# Linguistic Combinatorics: Infinity and Human Language

Linguistic Combinatorics: Infinity and Human Language

I’ve just started reading The Language Instinct by Steven Pinker. It’s a very readable book directed at laymen to the field of Linguistics. I had been enjoying how he lucidly shows that we at genetically-specified to acquire language and agreeing with this thesis. Then I came to the chapter, entitled How Language Works and here I had a problem. My problem lead me to begin thinking about what at first sight appears to be a simple question.

Are there an infinite number of ways we can combine words of any language (in our case English) to form meaningful sentences? Simple it seems huh? Not so fast. Pinker repeatedly tells us yes, we can make an infinite number of sentences in this or any other language. He uses algebraic combinatorics to show this. But, to me this doesn’t seem so. The implication of my dissent is that we have an upper supremum on what meaningful statements we can make in any language.

Take English, with 26 letters we can form a large finite set of words. I’ve read, from lexical sources estimates that English has approximately 500,000 to as high as 800,000 words. The combinations of those words arithmetically go well beyond named numbers. This set, if we specify that the sentences formed must be meaningful is limited. Pinker gives an example like this in the above-named chapter. The happy dog eats candy. He then goes on to show we could form another sentence by simply adding another happy to the given one. And based on this any given sentence could be infinitely extended by adding more words. So, using this example lets say we took the sentence The happy dog eats candy and added every single one of the 800,000 English words to the end of it, one at a time. We’d then have 800,001 sentences. But, many of those sentences would be meaningless. He correctly points out that integer sets become infinite by simply appending 1 to the end of any given number. What he forgets note is that the integers are mathematically called an infinite ring. That is we can take the numbers 0 to 9 and keep augmenting them by using a rule of repetition, not so with human languages. To see this, it is easy to imagine an integer that goes on forever. In fact, we all know a non-integer that does this, e.g. π. But, can you imagine an endless word that would be meaningful in any language? Of course not.

I’m not even sure if all human languages are potentially infinite. We know new words are invented all the time. But, that too is questionable because in order for word creation to make an infinite set of meaningful sentences we’d have to do it in infinite time. Moreover, the word creation couldn’t be infinite, unless we started making repetitive words using the augmentation rules like arithmetic. I believe we’d start creating meaningless words. Example: lets say we want a new word. Take the word fell and add another l to get felll, but that would not be a meaningful English word. Since the set of letters we have now is limited (26 in English) the corresponding combinations (words) are too. Unless we allow infinite repetition of letters, like we do with integer arithmetic, infinite creation of new words would lead to a meaningless arrays of symbols. There is a philosophic implication here: Within infinite sets, are finite sets. But, if we allow infinite members to be in a set (by repetition of letters or other devices) we begin to lose meaning. It’s worst if we have infinite symbols (I’m referring to the letter symbols). Say we wanted the 26 letter English alphabet increased infinitely. This could in fact be done. Add another curve to B, or an additional line to T, etc. We could increase the primitives that compose words infinitely. If we have an infinite variety of symbols, we could never make one symbol unique. If an infinitude of symbols could stand for one of our most basic pronouns I, how could we ever uniquely specify ourselves? By analogy, if we had an infinity of words, how could we ever specify say tree? This is similar to the Axiom of Choice in set theory mathematics. This axiom says in non-technical language that there must be a way to specify members of a set. For example, in a set (a,b,c) we must able to indicate that a is not b and b is not c, or c is not a, etc. The curious consequence of an infinite alphabet is that every member WOULD BE UNIQUE, and thus no member could be used uniquely.

Setting aside whether there are infinite words, languages as they stand now, certainly don’t allow an infinite set of sentences if those sentences are required to be meaningful in said language. Here is where I know the objection can be raised: just what do you mean by meaningful? In fact, Pinker again is himself helpful on this point. He gives an example from Noam Chomsky of a grammatical correct yet meaningless sentence. Colorless green ideas sleep furiously. This is an example of a sentence I’d say could be formed, but is not meaningful and thus not a valid sentence.

The profound outcome of what I’m suggesting is this: We can only say so much in a given language. There is only so much we can actually write and say. It’s huge in its finitude, that’s for sure, but not endless. Many would make the leap and declare: well, that means we can only have a finite number of thoughts too. No, it doesn’t. Pinker again is instructive here. He rightly shows that words and their supersets, sentences are not at heart what thought is. Thought is more a brain activity that recognizes manipulation of representations of reality. For instance, you can think left and right without words for those geometric directions. What it does imply is not every thought can be articulated. I can see this as being true. Intuitively, I had thoughts or to use the colloquial term, feelings that I can’t express in spoken or written language.

I’m actually not sure if we are limited in our thought process. We could be. If the idea that our brains are discrete state machines (sometimes called finite state machines), which can process units of input to our brains, is true, then there is an upper limit on what we can think. But, wait, whoa….I’m not gonna get into the argument here.

There is an adjunct argument to this that I will entertain. It’s called The Eternal Recurrence Theorem. It’s attributed to Henri Poincaré, a physicist and mathematician of the 19th century. Poincaré considered it from the viewpoint of closed physical systems, like the universe itself. He used differential equations to show that energy-conserving space in a volume of matter would invariably return to an original configuration of the atoms within it. To simplify this argument, lets take one estimate of the number of atoms in the universe I read. 10 to the 80th power is the value. With that many atoms interacting, that is bonding, colliding, decoupling, changing into one another, etc, we have an almost infinite series of combinations of these things. But, still not an infinity of such combinations. Poincaré reasoned that this process would go on forever, but at some point the process would repeat itself. It would run out of unique combinatorially configurations which it could assume, and thus return to its original configuration state. And if it did this, well must do it eternally, thus the term Eternal Recurrence. Yes, there really is nothing new under the Sun, to quote a now cliché phrase. I have to say that this idea did not originate with Poincaré, in fact, the ancient Egyptian people saw this long ago. The sun god Amon-Re was composed of constituent natures, which could form in specific portions by strict arithmetical rules and those rules lead to an eternal recurrence of the essence of this God. Kinda silly and rudimentary to we moderns, but still the same idea. Nevertheless, with this said, how could anybody, anywhere believe that we, with our limited number of symbols could express an infinity of meanings through a sentence structure?

Case closed.

Poincaré’s Theorem violates the second law of thermodynamics, because it does not take entropy into account properly.

closed systems tend over time to increase total entropy. TOTAL entropy is always increasing, because every interaction between matter-particles or particle-groupings represents a loss of order: some energy is always lost as a cost of work performed in the interaction, usually as heat or other light-based energy (photon emission). since no action is effortless, it is this tiny cost of the effort which subtracts from the available energy for structure-ordering, and thus causes their complexity to decrease naturally over each interaction with additional structures.

total energy is never lost, but it is always, AS A WHOLE, converted into states of progressively higher and higher entropy. thus, a new state can NEVER return to an exact previous state (the entirety of all states, i mean here by “state”, i.e. the universe as a whole); thus, recurrence is impossible, because in order to recur the universe would need to lose some of the entropy that it gained as a whole since the previous state occured, which cannot happen unless energy is introduced to the system from outside, which is impossible since we defined the universe properly as a closed system. re-define the universe as open to some external system or meta-universe, and perhaps recurrence can occur, HOWEVER then the impossibility of recurrence merely now applies to the new totality…

in short, Poincaré was wrong that the totality of a closed system will recur to exact or near-exact previous states… in addition, this is also why Nietzsche was wrong about his concept of eternal recurrence (who it seems Poincaré likely ‘borrowed’ the idea from and attempted to mathematize it). no system can recur unless it is an open system, i.e. unless entropy can be reduced by the influx of additional energy into the system itself, over time.

Yes, I admit you have pinpointed the key objection to Eternal Recurrence. Increasing entropy in a closed system does blow a hole in the idea. But, I won’t defend it. I wondered when writing that paragraph, if I’d hear this valid objection. I agree with the standard model of the universe as a closed system and of course accept the 2nd thermo law. Never mix disciplines I guess is the lesson for me. Thanks for the correction. My apologies offered.

I will point out that my reference to this flawed theorem in physics does not affect what I claim mathematically in reference to linguistic combinations. Especially if we remember these combinations have to be meaningful. As I read more of this work, I find him going further and further into the notion that we can make an infinite number of sentences. I was struck with the thought last night, what would an infinite sentence look like? Why we couldn’t even read it, it would require an infinite amount of time to read it, and it would never have a meaning—which is at the core of what a sentence is for. Pinker in his book is clearly only referring to a potential infinity of word combinations and sentences. But, even that is not strictly true because of the constraint that we make meaningful constructions. And what is so shocking to me at least, is we have a finite number of these we can make.!

“Pinker repeatedly tells us yes, we can make an infinite number of sentences in this or any other language. He uses algebraic combinatorics to show this.”

Pinker goes too far in illustrating quite a simple (and unfortunately for you, irrefutable) point.

Just 13 different words can be made in to an infinite number of meaningful sentences:

1. The dog ate food, which had been made from the remains of another dog.

2. The dog ate food which had been made from the remains of another dog that ate food which had been made from the remains of another dog.

3. The dog ate food which had been made from the remains of another dog that ate food which had been made from the remains of another dog that ate food which had been made from the remains of another dog that ate food which had been made from the remains of another dog.

``````...[b][i]Ad infinitum[/i][/b]
``````

What you show is exactly my point. An infinite sentence can be made I don’t claim it can’t. But such a sentence is NOT MEANINGFUL!!! In fact, Pinker gives an example using the same repetitive method. Again, I point out that this sentence is only potentially infinite. Since we’re finite beings, we could never experience its infinity. You’re missing my implication here. Pi is an endless number and can be understood as an endless string of numbers. But, a sentence on the hand loses its meaning if it becomes infinite. A sentence is by its very nature suppose to be finite to understand its message. As, I stressed several times in the original post, of course we can make infinite strings of symbols from a finite set of symbols, but the crux is meaning. Your sentence above loses all meaning with the repetitive phrasing. I’m proposing there is no infinite meaning for finite beings. Of course, there would be for an infinite being, and this being is a confirmed card-carrying atheist, so I won’t even consider that idea.

Another way to put my point is this: Infinity mathematically is a concept. We can understand the concept of infinity. We can use a method of numeration based on a repetitive model with a finite set of symbols to create an endless expanse of numbers. Meaning in language is not like the conceptual idea in math. It must be finite, there is no infinite meaning so to speak. A word that never ended would not be understood. The same goes for a sentence. Take your sentence with the seemingly endless reference to the dog eating remains that another dog leaves. How do we know at some point in the infinite string that a dog DOESN’T eat the remains that are left by another dog? We can’t and the implied notion of this going on forever is not true and thus the sentence’s meaning is at best ambiguous. In reality it’s fictitious because we know of no real world event like this that could go on forever. Again, its meaningfulness is lost.

No, what I have done is prove you wrong. Note, you said that:

I have proved that Pinker is quite entitled to the statement that there are an infinite number of sentences that can be made, that Pinker is right and you are wrong. The sentence I constructed can be expanded ad inifinitum without losing it’s meaning. There is no upper limit on how many times it can be expanded. Deal with it.

I also think you’re confusing two separate points:

1. An infinite number of meaningful sentences can be made.
2. An infinitely large sentence can be constructed.

The first I have already proved is true. It is what, from what you have said, that Pinker is arguing for and you have no argument against it. It simply states that there is no limit on how many different sentences you can create (just like there are an infinite amount of prime numbers). If you had an infinite amount of time to construct longer and longer sentences you would never reach a point in which you would have to stop. Obviously you don’t have inifinite time, but this is irrelevant.

The second is just silly - nobody argues for it. Note also dissmissing it does nothing to support your conlusion, that:

“The profound outcome of what I’m suggesting is this: We can only say so much in a given language”

Because to reach this conclusion you would have to refute 1). Which you haven’t and which you can’t (because it is easily demonstartable to be true).

Case Closed.

Actually, you have proved both.

Your proof of the first involves the construction of ever longer sentences, each preceded by an ordinal integer (X). As that integer “approaches infinity” so does the length of the corresponding sentence. In fact, the length of each sentence can be represented by an integer expressing the number of words in it (Y). Thus we get a one-to-one correspondence between the X and the Y; for every value of X there is a unique value of Y; if we are given one, we can calculate the other.

1. 14
2. 14+13
3. 14+13+13
4. 14+13+13+13
.
.
.
.
X. Y [Y= 13X+1]

As X approaches infinity, so does Y.

Not to be a stickler here, but a sentence isn’t a sentence until it is provided a period. An infinite sentence structure cannot be a sentence per se… or do ellipses count?

You might just as well note that a sentence isn’t a sentence until the last word is written (or spoken); or until the second-last word is written (or spoken); or until the third-last word is written (or spoken), etc.

Your objection simply amounts to the trite observation that you can never really “reach” infinity, sit back, fold your arms, and congratulate yourself on a job well done. That doesn’t refute infinity - it rather proves it!

Don’t get me wrong, I like the thought experiment. There’s just that niggling gnat of standard grammar flying round in my mind about it…

I would say, though, that I don’t think the reverse-ad nauseum response applies, as it can never be determined when the second, third, &c. last word is present until the last word is present. The last word is the last word… shit, sorry, trite…

Rather, I’m saying that there is a disjunction between the concepts of sentence and infinity. But no worries, I don’t have any grand prejudices against disjunctions… I just sometimes feel the need to acknowledge them…

There is a lot of loose language flying around, I appreciate that. But the sentence “An infinitely large sentence can be constructed” still clearly means “the construction of an infinitely large sentence is a possibity”.
You say to oughtist that: “Your objection simply amounts to the trite observation that you can never really “reach” infinity, sit back, fold your arms, and congratulate yourself on a job well done”

and indeed this is exaclty how oughtist ought to act. Because it is all that is necesseray to prove that an infinitely large sentence can not be constructed. Yes, the observation is “trite”, but that’s exactly why I called the original statment silly: it only takes such a vacant observation to serve as a disproof of it.

This is a silly debate.

By that reasoning, you could just as easily say that “An infinite number of meaningful sentences can be made” clearly means “The writing of an infinite number of meaningful sentences is a possibility”. And yet you yourself have proven it to be so.

It is no less reasonable to say that an infinitely large sentence can be constructed. Indeed, as I demonstrated, your proof is predicated on doing exactly that.

As a general proposition, that is true. But in the context of the specific proof offered by brevel_monkey, we are dealing with an infinite series of sentences generated by adding just 13 words at a time, always in the same sequence. For every sentence in the infinite list, we know what the last word will be: dog. We also know the second-last word will be “another”. And so on. This is true for the 19th sentence in the series and also for the 260 billionth sentence.

But, you may ask, since the sentences repeat the same words over and over, how can we tell when we really are at the end of the sentence? Similarly, how do I know when I see the word “of” whether it is the third-last or the sixteeth-last word in the sentence?

The answer is that each sentence is constructed according to a simple algorithm: Take the number of the sentence in the sequence, multiply it by 13 and add 1, and you will know exactly how long the sentence is supposed to be. That’s why, without writing them all out, I can confidently tell you that the 1000th sentence in the series contains 13,001 words; and furthermore, that if I were reading it and found that some words (and the period) were somehow missing from the end of the sentence, I would in principle be able to determine exactly how many words were missing, and in fact finish the sentence off myself.

So in this example, there is no indeterminacy at all as to where any given sentence ends, even if the sentence is incomplete.

Well, I’ll tell ya, all I know is that pneumonoultramicroscopicsilicovolcanoconiosis and floccinaucinihilipilificationism take us a long way, but not all the way… However, word games are well worth playing!!

But we don’t know what instance of the word(s) ar(is)e the infinite one(s)… meaning, that is, there is a formal process of repetition, of course, but the actual “writing” of the word(s) {wherein each word and it’s meaning is semi-independent of it’s previous instances [careful, I might go ontological here!]} is “meaningfully indefinite”, and thus endlessly lacking meaning. If we do not know the meaning of the word, then we cannot count it yet. Alternatively, at some point we say the sentence is meaningless…

We have the algorithm, but we don’t have the instantiation of meaning for the instantiation of the word(s). We have the blur of an infinite “meaning”, but what is a meaning if it is endless to begin with… crap, falling of into ontology again… well, do with that as you might (sorry, in a rush…

Your paraphrase significantly alters the meaning of the sentence. You have mistakenly ready it “It is possible to write down an infinite amount of sentences”, and yet this is clearly not what it meant. A correct paraphrase would be: “There are an infinite number of possible sentences”. This is what my example showed to be true.

This is an entirely unreasonable thing to say, though. An “infinitely large sentence” is impossible - sentences have to end in order to be sentences.

My proof is based on no such absurdity. All the proof shows, and all that is being argued for, is that there is no limit on how many meaningful sentences that can be constructed that imposed by language itself. So language itself is a potentially endless enterprise. Anyway: this all looks far too mathematical for me. I only lept in orinignally in defense of an age old liguistic doctrine that I happen to believe true. Debates about inifnity itself, just not my cup of tea (although they seem to keep happening recently).

Let’s look at an analogy from mathematics to see how meaning does not have to diminish as the length of a statement or expression approaches the “infinite.”

Consider the repeating decimal fraction 0.142857142857142857142857… which goes on with the digits 142857 recurring in succession “infinitely” (i.e., it does not end). Does this mean we can’t understand what the number means without seeing the “entire” sequence? No; we can prove that the longer the decimal continues, the closer its value approaches exactly the common fraction 1/7.

It’s not “the blur of an infinite meaning,” to use your words. The more infinite the decimal gets, the more exactly its meaning coincides with 1/7.

Actually, in the subject example, we know a priori exactly what each sentence in the sequence means — because we have the algorithm!

The meaning of the first sentence is self evident:

1. The dog ate food, which had been made from the remains of another dog.

The meaning of the second sentence is also easy to grasp:
2. The dog ate food which had been made from the remains of another dog that ate food which had been made from the remains of another dog.

As the list continues, and the length of each sentence grows, we begin to detect a pattern of meaning: each sentence recounts the tragic tale of X canine cannibals plus one dog whose eating preferences are never mentioned [again, X being the ordinal number attached to each sentence]. Each dog, starting with the dog whose eating preferences are unstated, becomes food for another dog, in succession, until X dogs have been eaten and only one remains. The syntax of the sentence is such that the sequence of events is presented in reverse chronological order, but that doesn’t make it any more difficult to understand.

Because we know the algorithm for generating the sentences, we can say with absolute confidence that the 1000th sentence tells the story of 1001 dogs who ate, and were eaten (except for the special cases of the first dog and the last), in sequence, until only one dog remained. We don’t even need to read the sentence in full, just as we don’t need to see 0.142857142857142857142857… to a thousand decimal places in order to know that it differs only infinitesimally from the faction 1/7.

Assuming for the moment that a sentence of “infinite length” is possible, we don’t need to read to the end of it in order to know that it tells the story of an infinite number of dogs, who ate each other, in succession, until only one was left. In fact, we don’t even need to read that sentence at all. Thus even something that is endless can have a clear and accessible meaning.

In actuality, the list of sentences would go on forever, with each sentence getting longer and the number preceding it getting larger. But you would never come to a sentence of infinite length preceded by an infinite number — you’d always be able to construct a longer sentence than any sentence you would find on the list, preceded by an ordinal number higher than any other number on the list. But that doesn’t mean that the number of sentences isn’t infinite; nor does it mean that the sentences don’t become infinitely longer.

Your example also demonstrated that the length of a sentence can be extended indefinitely, and in extreme cases, infinitely. That must be so, or your proof fails.

Indeed, in order to make each successive sentence unique, your example makes each one longer than the last. As the number of possible sentences in your example increases, so does the length of the last one. So you cannot maintain that the number of sentences can become infinitely large without the length of those sentences becoming infinitely large as well. If the sentence grows to such a length that it can no longer be considered a sentence, then your list of sentences grinds to a halt, and your proof fails.

It’s true that every sentence in the list has a beginning and an end (and a period). Thus every sentence in the list is finite. But the same is true of the number of sentences. Each sentence is preceded by a unique number that is finite, and yet there are an infinite number of them, as you have proved. It’s all part of the paradox of infinity; every term in an infinite sequence is itself finite.

The proof also shows, and I am arguing, that there is no limit to the length of a meaningful sentence that can be constructed. You never reach a point where you can no longer add those 13 words to the end of the previous sentence to make a new one.

Pinker was right.

infinite convergence (e.g. 1/7) is only possible with numbers, i.e. in the abstract.

if we are speaking of meaning, such as the content of words or sentences, then all “infinities” will, indeed must be, divergent… as the number of possible word and sentence combinations increases towards infinity, it will not “converge” on a real value, it will just continue a further summation.

however, it is irrelevant, since the idea that there could be an infinite amount of words, sentences, or combinations thereof, is a contradiction. there are a finite number of particles in the universe, so there are also a finite number of “things” in existence, be it people, ideas, matter, entities, planets, whatever… in order for there to be an INFINITE, i.e. unending, number of word or sentence combinations which generate meaning, there would need to be an infinite number of meanings, which is impossible since there are a finite number of things of which meaning can speak of, or relate to.

meaning is only MEANINGful when it relates to some aspect of reality. since there are a finite number of aspects of reality, there can never be an infinite number of meanings, so therefore there can also never be an infinite number of meaningful word or sentence combinations. of course, if we include meaningLESS word and sentence combinations, then sure, you can just keep adding a “the” or “blue” thrown in wherever, and make unending chains of language-symbols, which could be infinite in theory… but language presupposes meaning. word or sentence combinations are not considered language if they are meaningless.

nothing extended, i.e. REAL, can be infinite in nature. everything that exists, including the universe itself, is finite and limited. infinity as applied to energy would be a violation of thermodynamics. so, of course, if you want to meaningfully say something in language, and therefore speak about real aspects of reality (generate meaning), there are a finite number of ways to do this… sure, we will never, ever reach that limit, whatever it is, nor can we know what it is, but regardless there IS such a finite number-- just like we cannot know what the total number of particles in the universe is, even though there IS such a finite number.

Wow, what have I started here? First, let me make what I think is a clearer notion of what I’m getting at.

For all those whom referred to mathematical conceptual meanings to numbers in the infinite, I say: I couldn’t agree more. But the sense in which I wrote of meaning had to do with our perceptual ability to understand a given sentence. So, take the sentence “Unicorns exists”. Clearly not true perceptually, and thus I say it’s a meaningless sentence in that you would never experience an unicorn. But, conceptually, this is meaningful sentence, i.e. the idea of unicorns existing is meaningful. This is my objection to that reference about dogs eating the remains other dogs. No such real world event can exist, it has no perceptual reality. Yes, of course it can be constructed and be understood as concept of never-ending muts munching the remains that others have left (sorry but I don’t like dogs, thus the derogatory reference, cultural thing) and that would be meaningful. But, it can’t be understood as being a meaningful sentence perceptually. And that’s what sentences we make are all about. We say: I like this song; Oh, you look great kid!; I can’t believe you did that, etc. All sentences about real world perceptual experiences. No infinite sentence could deliver this kind of meaning. What I’m suggesting is we have to recognize that being human beings limits us in some ways. We don’t experience an infinity of perceptions, nor can we express such. This is not so hard to grasp. One of the reasons we developed the idea of deities is due to this tacit knowledge of our finitude. Spinoza in his Book of God used this very idea to prove God. Weird work using a logical style to prove an invalid conclusion, won’t go into details.

In fact, I could even go further conceptually and say we have no infinite unique symbolization. the integers 0-9 are really built from a limited number geometric shapes. for instance 3 is a double horseshoe shape. 9 is 1 with a horseshoe. So, at the most basic level we have primitives that use a kind of recursion to build our elemental figures and then a rule of repetition to continue them forever. But, there is no set of infinite unique symbols, our geometric world doesn’t allow this. Of course this is getting far afield from my point.

My original polemic with Pinker was directed at meaning as an experience in our real world, not things like 1/7 converging to a conceptual idea in math. Though, I thought that one was a good example of an infinitely understandable concept.

Okay I await comments, derisive, hostile and otherwise.

Well, you seem to have a very limited view of what a sentence is. If every sentence has to be about real world perceptual experiences, then abstract thought becomes virtually impossible, at least, if expressed in sentence form. So does any discussion of the imaginary.

“The unicorn ate the leprechaun” is every bit as meaningful a sentence as “My dog ate my homework”. It’s not even in the same league as Chomsky’s “Colorless green ideas sleep furiously,” which is just syntax with no conceptual meaning.

And surely, you cannot object to brevel_monkey’s proof on the basis that the sentence “The dog ate food, which had been made from the remains of another dog” is meaningless! Pinker certainly wouldn’t.

My suggestion is that precisely because we have a priori knowledge of what each (sub)sentence in the sequence means it is not a sentence. Sentences need to be read inorder to be understood (and, of course, speed reading is not a solution here). If we already know prior to reading it what it is saying, then there’s no meaning in making it a sentence. As I offered previously, we instead enter an ellipsis… and suddenly the infinite is contained and the impression of a sentence is preserved. Exactly at what point we do so depends on how quickly we think the reader would understand the device. Pretty quick, I’d suggest. Hence, the “writing” would stop. The “blur of meaning” would be captured, succinctly.