World Without Numbers Essay Checker

Here is a theory of time. It is neither new to me nor new in the world. I formulated it for publication in 1999 and had it formulated for me, so I could make it my own, sixteen hundred years ago by Augustine in 399 C.E. and some three quarters of a millennium before that by Aristotle, post-335 B.C.E.* There is a certain advantage in revisiting old thoughts, although they have become second-nature and have lost the footloose feel of thinking that is yet on the path to discovery: these long-held notions have also sloughed off some of their complexity and are more amenable to summary.

The theory is, first, that time is not a being, a thing, or a substance in the world, nor does it operate as a power, a force, or a destiny in our life. It has no external existence, and all speech attributing reality to it is unwittingly metonymic, meaning that the word “time” is used by a sort of obtuse poetry for processes that have better names of their own.

The theory has a second element, namely that it would be a better world, and we would be better off, if more people thought that time was unreal and spoke accordingly.

Before closing in on the gist of this theory, I want to acknowledge an intelligent resistance that a listener might feel arising within. If you have a notion proposed to you as true and are immediately told that it is also beneficial, shouldn’t you rear up and resist as a matter of principle? Don’t we keep ourselves honest by tinting our glasses grey? Isn’t a truth that comes embellished with utility very suspect? Of course it is, because it might be nothing but a Pollyannaish optimism, a self-pleasing thoughtless this-is-the-best-of-all-possible-worlds” optimism. What I’ll be proposing has behind it a sense that demands more reflection. I call it “ontological optimism.” Ontology is the account of being. The very notion of Being requires a complement: Appearance. The true Being of which true philosophers strive to give an account comes to our attention as opposed to what only appears or is merely incidental. The two greatest philosophers of classical antiquity, Plato and Aristotle, were ontological optimists. They do not, in the least, think that everything within this world is always for the best, but they do think that its sources, be they at work from beyond or within, are wonderfully good and therefore attractive to our knowledge-hungry souls.

I’ve briefly set out a reason for not foreclosing on a proposed truth because it is beneficial to believe it—although in the later history of inquiry into the nature of things there will be those who make pessimism—a sense that things are as bad as possible—the test of truthfulness, because the way things are is in truth ugly. To deal with this split in the human sense of the world requires a lifetime’s conversation. For now, I’ll posit a guarded optimism.

There is a second misgiving that a canny listener might have: Does every truth want announcing? Shouldn’t prudent people suppress some parts of what they feel compelled to believe? I’ll give an example with major consequences. Our Declaration of Independence claims that “all men are created equal” in respect to “certain unalienable rights, among which are life, liberty, and the pursuit of happiness.” Just read Lincoln’s speech on the Dred Scott Decision (1857) for his sense—a true believer’s sense—of the vulnerability of the document’s basic assertions, assumptions that have by now become even more questionable for us. For the Declaration grounds our equality in a common divine Creation, and that is no longer a faith to be taken for granted. Is the questionableness of the ultimate equality of human beings, then, a proper subject for public inquiry? Not on your life—not in principle and surely even less in fact. Some topics have to be left alone if we’re to live together. When you hear some of my claims about time you might wonder if time isn’t such a topic.

Of course, I’m speaking tongue-in-cheek, precisely because I think that a public reflection on the reality of time might lead to a revision of some current mantras which seem to me humanly deleterious, whereas the doctrine of equality seems to me humanly beneficial. And also, in all candor, because the kind of ontological reflection I mean to put before you is in fact very unlikely to be of major consequence to the world—though I share with all speakers at academic symposia a secret desire to be dangerous.

So I’ll barge on, telling first what time is not, and then what it is insofar as it is anything, and finally why an affirmation of its unreality, of a world without time, is advantageous to life.

First, What time is not: Look into the world and try to detect time. Our environment is full of time-telling, but the thing told is never in evidence. David Hume’s consequence-laden observation was that we never actually see a cause, only a constant conjunction of events. So also with time: We never observe it, only changes in space. Time is told either by location in space or by counting in…what? Wouldn’t the natural completion of that phrase be “counting in time?” That’s circular, to be sure, though in fundamental thinking circularities are often revealing, because they display ultimate involvements. In this case how we catch something bears on what it is.

Second, then, What time is: Basically time-instruments are in the analogue mode. Timaeus, in the Platonic dialogue named after him, says that what we call time is “a certain movable image of eternity…an eternal image going according to number.” (37d ff.) Time is an “image of,” or is analogous to, eternity because it is everlasting and has neither beginning nor end. It is a mere image because it appears as change, and so it doesn’t achieve the undifferentiated nowness of eternity; it is movable as traversing circular distances. Its generating and telling instruments are the visible heavenly bodies. In other words, the heavens both are and tell the time of the world; they are both cosmic time that goes on forever and a heavenly clock that needs no rewinding. The watches most of us wear on our wrists are in turn made in the heavens’ image; they are analogues of the circular motion of the sun (as it appears to us) or of the earth (as Copernican theory persuades us). Whether the time-piece is cosmic or miniscule, it tells time by an indicator, sometimes a heavenly body, sometimes “a hand” moving over a portion of a circle’s circumference. So even a little ladies’ watch is an analogue of the cosmos. There are also in our day digital time-pieces that involve counting and will open a can of worms. I will speak of them later. One difference between analogue and digital clocks comes across in a preference for the round watchface as expressed by a friend of mine who said: “I want to know what time it is, but I also like to see what time it isn’t.” Analogue watches tell time in terms of the everlasting revolutions of the heavens together with the conventional divisions of the human day.

Aristotle picks up on the “going” of the image “according to number”—or so it seems, when we read Book 4 (chaps. 10-14) of his Physics(which contains his account of time) in juxtaposition with the Timaeus. Probably he clued it out himself. In any case, he puts motion together with number to spectacular effect—the first instance I know of in any writing of time being effectively undone as a something. He doesn’t say: “I’m first; this is a conceptual revolution.” He would much rather make his thinking persuasive by presenting it as a tweaking of thoughtful predecessors. Yet, in brief, he has discovered that time is incidental to change. And since he thinks that all change is at bottom locomotion (chap. 7.7), this means that time is attendant on motion from place to place. Moreover, this motion is numerable. For although it is continuous, it is divisible into even measures at any of the points of the trajectory of a mobile object. Every motion, of course, implies a moving object which generates, one might say, a path, whose diagram is an open or closed orbital trajectory. Then time is the counted collection of all the measured linear units: 12 (EST), for example, is the counted number of dial-measures in which the sun reaches high noon, the zenith of its orbit, from a fixed starting point opposite. Or 13 (years) is the number of the sun’s yearly circuits on the ecliptic, the day after which a young Jew is said to be a man. For motion to be thus countable, it needs to have a recognizable “before and after:” here before, here now, here thereafter. Thus Aristotle defines time in this way: “Time is the number of motion with respect to before and after.”


Here, we might think, Aristotle has gotten himself into deep trouble. “Before and after” are, after all, primarily time-words: past and future divided by a non-time, a span-less, point-like “now.” Thus rewritten, “Time is the number of motion counted according to the progress of time” doesn’t sound very helpful. But Aristotle has a perfect defense: For him every motion that is not violently unnatural is a development of potentiality from implicitness to fulfillment. Therefore every motion—sublunar ones that begin and end and heavenly motions that never cease—every single motion has discernible phases even before time is brought in. So “before and after” can indeed be pre-temporal, as are the implicit stages of a development.

But there is a more serious stumbling block, and I will make a gift of my book on time to anyone who removes it for me in Aristotle’s terms. He emphasizes that time is the counted number, not the counting number. (4.2) So if I say “twelve o’clock high” I mean the twelve counted path-segments of the sun’s motion, not my counting thereof. But Aristotle is also quite clear about the fact that there can be no counted number without a counting consciousness. (Aristotle, of course, says “soul,” and so should I, though the word is at present proscribed, and “consciousness” is de rigueur, I think principally because it is from Latin and has three syllables and seems less naïve than “soul,” which is from good Old English and has but one.)

So the counted motion, which is time, requires a counting soul. Here is the problem: The counting soul does not just beat with a steady pulse: one, one, one…  That’s what the digital watch does, thereby electronically causing a prescribed series of numbers to appear on a spatially moving dial. The soul actually recalls the pulses accumulated. Its numbering is ordinal: first, second, third. It saves bygone pulses in their order and projects future ones, and it is present, here now, at each moment of counting. But if it is counted motion that is time, then the counting soul is pre-temporal. What then is the substrate of its serially ordered activity? Aristotle, in making time external and incidental, something that is found in nature only as a mere measure, has also made human counting an enigma. What name shall we give the psychic development that directs ordered, ordinal, counting?

One reason why Aristotle has effectively reduced time to nothing in itself is that it is in its conceptual structure dramatically unlike its representational analogue, the linear path, the visualizable trace, of a mobile object. The time-line segment before the now, called “the past,” is gone, erased; the future time path is not yet and invisible; the now is analogous to a point which has, as Euclid says, no parts and “in” which nothing can exist. If you cast yourself into time, you’re done for; there is no time span in which to exist—though plenty of spatial extension in which to move.

Immanuel Kant

Here’s an interesting addendum to the Aristotelian difficulty. It is taken up and solved more than two millennia later in his own terms by Kant in his Critique of Pure Reason(1787)—not the enigma of existence, namely, what span time’s “no-longer” and “not-yet” leave for us to be in—but time’s particular relation to counting. Recall that Kant thinks that all our experiences, whatever appears to us in an eventually apprehensible way, already comes directly formatted temporally and spatially. But this forming frame is, so to speak, amorphous and beneath awareness. It needs to be brought together (in Greek, “synthesized”) with thinking, with the understanding. Kant assigns to the imagination the mysterious work of joining intuition and understanding, distinctionless time and a determinating concept. Kant thinks that this latter is the concept of quantity, and that when intuited time is made determinate by quantity, counting is the result. The way I put it to myself is this: Time makes its appearance in consciousness by a kind of pulsing that is a now-counting: now1, now2, now3…, or one, two, three…. This analysis seems to me true to experience. Sheer temporal awareness seems to be a kind of pure enumeration of beats—it may actually be our heart-beat felt as a pulse, the throbbing of our arteries following the pumping of the heart. What makes a span of time, time lived through, is having laid up that cardinal count in memory, where it becomes ordinal: first beat, second beat, third beat. Thus the mere beating turns into a first, second, third moment of remembered past.

So Kant solves the problem by bringing time totally within the consciousness of a “subject,” that is, a thinking I. Time is not soul-numbered motion entering into the world from outside, but number itself arises as a conceptualizing of intuitional time within the subject. But then, so does everything within the reach of our comprehension arise within me, the subject; this elucidation of time is bought at the price of near-total subjectivity. Moreover, the deep origin of time as a form of our sensibility, though in us as subjects, is not for us as knower: The grounds of the possibility of our experiential knowledge are not within our experience. Thus one might say that for Kant, too, aboriginal time is a non-being, not a knowable something—that inferred ghost which he calls a noumenon.

Third, What time is insofar as it is anything: So I’ll leap back through the ages to Augustine, who seems to me the greatest phenomenologist of time, that is, the finest observer of the internal experience we have of it, and the first analyst of its elements.

That is not just my opinion. The most comprehensive and acute work on time in modernity that I know of, Husserl’s On the Phenomenology of Internal Time-Consciousness (1893-1917), is essentially an acknowledged elaboration of Augustine’s own answer in the Confessions to his famous phrasing of the enigma of time: “What, then, is time? If nobody asks me, I know; if I want to explain it to someone who asks, I don’t know” (10.14). Augustine allows that we all know time as an experience, sometimes an acutely and deliciously painful one: Here’s Shakespeare, Augustine’s rival in time-consciousness:

Being your slave, what should I do but tend
Upon the hours and times of your desire?
I have no precious time at all to spend,
Nor services to do till you require.
Nor dare I chide the world-without-end hour
Whilst I, my sovereign, watch the clock for you,
Nor think the bitterness of absence sour
When you have bid your servant once adieu. (Sonnet 57)

Who among us has not spent a world-without-end hour sitting by the telephone? Who is not acquainted with the swift “time’s up” of dense experience, short in felt duration, long in remembrance, or the dragging “are we done yet?” of bored disengagement, endless as a happening but miniscule in memory? Or the brute standing still of time in pain? Or the relative pace of experienced time that Rosalind describes in Shakespeare’s As You Like It:

Time travels in divers paces with divers persons. I’ll tell you who Time ambles withal, who Time trots withal, who Time gallops withal, and who he stands still withal. (3.2, 299-302).

That’s the experience described—but now to the experience explained. How does it arise? Here is Augustine’s answer, which I’ll frame as a diagram for you to envision.

Imagine a horizontal line of indefinite length. It represents all the world’s simultaneous motions, its goings-on, from the stars’ revolutions to the mosquitos’ dartings. For Augustine, the Christian, the line must have a beginning, Creation, and an end, Judgment Day. In God’s omnisciently comprehensive sight it is all there at once. But human beings experience it as an extension. Imagine a second vertical line, best drawn orthogonal to the world line, and moving along with it. The moving point of crossing is an “origin.” It represents our mind, existing now, in contact with the world and borne along by its motion. So it is not really a mathematical point but a living moment in a moving world. Later writers, beguiled by Aristotle’s analogy of the temporal now to the spatial point of no extent, will see the need to call it the “specious present.” But it is not a specious—that is, pretend—present, at all, but a real psychic event, albeit a mystery.

Where then in this diagram is past and future? The vertical line represents, as I said, the mind. And the mind has, as Augustine puts it, distentio–its lengthening, its existence, its longitude, we might say. Diagrammatically, it extends above and below its origin, its moment of existence, its contact with the world. The part of the vertical below the moment of existence in the present world represents a build-up of memory-moments, deeper and deeper in the soul, lower and lower on the upright.

Next, all the moments of memory are connectible by parallel oblique lines to the world line that the mind has traversed. If we imagine the forward motion of world and human being progressing toward the right, then the world line to the left of the origin represents motions and events left behind in the past, and each of our true memories down on the “distention” of mind connects to, projects on, a receding point to the left part of the world’s motion line. Of course, scrambled connections (crossed projections) and false memories (wandering projections) can occur. That is how we have a past; the past is a stack of nows now in our distended minds—and all one now in God’s collected mind.

Likewise with the future: Think of it as all the plans and expectations, further and further away from the present, rising upward on the upper half of the mind’s line and projectable by parallel-oblique lines onto the future motions of the world.

That there is in fact a past, though for us only partially and only indirectly recoverable and real only in memory, is common belief; whether there is in fact a real future and how our plans and expectations bear on it is a great theological problem—in fact, the problem of free will. But this much Augustine shows clearly and, I think, truly. He says that we must speak of “a present of bygones, a present of presences, a presence of future things,” (11.2) and continues: “For some such there are in the soul, and I do not see them elsewhere. The present of things gone is memory, the present of things present is sight, the present of things future is expectation.” (11.20, 28) In my words, time is entirely the effect of memory and expectation. Insofar as time is anything, it is a so-called epiphenomenon, an idle, ineffective affect supervening on the real operations of memory and expectation.

But no—“idle” is an inadequate word for our potent sense of time, which is to be understood as our sense of our mind’s longitude, its present lengthening into the before and after of the now of our existence—and of course that fact underwrites, overwrites, potently affects our life.

So now I can zero in on a sense of time that seems to me both spurious and deleterious. It is time not as an internal enlargement of existence but as an external being or force. Continuous time, thought of as being in the world, may be conceived as a continuous stream bearing things along, an absolutely primal, equable flow (of what? we may ask) that is unaffected by anything else in the world; this is Newton’s absolute time. (Principia [1686], First Scholium) You may even hear it, as Shakespeare (once again) makes Hamlet speak of one who “only got the tune of time,” a hum conveying its “most fond and winnowed opinions.” (5.2, 183) You may figure it as a linear, open-ended, unbounded mere going-on, or as a closed, ever-repetitive, bounded cycle. In these metaphors, the laws of motion apply indifferently whether time is run forwards or backwards. Or you may imagine the continuous temporal substrate as directed by a forward arrow, a principle of unidirectional change or development that prohibits reversal. This sort of time is not, one might say, “when-neutral;” you might call it change in the abstract, or the substrate of embodied change. In all these forms, some sort of quasi-event or pseudo-motion is imagined as continuous.

The other metaphor, the second figurative way of imagining time is, on the other hand, continual: The now, the present, continually divides the stream of time into gone-by and not-yet-arrived, into past and future. Thus time breaks into a lost past and a not-yet-gained future around a continually new-event-now. This new-now nullifies the past as living; it leaves the passed-away past, so to speak, set in stone. It is, quixotically, both hard-and-fast and intangible: You can’t change it—or so they say. It is indeed, often literally, set in stone; for instance, epigraphy is the discipline of deciphering inscriptions, often found on marbles. Its watchword is saxa loquuntur, “the stones speak.” But does that really mean you can’t change it?

For consider that these testimonials are not past, not in the past. They are in the present, and we must make of them what we can—or will. This curious circumstance, that the past is real only in the present, might be thought of as the incarnation of the memory that Augustine calls “the present of things gone.” You can see that a thoughtful consideration of the past opens a can of worms. What is memory, the storage house of time-expired presences? How invulnerable to change is the memorial past? What about that secondary, often public, memory that is built up from present testimonials of past events? What is more changeable than the past—perhaps even transformable into the present?

But this can of worms is replaced by a bucket of serpents when it comes to the future. For who would doubt that except for a God-inspired prophet, no one can have the future in mind? The future, by the very meaning we attach to it, cannot provide us with any testimonials; it hasn’t happened. All we have are our hopeful or fearful expectations, dim intimations of blessings or harms to come, and uncertain conjectures, projections of our past experiences embellished with change-vectors, their rates and directions of change, and, above all, an impetenetrability made less or more pliable by our weak or resolute will. The will is the human force whose very name announces future-directedness, by means of which we take hold in our minds of the yet-to-be and try to bring it about in the world to our satisfaction. To be sure, we may make vivid pictures of the future, but closer examinations will show that they are, depending on our mood, imaginary recollections from a golden age, or over-the-top distortions of present trends. But they are not images of originals that reside over there in the future—for there’s no there there.

Fourth, and finally: World without time: You can probably tell from my tone, that my desire to cancel time has much to do with the damage that can be done to us by the notion of a real future. Let me now enumerate three elements of a theory that presents time as unreal in the world, as not thing-like, not force-like—a theory by now surely exposed as part of a program of resistance to certain ways of life. Then I will complete my talk by fleshing out briefly these refusals to cooperate with “time.” So then, my three recalcitrances: (a) to the past as passed away, bygone; (b) to the present as mere passage, transition; (c) to the future as an imperative power.

(a) Insofar as the past is the span of time behind us, if time is something real, those spans are really dead, and their relics are mummies, either to be carefully prepared, with ointments of honey or baths of vinegar, to live the museum life of the embalmed departed, or to be discarded upon that notorious rubbish heap of history as no longer “relevant” to our time, the present. Thus, for those of a venerating temperament, the past becomes a silent tomb near which they sit rigidly in. For others, whose dispositions long for change, the past is a spent force, a deadweight on their innovative energy. To neither party is the past, if it is anything, the time-proof treasury that houses all our inheritance of thought and imagination, once human memory has reluctantly let go of what is too delicate, or cheerfully chucked out what is too trashy, for prolonged life. But how the past is properly present to us is a tricky and timely subject for another day. So much can be said in a sentence: Unless we want to cut ourselves out of humanity’s will and remove ourselves as beneficiaries of its estate, we had better give up thinking of the past as having a date of expiration.

(b) Those who feel the past as a march of obsolescence are in fact consigning their personal present to mere transition. For the life-principle of obsolescence is innovation, and innovation is not the heart-stopping or mind-boggling perpetual newness of an imagination-arousing work or a truth-revealing theory or a potent Newness is ever-fresh and invulnerable to obsolescence, because it is not a mere time-marker, a mere date-stamp, on the work of art or on the discovery of an explanation, or on the invention of a contrivance. Newness is rather inherent to these wonders insofar as they break into the ordinary course of on-going life and enhance or redirect it. Time cannot stale its infinite variety.

Innovation, on the other hand, is systematic, intentional novelty, willful newness. In the innovative mindset (this is a derogatory term: fully alive people don’t have mind-sets), small novel differences often trump great solid worth. People succumb to the persuasion that “we live in a time of change,” giving to time an independent power, as if it were an accelerator that puts life in overdrive without the need of my foot on the figurative pedal—a vehicle racing through each present to the next, a car in need of a factory recall. Otherwise put: People accept that they live in “a time of…” and that it is prudent to “get with it,” to clue out what this time-tyrant commands and to do it—in our case, to treat each moment of life as just a bridge to the next novelty. But there is no such time-potentate. There are only people willing to go along—not, to be sure, with the non-existent times, but with what each person thinks the others think, or whither his or her option-dissipated likes weakly tend. What a humanly actual present—I am tempted to say, a time-less present—might be, what, in short, it means actually to exist, is, once again, worth a long conversation.

(c) So then, finally, the future, the chief and least existent venue of real time. You all know the vocabulary of future-possessed. Some say: “The future is here”—really absurd speech; if it’s here it’s too late. They might have meant: Be proactive! Clue out what is coming and preempt or prevent it. The original meaning of “prevent” was “go before,” as in the Psalm 18, in which David is fearfully imagining: “The sorrows of death compassed me about: the snares of death prevented me.” He means “came before me, confronted, me.” (18, 5) In that sense, the anticipation of the future, in literally “foregoing” it, also “prevents” it; it forecloses the future. Human beings are surely entitled, even required, to prevent the future in the sense that by anticipating their version of it they’ll bring it about or keep it from happening—as long as they understand that they are going towards something, an “it,” that is not there to meet them. How we think about our plans makes a great difference: whether we justify our intentions as accepting, managing, and yes, serving, what is coming at us in the false, even craven, belief that there is a real future; or whether we, believing the Future (capital F) to be a false reification, a confusion between an abstraction and a reality, make ourselves think now, in our present, about what is best and most desirable and also humanly possible—and then do that.

And, once again, there is endlessly more to say about the future. But instead of pursuing it, I will end with this observation: Being future-recalcitrant is the very opposite of being reactionary, for the non-existence of the future—or at least our ineradicable ignorance of it—is the very condition of our practical freedom.

Books by Eva Brann may be found in The Imaginative ConservativeBookstore. This lecture was delivered at the Symposium on Time held at Belmont University in Nashville, TN on September 23, 2014. It appeared in The St. John’s Review (Volume 57, No. 1, 2015) and is republished here by permission of the author. Miss Brann welcomes questions/comments via mail: Dr. Eva Brann, St. John’s College, 60 College Avenue, Annapolis, MD, 21401-1655 (she does not use computers).

*See Eva Brann, What Then Is Time?(Lanham, MD: Rowman and Littlefield, 1999).

Published: Dec 9, 2015

Eva Brann

Eva Brann is a Senior Contributor to The Imaginative Conservative, a distinguished and long-serving tutor at St. John's College, and the 2005 National Humanities Medal recipient. Dr. Brann's works include: Paradoxes of Education in a Republic, The Past-Present: Selected Writings of Eva Brann, What, Then, Is Time?, The World of the Imagination: Sum and Substance, Homeric Moments, Feeling Our Feelings, The Logos of Heraclitus, Un-Willing: An Inquiry into the Rise of Will’s Power and an Attempt to Undo It, The Music of the Republic: Essays on Socrates' Conversations and Plato's Writings, and Then & Now: The World's Center and the Soul's Demesne. Dr. Brann has also published translations of Plato’s Sophist and Phaedo.

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Try to imagine a world without numbers. No more addition or subtraction, algebra nor calculus. No more high school geometry. It would be pretty hard to get by without basic counting, such as being able to tell whether you had caught five fish or ten fish. Yet one tribe in Brazil seems to get by just fine with practically no comprehension of any mathematical concepts.

The inhabitants of the banks of the Maici river live in a world unlike our own. The difference goes beyond the lack of computers, cell phones and cars; one would be hard pressed to find that technology in the middle of any forest. Rather, for the Pirahã, numbers are just not a big part of their life. They can barely count, and anything more difficult than that is right out. That’s not all that’s different about them; They lack any examples of art or fiction, and their language has a grammar so radical that it could possibly disprove the theory that certain principles of grammar are shared by all languages— the universal grammar theory. The Pirahã certainly have a unique way of life.

The Pirahã are terrible mathematicians, unable to do even simple addition. Then again, it’s difficult to do any sort of calculation when you have no concept or words for exact numbers. There are really only three numeric words in Pirahã – “one,” “two,” and “many.” To add to the confusion, “one” doesn’t always mean exactly one – it could mean one fish, a small fish, or only a few fish.

There used to be a belief, however, that number words were not necessary for a concept of mathematics. Other tribes with similarly limited numerical vocabularies have managed to practice some mathematical concepts, however researchers have failed to teach the Pirahã even the most basic math. After eight months of lessons, none of the Pirahã could do anything more complicated than counting up to three. The rest of the mathematics is far beyond their grasp. This is not to say that they do not understand what math is— just that they cannot seem to do any of it.

Numbers are not the only limited part of their vocabulary. Their language lacks quantifiers such as “all,” “every,” “most,” “few,” etc. There are no basic color words— red could be described as “blood-like” but there is no single word for “red.” Also limited is their kinship system, for which there are only terms for direct biological descendants (daughter, son) and for people of differing generations (i.e., one generation older). There are even some claims by researchers that the Pirahã borrowed their pronoun set from a neighboring tribe and did not even have any before recent times!

Of course, it would be difficult to develop a complex vocabulary when limited to just ten consonants and vowels, a number which makes the Pirahã language the world’s most phonetically limited language. But while the language cannot be written, it can be whistled, hummed, or put into music.

When one starts to look at the grammar of their language, it becomes even stranger still. For one thing, it lacks the concept of perfect tense. Of more interest to linguists is the discovery that the Pirahã language does not allow for one phrase to be embedded inside another, which means the language is not recursive. This property of the Pirahã language runs counter to the theory of universal grammar, since recursion is one of the properties of the theory.

As far as researchers know, there are no fictional stories nor mythologies in the Pirahã culture. All stories are descriptions of experiences, and these stories only go back one or two generations at most. There is no collective memory of the Pirahã people; no history of their people is recorded by them. There is practically no art in their culture; whatever drawings they make are only used to describe the spirit world that they have experienced and are not drawn for aesthetic purposes.

Another extraordinary quality of the Pirahã is their amazing physical endurance. They take short naps from fifteen minutes to a few hours, usually sleeping no more than two hours a day. They only occasionally sleep through the night. On top of that, they often starve themselves— even if they have enough food— just from a desire to be more strong.

One might think that this unique way of life would disappear if introduced to modern life, but this is not the case. They do not live in isolation; they have been in contact with other Brazilians for over two hundred years, and they have sold goods to traders for quite a while. Rather than being absorbed by their neighbors, they resist. The reason for this is because the Pirahã see themselves as intrinsically better than the people around them, and so they do their best to avoid being like others. Maybe they resisted progress so fiercely that they have succeeded in keeping their culture different from those around them. Then again, maybe they really are superior, and we just lack the mental faculties to realize it.

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