Sunday, 28 December 2014

The axiom of choice

I have an invisible OCD. I call it 'thinking'. I'm drawn to abstract structures: language, music, ethical discourse as logic systems, mathematical equations and algorithms, architecture—anything, really, that can be derived from a set of first principles.

One of these things that I have obsessed over is called 'set theory' where the 'axiom of choice' resides.

Set theory, among all mathematics, has got to have the ugliest symbolism. If we were to assiduously follow GH Hardy's edict that 'beauty' be the final arbiter of mathematics, the only saving grace of set theory would be the implications of its statements.

In not so many words, the axiom of choices says:

Axiom of Choice Let C be a collection of nonempty sets. Then we can choose a member from each set in that collection. In other words, there exists a function f defined on C with the property that, for each set S in the collection, f(S) is a member of S. (


Eric Schechter of Vanderbilt University (just quoted above) says of "the last great controversy of mathematics" (ie, the axiom of choice) that:

The controversy was over how to interpret the words "choose" and "exists" in the axiom:

  • If we follow the constructivists, and "exist" means "find," then the axiom is false, since we cannot find a choice function for the nonempty subsets of the reals.
  • However, most mathematicians give "exists" a much weaker meaning, and they consider the Axiom to be true: To define f(S), just arbitrarily "pick any member" of S. (ibid)
I, personally, think that the words "choose" and "exist" are merely consequential grammatical elements of the broader vulgate statement of the axiom and adjunct to the main notion of "property"—"...a function f defined on C with the property that..."

This abstract notion of 'property' appears highly flexible and general, yet highly constrained—a given result is never mere whimsy but always derived from a set of rules/operations that do not quarter any exception (else it would not comprise of a set as such).

Mario Livio the author of The Equation That Couldn't Be Solved (2005) writes of this notion of 'property':

The properties that define a group are:

1. Closure. The offspring of any two numbers combined by the operation must itself be a member. In the group of integers, the sum of any two integers is also an integer (e.g., 3 + 5 = 8).
2. Associativity. The operation must be associative—when combining (by the operation) three ordered members, you may combine any two of them first, and the result is the same, unaffected by  way they are bracketed. Addition, for instance, is associative: (5 + 7) + 13 = 25 and 5 + (7 + 13) = 25, where the parentheses, the "punctuation marks" of mathematics, indicate which pair you add first.
3. Identity element. The group has to contain an identity element such that when combined with any member, it leaves the member unchanged. In the group of integers, the identity element is the number zero. For example, 0 + 3 = 3 + 0 = 3.
4. Inverse. For every member in a group there must exist an inverse. When a member is combined with its inverse, it gives the identity element. For the integers, the inverse of any number is the number of the same absolute value, but with the opposite sign: for e.g., the inverse of 4 is -4 and the inverse of -4 is 4; 4 + (-4) = 0 and (-4) + 4 = 0. (Mario Livio, 2005. p. 46)

On a clock calculator (modulo 6), Gauss found that any given prime number has congruence with either 5 or 1 for prime numbers greater than 3. How many rotations are required to obey this congruence is not predictable, but there is an interesting property in that for any twin primes the first must occur at 5 o'clock and the second must occur at the immediately following 1 o'clock.


Saturday, 27 December 2014

The Wretched of the Earth

“Today I believe in the possibility of love; that is why I endeavor to trace its imperfections, its perversions.”
― Frantz Fanon, Black Skin, White Masks

Years ago I was introduced to Franz Fanon's writings (The Wretched of the Earth) by someone who was of that generation trying to "discover its mission, fulfill it, or betray it." As a self-professed Marxist in a pre-USSR collapse he tried real hard to distinguish himself different from the herd but I think it was more indicative of a certain dissatisfaction with academia (ie, unfulfilled ambitions) than being in a counter-culture; what could not be articulated (conscious or otherwise) expressed itself as being-out-of-place by choice for its own sake, righteous indignation included―righteous indignation especially.

Looking back I don't think he was far off the mark. The terminology was only starting to gel: if the problem was the "establishment" then being "anti-establishmentarian" must be the cure; if the shots were in the dark, the motivations were nonetheless profound.

I think this unwitting profundity was an implicit recognition of how prophetic Eisenhower's Farewell Address really was:

We . . . must avoid the impulse to live only for today, plundering for our own ease and convenience the precious resources of tomorrow. We cannot mortgage the material assets of our grandchildren without risking the loss also of their political and spiritual heritage. We want democracy to survive for all generations to come, not to become the insolvent phantom of tomorrow.

The only problem was that, being a self-professed Marxist, he could not bring himself to attributing such quintessential insight of the times to come as having been breath life by such a person as Eisenhower.

Now this conjunction of an immense military establishment and a large arms industry is new in the American experience. The total influence -- economic, political, even spiritual -- is felt in every city, every Statehouse, every office of the Federal government. We recognize the imperative need for this development. Yet, we must not fail to comprehend its grave implications. Our toil, resources, and livelihood are all involved. So is the very structure of our society.

In the councils of government, we must guard against the acquisition of unwarranted influence, whether sought or unsought, by the military-industrial complex. The potential for the disastrous rise of misplaced power exists and will persist. We must never let the weight of this combination endanger our liberties or democratic processes. We should take nothing for granted. Only an alert and knowledgeable citizenry can compel the proper meshing of the huge industrial and military machinery of defense with our peaceful methods and goals, so that security and liberty may prosper together. (ibid)

Or, perhaps he never recognized the archetypal struggle as such being that he insisted upon the differences in class as the defining factor of it rather than the existential nature (and outcome) of an unexamined value system. It is, after all, a rare thing this making of conscious choice especially when ideology blocks the vista of possibilities in the making of that conscious choice affords.

We do not, as a matter of course, make conscious choices. We instead respond to, react against and/or ignore choices we could have made:

Someone has likened emotions to the red light on the dashboard of a car indicating an engine problem. You can respond to the red light's warning in several ways. You can cover it with a piece of duct tape. "I can't see the light now," you say, "so I don't have to think about the problem." You can smash the light with a hammer. "That'll teach you for glaring in my face!" Or you can respond to the light as the manufacturers intended by looking under the hood and fixing the problem.

You have the same three options in responding to your emotions. You can respond by covering them, ignoring them or stifling them. That is called suppression. You can respond by thoughtlessly lashing out, giving someone a piece of your mind or flying off the handle. I call that indiscriminate expression. Or you can peer inside to see what is going on. That is called acknowledgement. (Neil T Anderson, 2000. pp. 173-174)

Making a conscious choice, then, requires an active and on-going examination of our value systems. This is a very hard thing to do, especially if like me, your handicap is an inherent inability to deal with strong emotions and thus prone to "flying off the handle" to rid of them.

I do not trust myself to make conscious, good choices. That is my cross to bear: most, if not all, of my unfettered thoughtless choices have resulted in "life experiences". Looking back, it's a wonder and a miracle I have survived thus far.

This is what makes me a Christian: I have had to assume the Micah principle (ie, Micah 6: 8 "He has shown you, O mortal, what is good. And what does the Lord require of you? To act justly and to love mercy and to walk humbly with your God.") and submit to the Lord in genuine humility because, on my own, I am truly incapable of making conscious choices without the guidance of the Christ's Gospel. This is my confession, my acknowledgement.

I know that "religion" turns people off. I have no religion; I lost it long ago. I do not go to church; I do not intentionally and unkindly judge people; I do not make public display of "doing good". I seek no status within the community. I'm really not part of the Christian community at all. The Gospel of the Lord is my meditation.

The literature of fishermen, tax collectors, and the generally rejected of the religious community makes me go "wow". There is something divine in that, in realizing that this literature was created by people of the most unlikely pedigree, The Wretched of the Earth.


Sunday, 21 December 2014

Christmas: the one thing that can be all things to all people

I never liked Christmas much. It is a season of disappointments; a season of darkness, literally and figuratively. No amount of contrived gaudy gaiety can redeem such jet-black night.

As a believer in the Christ as my Lord Savior I see no contradiction, no lack of generosity, no crippling pessimism: it is said that it is darkest before dawn, and what fitting metaphor:

In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. In him was life, and that life was the light of all mankind. The light shines in the darkness, and the darkness has not overcome it. (John 1: 1-5)

Hanukkah is encapsulated by an acronym that says: A great miracle happened there.

I am no saint. This meditation is what stirs and animates my love—for my kids, my family, those that have touched my life both positively and negatively.

I recently came across Isaiah Berlin (6 June 1909 – 5 November 1997). I think I've always sought out those thinkers who have a sense of irony, and what exquisite irony this man weld. If Christ-like irony be the measure of a humble man, Berlin is worthy of our attention:

Certainly no politics are more real than those of academic life, no loves deeper, no hatreds more burning, no principles more sacred. (To Freya Stark, 12 June 1944)

Nobody is so fiercely bureaucratic, or so stern with soldiers and regular civil servants, as the don disguised as temporary government official armed with an indestructible superiority complex. (ibid)

Doesn't that one describe the dullard, Harper, to the tee? (actually, for someone who described his own writings as having so little politics, Berlin cuts rather deeply to the quick and counts certainty a great evil to be rightly and promptly ridiculed)

Here is a personal lesson for me (someone so obviously prone to easy intellectual pride and vanity):

I am a hopeless dilettante about matters of fact really and only good for a column of gossip, if that. (To Walter Turner, 12 June 1945)

Pluralism, which he advocated for mightily and so capably, was often criticized as merely a form of relativism. Rather than pulling a conniption or walking away in disbelief and disappointment, he responded thusly:

Injustice, poverty, slavery, ignorance – these may be cured by reform or revolution. But men do not live only by fighting evils. They live by positive goals, individual and collective, a vast variety of them, seldom predictable, at times incompatible. (‘Political Ideas in the Twentieth Century’ (1950), L 93 [FEL 40])

Unless there is some point at which you are prepared to fight against whatever odds, and whatever the threat may be, not merely to yourself but to anybody, all principles become flexible, all codes melt, and all ends-in-themselves for which we live disappear ... (To Philip Toynbee, 24 January 1958)

What the historian says will, however careful he may be to use purely descriptive language, sooner or later convey his attitude. Detachment is itself a moral position. The use of neutral language (‘Himmler caused many persons to be asphyxiated’) conveys its own ethical tone. (Introduction to ‘Five Essays on Liberty’ (1969) , L 22–3 [FEL xxix])

This final quote in defense of pluralism is what originally caught my eye:

Those, no doubt, are in some way fortunate who have brought themselves, or have been brought by others, to obey some ultimate principle before the bar of which all problems can be brought. Single-minded monists, ruthless fanatics, men possessed by an all-embracing coherent vision do not know the doubts and agonies of those who cannot wholly blind themselves to reality. (ibid. 47 [lv])

I cannot honestly bring myself to believe that the dark hours of the winter solstice as marking the birth of our Savior though I can honestly say that giving gifts to my loved ones brings me sincere joy. This season, however, is full of metaphorical meaning for me. And I am of the belief that no one can sincerely account for one's years to one's self without some measure of objective standard no matter how amorphous, dynamic and vague its resolution.

These nuggets just quoted contrast and gauge how I'd like to measure myself up to the Gospel of my Lord.

Merry Christmas and a Prosperous New Year,


Sunday, 14 December 2014

"I open my eyes and my eyes are filled"

-the title of this entry is taken from David Berlinski (2009)

Much of the features of the human brain seems to obey the principles of quantum physics: how we see the world (matter) in all its richness of colour (wave-like); how our actions and mental states can be apparently influenced by our notions of past, present and future; etc. Even the way we so effortlessly express and comprehend language has pseudo-quantum physical like features.

In thinking about language I'm always struck by the human mind's ability to take in and express fully-formed and/or spontaneously forming ideas in the act of speaking and listening. This may be just an illusion of timing—I concede this only contingently because whether it be an illusion or not it is a fine and good thing to have. At any rate, the notion of completion (quantum, if you will) seems built-in to our aesthetic/semantic sensibilities such that an incomplete thought always leaves us scrambling to complete it: our "linguistic turn" demands satisfaction.

The morpho-syntactic structure of the Inuit language is highly mathematical where the interaction between phonology and morphology is so beautifully regular that we (those that speak the language) can and do anticipate, and can and do predict the place and manner of articulation the variant will take on depending on the following morpheme—cause apparently follows effect in this case because most of the phonological assimilation rules in the Inuit language are "regressive" (ie, the cause/effect goes backwards).

ani- becomes anijumajunga  "I would like to exit (now)"

pisuk- becomes pisugumajunga  "I would like to (take a) walk"

isiq- becomes isirumajunga  "I would like to enter (now)"

the bold text are examples of "progressive" assimilation (basic form remains [juma] when it follows a root ending in a vowel; /k/ changes to [g] in the second case; /q/ changes to [r] in the third). In all cases, the place of articulation of the initial segment is left unchanged, but the voicing is changed (as is typical of Inuit language assimilation rules)

But, in the case of

pisuktunga  "I am walking"

pisuglanga "let me walk"

the assimilation rules are "regressive"—again, following the general rules of Inuktitut, the place of articulation of the final segment of the root verb (pisuk-) remains unchanged but the change in voicing is affected by the following morphemes ([-tunga] and [-langa]) that differ not only in semantic content but, more importantly, whose initial segments differ in voicing.

This morpho-phonological feature of the Inuit language is not so uniquely strange to the Inuit language. English, to some extent, also has this feature—in fact, all human languages do; the only qualification seems to be that the phonological change be phonetic and not phonemic (ie, have no semantic significance in the change).

In English, the word "miss" ends with a segment /s/:

"I miss her"  -no change in the final /s/ (say it out loud);

but, /s/ becomes [sh] in

"I miss you" (compare it with "I miss her")

This change in /s/ is called "fronting" and it anticipates the following "you" which is articulated relatively close to the lips in comparison to "how" which is pronounced further back in the sound-production apparatus (ie, the mouth as a whole).

The production of speech (and expression/comprehension of thoughts) is largely psychological where the encoding and decoding processes happen too fast for the conscious mind to discern. The currency of speech comprises of idealized quanta of fully formed thoughts. This interplay apparently pays little attention to individual sounds, words and phrases which smear out and bleed into each other forwards and backwards, and this process must be unhindered lest meaningfullness just sort of evaporates—I mean, try and repeat the same word over and over again or stare at an individual word for a while and our mind's eye will just naturally glaze over because there is no real meaning to hold its attention.

The various narratives and semiotic frameworks (ie, our prior experiences) determine our ability to interpret and decode meaning and comprehension/take-away is often idiosyncratic rather than collective: our ability to learn and acquire new frameworks demands it. Collective follows idiosyncratic.

When the process of language acquisition is disrupted in a sustained way—as what happens in inappropriate "pedagogies" like the so-called "whole language" approach—what comes naturally is lost. Whether this is permanent or not, I don't know. It certainly has devastating consequences as histories of "colonialized" peoples bears this out time and again.

I think this disruption can be overcome simply because it is proven time and again that the human mind is extremely resilient and seems to naturally seek ways of transcendence and compensation, after its own way and fashion.

The ability to switch back and forth between various narratives/semiotic frameworks seems to be the key. Intelligence, at the end of the day, is a given. But the more learned and educated a person becomes the more natural and well-oiled the ability to shift intellectual gears become. Exposure to new and well-articulated ideas and experiences facilitates language acquisition; not so much with rote memorization.


Saturday, 13 December 2014

Why 'dialectics' is important to vitality of civilization

The term "dialectics" is defined:

Dialectic (also dialectics and the dialectical method), from Ancient Greek διαλεκτική, is a method of argument for resolving disagreement that has been central to European and Indian philosophy since antiquity. The word dialectic originated in ancient Greece, and was made popular by Plato in the Socratic dialogues. The dialectical method is discourse between two or more people holding different points of view about a subject, who wish to establish the truth of the matter guided by reasoned arguments.

The term dialectics is not synonymous with the term debate. While in theory debaters are not necessarily emotionally invested in their point of view, in practice debaters frequently display an emotional commitment that may cloud rational judgement. Debates are won through a combination of persuading the opponent; proving one's argument correct; or proving the opponent's argument incorrect. Debates do not necessarily require promptly identifying a clear winner or loser; however clear winners are frequently determined by either a judge, jury, or by group consensus. The term dialectics is also not synonymous with the term rhetoric, a method or art of discourse that seeks to persuade, inform, or motivate an audience. (

The Wikipedia entry on Dialectic continues:

Different forms of dialectical reasoning have emerged throughout history from the Indosphere (Greater India) and the West (Europe). These forms include the Socratic method, Hindu, Buddhist, Medieval, Hegelian dialectics, Marxist, Talmudic, and Neo-orthodoxy. (ibid)

The Talmudic dialectical method (of Rabbinic Judaism), especially the Avot Tractate, or, "The ethics of the fathers", relies on the four principles of interpretation called, PaRDeS (an acronym of the four levels of exegeses) but it places extreme importance to fidelity to the Holy Scriptures, to not only in what it says but to every stroke and sequential integrity of the actual Hebrew letters:

Each type of Pardes interpretation examines the extended meaning of a text. As a general rule, the extended meaning never contradicts the base meaning [emphasis mine]. The Peshat means the plain or contextual meaning of the text. Remez is the allegorical meaning. Derash includes the metaphorical meaning, and Sod represents the hidden meaning. There is often considerable overlap, for example when legal understandings of a verse are influenced by mystical interpretations or when a "hint" is determined by comparing a word with other instances of the same word. (

Ideology and its twin, Dogma, are two demons that ever seek to lull the unwary into dead-ends and they seem to be inherently built-in to any rational discourse especially where definitive answers/solutions are necessarily rare and only hard-won by sheer effort and perseverance. There seems to have been two spectacular instances where the twin demons apparently won in the venerable discourse of scientific thought: the so-called String Theory and Darwinian evolution.

In the Darwinian theory of evolution, the will to monopoly (through no fault of anyone, really) seems to have asserted itself right from the get-go. In David Berlinski's book, The Devil's Delusion: Atheism and Its Scientific Pretensions (2009), there is a beautifully crafted passage (is there any other way he writes?) that illustrates this need for dialectical exchange and the consequences when it is ignored (quoted here in its entirety just because no other way is possible):

Together with Charles Darwin, Alfred Wallace created the modern theory of evolution. He has been unjustly neglected by history, perhaps because shortly after conceiving his theory, he came to doubt its provenance. Darwin, too, had his doubts. No one reading On the Origins of Species could miss the note of moral anxiety. But Darwin's doubts arose because, considering its consequences, he feared his theory might be true; with Wallace, it was the other way around. Considering its consequences, he suspected his theory might be false.

In an interesting essay published in 1869 and entitled "Sir Charles Lyell on Geological Climates and the Origins of Species," Wallace outlined his sense that evolution was inadequate to explain certain obvious features of the human race. The essay is of great importance. It marks a falling-away in faith on the part of a sensitive biologist previously devoted to ideas he had himself introduced. Certain of "our physical characteristics," he observed, "are not explicable on the theory of variation and survival of the fittest." These include the human brain, the organs of speech and articulation, the human hand, and the external human form, with its upright posture and bipedal gait. It is only human beings who can rotate their thumb and ring finger in what is called ulnar opposition in order to achieve a grip, a grasp, and degree of torque denied any of the great apes. No other item on Wallace's list has been ticked off against real understanding in evolutionary thought. What remains is fantasy of the sort in which the bipedal gait is assigned to an unrecoverable ancestor wishing to peer (or pee) over tall savannah grasses.

The argument that Wallace made with respect to the human body he made again with respect to the human mind. There it gathers force. Do we understand why alone among the animals, human beings have acquired language? Or a refined and delicate moral system, or art, architecture, music, dance or mathematics? This is a severely abbreviated list. The body of Western literature and philosophy is an extended commentary on human nature, and over the course of more than four thousand years, it has not exhausted its mysteries. "You could not discover the limits of soul," Heraclitus wrote, "not even if you traveled down every road. Such is the depth of its form."

Yet there is no evident distinction, Wallace observed, between the mental powers of the most primitive human being and the most advanced. Raised in England instead of the Ecuadorian Amazon, a native child of the head-hunting Jivaro, destined otherwise for a life spent loping through the jungle, would learn to speak perfect English, and would upon graduation from Oxford or Cambridge have the double advantage of a modern intellectual worldview and a commercially valuable ethnic heritage. He might become a mathematician, he would understand the prevailing moral and social codes perfectly, and for all anyone knows (or could tell), he might find himself a BBC commentator, explaining lucidly the cultural significance of head-hunting and arguing its protection.

From this it follows, Wallace argued, that characteristic human abilities must be latent in primitive man, existing somehow as an unopened gift, the entryway to a world that primitive man does not possess and would not recognize.

But the idea that a biological species might possess latent powers makes no sense in Darwinian terms. It suggests forbidden doctrine that evolutionary  advantages were front-loaded far away and long ago; it is in conflict with the Darwinian principle that useless genes are subject to negative selection pressure and must therefore find themselves draining away into the sands of time.

Wallace identified a frank conflict between his own theory and what seemed to him obvious facts about the solidity and unchangeability of human nature.

The conflict persists; it has not been resolved. (Berlinski, 2009, pp. 157-159)

As if the idiocy of over-extending an incomplete scientific theory into fields not of its purview, and the ill-advised-ness of pontificating and issuing papal bulls prematurely (as the Dawkinses and the Pinkers of this world have done) were not abundantly clear yet, Berlinski continues further down:

Writing in the 1960s and 1970s, the Japanese mathematical biologist Motoo Kimura argued that on the genetic level—the place where mutations take place—most changes are selectively neutral. They do not help an organism survive; they may even be deleterious. A competent mathematician and a fastidious English prose stylist, Kimura was perfectly aware that he was advancing a powerful argument against Darwin's theory of natural selection. "The neutral theory asserts," he wrote in the introduction to his masterpiece, The Neutral Theory of Molecular Evolution, "that the great majority of evolutionary changes at the molecular level, as revealed by comparative studies of protein and DNA sequences, are caused not by Darwinian selection but by random drift of selectively neutral or nearly neutral mutations." (ibid, p. 194)

Most people who know me, or have read enough entries in this blog, may have already surmised that I'd say: BURNED! to both sides of the Creationists/Evolutionist divide, the right-wing nuts who use social Darwinism to justify their arrested-development of becoming fully human.


Dialectics, then—rather than promising definitive answers—seek to draw in as wide a range and diversity of thought in knowledge acquisition as possible, as long as advocacy is rationally articulated and done in good faith.

Had the theory(ies) of evolution been sifted through the dialectic sieve, people like the Nazis, the Stephen Harpers, the Ayn Rands, the Tea Party militants, the so-called Moral Majority movements of this world may have been proven much less virulent, even peripheral to Western civilization. The United States of America—that brightly shining mansion on the hill—may have been given half a chance to truly be the promise of the suffering humanity rather than the sorry, pathetic husk it has become in pursuit of its manifest destiny, after the image of the military-industrial complex.


A curious case of the "four" (in the Inuit language)

The universe appears to be just one of those things.
-Frank Wilczek

The other day, I was doing an informal presentation on the Inuit language consonant chart to one of my colleagues at the Arctic College in preparation for Inuit Language courses we're simultaneously holding for the next couple of weeks (I'm teaching one of the four classes) when she asked me how I would explain the dialectal variants of the number 4—in some instances, it occurs as "tisamat" and in others as "sitamat".

Rather than giving an unsatisfying "explanation" that it is probably "just one of those things", I decided that I would try looking at it in terms of autosegmental analysis. -I've mentioned "autosegmental phonology" before in this blog which I believe has productive possibilities for the analysis of the Inuit language variations.

Says Wikipedia on autosegmental phonology:

The working hypothesis of autosegmental analysis is that a large part of phonological generalizations can be interpreted as a restructuring or reorganization of the autosegments in a representation. Clear examples of the usefulness of autosegmental analysis came in early work from the detailed study of African tone languages, as well as the study of vowel and nasal harmony systems. (

More specifically, using this gambit:

There are situations in which the rule applies not to a particular value of a feature, but to whatever value the feature has. In these situations, it is necessary to include the presence of the feature, but not to specify its value. (ibid)

I thought some light may be shed on this interesting problem.

How I'd explain the implications of the above insight would be to say that a given word comprises of a series of obligatory slots to which consonants and vowels are assigned. For example, the word for "four" in Inuktitut may be rendered (in highly abstract terms, of course) as comprising of this series of consonants and vowels:

CiCamat—ie, the word is sometimes 'tisamat' and sometimes 'sitamat' depending on how your dialect pronounces the word.

Let me draw your attention to the capitalized "C"s (consonants), where the first consonant is sometimes /t/ and sometimes /s/ while the second consonant slot takes what the first doesn't choose (it comes out as [t] if the first chooses /s/; [s] if the first chooses /t/).

The choice in the expression of the second consonant between the two seems to be psychologically real, and, in fact, it seems to be set in stone: "after thy father, thou may be such but not some other".

I think what is happening here is that the sequence of the first two vowels in the word: the /i/ and the /a/ respectively are exerting some irresistible force in the sequence of this particular slot assignment. I say this because one may have:

sitamat   but not  *satimat


tisamat  but not  *tasimat

In obeying the slot assignments, in fact, one may mispronounce the first two consonants (in this case, change the voicing feature of the consonants in questions while keeping to the vowels as they are) and not lose the meaning:

zidamat  (the hypothetical version of 'sitamat'); and,

dizamat (the hypothetical version of 'tisamat').


Ferdinand de Saussure—and the structuralist school after him—claimed that the production of words in human languages is a completely arbitrary affair:

Saussure posited that linguistic form [ie, a given word] is arbitrary, and therefore that all languages function in a similar fashion. According to Saussure, a language is arbitrary because it is systematic, in that the whole is greater than the sum of its parts.(


There is something incomplete about this perspective. Having seen that /dog/ may express itself as: qimmiq; chien; dog (or, schweinhund as my friend, Kalman, likes to pepper his speech in mimicking a German accent), Saussure makes a rather vague (and odd) claim that "language is arbitrary because it is systematic" and no less "greater than the sum of it parts". He goes from word to language with little or no intermediary steps in between. That he started from word outward apparently gave him no pause for thought, let alone in treating a given word as having no internal structure at all but fully-formed and permanent.

Language structures do have internal logic systems that interplay elemental phono-morpho-syntax with history and linguistic evolution in highly constrained and rigid ways. Rather.

The analysis of "four" in Inuktitut above instead suggests that these systematic linguistic structures are "information-rich" (ie, greater than the sum of their parts) not only because they are capable of encoding meanings (semantic content) but evolve according to lock-stepped iterative processes, much like how plants grow and evolve or how chemical elements combine to make compounds, each according to the available physical properties of its elements and their unique emergent possibilities when combined a certain way.