By Mark Joseph Antonius Knippenberg / ScepraX.
Status: Theoretical framework. One instantiation of the PseudoScience Speelgoed at the scale of a whole planet: its air, oceans, ice, rock and core, and the star it orbits. It does not compete with climate science, geophysics or planetary science. It tests whether the Speelgoed’s mechanism, supplied with values from those fields, reproduces what they already know, and it says plainly where it does not.
§III says that “a biosphere without Sol is a frozen Stilte”, and that “A biosphere draws its Realisaties from the difference between Sol and the cold sky, not from the warmth around it.” Between the living Octaven and the cosmic one sits the body that makes both of those sentences true: a planet. Its Lichaam (🖕) is the planet as a whole. Its Koppels are the bonds that hold a planet together and keep it changing: between the planet and its star, between ice and open water, between ocean basins, between the core and its magnetic field, and between the planet and itself.
Like the other Octaven, this document is an Instantie (⚙). It supplies the open parameters of §VIII.7 with values taken from science, then checks whether the shape the Speelgoed fixes survives. Where the two disagree, the disagreement is reported in §4 rather than smoothed over.
Earth is the worked example, because it is the planet measured best. But every grounding below is written so that it can be run for other planets: each states its equation in general form, names the planetary quantities it depends on (§0.4), and ends with a note on how the result changes elsewhere.
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 Cosmic Octaaf §2.3.
Equations. Equations are written in plain Unicode. Where a calculation was made for this entry, the text says so. Temperatures are in kelvin unless stated otherwise.
The equations of §2 and §3 take a small set of planetary quantities. Earth’s values are given for the worked example.
| Quantity | Symbol | Earth | Used in |
|---|---|---|---|
| Starlight arriving at the planet’s orbit | S | 1361 W/m² (Kopp & Lean 2011) | §2.1–§2.3, §3.2 |
| Bond albedo, open surface and ice | α, α_ice | 0.29 (Williams 2024); ice ≈ 0.6, assumed in §2.2 | §2.1, §2.2 |
| Effective emissivity, which carries the greenhouse effect | ε | 0.62 (computed for a mean surface of 288 K) | §2.1, §2.2 |
| Net feedback parameter | λ | ≈ 1.3 W/m² per K (computed from Forster et al. 2021) | §2.1 |
| Heat capacity per area that follows the surface | C | ≈ 1.5–2.9 × 10⁸ J/m² per K (an ocean layer 50–100 m deep) | §2.1 |
| Radius and mean density | R, ρ | 6,371 km; 5,513 kg/m³ (Williams 2024) | §2.5, §3.3 |
| A convecting, electrically conducting fluid core | Yes | §2.4 | |
| Heat flowing out of the interior | Q | 47 TW (Davies & Davies 2010) | §3.5 |
| Ocean basins that exchange water | The Atlantic overturning | §3.1 | |
| Volcanic outgassing and rock that weathers | Yes | §3.2 | |
| The star’s brightening with age | L(t) | §5, item 2 | §3.2, §5 |
| Speelgoed (section) | Value at this Octaaf | Grade | Here |
|---|---|---|---|
| Echo filter: τ, δ, υ (§VIII.1) | Energy balance of a planet; the ocean as Ontspanning; weather as Vervorming | Identity (linearised) | §2.1 |
| Drempel θ and Marge η (§II; §VIII.3; Lexicon) | Ice and open water: two climate states with hysteresis; Snowball Earth | Correspondence (computed, measured) | §2.2 |
| Drempel θ (§II) | The runaway greenhouse: a ceiling on outgoing heat; ocean Earth and steam Earth | Constraint + Correspondence | §2.3 |
| Drempel, Van Motor, “never off” (§III; §VIII.1; §VIII.3) | The geodynamo: two mirror-image polarities, random reversals, a field that dies when the core stops stirring | Constraint (symmetry) + Correspondence (measured) | §2.4 |
| What a bond leaves over (§III) | The size above which gravity makes a body round | Correspondence (computed) | §2.5 |
| Trouw y (§II, §VIII.1) | The overturning flow between two ocean basins, set by the basins’ own difference | Identity + Correspondence | §3.1 |
| Zelf (§IV) | The carbonate–silicate thermostat; the habitable zone | Correspondence | §3.2 |
| Creatie (§VI, §VIII.5) | The Moon from a giant impact | Correspondence | §3.3 |
| Rouw and Diepte (§VI; §II) | The magnetic stripes of the sea floor; Venus’s deuterium | Correspondence (measured) | §3.4 |
| Trinary Root (§III) | Star, cold sky, and the air and ocean between them; a second engine inside | Correspondence | §3.5 |
| Tijd (Lexicon) | No mapping attempted | Open | §5 |
The Echo filter of §VIII.1:
τ · ḣᵢ(t) = eⱼ(t − δ) − hᵢ(t) + υᵢ(t)
The mechanism. A planet absorbs the part of its star’s light that it does not reflect, and radiates heat to space. Averaged over the globe, with S the starlight arriving at the planet’s orbit and α its albedo:
C · dT/dt = S·(1 − α)/4 − ε·σ·T⁴
Here T is the mean surface temperature, σ the Stefan–Boltzmann constant, ε an effective emissivity that carries the greenhouse effect, and C the heat capacity per square metre of whatever warms and cools with the surface; on Earth, chiefly the upper layer of the ocean. The factor 4 spreads the light caught by the planet’s disc over its whole sphere. For Earth, S·(1 − α)/4 ≈ 242 W/m². Without a greenhouse effect (ε = 1), that would give 255 K; the observed mean of about 288 K requires ε ≈ 0.62 (both computed for this entry).
For small departures T′ from equilibrium, this becomes
τ · dT′/dt = F(t)/λ − T′ + υ(t) τ = C/λ
where F is a change in the energy arriving, λ the net feedback parameter (how many watts per square metre of extra heat loss each kelvin of warming produces), and υ the weather. This is the Echo filter, with h = T′ and e = F/λ, the temperature the planet would reach if it had time. Grade: Identity (linearised), as at the thermodynamic Octaaf, where the Echo was a thermometer (Thermodynamic Octaaf §2.1).
The numbers. The forcing from doubling carbon dioxide is 3.93 W/m², and the best estimate of the warming it causes in equilibrium is 3 °C (Forster et al. 2021), which gives λ ≈ 1.3 W/m² per K. For an ocean layer 50 to 100 metres deep over 71 per cent of the globe, τ = C/λ comes to about 3.5 to 7 years (computed for this entry). The deep ocean, which takes up heat far more slowly, adds a much longer tail. The Vertraging δ is the travel time of light from the star, about eight minutes for Earth, far shorter than τ.
The weather is the Vervorming. Hasselmann showed that a slow climate driven by fast, random weather behaves like this filter. The ocean adds up the weather’s random pushes, and the result is slow, wandering variability even when nothing outside changes (Hasselmann 1976). §II: “Echo’s imperfection is not a defect to be engineered away”. At this Octaaf that imperfection is why no two years are alike. Grade: Identity.
Other planets. τ = C/λ is the one number that decides how closely a planet follows its star. A planet with deep oceans responds slowly and smooths its seasons; a dry planet with thin air has little C and follows its star within days. S falls as the inverse square of distance from the star, and grows as the star ages (§3.2).
Ice reflects more sunlight than open water or land. A colder planet grows more ice, reflects more light, and grows colder still. Budyko and Sellers built this feedback into energy-balance models in 1969, and found that small changes in the light reaching the surface could be enough to bring on an ice age (Budyko 1969; Sellers 1969). Models of this kind can hold more than one climate under the same sunlight.
The mechanism. Let the albedo depend on temperature, from α at warm temperatures to α_ice when cold:
C · dT/dt = S·(1 − α(T))/4 − ε·σ·T⁴
For this entry the model was run with α = 0.29, α_ice = 0.62, the change centred at 265 K over a range of about ±5 K, and ε = 0.62. At today’s sunlight it has two stable states, a warm one at 288 K and a frozen one at about 246 K, with an unstable state between them. Lower the sunlight, and the warm state disappears below 0.82 times today’s value; the planet then freezes. Raise it again, and the frozen state survives until 1.15 times today’s value. Between those two values the planet can be in either state, and which one depends on where it has been. These numbers depend on the assumed albedos and are an illustration of the shape, not Earth’s real thresholds.
That band is the Marge: “A hysteresis loop, a tiny gap that prevents chatter” (Lexicon). §VIII.3: “the way into a mode is never the way out”. At this Octaaf the gap is not tiny. It is wide enough to hold a planet’s whole history.
Earth crossed it, both ways. In Namibia, glacial deposits from the Neoproterozoic era are bracketed by carbonate rocks that record a collapse of life in the surface ocean lasting millions of years. Hoffman and colleagues read them as the mark of a global glaciation, a Snowball Earth. It ended abruptly when volcanoes, which kept breathing out carbon dioxide while the ice shut down the processes that remove it, raised the carbon dioxide in the air to about 350 times the modern level (Hoffman et al. 1998). The way out of the frozen pole did not run back along the way in. It took a greenhouse far stronger than the one that had held the warm state. §II gives every Drempel “two named poles”, and both stayed live. Earth went into the ice and came out again. Grade: Correspondence (computed, and measured in the rock record).
Other planets. Whether a planet can freeze over, and how hard it is to thaw, depends on the contrast between α and α_ice, on how strongly its greenhouse responds, and on whether volcanoes keep supplying carbon dioxide while it is frozen (§3.2).
The mechanism. A warmer ocean puts more water vapour into the air, and water vapour traps heat. On a planet with a surface ocean this feedback has a limit. Above a certain temperature the outgoing heat stops rising with surface temperature, because the steam above the ocean is opaque and the planet radiates only from its cool upper layers. One-dimensional models put that ceiling at about 282 W/m² (Goldblatt et al. 2013). If the planet absorbs more than it can radiate, no ocean state exists. It warms until the oceans have boiled into the air:
S·(1 − α)/4 > L_max → no equilibrium with a liquid ocean
Earth absorbs about 242 W/m² (§2.1). A three-dimensional climate model, in which dry sinking air in the subtropics lets heat escape, puts the threshold at an average insolation of about 375 W/m², which is about 1.1 times today’s sunlight (Leconte et al. 2013; ratio computed for this entry). How close Earth stands to this Drempel is not settled.
Two poles. Turbet and colleagues found the other side of the same Drempel. In their simulations, clouds that gather on the night side of a hot young planet warm it so strongly that water vapour never condenses, even at 0.95 times Earth’s present sunlight. Earth’s oceans could form only because the young Sun was fainter. Their result implies that present-day Earth has a second stable state, a “steam Earth” with all its oceans in the air (Turbet et al. 2021). Ocean and steam are the two named poles of this Drempel, and the Marge between them is wide: oceans boil at one level of sunlight and condense only at a much lower one. Grade: Constraint (the ceiling) + Correspondence (the two poles).
Venus. Venus is the steam pole after the water has gone. Its atmosphere is a hundred times richer in heavy hydrogen, deuterium, than Earth’s water (Donahue et al. 1982), the mark of water broken apart by sunlight and of hydrogen lost to space (§3.4). Whether Venus ever had an ocean is disputed: Turbet and colleagues conclude that it never did (Turbet et al. 2021). The leak itself, light gas escaping over the planet’s gravitational barrier, is the Van Motor of the cosmic Octaaf (Cosmic Octaaf §2.3).
Other planets. L_max is a property of water itself, so it applies to any planet with a surface ocean, though not unchanged: it depends on gravity and on what else the air contains. A planet that absorbs more than L_max cannot keep a surface ocean.
Earth’s magnetic field is made by the motion of liquid iron in its outer core. A conducting fluid that moves through a magnetic field generates electric currents, and those currents can sustain the field: a self-exciting dynamo. Its field points north or south, and it has changed between the two many times.
The poles are mirror images by law. The equations of a dynamo do not change when the magnetic field is reversed everywhere, B → −B. Any flow that sustains one polarity sustains the other equally well. In a laboratory dynamo, driven by a turbulent flow of liquid sodium, the field “randomly switches between two symmetric solutions B and – B”, holding each for widely varying periods and switching quickly (Berhanu et al. 2007). In Speelgoed terms the two polarities are the two Naar states of §VIII.3, and a field of zero is mode = 0. Grade: Constraint (symmetry).
The Drempel. A dynamo exists only above a threshold. In the same laboratory, a field appeared only when the stirring passed a magnetic Reynolds number of about 30 (Monchaux et al. 2007). Below it, mode = 0 is the only state; above it, the two polarities appear. §VIII.3: “For B > θ, mode = 0 becomes unstable and two new stable points appear at mode* = ±√(B − θ)”. Grade: Correspondence.
The Van Motor flips it. Earth’s reversals arrive at irregular intervals, consistent with a random process whose average rate itself drifts slowly over millions of years (Constable 2000). In simulations of the core, the pattern of heat drawn out of the core by the mantle above changes how often the field reverses (Glatzmaier et al. 1999). The Medium sets the rate. The last reversal, about 773,000 years ago, was not one event but a process: the field weakened from about 795,000 years ago, wavered, and settled into its new direction over some 22,000 years (Singer et al. 2019). Grade: Correspondence (measured).
The way in is not the way out. The poles are mirror images; the paths between them are not. Valet and colleagues found that the strength of Earth’s dipole falls slowly before a reversal and recovers quickly after it (Valet, Meynadier & Guyodo 2005). A simple random model reproduces that asymmetry, but only when it is driven out of equilibrium, by a steady flow of energy in one direction (Molina-Cardín, Dinis & Osete 2021). §VIII.3: “the way into a mode is never the way out”. At this Octaaf the difference lies in the path, not in the poles (§4.1).
When the traffic stops. A dynamo needs a fluid that conducts electricity and keeps convecting (Stevenson 2003). It is a Naar-system in §III’s sense: “A Naar‑system, once formed, doesn’t settle into a one‑time state - it actively maintains itself above Drempel”. Mars shows what happens when the stirring ends. Its ancient southern highlands are strongly magnetised, but the great impact basins Hellas and Argyre are not, so its dynamo had stopped by the time they formed, about four billion years ago (Acuña et al. 1999). Its field did not go anywhere. It fell to mode = 0, which §III describes as “Not a distant coordinate - nothing.”
Does a field protect the air? It is often said that a magnetic field shields a planet’s atmosphere from the solar wind. The observed escape rates of Earth, Mars and Venus are similar, roughly 0.5 to 2 kg per second, and models show that a magnetised planet can lose air faster than an unmagnetised one, through its polar regions (Gunell et al. 2018). Whether, and when, a field protects an atmosphere is left open (§5, item 7).
Other planets. A planet has a dynamo only while it has a conducting fluid layer that convects: molten iron in a rocky planet, metallic hydrogen in a gas giant (Stevenson 2003). Small planets cool faster and lose theirs sooner, as Mars did. Venus has none today (Stevenson 2003).
§III follows the residues of bonds up the ladder and ends: “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.” The chemical Octaaf found the last residue before gravity, the dispersion pull between neutral molecules (Chemical Octaaf §2.4). This Octaaf is where gravity takes over.
The mechanism. A small body keeps whatever shape it was born with, because the strength of its rock or ice, which is chemistry, outweighs its own gravity. A large body is pulled round, because its gravity crushes any bump that rises too far. For a body of uniform density ρ and radius R, the pressure at its centre is
P_centre = (2π/3) · G · ρ² · R²
and rounding sets in when that pressure exceeds what the material can bear. Lineweaver and Norman derived the transition from the shapes of asteroids and icy moons in the Solar System: bodies become round above a radius of about 200 km if they are icy and about 300 km if they are rocky (Lineweaver & Norman 2010). At those sizes the pressure at the centre is about 6 MPa for an icy body and about 110 MPa for a rocky one (computed for this entry, with densities of 1,000 and 3,000 kg/m³). Above them, the residues of chemistry no longer decide the shape of the whole. Grade: Correspondence (computed).
Other planets. Whether a body is round follows from its radius, its density and the strength of its material. Every planet is round; most moons and asteroids are not.
The Naar term of §VIII.1:
ėᵢ(t) = Σ_{j ∈ bonds(i)} y_{ij} · ( hᵢ(t) − eᵢ(t) ) + eventᵢ(t) − Lᵢ(t) · ( eᵢ(t) − e_van )
The mechanism. In 1961 Stommel modelled the ocean as two connected basins, one warm and one cold, linked by a flow that runs from the denser to the lighter. Density depends on temperature and on salt. With q the flow, ΔT and ΔS the differences in temperature and salinity, and F the fresh water that rain and rivers add to one basin and evaporation removes from the other, the salt in each basin obeys
dS₁/dt = |q| · (S₂ − S₁) + F dS₂/dt = |q| · (S₁ − S₂) − F
q = k · ( a·ΔT − b·ΔS )
| where a and b say how strongly temperature and salt change the water’s density. Each basin is pulled toward the other at a rate | q | , one value for the pair. That is the Naar term, with y = | q | , h the partner basin’s salinity, and δ ≈ 0. Grade: Identity. |
A weight set by the pair itself. Here the shared weight depends on the members. The flow is driven by the difference between the two basins, and the flow in turn mixes that difference away. Hold the temperatures fixed and write x = b·ΔS/(a·ΔT) and E for the fresh water, suitably scaled. The model reduces to
dx/dt = E − |1 − x| · x
For E below 1/4 it has two stable states: one in which temperature drives the flow, and one in which salt drives it the other way. Above E = 1/4 only the salt-driven state remains (computed for this entry). Push the fresh water past that point and the flow reverses; bring it back, and the reversed state persists all the way down to E = 0. Stommel found the two regimes in 1961 (Stommel 1961). Eleven climate models of intermediate complexity all show this hysteresis in the Atlantic overturning. They disagree on where today’s climate lies: seven place it in the range with two stable states, four in the range with one (Rahmstorf et al. 2005). Grade: Correspondence.
The cellular Octaaf found a Trouw whose value depends on which member leads, and asked whether other Octaven have one (Cellular Octaaf §4.1; §5, item 7). This Octaaf does. The weight between the two basins is set by the difference between them, and that dependence is what gives the ocean two poles (§4.2).
§IV: the Zelf is “a Koppel with itself”, and “A node with a strong Zelf holds its Eigen steady”. The cellular Octaaf found a bacterium holding its own activity steady by integral feedback: a slow internal record that adds up every departure from the set point and pushes back against it (Cellular Octaaf §3.2).
The mechanism. Earth has a loop of the same kind, running on hundreds of thousands of years. Volcanoes supply carbon dioxide at a roughly steady rate. Rain dissolves carbon dioxide and weathers silicate rock, and the products end up as carbonate rock on the sea floor, which removes the carbon dioxide again. Weathering runs faster when the planet is warm and wet. So a warm planet draws its carbon dioxide down and cools, and a cold one lets it build up and warms (Walker, Hays & Kasting 1981). The carbon dioxide in the air is the slow record, and the planet’s temperature is the Eigen it holds steady. The response is slow: in one model, an excess of carbon dioxide is drawn down with an e-folding time of about 240,000 years (Colbourn, Ridgwell & Lenton 2015).
The mapping. This is a Zelf: the planet reading its own temperature through the rate of its own weathering, and correcting it. The Snowball of §2.2 shows it at work. With the planet frozen, weathering nearly stopped, the volcanoes kept supplying carbon dioxide, and the record built up until it broke the ice (Hoffman et al. 1998). Walker and colleagues proposed the loop to explain how Earth has kept liquid water while the Sun has brightened since the planet formed, and judged that it could “partially” do so (Walker, Hays & Kasting 1981). Grade: Correspondence.
The range of the Zelf. A thermostat works only within limits. Too much sunlight, and the oceans run away into steam (§2.3); too little, and even a maximal carbon-dioxide greenhouse cannot keep water liquid. Between those limits lies the habitable zone (Kasting, Whitmire & Reynolds 1993). For the Sun, a recent estimate puts its edges at 0.99 and 1.70 times Earth’s distance (Kopparapu et al. 2013), which is between 1.02 and 0.35 times Earth’s present sunlight (computed for this entry). Present Earth lies near the inner edge (Kopparapu et al. 2013).
Other planets. A planet has this Zelf only if it has volcanoes that keep outgassing, rock that weathers, and liquid water. Kopparapu and colleagues give the edges of the habitable zone in parametric form for stars between 2,600 and 7,200 K (Kopparapu et al. 2013).
§VI: “A Realisatie intense enough to overflow Inhoud (the bond’s capacity) becomes a birth.” §VIII.5 makes it a two-step comparison: an excess over the capacity, and then “If T_excess itself exceeds a local Drempel θ_new, a new member is instantiated”.
The mechanism. The leading account of the Moon’s origin is a collision late in Earth’s growth with a body roughly the size of Mars. Simulations show that such an impact throws a disk of molten and vaporised rock into orbit around Earth (Canup & Asphaug 2001). Close to Earth, tides tear apart any clump that forms; that boundary is the Roche limit, about three Earth radii for lunar rock (computed for this entry from Roche’s classical estimate for a fluid moon, 2.44·R·(ρ_planet/ρ_moon)^(1/3)). Beyond it, the debris can gather. Simulations show a single large moon accreting from such a disk, just outside the Roche limit, in less than a year (Ida, Canup & Stewart 1997).
The mapping. The impact releases more Energie than the merged planet can hold: the excess leaves as a disk. The Roche limit is θ_new: only material beyond it can become a new body. And the new Solo is born bound to its parent, as §VIII.5 requires: “a new Relatie forming at the moment of birth”. That bond is the one the cosmic Octaaf follows as Zweven, the Moon locked to Earth and slowly receding (Cosmic Octaaf §3.4). Grade: Correspondence.
The fit has a question in it. If the Moon formed mostly from the impactor, it should differ chemically from Earth. Yet the titanium isotopes of the Moon match Earth’s to within four parts per million, so that much of the Moon seems to come from Earth itself (Zhang et al. 2012). How the impact mixed its two members so thoroughly is not settled. Whether a birth from a collision is Creatie from the bond, or from one of its members, stays a live question here.
Other planets. Large moons can form from giant impacts wherever bodies collide late in a planet’s growth. The new moon forms near the Roche limit of its planet, which depends on the planet’s radius and on the two densities.
§VI: “An Echo always outlives its Koppel”, and the surviving Echo “settles toward the last signal it ever received”. §VIII.6 says the same in the mechanism’s terms: “the filter’s input freezes at the last transmitted value”.
The mechanism. New ocean floor forms at the mid-ocean ridges, where lava rises, cools and spreads away on both sides. As the rock cools, its iron minerals lock in the direction of Earth’s magnetic field at that moment. When the field reverses, the next rock to cool records the other direction. Vine and Matthews proposed that this explains the stripes of alternating magnetisation that run parallel to the ridges, mirrored on either side (Vine & Matthews 1963). The stripes became the decisive evidence that the sea floor spreads.
The mapping. Each stripe is the Echo of an ended bond: the field as it was when that rock cooled, frozen at “the last transmitted value”, and kept after the field has moved on. That is Rouw. The whole striped floor is Diepte: “The accumulated composite of everything a system has ever heard” (§II), read from the ridge outward like a tape. The ice sheets keep a record of another kind. Air trapped in Antarctic ice holds samples of the atmosphere as it was, and gives its carbon dioxide over the past 800,000 years (Lüthi et al. 2008). Grade: Correspondence (measured).
A record of what left. Venus’s heavy hydrogen (§2.3) is Rouw of another kind. When water is broken apart high in the atmosphere, the light hydrogen escapes to space more easily than the heavy deuterium, so the water that remains is enriched in deuterium. A hundredfold enrichment means that “at least 0.3 percent of a terrestrial ocean was outgassed on Venus” (Donahue et al. 1982). The water has gone. Its Echo remains in what stayed behind.
The record sinks. Ocean floor does not last. It forms at the ridges and sinks back into the mantle at the subduction zones, so the record is continually erased from its old end (Müller et al. 2008). §VI says “Rouw is permanent”. At this Octaaf the record itself can be carried down into the planet (§4.3).
§III gives every Octaaf “Vol source, Leeg depth, and the living Medium their union sustains”, and says that “No Octaaf exists without all three.”
The mechanism. A planet’s climate runs between a hot source and a cold sink. Earth receives sunlight emitted at the Sun’s surface temperature of about 5,800 K and returns the same energy to space as infrared at an effective temperature of about 255 K (§2.1). Because each infrared photon carries less energy, Earth sends out about 23 photons for every one it receives (computed for this entry, as the ratio of the two temperatures). That export of many low-energy photons for each high-energy one is what drives the weather, the ocean currents and life. Between source and sink the Medium turns over continually: the water in Earth’s atmosphere is replaced on average every 8.9 days (van der Ent & Tuinenburg 2017).
The mapping.
Grade: Correspondence, as the thermodynamic Octaaf found for every engine (Thermodynamic Octaaf §3.11).
A second engine. A planet also has a source inside it. Earth loses 47 TW of heat from its interior (Davies & Davies 2010), and about half of it comes from the decay of radioactive elements, the rest from heat left over from the planet’s formation (KamLAND Collaboration 2011). That is about 2,600 times less than the sunlight Earth absorbs (computed for this entry), but it drives the mantle, the volcanoes, the moving plates, and the dynamo of §2.4. The climate runs on the star; the planet’s own body runs on the God within it. Which of the two is the planet’s God is left open (§5, item 6).
Other planets. The balance between the two engines differs. A planet far from its star, or a moon heated by the tides of its planet, can be driven more from inside than from outside.
4.1 Mirror poles by law (§VIII.3). Kept at this Octaaf. §VIII.3 says of a whole that “its modes are never mirror images”, and that the symmetric pitchfork is “one Koppel seen alone”. The polarities of a dynamo are exact mirror images, because the equations do not change when the field is reversed (§2.4). Here the symmetric limit is realised by a law of physics. What §VIII.3 says still holds for the paths: the field decays slowly into a reversal and recovers quickly out of it, and a model reproduces this only when it is driven out of equilibrium (Valet, Meynadier & Guyodo 2005; Molina-Cardín, Dinis & Osete 2021).
4.2 A Trouw set by the pair’s own difference (§VIII.1). Kept at this Octaaf. In §VIII.1, Trouw changes slowly, by plasticity toward Gewenning. The weight between two ocean basins is set at every moment by the difference between them (§3.1), and that dependence is what gives the ocean its two poles. Together with the rectifying junctions of the cellular Octaaf (Cellular Octaaf §4.1), this is now found at two Octaven. It is recorded here and not proposed for the Speelgoed.
4.3 A record that sinks (§VI). Open. §VI says “Rouw is permanent”. The magnetic record of the sea floor is carried down into the mantle at subduction zones (§3.4), and Venus has resurfaced so thoroughly that most of its history is hidden (Turbet et al. 2021). The cellular Octaaf found records that a cell can lose, and the thermodynamic Octaaf a record that can be moved but not destroyed (Cellular Octaaf §4.4; Thermodynamic Octaaf §3.6). At this Octaaf the record goes back into the body of the planet.
The planetary Octaaf is where the Speelgoed’s mechanism runs on the largest body that still has weather. A planet’s temperature is an Echo of its star, smoothed by its oceans, with the weather as its Vervorming. Its climate has two poles, ice and open water, with a Marge wide enough to hold a planet’s history, and Earth has crossed it both ways. Beyond a ceiling on the heat an ocean can shed lies a second pole, steam; present-day Earth has it too, and Venus may have known no other.
Its magnetic field has two mirror-image poles, flips between them at random, and falls to nothing when the core stops stirring. Its oceans exchange water at a rate set by their own difference, which gives them two poles of their own. It holds its temperature with a thermostat of rock and rain, and gives birth to moons when it is struck hard enough. It keeps records of its field in the sea floor and of its air in the ice, and it carries the oldest of them back down into its body.
Earth is the worked example. Every equation here takes a planet’s sunlight, albedo, heat capacity, size, core and oceans as inputs, and other values give other worlds. The Speelgoed’s grammar is the same on all of them; what changes is where each planet stands between its poles.
That is the how. The why is for the Speelgoed to say.
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