Every Voice Is an Equation

Speech can be written as mathematics, and the brain decodes it in milliseconds. Put the same test to the rest of existence, using modern code and the number systems of the ancient world, and the results reveal a precise boundary: what can be reduced to code, what never can, and what remains undiscovered.

An Idea Older Than Writing

The belief that nature can be counted predates written language. In the Lebombo Mountains on the border of South Africa and Eswatini, archaeologists recovered a baboon fibula 7.7 centimeters long bearing 29 notches, a figure close to the length of a lunar month; researchers have proposed that it served as a lunar calendar.¹ Around 20,000 years Before Christ (BC), near Lake Edward in today’s Democratic Republic of the Congo, the Ishango bone was marked with columns of notches. One column reads 11, 13, 17, 19, the prime numbers between 10 and 20; another appears to record doubling. The bone is displayed at the Royal Belgian Institute of Natural Sciences in Brussels.¹ Summed for this report, two of its columns each total exactly 60, and the third totals 48.

Evidence that early societies modeled the sky numerically follows. The Nebra sky disc, a bronze-and-gold plate buried in present-day Germany around 1600 BC, is considered the oldest known depiction of cosmic phenomena and is believed to encode the earliest known leap rule for reconciling lunar and solar calendars.² In one leading interpretation, a thick crescent Moon about four and a half days old appearing beside the Pleiades in spring signaled that a thirteenth month should be added; proponents describe this as an interpretation rather than a proof.³ The underlying problem is arithmetic: twelve lunar months fall about 10.9 days short of a solar year, causing an uncorrected calendar to drift. Other civilizations reached the same principle independently. In India, the Sulba Sutras set out geometric rules for constructing Vedic altars; the mathematician Baudhayana, active around 800 BC, stated a rule for the diagonal of a square and gave the square root of 2 as 1 + 1/3 + 1/12 − 1/408, or 1.414216, accurate to five decimal places.⁴ That figure is identical to the value the Babylonian averaging method produces on its third step, as described later in this report. In China, the Luoshu, the earliest known magic square, arranges the numbers one through nine so that each row, column and diagonal totals 15, with odd numbers representing heaven and yang and even numbers earth and yin.⁵ All eight lines were verified for this report. Between 350 and 50 BC, Babylonian astronomers calculated Jupiter’s motion using the area of a trapezoid, a geometric method previously credited to European scholars more than 1,400 years later.⁶ The Greeks articulated the idea as philosophy. According to Aristotle, the Pythagoreans of the sixth century BC held that “the elements of numbers were the elements of all things” and that “the whole heaven was harmony and number.”⁷ In 1623, in a polemic about comets titled Il Saggiatore (The Assayer), the Italian astronomer Galileo Galilei gave the principle its most cited form: the universe is a great book, open before us but unreadable until one learns its language, which is mathematics, written in triangles, circles and other geometric figures.⁸ Galileo did not originate the idea. He inherited it and converted it into a scientific method of measurement, calculation and testing. Four centuries later, that principle is easiest to examine in ordinary conversation. Every spoken word is a physical event that can be measured and written as an equation, and every listener carries a biological system that solves those equations faster than most machines could until recently. This report traces that process from start to finish, then puts the question “is everything code?” to direct mathematical testing, in modern code and in the number systems of the ancient world.

The Physics of a Word

Speech begins as pressure. A speaker sets air molecules in motion, and the disturbance travels outward at about 343 meters per second. The simplest possible sound, a pure tone such as a tuning fork produces, is described by a single equation: The human voice is more complex. The vocal folds, two bands of tissue in the throat, open and close roughly 100 to 250 times per second in normal speech. Each cycle releases a pulse of air, and the sequence produces a buzz. Mathematically, that buzz is a series of sine waves at whole-number multiples of the base pitch, known as harmonics: The base pitch, however, does not determine which word is spoken. “Cat” said high or low remains “cat.” Pitch conveys emotion, emphasis and whether a sentence is a question. The identity of the word is carried by something else.

The Vocal Tract as an Instrument

The scientific foundation for that distinction was laid in Tokyo. In 1941, researchers Tsutomu Chiba and Masato Kajiyama published The Vowel: Its Nature and Structure, using X-ray images to measure the throat and mouth during each vowel and building physical tube models that reproduced those vowels when supplied with a buzz.⁹ Researchers at Sophia University in Tokyo have since reconstructed the models, demonstrating that a narrow constriction near the front of the mouth produces “ee,” while an open front and constricted back produce “ah.”¹⁰ Swedish engineer Gunnar Fant of the Royal Institute of Technology (KTH) in Stockholm formalized the work as the source-filter theory, which derives the acoustic properties of speech from first principles and applies across languages, in speech and in singing.¹¹ In its simplest form: The vocal tract is a tube roughly 17 centimeters long, closed at the vocal folds and open at the lips. Such a tube resonates at predictable frequencies and amplifies nearby harmonics: The calculation yields peaks near 500, 1,500 and 2,500 Hz. These resonances are called formants, and this set corresponds to the neutral vowel “uh.” Moving the tongue, jaw or lips reshapes the tube and shifts the formants. Those shifts distinguish one word from another.

Vowel	As in	First formant (F1)	Second formant (F2)
ee	“beet”	about 270 Hz	about 2,300 Hz
ah	“father”	about 730 Hz	about 1,100 Hz
oo	“boot”	about 300 Hz	about 870 Hz
uh	“but”	about 500 Hz	about 1,500 Hz

Opening the jaw raises the first formant; moving the tongue forward raises the second. The values shown are typical of adult male voices. Children and most women have shorter vocal tracts and correspondingly higher values. Listeners rely on the relationship among the peaks rather than their absolute values, which is why a child and an adult saying “ee” are heard as producing the same vowel.

Second formant, F2: tongue front (2,500 Hz) → back (700 Hz)First formant, F1: jaw closed → openee (270, 2300)oo (300, 870)uh (500, 1500)ah (730, 1100)

Consonants: Noise, Bursts and Silence

Consonants introduce a wider range of mathematics. Speech scientists generally identify four sound sources: the voiced glottal source, an aspiration source, a frication (hissing) source and a transient source such as a pop or click.¹² Each alters the underlying equation:

• Hissing sounds (s, sh, f). No regular vibration is involved. Air forced through a narrow gap becomes turbulent, producing noise close to random. An “s” concentrates energy above about 4,000 Hz; a “sh” sits lower, roughly 2,000 to 4,000 Hz, because the constriction is further back and lip rounding enlarges the space in front.
• Stops (p, t, k, b, d, g). Airflow is fully blocked, creating a brief silence, then released in a burst. The difference between “pat” and “bat” depends largely on voice onset time, the interval between the burst and the start of vocal-fold vibration: near zero for an English “b,” roughly 40 to 80 milliseconds for a “p.”
• Nasals (m, n, ng). Air passes through the nasal cavity, which effectively adds a second tube. The interaction produces “anti-resonances,” frequencies at which sound is cancelled.

Consonants also shape adjacent vowels. In “bah,” “dah” and “gah,” the vowel is the same, but the second formant enters from a different starting frequency in each case. That transition, lasting tens of milliseconds, is a principal cue listeners use to identify the consonant.

The Mathematics of “Meow”

Applied to a single word, the framework is concrete. Spoken by a person, “meow” proceeds in three stages:

• The “m.” Lips closed, air directed through the nose, producing a low murmur with its main resonance at a few hundred Hz and anti-resonances suppressing higher frequencies.
• The “ee” onset. The lips open and the tongue moves forward; the second formant rises toward roughly 2,000 Hz.
• The “ow” glide. The jaw lowers and the lips round; the first formant rises and falls while the second descends toward about 900 Hz.

Expressed mathematically, “meow” is a falling curve in the second formant combined with a rise and fall in the first, beginning from a nasal resonance. Another word would trace another curve. Cats produce their own version of this signal, and science is beginning to read it. At Lund University in Sweden, phonetician Susanne Schötz and colleagues in the “Meowsic” project (Melody in Human-Cat Communication) have recorded and analyzed hundreds of cat vocalizations, measuring how pitch and melody change with context.¹³ Schötz has reported that a meow ending on a rising note at the food bowl signals a clear request, and that cats appear capable of imitating melodic patterns in their owners’ speech.¹⁴ For anyone responsible for an animal’s care, the implication is practical: changes in the pitch, length or frequency of vocalizations can signal stress, discomfort or illness before other symptoms appear.

The Ear as a Frequency Analyzer

Decoding begins in the cochlea, a fluid-filled spiral in the inner ear about the size of a pea and roughly three and a half centimeters long when uncoiled. Within it lies the basilar membrane. Hungarian physicist Georg von Békésy, who received the 1961 Nobel Prize in Physiology or Medicine for this work, showed that incoming sound creates a wave that travels along the membrane, peaking at a different location for each frequency because the membrane’s stiffness and width vary along its length.¹⁵ High frequencies peak near the entrance; low frequencies travel to the far end. The significance is mathematical. Separating a complex wave into its component frequencies is the function of the Fourier transform, named for French mathematician Joseph Fourier. The cochlea performs a physical equivalent continuously and in real time. About 3,500 inner hair cells line the membrane, each responsive to its own portion of the roughly 20 to 20,000 Hz range of human hearing. Those cells convert mechanical motion into electrical signals. Nerve cells transmit information as spikes, brief all-or-nothing electrical pulses, encoding it in their rate and precise timing. At the most fundamental level, the auditory nerve delivers a stream of timed pulses, a format closer to binary code than to language as we experience it.

Rhythm in the Brain

In the auditory cortex, timing becomes central. Neurons fire in coordinated patterns called oscillations, measurable from the scalp by electroencephalography (EEG), which records electrical activity through small sensors. Neuroscientist Anne-Lise Giraud and colleague David Poeppel proposed in a widely cited 2012 review that these oscillations align with the rhythms of speech and divide incoming sound into units, syllables and individual sounds, that the brain can then decode.¹⁶ The correspondence is close. People speak at about four to five syllables per second, while the brain’s theta rhythm runs at about four to eight cycles per second; faster gamma rhythms match the pace of individual speech sounds. An earlier study led by Giraud, combining EEG with brain imaging, found that gamma activity correlated most strongly with the left auditory cortex and theta activity with the right, and that both were linked to the region controlling the mouth.¹⁷ Perception and production of speech, the evidence suggests, operate on a shared timing system.

Templates, Prediction and Meaning

The brain also classifies what it hears against stored references. Finnish psychologist Risto Näätänen and colleagues demonstrated this using the mismatch negativity (MMN), an automatic electrical response triggered when a sound departs from an established pattern, even without conscious attention. Their key finding was that the response depends on the listener’s native language. The brain maintains abstract representations of its language’s speech sounds, which Näätänen termed phoneme traces. These form rapidly after birth and are functioning by six to twelve months of age.¹⁸ The capacity persists into adulthood: in a University of Turku study, native Finnish speakers learned to perceive an unfamiliar consonant contrast after three days of listen-and-repeat training, with corresponding changes in their automatic brain responses.¹⁹ In effect, the brain treats speech as a noisy signal to be measured, matched to the nearest stored category and resolved. That is why listeners hear a distinct “b” or “p” even though real speech produces a continuous range of timing values between them. From there, decoded sounds pass to networks responsible for words, grammar and meaning. The modern study of where that happens dates to Paris in 1861, when surgeon Paul Broca examined the brain of patient Louis Victor Leborgne, who for years had been able to produce little beyond the syllable “tan.” Broca found damage in the left frontal lobe, the area now named for him.²⁰²¹ German neurologist Carl Wernicke later identified a region further back in the left hemisphere associated with comprehension. Current research describes a more distributed network, but the principle holds: distinct circuits handle distinct stages of the process.

Is Everything a Code?

The mathematical description of speech is part of a much broader pattern. Music. The ancient Greek thinker Pythagoras is credited with observing that consonant musical intervals arise from simple whole-number ratios: half a string’s length produces an octave (2:1), two-thirds a fifth (3:2). Biology. Living organisms are built from instructions in deoxyribonucleic acid (DNA), written in four chemical letters. Cells read them in groups of three; since 4 × 4 × 4 = 64, there are 64 possible codons, mapped to 20 amino acids and stop signals. Researchers translate DNA into protein sequences with tools such as the Swiss Institute of Bioinformatics’ Expasy Translate.²² Natural patterns. Sunflower seeds and pinecone scales frequently arrange themselves in spiral counts from the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55…), with successive seeds about 137.5 degrees apart, an angle linked to the golden ratio. Word frequencies in large texts follow Zipf’s law: the most common word appears roughly twice as often as the second and three times as often as the third. Measurement. Since 20 May 2019, all official units of measurement have been defined by fixing seven constants of nature to exact values, under a decision of the General Conference on Weights and Measures, organized by the International Bureau of Weights and Measures (BIPM) near Paris.²³ The second is defined by 9,192,631,770 oscillations of a cesium atom, the meter by the speed of light at exactly 299,792,458 meters per second, the kilogram by the Planck constant. Germany’s national metrology institute described the change as placing every unit on the firm foundation of the constants themselves.²⁴ The International System of Units (SI) no longer depends on any physical artifact. The universe as computation. German computing pioneer Konrad Zuse proposed in his 1969 book Rechnender Raum (Calculating Space) that space itself might function as a grid of computing cells, with physical law as its program.²⁵ Whether that view holds is a testable question. The Foundation put it to the test.

The Tests

For this report, something “has a code” if a finite set of rules, an equation or computer program, can fully produce or predict it. An artificial intelligence (AI) model, Claude, wrote and ran five mathematical tests in the Python programming language. All figures below are output from those runs. Test 1: Compression. Rule-governed data can be described in fewer symbols than the original; random data cannot. Three samples of 16,000 bytes each were compressed:

Sample	Compressed to	Finding
One second of a synthesized “ee” vowel	3.1% of original	Highly coded
The text of this report	38.7% of original	Partly coded
Random noise from the computer’s hardware	100.4% of original	No code found

The vowel, composed entirely of harmonics and formants, reduced to under 500 bytes. Language compressed partially, reflecting both pattern and choice. Random noise did not compress at all. Test 2: Hidden variables in quantum physics. Entangled particles behave as a single unit even when separated. Physicists long debated whether each particle carries hidden instructions that predetermine its measurement results. Physicist John Bell devised a test. The program evaluated all 16 possible hidden-instruction strategies for a pair of particles; the highest score any can achieve on Bell’s test is 2. Quantum mechanics predicts 2.83 (two times the square root of two). Experiments consistently exceed 2. The 2022 Nobel Prize in Physics was awarded to Alain Aspect, John Clauser and Anton Zeilinger for this work, with the Nobel committee concluding that quantum mechanics “cannot be replaced by a theory that uses hidden variables.”²⁶ (The result specifically excludes instructions carried locally by each particle; theories involving instantaneous connections across distance remain debated.) The implication is that individual quantum events are genuinely random: their probabilities follow an equation, but single outcomes do not. Test 3: Long-term prediction. The logistic map (x → 4x(1 − x)) is a simple equation that behaves chaotically. Starting from two values differing by one part in a trillion, the program’s predictions diverged completely after 37 steps. Doubling precision roughly doubles the forecast horizon: about 40 steps at 12 digits, 80 at 24, 159 at 48. French mathematician Henri Poincaré encountered the same limit in the 1890s while studying three orbiting bodies, finding no general closed-form solution.²⁷ Chaotic systems follow rules, but predicting them indefinitely would require infinite precision. Test 4: Counting programs against numbers. Programs are finite strings of symbols and can therefore be counted. With 95 keyboard characters there are about 10²⁰ programs up to 10 characters, 10¹⁹⁸ up to 100 and 10^1,978 up to 1,000: enormous but countable. The real numbers between 0 and 1 are not countable, as German mathematician Georg Cantor proved in the nineteenth century. The program reproduced his diagonal method, taking ten program-generated numbers (including π, e and √2) and altering one digit of each to construct a new number, 0.2251584141…, absent from the list. Any such list, however long, omits numbers. It follows that almost every number cannot be produced by any program or equation. Test 5: Verification versus proof. The Collatz problem asks whether repeatedly halving even numbers and tripling-plus-one odd numbers always reaches 1. The program confirmed it for every number from 1 to 1,000,000 (the longest path, from 837,799, takes 524 steps). No accepted proof yet exists that it holds for all numbers. Checking, however extensive, is not proof, and mathematics has established that certain questions cannot be resolved by any program.

The Ancient Calculators

The question of whether the world can be counted predates the computer by several thousand years. To test the findings against that longer record, the numbers in this report were recalculated using the mathematical systems of major ancient civilizations, with the AI carrying out each calculation according to that culture’s own methods. Babylon: base 60. Mesopotamian mathematicians counted in sixties, the origin of the 60-minute hour and the 360-degree circle. A clay tablet known as Plimpton 322, dated to about 1822 to 1762 BC, contains fifteen rows of ratios that researchers at the University of New South Wales in Sydney argued in 2017 constitute “the world’s first trig table,” and an exact one.²⁸ Another tablet, YBC 7289, gives the square root of 2 as 1;24,51,10 in base 60, or 1.41421296, within six ten-millionths of the true value.²⁹ Applying the Babylonian averaging method from a starting guess of 1 reproduced those exact digits on the third step. In base 60, the 504.41 Hz vocal-tract resonance calculated earlier becomes 8,24;24,42, and the quantum score of 2.83 becomes 2;49,42,20. The fine-structure constant, 1/137, does not terminate: it begins 0;0,26,16,38,32,24 and continues indefinitely, because 137 shares no factor with 60. The Sydney researchers noted that some of the tablet’s ratios likewise could not be written exactly in base 60, requiring the scribes to work around them. Egypt: doubling and unit fractions. The Rhind Papyrus, copied by the scribe Ahmes around 1680 to 1620 BC, contains 87 problems with solutions.³⁰ Egyptian scribes multiplied by repeated doubling and expressed fractions as sums of unit fractions.³¹ Using that method, 16 doubled twice yields 64, matching the number of DNA codons; a rough calendar of 235 months of 29 days each comes to 6,815 days, assembled from the doubled rows for 16, 8, 4 and 1. The papyrus’s rule for a circle’s area, a square with sides eight-ninths of the diameter, implies π equals 256/81, about 3.1605, an error of 0.6%.³⁰ Dark matter’s 26.8% share of the universe is exactly 1/4 + 1/56 + 1/7000. The square root of 2, by contrast, produced a series, 1 + 1/3 + 1/13 + 1/253 + 1/218,201 + …, whose denominators exceeded twenty-two digits after six terms without closing. Greece: proving the limits. Greek mathematicians proved that the square root of 2 cannot be expressed as a ratio of whole numbers, the earliest known demonstration that a quantity has no exact representation in its era’s number system. Archimedes bounded π by enclosing a circle between polygons of 6 to 96 sides, concluding that it lies between 223/71 and 22/7.³² Rerunning his procedure narrowed the range from 3.0–3.46 at six sides to 3.141032–3.142715 at ninety-six. Greek engineers also built the Antikythera mechanism, a bronze calculating device from the first century BC with an estimated 35 gears, used to predict eclipses and track the Moon with cycles drawn from Babylonian astronomy.³³ Its Metonic gearing reflects that 235 lunar months approximately equal 19 years; the calculation gives 6,939.69 days against 6,939.60, a difference of about two hours over nineteen years. China: refining π. Liu Hui extended the polygon method to 3,072 sides, obtaining 3.14159, and Zu Chongzhi (430–501) expressed π as 355/113.³⁴ Recalculated, Liu Hui’s polygon gives 3.14159211, and 355/113 equals 3.141592920, accurate to six decimal places. India: zero as a number. In 628, the astronomer Brahmagupta set out the first known rules for arithmetic with zero as a number, and used the square root of 10 as a practical value for π.³⁵ That value, 3.1623, served construction and astronomy. Indian place-value numerals are the ancestors of modern digits and, by extension, of the binary code used in this report’s tests, in which 64 is written 1000000. Baghdad: the algorithm. In the ninth century, at Baghdad’s House of Wisdom, the Persian mathematician al-Khwarizmi wrote the treatise on al-jabr that named algebra, and the Latin form of his name, Algoritmi, gave rise to the word algorithm.³⁶ Each test in this report was an algorithm in that original sense. His completing-the-square method solves the classic x² + 10x = 39 to give x = 3, and identifies the single fixed point of the chaotic equation in Test 3, x = 3/4. The Maya: base 20 and an early zero. Maya mathematicians used a base-20 system written with three signs, a dot for one, a bar for five and a shell for zero, and employed place value with zero in inscriptions dating to around the time of Christ, earlier than in the Old World.³⁷ Their calendar counted 20 days to a uinal, 18 uinals to a 360-day tun, 20 tuns to a katun and 20 katuns to a baktun.³⁷ In that count, 16 October 2026, the date of this report, is 13.0.14.0.7 under the most widely used correlation (13.0.14.0.5 under an alternative two days apart). Carbon-14’s half-life of 5,730 years becomes 14.6.10; the busy beaver value 47,176,870 becomes 14.14.17.2.3.10; and the 9,192,631,770 cesium oscillations that define a second become 7.3.12.13.18.19.8.10. The Dresden Codex tracks Venus on a 584-day cycle, five of which equal 2,920 days, or eight 365-day years. The true average is 583.92 days, an error of 0.08 day per cycle, which the Maya addressed by building correction points into the table.³⁸ Lacking fractions, they adjusted the system instead. The Inca: recording in knots. Inca administrators recorded censuses, taxes and supplies on quipus, knotted cords using a standardized base-10 system in which knot position and type indicated units, tens, hundreds and thousands.³⁹ On a quipu, 5,730 appears as five knots, seven knots, three knots and a blank units position. Some quipu combinations are thought to have encoded formulas whose meaning has been lost.³⁹

What Cannot Be Reduced to Code

Together, the tests and the research define a specific list, in three categories.

A Number on Everything

An important distinction applies to the entire list: even what cannot be coded still carries numbers.

• A single atom’s decay cannot be timed, but a carbon-14 atom has exactly a 50% probability of decaying within 5,730 years.
• Chaitin’s Omega is itself a number, with about 40 binary digits determined; the remainder exist but cannot be computed.
• Uncomputable numbers are numbers without a formula.
• Weather is measured entirely in numbers, and its unpredictability has a measurable rate: how quickly forecast errors double.
• Dark matter and dark energy are unexplained, yet their shares of the universe are known: 26.8% and 68.3%.
• The fine-structure constant is an unexplained value that is itself a number, about 1/137.
• Gödel’s unprovable statements were identified by assigning every mathematical statement a number.

Assigning a number, however, is not the same as explaining. A number can label anything, as a barcode labels a product without describing its taste. Consciousness illustrates the gap most clearly: brain-wave frequencies, reaction times and pain ratings quantify activity surrounding an experience, but none constitutes the experience itself. The accurate conclusion is that numbers attach to nearly everything, including what cannot be coded; what is not always possible is converting those numbers into a rule that fully explains or predicts.

Still Discovering

Much of this knowledge is recent, and much remains incomplete. Developments from the past decade include:

• 2015: evidence that adults form new speech-sound templates within three days of training.¹⁹
• 2017: reinterpretation of a 3,800-year-old Babylonian tablet as the earliest exact trigonometric table.²⁸
• 2019: redefinition of all units of measurement by constants of nature.²³
• 2022: a Nobel Prize for experiments ruling out hidden instructions carried by particles.²⁶
• 2023: new Paris Observatory research on why the chaotic Solar System remains stable.⁴⁷
• 2024: resolution of the fifth busy beaver number after roughly 60 years.⁴²
• July 2026: a new clue to the form of the fine-structure constant.⁵⁰

The historical record is also still being read. The Antikythera mechanism has been only partly reconstructed, with several gears inferred rather than recovered.³³ The meaning of some quipu patterns has been lost.³⁹ Scholars continue to debate how the Maya corrected their Venus table.³⁸ Research into cat vocalizations continues at Lund University.¹³ And the search for dark matter is ongoing. Items now listed as “not yet coded” may be explained in the future; every equation in this report was once unknown.

Why It Matters

Speaking is physics. The lungs supply energy, the vocal folds produce a harmonic series, and the tongue, jaw and lips continuously reshape a 17-centimeter resonator. The listener reverses the process: frequency analysis in the cochlea, timed pulses along the auditory nerve, rhythmic segmentation in the cortex, comparison against stored templates and, ultimately, meaning. The process does not feel mathematical, but it is, and the decoder that runs it is present in every listener. The same is true of most of the physical world. At its edges, where randomness, infinity and conscious experience reside, the code ends, and mathematics can identify exactly where. Galileo described nature as a book written in mathematics. The evidence now shows both how much of that book can be read and, with precision, which pages cannot.