understanding up and down our hierarchical consciousness is what makes the world around us, it gives it dimensions, it gives us glimpse into what “is”.

When I start a blog I always wish to keep it purely in one genre, but I always end up mixing and it is at this point that I must talk about the Hindu philosophy. This philosophy has always been assaulted upon for being vague, for not “giving out” what it wants to say, consider for example what Ayn Rand says about Indian philosophy, though I do not remember the exact text now, I remember that she was against the idea of describing God as not what He is not, rather than  describing in precise words what he is, she called it a flaw in logic. I do not know whether Miss Rand knew about Boolean algebra, but contra-positive also has the same truth value as implication. By describing what it is not, the philosophy is deliberately blurring the idea, it telling you to stop searching in avenues that are fruitless, it’s like NP completeness, either you go head long into attacking the problem of P=NP, or you just leave the avenue and search the greener pasture. Describing God, I think is something similar. Here’s how: from what I wrote in most part of  this blog, reality is neither precept, nor simply a thought, nor is it conjuncture weaved to explain the vast complex world around us. It is a higher level assimilation that cannot be framed in any particular analogy, or described in temporal dimensions.Hindu philosophy has always equated many deep concepts, in most of our texts, words “It”, “truth”, “Real”,”Reality”, “Existence”, “Universe” are all synonyms to the generalized word “God”, so describing the “reality” as an abstracted assimilation the way i described is not a flaw in philosophy, but a contra-positive.

As a parting thought think of what this self referential sentence means: “As you are reading me, I am just a bunch of state changes in the configurations of the neurons of your brain”
Here I must conclude. I know this has been a long read and the material has spread across many subjects not all of which may be understandable to everyone. But it has been my effort to keep it general, and therefore please do not gauge my knowledge either in Math or philosophy by this blog. And for the curious: I was reading “Model Based Agents” in AI when this blog started brewing in my head.
Thanks for reading, Adios!

This blog is about a very important aspect of mathematics, in fact so important that we apply this concept in our life consistently. It is about “transformation”, in this case, viewing the life as something else to make certain emancipating conclusions.

My university required me to submit my degree certificate, so my parents obtained them from my previous university and couriered them to me, which arrived yesterday. Th last day for that submission being only 3 days away I was pretty tensed, so I hurried over and submitted them, after finishing the formalities I went to study center and was securely packing the degree certificate, along with my transcripts (which listed all my marks from first to last semester), when I read that certificate ” ..he  has been declared eligible to the award of Bachelor of Engineering degree in … “, a sense of exhilaration coursed through me reading that. In the rush of the life we so often forget what path we have tread to come here, how eventful that path has been.

Now I was rooted, I re-read all my marks cards, and certificates from tenth standard till final semester, sure these are not the most impressive marks one can see, but they were mine and those bunch of numbers were actually  life buoys in the nearly forgotten of sea of time that lies behind me. To a prospective employer or someone similar they are “metrics” to gauge me, but for me they are the quintessence of a small struggles,  battles at times, in the past, some won, some nearly lost, but gory all. I saw the pathetic marks I had obtained in Mu-p, I remembered the struggle I had put up to pass that subject and yet maintain FCD. When I saw the tenth marks card, I was filled with memories of preparation, of reading History on top of Arun’s house terrace (I still get nightmare in which one day I wake up and realize that day is Social Studies exam and I have not prepared at all or something similar). Then I saw the Chemistry marks in 12th, I was so reminded of Babuji’s classes and the pages from Physical Chemistry text.. All those were tense times, moments when those exams looked like insurmountable obstructions, they were moments of complete panic and near hysteria,  now naught more that a  speck in the past. When I sit to think of those exams, the severity of the moment comes back, not diminished only distanced, somehow dulled.

While mentioning this to a friend, Swathi, I came to a comparison of this phenomenon. Life, I feel, is like mountain climbing. There are moments when you come to face to face with a large boulders with flat faces, at the moment the boulder fills your vision, you find only the sheer rock in front of you and an abyss behind, you feel that nothing at all matters other than getting past that boulder, nothing is more important, and you give anything to get past it because you fear that nothing exists but this challenge, then struggle against the cold rock, bruise your limbs, you toil, you sweat and you bleed, nearly miss it and then, in one glorious moment you peak it, then the moment is past, you keep walking forgetting your terror of abyss and rock face, you forget the moment of exhilaration, you only watch the “present” because someone told you it’s a gift, and you struggle ahead forgetting that adrenaline of climb that terror, only paying attention to the path you’re walking on. . But at one point you stand, braze your feet and look back, those rocks and boulders and abysses, are still very much there, and when you can think, even the terror you felt becomes so real again, it course through your veins, teh you realize the moment has passed, that you have made it, you have surmounted it, the difficulty that seemed to overpower you behind that rock face is very much real but  real only in your head, the rock itself is distanced, now a pebble in your vision. And in those moments when you stand and breathe and look back do you realize that no problem that threatens to over power you exists outside of your head, In that moment when you realize this, I think, you truly live.

This is the transformation that measures our life, the transformation from the terrified squealing climber behind the rock face to the man standing after having conquered it, realizing that yes the terror was real only as real as you made it in your head. It is not scaling the entire mountain, nor somehow making it to the top, but realizing this. The realization that there were many problems in the past and there will be more in the future, I believe, is the true emancipation of a soul.

Thanks for reading,

Here’s to Life,

Cheers!

When one is postulating correlations or causations extant in reality, one should always remember that the human brain is mainly a pattern recognition engine. And it is such a persistent pattern recognition engine that it often perceives patterns where none exist.

Jeff Walther

Yes,  our brain is a very good patter recognition engine:

I recognized a pattern in my “Algorithm Design” textbook, by Kleinberg and Tardos:

(Chapter 8, NP and Computational Intractability, Section 8.3, 4th paragraph under “Problems and Algorithms)

last sentence of paragraph:

We say that A solves the problem X if for all strings s, we have A(s) = yes if and only if  s∈X

On a similar note, I fund this pic somewhere on the web:

That’s all for the post, keep matching patterns,

Cheers!

“The discussion of which is beyond the scope of this text” I read this line first in my 8th standard mathematics text. I wondered when I will actually come to the level where I will read those mysterious things that are beyond the scope of the book I was holding. I forgot what the text was discussing so I didn’t found out if I ever came to that level. And 10 or so years later here I was studying Applied Cryptography, and one sentence lashed at me again from a text: ” the discussion of which is beyond the scope of this book ” Wow! I think even the best brains in this world, in mathematics  in physics and in philosophy, also get stumped by this sentence every once in a while. As Socrates said “The more a man knows, the more he realizes how less he knows”. By the way,this can be mathematically accurate only if we consider that  ”all that is to be known” as an infinite set, or simply that knowledge is free flowing ad infinitum to quote the opening of Ishaavashya Upanishad of Yajur Veda: “Poorrnamadah purnamidam, purnaat purnamudachyate purnasya purnaamadaya purnamevavashishyate” (This is Complete , this is Complete, from that Complete a if a Complete is extracted, a Complete remains, adding to that Complete leaves it as Complete (as before), shanti shanti shanti).  I am sure Adi Shankarachrya, while writing this made sure to call it as just ‘Complete’ and nothing more, possibly to leave the lesser mortals like us to eternally contemplate what he was referring to by ‘Complete’, was it knowledge, the Brahman, the Truth, what was it that will ever drive man in pursuit of that which cannot be completely extracted?

PS: I did not intend to make this quick post philosophical, but well, here it did become one..

The gentle zephyr sifted through the northern window of the citadel.  The reclusive tower of the citadel rose eight fathoms and a half above the tallest roofs of the beautiful white city of Nossar. The city was built by the adept hands of men Linar. It was said that the mortar mixed by the men of Linar held magic. The formidable city had withstood the sands of time, it had seen thousands of winters, dozens of great wars, and The Fault, and this was the testament to the claim.
The guards in the citadel were drowsy; the keen wind was soporific, obliterating any possibility of an alert watch. They were the best of the archers in the city selected and trained by the masters of The Yard, they were keen of sight, could gaze into leagues of battlement, but they were no guards. They were summoned by the king and commanded to keep a watch for a brown eagle flying westwards. The convoluted command had not given place for much doubt, for the air was rife with the rumor that The Sybil had spoken. The command to watch for this omen was all but unexpected. The connection was uncanny.
The high Seer seldom spoke, but when he did everyone took notice, for the great orb never lied, and as skeptics  were noticing, it spoke naught but of foreboding ill.  The last The High Seer had spoken it was in a spring two hundred and forty four years ago. The whole kingdom was thrown into a torpor. The then king, King Enueal the third, had ordered every host to ready for the eventuality, every able bodied man of the kingdom was armed, every armoury was emptied. The war beasts were untethered, and readied for war. The husbandmen of country were asked to fortify their villages. Hosts were armies were readied all through the Empire, from the Northern high passes to southern sea, from the Forest in the east to Fiery mountains in the west where the dragons.
The Empire had all but given up to mass hysteria, only the king’s rule had kept the Empire from disintegrating. He had journeyed through the empire under sun and moon, against biting chill and scorching heat, and his captains had been the sinew of the effort.
But no preparation was to stand against the fate, and the doom did befall. The Seer’s words were chilling when they had come, but they were accurate to the last syllable. The Fault had occurred. But this time, the king had taken up the challenge more surreptitiously. No one knew the exact words The Sybil had spoken, but the terseness was no less than last time.
The Empire was waiting with bated breath. The very air seemed to be heavy in the Upper Hall; the assembled captains had come back to report in on the errands they were sent on, in the preparations. But far away from the stifling air of the expectant city, far away indeed from the heavy wi-fi traffic of the city sat a Sage, keen blue eyes, a fleck of frost on his brow, gray and wrinkled into a thousand lines of age. The robe he wore was white but somehow it looked refulgent against the gray of the bower he sat in. He had chosen this place, under the white cedar tree, for the tranquility it offered. There he sat his fingers lithe on the keyboard keying in the final commands. And when the packet began to flow in, a smile broke upon the thin lips. He knew exactly what the seer had said, “Every ISP shall fail, every server shall crash, every table Reset. No Ethernet shall stand. The Network shall fall”, and as the fate would have it, he now knew exactly how to avert this crisis.

PS: The inspiration for this write up comes from Lord of the Rings – JRR Tolkien, Computer Networks – Andrew Tannenbaum, and a boring ETM Lecture of a Friday Morning, and as you might have guessed by now, I am not writing any new Novel, the title was simply a last thought, to complete the craziness.