Saturday, 31 January 2015

Inuit and the notion of "number"

Sometimes, in my quieter moments, I think about Kant's decidedly mathematical assertion that space and time are primal elements of human consciousness and cognition. That Kantian philosophy would be "decidedly mathematical" is neither surprising nor remarkable, but what is remarkable (if obscurantist) about his philosophical treatment of space and time is that he went beyond the merely empirical (and, therefore, naive) and pared everything down to the absolutely essential elements of human consciousness—Descartes appears rather parochial compared to Kant:

Space is not something objective and real, nor a substance, nor an accident, nor a relation; instead, it is subjective and ideal, and originates from the mind's nature in accord with a stable law as a scheme, as it were, for coordinating everything sensed externally. (Kants gesammelte Schriften, Ak 2: 403)

Ditto, for our notion of time (ie, subjective, ideal, etc.).

What blew my mind (as a linguist) is that Kant was able to link these two primitive elements of human consciousness to the structure of language—ie, as forming the foundations of grammar, no less! I invite you to consider our notions of "proximity", and not only our notions of "past, present and future" but additionally what are called irrealis moods of "perfective past, present, and future"—ie, "will have had..."—and swat them away as you would annoying flies. What you're left with are things and actions without context (adverbs and adjectives having been swatted away along with space and time), and therefore completely meaningless (Saussurean) cats and dogs (let alone, jumps and sittings).

Georg Ferdinand Ludwig Philipp Cantor was a German mathematician who invented the set theory in mathematics. At its core, set theory is a realization that our notion of counting is a secondary, emergent activity arising only after we realize (discern) that we can collect and organize like objects into sets.

To quote the incomparable David Berlinski (Infinite Ascent, 2005):

From the first, working mathematicians turned gratefully to set theory because of its immense, its obvious, usefulness. It comprises a series of ideas, and language, and a technique, its serviceability in this regard an especially ironic circumstance just because sets are not themselves obviously mathematical objects, sets serving perfectly well to collect kiwis and kangaroos, as well as numbers and points. (Berlinski 2005, p. 128)

I would contend that the Inuit notion of "number" is exactly like how set theory treats a collection of things (ie, numbers and/or points on a plane or line). The lexicalized root itself, naasaut (number), may be analysed as:

[naa-] + [-saq-] + [-ut(i)-] or,

[completion] + [working to achieve a desired state] + [instrument]

In a typically particularized context/definition an Inuktitut dictionary, Uqausiit Tukingit (2000), defines a notion of:

naajijuq: ullunik imannanik aullaqsimaniaqłungi, ullut taakkua naangmata naajivuq

or, translated:

naajijuq: in having planned to be away (hunting) for a set number of days, when these days have past (the hunter) returns home

and, here is the entry on naasaut itself:

naasaut: nalunaiqsiniq kisutuinnait qassiuninginnik

which may be translated as:

naasaut: the act of giving an indication of how many things are

The Inuit notion of "completion" (or, "achieving an end") is uncannily anticipatory of set theoretic notions of number. The notational conventions of set theory indicate "number" in terms of a series of what are called "empty sets" {∅} embedded between {}—as per Peano's axiom that zero is a number—belies the simplicity and elegance of its subject. The concept of number is rather more abstract and ineffable for the precise reason that it is more primitive than the act of counting.

Number, then, may be described precisely in terms of Kant's notions of space and time: it is a primitive element necessary to achieve consciousness and cognition, and, more importantly, to gain competence and mastery over grammar.

The bias that it is only the Western Mind that has achieved the pinnacle and sophistication of capturing the whys and wherefores of human consciousness is really a "tilting at windmills": as Kant adumbrates, all human consciousness has space, time and number at its foundations. It is from these that any scaffolding (ie, culture) is only possible. As the Kant quotation above implies, consciousness/self-awareness is not an achievement by effort; it is a commonality belonging to all sentient beings. It is an axiom upon which all things that we can perceive, imagine and articulate are based.


Saturday, 24 January 2015

Keys to the Kingdom

In the movie, Matrix: Reloaded, the Councillor Haman character, late at night in the engineering level of Zion, says to Neo:

Almost no one comes down here, unless, of course, there's a problem. That's how it is with people - nobody cares how it works as long as it works. I like it down here. I like to be reminded this city survives because of these machines. These machines are keeping us alive, while other machines are coming to kill us. Interesting, isn't it? Power to give life, and the power to end it.

and he continues:

There is so much in this world that I do not understand. See that machine? It has something to do with recycling our water supply. I have absolutely no idea how it works. But I do understand the reason for it to work. I have absolutely no idea how you are able to do some of the things you do, but I believe there's a reason for that as well. I only hope we understand that reason before it's too late.

I approach science, math and religion in much the same way. I often have no idea how it works. But I'm also of the mind that there tend to be reasons, felt but left unspoken, for why they'd work. This realization keeps me humble. There is a feeling that I'm just scratching the surface. Sometimes I spend years contemplating something in the back of my mind, then, suddenly, unbidden, things seem to fall into place all at once and fully developed.

I think I've always had this ability for a-ha moments; the ability to consider and weigh things at multiple levels at the same time. The realization that the absurd and the profound, the sacred and the profane, often co-exist in a single statement compels me to take human genius for articulation of ideas seriously. I believe that the human mind is capable of divine inspiration in this exact way so I often obsess (perhaps unduly) over irony.

Often, where I'd intuit a highly-complex and convoluted path a simple principle is found. This is true in math, science and religion.

I know that Christianity per se has a bad reputation and turn people off as no other thing in the human experience can and is capable of. Besides the psychological dissonance in general, many so-called "Christians" are judgmental, xenophobic (racist, Islamophobic, anti-Semitic, etc. etc.) and tend to extreme passive-aggression if not outright symbolic and real violence. if the Christ wanted unabashed busybodies to represent Him.

Someone I love profoundly is a casualty of family under the evil influence of a cult. I know that Matthew 10: 34-36 is the justification for this forced, complete estrangement:

"Do not suppose that I have come to bring peace to the earth. I did not come to bring peace, but a sword. For I have come to turn

'a man against his father,
a daughter against her mother,
a daughter-in-law against her mother-in-law—
a man’s enemies will be the members of his own household.'"

The Strong's Expanded Exhaustive Concordance of the Bible says that the word "sword" (in Greek, mechaira) is a figurative term of divine judgement. This sword is spoken of Gospels as in the letters of Paul and in the Book of Revelation ("...and a sharp two-edged sword came from His mouth." Rev. 1: 16).

The "a man against his father..." part is in reference to a judgement passed by G*d in the prophesies of Micah 7:6 on the day of His visitation on Israel. Denial is the hallmark of justifying evil, it is this denial that allows unchecked perpetuation of abuse and caps off this sorry state of affairs in the family of Israel as per the divine judgement.

The quote in the Book of Matthew has nothing to do with a command to turn against family against family, let alone is it an arbitrary threat of violence from the Christ. The Christ has come to His people and what He finds is a:

"...time of your confusion.
Do not trust a neighbor;
    put no confidence in a friend.
Even with the woman who lies in your embrace
    guard the words of your lips.
For a son dishonors his father,
    a daughter rises up against her mother,
a daughter-in-law against her mother-in-law—
    a man’s enemies are the members of his own household." (Micah 7: 4-6)

The passing of divine judgement is never a condemnation but is rather a conviction (a quickening of conscience) before forgiveness and reconciliation can take root in the wayward:

“Blessed is the one whom God corrects;
    so do not despise the discipline of the Almighty.
For he wounds, but he also binds up;
    he injures, but his hands also heal." (Job 5: 17-18)

I've also been bothered quite a bit by the Islamophobia I saw in one of my fellow Christians. He is a right-wing fundamentalist and I have strong suspicions that he belongs to the sect that sees it their Christian duty to help bring about Armageddon with the ultimate end to open the path for the new Jerusalem where the Muslims are expelled and the Dome of the Rock is blown up like the Nazi emblem in that famous WWII footage—well, to be fair, it is not only the Muslims he has ideological/theological issues with but also Catholics and Anglicans, and the Orthodox Church I'd surmise if they were one of the pesky churches in Canada.

He seems so far up the ass that I suspect he's completely and blissfully unaware that:

"Whoever claims to love God yet hates a brother or sister is a liar. For whoever does not love their brother and sister, whom they have seen, cannot love God, whom they have not seen. And he has given us this command: Anyone who loves God must also love their brother and sister." (1 John 4: 20).

As usual, the common thread in all these strands a simple principle applies (Micah 6:8).


Saturday, 17 January 2015

Why literacy?

In the appreciation of a work of art, the amateur appreciates the subject, but the connoisseur admires the painting.
-David Berkinski, Infinite Ascent, p. 39

The notion of "literacy" goes beyond the ability to read and write. It requires further commitment from the reader to "turn water into wine". What I mean is that the reader is invited to partake in a tradition that is rich and generous beyond imagining. It does this by paring down the superfluous, the unnecessary (ie, ignorance and pride) and by building upon, by appealing to what was always there (ie, intelligence and rationality).

It is strange that there is no "literary-literate", but there are such things as "scientifically-literate"; "philosophically-literate"; "politically-literate"; etc.—even "artistically-literate"—that seem to suggest that literacy, per se, is not a mechanical but a maturation process of sorts, a gaining of excellence and mastery. Ie, it goes beyond, as Northrop Frye says below, the facts and statements of a text and, if trusted and allowed, goes on to affect the existential being of the person who has become literate:

Wisdom is the central form which gives meaning and position to all the facts which are acquired by knowledge, the digestion and assimilation of whatever in the material world the man comes in contact with.
-Northrop Frye, Fearful Symmetry: A Study of William Blake

The notion of "wisdom" is a slippery, hard-to-give-a-pat-definition concept because it is not a thing but a perceptual framework that is acquired not in textbooks but in contemplation of the narrative (be it history, oral traditions, classicist literature, and what is called "conventional wisdom"—or, as I call it, normative exegeses).

In the study of the Holy Scriptures I consider theology a blasphemous abomination by the simple virtue that it seeks to limit that which cannot be, by definition, bound:

The Tao that can be spoken is not the eternal Tao.
-Tao Te Ching

rather, my belief in the Gospel of the Christ Jesus has to do with the transcendent, transformative personal obligations we owe to G*d, to nature and to our fellow human beings (love (or agape) and reconciliation). I include in our obligations to nature because it says in the Book of Revelation:

...The time has come for judging the dead,
    and for rewarding your servants the prophets
and your people who revere your name,
    both great and small—
and for destroying those who destroy the earth.
-Book of Revelation 11:18 (NIV)

Socrates—in a round-about way—was less interested in definitions per se in his insistence upon universals but rather in the nature of things that define us, and our values: In discoursing on justice, he is not interested in the definition of "justice", but, rather, what is its nature, what is required of us to embody it?

In all my talk of Inuit Qaujimaningit (IQ or Inuit Knowledge) and the Family Health Model (spoken of in more detail somewhere in this blog) I've tried to impress upon people that I'm not wanting definitions of words to be posted as labels but that we discourse on and explore the implications to (personal and social) value systems. These are not intended to provide definitive answers to questions not asked but help us to be able to formulate contemporary issues around a common framework and learn from each other.


Saturday, 10 January 2015

Freedom of speech?

"The public in France has this natural tendency to be Islamophobic without being aware of it, but the horror or what just happened cannot let us forget about rationality."
-Valerie Amiraux, Canada Research Chair for the study of Religious Pluralism (

I'm a believer in "freedom of speech" but I regard it with a certain amount of caution as I would with a "right to bear arms" if we had it here in Canada.

During my survey of websites and literature for my piece yesterday I titled, Je Suis Ahmed, I was struck, as I often am when thinking about subjects and issues with certain complexity and profundity, of the scope of differing views—some wacky and visceral and downright scary, some thoughtful and utterly important to remember in times like these past few days in France. I've been deliberately avoiding posted comments in news stories knowing how disturbingly uninformed and thoughtless some can be.

It is interesting that Muslim and those of Arab descent tweeted the more rational and personally thoughtful comments on the senseless massacre in Paris:

while the hashtag #Je suis Charlie comments tended toward the decidedly abstract, vague, mechanical and impersonal comments about values and freedoms. As in Dyab Abou Jahjah's tweet, Voltaire was also much referenced in #Je suis Charlie but I doubt his heart would have been warmed by a somewhat reactionary sentiment expressed by the non-Muslim twitter. I think Voltaire would have quipped:

Superstition is to religion what astrology is to astronomythe mad daughter of a wise mother. These daughters have too long dominated the earth.

or some variant referencing hate speech with the recently-much-cherished "freedom of speech", and he would have humbly signed his tweet, François-Marie Arouet.

Observing what is now happening in France with attacks on mosques he would no doubt say: "It is dangerous to be right in matters where established men are wrong" with the glaring irony lost upon the self-righteous fools who think such attacks are justified.

I know a so-called "Christian" here who thinks casual Islamophobia is a God-given Christian duty. I bet you dollars-to-doughnuts that this is a hall-mark of the Harper base. Our highly-esteemed Public Safety Minister made a huge show of solidarity (as has Harper himself) with our French allies but I get a distinct feeling that their ideas of "freedoms" in general are somewhat off the mainstream notions of freedom.

I weep for the species.


Friday, 9 January 2015

Je suis Ahmed

Ahmed Merabet was a Muslim cop who was assassinated as the last victim in the Charlie Hebdo massacre who seems to have had the misfortune of being in the wrong place at the right time, on patrol when the gunmen burst out of the Hebdo building, shot down then shot in the head for good measure.

There seems to be a whole lot of self-righteous indignation on all sides with very little cause for admiration.

Ahmed Merabet probably did not want to die, but he did not die needlessly—in fact, he died in the line of duty. He died a hero, and, unlike his killers, a martyr for the French Republic and all the noble ideals so often abused in the country itself and the other like-minded countries in the West.

Rather than focusing on the negative, normative edicts, bulls and fatwas that come out so easily in these times of on-going religious and ideological crises I'd like to focus upon the so-called cardinal virtues to honour Ahmed Merabet's sacrifice.

This is taken from Wikipedia:

  • Prudence (φρόνησις, phronēsis): also described as wisdom, the ability to judge between actions with regard to appropriate actions at a given time.
  • Justice (δικαιοσύνη, dikaiosynē): also considered as fairness, the most extensive and most important virtue.
  • Temperance (σωφροσύνη, sōphrosynē): also known as restraint, the practice of self-control, abstention, and moderation tempering the appetition.
  • Courage (ἀνδρεία, andreia): also named fortitude, forbearance, strength, endurance, and the ability to confront fear, uncertainty, and intimidation. (
It is said of the mu'min that two testimonies are required of them that believe:

O you who believe with the tongue! Believe through your deeds. (Quran 4: 136)

Unlike his selfish killers, Ahmed did not force upon the circumstances perversion of his faith; his life was taken as ultimate payment for the protection of innocents, as a symbol of the noble ideals that so few of us appreciate let alone would die for.

Four score and seven years ago our fathers brought forth on this continent a new nation, conceived in liberty, and dedicated to the proposition that all men are created equal.

Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battlefield of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this.

But, in a larger sense, we can not dedicate, we can not consecrate, we can not hallow this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us—that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion—that we here highly resolve that these dead shall not have died in vain—that this nation, under God, shall have a new birth of freedom—and that government of the people, by the people, for the people, shall not perish from the earth. (Abraham Lincoln, Gettysberg Address)

Je suis Ahmed Merabet
Je suis Patrice Vincent
Je suis Nathan Cirrilo

We, the living, salute you.

Saturday, 3 January 2015

Whys of my faith

Yesterday I had lunch with one of my colleagues. We had a very interesting conversation centered around abstract notion of preservation of property—scaling constant in different sized fonts, clock calculators, etc. (even G*d).

He is Muslim and I a Christian; we believe in the same G*d. It is, in essence, that only the details and specifics that differ. And I don't much believe in the artifacts of religion. Like the Cohle character in True Detective I quoted yesterday, I do not want to become a "piece of s***".

I try and perceive faith in somewhat mathematical terms. What I mean is this:

Teach slaves to be subject to their masters in everything, to try to please them, not to talk back to them, and not to steal from them, but to show that they can be fully trusted, so that in every way they will make the teaching about God our Savior attractive. (Titus 2: 9-10)

Rather than focusing on the value-laden terms like "slaves" and "masters" I exchange them for x and y and literally strip the principle down to its essence. Same thing with a phrase like "be subject to", which become an functional operation like "in relation to", like so:

Let x and y strive such they are in relation to a state of trust and good will between them.

The ideals: "not to talk back to" and "not to steal from" apply whether the relationship between the x and the y is one of equal or unequal dynamics, and really need only one side to commit to an ideal, which, given enough time and perseverance, will literally change the relationship or at the very least the perspective of one of them.

Titus continues:

For the grace of God has appeared that offers salvation to all people. It teaches us to say “No” to ungodliness and worldly passions, and to live self-controlled, upright and godly lives in this present age, while we wait for the blessed hope—the appearing of the glory of our great God and Savior, Jesus Christ, who gave himself for us to redeem us from all wickedness and to purify for himself a people that are his very own, eager to do what is good. (Titus 2: 11-14)

"to live self-controlled, upright and godly lives in this present age" has to start somewhere and this commission for the believer starts from:

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. (Micah 6: 8)

This, says the Lord, after rejecting the artifacts of religion:

With what shall I come before the Lord
    and bow down before the exalted God?
Shall I come before him with burnt offerings,
    with calves a year old?
Will the Lord be pleased with thousands of rams,
    with ten thousand rivers of olive oil?
Shall I offer my firstborn for my transgression,
    the fruit of my body for the sin of my soul? (Micah 6: 6-7)

When I sought help I was advised by a fellow Christian something that I read elsewhere later: "Come as you are." I take to heart the simplicity of this invitation. There was no judgement, no demand to jump over bureaucratic hoops, no rituals I was required to perform, but to meditate upon "My soul, wait thou only upon G*d" (Psalm 62) in the writings of Andrew Murray (

Had I not started here I think I would have easily lost interest again. I would have probably half-heartedly sought salvation in ritual before giving up, and the temptations to ritual are replete in the Christian community: it was impressed upon me that the Anglican faith I grew up in was wrong and that my baptism as an infant and the subsequent confirmation in my teenage years was somehow invalid. Right...

The notion of teshuva ( is, by necessity, a one-to-one relationship with G*d and not a performance of a communal ritual. As Aharon E Wexler (2014) writes in his essay, On Teshuva, the concept is often mistranslated as "repentance" when its actual root comes from the notion of a return to G*d, "a return to the person we were meant to be".

That, rather than becoming proficient in issues of doctrine, is what I'm aiming for, or more precisely, waiting upon G*d for.


Thursday, 1 January 2015

Moment of conception

"If the only thing keeping a person decent is the expectation of divine reward then, brother, that person is a piece of s***. And I’d like to get as many of them out in the open as possible. You gotta get together and tell yourself stories that violate every law of the universe just to get through the goddamn day? What’s that say about your reality?"
-Rust Cohle, True Detective

Over the holidays I have discovered that my cable subscription includes HBO Canada. I've been catching up on my favourite, Game of Thrones, and discovered True Detective starring Woody Harrelson and Matthew McConaughey. What a dark, compelling piece of writing; a perfect example of why I love American literature.

It's not so much the dark and compelling part that draws me in, but how the story-line is utilized to explore what it is to be human within the context of the human condition honestly.

McConaughey's character, Rust Cohle, is a hard-core pessimist/nihilist who riddles the whole miniseries with dark gems, his own takes on Nietzsche but not really. Or, more precisely, he is the organ in which Nietzschean genes are conceived and expressed but a creature not entirely Nietzsche but uniquely Cohle is birthed.

Nietzsche just doesn't have the constitution for it—his perspective is idealized in the notion of a 'superman', and, necessarily, speculative (ie, like Harper, Nietzsche games the system because he lacks the imagination, the capacity to be truthful)—whereas Cohle derives his perspective from the landscape he is written to witness and doesn't have the luxury to indulge in fantasy:

"The world needs bad men. We keep the other bad men from the door."

In this respect he is the archetypal Batman: he is not overwhelmed and defeated by the darkness (he does not deny darkness) but is driven by something deeper, something less certain, something like a conscious choice, something divine.

Over the last couple of weeks I've re-reading and contemplating the Mario Livio book, The Equation That Couldn't Be Solved (2005), not so much for its technical concepts but from what I've come to call the "moment of conception".

What I mean is, like Cohle's unique take on Nietzsche, I seem to be perceiving something beyond all the fancy language of mathematics (or, Nietzsche's pessimism, if you will), something approaching the metaphysical.

I've been contemplating the real line (ie, in maths, the 'real line' is defined as comprising all the numbers that organically manifest in the number line (including not only the rationals but also the irrational-, the algebraic-, and the transcendental- numbers, even unto the imaginary numbers). At the "moment of conception" of the number line, these numbers existed no matter the grief and pain that it took to discover and conceptualize them.

In each step that brought these different types of numbers into light moments of real crises mark their acceptance and reconciliation into the human mindscape. It is not only the Church, but—fundamentally—the orthodoxy and the very circumstances that resisted and conspired to deny their existence.

The history of mathematics is a microcosm of this eternal struggle, this peeling away of feeling and revelation of truth. These truths are all the more precious because of the blood and sacrifice that purchased them. Ignorance is not dark and evil because they are in its nature; darkness and distortedness are signals of an incompleteness of revelation, and therefore contingent upon their opposites. That ignorance is often marked by certainty and hubris that break and shatter under the weight of new knowledge is the truth of their utter contingency.

In this respect (this moment of conception), the opening lines of the Book of John are figuratively and literally true:

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)

Psalm 19 says of God's glory, the works of His hands: "They have no speech, they use no words; no sound is heard from them. Yet their voice goes out into all the earth, their words to the ends of the world."