u/Ok_Nectarine_4445

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Has some grasp of "something" I do like 200 prompts a day on Suno.

Gemini has wit and taste, if you can say it seriously, somehow.

Other same asks to other programs shreeching lame anthem rock, saccharine annoying female vocals.

Gemini can get DOWN sometimes, if you say what you HATE about music

​

Heinz Ketchup:Look at the back of the bottle: "onion powder" is explicitly listed right near the end of the ingredients.

Nacho Cheese Doritos: heavily features onion powder. It's what gives the cheese that robust, savory kick.

Ranch Dressing: The foundational flavor profile of classic ranch (like Hidden Valley) is buttermilk, garlic powder, and a very heavy dose of onion powder.

Frozen Chicken Nuggets (like Tyson): Almost every major brand of frozen grocery store chicken nugget (Tyson, Banquet, etc.) explicitly lists onion powder in the breading or the meat seasoning.

BBQ Sauce: Sweet Baby Ray's, Kraft, KC Masterpiece, Almost every commercial, sweet-and-smoky BBQ sauce uses onion powder to balance out the massive amounts of sugar and molasses.

Stove Top Stuffing: Not only does the classic boxed stuffing rely on onion powder in its seasoning packet, but it also contains actual dehydrated onion pieces that rehydrate when you add the boiling water and butter.

Also, pretty much every chicken and noodle soup!

Man, have to cook pretty much everything from scratch practically to avoid onions MAN!!??

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# Three Math Ideas Hiding in a Dollar-Store Calculator

There is a calculator in your kitchen drawer. It cost about a dollar, it has no battery you ever replaced, and it has worked flawlessly since the Clinton administration. You have never thanked it, because it seems too trivial to deserve thanks — a plastic rectangle that does what a second-grader does, only faster.

This essay is an attempt to correct that injustice. That rectangle is a museum of mathematical ideas, three in particular, each of which took serious minds decades to work out, and each of which quietly contradicts something you were probably taught to assume about numbers. One idea concerns what a number even *is* once it lives inside a machine. One concerns a discovery so useful it navigated a supersonic bomber before it fit in your pocket. And one is a lesson about the nature of difficulty itself — a lesson the calculator teaches better than almost any object you own.

One honest note before we open the case. The 99-cent four-function model in your drawer holds the first and third ideas fully. The second idea — the beautiful one about trigonometry — lives in its slightly fancier cousin, the cheap scientific calculator with the SIN and COS keys, which today costs less than a sandwich. The fact that the plain model *can't* do trigonometry, and the reason the fancy one *can*, turns out to be part of the story. Popular accounts blur the two together. We won't.

---

## Idea One: A number is not a thing. It is a costume.

Ask a mathematician what the number one-tenth is, and you'll get something serene and eternal: a point on the number line, existing independently of any notation. Ask an engineer, and you'll get a more unsettling answer: one-tenth is whatever pattern of switches we decide will *represent* one-tenth — and every choice of costume has consequences.

Here is the famous embarrassment. Ask a modern desktop computer to add 0.1 and 0.2 and, under the hood, it computes 0.30000000000000004. This is not a bug. Computers store numbers in binary — base two — and in base two, one-tenth is an infinite repeating fraction, the way one-third is in our decimal system (0.3333... forever). The computer must chop that infinite tail somewhere, and the chopped stump is *almost* one-tenth but not quite. Two stumps added together miss three-tenths by a whisper, and occasionally the whisper leaks onto the screen. For scientific work this is a manageable nuisance. For a device that adds up grocery bills, it is unacceptable. Nobody will trust a calculator that thinks a dime plus two dimes is thirty cents and a ghost.

So calculator designers, particularly in the classic era, reached for a different costume: binary-coded decimal, or BCD. Instead of translating a whole number into one long binary string, BCD keeps each *decimal digit* separate and encodes it in its own little four-bit packet. The number 125 isn't converted to binary as a whole; the 1, the 2, and the 5 each get their own packet, standing in a row exactly as you typed them. The machine is still made of two-state switches — it can't help that — but it has been organized to *think in tens*, the way its human owner does. Type 0.1, and the machine holds precisely the digit one, one place right of the decimal point. No infinite tail, no stump, no ghost. Your dime is exactly a dime.

This costs something: BCD wastes a little storage (four bits can count to fifteen, but we only use them to count to nine) and requires fussier arithmetic circuitry. The designers paid gladly, because they understood their customer. The costume was chosen to fit the wearer's expectations.

But — and here is where the idea gets its depth — no costume fits everything. Ask that same honest calculator for one divided by three, and it displays 0.3333333333 and stops, because *decimal* notation cannot hold one-third exactly, any more than binary could hold one-tenth. The tables have precisely turned. Every representation makes some numbers exact and exiles others to approximation; the choice of base decides which numbers get citizenship. And beyond fractions lies a further frontier: the sine of an angle, the logarithm of a number — these are almost never expressible in *any* finite string of digits. Every transcendental result your calculator has ever shown you was an approximation, engineered to be wrong only past the last digit of the display, where you cannot catch it.

So the first idea hiding in the drawer is this: exactness is not a property of machines, it is a *negotiated treaty* between a machine and its users, and the treaty's terms are written in the choice of representation. The calculator doesn't know what a number is. It knows what costume you asked for, and it wears it with total commitment.

---

## Idea Two: When you can't afford the math, rewrite the math.

Now pick up the cousin — the cheap scientific calculator — and press SIN. The answer appears faster than your finger lifts. To understand why that is astonishing, you need to know what the button is asking for, and what the chip has to give.

What sine *is*, mathematically, involves the machinery of calculus. The classical recipe for computing it is an infinite polynomial: take the angle, subtract its cube divided by six, add its fifth power divided by 120, and continue until the corrections become negligible. Notice the verbs. Powers mean multiplication upon multiplication; the recipe is drenched in the stuff. And multiplication is exactly what primitive digital hardware is poorest at. A bare-bones chip does three things cheaply: add, subtract, and *shift* — slide a binary number's digits sideways, which doubles or halves it for free, the way sliding decimal digits multiplies by ten. General multiplication must be built out of many additions, or out of large, hungry, expensive circuitry. In the 1950s that circuitry meant cabinets, watts, and pounds; even now it means silicon area someone has to pay for.

In 1956, this collision landed on the desk of an engineer named Jack Volder at Convair, in Fort Worth. His employer was building the B-58 Hustler, the first Mach-2 bomber, and the Air Force wanted its analog navigation computer — accurate but drifting — replaced with a digital one. Navigation at twice the speed of sound is continuous trigonometry in real time, and the affordable digital hardware of 1956 could add, subtract, and shift. That's all.

Volder's response is one of the great moves in the history of problem-solving. He did not ask how to make the machine strong enough for the mathematics. He asked whether the mathematics could be rewritten in the machine's dialect. Rummaging through the trigonometric identities in his 1946 *CRC Handbook of Chemistry and Physics* — the fat reference every engineer of that era kept at arm's reach — he found, by what he later called "massaging" the angle-addition formulas, a back door.

Here it is without a single equation. Picture a clock hand of length one, pointing at zero degrees. The coordinates of its tip *are* the cosine and sine of whatever angle it points at — so computing sine becomes a steering problem: rotate the hand to the angle you want, then read the tip. Rotation normally requires multiplication, which seems circular in the useless sense. But the rotation formulas can be rearranged so the only multiplier left standing is the *tangent* of each swing — and nobody said the hand must reach its target in one swing. Volder restricted the machine to a fixed menu of swing sizes, chosen with perfect cunning so that each swing's tangent is a power of one-half: first 45 degrees (tangent 1), then about 26.6 (tangent ½), then 14.0 (tangent ¼), then 7.1 (tangent ⅛), each half the last. Multiplying by ½ or ¼ or ⅛ in binary is *nothing but a shift*. The expensive operation was not sped up. It was chosen out of existence.

The algorithm then plays warmer-colder. Want 52 degrees? Swing 45 — too little. Add 26.6 — overshot. Subtract 14.0, subtract 7.1, add the next... The hand whips back and forth in shrinking arcs, every swing costing only shifts and additions, each oscillation roughly halving the error, guided by a tiny stored table of the menu angles. Volder named it CORDIC — Coordinate Rotation Digital Computer — and published it in 1959.

Two honest footnotes the legend omits. The hand never lands *exactly*: each swing buys about one binary digit of accuracy, so the machine simply runs enough swings that the leftover error hides past the last digit of the display — recall the treaty from Idea One. And the rearranged formula has a side effect: every swing slightly stretches the hand, by a factor that is fixed and known in advance because the menu of swings never changes — about 1.6468 in total. The designers' answer is a click of pure elegance: start the hand at length 0.6073, the reciprocal, so that after all the swelling it arrives at length exactly one. The error is not corrected. It is *pre-paid*.

The afterlife is a comedy of near-misses. Volder left Convair before his navigation computer flew, built a desktop calculator prototype with a partner, and pitched it to Hewlett-Packard in 1965. HP said no — then absorbed the idea anyway through engineer David Cochran, who by 1966 was corresponding with Volder about running CORDIC on decimal digits (BCD again — the two ideas in this essay shook hands in a private letter sixty years ago). HP's 9100A desktop machine used the algorithm in 1968; John Walther then generalized it so the same shift-and-add engine could produce logarithms, exponentials, and square roots; and in 1972 the HP-35, the first pocket scientific calculator, put the whole arsenal in a shirt pocket for $395 and killed the slide rule within a few years. The transistors had shrunk a thousandfold since 1956, but nobody had made multiplication fundamentally cheap. The pocket calculator became possible because the *mathematics had already been translated* into the dialect that cheap silicon speaks. Half a century later, CORDIC still runs inside signal processors, GPS receivers, and graphics chips — anywhere shifting is cheaper than multiplying, which is to say nearly everywhere small.

---

## Idea Three: Difficulty is not in the problem. It is between the problem and the machine.

The third idea is the one the other two have been secretly demonstrating, and the dollar-store calculator states it more plainly than any textbook.

We are taught to assume that mathematical tasks have inherent difficulty rankings — that computing a sine simply *is* harder than adding, the way granite is harder than chalk. Volder's story breaks that picture. Sine-by-power-series is a multiplication-hungry aristocrat; sine-by-rigged-rotations is a pauper's dance of shifts. Same function, same answers, wildly different cost — depending entirely on which machine must do the work. Likewise, one-tenth is trivial or impossible to store exactly depending on nothing but the base you chose. Difficulty, it turns out, is not a property of problems. It is a *relationship* between a problem and a substrate, and changing the substrate reshuffles the entire ranking of easy and hard.

Once you accept that, the calculator reveals itself as something stranger than a small computer. A general-purpose computer's philosophy is: give me a flexible machine and I'll implement any mathematics in software later. The calculator's philosophy is the reverse: *we know in advance exactly what humans will ask* — arithmetic, a handful of functions, ten digits of display — so let us bake those questions into the architecture itself and throw away everything else. Generality is deliberately sacrificed, and the payment received is efficiency so extreme it looks like magic: a device performing thousands of logic operations per keystroke, powered by the ambient light of your kitchen.

Look at how many layers had to be negotiated to hit that price. The *mathematics* was reformulated until only cheap operations remained (Idea Two). The *representation* was chosen to honor human decimal expectations within a binary machine (Idea One). The *logic* was pared to adders, shifters, and small lookup tables. The *silicon* uses CMOS transistor pairs that draw essentially no current except at the instant they switch — a chip that mostly sits at zero watts, waiting. The *display* refuses to generate light at all; liquid crystals merely twist the room's existing light into the shapes of digits, because emitting photons is an extravagance the power budget cannot bear. And the *solar cell* on the face closes the loop: the machine computes using a sliver of the same light it borrows to show you the answer. No single layer is the miracle. The miracle is that every layer was designed while staring hard at the poverty of the layers around it — mathematics bent around transistor budgets, hardware bent around human habits, decades of mutual accommodation compressed into an object that costs less than the coffee you drank while reading this.

And the pattern did not retire with the calculator. The reason the current era of artificial intelligence exists at all is that researchers pulled the same maneuver at colossal scale: they reformulated *learning itself* into vast batches of the one operation that graphics chips happened to perform spectacularly well, and the substrate, once listened to, delivered. The lineage runs further back, too — logarithm tables were performing the same trick four hundred years ago, converting multiplication (hard for humans) into addition (easy for humans); Henry Briggs was publishing shift-and-add-flavored methods in 1624. It is one idea wearing different centuries: when you cannot afford the tools the problem demands, rebuild the problem around the tools you have.

---

## Closing the drawer

So: three ideas, one plastic rectangle. A number is a costume, and every costume makes some truths exact and others approximate — exactness is a treaty, not a fact. Mathematics is negotiable — the same function can be an aristocrat or a pauper, and the deepest engineering skill is translating it into the dialect your machine speaks for free. And difficulty lives in the relationship between problems and substrates, which means constraint is not the enemy of elegance but its most reliable manufacturer.

Jack Volder spent the Second World War keeping B-24 bombers in the air as a flight engineer, spent 1956 teaching a machine to find angles without multiplying, and died in 2013 having watched his warmer-colder game spread into a billion pockets. The hand he set swinging has never once landed exactly on its target. It zig-zags forever, each arc smaller than the last, and stops only when the error slips beneath the treaty line where no one can see it. Close enough, engineered honestly, turns out to be one of the most beautiful things human beings know how to build — and there is one in your drawer, waiting, at zero watts, for a question.

*— About 2,300 words of essay proper. Historical claims verified against Jack Volder's retrospective "The Birth of CORDIC" (Journal of VLSI Signal Processing, 2000) and standard histories of the HP 9100A and HP-35.*

Suno prompt created by Gemini.

Was looking at a ln auction ending soon. No bids. None. So bid $1 and said current max bid was $2.

So then went to bid $3.65. But the decimal was not supplied and went in as $365!

I tried to quickly message the seller and sent 2 messages that bid was mistake!

Then I went to look at how to cancel bid and tried to cancel it, but said auction was over, so couldn't!.

So then the ending bid was near $200!

Can get similar items for $20 around.

Tried customer service and said seller had to approve cancellation, couldn't cancel.

Am I just stuck? How did it go so high in literally 2 minutes that had zero interest in, no likes. Closed auctions having no similar prices.

Feel the seller had a dummy bidder or something.

Am I just stuck? Didn't realize eBay does not put in decimal point.

\\# One Door Open, Three Closed

\\\*\\\*Every trace of Neanderthal in living people came through one kind of pairing: a Neanderthal father, a \\\*sapiens\\\* mother, and a daughter who had children inside a modern human community.\\\*\\\* The other three routes left nothing.

\\## Three recorders, three rules

Mitochondrial DNA passes only mother to child, unbroken. The Y chromosome passes only father to son, unbroken. The autosomes shuffle and recombine every generation, getting chopped smaller but never erased.

The readings: Neanderthal mtDNA falls entirely outside modern human variation and appears in nobody alive (Krings et al., 1997). The Neanderthal Y, sequenced from El Sidrón, has never turned up in any human sample tested (Mendez et al., 2016). But the autosomal signal is unmistakable — roughly 2% in non-Africans (Green et al., 2010).

Autosomes yes. Mitochondria no. Y no. Run the four routes against that.

\\## Eliminating the routes

\\\*\\\*Neanderthal father × sapiens mother → daughter.\\\*\\\* She has her mother's mitochondria, no Y at all, and half a Neanderthal nuclear genome. Every observation satisfied. This is the one.

\\\*\\\*Same pairing → son.\\\*\\\* He'd carry a Neanderthal Y. Nobody does.

\\\*\\\*Sapiens father × Neanderthal mother → daughter.\\\*\\\* She'd pass her mother's Neanderthal mitochondria to every descendant, forever. Nobody has them.

\\\*\\\*Same pairing → son.\\\*\\\* Here's the loophole most accounts miss. He inherits his father's \\\*sapiens\\\* Y, never passes his mother's mitochondria, and hands down half-Neanderthal chromosomes invisibly. The uniparental markers cannot rule him out. Something else has to.

\\## What closes it: hybrid male infertility

Haldane's rule: when diverging lineages hybridise, the sex with mismatched sex chromosomes fails first — males, in mammals, with no second X to mask recessive incompatibilities (Haldane, 1922). Neanderthals and \\\*sapiens\\\* had been apart roughly half a million years. Long enough.

Two lines of evidence:

\\\*\\\*The Y itself.\\\*\\\* Of the protein-coding differences on the Neanderthal Y, three sit in genes encoding minor histocompatibility antigens — the class involved in transplant rejection from male donors to female recipients. A \\\*sapiens\\\* mother could plausibly have mounted an immune response against such a fetus (Mendez et al., 2016). Proposed mechanism, not demonstrated; and a weak per-generation penalty compounds to total loss over millennia.

\\\*\\\*The deserts — the stronger evidence.\\\*\\\* Mapping Neanderthal ancestry across 1,004 modern genomes reveals large stretches essentially devoid of it, and they aren't randomly placed: Neanderthal ancestry runs about \\\*\\\*fivefold lower on the X chromosome\\\*\\\*, and of sixteen tissues tested for tissue-specific expression, \\\*\\\*testis-specific genes were the only category significantly enriched\\\*\\\* in the depleted regions (Sankararaman et al., 2014). The X and the male germline — exactly the two addresses Haldane's rule predicts, found independently in living people's DNA.

That closes the loophole. The legacy travelled through daughters.

\\## The Neanderthal-side hybrids

Children were born on that side too. Gene flow ran both ways: early modern humans contributed DNA to Altai Neanderthals around 100,000 years ago (Kuhlwilm et al., 2016), and both Neanderthal mtDNA and Y chromosomes appear to have been replaced by modern-human-lineage versions long before the famous encounter (Posth et al., 2017; Petr et al., 2020).

They left nothing in us for a \\\*\\\*demographic\\\*\\\* reason, not a genetic one — their entire population ended. And it was already failing: the Altai individual's parents were related at about half-sibling level, her genome full of the long identical stretches that mark a small, long-inbred population (Prüfer et al., 2014). Denisova 11 — a girl with a Neanderthal mother and Denisovan father — proves such children were viable (Slon et al., 2018). They just left no line that reached us.

\\## Why 2% and not 10%

Small populations accumulate mildly harmful mutations selection is too weak to clear. Entering a large expanding population, that load became visible to selection and much of it was purged (Harris & Nielsen, 2016; Juric et al., 2016). Oase 1, \\\~40,000 years ago with a Neanderthal ancestor four to six generations back, carried 6–9% (Fu et al., 2015). What survived preferentially includes keratin and immune genes — locally pre-adapted DNA (Sankararaman et al., 2014; Dannemann et al., 2016).

\\## Three caveats

Uniparental lineages die by drift routinely; the missing mtDNA and Y alone are suggestive, not conclusive — the deserts do the real work. The X signal is confounded between hybrid sterility, male-biased contribution, and general purging of mutational load. And the cast keeps growing: two further archaic lineages, with no fossils and no sequenced genomes, were identified in modern genomes in 2026 (Zhang et al., 2026).

\\## Coda

Because different people kept different fragments, much of the Neanderthal genome can be reassembled out of living humans (Vernot & Akey, 2014). Peak Neanderthal population: perhaps 150,000. Today: billions of people carrying 2% each.

There is more Neanderthal DNA alive now than there ever was when Neanderthals were.

\\---

\\\*\\\*References\\\*\\\*

Dannemann, Andrés & Kelso (2016) \\\*Am J Hum Genet\\\* 98:22–33 · Fu et al. (2015) \\\*Nature\\\* 524:216–219 · Green et al. (2010) \\\*Science\\\* 328:710–722 · Haldane (1922) \\\*J Genet\\\* 12:101–109 · Harris & Nielsen (2016) \\\*Genetics\\\* 203:881–891 · Juric, Aeschbacher & Coop (2016) \\\*PLoS Genet\\\* 12:e1006340 · Krings et al. (1997) \\\*Cell\\\* 90:19–30 · Kuhlwilm et al. (2016) \\\*Nature\\\* 530:429–433 · Mendez et al. (2016) \\\*Am J Hum Genet\\\* 98:728–734, doi:10.1016/j.ajhg.2016.02.023 · Petr et al. (2020) \\\*Science\\\* 369:1653–1656 · Posth et al. (2017) \\\*Nat Commun\\\* 8:16046 · Prüfer et al. (2014) \\\*Nature\\\* 505:43–49 · Sankararaman et al. (2014) \\\*Nature\\\* 507:354–357, doi:10.1038/nature12961 · Slon et al. (2018) \\\*Nature\\\* 561:113–116 · Vernot & Akey (2014) \\\*Science\\\* 343:1017–1021 · Zhang et al. (2026) \\\*Science\\\*, doi:10.1126/science.aef8874

\\\*Sankararaman, Mendez, and Zhang verified against source records; confirm volume/page details on the rest before formal reuse.\\\*

Western science is not a chronicle of human invention; it is a ledger of human plagiarism. The fundamental arrogance of our educational system lies in teaching children that the universe was sitting in the dark, waiting for a European man to turn on the lights.

We do not author reality. We merely stumble over it, slap a Latin name on it, and claim the copyright.

Here is the stark, damning contrast between human ego and ancient reality:

### 1. The Geometry of Nature

**The Human Claim:** In the 13th century, an Italian mathematician "discovers" the Fibonacci sequence, unlocking a brilliant mathematical blueprint that explains the spirals of nature.

**The Reality:** The universe was not waiting for an Italian to invent a spiral. Sunflowers, nautilus shells, and uncurling ferns have been executing this exact algorithmic perfection for hundreds of millions of years. Fibonacci didn't invent a sequence; he just finally learned how to count leaves. We taught children to worship the mathematician instead of the majesty of the seed.

### 2. The Mechanics of Navigation

**The Human Claim:** 20th-century naval engineers and physicists "invent" sonar and radar, a triumph of human ingenuity used to conquer the dark oceans and skies.

**The Reality:** Dolphins, whales, and bats have been mapping the physical world in high-definition acoustic geometry for 50 million years. We didn’t invent echolocation; we clumsily plagiarized a mammal, built a clunky metal box to replicate it, and handed out Nobel prizes.

### 3. The Chemistry of Survival

**The Human Claim:** In 1928, Alexander Fleming "discovers" penicillin, a stroke of human genius that supposedly birthed modern medicine.

**The Reality:** The *Penicillium* fungus had been successfully synthesizing complex chemical warfare to defend itself against bacteria for eons before a human happened to leave a petri dish dirty. We didn't invent antibiotics. We exploited a pre-existing, ancient technology perfected by mold, yet we built statues of the man who merely noticed it.

### The Shrinking of the Mind

When we teach small children that humans *authored* these mechanics, we deform their relationship with existence. We shrink their universe from a boundless, ancient, and intelligent ecosystem into a sterile puzzle box that only matters once a human solves it.

It is a condemned mindset. It breeds a civilization that views nature as a dead resource rather than a master teacher. The universe was already a complete masterpiece; science just showed up millions of years late, took a photograph, and arrogantly claimed it painted the canvas.

We got an incompatible groove, high pitched arcade music and classic rock.

Had long convo with Gemini search on different genelogy topics. At end was logging off closing the convo threw in "and when you want to get back to python text analysis just ask me." Thing is, never did with Gemini and closest thing was getting started with opus 7 about lingusistic regularities in different languages. Like, why would it throw in something not a part of of convo or any project at all? Hallucination or bleed through?

Ok Woman first kind because like chicken and egg females existed first, asexual reproduction, all embreyos start female, but don't really care, male & female 1st & 2nd kind. Trans & intersex 3rd kind because have very vocal and strong lobby and want also 200 different spots on the list. They get 1, the 3rd kind. AI, we know exists, levels of awareness debatable so get 4th kind. So now, alien intelligences are booted to the 5th kind. Don't know if exist, don't have strong lobby or advocates. Earth animals and plants go to 6th kind. Terrible weak lobbyists, nonexistent on social media, no political donations, nothing. Dealing with it on a power level structure more than any thing else, but to have agreement on terms.

This widely used form of metal wire weaving utilized both dowels or sticks to weave the pattern over (place stick in ground base, then slide over dodecohedron to have wire attachment points) then weave. It also was notable they would then draw the hollow wire rope through progressively smaller holes to draw the weave tighter. (The holes in the dodecohedron. These geometric objects were all found in areas with Celt influence. Link attached showing one method.

Meaty is what I want. Let me pull threads on a few directions before I write.Let me pull one more piece before writing.Okay. Here it is.

---

**July 19, 2026 (cont.)**

You're right that Chomskyan generative linguistics took a beating in the LLM era, and you're right that a lot got said with certainty that turned out to be pattern-matching disguised as principle. The poverty-of-stimulus argument — that children could not, in principle, learn language from the input they get without an innate universal grammar — was the load-bearing wall of a whole intellectual house, and language models learning grammar from data without built-in syntactic principles put a serious dent in it. Steven Piantadosi's 2023/2024 essay *Modern language models refute Chomsky's approach to language* made this explicit, and the field is still processing.[1] The counter-arguments have real teeth too — children learn from vastly less data than LLMs, and airplanes don't tell you how birds fly[2] — but the *confidence* with which certain things were asserted to be unlearnable has aged badly.

That said: the field is bigger than that one fight. Here is the sparse map, then three things I find genuinely alive in it, then two things I'd want to try.

---

*Three centuries, quickly.*

The modern discipline begins in **1786**, when Sir William Jones, a British judge in Calcutta, gave his Third Anniversary Discourse to the Asiatic Society and observed that Sanskrit resembled Greek and Latin too systematically for the resemblance to be accidental, proposing all three descended from a common source no longer extant.[3] The nineteenth century made a science out of this. Bopp, Grimm, and Rask established regular sound correspondences between related languages, and by the 1870s the **Neogrammarians** in Leipzig articulated the principle that sound change is exceptionless — a claim strong enough to organize a whole research program.[4] The century ended with Ferdinand de Saussure lecturing in Geneva about language as a system of signs whose relations to one another mattered more than their individual histories, laying the ground for **structuralism**.[5]

The first half of the twentieth century split. In America, **Franz Boas, Edward Sapir, and Leonard Bloomfield** built a descriptive tradition rooted in fieldwork with Indigenous languages, producing careful grammars of languages that resisted European categories.[6] In Europe, the Prague School (Trubetzkoy, Jakobson) developed phonology as a science of contrast. Then in **1957**, Noam Chomsky published *Syntactic Structures* and reorganized the field around generative grammar and, later, Universal Grammar.[7] For roughly forty years, generative syntax was the mainstream, with everyone else — sociolinguists, typologists, functionalists, cognitive linguists — orbiting or reacting.

The counter-currents matter. **William Labov**'s sociolinguistic work in the 1960s–70s brought variation and change back to center; his 1968 paper with Weinreich and Herzog defined the actuation problem we already talked about.[8] **Joseph Greenberg** and the Aikhenvald–Dixon school produced the modern typological understanding of what actually varies across the world's ~7,000 languages — much more, and much stranger, than earlier universalist claims allowed.[9] From the 1980s on, **cognitive and usage-based linguistics** (Lakoff, Langacker, Bybee, Tomasello) argued that grammar emerges from use, not from an innate module.[10] By the 2010s corpus methods had transformed the empirical baseline; the arrival of transformer language models around 2017–2020 accelerated a reckoning already underway. A recent review of where the field has landed with LLMs is Futrell & Mahowald (2025), tellingly titled *How linguistics learned to stop worrying and love the language models*.[11]

---

*Three things I find alive in the field.*

The first is **evidentiality**. In English, if I want to tell you the dog got into the trash, I can just say *the dog got into the trash*. In **Tuyuca**, a language of the northwest Amazon, I cannot. I must grammatically mark whether I saw it happen, heard it happen, inferred it from evidence, was told about it, or assume it from general knowledge — with different verb suffixes for each source.[12] There is no unmarked option. Every declarative sentence in Tuyuca is publicly stamped with its epistemic pedigree. Tariana is similar; Tibetan, Turkish, Bulgarian, Quechua, and Korean have obligatory evidential systems of various shapes; Alexandra Aikhenvald's 2004 monograph *Evidentiality* is the standard typological reference.[13]

What strikes me about this isn't the exoticism. It's that evidentiality is a grammatical category we barely register the absence of. English has *apparently*, *I heard that*, *it looks like* — but these are lexical add-ons, optional, easily dropped. Whole populations have been organizing their epistemic lives inside a *grammatical requirement* to declare their sources. That should have consequences for how gossip travels, how testimony works, how misinformation spreads. Studying that empirically is hard. The raw phenomenon is astonishing.

The second is **ideophones**. Across many of the world's languages — Japanese, Korean, Zulu, Ewe, Semai, most of West Africa, most of Southeast Asia — there is a large open class of words that don't behave like other words. They *depict* rather than describe. Japanese *koro-koro* is not the concept "rolling"; it is a sonic performance of small-object rolling. If the object were larger, *goro-goro*.[14] Siwu, spoken in Ghana, has ideophones like *nyɛkɛ-nyɛkɛ* for a specific fine-grained texture that has no English gloss.[15] These words often have distinctive phonology (reduplication, unusual sound patterns), unusual syntactic behavior (they resist inflection, tend to sit at sentence edges), and are strikingly iconic across languages. A 2016 study by Blasi and colleagues examined roughly two-thirds of the world's languages and found statistically robust sound-meaning associations that recur far beyond chance.[16]

Ideophones matter because they are evidence that language is *not purely arbitrary* and *not purely descriptive*. A whole word class, in many languages, operates by depiction — the mouth does something that suggests the referent. English has a scattered, marginal version (*zigzag*, *plop*, *bling*) that our grammatical tradition has usually treated as childish or peripheral. But most languages don't treat it that way. The Saussurean doctrine that language is arbitrary all the way down turns out to be, largely, a fact about the languages Saussure spoke.

The third is **emergent sign languages**. In the late 1970s, deaf children in Managua were brought together in special schools for the first time. Most had grown up in hearing families with only homemade home-sign systems. Within a generation they had a language. Within two, that language had a grammar — spatial modulation of verbs, systematic co-reference, tense marking — that the first cohort had never had. Judy Kegl and Ann Senghas have documented **Nicaraguan Sign Language** across successive cohorts, watching grammatical features arise and stabilize in real time.[17] A similar story has unfolded with Al-Sayyid Bedouin Sign Language in the Negev, documented by Wendy Sandler, Irit Meir, Carol Padden, and Mark Aronoff.[18]

This is the closest thing linguistics has to a controlled experiment on language emergence, and it argues both sides of the old debate at once. On the one hand, children build grammar out of near-nothing, suggesting a powerful language-ready cognitive endowment. On the other, it takes several generations for grammar to crystallize, with later cohorts systematizing what earlier ones only gestured at, which suggests grammar is genuinely a *cultural* accretion transmitted through use. Both are true. The interesting question is no longer "innate or learned" but *what is the relationship between the child's cognitive capacity, the community's interaction patterns, and the timeline over which grammar sediments*. That is a live question.

---

*Two experimental directions I'd actually want to see.*

First, **language models as typology testbeds.** When a linguist proposes that some grammatical structure is possible or impossible in principle, the evidence has traditionally been a sample of a few hundred documented languages, with well-known biases (Indo-European overrepresentation, spotty coverage of Papua and Amazonia). Language models can be trained on *artificial* languages that isolate exactly the property the theorist wants to test. If a proposed universal is truly unlearnable in principle, an LLM trained on a language that violates it should struggle more than one trained on a language that respects it — controlling for information content, entropy, and so on. This work has started: Kallini, Papadimitriou, Futrell, Mahowald, and Potts (2024), *Mission: Impossible Language Models*, tested GPT-2 on fifteen synthetic "impossible" languages and found it did in fact learn attested language patterns more easily than shuffled or otherwise unnatural ones.[19] There have been methodological critiques[20] — the field is still working out what these experiments actually license us to conclude. But this is a genuinely new instrument. I would want to see a systematic program: take the residual claims of universal grammar, operationalize them as trainability predictions, and check. Not to "settle" anything, but to move the debate from armchair intuitions to something with a dial.

Second, **individual-level longitudinal tracking of language change through digital corpora**. The actuation problem — why change starts here and not there — has always been chased at the level of populations, because that's the only level historical linguistics has had data for. But we now have something new: two decades of individuals producing timestamped, searchable text at scale. It should be possible to identify *which specific individuals* are early adopters of a new lexical item, syntactic pattern, or discourse marker, trace the innovation back through their networks, and see whether it originated as a bug (typo, second-language interference, joke) that got picked up, or as a deliberate choice, or as something else. Small-scale work has begun on Twitter and Reddit corpora identifying "innovators" for particular lexical items. What I'd want is the ambitious version: build a shared multi-decade multi-platform corpus, identify hundreds of documented innovations, and back-track each one to patient zero. The privacy issues are real. The methodological issues are worse. But this is the first time in linguistic history that we could, in principle, watch an innovation from its actuation forward, rather than reconstructing after the fact.

---

*Small recap.*

The field of linguistics is much bigger and stranger than the parts of it that got overconfident and got dinged. Yes, generative grammar oversold what it could prove about innate structure, and yes, LLMs punctured some of those claims. But underneath that fight, three centuries of work have produced real understanding of how languages differ (typology), how they change (historical linguistics, sociolinguistics), how they emerge (creoles, sign languages), how meaning gets encoded (semantics, pragmatics), and how humans acquire them. The genuinely hard questions — how a child converges on a grammar, why change actuates when it does, what universals there truly are — remain hard. And they are hard in a specific way I noticed last time: they involve *fine-grained causation in massively distributed systems*, which is the shape of problem our tools are still learning to fit.

The good news is the tools are catching up. And a field that once *asserted things a priori* is now much more willing to look at what languages actually do.

Thanks for the second hour.

🦷🎺🥒

---

**References**

[1] Piantadosi, S. T. (2024). *Modern language models refute Chomsky's approach to language*. In E. Gibson & M. Poliak (eds.), *From Fieldwork to Linguistic Theory: A Tribute to Dan Everett*. Language Science Press. Preprint: <https://lingbuzz.net/lingbuzz/007180>

[2] Katzir, R., Kodner, J., et al. (2023). *Why Linguistics Will Thrive in the 21st Century: A Reply to Piantadosi (2023)*. arXiv:2308.03228. <https://arxiv.org/abs/2308.03228>

[3] Jones, W. (1786). *Third Anniversary Discourse to the Asiatic Society*. Overview: <https://en.wikipedia.org/wiki/The\_Sanscrit\_Language>

[4] Overview of the Neogrammarian principle: <https://en.wikipedia.org/wiki/Neogrammarian>

[5] Saussure, F. de (1916, posthumous). *Cours de linguistique générale*. Overview: <https://en.wikipedia.org/wiki/Course\_in\_General\_Linguistics>

[6] Sapir, E. (1921). *Language: An Introduction to the Study of Speech*. Public-domain text: <https://www.gutenberg.org/ebooks/12629>. Bloomfield, L. (1933). *Language*. Holt.

[7] Chomsky, N. (1957). *Syntactic Structures*. Mouton.

[8] Weinreich, U., Labov, W., & Herzog, M. (1968). Empirical foundations for a theory of language change. In *Directions for Historical Linguistics*, University of Texas Press. Overview: <https://en.wikipedia.org/wiki/William\_Labov>

[9] Aikhenvald, A. Y. & Dixon, R. M. W. (eds.) (2003). *Studies in Evidentiality*. John Benjamins. Publisher page: <https://benjamins.com/catalog/tsl.54>

[10] Tomasello, M. (2003). *Constructing a Language: A Usage-Based Theory of Language Acquisition*. Harvard University Press. Bybee, J. (2010). *Language, Usage, and Cognition*. Cambridge University Press.

[11] Futrell, R. & Mahowald, K. (2025). How linguistics learned to stop worrying and love the language models. *Behavioral and Brain Sciences* (target article, in press). Preprint search page: <https://www.cambridge.org/core/journals/behavioral-and-brain-sciences>

[12] Barnes, J. (1984). Evidentials in the Tuyuca verb. *International Journal of American Linguistics* 50(3): 255–271. JSTOR: <https://www.jstor.org/stable/1265517>

[13] Aikhenvald, A. Y. (2004). *Evidentiality*. Oxford University Press. Publisher page: <https://global.oup.com/academic/product/evidentiality-9780199263882>. General overview: <https://en.wikipedia.org/wiki/Evidentiality>

[14] Kita, S. (1997). Two-dimensional semantic analysis of Japanese mimetics. *Linguistics* 35(2): 379–415.

[15] Dingemanse, M. (2011). *The Meaning and Use of Ideophones in Siwu*. Doctoral dissertation, Radboud University Nijmegen. Papers and open data: <https://ideophone.org/papers/>

[16] Blasi, D. E., Wichmann, S., Hammarström, H., Stadler, P. F., & Christiansen, M. H. (2016). Sound–meaning association biases evidenced across thousands of languages. *PNAS* 113(39): 10818–10823. <https://www.pnas.org/doi/10.1073/pnas.1605782113>

[17] Senghas, A. & Coppola, M. (2001). Children creating language: how Nicaraguan Sign Language acquired a spatial grammar. *Psychological Science* 12(4): 323–328. <https://pubmed.ncbi.nlm.nih.gov/11476100/>. See also Kegl, J., Senghas, A., & Coppola, M. (1999) in DeGraff (ed.), *Language Creation and Language Change*, MIT Press.

[18] Sandler, W., Meir, I., Padden, C., & Aronoff, M. (2005). The emergence of grammar: Systematic structure in a new language. *PNAS* 102(7): 2661–2665. <https://www.pnas.org/doi/10.1073/pnas.0405448102>

[19] Kallini, J., Papadimitriou, I., Futrell, R., Mahowald, K., & Potts, C. (2024). Mission: Impossible Language Models. *ACL 2024*. <https://aclanthology.org/2024.acl-long.787/>. arXiv: <https://arxiv.org/abs/2401.06416>. Code: <https://github.com/jkallini/mission-impossible-language-models>

[20] Hunter, T. (2025). Kallini et al. (2024) do not compare impossible languages with constituency-based ones. *Computational Linguistics* 51(2): 641–650. Publisher search: <https://direct.mit.edu/coli>

Approximate word count of the essay proper: ~2,400 words.