By Mark Joseph Antonius Knippenberg / ScepraX.
Status: Theoretical framework. One instantiation of the PseudoScience Speelgoed at the scale of atoms, molecules, and the bonds between them. It does not compete with chemistry. It tests whether the Speelgoed’s mechanism, supplied with values from chemistry, reproduces what chemistry already knows, and it says plainly where it does not.
The Speelgoed’s own examples live at this Octaaf. §V.5 walks from Hydrogen to Oxygen. §III binds the two into Water, and then binds Water and Carbon Dioxide into Sugar. The Lexicon calls Water “a Koppel of two gases that becomes a liquid of profound Greep”. And of its reading of the ladder, §III says: “It fits the physics from quarks to Water”. This entry tests that stretch. It covers two rungs of §III’s ladder, the Atom Octaaf and the Molecule Octaaf, because one science covers both. Its Lichaam (🖕) is an atom or a molecule. Its Koppels are the bonds between them.
Chemistry is also the first science that described its bonds in the language of preference. Eighteenth-century chemists ranked substances in tables by their “affinity” for one another (Geoffroy 1718; Bergman 1775), and in 1809 Goethe borrowed that chemistry for a novel about two couples who exchange partners, Die Wahlverwandtschaften, “elective affinities” (Goethe 1809). The idea that bonds between people and bonds between substances share a grammar is therefore old. The Speelgoed’s claim is narrower and can be tested: one mechanism, with values that each science supplies. Even the word Octaaf has a predecessor in chemistry (§3.7).
Like the other Octaven, this document is an Instantie (⚙). It supplies the open parameters of §VIII.7 with values taken from chemistry, then checks whether the shape the Speelgoed fixes survives. Where the two disagree, the disagreement is reported in §4 rather than smoothed over.
Five features set this Octaaf apart:
Every mapping carries one of five grades, defined as in the other Octaven.
| Grade | Meaning |
|---|---|
| Identity | The Speelgoed equation and the scientific model are the same equation under a stated substitution of symbols. |
| Constraint | The science fixes, bounds, or forbids a choice the Speelgoed leaves open to its Instantie. |
| Correspondence | Same structure and same qualitative behaviour, but no shared equation. |
| Tension | The Speelgoed as written conflicts with established findings. A repair is proposed. |
| Open | Not resolved. |
An Identity shows that the Speelgoed uses the same mathematics as the science at this Octaaf. That is a test of consistency, not evidence that the Speelgoed explains more than the science already does. Which quantity a Speelgoed term is mapped to is also a choice, and the same term may map to different quantities at different Octaven.
Quotations. Quotations from the Speelgoed leave out its bold markup and the symbols it puts in brackets after a term. Otherwise they are verbatim.
References. References such as §II or §VIII.1 point to the PseudoScience Speelgoed. References such as §2.1 point to sections of this document. References to companion entries are written in full, for example Thermodynamic Octaaf §2.2.
Units. Bond energies are given per mole of bonds, in kJ/mol, and where spectroscopists measured them, also in cm⁻¹ (1 cm⁻¹ ≈ 0.01196 kJ/mol).
Equations. Equations are written in plain Unicode. Where a calculation was made for this entry, the text says so.
| Speelgoed (section) | Value at this Octaaf | Grade | Here |
|---|---|---|---|
| Vol and Leeg (§IV, §VI; Lexicon) | A lean toward giving or receiving electrons, read within each bond; not a charge | Correspondence | §2.1 |
| Drempel θ (§II; §VIII.3) | Chiral symmetry breaking: a pitchfork between two mirror-image hands, with the mixture of both as mode = 0 | Identity (model, near the threshold) + Correspondence (measured) | §2.2 |
| Van Motor, L = L₀·exp(−J) (§III, §VIII.1) | Racemisation in living teeth; every reaction runs both ways; Water comes apart and re-forms | Correspondence (measured) + Constraint | §2.3 |
| What a bond leaves over (§III) | Covalent bond, hydrogen bond, dispersion | Correspondence, with a refinement | §2.4 |
| Drempel and its poles (§II); Kruispunt (§IV) | Catalysis: the barrier lowered in both directions alike; Sabatier’s principle | Constraint + Correspondence | §2.5 |
| Trouw y (§II, §VIII.1) | Atom rung: the exchange coupling between two atoms, its sign set by how their spins pair. Molecule rung: the residue of §2.4 | Identity (as at the quantum Octaaf) | §3.1 |
| Trek and Zin (§IV; Lexicon) | Readiness to bond, and the binding constant toward one partner: elective affinity, molecular recognition | Correspondence (measured) | §3.2 |
| Godin (§III; Lexicon) | Dioxygen: a strong receiver held back by its own first step | Correspondence | §3.3 |
| Creatie and Inhoud (§VI, §VIII.5) | A crystal born from a supersaturated solution: solubility as Inhoud, the nucleation barrier as θ_new | Correspondence | §3.4 |
| Masker (§VII; Lexicon) | Protecting groups | Correspondence | §3.5 |
| Rouw and Diepte (§VI; §II) | Molecular imprinting: a cavity that outlives its template | Correspondence (measured) | §3.6 |
| Levelling (§V.5; Lexicon) | The count of the periodic table; the octet; Newlands’ octaves | Correspondence (count) | §3.7 |
| Trinary Root (§III) | Atom rung: Hydrogen gives, Oxygen receives. Molecule rung: Water gives, Carbon Dioxide receives, Light pays | Correspondence; the Medium of the first rung Open | §3.8 |
| Tijd (Lexicon) | No mapping attempted | Open | §5 |
Vol and Leeg are not charges. The Lexicon defines Vol as “The self-sufficient end of the dependency spectrum” and Leeg as “The dependent end of the dependency spectrum”. §IV says that Vol/Leeg decides “which side of the Relatie a member tends to sit on”, and §VI adds that “neither is ever a pure giver or pure receiver”. The spectrum is about what a member does in a bond: whether it gives or receives, and how much it needs the bond to be whole. It is a matter of affinity and preference, not a property a member carries alone.
Full and empty. At this Octaaf the words can be read almost literally. Chemistry describes an atom by its outer shell of electrons, and a shell can be full or have places empty. Lewis proposed in 1916 that atoms bond by sharing pairs of electrons until each has a full outer shell: two electrons for hydrogen, eight for most light atoms after it (Lewis 1916; Langmuir 1919). An atom whose shell is already full, such as helium or neon, needs nothing and bonds with almost nothing. It is Vol, as the cosmic Octaaf found for helium (Cosmic Octaaf §3.11). An atom with empty places seeks partners to fill them. Oxygen has two, and §III says it plainly: “Oxygen craves the electrons that would fill its outer shell”.
Giving and receiving. Within a bond, the shared electrons do not sit evenly between the members. Chemists keep a ledger of who has given to whom, the oxidation state: each shared pair is credited to the member that holds it more strongly, a comparison made within the pair (Karen, McArdle & Takats 2016). The member credited with the pair has received; the other has given. Chemistry names the roles. A reductant gives electrons and an oxidant receives them. In a shared pair, a Lewis base gives the pair, and a Lewis acid offers the empty place that receives it (Lewis 1923). In water, the ledger has hydrogen giving and oxygen receiving. Hydrogen is Vol and Oxygen is Leeg, as §III says.
Not charge. Charge does not decide the roles. Ammonia and boron trifluoride are both neutral: ammonia gives a pair, and boron trifluoride, with an empty place, receives it. Permanganate, MnO₄⁻, is a negative ion and one of the strongest receivers in the laboratory, while the iron(II) ion, Fe²⁺, is positive and gives (Bard, Parsons & Jordan 1985). And the ledger itself is bookkeeping, not a measured charge (Karen, McArdle & Takats 2016). No real bond between unlike atoms is purely shared or purely handed over (Pauling 1932), just as “nobody sits at a pure pole on a continuous spectrum” (§IV).
Read in each bond. Whether a member gives or receives depends on its partner. Water receives from sodium, which hands it electrons and sets free hydrogen gas. It gives up its own electrons only to the strongest receivers, such as fluorine (Greenwood & Earnshaw 1997), or when Light pays for the transfer (§3.8). Chemists measure the lean of one member against another as a standard reduction potential, a free energy per electron. The scale has a fixed zero, by convention: the hydrogen electrode (Bard, Parsons & Jordan 1985). Every member’s lean is read from the first rung of §V.5.
Grade: Correspondence. How far “fully” reaches at this Octaaf is recorded in §4.1.
Many molecules come in two forms that are mirror images of each other, like a left and a right hand: the same atoms, joined in the same order, that cannot be laid on top of each other. The two forms, called enantiomers, have the same energy, the same boiling point, and the same reactions with any partner that is not itself handed. Life uses one hand only: the amino acids of its proteins are left-handed, and the sugars of its RNA and DNA right-handed (Quack, Seyfang & Wichmann 2022).
In Speelgoed terms, the two hands are the two Naar states of §VIII.3, mode* = +√(B − θ) and mode* = −√(B − θ). An equal mixture of both, which chemists call racemic, has no hand at all. It is mode = 0, Van-mode, which §III describes as “Not a distant coordinate - nothing.”
The pitchfork. Frank showed in 1953 that a racemic mixture can be unstable. If each hand speeds its own formation and the two hands destroy each other when they meet, a small excess of one hand grows (Frank 1953). Kondepudi and Nelson studied an open version, supplied with raw material at a steady rate, and found a symmetry-breaking bifurcation (Kondepudi & Nelson 1985). For this entry, a scheme of that kind was written out:
S + T ⇌ X_L S + T ⇌ X_D
S + T + X_L ⇌ 2 X_L S + T + X_D ⇌ 2 X_D
X_L + X_D → P
Here X_L and X_D are the two hands, S and T the raw materials, held at a fixed product λ = [S]·[T] by the supply, and P an inert product. Write α = ([X_L] − [X_D])/2 for the excess of one hand. The racemic state is unstable above a threshold λ_c, and only if the two hands destroy each other faster than the self-copying step runs backward. A standard reduction, repeated numerically for this entry, gives the new states near the threshold as
α* = ±c·√(λ − λ_c)
with c a constant set by the rate constants. That is §VIII.3: “For B > θ, mode = 0 becomes unstable and two new stable points appear at mode* = ±√(B − θ)”, with B − θ = λ − λ_c. Grade: Identity, near the threshold and in the symmetric case.
Both hands live, measured. Sodium chlorate is made of ions that have no hand, but its crystals are handed. Kondepudi, Kaufman and Singh grew them from solution. Without stirring, statistically equal numbers of left- and right-handed crystals formed. With stirring, 99.7 per cent of the crystals in a given sample had the same hand, either left or right (Kondepudi, Kaufman & Singh 1990). Each run settles on one pole, and the other pole stays as available as before. §VII: “the same system with the same orders will not produce the same outcome twice”.
Never quite mirror images. The symmetric pitchfork is a limit. A small bias toward one hand unfolds it, and the favoured hand is then the likelier outcome. Soai and colleagues found a reaction whose product speeds its own formation in its own hand, so that a small excess of one hand grows round after round (Soai et al. 1995). And §VIII.3 says of every whole that “its modes are never mirror images”. For molecules, physics predicts the same. The weak nuclear force does not respect mirror symmetry, and it should give the two hands slightly different energies: 10⁻¹¹ to 10⁻¹⁰ J/mol by calculation, depending on the molecule (Quack, Seyfang & Wichmann 2022). That is about 10⁻¹⁴ of the thermal energy at room temperature, computed for this entry, and it has not yet been detected. Grade: Identity (model, near the threshold) + Correspondence (measured). Which hand life chose, and why, is left open (§5, item 2).
The thermodynamic Octaaf identified the Van Motor with the Arrhenius–Kramers law and showed that it is never off at any temperature above absolute zero (Thermodynamic Octaaf §2.2). At this Octaaf it can be watched at work.
The held hand slips. A living body keeps its single hand by traffic: its proteins are built from left-handed amino acids, broken down, and rebuilt (Cellular Octaaf §2.2). Where a protein is never renewed, the Van Motor shows. In the enamel of human teeth, aspartic acid slowly turns into its mirror form, with a rate constant of 8.29 × 10⁻⁴ per year, so that the mirror form accumulates with age in living people. The same increase was not seen in haemoglobin, a protein the body keeps renewing (Helfman & Bada 1975). In dentine and enamel, the mirror form gains about 0.1 per cent of the aspartic acid per year (Helfman, Bada & Shou 1977). The held pole lasts as long as it is renewed. Left alone, the aspartic acid drifts back toward mode = 0, the mixture with no hand. §VIII.1: “Escape toward Van is exponentially suppressed by how strongly the node is held - suppressed, never abolished.”
Water comes apart. Forming liquid water from hydrogen and oxygen at 25 °C releases 237.1 kJ of free energy per mole; this was computed for this entry from the CODATA values (Cox, Wagman & Medvedev 1989). The equilibrium constant is about 3.5 × 10⁴¹, also computed for this entry. That is enormous, but it is finite. In a sealed space above pure water, the oxygen set free by water’s own dissociation would settle at about one molecule in every 300 cubic metres (computed for this entry). A reaction said to “go to completion” approaches a limit. The other pole is never empty.
Water is traffic. Water also comes apart into ions. In pure water at 25 °C, about one molecule in 550 million is ionised at any moment (computed from the ionisation constant; Bandura & Lvov 2006). The ions find partners again within about 70 microseconds, because their recombination is one of the fastest reactions known (Eigen & De Maeyer 1955). For the balance to hold, each water molecule must come apart, on average, about once every eleven hours, some 800 times a year (computed for this entry). The bonds between neighbouring molecules change faster still: liquid water rebuilds its network of hydrogen bonds on a timescale of picoseconds, trillionths of a second. Simulations show a molecule switching partners by a sudden, large turn, not by small steps (Laage & Hynes 2006), and experiments support that picture, most clearly in salt solutions (Laage et al. 2012).
§III: “persistence is paid for out of that ongoing traffic, not out of one founding crossing”. A glass of water looks still. Every molecule in it has come apart and re-formed hundreds of times in a year, and its hydrogen bonds change partners within trillionths of a second. Grade: Correspondence (measured). “The Van Motor is never off” (§VIII.1) holds at this Octaaf as an equilibrium constant that is never infinite. Grade: Constraint, and the Speelgoed passes it.
§III reads a pattern along the ladder: “each God/Godin bond tends to cancel the charge that ruled its own Octaaf”, and “What the next Octaaf feels is a residue.” For the rungs of this entry it names two residues: “The bonds between atoms are what the electric force can still do between neutral atoms once they come close, and the hold of Water on Water is what is left of it between neutral molecules.” Chemistry measures each step.
One hydrogen bond is worth only about five times the thermal energy at room temperature (computed for this entry), but every molecule in liquid water holds several at once, which the Lexicon names “a liquid of profound Greep”. Grade: Correspondence.
A refinement. §III ends its chain this way: “Where every charge that can cancel has cancelled, only the pull that cannot cancel remains: gravity, which only attracts, and therefore rules the largest scales.” At this Octaaf a pull that no cancelling of charge removes appears earlier. Dispersion needs no net charge and no lasting separation of charge; it comes from fluctuations, so no cancelling of charge removes it. Between two molecules in empty space it only attracts. It weakens so fast with distance that gravity still rules the largest scales. And it depends on the Medium. Between two different bodies immersed in a liquid it can push them apart, as Munday, Capasso and Parsegian measured between a gold sphere and a silica plate in bromobenzene (Munday, Capasso & Parsegian 2009). What two members feel for each other depends on what lies between them. This is recorded in §4.2.
Neither argon atom shows a lasting Eigen: no permanent separation of charge. What binds them is each atom’s fluctuation being followed by the other’s. Whether that is a Koppel held by Echoes alone is left as a question (§5, item 3).
A catalyst takes part in a reaction and comes out unchanged. Ostwald defined catalysis as “the acceleration of a chemical reaction, which proceeds slowly, by the presence of a foreign substance”, and stressed that the catalyst does no work: whatever energy is spent adding it is recovered when it is taken away (Ostwald 1894). It follows that a catalyst cannot shift an equilibrium. If it could, adding and removing it would drive a reaction back and forth and deliver work for nothing, a perpetual motion machine. A catalyst offers a route with a lower barrier. The difference between the barrier of the forward crossing and that of the return is fixed by the two poles, so any route that lowers one lowers the other by the same amount. In the thermodynamic Octaaf’s terms, the Greep J = ΔG‡/k_BT falls equally in both directions (Thermodynamic Octaaf §2.2).
The effect can be enormous. Without an enzyme, orotic acid loses its carbon dioxide in neutral water at room temperature with a half-life of 78 million years. The enzyme that performs the same step on its relative orotidine 5’-phosphate, on the way to the letters of RNA and DNA, speeds the reaction by a factor of 10¹⁷ (Radzicka & Wolfenden 1995). The poles do not move.
The mapping. §II gives every Drempel “two named poles”. At this Octaaf the depth of the poles and the height of the barrier between them are separate quantities, and a third member can change the height without touching the depths. It cannot favour either pole. Grade: Constraint.
Where the crossing happens. A catalyst works by binding: the reactants attach to it, cross, and leave. Sabatier saw what this demands (Sabatier 1913). A surface that binds too weakly never holds the reactants long enough to change them. One that binds too strongly holds whatever lands on it and does not let go, so the next arrival finds the place taken. The best catalysts sit between. Plotted against binding strength, catalytic activity rises and falls in the shape of a volcano. For making hydrogen gas, the peak lies where hydrogen binds to the surface with a free energy near zero, and platinum sits near the top (Nørskov et al. 2005).
This is the Vermenigvuldiging of §IV. The catalyst’s binding site is a Kruispunt. Free, its Signaal is at Munt; occupied, at Kop. An arriving molecule is the traveller. A site that binds too strongly stays at Kop, and each new arrival meets a Weigering: “a bond that keeps meeting the same claimed gate is drained one Weigering at a time”. When a catalyst’s sites are held by something that will not leave, chemists call it poisoned. A site that binds too weakly never lets the traveller’s Reactie pass its Drempel, and “nothing resolves”. Grade: Correspondence.
§III: “The bonds between atoms are what the electric force can still do between neutral atoms once they come close.” The first quantum explanation of how two neutral atoms bond came from Heitler and London (Heitler & London 1927). Two hydrogen atoms, each with one electron, approach each other. The electrons are identical and can trade places, and the energy of the pair depends on how their spins are arranged. With the spins opposed, the atoms bind into a hydrogen molecule. With the spins aligned, they repel, and no chemical bond forms (Kołos & Wolniewicz 1965).
The members are the same in both cases. Neither atom alone decides whether the pair attracts or repels; only the arrangement of the pair does. The difference between the two arrangements can be written as a single coupling between the two spins, the exchange coupling, which is the kind of coupling the quantum Octaaf identified with Trouw: one value per pair, of either sign (Quantum Octaaf §2.5). §II: “Positive Trouw pulls the Eigen toward its Echo of the partner; negative Trouw pushes it away.” Grade: Identity, as at the quantum Octaaf.
The shared weight can be measured only on the pair. The energy needed to separate the two atoms of a hydrogen molecule is known to ten significant figures: 36,118.06962 cm⁻¹, or 432.07 kJ/mol (Hölsch et al. 2019; conversion computed for this entry). §II: “Trouw is shared-one value per Koppel”.
Two rungs, two Trouws. §III: “Each Octaaf’s Trouw is what the Octaaf below it left over.” At the Atom rung, Trouw is the coupling that makes the bond. At the Molecule rung the members are molecules, and their Trouw is what that bond left over: the hydrogen bond and the dispersion pull of §2.4.
§IV defines Trek as “the general, unaimed pull toward relationship-the background readiness to bond”, and Zin as the same pull once it is “aimed at one specific other system”. Its example: “General hunger is Trek. Wanting this specific meal, right now, is that same value, aimed-Zin.”
Chemistry began as a science of preference. In 1718 Geoffroy published a table of rapports. Each column was headed by one substance, with other substances listed below it in the order of their affinity for it, and a substance higher in a column would displace one lower down from its partner (Geoffroy 1718). Bergman extended the tables and called the effect elective attraction (Bergman 1775). In Goethe’s novel, the Captain explains how two compounds, AB and CD, can exchange partners to form AD and BC, and the novel’s two couples then do the same (Goethe 1809).
Zin, measured. Modern chemistry measures a preference as a binding constant: how strongly one member holds one particular partner. Pedersen found that ring-shaped molecules, the crown ethers, wrap around metal ions and hold them in their central cavity (Pedersen 1967), and a ring holds one ion more firmly than another. Fischer described the specificity of enzymes with an image every chemist knows: lock and key (Fischer 1894). Pearson found a preference by kind: “hard” acids, small and not easily deformed, prefer hard bases, and “soft” acids prefer soft ones (Pearson 1963).
The mapping. The binding constant toward one partner is a Zin: the pull aimed at one specific other. A preference is two Zins compared. Trek is the same member’s readiness to bind at all, before a partner is chosen. Grade: Correspondence (measured).
One value or two? The Speelgoed says that Trek and Zin are “same value, same slot”. Chemistry long taught that they trade against each other: the more reactive a species, the less choosy. That rule, the reactivity–selectivity principle, has met so many exceptions that Mayr and Ofial called it “an imperishable myth” (Mayr & Ofial 2006). Whether the readiness to bond with anything is the same pull that chooses is left open (§5, item 5).
The Lexicon’s Godin “Embodies the principle of endless craving”. It is “the pure, undirected pull - Trek without aim - made into a being”, and “It enables burning.” §III names Oxygen the Godin of the Atom Octaaf.
The craving. Burning almost any fuel with oxygen releases about 418 kJ for every mole of O₂ consumed (Schmidt-Rohr 2015; Cellular Octaaf §2.4). Even bound to its own kind, oxygen stays unsatisfied. The O₂ molecule has two unpaired electrons, which make it paramagnetic: liquid oxygen is drawn to a magnet (Greenwood & Earnshaw 1997). Of the main gases of the air, it is the only one with unpaired electrons.
Held back. Yet wood, sugar and living bodies sit in an atmosphere that is one-fifth oxygen without bursting into flame. Textbooks often explain this by spin: O₂’s two unpaired electrons point the same way, while most molecules have none, so a direct reaction is “spin-forbidden”. Borden and colleagues traced the persistence to the energy of the first steps. The two unpaired electrons of O₂ are spread over both atoms and stabilised by about 100 kcal/mol, compared with two separate OH radicals. That makes the first steps open to O₂ uphill: taking a single hydrogen atom from another molecule, or bonding to another O₂. What makes burning so favourable is only reached later, when the weak O–O bond itself breaks (Borden et al. 2017). The craving is real, but it cannot be satisfied halfway.
The mapping. A Godin whose pull is enormous and undirected, held back by its own first step. The Van Motor is not stopped by that: iron still rusts and oils still turn rancid in air, slowly. And once a fire starts, the crossing feeds itself. The restraint matters beyond oxygen. The unreactivity of O₂ toward these first steps, Borden and colleagues write, “maintains its abundance in the ecosphere and thus its availability to support aerobic life”. The Godin’s restraint is what lets the next Octaaf breathe. Grade: Correspondence.
§VIII.5 makes Creatie a two-step comparison. First an excess over the capacity Q, and then: “If T_excess itself exceeds a local Drempel θ_new, a new member is instantiated”.
The mechanism. A solution can hold only so much of a dissolved substance at a given temperature: its solubility. Cool a saturated solution, or let its solvent evaporate, and it holds more than it can; it is supersaturated. Yet a supersaturated solution can stay clear for a long time. A crystal has to start as a small cluster, and a small cluster has so much surface for its size that it tends to dissolve again. Only a cluster larger than a critical size grows. In classical nucleation theory, the barrier to forming one is
ΔG* = 16π·γ³·v² / ( 3·Δμ² ) Δμ = k_B·T·ln S
where γ is the energy per area of the crystal’s surface, v the volume of one molecule in the crystal, S the supersaturation, and Δμ the excess free energy per molecule (Becker & Döring 1935; Mullin 2001). The barrier falls steeply as the excess grows. Below a certain supersaturation, crystals practically never form on their own; above it, they appear. The range between saturation and that point is called the metastable zone (Mullin 2001).
The mapping. The solubility is Inhoud, “The absorption capacity Q of a Koppel; excess beyond it triggers Creatie” (Lexicon). The supersaturation is the excess, measured as a free energy. The nucleation barrier is θ_new. The new crystal is a new Solo, and it is not disconnected: from the moment it forms, it exchanges molecules with the solution it came from, growing and dissolving at once. Grade: Correspondence.
Born bound. Kondepudi’s stirred sodium chlorate (§2.2) shows the last clause of §VIII.5: “a new Relatie forming at the moment of birth”. Stirring breaks small fragments off the first crystal, the fragments seed new crystals, and the new crystals carry the first one’s hand (Kondepudi, Kaufman & Singh 1990).
The Lexicon’s Masker is “A presented Eigen broadcast at the source, standing in a Koppel where the Bloot one should be”. It has “Same garment, two wearers”, and of the second it says: “an Engel wears it to protect, the hidden Eigen is real, and the Pijn is the gift.”
The mechanism. A chemist building a complex molecule step by step often has a reactive group that must survive a step meant for another part of the molecule. The group is masked: turned into a form that the reagents of that step leave alone, and restored afterwards. An alcohol becomes a silyl ether, an amine a carbamate, a ketone an acetal. Chemists have catalogued a great many such protecting groups, each with its own way on and off (Wuts 2014).
The mapping. The reagent reads the mask and treats the group as what it presents. The group’s own identity is kept underneath and returns intact when the mask is removed. This is the Engel’s Masker, worn to protect. It also prices itself, as §VII says: “A Masker prices itself”. Every mask costs a step to put on and a step to take off, and chemists count protecting groups among the main costs of a synthesis (Young & Baran 2009): “Its standing cost is Pijn” (Lexicon). And it holds “only until a commitment is demanded that the true Eigen must actually make” (§VII). Before the group can form the bond it was kept for, the mask must come off. Grade: Correspondence.
The fit has a limit. A chemical mask is not a pretence. While it is on, the group really is something else. What it hides is what the group will be again.
§VI: “An Echo always outlives its Koppel”, and the Echo of an ended bond “settles toward the last signal it ever received”.
The mechanism. In molecular imprinting, a polymer is formed around a template molecule. Smaller molecules that bind to the template gather around it and are locked in place as the polymer sets. Then the template is washed out. What remains is a cavity with the template’s shape and its pattern of binding points. Wulff and Sarhan made such polymers around a handed template. After it was removed, the polymer preferred the template’s own hand over its mirror image (Wulff & Sarhan 1972). Vlatakis and colleagues imprinted polymers with the drugs theophylline and diazepam. The imprints bound their templates with a selectivity similar to that of antibodies, and an assay built on them measured drug levels in human serum as accurately as an established immunoassay (Vlatakis et al. 1993).
The mapping. The cavity is the Echo of an ended bond: a trace of the partner’s shape, set at the moment the bond ended and kept after the partner has gone. That is Rouw. The polymer is rigid, so this Echo hardly drifts. And it decides what the polymer binds next, which is what §II says of Diepte: “the hidden charge that colours every subsequent perception and decision”. §VI also says of Rouw: “touch it, and it answers”. An imprinted cavity is silent until a molecule of the template’s shape comes near, and then it binds. Grade: Correspondence (measured).
Most bonds at this Octaaf leave no such record in their members. That is recorded in §4.3.
§V.5: “To reach a higher Octaaf in the simple atom ladder, the God of the lower Octaaf walks the first eight positions of the periodic table”, from “Hydrogen (1) - the God” to “Oxygen (8), the Godin”. The Lexicon makes “the eight-step walk” the spine of every Octaaf.
The count. The positions are atomic numbers: the charge of the nucleus, which Moseley showed to be the order of the elements (Moseley 1913). Oxygen is the eighth. The number eight matters in chemistry for a second reason. The outer shell of the light atoms after helium is full at eight electrons (Lewis 1916; Langmuir 1919). Oxygen has six and craves two, which is why one oxygen binds two hydrogens. Grade: Correspondence (count).
The first octave. The word has a predecessor. In 1865 Newlands arranged the known elements by atomic weight and noticed that their properties recur at every eighth element: “members of the same group stand to each other in the same relation as the extremities of one or more octaves in music”. He called it the law of octaves (Newlands 1865). When he presented it to the Chemical Society in 1866, Professor Foster asked whether he had examined the elements “according to the order of their initial letters” (Chemical News 1866). In 1887, five years after it had honoured Mendeleev and Meyer, the Royal Society awarded Newlands its Davy Medal for the discovery of the periodic law.
A count, not a path. At this Octaaf no process turns Hydrogen into Oxygen. Chemistry rearranges partners; it never changes what an element is. The walk is a path in the nuclei of atoms, inside the stars. Stars fuse hydrogen into helium, and helium into carbon and oxygen (Burbidge et al. 1957), and the oxygen of water was made there (Cosmic Octaaf §3.11). Even there the walk skips rungs. Stars do not make beryllium and boron by burning; most of those come from cosmic rays breaking larger nuclei apart in space (Reeves, Fowler & Hoyle 1970).
The descent. §V.5: “Water descends into its members: Oxygen and Hydrogen.” That part is chemistry. Water can be split into hydrogen and oxygen, at a cost of at least 237.1 kJ per mole (§2.3), so the parting draws Verlies, as §V.5 says. The reverse walk through the elements is again a count. The parting of water that matters most happens at the next rung, in photosynthesis (§3.8).
§III follows the ladder through both rungs of this entry: “There, Hydrogen is the God-fully Vol-and Oxygen is the Godin-fully Leeg-and their bond is Water”, and “In that octaaf, Water is the God; Carbon Dioxide, emptied of usable energy, is its Godin; with Light as their Medium they form Sugar”. Read with the lean of §2.1, both rungs hold.
The Atom rung. In water, hydrogen has given and oxygen has received (§2.1). Their union releases Energie: 237.1 kJ of free energy per mole (§2.3). §III gives every Octaaf “Vol source, Leeg depth, and the living Medium their union sustains”, but it names no Medium for this rung, and §V.5 says only that Hydrogen and Oxygen “form a bond with each other and their Medium”. It is left open (§5, item 1).
The Molecule rung. In photosynthesis, Water gives and Carbon Dioxide receives. Plants take electrons from water and pass them, along a chain, to carbon dioxide, which becomes sugar. The carbon in carbon dioxide has already given away all four of its outer electrons, as far as the ledger of §2.1 can count; it has nothing left to give. That is what “emptied of usable energy” means in chemistry. The transfer runs uphill, and Light pays for it. In the dark, water gives its electrons only to the strongest receivers (§2.1). §III: “Water without Light is Leeg, explicitly not in its Vol state.” At this Octaaf that sentence is chemically accurate.
The Godin set free. In 1941 Ruben and colleagues gave plants water or carbon dioxide labelled with the heavy isotope oxygen-18, and showed that the oxygen plants release comes from the water, not from the carbon dioxide (Ruben et al. 1941). So the Oxygen that received from Hydrogen at the Atom rung, and was taken into Water, the God of the next rung, gives back at that rung what it once received, and leaves as O₂. The electrons that hydrogen gave to oxygen pass on to carbon. §III: “A Godin at one Octaaf is integrated into the God of the next Octaaf”. At this Octaaf the Godin is released again, and breathing closes the loop: sugar burns with oxygen back to carbon dioxide and water (Cellular Octaaf §2.4).
Grade: Correspondence. The Medium of the Atom rung is Open.
4.1 “Fully” Vol and “fully” Leeg (§III). Constraint (scope). At this Octaaf, Vol and Leeg are read within a bond (§2.1). In water all the giving runs from Hydrogen to Oxygen, so each is fully what §III calls it there. Across all of chemistry, neither stands at a pole: fluorine receives more strongly than oxygen, and many metals give more readily than hydrogen. §III already says this: “Being God or Godin is a claim about one bond, not a rank a thing keeps.” No change is proposed.
4.2 Before gravity, dispersion (§III). Kept at this Octaaf. §III ends its chain of residues with gravity, “the pull that cannot cancel”. At this Octaaf a pull that no cancelling of charge removes appears first: dispersion (§2.4). It weakens quickly with distance, so gravity still rules the largest scales, and §III calls its chain “a reading of the ladder, not a rule of the mechanism”. Two details are recorded here: the uncancellable pull at this Octaaf is electromagnetic, and across a Medium it can repel.
4.3 Members without memory (§II, §VI). Open. §II says that a system is “in the most literal mechanical sense, accumulating every relationship it has ever maintained”, and §VI that “An Echo always outlives its Koppel”. The members of this Octaaf do not keep such a record. Two water molecules are identical, whatever bonds each has had; a molecule formed a moment ago and one formed a billion years ago cannot be told apart. Where an ended bond leaves a record, it goes into the Medium, as heat and light, where the quantum and thermodynamic Octaven found it (Quantum Octaaf §3.6; Thermodynamic Octaaf §3.6), or into a structure built to keep it (§3.6).
4.4 The seven steps are a count (§V.5). Kept at this Octaaf. At this Octaaf the walk from Hydrogen to Oxygen, and the walk back, are counts on the periodic table. No chemical process changes one element into another. The walk is a path in the stars, and even there it skips rungs (§3.7).
The chemical Octaaf is where the Speelgoed’s own examples live. Its Vol and Leeg are full and empty: a lean toward giving or receiving, read within each bond, never a charge. Read that way, §III’s ladder holds at both of its rungs. Hydrogen gives to Oxygen, and Water is born. Water gives to Carbon Dioxide when Light pays, Sugar is born, and the Oxygen that once received is set free.
Its Drempel chooses between two hands. A reaction in which each hand copies itself passes through the pitchfork of §VIII.3, and a stirred crystallisation picks one hand per run, but not the same hand every run. Its Van Motor is never off. Water comes apart and re-forms, and the living body slowly loses its single hand wherever it stops renewing itself. Its catalysts lower a Drempel without favouring either pole, and work best when they bind neither too weakly nor too strongly. Its bonds leave residues, and the last of them, dispersion, binds even atoms that have nothing to share.
Chemistry has always spoken of affinity and preference. Geoffroy ranked them in a table, and Goethe told a love story with them. This entry finds the Speelgoed’s grammar in the same place, with numbers attached. At its foot, two questions stay open: the Medium of the first rung, and why life chose one hand. The other hand is still there.
That is the how. The why is for the Speelgoed to say.
Bandura, A. V., & Lvov, S. N. (2006). The ionization constant of water over wide ranges of temperature and density. Journal of Physical and Chemical Reference Data, 35(1), 15-30. doi:10.1063/1.1928231
Bard, A. J., Parsons, R., & Jordan, J. (Eds.). (1985). Standard Potentials in Aqueous Solution. New York: Marcel Dekker. 2017 reissue: doi:10.1201/9780203738764
Becker, R., & Döring, W. (1935). Kinetische Behandlung der Keimbildung in übersättigten Dämpfen. Annalen der Physik, 416(8), 719-752. doi:10.1002/andp.19354160806
Bergman, T. (1775). Disquisitio de attractionibus electivis. Nova Acta Regiae Societatis Scientiarum Upsaliensis, 2, 159-248. English translation (1785), Internet Archive
Borden, W. T., Hoffmann, R., Stuyver, T., & Chen, B. (2017). Dioxygen: What makes this triplet diradical kinetically persistent? Journal of the American Chemical Society, 139(26), 9010-9018. doi:10.1021/jacs.7b04232
Burbidge, E. M., Burbidge, G. R., Fowler, W. A., & Hoyle, F. (1957). Synthesis of the elements in stars. Reviews of Modern Physics, 29(4), 547-650. doi:10.1103/RevModPhys.29.547
Chemical News (1866). Report of the meeting of the Chemical Society, 1 March 1866. Chemical News, 13, 113. Text and context, Le Moyne College
Cox, J. D., Wagman, D. D., & Medvedev, V. A. (1989). CODATA Key Values for Thermodynamics. New York: Hemisphere. codata.info
Eigen, M., & De Maeyer, L. (1955). Untersuchungen über die Kinetik der Neutralisation. I. Zeitschrift für Elektrochemie, 59(10), 986-993. doi:10.1002/bbpc.19550591020
Fischer, E. (1894). Einfluss der Configuration auf die Wirkung der Enzyme. Berichte der deutschen chemischen Gesellschaft, 27(3), 2985-2993. doi:10.1002/cber.18940270364
Frank, F. C. (1953). On spontaneous asymmetric synthesis. Biochimica et Biophysica Acta, 11, 459-463. doi:10.1016/0006-3002(53)90082-1
Geoffroy, É.-F. (1718). Table des différents rapports observés en chimie entre différentes substances. Mémoires de l’Académie royale des sciences, 202-212. Biodiversity Heritage Library
Goethe, J. W. von (1809). Die Wahlverwandtschaften. Tübingen: Cotta. Project Gutenberg
Greenwood, N. N., & Earnshaw, A. (1997). Chemistry of the Elements (2nd ed.). Oxford: Butterworth-Heinemann. doi:10.1016/C2009-0-30414-6
Heitler, W., & London, F. (1927). Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik. Zeitschrift für Physik, 44(6-7), 455-472. doi:10.1007/BF01397394
Helfman, P. M., & Bada, J. L. (1975). Aspartic acid racemization in tooth enamel from living humans. Proceedings of the National Academy of Sciences, 72(8), 2891-2894. doi:10.1073/pnas.72.8.2891
Helfman, P. M., Bada, J. L., & Shou, M.-Y. (1977). Considerations on the role of aspartic acid racemization in the aging process. Gerontology, 23(6), 419-425. doi:10.1159/000212218
Herman, P. R., LaRocque, P. E., & Stoicheff, B. P. (1988). Vacuum ultraviolet laser spectroscopy. V. Rovibronic spectra of Ar₂ and constants of the ground and excited states. The Journal of Chemical Physics, 89(8), 4535-4549. doi:10.1063/1.454794
Hölsch, N., Beyer, M., Salumbides, E. J., Eikema, K. S. E., Ubachs, W., Jungen, C., & Merkt, F. (2019). Benchmarking theory with an improved measurement of the ionization and dissociation energies of H₂. Physical Review Letters, 122(10), 103002. doi:10.1103/PhysRevLett.122.103002
Karen, P., McArdle, P., & Takats, J. (2016). Comprehensive definition of oxidation state (IUPAC Recommendations 2016). Pure and Applied Chemistry, 88(8), 831-839. doi:10.1515/pac-2015-1204
Kołos, W., & Wolniewicz, L. (1965). Potential-energy curves for the X ¹Σg⁺, b ³Σu⁺, and C ¹Πu states of the hydrogen molecule. The Journal of Chemical Physics, 43(7), 2429-2441. doi:10.1063/1.1697142
Kondepudi, D. K., Kaufman, R. J., & Singh, N. (1990). Chiral symmetry breaking in sodium chlorate crystallization. Science, 250(4983), 975-976. doi:10.1126/science.250.4983.975
Kondepudi, D. K., & Nelson, G. W. (1985). Weak neutral currents and the origin of biomolecular chirality. Nature, 314(6010), 438-441. doi:10.1038/314438a0
Laage, D., & Hynes, J. T. (2006). A molecular jump mechanism of water reorientation. Science, 311(5762), 832-835. doi:10.1126/science.1122154
Laage, D., Stirnemann, G., Sterpone, F., & Hynes, J. T. (2012). Water jump reorientation: From theoretical prediction to experimental observation. Accounts of Chemical Research, 45(1), 53-62. doi:10.1021/ar200075u
Langmuir, I. (1919). The arrangement of electrons in atoms and molecules. Journal of the American Chemical Society, 41(6), 868-934. doi:10.1021/ja02227a002
Lewis, G. N. (1916). The atom and the molecule. Journal of the American Chemical Society, 38(4), 762-785. doi:10.1021/ja02261a002
Lewis, G. N. (1923). Valence and the Structure of Atoms and Molecules. New York: Chemical Catalog Company. Internet Archive
London, F. (1937). The general theory of molecular forces. Transactions of the Faraday Society, 33, 8-26. doi:10.1039/TF937330008b
Maksyutenko, P., Rizzo, T. R., & Boyarkin, O. V. (2006). A direct measurement of the dissociation energy of water. The Journal of Chemical Physics, 125(18), 181101. doi:10.1063/1.2387163
Mayr, H., & Ofial, A. R. (2006). The reactivity–selectivity principle: An imperishable myth in organic chemistry. Angewandte Chemie International Edition, 45(12), 1844-1854. doi:10.1002/anie.200503273
Moseley, H. G. J. (1913). The high-frequency spectra of the elements. Philosophical Magazine, 26(156), 1024-1034. doi:10.1080/14786441308635052
Mullin, J. W. (2001). Crystallization (4th ed.). Oxford: Butterworth-Heinemann. doi:10.1016/B978-0-7506-4833-2.X5000-1
Munday, J. N., Capasso, F., & Parsegian, V. A. (2009). Measured long-range repulsive Casimir–Lifshitz forces. Nature, 457(7226), 170-173. doi:10.1038/nature07610
Newlands, J. A. R. (1865). On the law of octaves. Chemical News, 12, 83. Text and context, Le Moyne College
Nørskov, J. K., Bligaard, T., Logadottir, A., Kitchin, J. R., Chen, J. G., Pandelov, S., & Stimming, U. (2005). Trends in the exchange current for hydrogen evolution. Journal of The Electrochemical Society, 152(3), J23-J26. doi:10.1149/1.1856988
Ostwald, W. (1894). [Review]. Zeitschrift für physikalische Chemie, 15, 705-706. English translation
Pauling, L. (1932). The nature of the chemical bond. IV. The energy of single bonds and the relative electronegativity of atoms. Journal of the American Chemical Society, 54(9), 3570-3582. doi:10.1021/ja01348a011
Pearson, R. G. (1963). Hard and soft acids and bases. Journal of the American Chemical Society, 85(22), 3533-3539. doi:10.1021/ja00905a001
Pedersen, C. J. (1967). Cyclic polyethers and their complexes with metal salts. Journal of the American Chemical Society, 89(26), 7017-7036. doi:10.1021/ja01002a035
Quack, M., Seyfang, G., & Wichmann, G. (2022). Perspectives on parity violation in chiral molecules: Theory, spectroscopic experiment and biomolecular homochirality. Chemical Science, 13(36), 10598-10643. doi:10.1039/d2sc01323a
Radzicka, A., & Wolfenden, R. (1995). A proficient enzyme. Science, 267(5194), 90-93. doi:10.1126/science.7809611
Reeves, H., Fowler, W. A., & Hoyle, F. (1970). Galactic cosmic ray origin of Li, Be and B in stars. Nature, 226(5247), 727-729. doi:10.1038/226727a0
Rocher-Casterline, B. E., Ch’ng, L. C., Mollner, A. K., & Reisler, H. (2011). Communication: Determination of the bond dissociation energy (D₀) of the water dimer, (H₂O)₂, by velocity map imaging. The Journal of Chemical Physics, 134(21), 211101. doi:10.1063/1.3598339
Ruben, S., Randall, M., Kamen, M., & Hyde, J. L. (1941). Heavy oxygen (O¹⁸) as a tracer in the study of photosynthesis. Journal of the American Chemical Society, 63(3), 877-879. doi:10.1021/ja01848a512
Sabatier, P. (1913). La catalyse en chimie organique. Paris: Béranger. 2013 reissue: doi:10.14375/np.9782369430186
Schmidt-Rohr, K. (2015). Why combustions are always exothermic, yielding about 418 kJ per mole of O₂. Journal of Chemical Education, 92(12), 2094-2099. doi:10.1021/acs.jchemed.5b00333
Soai, K., Shibata, T., Morioka, H., & Choji, K. (1995). Asymmetric autocatalysis and amplification of enantiomeric excess of a chiral molecule. Nature, 378(6559), 767-768. doi:10.1038/378767a0
Vlatakis, G., Andersson, L. I., Müller, R., & Mosbach, K. (1993). Drug assay using antibody mimics made by molecular imprinting. Nature, 361(6413), 645-647. doi:10.1038/361645a0
Wulff, G., & Sarhan, A. (1972). Use of polymers with enzyme-analogous structures for the resolution of racemates. Angewandte Chemie International Edition in English, 11(4), 341-344. doi:10.1002/anie.197203341
Wuts, P. G. M. (2014). Greene’s Protective Groups in Organic Synthesis (5th ed.). Hoboken, NJ: Wiley. doi:10.1002/9781118905074
Young, I. S., & Baran, P. S. (2009). Protecting-group-free synthesis as an opportunity for invention. Nature Chemistry, 1(3), 193-205. doi:10.1038/nchem.216