Composition

The same 11 elements viewed through 6 different norms. Each one tells a different story about what you are.

11
Major Elements
6
Mathematical Lenses
7×1027
Atoms in 70 kg Body
99.9%
Mass from Top 11
222×
Max Cosmic Enrichment (K)
φ² ± 1%
O/C Atom Ratio

Raw Data

The human body contains ~60 elements. These 11 account for 99.9% of body mass.
Each row below is a single ground truth. Everything else on this page is a projection — the same data viewed through a different linear operator.
ElementZMass %A (u)rvdW (pm)BE/nucleon (MeV)
H19.51.0081200
C618.512.0111707.680
N73.214.0071557.476
O865.015.9991527.976
Na110.222.9902278.111
Mg120.124.3051738.261
P151.030.9741808.481
S160.332.0651808.493
Cl170.235.4531758.520
K190.439.0982758.557
Ca201.540.0782318.551

§1 — Six Lenses

The same composition data projected through six different operators. Each lens applies a different weighting to the raw mass fractions, producing six different rankings of the same elements. The mathematical structure is a family of measures on the same finite set, each emphasizing different physical properties.
Six Lenses — The same elements, six different stories

Lens 1: By Mass

wi = mass%i    (identity transform)
O65.0%
C18.5%
H9.5%
N3.2%
Ca1.5%

You are mostly oxygen by weight — because water is 89% oxygen by mass. The heaviest atom dominates when you weigh things.

Lens 2: By Atom Count

ni ∝ mass%i / Ai
H61.3%
O26.4%
C10.0%
N1.49%
Ca0.24%

Six out of every ten atoms in your body are hydrogen. Dividing by atomic weight inverts the hierarchy: the lightest atom wins.

Lens 3: By Volume

Vi ∝ ni × rvdW³
H40.7%
O35.6%
C18.9%
N2.12%
Ca1.15%

Carbon has a larger van der Waals radius than oxygen (170 vs 152 pm), so it takes up proportionally more space. The volume lens is the most equitable — H, O, and C are all within a factor of 2.

Lens 4: By Electron Count

ei ∝ ni × Zi
O59.5%
H17.3%
C16.9%
N2.93%
Ca1.37%

Oxygen reclaims the throne. With Z=8, each oxygen atom brings 8 electrons. Your chemistry is driven by oxygen's electrons — the engine of oxidative metabolism.

Lens 5: By Nuclear Binding Energy

Ei ∝ ni × (BE/A)i × Ai
O72.4%
C19.8%
N3.34%
Ca1.79%
H0.00%

Hydrogen vanishes entirely — a lone proton has zero binding energy. The nuclear energy budget is 72% oxygen. Calcium punches above its weight: 0.24% of atoms but 1.79% of binding energy.

Lens 6: By Cosmic Enrichment

εi = nbody,i / nuniverse,i
K222×
P210×
Cl36.7×
Ca34.8×
Na28.3×
O25.4×
C21.8×
N14.9×
S1.4×
H0.83×
Mg0.46×

The hierarchy inverts completely. The trace elements — potassium and phosphorus — are enriched 200× over cosmic abundance. You are not a sample of the universe. You are a 200-fold concentrate of odd-Z products of stellar nucleosynthesis. Hydrogen and magnesium are actually depleted.

§2 — Ratio Analysis

Examine consecutive ratios in the atom-count ranking: H → O → C → N → Ca.
Are there patterns? Do mathematical constants appear? We check honestly.
RatioValueNearest ConstantRelative ErrorVerdict
H / O (atom%)2.320√5 ≈ 2.2363.7%Loose fit
O / C (atom%)2.638φ² ≈ 2.6180.75%Within 1%
C / N (atom%)6.742e + π ≈ 5.86015%No fit
N / Ca (atom%)6.1042π ≈ 6.2832.9%Plausible coincidence
O / C (mass%)3.514e + ¾ ≈ 3.4681.3%Forced
C / H (mass%)1.94722.6%Simple arithmetic
H / N (mass%)2.96931.0%Simple arithmetic
The O/C atom ratio: the two most important non-hydrogen elements in biochemistry — the backbone of sugars (CnH2nOn) and the framework of proteins — exist in your body at a ratio of 2.638, within 0.75% of φ² = φ + 1 ≈ 2.618. This is the only ratio that passes a reasonable significance test. The others are either too loose or can be fit to any constant with enough shopping.
Why might O/C ≈ φ²? The average oxidation state of biological carbon determines how many oxygens accompany each carbon. Carbohydrates have O/C = 1. Fats have O/C ≈ 0.1. Proteins have O/C ≈ 0.4. Water adds oxygen without carbon. The aggregate ratio reflects the macronutrient mix: approximately 55% carbohydrate, 30% fat, 15% protein by calories, plus the large reservoir of body water. The φ² agreement is specific enough to note but far from inevitable — a different diet would shift it.

§3 — Zipf / Power Law Analysis

If composition follows a power law, then percentage ∝ rank−α, and log(percentage) vs log(rank) is linear with slope −α.
We fit this for all three extensive lenses.
log-log Rank vs Percentage — Power law fits
LensZipf Exponent αR²Interpretation
Mass %2.7910.975Strong power law; steeper than Zipf's law for language (α ≈ 1)
Atom %3.6720.948Very steep; even more concentrated than mass
Volume %3.0950.921Volume softens concentration; R² drops
Biological composition is more concentrated than language. Zipf's law for word frequencies has α ≈ 1.0. City sizes: α ≈ 1.1. Gene expression: α ≈ 1.5. Body composition: α ≈ 2.8–3.7. This means the top element dominates far more aggressively than the top word dominates a text. Biology uses very few elements very intensively.

§4 — Information Entropy

Shannon entropy: H = −Σi pi log₂ pi    (bits)
Maximum entropy Hmax = log₂(N) = log₂(11) ≈ 3.459 bits (uniform distribution).
Efficiency η = H / Hmax. Low efficiency ⇒ dominated by few elements. High efficiency ⇒ spread across many.
Shannon Entropy per Lens
LensH (bits)Hmax (bits)Efficiency ηEffective Neff = 2H
Mass %1.5963.45946.1%3.02
Atom %1.4303.45941.3%2.69
Volume %1.8303.45952.9%3.56
Electron %1.7053.45949.3%3.25
Binding Energy %1.2613.32238.0%2.40
Cosmic Enrichment2.2993.45966.5%4.92
The effective number of elements. Despite using 11 major elements, each lens behaves as if only 2.4–4.9 elements matter. The binding energy lens is the most concentrated (Neff = 2.4: essentially just O and C). The cosmic enrichment lens is the most spread out (Neff = 4.9) because the trace elements have enormous enrichment factors. Volume is the most "democratic" extensive lens (η = 52.9%).

§5 — The Cosmic View

Three compositions of the same elements, three completely different distributions. The universe is hydrogen soup. The Earth's crust is an oxygen-silicon oxide. Your body is an oxygen-carbon-hydrogen solution. You are not made of what is most common, either cosmically or geologically. You are made of the specific products of stellar nucleosynthesis optimized for carbon-water chemistry.
Universe vs Earth's Crust vs Human Body — top elements by mass
Three sources, three stories. The universe is 98% hydrogen + helium — the products of Big Bang nucleosynthesis. The Earth's crust is 74% oxygen + silicon — the products of rocky planet differentiation. Your body is 83.5% oxygen + carbon — the products of biological selection from an aqueous solvent. The overlap between these three distributions is remarkably small. Life chose its ingredients with extreme specificity.

§6 — What's Actually Interesting

After six lenses, three analyses, and many numbers — what genuinely emerges?

Finding 1: Identity depends on the norm

The question "what are you made of?" has no unique answer. By mass, you are oxygen. By count, you are hydrogen. By volume, it is nearly a tie. By electrons, oxygen again. By nuclear energy, hydrogen does not exist. By cosmic enrichment, you are potassium.

This is not a curiosity — it is the central fact. The choice of norm determines the answer, and no norm is privileged. A mass-centric view is convention, not truth.

Golden Spiral — Element abundances mapped onto φ

Finding 2: O/C ≈ φ²

The atom ratio of the two most important non-hydrogen elements in biochemistry approximates the square of the golden ratio to within 0.75%. This is probably coincidence — but it is a specific coincidence. It arises from the stoichiometry of the macronutrient mix (carbohydrates, fats, proteins) plus body water. A different diet shifts the ratio. A herbivore would have a higher O/C; a carnivore, lower.

Finding 3: Composition is super-Zipfian

Body composition follows a power law with exponent α ≈ 2.8–3.7, far steeper than the α ≈ 1 of linguistic Zipf's law. Biology uses very few elements very intensively. The effective number of elements (2H) ranges from 2.4 to 4.9 across lenses, despite 11 major elements being present. This suggests a design principle: life minimizes its elemental vocabulary while maximizing functional diversity.

Finding 4: You are a 200× potassium concentrate

The cosmic enrichment lens reveals the most surprising ranking. Potassium and phosphorus — trace elements by mass — are enriched 200× over cosmic abundance. These are the elements the universe makes least efficiently (odd-Z, requiring specific supernova conditions) that biology demands most insistently (nerve impulses require K+; DNA requires phosphate backbones). You are, in a precise sense, a monument to stellar inefficiency.

Finding 5: The dual identity of water

By atom count, you are a hydrogen machine (61%). By electron count, you are an oxygen machine (60%). These are the same fact viewed from two sides: H2O has 2 hydrogen atoms contributing 2 electrons, and 1 oxygen atom contributing 8. Water is simultaneously hydrogen-dominated (by count) and oxygen-dominated (by chemistry). The lens determines which face you see.

Uncertainty: These ratios are descriptive, not explanatory. Finding φ² in the O/C ratio does not mean biology "uses" the golden ratio — it means two physical quantities happen to have that ratio for biochemical reasons (the stoichiometry of amino acids, nucleotides, and lipids). We present the pattern without claiming teleology.

Assumption: Composition data assumes a "standard" 70 kg adult. Individual variation (body fat percentage, hydration, bone density) can shift mass fractions by ±5–10% for major elements.

Implication: If the dietary macronutrient ratios change significantly (ketogenic diet, for example), the O/C ratio would shift toward ~2.0, breaking the φ² approximation. The pattern is contingent on typical omnivorous composition.