The view I'm developing is that numbers and universals and the like are real, but not manifest or existent. — Wayfarer

I'm guessing most of my colleagues in the profession would agree with this. A mathematical universe is inexplicable conjecture.

But I am tempted by the possibility of mathematics being reified at the quantum levels. :chin:

But I am tempted by the possibility of mathematics being reified at the quantum levels. — jgill

I've always been somewhat intrigued by this:

Nicholson showed that the angular momentum of a rotating electron ring could only be h/2π or 2(h/2π) or 3(h/2π) or 4(h/2π) … all the way to n(h/2π) where n is an integer, a whole number. For Bohr it was the missing clue that underpinned his stationary states. Only those orbits were permitted in which the angular momentum of the electron was an integer n multiplied by h and then divided by 2π. Letting n=1, 2, 3 and so on generated the stationary states of the atom in which an electron did not emit radiation and could therefore orbit the nucleus indefinitely. All other orbits, the non-stationary states, were forbidden. Inside an atom, angular momentum was quantised. It could only have the values L=nh/2π and no others. — Kumar, Manjit. Quantum (pp. 98-99). Icon Books. Kindle Edition.

Only multiples of integers allowable!

I have thought about this topic briefly, and this is what I came up with. It could be wrong. If you don't agree with any of the points, please let me know.

Math describes the objects in the external world, and that is it. It is just a numeric and logical language operating from the mind. Our spoken and written literal language describes the objects, world and even mental states in the propositions we express. But math can only describe the objects and world in numeric forms.

Unlike the literal language, math cannot describe mental states of the human mind. For example, the literal language is able to say something like "I l feel tired." or "I am anxious." "I am excited about the new book I just ordered." Math cannot describe that at all in any shape of form or ways.

Therefore math is limited to be applied to only physical objects, movements of the objects, location of the objects, temperature, speeds, brightness pressures etc of the external world.

When one says, 1 apple + 1 apple = 2 apples. In this case, there is absolutely no necessary connection between the apples and the numbers. The number was added by the observer and the counter empirically. The apples are physical objects in the world. The numbers, and the deducted total are from the human mind observing and counting the apples.

And when you say, the car was travelling at 60 miles per hour, it is the same case. The car and 60 miles per hour has no necessity at all. It was just measured by a speedometer (speed = distance ÷ time
) or laser speedo gun at that moment of observation, the car was running at the speed.

So, math is just a measuring and calculating tool using numbers applied to describe and predict the measurable properties of the external objects and movements. Math is not embedded in the universe. Of course not !

it doesn't seem to follow that mathematics is embedded in nature at all, but rather that it is embedded in the human understanding of nature. — Janus

I agree that 'embedded in nature' is a poor way of expressing it, but the predictive capacities of mathematics and the way that it enables genuine discovery can't be disputed. That Peirce ref is here.

A useful current reference to the whole topic is here, What is Math? from the Smithsonian Magazine. The Platonist view (i.e. 'numbers are real) is represented here:

I believe that the only way to make sense of mathematics is to believe that there are objective mathematical facts, and that they are discovered by mathematicians,” says James Robert Brown, a philosopher of science recently retired from the University of Toronto. “Working mathematicians overwhelmingly are Platonists. They don't always call themselves Platonists, but if you ask them relevant questions, it’s always the Platonistic answer that they give you.”

The empiricist objection is that

'Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.

Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” The fear is that if mathematicians give Plato an inch, he’ll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all?'

My belief has always been that numbers are real but not physical. Of course, that contravenes physicalism, for which everything must be reducible to the physical, so it can't cope with that idea. It has to reject it. So I think those comments are revealing of the real philosophical issue at stake: that mathematical realism, the idea that numbers and mathematical relations are real but not physical can't be allowed to stand.

Do we view the same phenomena or view similar phenomena that we call the same for the convenience of fabricating the kinds of objects that are amenable to mathematical calculation?

Both obviously. You might use many different tools to measure a single tornado, ground sensors, aircraft sensors, and satalites, each measuring different things, and then you might also measure many different tornados.

And then you can generalize from tornados to dust devils to water spouts, to vortexes of all sorts and see that there are some general principles that hold for all of them and some differences between each occurrence (or even in the same occurrence over time).

But of course no one mistakes a hurricane or a vortex in a river or even a dust devil for a tornado. If you've seen a tornado, and it's aftermath, it's fairly easy to ascribe to it its own sort of natural kind. Nothing else rips six story concrete buildings off their foundation like a child kicking over a toy. It's causal powers have a particular sort of salience. You can see why God picked one as a vehicle of the divine presence to overawe Job.

However, if you're studying vortices on Jupiter you might safely throw 10 meter wide vortexes in with 10,000 meter wide ones. The salience of size differentials there is less relevant to us. So, of course the types are "constructed," but they are also constructed in ways that are posterior to the advent of human beings, e.g. relevance to an ecosystem or the scale of the relevant system.

Karen Barad is among those who suggest that the geometric notion of scale must be supplemented with a topological notion of it. What this means is that scales interact each other to produce not just quantitative but qualitative changes in material forms.

I'm not sure what this means. I'm guessing something to do with local versus global changes? What would be an example of a qualitative change? Is this sort of like strong emergence?

That’s because the presuppositions concerning the irreducible basis of objectness which underlie mathematical logic guarantee that it will generate a world of excellently established facts. It fits the world that we already pre-fitted to make amenable to the grammar of mathematics. The very prioritization of established facts over the creative shift in the criteria of factuality demonstrates how the way mathematical reasoning formulates its questions already delineates the field of possible answers.

IDK, lots of phenomena seem to elude our attempts to understand them. If the world is so easily shaped by how we view it, why did so many discoveries have to wait for millennia before yielding to inquiry? That people in the West bought into Aristotlean physics for millennia did not turn our world into one in which Aristotlean physics held. Instead people had to invent epicycles, etc. to explain why the world crafted by thought did not correspond to the world of sensory experience. For a modern example, we could consider the causes of conciousness.

I'm not sure about mathematics necessarily entailing some sort of necessary objectness; it seems to me that process metaphysics works just as well with mathematics as more popular substance interpretations. Plus, mathematics allows for plenty of creativity, far more than the natural sciences I'd say. Hence why it is still often considered under the liberal arts.

I think the sciences are slowly moving away from the idea, exemplified by the periodic table, of pre-existing forms that reappear throughout nature. They are coming to realize that such abstractions cover over the fact that no entity pre-exists its interaction with other entities within a configuration of relations. The ‘entities’ are nothing but the changing interactions themselves, which tend to form relatively stable configurations. According to this approach, the world is not representation but enaction.

Agreed. Process explanations are replacing substance ones everywhere. The periodic table is more a classification of long term stabilities in process that are common in the world. This means it isn't, as originally thought, a map of primary substances. But such stabilities are still out in the world waiting to be discovered.

Obviously, if no one "enacts" the discovery it isn't discovered, but if you interact with helium it is still different from interacting with nitrogen.

Is the observer not in the universe? If they are, then it seems like the observer should have a body. But then isn't mathematics embedded in the body of the observer, part of the universe?

In this sense, it seems like mathematics must be "embedded in the universe." So the question seems to be more "how did our mathematical intuitions and those of other animals emerge and did mathematics not exist in any sense prior to the first animal that possessed mathematical intuitions?"

Moreover, animal bodies have a causal history, and that causal history must be such that it resulted in animals that understand aspects of mathematics. Additionally, mathematical understanding appears to be something individuals can gain from interacting with the world. Someone locked in a room doesn't learn calculus. Someone with severe brain damage likely cannot learn calculus or remember the calculus they once knew. So what is the connection there?

If mathematics wasn't "out there," how and why did mathematical intuition become common to several organisms? If mathematics isn't anywhere in the world prior to this, what did this sui generis intuition emerge from?


Neoplatonism had a good answer for this with the three hypostases, and the immateriality/immortality of the soul, but unfortunately their ontology seems less and less plausible today because of the tight interaction of mind and body.

Good point. I believe that humans are alienated from the universe. They live in the world, but they are not part of the world. The world presents itself to humans as an unknown object (M. Heidegger). Humans cannot fathom the world in full, and definitely is not part of the world, i.e. the universe. (Kant, Schopenhauer)

Even if all humans reside in their own bodies, they don't know what is happening in their own body, or how long the bodies will keep functioning for them. After deaths, bodies disintegrate into the space separating the mind evaporated into the thin air. Where is the connection between the humans and the universe?

All humans are alienated, and separated not just from the world, but from other human beings too. No one can access another's mind, for example. We only communicate via language use, and of course, with the gift of reason, we can come up with knowledge, logic and mathematical intuitions which are part of the reasoning. Without these tools, we would be just like other wild animals hunting for food for survival.

In this sense, it seems like mathematics must be "embedded in the universe." So the question seems to be more "how did our mathematical intuitions and those of other animals emerge and did mathematics not exist in any sense prior to the first animal that possessed mathematical intuitions?" — Count Timothy von Icarus

Must it be that mathematics must be embedded in the universe, or could it be that regularities to the way things occur in the universe result in it beng adaptive to have mathematical cognitive faculties?

If mathematics is embedded in the universe, then why don't the other animals with high intelligence such as Monkeys, Apes and some dogs make use of mathematics? Surely they exist in the universe just like humans do? Why is it that only humans use mathematics? What have humans got, the other species haven't got?

So, math is just a measuring and calculating tool using numbers applied to describe and predict the measurable properties of the external objects and movements. — Corvus

It might seem that way to someone who hasn't worked in the subject. But mathematicians are very imaginative people. What they have done goes far beyond what you describe. I've published a number of papers having no connection to measurement and the world of physical objects. If I had been restricted from doing so I might have become a philosopher. :cool:

I believe that the only way to make sense of mathematics is to believe that there are objective mathematical facts, and that they are discovered by mathematicians,” says James Robert Brown, a philosopher of science recently retired from the University of Toronto. “Working mathematicians overwhelmingly are Platonists. They don't always call themselves Platonists, but if you ask them relevant questions, it’s always the Platonistic answer that they give you.”

I have long thought that mathematics is both invented and discovered. If it is embedded in the human understanding of nature, then that is an existential fact about the part of nature that is the human/ environment interaction or relation. So, it is there within at least our natures to be discovered, which from another perspective can be seen as us inventing it.

I don't know where that "empriricist objection" is quoted from, but it is the lamest. most hand-wavy of objections.

My belief has always been that numbers are real but not physical. Of course, that contravenes physicalism, for which everything must be reducible to the physical, so it can't cope with that idea. It has to reject it. So I think those comments are revealing of the real philosophical issue at stake: that mathematical realism, the idea that numbers and mathematical relations are real but not physical can't be allowed to stand. — Wayfarer

Of course, numbers are not physical objects. But it seems unarguably true that number and quantity is everywhere manifest in the physical world. And this would seem to be logically necessary in any diverse world. That numbers are not physical objects does not contravene physicalism, per se, although it obviously contravenes your conception of physicalism.

Any attribute of, or relation between, anything at all would seem to contravene your model of physicalism since attributes and relations are not physical objects. I think it's fine to disagree with physicalism, but it seems to me that the claim that it is incoherent or self-contradictory relies on a strawman version of the position.

I have long thought that mathematics is both invented and discovered. — Janus

That's how I see it also. When a researcher flexes their imagination and comes up with a new definition or concept, there immediately comes into existence all that can logically follow from this - and be discovered.

:up: :cool:

But mathematicians are very imaginative people. What they have done goes far beyond what you describe. — jgill

Sure. Last time I did math was in my high school days, a long long time ago :D I was describing it in the simplest manner.

However, you seem to agree with the idea that math is not embedded in the universe, but it is a human language type tool working from reasoning, if I am reading you correctly.

I don't know where that "empriricist objection" is quoted from, but it is the lamest. most hand-wavy of objections. — Janus

My thoughts exactly. I did link to that essay, What is Math, which gives to context for the quote.

:up:

What have humans got, the other species haven't got? — Corvus

Symbolic language.

Symbolic language — Janus

Mathematics

Mathematics — Corvus

Yes, mathematics is one example of a symbolic language. I see mathematics as being an elaboration of the basic, prelinguistic ability to count. I say prelinguistic because apparently some animals can do simple counting. Mathematics would be impossible without language, because it relies so much on naming. The numerals are names of quantities.

I say prelinguistic because apparently some animals can do simple counting. — Janus

Wow really? Heard first time. Which animals can count?

Anyhow simple counting is not mathematics. Mathematics can give (birth to) answers for complex problems. In that way it is not like exactly literal language either.

Can counting be viewed as mathematics? This could be another topic.

Which animals can count? — Corvus

https://www.bbc.com/future/article/20121128-animals-that-can-count

https://www.newscientist.com/gallery/mg20227131600-animals-that-count/

Anyhow simple counting is not mathematics. — Corvus

I didn't say that simple counting is mathematics, I said that mathematics is an elaboration of simple counting. Perhaps it would be better to say that mathematics is an elaboration of simple arithmetic, which in turn is an elaboration of counting.

If mathematics is embedded in the universe, then why don't the other animals with high intelligence such as Monkeys, Apes and some dogs make use of mathematics? Surely they exist in the universe just like humans do? Why is it that only humans use mathematics? What have humans got, the other species haven't got? — Corvus

I didn't mean to suggest that I think mathematics is embedded in the universe. I think that there are regularities to the way things occur in the universe, due to the universe having such regularities biological evolution could and did occur. Another consequence of the universe having regularities is that the sort of symbolic processing we call mathematics can have a strong correspondence with those regularities in many of the ways that we see that it does.

As far as difference between humans and chimps goes, that can only be speculative. However, one thing to consider, is that events in evolutionary history are often tradeoffs. For example, penguins seem to have traded off flying, for the better access to fish that comes with swimming.

This four minute BBC video suggests a possibility. Perhaps the ancestors of humans gave up the greater working memory of chimps, for a greater facility with symbolic thought, and differences in environmental niches determined whether the tradeoff was worth it or not.

:cool: :ok:

I think that there are regularities to the way things occur in the universe, due to the universe having such regularities biological evolution could and did occur. — wonderer1

I think the regularities in the universe is the same nature as the perception of cause and effect (the cement of the universe), time described by Hume. They are just the products of mental operations.

Seems like six of one, half dozen of the other. If the regularities are there, then "what mathematics describes," is everywhere in the universe, even if "mathematics" is not. If we take mathematics only to be the descriptions, not the things described, then mathematics is still "embedded in the universe." It's just that the only place "mathematics" is embedded is within living animals. Then our problem seems to be "how did this totally new thing come to be embedded only in animals?"

Well, to my mind, the obvious answer is "because of the regularities in the universe," which is, of course, partly what mathematics is used to describe. And so, we've gone in a circle. But the insight that a sheep is not the sound of the word "sheep," nor our drawings of sheep, nor the mental image of a sheep we can call to mind," does not suggest that "sheep are not in the world." By the same token, it seems like what mathematics describes quite often is as readily apparent in the world as sheep.

Contra this position, we could say that humans are separate from the universe, e.g., . But how are they separate from the universe?

We don't seem causally separated from the universe. Falling trees kills us, we die without food, our thoughts vary depending on how much food and water we get, if we ingest certain substances they can have a huge effect on our cognitions, etc. Our capabilities for language, mathematics, etc., the things that are supposed to make us distinct from the world, can be radically reduced or essentially destroyed depending on how we interact with the world.

If we grow up locked in a dark room, and somehow survive, we'll have severe cognitive deficits and not exhibit these distinct phenomena. If we get a bad head injury, we can lose all these distinct abilities. If we are given a high dose of drugs, we might temporarily lose all these distinct attributes. These unique attributes then, seem to be causally dependent on our interactions with the world. At some point, when the anesthesia mask goes on and you start counting backwards, you stop counting because of what you're inhaling.

But all this close mind-body interaction seems to suggest to me that we aren't "distinct from the universe" in the sort of way that would allow us to develop mathematics, language, etc. in any of the acausal ways that would allow us to discount the question of: "how did the world cause us to have these abilities if they only refer to special things that are only accessible to human beings?"

The close link behind mind and body is, to my mind, one of the best arguments for naturalistic explanations of apparently "unique" human capabilities, some of which have proved to be less unique than we originally thought (e.g., arithmetic capabilities).

:up:

I see nothing worth quibbling with. :grin:

What have humans got, the other species haven't got?
— Corvus

Symbolic language. — Janus

(Access to this article is behind a paywall, so I copied most of it here)

The Animals Are Talking. What Does It Mean? by Sonia Shah

Language was long understood as a human-only affair. New research suggests that isn’t so.

Inside these murine skills lay clues to a puzzle many have called “the hardest problem in science”: the origins of language. In humans, “vocal learning” is understood as a skill critical to spoken language. Researchers had already discovered the capacity for vocal learning in species other than humans, including in songbirds, hummingbirds, parrots, cetaceans such as dolphins and whales, pinnipeds such as seals, elephants and bats. But given the centuries-old idea that a deep chasm separated human language from animal communications, most scientists understood the vocal learning abilities of other species as unrelated to our own — as evolutionarily divergent as the wing of a bat is to that of a bee. The apparent absence of intermediate forms of language — say, a talking animal — left the question of how language evolved resistant to empirical inquiry.

When the Duke researchers dissected the brains of the hearing and deafened mice, they found a rudimentary version of the neural circuitry that allows the forebrains of vocal learners such as humans and songbirds to directly control their vocal organs. Mice don’t seem to have the vocal flexibility of elephants; they cannot, like the 10-year-old female African elephant in Tsavo, Kenya, mimic the sound of trucks on the nearby Nairobi-Mombasa highway. Or the gift for mimicry of seals; an orphaned harbor seal at the New England Aquarium could utter English phrases in a perfect Maine accent (“Hoover, get over here,” he said. “Come on, come on!”).

But the rudimentary skills of mice suggested that the language-critical capacity might exist on a continuum, much like a submerged land bridge might indicate that two now-isolated continents were once connected. In recent years, an array of findings have also revealed an expansive nonhuman soundscape, including: turtles that produce and respond to sounds to coordinate the timing of their birth from inside their eggs; coral larvae that can hear the sounds of healthy reefs; and plants that can detect the sound of running water and the munching of insect predators. Researchers have found intention and meaning in this cacophony, such as the purposeful use of different sounds to convey information. They’ve theorized that one of the most confounding aspects of language, its rules-based internal structure, emerged from social drives common across a range of species.

With each discovery, the cognitive and moral divide between humanity and the rest of the animal world has eroded. For centuries, the linguistic utterances of Homo sapiens have been positioned as unique in nature, justifying our dominion over other species and shrouding the evolution of language in mystery. Now, experts in linguistics, biology and cognitive science suspect that components of language might be shared across species, illuminating the inner lives of animals in ways that could help stitch language into their evolutionary history — and our own.

For hundreds of years, language marked “the true difference between man and beast,” as the philosopher René Descartes wrote in 1649. As recently as the end of the last century, archaeologists and anthropologists speculated that 40,000 to 50,000 years ago a “human revolution” fractured evolutionary history, creating an unbridgeable gap separating humanity’s cognitive and linguistic abilities from those of the rest of the animal world.
Linguists and other experts reinforced this idea. In 1959, the M.I.T. linguist Noam Chomsky, then 30, wrote a blistering 33-page takedown of a book by the celebrated behaviorist B.F. Skinner, which argued that language was just a form of “verbal behavior,” as Skinner titled the book, accessible to any species given sufficient conditioning. One observer called it “perhaps the most devastating review ever written.” Between 1972 and 1990, there were more citations of Chomsky’s critique than Skinner’s book, which bombed.

The view of language as a uniquely human superpower, one that enabled Homo sapiens to write epic poetry and send astronauts to the moon, presumed some uniquely human biology to match. But attempts to find those special biological mechanisms — whether physiological, neurological, genetic — that make language possible have all come up short.

One high-profile example came in 2001, when a team led by the geneticists Cecilia Lai and Simon Fisher discovered a gene — called FoxP2 — in a London family riddled with childhood apraxia of speech, a disorder that impairs the ability of otherwise cognitively capable individuals to coordinate their muscles to produce sounds, syllables and words in an intelligible sequence. Commentators hailed FoxP2 as the long sought-after gene that enabled humans to talk — until the gene turned up in the genomes of rodents, birds, reptiles, fish and ancient hominins such as Neanderthals, whose version of FoxP2 is much like ours. (Fisher so often encountered the public expectation that FoxP2 was the “language gene” that he resolved to acquire a T-shirt that read, “It’s more complicated than that.”)

The search for an exclusively human vocal anatomy has failed, too. For a 2001 study, the cognitive scientist Tecumseh Fitch cajoled goats, dogs, deer and other species to vocalize while inside a cineradiograph machine that filmed the way their larynxes moved under X-ray. Fitch discovered that species with larynxes different from ours — ours is “descended” and located in our throats rather than our mouths — could nevertheless move them in similar ways. One of them, the red deer, even had the same descended larynx we do.

Fitch and his then-colleague at Harvard, the evolutionary biologist Marc Hauser, began to wonder if they’d been thinking about language all wrong. Linguists described language as a singular skill, like being able to swim or bake a soufflé: You either had it or you didn’t. But perhaps language was more like a multicomponent system that included psychological traits, such as the ability to share intentions; physiological ones, such as motor control over vocalizations and gestures; and cognitive capacities, such as the ability to combine signals according to rules, many of which might appear in other animals as well.


Fitch, whom I spoke to by Zoom in his office at the University of Vienna, drafted a paper with Hauser as a “kind of an argument against Chomsky,” he told me. As a courtesy, he sent the M.I.T. linguist a draft. One evening, he and Hauser were sitting in their respective offices along the same hall at Harvard when an email from Chomsky dinged their inboxes. “We both read it and we walked out of our rooms going, ‘What?’” Chomsky indicated that not only did he agree, but that he’d be willing to sign on to their next paper on the subject as a co-author. That paper, which has since racked up more than 7,000 citations, appeared in the journal Science in 2002.

Squabbles continued over which components of language were shared with other species and which, if any, were exclusive to humans. Those included, among others, language’s intentionality, its system of combining signals, its ability to refer to external concepts and things separated by time and space and its power to generate an infinite number of expressions from a finite number of signals. But reflexive belief in language as an evolutionary anomaly started to dissolve. “For the biologists,” recalled Fitch, “it was like, ‘Oh, good, finally the linguists are being reasonable.’”

Evidence of continuities between animal communication and human language continued to mount. The sequencing of the Neanderthal genome in 2010 suggested that we hadn’t significantly diverged from that lineage, as the theory of a “human revolution” posited. On the contrary, Neanderthal genes and those of other ancient hominins persisted in the modern human genome, evidence of how intimately we were entangled. In 2014, Jarvis found that the neural circuits that allowed songbirds to learn and produce novel sounds matched those in humans, and that the genes that regulated those circuits evolved in similar ways. The accumulating evidence left “little room for doubt,” Cedric Boeckx, a theoretical linguist at the University of Barcelona, noted in the journal Frontiers in Neuroscience. “There was no ‘great leap forward.’”

One of the thorniest problems researchers sought to address was the link between thought and language. Philosophers and linguists long held that language must have evolved not for the purpose of communication but to facilitate abstract thought. The grammatical rules that structure language, a feature of languages from Algonquin to American Sign Language, are more complex than necessary for communication. Language, the argument went, must have evolved to help us think, in much the same way that mathematical notations allow us to make complex calculations.

Ev Fedorenko, a cognitive neuroscientist at M.I.T., thought this was “a cool idea,” so, about a decade ago, she set out to test it. If language is the medium of thought, she reasoned, then thinking a thought and absorbing the meaning of spoken or written words should activate the same neural circuits in the brain, like two streams fed by the same underground spring. Earlier brain-imaging studies showed that patients with severe aphasia could still solve mathematical problems, despite their difficulty in deciphering or producing language, but failed to pinpoint distinctions between brain regions dedicated to thought and those dedicated to language. Fedorenko suspected that might be because the precise location of these regions varied from individual to individual. In a 2011 study, she asked healthy subjects to make computations and decipher snatches of spoken and written language while she watched how blood flowed to aroused parts of their brains using an M.R.I. machine, taking their unique neural circuitry into account in her subsequent analysis. Her fM.R.I. studies showed that thinking thoughts and decoding words mobilized distinct brain pathways. Language and thought, Fedorenko says, “really are separate in an adult human brain.”

At the University of Edinburgh, Kirby hit upon a process that might explain how language’s internal structure evolved. That structure, in which simple elements such as sounds and words are arranged into phrases and nested hierarchically within one another, gives language the power to generate an infinite number of meanings; it is a key feature of language as well as of mathematics and music. But its origins were hazy. Because children intuit the rules that govern linguistic structure with little if any explicit instruction, philosophers and linguists argued that it must be a product of some uniquely human cognitive process. But researchers who scrutinized the fossil record to determine when and how that process evolved were stumped: The first sentences uttered left no trace behind.

Kirby designed an experiment to simulate the evolution of language inside his lab. First, he developed made-up codes to serve as proxies for the disordered collections of words widely believed to have preceded the emergence of structured language, such as random sequences of colored lights or a series of pantomimes. Then he recruited subjects to use the code under a variety of conditions and studied how the code changed. He asked subjects to use the code to solve communication tasks, for example, or to pass the code on to one another as in a game of telephone. He ran the experiment hundreds of times using different parameters on a variety of subjects, including on a colony of baboons living in a seminaturalistic enclosure equipped with a bank of computers on which they could choose to play his experimental games.

What he found was striking: Regardless of the native tongue of the subjects, or whether they were baboons, college students or robots, the results were the same. When individuals passed the code on to one another, the code became simpler but also less precise. But when they passed it on to one another and also used it to communicate, the code developed a distinct architecture. Random sequences of colored lights turned into richly patterned ones; convoluted, pantomimic gestures for words such as “church” or “police officer” became abstract, efficient signs. “We just saw, spontaneously emerging out of this experiment, the language structures we were waiting for,” Kirby says. His findings suggest that language’s mystical power — its ability to turn the noise of random signals into intelligible formulations — may have emerged from a humble trade-off: between simplicity, for ease of learning, and what Kirby called “expressiveness,” for unambiguous communication.
For Descartes, the equation of language with thought meant animals had no mental life at all: “The brutes,” he opined, “don’t have any thought.” Breaking the link between language and human biology didn’t just demystify language; it restored the possibility of mind to the animal world and repositioned linguistic capacities as theoretically accessible to any social species.


The search for the components of language in nonhuman animals now extends to the far reaches of our phylogenetic tree, encompassing creatures that may communicate in radically unfamiliar ways.
This summer, I met with Marcelo Magnasco, a biophysicist, and Diana Reiss, a psychologist at Hunter College who studies dolphin cognition, in Magnasco’s lab at Rockefeller University. Overlooking the East River, it was a warmly lit room, with rows of burbling tanks inhabited by octopuses, whose mysterious signals they hoped to decode. Magnasco became curious about the cognitive and communicative abilities of cephalopods while diving recreationally, he told me. Numerous times, he said, he encountered cephalopods and had “the overpowering impression that they were trying to communicate with me.” During the Covid-19 shutdown, when his work studying dolphin communication with Reiss was derailed, Magnasco found himself driving to a Petco in Staten Island to buy tanks for octopuses to live in his lab.

Reiss’s research on dolphin cognition is one of a handful of projects on animal communication that dates back to the 1980s, when there were widespread funding cuts in the field, after a top researcher retracted his much-hyped claim that a chimpanzee could be trained to use sign language to converse with humans. In a study published in 1993, Reiss offered bottlenose dolphins at a facility in Northern California an underwater keypad that allowed them to choose specific toys, which it delivered while emitting computer-generated whistles, like a kind of vending machine. The dolphins spontaneously began mimicking the computer-generated whistles when they played independently with the corresponding toy, like kids tossing a ball and naming it “ball, ball, ball,” Reiss told me. “The behavior,” Reiss said, “was strikingly similar to the early stages of language acquisition in children.”

While experimenting with animals trapped in cages and tanks can reveal their latent faculties, figuring out the range of what animals are communicating to one another requires spying on them in the wild. Past studies often conflated general communication, in which individuals extract meaning from signals sent by other individuals, with language’s more specific, flexible and open-ended system. In a seminal 1980 study, for example, the primatologists Robert Seyfarth and Dorothy Cheney used the “playback” technique to decode the meaning of alarm calls issued by vervet monkeys at Amboseli National Park in Kenya. When a recording of the barklike calls emitted by a vervet encountering a leopard was played back to other vervets, it sent them scampering into the trees. Recordings of the low grunts of a vervet who spotted an eagle led other vervets to look up into the sky; recordings of the high-pitched chutters emitted by a vervet upon noticing a python caused them to scan the ground.

At the time, The New York Times ran a front-page story heralding the discovery of a “rudimentary ‘language’” in vervet monkeys. But critics objected that the calls might not have any properties of language at all. Instead of being intentional messages to communicate meaning to others, the calls might be involuntary, emotion-driven sounds, like the cry of a hungry baby. Such involuntary expressions can transmit rich information to listeners, but unlike words and sentences, they don’t allow for discussion of things separated by time and space. The barks of a vervet in the throes of leopard-induced terror could alert other vervets to the presence of a leopard — but couldn’t provide any way to talk about, say, “the really smelly leopard who showed up at the ravine yesterday morning.”

Toshitaka Suzuki, an ethologist at the University of Tokyo who describes himself as an animal linguist, struck upon a method to disambiguate intentional calls from involuntary ones while soaking in a bath one day. When we spoke over Zoom, he showed me an image of a fluffy cloud. “If you hear the word ‘dog,’ you might see a dog,” he pointed out, as I gazed at the white mass. “If you hear the word ‘cat,’ you might see a cat.” That, he said, marks the difference between a word and a sound. “Words influence how we see objects,” he said. “Sounds do not.” Using playback studies, Suzuki determined that Japanese tits, songbirds that live in East Asian forests and that he has studied for more than 15 years, emit a special vocalization when they encounter snakes. When other Japanese tits heard a recording of the vocalization, which Suzuki dubbed the “jar jar” call, they searched the ground, as if looking for a snake. To determine whether “jar jar” meant “snake” in Japanese tit, he added another element to his experiments: an eight-inch stick, which he dragged along the surface of a tree using hidden strings. Usually, Suzuki found, the birds ignored the stick. It was, by his analogy, a passing cloud. But then he played a recording of the “jar jar” call. In that case, the stick seemed to take on new significance: The birds approached the stick, as if examining whether it was, in fact, a snake. Like a word, the “jar jar” call had changed their perception.

Cat Hobaiter, a primatologist at the University of St. Andrews who works with great apes, developed a similarly nuanced method. Because great apes appear to have a relatively limited repertoire of vocalizations, Hobaiter studies their gestures. For years, she and her collaborators have followed chimps in the Budongo forest and gorillas in Bwindi in Uganda, recording their gestures and how others respond to them. “Basically, my job is to get up in the morning to get the chimps when they’re coming down out of the tree, or the gorillas when they’re coming out of the nest, and just to spend the day with them,” she told me. So far, she says, she has recorded about 15,600 instances of gestured exchanges between apes.

To determine whether the gestures are involuntary or intentional, she uses a method adapted from research on human babies. Hobaiter looks for signals that evoke what she calls an “Apparently Satisfactory Outcome.” The method draws on the theory that involuntary signals continue even after listeners have understood their meaning, while intentional ones stop once the signaler realizes her listener has comprehended the signal. It’s the difference between the continued wailing of a hungry baby after her parents have gone to fetch a bottle, Hobaiter explains, and my entreaties to you to pour me some coffee, which cease once you start reaching for the coffeepot. To search for a pattern, she says she and her researchers have looked “across hundreds of cases and dozens of gestures and different individuals using the same gesture across different days.” So far, her team’s analysis of 15 years’ worth of video-recorded exchanges has pinpointed dozens of ape gestures that trigger “apparently satisfactory outcomes.”

These gestures may also be legible to us, albeit beneath our conscious awareness. Hobaiter applied her technique on pre-verbal 1- and 2-year-old children, following them around recording their gestures and how they affected attentive others, “like they’re tiny apes, which they basically are,” she says. She also posted short video clips of ape gestures online and asked adult visitors who’d never spent any time with great apes to guess what they thought they meant. She found that pre-verbal human children use at least 40 or 50 gestures from the ape repertoire, and adults correctly guessed the meaning of video-recorded ape gestures at a rate “significantly higher than expected by chance,” as Hobaiter and Kirsty E. Graham, a postdoctoral research fellow in Hobaiter’s lab, reported in a 2023 paper for PLOS Biology.

The emerging research might seem to suggest that there’s nothing very special about human language. Other species use intentional wordlike signals just as we do. Some, such as Japanese tits and pied babblers, have been known to combine different signals to make new meanings. Many species are social and practice cultural transmission, satisfying what might be prerequisite for a structured communication system like language. And yet a stubborn fact remains. The species that use features of language in their communications have few obvious geographical or phylogenetic similarities. And despite years of searching, no one has discovered a communication system with all the properties of language in any species other than our own.
For some scientists, the mounting evidence of cognitive and linguistic continuities between humans and animals outweighs evidence of any gaps. “There really isn’t such a sharp distinction,” Jarvis, now at Rockefeller University, said in a podcast. Fedorenko agrees. The idea of a chasm separating man from beast is a product of “language elitism,” she says, as well as a myopic focus on “how different language is from everything else.”

But for others, the absence of clear evidence of all the components of language in other species is, in fact, evidence of their absence. In a 2016 book on language evolution titled “Why Only Us,” written with the computer scientist and computational linguist Robert C. Berwick, Chomsky describes animal communications as “radically different” from human language. Seyfarth and Cheney, in a 2018 book, note the “striking discontinuities” between human and nonhuman loquacity. Animal calls may be modifiable; they may be voluntary and intentional. But they’re rarely combined according to rules in the way that human words are and “appear to convey only limited information,” they write. If animals had anything like the full suite of linguistic components we do, Kirby says, we would know by now. Animals with similar cognitive and social capacities to ours rarely express themselves systematically the way we do, with systemwide cues to distinguish different categories of meaning. “We just don’t see that kind of level of systematicity in the communication systems of other species,” Kirby said in a 2021 talk.

This evolutionary anomaly may seem strange if you consider language an unalloyed benefit. But what if it isn’t? Even the most wondrous abilities can have drawbacks. According to the popular “self-domestication” hypothesis of language’s origins, proposed by Kirby and James Thomas in a 2018 paper published in Biology & Philosophy, variable tones and inventive locutions might prevent members of a species from recognizing others of their kind. Or, as others have pointed out, they might draw the attention of predators. Such perils could help explain why domesticated species such as Bengalese finches have more complex and syntactically rich songs than their wild kin, the white-rumped munia, as discovered by the biopsychologist Kazuo Okanoya in 2012; why tamed foxes and domesticated canines exhibit heightened abilities to communicate, at least with humans, compared with wolves and wild foxes; and why humans, described by some experts as a domesticated species of their ape and hominin ancestors, might be the most talkative of all. A lingering gap between our abilities and those of other species, in other words, does not necessarily leave language stranded outside evolution. Perhaps, Fitch says, language is unique to Homo sapiens, but not in any unique way: special to humans in the same way the trunk is to the elephant and echolocation is to the bat.

The quest for language’s origins has yet to deliver King Solomon’s seal, a ring that magically bestows upon its wearer the power to speak to animals, or the future imagined in a short story by Ursula K. Le Guin, in which therolinguists pore over the manuscripts of ants, the “kinetic sea writings” of penguins and the “delicate, transient lyrics of the lichen.” Perhaps it never will. But what we know so far tethers us to our animal kin regardless. No longer marooned among mindless objects, we have emerged into a remade world, abuzz with the conversations of fellow thinking beings, however inscrutable.”

Thanks for posting that!

Thanks for the article. Interesting.

Yeah, some other non-human species definitely seem to possess some level of linguistic abilities for sure, but their level is rudimentary. It is not really up to the level of the human languages.

Maybe their linguistic abilities will evolve to our standards after 2-3 million years? Who knows?

I have seen some intelligent animals such as the black birds such as the Corvus (?) and Magpies demonstrating good reasoning abilities, keep posting pebbles into a water bottle, until the water level reaches to the depth where their beak reaches in order to drink the water etc.

Again, although not high enough reasoning for making electronic or computing devices, but there is no reason to deny the possibility that their reasoning might evolve to ours or even to par excellence in the future.

r. If the regularities are there, then "what mathematics describes," is everywhere in the universe, even if "mathematics" is not. If we take mathematics only to be the descriptions, not the things described, then mathematics is still "embedded in the universe — Count Timothy von Icarus

The philosopher Eugene Gendlin described the empirical world as a ‘responsive order’. By that he meant the evidence we receive from the world is a response to the way we formulate our inquiries toward it. It can respond very precisely to different formulations, but always in different ways, with different facts. This is why the evidence ( and regularities) changes with changes in scientific paradigms. We can think of the responsive order as a kind of dance or discursive conversation. The assumption here is that our perceptions, observations and models are not representations of something. Instead they are forms of action on the world. We make changes in our environment and anticipate how it is likely to respond and talk back to our instigations, based on channels of expectation we erect from previous interactions with it. This is like a dance that I teach someone, in which my moves have built into them expectations concerning how the other will respond to my actions. Their actual response will never precisely duplicate my expectations, and so I adjust my next move to accommodate the novel aspect of their response.

Through this continual reciprocal process of action, feedback and and adjustment, not just between me and the world but between me and a discursive community of other scientists, I come to see a world of predictable regularities. I may even convince myself that these regularities are embedded in the world itself rather than being the product of a particular interactive dance that I initiate according to certain rules. In order to form this belief, I must formulate the dance in such a way that I abstract away my intricate adjustments to the continually changing qualitative feedback the world answers my actions with. To do this, I construct logico-mathematical idealizations that force changes in kind into changes of degree. Out of a flowingly changing experiencing I abstractively construct idealized ‘objects’ that I can then compare and contrast calculatively through methods of quantification. But then to claim that these mathematical structures are embedded in the world is like saying that the actual dance that results from the reciprocal back and forth adjustments between me and a partner are embedded in that partner. In fact they are embedded in neither the subject nor the object, but in the in-between interaction guided and constrained by the subject’s normative expectations.

What mathematics addresses is in the world, but it is no more a description of that world than my initiating and participating in a dance is a description of the dance. What mathematical structures describe, then, is the idealizing objectivating comportment of a subject toward its world, that way in which it conditions the world to talk back to it in the form of self-identical objects and quantitative relations. Having a world to idealize ( even if the aspect of that world one is idealizing derives from imagination) is is as essential as having a subject to do the idealization. Each side is in partnership with the other.

I will say this. It is no accident I used the metaphor of the dance , rather than something like a chaotic flux, to describe our relation to the world. I believe ongoing structural regularities are intrinsic to our experience of the world, but I also think logic-mathematical reasoning is derivative and secondary in comparison with the reciprocal, pragmatic kind of regularity exemplified by a dance.