How big is your language?

This blog post first appeared, as written by me, on The Copernican science blog on December 20, 2012.

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It all starts with Zipf’s law. Ever heard of it? It’s a devious little thing, especially when you apply it to languages.

Zipf’s law states that the chances of finding a word of a language in all the texts written in that language are inversely proportional to the word’s rank in the frequency table. In other words, this means that the chances of finding the most frequent word is twice as much as are chances of finding the second most frequent word, thrice as much as are chances of finding the third most frequent word, and so on.

Unfortunately (only because I like how “Zipf” sounds), the law holds only until about the 1,000th most common word; after this point, a logarithmic plot drawn between frequency and chance stops being linear and starts to curve.

The importance of this break is that if Zipf’s law fails to hold for a large corpus of words, then the language, at some point, must be making some sort of distinction between common and exotic words, and its need for new words must either be increasing or decreasing. This is because, if the need remained constant, then the distinction would be impossible to define except empirically and never conclusively - going against the behaviour of Zipf's law.

Consequently, the chances of finding the 10,000th word won’t be 10,000 times less than the chances of finding the most frequently used word but a value much lesser or much greater.

A language's diktat

Analysing each possibility, i.e., if the chances of finding the 10,000th-most-used word are NOT 10,000 times less than the chances of finding the most-used word but…

• Greater (i.e., The Asymptote): The language must have a long tail, also called an asymptote. Think about it. If the rarer words are all used almost as frequently as each other, then they can all be bunched up into one set, and when plotted, they’d form a straight line almost parallel to the x-axis (chance), a sort of tail attached to the rest of the plot.


• Lesser (i.e., The Cliff): After expanding to include a sufficiently large vocabulary, the language could be thought to “drop off” the edge of a statistical cliff. That is, at some point, there will be words that exist and mean something, but will almost never be used because syntactically simpler synonyms exist. In other words, in comparison to the usage of the first 1,000 words of the language, the (hypothetical) 10,000th word would be used negligibly.

The former possibility is more likely – that the chances of finding the 10,000th-most-used word would not be as low as 10,000-times less than the chances of encountering the most-used word.

As a language expands to include more words, it is likely that it issues a diktat to those words: “either be meaningful or go away”. And as the length of the language’s tail grows, as more exotic and infrequently used words accumulate, the need for those words drops off faster over time that are farther from Zipf’s domain.

Another way to quantify this phenomenon is through semantics (and this is a far shorter route of argument): As the underlying correlations between different words become more networked – for instance, attain greater betweenness – the need for new words is reduced.

Of course, the counterargument here is that there is no evidence to establish if people are likelier to use existing syntax to encapsulate new meaning than they are to use new syntax. This apparent barrier can be resolved by what is called the principle of least effort.

Proof and consequence

While all of this has been theoretically laid out, there had to have been many proofs over the years because the object under observation is a language – a veritable projection of the right to expression as well as a living, changing entity. And in the pursuit of some proof, on December 12, I spotted a paper on arXiv that claims to have used an “unprecedented” corpus (Nature scientific report here).

Titled “Languages cool as they expand: Allometric scaling and the decreasing need for new words”, it was hard to miss in the midst of papers, for example, being called “Trivial symmetries in a 3D topological torsion model of gravity”.

The abstract of the paper, by Alexander Petersen from the IMT Lucca Institute for Advanced Studies, et al, has this line: “Using corpora of unprecedented size, we test the allometric scaling of growing languages to demonstrate a decreasing marginal need for new words…” This is what caught my eye.

While it’s clear that Petersen’s results have been established only empirically, that their corpus includes all the words in books written with the English language between 1800 and 2008 indicates that the set of observables is almost as large as it can get.

Second: When speaking of corpuses, or corpora, the study has also factored in Heaps’ law (apart from Zipf’s law), and found that there are some words that obey neither Zipf nor Heaps but are distinct enough to constitute a class of their own. This is also why I underlined the word common earlier in this post. (How Petersen, et al, came to identify this is interesting: They observed deviations in the lexicon of individuals diagnosed with schizophrenia!)

The Heaps’ law, also called the Heaps-Herdan law, states that the chances of discovering a new word in one large instance-text, like one article or one book, become lesser as the size of the instance-text grows. It’s like a combination of the sunk-cost fallacy and Zipf’s law.

It’s a really simple law, too, and makes a lot of sense even intuitively, but the ease with which it's been captured statistically is what makes the Heaps-Herdan law so wondrous.

[caption id="attachment_24742" align="aligncenter" width="472"] The sub-linear Heaps' law plot: Instance-text size on x-axis; Number of individual words on y-axis.[/caption]

Falling empires

And Petersen and his team establish in the paper that, extending the consequences of Zipf’s and Heaps’ laws to massive corpora, the larger a language is in terms of the number of individual words it contains, the slower it will grow, the lesser cultural evolution it will engender. In the words of the authors: “… We find a scaling relation that indicates a decreasing ‘marginal need’ for new words which are the manifestations of cultural evolution and the seeds for language growth.”

However, for the class of “distinguished” words, there seems to exist a power law – one that results in a non-linear graph unlike Zipf’s and Heaps’ laws. This means that as new exotic words are added to a language, the need for them, as such, is unpredictable and changes over time for as long as they are away from the Zipf’s law’s domain.

All in all, languages eventually seem an uncanny mirror of empires: The larger they get, the slower they grow, the more intricate the exchanges become within it, the fewer reasons there are to change, until some fluctuations are injected from the world outside (in the form of new words).

In fact, the mirroring is not so uncanny considering both empires and languages are strongly associated with cultural evolution. Ironically enough, it is the possibility of cultural evolution that very meaningfully justifies the creation and employment of languages, which means that at some point, languages only become bloated in some way to stop germination of new ideas and instead start to suffocate such initiatives.

Does this mean the extent to which a culture centered on a language has developed and will develop depends on how much the language itself has developed and will develop? Not conclusively – as there are a host of other factors left to be integrated – but it seems a strong correlation exists between the two.

So… how big is your language?

Hypothesis of unequal perception

Let’s say there are two people talking: X and Y. X has three kinds of knowledge: Basic, Pertinent, Abstracted. Y has only two kinds of knowledge: Basic, Pertinent.

S₁: If Y argues that X’s knowledge of the abstracted does not qualify him to be more knowledgeable than Y on qualitative terms because it is not useful knowledge,

S₂: If X argues that Y’s lack of knowledge of the abstracted qualifies X to be regarded as qualitatively more knowledgeable than Y, and refutes Y by claiming Y cannot judge the usefulness of knowledge of the abstracted because Y does not have it,

A₁: If Y counter-claims that X’s refutation of Y is simply because X possesses some other kind of knowledge and hopes that it will be useful,

C: Then Y’s independence of the knowledge of the abstracted and X’s dependence on the knowledge of the abstracted are either

• C₁: Meaningless


• C₂: Meaningful; if meaningful, then cannot be established in terms consistent with the other’s perception because there will always be reasonable circumstances in which the claimant can be tautological and the defendant, contradictory (i.e., incompleteness).

Effectively, this conclusion signifies the incapacity of anybody, through any logical means, to establish that there exists an absolute perception that everyone adheres to concerning an arbitrary object.

Here, the assumptions are

• V₁: That the object being perceived may be engaged with the human senses through the knowledge of the object’s function and purpose


• V₂: That the act of perceiving is contingent upon pre-existing knowledge and isn’t therefore a “learning experience”


• V₃: That there is no way to demonstrate the usefulness of any knowledge independent of the perception modality (i.e., if there is no way to establish literally and meaningfully the significance of some knowledge – in the form of grammatically secured sentences or actions – then that knowledge pertains to a logically inconsistent hypothesis. E.g., sentiments.)

An experiment in propositional calculus

Q: Are truths simply objective reasons whose truth-values may or may not be verifiable?

A:

This question seems to possess a native paradox, but that simply arises from a logical error in the semantics: we can’t address unverifiable statements as “truths”. Instead, they are logically contingent statements.

Even so: As Wittgenstein says in the preface of his Tractatus Logico-Philosophicus, “In order to draw a limit of thinking, we should have to think both sides of this limit.” Similarly, in order to establish the objectivity of a statement, its subjectivity must be conclusively denied as well as its independence of subjective considerations verified.

The attainment of these conditions can be explored through Sir Ayer’s verification principle, the tenets of which were established in his 1926 opus, Language, Truth and Logic. However, it must be noted that Ayer denied, reasonably, that unempirical hypotheses may be formed on the basis of empirical engagements with reality. By extension, there exists an inherent denial of any transcendent reality, which in turn eliminates the presence of any objective truths.

At the same time, however, there exist objective literal truths, which are closer to being tautologies than truths themselves simply because they are a repetition of meaning whose propositional variables are actually fixed and whose truth-value is also fixed.

During an argument, negation and affirmation are used to establish the value of a propositional formula. The formula could be any statement whose propositional variables can assume different values. For instance, the statement S has an unverified propositional value.

S: Smoking is disagreeable; drinking is agreeable.

To some, S will make sense while, to some others, S won’t make any sense at all. In order to establish the truth-value of S, we explore the existence of a logical system that is consistent with the value of S being both true and false. This is unlikely because it contradicts our logical framework itself. Then, the next step is to understand the structure of a logical system in which S is either true or false and such that the value of one propositional variable impacts the value of the second propositional variable directly.

In other words, we make S a formula with two variables, X and Y, and find out how the values of X and Y are consistent/inconsistent with each other while they exist in the framework of the same set of logical principles.

S: X • Y

If we now hypothesize that X cannot retain its value while Y’s value is held fixed, then we pursue the negation of this hypothesis in order to establish that S is true. If we affirm the hypothesis, then we will prove that S is false. In the course of either of these arguments, we repeatedly hypothesize and evaluate the truth-value of each, and proceed until we have with a hypothesis that corroborates or denies the parent hypothesis and so renders the statement as either true or false.

However, if a rhetorical tautology cannot be assumed to constitute a reason (because it is a repetition of meaning), and if Wittgenstein’s proposition that tautologies are statements deducible logically and therefore meaningless is true, then the tenets of propositional logic are neither tautologies nor analytic truths.

Moreover, no literal significance can be assigned to logically valid statements according to Sir Ayer! In this context, the existence of any literal significance of logically valid statements depends not on their analytic proposition but their synthetic proposition – as affirmed by Sir Ayer. (Here, according to George Berkeley: “esse est percipi”!)

Frakking in the fog

On February 20, Monday, Chennai was blanketed with a heavy fog that appeared out of nowhere during its early hours. Visibility was reduced to some 20 metres and the sun was completely blocked out. I'm inclined to blame global warming for this occurrence, although I don't know how I could go about proving my point. It definitely wasn't a smog because it didn't look polluted; moreover, if it had been a smog, it should have appeared earlier, too, especially during the post-monsoon and winter seasons.

That's not my point. My point here is to speculate on something a friend of mine, N, claimed to have seen through the fog on her way to college from home: a more than frequent incidence of copulating dogs and pigs, especially the latter. What was it about the sudden change in the weather that could have caused this?

[caption id="attachment_21651" align="aligncenter" width="448" caption="Dogs frakking on a beach"][/caption]

I'm torn between two possibilities. The first is that this phenomenon could've easily been a coincidence. Those dogs and pigs might've done it anyway because the reproductive cycle for female dogs lasts about 6 months each time. Each cycle has four stages: proestrus, estrus, diestrus and anestrus. The second one, estrus, lasts about 12 days and is when copulation occurs. If the animal is sexually active for 12 days in six months, and has an attracted male around her, things are going to happen fog or no fog.

The second possibility - which, again, I have no way to explore - is that the fog might've acted like a curtain that the animals could've drawn about themselves to do their private business. Usually, dogs are more likely to "do it" in relatively secluded areas like parks and infrequently used roads, and during those times of day when coitus interruptus is less likely to occur. The fog just could have been the perfect proxy.

I'm not convinced by the second reason because, well, the first reason seems more convincing and actually overwhelms the argument of the second. At the same time, if estrus and the fog coincided, then copulating activity could've been heightened for that Monday alone. How unfortunate that someone didn't go around the city looking for all those frakking in the fog, and how lucky I am to have a friend like N.

Most of your superheroes are fail.

Superman is not a superhero. He's a normal-sized Kryptonian who, lucky for him, found the planet Earth whose inhabitants' physical powers were inferior to his, whose inhabitants' physical powers were proportionate to the problems they had caused on their home planet. Was Superman a superhero on Krypton? He couldn't have been because in order to have been, the difference between his physical powers and those of his Kryptonian peers would have had to be the same as the difference between his physical powers and that of his Earth-bound peers. And that's not the case.

As an extension of this argument, it can be said that everyone on Earth is a superhero - just that we haven't found a race of beings physically inferior to us.

Another thing about superheroism is a matter of intention. When Superman was forced to leave Krypton, did he chalk out a course for a planet where he knew he could be a superhero? No; he landed up on Earth accidentally. Assuming his story was real and happening in a parallel universe: Superman was lucky. And as far as I'm concerned, intention is important: the end result of all of a superhero's actions ought to have been intended because, otherwise, the uniqueness that comes with being 'super' vanishes. Even theists are unwilling to accept luck for how aimless it tends to be and instead attribute certain events to a supernatural being's intentions.

Just FYI.

The futurity of art

I suffer from a terrible lack of insight. Unless I find that something is structured in a way that I can recognize the structure itself, I cannot "read" it (and I don't know how better to put it).

For example, consider web design. Ignoring the programming aspect of it, anything on the web is designed keeping in mind the content that will be contained on the page. If it is purely written content, the primary objective is to provide the reader with an "environment" that contains no distractions irrespective of how many and what kind of widgets feature on the sidebar(s). The font has to be legible and stylistic at the same time, each post should be clearly demarcated from the next, keywords of the post should be visible to the reader as well as to any search engines that might crawl the page.

Keeping all this in mind, any insights I can and will provide will pertain to striking a fine balance between principle and technique, or requirement and style. However, the same cannot be said of art or creative writing because products in such arenas are products despite any disregard they may have expressed toward principle/technique because they are expressions of individual beliefs and tastes. In such cases, what is insight? I cannot say without a perfect knowledge of the subjective perspectives involved, and even then, things like the indeterminacy of translation limit the "quantity" of insight I am in a position to provide.

However, the necessity of insight persists because, in the absence of such information, development on the copy is impossible. In retrospect, this points to a consequential sort of lack-of-originality amongst those who employ another author's mythos to base their own works upon; at least, it is so that there is only any scalar development and no directional development: the plot will move forward in time or in space, but it will not move in any direction in terms of the ideological elements that it espouses.

For example, if I were a fan of Ludlum's Bourne series and if I were to speak about my liking of van Lustbader's continuation of the same series, then I will be not be professing any opinion on the subject of the series' essentially abstract constituents but only on van Lustbader's writing skills. In furtherance of the same line of thought, the creations of Ludlum will go from being fictitious to being meta-fictitious; van Lustbader's books will become individuations of Ludlum's mythos but can never aspire to become one of the mythos itself.

[caption id="" align="aligncenter" width="510" caption="Magritte's 'The Treachery of Images', 1928-1929, questioned the viewer's perception of reality. The picture of the pipe in this painting is only a metaphysical representation of the pipe; the pipe itself is alluded to by the comment at the bottom."][/caption]

However, the more important deduction is that van Lustbader's works now form the basis of other subjective interpretations, thereby ensuring the propagation of the "art of authorship" as such but not of the articulated entity itself. Someday, the memory of Ludlum's works will fade; at the same time, the mortality of such memories will concern only the processes involved in the creation of the mythos (and therefore only the structured) and not the mythos itself. In other words, the mythos will lose its history but retain its form and function, or its futurity, which will persist in the works of van Lustbader.

That is the problem with structure: its cause is pure principle while its effect is pure technique. Such a particular state of being stresses on inductive memory as opposed to requiring deductive memory: insofar as deduction is concerned, the advantage of inheritable logic is present. Although the inductive nature of logic itself can be disputed, the relationships it derives its strength from are fairly ingrained into our minds because they are the foremost tools employed to deconstruct reality. Furthermore, inductive memory is essentially biological. Propagation, therefore, is limited by natural constraints. (This recourse to human memory also implies that the changing face of art is necessary for a healthy futurity.)

One ear less

How long would humankind last if each human had only one ear, and if it did, how different would the world be?

1. Lack of physical balance?


2. Absence of symmetric infrastructure and technology?


3. "Lopsided" conversations?


4. Dissociation of beauty from symmetry?


5. A much-less messy self-portrait by van Gogh?

Questions on micropolitical subjectivism & frameworks

First off, bounded rationality: this concept I came across in another form in computational linguistics. In the late 19th century, Benjamin Whorf and Edward Sapir put forth their eponymous hypothesis that “the difference in the significance of languages is the difference in the significance of the perceptions of its speakers.” In '57, Chomsky came up with universal grammar: all languages are accompanied by psychological nativism and a poverty of the stimulus.

These rules struck at the heart of the empiricist position of language acquisition. So, by being born with preset capabilities, are we also beset by preset deficiencies that limit the scope of our successes? Here, we come to bounded rationalism as an immediate consequence of the existence of a universal grammar - and perhaps also to Nietzsche's 'Amor fati'. But this is a purely psychosocial argument.

Secondly, structuralism and rationalist theory: here, mathematics avails a solution I've been fond of in the past—John Nash's game theory. Herbert Simon's three steps to arrive at a decision are identification of alternatives, consequences of alternatives, and evaluation of relevance of consequences. All three are modeled on the necessity of a stable system, the condition that finite variables exist, and the condition that only a finite number of consequences are possible. In that case,

1. Does the macropolitical structure transform into a metastructure when it comes to assessing the symbolism of a micropolitical reality?


2. What does that entail?


3. If it doesn't, then is the new mediator subjectivism?


4. In that case, is the purpose of subjectivist knowledge to reconcile the self-reflexive identity against the backdrop of a macropolitical entity?


5. Or, is subjective knowledge purely a micropolitical issue?

This, I think, leads to Carnap's question: can ontological questions have objective answers? Here, as an engineer, I'm reminded of metaphysical naturalism as well.

Finally, the question I find most pressing is whether or not it is necessary for us to adopt a framework - a structuralist tool - in the context of which we view this world. For example, consider the statement "The sun rises in the east after it has set in the west." This means that an eastern sunrise follows a western sunset, ergo there's east and west and there's a sun. All these answers are within the framework of the statement.

However, a question like "Is there really a sun?" prompts us to question the validity of the framework itself, thereby asking us to step outside and evaluate it. Now, how do we evaluate it?

Questions on micropolitical subjectivism & frameworks

First off, bounded rationality: this concept I came across in another form in computational linguistics. In the late 19th century, Benjamin Whorf and Edward Sapir put forth their eponymous hypothesis that “the difference in the significance of languages is the difference in the significance of the perceptions of its speakers.” In '57, Chomsky came up with universal grammar: all languages are accompanied by psychological nativism and a poverty of the stimulus.

These rules struck at the heart of the empiricist position of language acquisition. So, by being born with preset capabilities, are we also beset by preset deficiencies that limit the scope of our successes? Here, we come to bounded rationalism as an immediate consequence of the existence of a universal grammar - and perhaps also to Nietzsche's 'Amor fati'. But this is a purely psychosocial argument.

Secondly, structuralism and rationalist theory: here, mathematics avails a solution I've been fond of in the past—John Nash's game theory. Herbert Simon's three steps to arrive at a decision are identification of alternatives, consequences of alternatives, and evaluation of relevance of consequences. All three are modeled on the necessity of a stable system, the condition that finite variables exist, and the condition that only a finite number of consequences are possible. In that case,

1. Does the macropolitical structure transform into a metastructure when it comes to assessing the symbolism of a micropolitical reality?


2. What does that entail?


3. If it doesn't, then is the new mediator subjectivism?


4. In that case, is the purpose of subjectivist knowledge to reconcile the self-reflexive identity against the backdrop of a macropolitical entity?


5. Or, is subjective knowledge purely a micropolitical issue?

This, I think, leads to Carnap's question: can ontological questions have objective answers? Here, as an engineer, I'm reminded of metaphysical naturalism as well.

Finally, the question I find most pressing is whether or not it is necessary for us to adopt a framework - a structuralist tool - in the context of which we view this world. For example, consider the statement "The sun rises in the east after it has set in the west." This means that an eastern sunrise follows a western sunset, ergo there's east and west and there's a sun. All these answers are within the framework of the statement.

However, a question like "Is there really a sun?" prompts us to question the validity of the framework itself, thereby asking us to step outside and evaluate it. Now, how do we evaluate it?

The invisible bridge

In a college of journalism, you'd think the blog posts would have to be better researched, better articulated and better delivered. While the latter two are a matter of personal choice, the first - good research - becomes unnecessary. When I was in an engineering institution for my UG, I blogged so frequently and so much that people began to take notice: I was "the blogger". At that point, the things I wrote about had nothing to do with engineering and it is quite a surprise how there are many engineers who'd have trouble understanding Foucault or Nietzsche or Machiavelli. Consequently, I began to research my posts well, ensuring no wrong information got out - directly or as a matter of interpretation.

Here, at ACJ: one misstep and I'm screwed. Both honest and crazy intellectuals will pounce on the slightest of mispronunciations and attempt to secure an argumentative victory. I don't rant out facts and statistics like I used to not because I've forgotten them but because it seems as though just listening to those around me is going to vindicate half the fee-amount I paid. At first, all the hooked-up contentiousness seemed sensational. Now, it seems abjectly pointless. Even in institutions such as this, apparently, there are some people caught between the states of "good journalist" and "bad journalist". I could be one of them, but I must admit hypocrisy - my friends will observe - has not bothered me. Being against my journalistic cause as it may seem to be, I'd clarify that this is a different kind of hypocrisy. Yes, another kind.

Enough of that BS now. Picking up from where I left off: blogging in an encouraging environment seems to be weaker than blogging in a discouraging environment. From an engineering standpoint, that's only sensible: the work done by a system working between two states that have a significant difference in enthalpies is much higher than the work done by a system working between two states that have a small difference in enthalpies. However, that also entails the input to be greater (because a greater "quantity" of work needs to be done to increase the potential energy of the system to so-so much). Similarly, blogging in a discouraging environment is bound to produce greater results if only I'd persist with it (keeping the time-frame finite, the results are only going to be better than what they were during the period of encouragement - which should do).

I love thinking like how an engineer would about things: systematically, without any fuss whatsoever, always knowing full well that if something's wrong, I'm also going to know if or if not it's going to be in my hands to fix it. If it is, then I will. If it isn't, then I won't. The mathematics at work behind all this structure and formality ensures that if things are right in principle, the rest will fall into place. That's the invisible bridge that spans the distance between cause and effect. Science is the grammar when literature's the right reasons, and if you see the problem - any problem - all you have to understand is that you're looking at many invisible bridges waiting to be stepped on.

The invisible bridge

In a college of journalism, you'd think the blog posts would have to be better researched, better articulated and better delivered. While the latter two are a matter of personal choice, the first - good research - becomes unnecessary. When I was in an engineering institution for my UG, I blogged so frequently and so much that people began to take notice: I was "the blogger". At that point, the things I wrote about had nothing to do with engineering and it is quite a surprise how there are many engineers who'd have trouble understanding Foucault or Nietzsche or Machiavelli. Consequently, I began to research my posts well, ensuring no wrong information got out - directly or as a matter of interpretation.

Here, at ACJ: one misstep and I'm screwed. Both honest and crazy intellectuals will pounce on the slightest of mispronunciations and attempt to secure an argumentative victory. I don't rant out facts and statistics like I used to not because I've forgotten them but because it seems as though just listening to those around me is going to vindicate half the fee-amount I paid. At first, all the hooked-up contentiousness seemed sensational. Now, it seems abjectly pointless. Even in institutions such as this, apparently, there are some people caught between the states of "good journalist" and "bad journalist". I could be one of them, but I must admit hypocrisy - my friends will observe - has not bothered me. Being against my journalistic cause as it may seem to be, I'd clarify that this is a different kind of hypocrisy. Yes, another kind.

Enough of that BS now. Picking up from where I left off: blogging in an encouraging environment seems to be weaker than blogging in a discouraging environment. From an engineering standpoint, that's only sensible: the work done by a system working between two states that have a significant difference in enthalpies is much higher than the work done by a system working between two states that have a small difference in enthalpies. However, that also entails the input to be greater (because a greater "quantity" of work needs to be done to increase the potential energy of the system to so-so much). Similarly, blogging in a discouraging environment is bound to produce greater results if only I'd persist with it (keeping the time-frame finite, the results are only going to be better than what they were during the period of encouragement - which should do).

I love thinking like how an engineer would about things: systematically, without any fuss whatsoever, always knowing full well that if something's wrong, I'm also going to know if or if not it's going to be in my hands to fix it. If it is, then I will. If it isn't, then I won't. The mathematics at work behind all this structure and formality ensures that if things are right in principle, the rest will fall into place. That's the invisible bridge that spans the distance between cause and effect. Science is the grammar when literature's the right reasons, and if you see the problem - any problem - all you have to understand is that you're looking at many invisible bridges waiting to be stepped on.

The function of a "unit cell" in the perception lattice

Old post, now archived thus.

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Beginning from the quantification of perception, we see, hear and feel the objects around us. We understand animation, we derive motion, we negotiate shapes, and we respond to changes. There is nothing to philosophy if only for our ability to become opinionated and a sense of good and bad, whence we also derive judgment and the skills of decision-making. Just as we have left and right to orient us in the physical realm, we have problems and solutions to orient us in the mental realm.

A problem is perceived in its deviation from normality, and in the exposition of abnormality to alert us to one change in particular and in even greater specificity, its incompatibility with normality as we see it. Problems can arise in many forms - as many as we have come to perceive. It is the solution we come to, the one particular decision to alter things as they are and to set them in positions that would resemble in positions they were. We try to reinstate normality as it should be, devoid of anything erroneous, error-prone or error-causing and greatly limitable by one's own actions as they will be.

While walking on a straight road, the need to perceive a change in direction is responded to by taking a perpendicular turn at the most. The sense of left and right, henceforth, seem to more pronounced owing to the presence of an original path that now takes up the first slot in the history of the journey. While travelling on a straight road, without having to take any turns at any points of space and time, the journey consisted of an abode and destination separated by a distance consisting solely of linear displacements; in other words, there was a problem, and there was only one feasible solution.

But once you have taken a turn, say to the right, then you have an angularity associated with your journey: you have reoriented yourself, and analogously, you have altered your direction in favour of a new solution to the same problem. The presence of an original plays an important role in that it gives rise to comparative decision-making, and a variety of opinions with significant variations between them.

The traversal of a straight road gives rise to no such notions because of its inherent inability to deliver comparability. And this is where a theory of nothing, which is only a set of some questions that seem to answer themselves at first, is born. Man’s natural need to quantify the objects, changes and adaptations around him is only understandable. Only with quantification comes perception. This is because, at the most fundamental of levels, the changes around us are used to keep track of time. When an object moves from point A to point B, it marks a change of position and gives rise to displacement. Therefore, the quantification of the phenomena around us empowers us with the tool of recollection, which can be put to immense use when we use comparative decision-making.

The same problem may have given rise to multiple solutions, but when a problem with only one possible solution occurs repeatedly, the problem can be filed away as a one-time occurrence and the solutions that were used previously to tackle it can be thought of as multiple and, therefore, employed again. This concept, in its turn, brings us to the breakdown of time into logically similar categories. When you leave your home for work, the morning may be divided as:

1. You at home,


2. You while driving, and


3. You at work.

By the logical organization of time periods, alternatively ‘time spans’, you find a sense of progress. When the same tasks are performed on a fairly regular basis, the scenario transforms into a routine and the requirement of a logical categorization becomes suppressed by the commoditized grouping of these tasks into blocks characterized by the observation of relatively progressive changes in a parallel walk of life.

For example, when you work at the office, you perform the tasks assigned to you (as conforming to a division of labour). However, the progress is observed in your personal life when you earn money, and in your employer’s business, which seems to want you to work efficiently for it to profit from the collective efficiency. Subsequently, an instance of multiparallelism can be drawn out between all such cases of analogous systems.

In the said cases, quantification has been observed only because it was being looked for; what about when one desires quantification in some other region of perception but is unable to find it? Does that mean that what one perceives is nonexistent? That is absurd because the validity of my perception is then annulled!

In trying to come to terms with change and the relativity of existence itself, we have subconsciously but inevitably generated the need for quantification. But of course, the coexistent fundamentality of the very notion is an excuse enough and has, therefore, qualified itself as a positive sign of progress.

Our understanding of the people and social machinery around us only deepens our faith in the social pedestal upon which we stand, and thereby also increases our commitment to the understanding of other parallel phenomena. So, pre-quantification, we have change, orientation, progress, and some parameters with which we are enabled to measure them. If these parameters were to be absent one at a time, then the ease of quantification becomes reduced, but on the other hand, even the presence of one of these parameters at times becomes a cause for problem. It is the combination of them that may possess any expectations of standing true.

However, when something as abstract as any other fundamental elemental constituent of logic, like logic itself, is subjugated to the detection of such parameters and the establishment of quantified judgment becomes very complicated owing to logically overriding incompatibilities. Therefore, in dealing with such terms with immense applications in reasoning, we have to define the most fundamental of these terms such that those incompatibilities arising out of hierarchal disturbances in the logical structure of reasoning itself are not dealt with.

In other words, we have to define the smallest units of existence which posses the least amount of elemental reasonability and, therefore, can be parallelized to arrive at a logical conclusion to any statement or problem.

The function of a "unit cell" in the perception lattice

Old post, now archived thus.

--

Beginning from the quantification of perception, we see, hear and feel the objects around us. We understand animation, we derive motion, we negotiate shapes, and we respond to changes. There is nothing to philosophy if only for our ability to become opinionated and a sense of good and bad, whence we also derive judgment and the skills of decision-making. Just as we have left and right to orient us in the physical realm, we have problems and solutions to orient us in the mental realm.

A problem is perceived in its deviation from normality, and in the exposition of abnormality to alert us to one change in particular and in even greater specificity, its incompatibility with normality as we see it. Problems can arise in many forms - as many as we have come to perceive. It is the solution we come to, the one particular decision to alter things as they are and to set them in positions that would resemble in positions they were. We try to reinstate normality as it should be, devoid of anything erroneous, error-prone or error-causing and greatly limitable by one's own actions as they will be.

While walking on a straight road, the need to perceive a change in direction is responded to by taking a perpendicular turn at the most. The sense of left and right, henceforth, seem to more pronounced owing to the presence of an original path that now takes up the first slot in the history of the journey. While travelling on a straight road, without having to take any turns at any points of space and time, the journey consisted of an abode and destination separated by a distance consisting solely of linear displacements; in other words, there was a problem, and there was only one feasible solution.

But once you have taken a turn, say to the right, then you have an angularity associated with your journey: you have reoriented yourself, and analogously, you have altered your direction in favour of a new solution to the same problem. The presence of an original plays an important role in that it gives rise to comparative decision-making, and a variety of opinions with significant variations between them.

The traversal of a straight road gives rise to no such notions because of its inherent inability to deliver comparability. And this is where a theory of nothing, which is only a set of some questions that seem to answer themselves at first, is born. Man’s natural need to quantify the objects, changes and adaptations around him is only understandable. Only with quantification comes perception. This is because, at the most fundamental of levels, the changes around us are used to keep track of time. When an object moves from point A to point B, it marks a change of position and gives rise to displacement. Therefore, the quantification of the phenomena around us empowers us with the tool of recollection, which can be put to immense use when we use comparative decision-making.

The same problem may have given rise to multiple solutions, but when a problem with only one possible solution occurs repeatedly, the problem can be filed away as a one-time occurrence and the solutions that were used previously to tackle it can be thought of as multiple and, therefore, employed again. This concept, in its turn, brings us to the breakdown of time into logically similar categories. When you leave your home for work, the morning may be divided as:

1. You at home,


2. You while driving, and


3. You at work.

By the logical organization of time periods, alternatively ‘time spans’, you find a sense of progress. When the same tasks are performed on a fairly regular basis, the scenario transforms into a routine and the requirement of a logical categorization becomes suppressed by the commoditized grouping of these tasks into blocks characterized by the observation of relatively progressive changes in a parallel walk of life.

For example, when you work at the office, you perform the tasks assigned to you (as conforming to a division of labour). However, the progress is observed in your personal life when you earn money, and in your employer’s business, which seems to want you to work efficiently for it to profit from the collective efficiency. Subsequently, an instance of multiparallelism can be drawn out between all such cases of analogous systems.

In the said cases, quantification has been observed only because it was being looked for; what about when one desires quantification in some other region of perception but is unable to find it? Does that mean that what one perceives is nonexistent? That is absurd because the validity of my perception is then annulled!

In trying to come to terms with change and the relativity of existence itself, we have subconsciously but inevitably generated the need for quantification. But of course, the coexistent fundamentality of the very notion is an excuse enough and has, therefore, qualified itself as a positive sign of progress.

Our understanding of the people and social machinery around us only deepens our faith in the social pedestal upon which we stand, and thereby also increases our commitment to the understanding of other parallel phenomena. So, pre-quantification, we have change, orientation, progress, and some parameters with which we are enabled to measure them. If these parameters were to be absent one at a time, then the ease of quantification becomes reduced, but on the other hand, even the presence of one of these parameters at times becomes a cause for problem. It is the combination of them that may possess any expectations of standing true.

However, when something as abstract as any other fundamental elemental constituent of logic, like logic itself, is subjugated to the detection of such parameters and the establishment of quantified judgment becomes very complicated owing to logically overriding incompatibilities. Therefore, in dealing with such terms with immense applications in reasoning, we have to define the most fundamental of these terms such that those incompatibilities arising out of hierarchal disturbances in the logical structure of reasoning itself are not dealt with.

In other words, we have to define the smallest units of existence which posses the least amount of elemental reasonability and, therefore, can be parallelized to arrive at a logical conclusion to any statement or problem.

The function of a "unit cell" in the perception lattice

Old post, now archived thus.

--

Beginning from the quantification of perception, we see, hear and feel the objects around us. We understand animation, we derive motion, we negotiate shapes, and we respond to changes. There is nothing to philosophy if only for our ability to become opinionated and a sense of good and bad, whence we also derive judgment and the skills of decision-making. Just as we have left and right to orient us in the physical realm, we have problems and solutions to orient us in the mental realm.

A problem is perceived in its deviation from normality, and in the exposition of abnormality to alert us to one change in particular and in even greater specificity, its incompatibility with normality as we see it. Problems can arise in many forms - as many as we have come to perceive. It is the solution we come to, the one particular decision to alter things as they are and to set them in positions that would resemble in positions they were. We try to reinstate normality as it should be, devoid of anything erroneous, error-prone or error-causing and greatly limitable by one's own actions as they will be.

While walking on a straight road, the need to perceive a change in direction is responded to by taking a perpendicular turn at the most. The sense of left and right, henceforth, seem to more pronounced owing to the presence of an original path that now takes up the first slot in the history of the journey. While travelling on a straight road, without having to take any turns at any points of space and time, the journey consisted of an abode and destination separated by a distance consisting solely of linear displacements; in other words, there was a problem, and there was only one feasible solution.

But once you have taken a turn, say to the right, then you have an angularity associated with your journey: you have reoriented yourself, and analogously, you have altered your direction in favour of a new solution to the same problem. The presence of an original plays an important role in that it gives rise to comparative decision-making, and a variety of opinions with significant variations between them.

The traversal of a straight road gives rise to no such notions because of its inherent inability to deliver comparability. And this is where a theory of nothing, which is only a set of some questions that seem to answer themselves at first, is born. Man’s natural need to quantify the objects, changes and adaptations around him is only understandable. Only with quantification comes perception. This is because, at the most fundamental of levels, the changes around us are used to keep track of time. When an object moves from point A to point B, it marks a change of position and gives rise to displacement. Therefore, the quantification of the phenomena around us empowers us with the tool of recollection, which can be put to immense use when we use comparative decision-making.

The same problem may have given rise to multiple solutions, but when a problem with only one possible solution occurs repeatedly, the problem can be filed away as a one-time occurrence and the solutions that were used previously to tackle it can be thought of as multiple and, therefore, employed again. This concept, in its turn, brings us to the breakdown of time into logically similar categories. When you leave your home for work, the morning may be divided as:

1. You at home,


2. You while driving, and


3. You at work.

By the logical organization of time periods, alternatively ‘time spans’, you find a sense of progress. When the same tasks are performed on a fairly regular basis, the scenario transforms into a routine and the requirement of a logical categorization becomes suppressed by the commoditized grouping of these tasks into blocks characterized by the observation of relatively progressive changes in a parallel walk of life.

For example, when you work at the office, you perform the tasks assigned to you (as conforming to a division of labour). However, the progress is observed in your personal life when you earn money, and in your employer’s business, which seems to want you to work efficiently for it to profit from the collective efficiency. Subsequently, an instance of multiparallelism can be drawn out between all such cases of analogous systems.

In the said cases, quantification has been observed only because it was being looked for; what about when one desires quantification in some other region of perception but is unable to find it? Does that mean that what one perceives is nonexistent? That is absurd because the validity of my perception is then annulled!

In trying to come to terms with change and the relativity of existence itself, we have subconsciously but inevitably generated the need for quantification. But of course, the coexistent fundamentality of the very notion is an excuse enough and has, therefore, qualified itself as a positive sign of progress.

Our understanding of the people and social machinery around us only deepens our faith in the social pedestal upon which we stand, and thereby also increases our commitment to the understanding of other parallel phenomena. So, pre-quantification, we have change, orientation, progress, and some parameters with which we are enabled to measure them. If these parameters were to be absent one at a time, then the ease of quantification becomes reduced, but on the other hand, even the presence of one of these parameters at times becomes a cause for problem. It is the combination of them that may possess any expectations of standing true.

However, when something as abstract as any other fundamental elemental constituent of logic, like logic itself, is subjugated to the detection of such parameters and the establishment of quantified judgment becomes very complicated owing to logically overriding incompatibilities. Therefore, in dealing with such terms with immense applications in reasoning, we have to define the most fundamental of these terms such that those incompatibilities arising out of hierarchal disturbances in the logical structure of reasoning itself are not dealt with.

In other words, we have to define the smallest units of existence which posses the least amount of elemental reasonability and, therefore, can be parallelized to arrive at a logical conclusion to any statement or problem.

Judgment of actions: A thought experiment

1. There is a man sitting under a table


2. The following objects are placed on the table: a small vat of a concentrated acid and a guillotine-like blade


3. A curtain is drown over the table to separate the objects to a half of the table


4. If the vat of acid spills, it will burn a hole through the wood and kill the man underneath


5. If the blade is dropped, it will slice through the wood and kill the man underneath


6. On either side of the curtain, two men, A and B, are made to sit


7. Both of them are independently made aware of the man under the table


8. A is given responsibility over the vat of acid and B is given responsibility over the blade


9. A is informed about the consequences of spilling the acid


10. B is informed about the consequences of dropping the blade


11. At some point, A accidentally tips the vat of acid but saves it from spilling over the table just in time


12. However, the table has been upset enough to bring the blade down upon it, killing the man


13. Is A's acquittal in a trial court dependent on or independent of his knowledge of the blade's existence?

Judgment of actions: A thought experiment

1. There is a man sitting under a table


2. The following objects are placed on the table: a small vat of a concentrated acid and a guillotine-like blade


3. A curtain is drown over the table to separate the objects to a half of the table


4. If the vat of acid spills, it will burn a hole through the wood and kill the man underneath


5. If the blade is dropped, it will slice through the wood and kill the man underneath


6. On either side of the curtain, two men, A and B, are made to sit


7. Both of them are independently made aware of the man under the table


8. A is given responsibility over the vat of acid and B is given responsibility over the blade


9. A is informed about the consequences of spilling the acid


10. B is informed about the consequences of dropping the blade


11. At some point, A accidentally tips the vat of acid but saves it from spilling over the table just in time


12. However, the table has been upset enough to bring the blade down upon it, killing the man


13. Is A's acquittal in a trial court dependent on or independent of his knowledge of the blade's existence?

Exploring sentence structures, induction, and emphasis

Key

• “→” indicates first-level nesting (i.e., child), “→→” indicates second-level nesting (i.e., grandchild), and so on


• Each phrase is a semantic child only of the previously latest parent


• Two or more phrases are siblings if and only if at least one of them has a child phrase


• In the notation “n/state”, “n” is the level assigner and “state” is the state-marker


• In the notation “state/n”, “n” is the level to which the “state” corresponds

Analysis

“How is one difference of opinion sufficient to qualify the truth of a rift in the Anna Hazare camp—between Hegde and Hazare himself—in the eyes of the media?”

How is
1→one difference
2→→of opinion
3→sufficient
4→→to qualify
5→→the truth
6→→→of a rift
7→→→in the Anna Hazare camp
8→→→→between Hegde and Hazare himself
9→→→in the eyes of the media?

In the above example,

• 1 and 3 are siblings


• 2 is the child of 1


• 4 to 5 is a passive transition


• 6 to 7 is a passive transition


• 6→7 is the child of 4→5 is the child of 3


• 8 is the child of 7


• 7 and 9 are siblings

Thus,

1/origin → _child → sibling/1 → 2/origin → 3/child → _grandchild → sibling/3

Notes on the example

Reduction of complexity The most deeply nested child will receive the least emphasis. Consequently, more important points have to be nested earlier on. If one complex idea is to be delivered, it would be wiser to break the sentences down: that way, deeply-nested child phrases are eliminated and the subject is grasped easily. However, this breakdown increases the amount of physical space necessary to hold the text.

Siblings limit Sentence lengths are harder to analyse because different people have different attention spans, and when the payoff involved is space, passive transitions can be employed to keep from creating more children or more siblings. At the same time, it is advisable to limit the number of siblings in each sentence to two.

Fragmentation If a child phrase is being included, the norm is to fit it into the sentence between two commas or two M-dashes. This is also the reason commas are powerful because they induce a pause in the reader’s flow, as if breaking his/her speed and having him/her scrutinize the child phrase. At the same time, inserting too many such breaks makes the text read fragmented, and fragmented texts make for frustrating reading.

Transitive phrases Consider the previous sentence: “At the same time, inserting too many such breaks makes the text read fragmented, and fragmented texts make for frustrating reading.” In this case, the comma is used for a different purpose:

1/origin → 2/origin → 3/origin

Essentially, the phrase “At the same time” is used to conduct a transition from the previous sentence to the current one and so the first comma marks the end of the transition and the beginning of the body. Similarly, the insertion “, and” indicates a fusing of the current sentence—the body—and “fragmented texts make for frustrating reading.” In fact, in order to broaden the emphasis on the idea, “, and” can be removed and substituted with a period.

Exploring sentence structures, induction, and emphasis

Key

• “→” indicates first-level nesting (i.e., child), “→→” indicates second-level nesting (i.e., grandchild), and so on


• Each phrase is a semantic child only of the previously latest parent


• Two or more phrases are siblings if and only if at least one of them has a child phrase


• In the notation “n/state”, “n” is the level assigner and “state” is the state-marker


• In the notation “state/n”, “n” is the level to which the “state” corresponds

Analysis

“How is one difference of opinion sufficient to qualify the truth of a rift in the Anna Hazare camp—between Hegde and Hazare himself—in the eyes of the media?”

How is
1→one difference
2→→of opinion
3→sufficient
4→→to qualify
5→→the truth
6→→→of a rift
7→→→in the Anna Hazare camp
8→→→→between Hegde and Hazare himself
9→→→in the eyes of the media?

In the above example,

• 1 and 3 are siblings


• 2 is the child of 1


• 4 to 5 is a passive transition


• 6 to 7 is a passive transition


• 6→7 is the child of 4→5 is the child of 3


• 8 is the child of 7


• 7 and 9 are siblings

Thus,

1/origin → _child → sibling/1 → 2/origin → 3/child → _grandchild → sibling/3

Notes on the example

Reduction of complexity The most deeply nested child will receive the least emphasis. Consequently, more important points have to be nested earlier on. If one complex idea is to be delivered, it would be wiser to break the sentences down: that way, deeply-nested child phrases are eliminated and the subject is grasped easily. However, this breakdown increases the amount of physical space necessary to hold the text.

Siblings limit Sentence lengths are harder to analyse because different people have different attention spans, and when the payoff involved is space, passive transitions can be employed to keep from creating more children or more siblings. At the same time, it is advisable to limit the number of siblings in each sentence to two.

Fragmentation If a child phrase is being included, the norm is to fit it into the sentence between two commas or two M-dashes. This is also the reason commas are powerful because they induce a pause in the reader’s flow, as if breaking his/her speed and having him/her scrutinize the child phrase. At the same time, inserting too many such breaks makes the text read fragmented, and fragmented texts make for frustrating reading.

Transitive phrases Consider the previous sentence: “At the same time, inserting too many such breaks makes the text read fragmented, and fragmented texts make for frustrating reading.” In this case, the comma is used for a different purpose:

1/origin → 2/origin → 3/origin

Essentially, the phrase “At the same time” is used to conduct a transition from the previous sentence to the current one and so the first comma marks the end of the transition and the beginning of the body. Similarly, the insertion “, and” indicates a fusing of the current sentence—the body—and “fragmented texts make for frustrating reading.” In fact, in order to broaden the emphasis on the idea, “, and” can be removed and substituted with a period.

Philosophy and the scientific method

Philosophy's widely been called the classification of thoughts; although that seems like a simple definition, those requirements in place to ensure that it is also accessible to the principles of scientific enquiry make it a daunting and esoteric subject to pursue. While intriguing challenges central to the human nature are presented in no small numbers along the way, the latter quality has prevented it from embraced by the masses as another context within which to investigate the Universe.

At the core of the philosophical argument lies its ability to define principles—any principles—which are, in turn, what enable the classification of thoughts. Would that the Universe contained all of its information as a garble of colours and noise, the process of learning would've been substituted by the process of discovery entirely. However, the case has been demonstrably polar: there are patterns everywhere, patterns that show a remarkable similitude to each other in that they are all principled, in that they all display characteristics of endurance and not grant any incidents of epistemological construction the misfortune of stagnation as structures of the past.This is one of the foremost reasons that inquiry into these matters has proved crucial for social, economic and political progress irrespective of "germane concerns" such as ethnicity, culture or racial history.

In order to both discover and establish (or, recognise and understand) such a replicable ontology, an underlying experimental process is necessary that abides by the principles of scientific investigation and, essentially, empiricism so as to prevent the case of reductio ad absurdum as well as to be able to verify the credibility of any hypothesis without interfering with its functions.

Philosophy and the scientific method

Philosophy's widely been called the classification of thoughts; although that seems like a simple definition, those requirements in place to ensure that it is also accessible to the principles of scientific enquiry make it a daunting and esoteric subject to pursue. While intriguing challenges central to the human nature are presented in no small numbers along the way, the latter quality has prevented it from embraced by the masses as another context within which to investigate the Universe.

At the core of the philosophical argument lies its ability to define principles—any principles—which are, in turn, what enable the classification of thoughts. Would that the Universe contained all of its information as a garble of colours and noise, the process of learning would've been substituted by the process of discovery entirely. However, the case has been demonstrably polar: there are patterns everywhere, patterns that show a remarkable similitude to each other in that they are all principled, in that they all display characteristics of endurance and not grant any incidents of epistemological construction the misfortune of stagnation as structures of the past.This is one of the foremost reasons that inquiry into these matters has proved crucial for social, economic and political progress irrespective of "germane concerns" such as ethnicity, culture or racial history.

In order to both discover and establish (or, recognise and understand) such a replicable ontology, an underlying experimental process is necessary that abides by the principles of scientific investigation and, essentially, empiricism so as to prevent the case of reductio ad absurdum as well as to be able to verify the credibility of any hypothesis without interfering with its functions.