tower / commit
docs(canon): the far end is cold — ice at the far cap, frosted panes, Tower sets the hull's heat loss (D-090)
README.md | 11 ++++++ content/world.json | 2 +- decisions.md | 56 +++++++++++++++++++++++++++++ design.md | 103 ++++++++++++++++++++++++++++++++++++++++++++++++++--- 4 files changed, 166 insertions(+), 6 deletions(-) diff --git a/README.md b/README.md index 279cafd..eaa8c5f 100644 --- a/README.md +++ b/README.md @@ -409,6 +409,17 @@ triangles, 8.3 km on a side, six meeting at the axis. That is the pitch of the c caps once had, so the frame is still the only object in the world with a known size and the only rule anyone has for judging distance, read against sky. +**The far end of the world is cold.** The far cap's glass is single, and glass does not let +heat out as light: it soaks it up and radiates it to space from its outer face, 1–2 TW over +the whole cap. So the window is a cold wall, with a cold wind running down it onto the +Deepward Sea, and Tower keeps that end dim and lets it freeze: open water at freezing, then +pack ice, then fast ice frozen to the foot of the cap, dusk by day and dark by night. The +glass frosts too, and Tower clears it one pane per turn of the world, in an order reshuffled +every 35.1-hour loop, so close to the window is white with a scatter of clear, starry +triangles. None of this is drawn yet. Tower can do this because it controls how much heat +the hull loses where, up to about 5 TW (design.md §1.9.4, §1.9.6; D-090). The sun cap is +double-glazed and does none of this: the Sunward Sea is a temperate one. + **Tower has a sun, and it crosses the world once a day.** The mirrorlets that fly in the beam gather into one shoal and throw the beam's light out sideways there, which makes a single blazing sun at one point on the beam. It lights at the **sun cap** at sunrise, moves diff --git a/content/world.json b/content/world.json index bf3d1a4..3ac16ee 100644 --- a/content/world.json +++ b/content/world.json @@ -35,7 +35,7 @@ "id": "deepward-sea", "name": "The Deepward Sea", "blurb": "", - "notes": "The same at the far cap, and the larger of the two. A 314 km shoreline with a 50 km cliff behind it, and the only windows in the world at its foot (§1.4).", + "notes": "The same at the far cap, and the larger of the two. A 314 km shoreline with a 50 km cliff behind it, and the only windows in the world at its foot (§1.4). The window is a cold wall, so this is a polar sea: ice-cold throughout, open to z 512 km, pack ice to 525, and dim fast ice frozen to the cap beyond (§1.9.6, D-090). Not drawn yet.", "public": true, "seed": 1346489887, "kind": "sea", diff --git a/decisions.md b/decisions.md index d50ebc3..ec19cc2 100644 --- a/decisions.md +++ b/decisions.md @@ -2997,3 +2997,59 @@ of their own; Pisa's day lengths, daylight saving and clock have tests of their moved; at the new hour the director looked up at the sun, which put the chase camera below the ship, and the sea pushed it back up beside the ship, looking past it. A ship's chase camera now looks no more than 20° up (`maxPitch` 0.35 in `shipLeg`). + +## D-090 — The far end is cold: ice at the far cap, a frosted window, and Tower sets the hull's heat loss + +*Amends §1.9.4, which said nothing breaks Tower's thermal uniformity.* + +**Worked out with the author**, 2026-09-28, starting from a question: if Tower sent no light +to the sea by the far cap, would it freeze? Canon only; nothing drawn yet. + +**What the question found.** Two things canon had missed. + +- **The far cap is a radiator.** D-045 glazed the whole cap, and glass is opaque to thermal + infrared, so the window absorbs the world's heat and its outer face radiates it to space: + 80–250 W/m² for a pane 0.1–1 m thick, **0.65–1.9 TW** over the cap. That is a cold wall the + size of the cap, and it contradicted §1.9.4's "nothing breaks the thermal uniformity". Air + cooled against it slides down the cap and goes sunward over the Deepward Sea as a steady + cold wind. +- **The hull cannot lose heat by itself.** 1 km of rock conducting 320 W/m² would need about + 100,000 K across it. So the heat reaches the skin because Tower sends it there. + +**Decided by the author:** + +1. **Tower controls the hull's heat loss, region by region, up to about 5 TW** — a tenth of + the beam. "Not infinite, but some control." Light makes the weather; heat rejection is how + Tower keeps the books. +2. **The far end is kept dim and freezes in bands**, sunward to cap: open water z 496–512 km, + pack ice 512–525, fast ice frozen to the cap 525–540, then the window. +3. **The rod stays as D-079 has it**, running past the sun to the cap. So the fast ice gets + dusk by day, tens of W/m², not darkness — "no big deal if we don't have complete + darkness". Stars by day, which a truly dark end would have given, are given up with it. +4. **The sun still goes to the cap** (D-074), so it goes out over the ice each evening. +5. **The far cap is single-glazed and frosts. Tower clears it one pane per turn of the + world**, 7 min 29 s, in a random order that is reshuffled every loop but always the same + for a given loop. 282 panes (216 whole, 66 cut by the rim) make a loop of 35.1 hours. + +**Consequences worked out, now in §1.9.6:** + +- **The whole Deepward Sea is at about freezing**, not only the ice. §1.9.1 means there is no + Coriolis to hold cold water in place; a 1 K difference drives an exchange of ~0.45 m/s, + which mixes the 44 km sea to within about a kelvin. No Tower sea can be frozen in one corner. +- **The air pays the window, not the sea.** Paid by the sea, the open water would need + 140–400 W/m², daylight. So the weather is one overturning cell — warm air deepward aloft, + the window wind sunward below — and the strength of that cell sets the ice edge. +- **The hull is turned down under the sea**, or the sea would freeze from its bed up. The far + end takes about 2 TW of the 5. +- **The fast ice holds**: ~1,500 N per metre of wind against ~3 MN of ice, and Tower has no + tides. Storms on the weather plan (D-067) are what could break it out. +- **The Deepward Sea's ninety ships** keep the 16 km of open water. + +**Numbers that are rough:** the window wind (5–15 m/s) and the frost rate (millimetres a day, +to a factor of ten). The frost rate decides how many panes are clear at once; one in ten is a +guess. + +**The sun cap is double-glazed** (author, 2026-09-29). Single glazing there would have done +all the same things — radiated, frosted, and sent a cold wind onto the Sunward Sea. Double, its +inner pane stays near the air's temperature, so the Sunward Sea stays temperate and the far end +is the world's only cold place. diff --git a/design.md b/design.md index cce3a4d..88980b9 100644 --- a/design.md +++ b/design.md @@ -356,6 +356,16 @@ The only views out are at the **end caps**, and they are peculiar: haze, so from anywhere but the deepward end the airlight in front of it swamps whatever is behind, and the cap reads as a disc of sky. The stars are there at noon and unseeable, which is a fact about eyes and not about the glass. +- **The far cap is single-glazed, and it frosts** (D-090). The glass is the coldest + surface in the world and collects frost on its inner face, so Tower clears it one pane + at a time, one pane per turn of the world in an order reshuffled every 35.1-hour loop. + Close to, the window is a white lattice with a scatter of clear, black, starry + triangles, and which ones are clear keeps changing. §1.9.6 has the numbers, and the + cold wind and ice the window makes at its foot. +- **The sun cap is double-glazed** (author, 2026-09-29; D-090). Its inner pane stays + near the air's temperature, so it neither frosts nor chills the world: the Sunward Sea is + a temperate sea and the Deepward Sea the only cold one. The two caps are glazed + differently on purpose. - **The beam does not go through it.** §1.3.3 puts the surviving quarter of the beam on a 3.2 km bullseye at the centre of the cap, and that bullseye is a mirror rather than glass: it returns the residual up the column for a second pass. The @@ -548,15 +558,25 @@ Two corollaries: #### 1.9.4 There is no passive climate at all **Tower has no latitude** — every point is equidistant from the light — and with the -hull sealed it has no windows either. Nothing breaks the thermal uniformity. A -uniform hull radiates at 274 K everywhere, so left alone the world settles into a -flat calm: no gradient, no wind, no evaporation, no rain, no rivers. +hull sealed it has no windows in its walls either. A uniform hull radiates at 274 K +everywhere, so left alone the world settles into a flat calm: no gradient, no wind, no +evaporation, no rain, no rivers. **The one exception is the far cap**, whose window is +a cold wall the size of the cap (§1.9.6, D-090); it makes a gradient at the deepward +end whatever Tower does. **So every weather system in Tower is deliberate.** Tower makes climate the only way left to it — by aiming light. It warms where it wants convection and shades where it -wants condensation; the hull's uniform loss is the sink. Every cloud, every +wants condensation; the hull's loss is the sink. Every cloud, every rainfall, every jet stream is something Tower is doing, continuously, on purpose. +**Tower also sets the sink** (D-090). The loss through the hull cannot be passive: +1 km of rock conducting the mean 320 W/m² would need a difference of some 100,000 K +across it, so heat reaches the outer skin because Tower sends it there. It follows +that Tower can send less of it from one place and more from another. **It can move +about 5 TW** — a tenth of the beam — between regions this way: enough to hold the far +end cold and a few projects besides, not enough to run the climate on. Light is still +how Tower makes weather; heat rejection is how it keeps the books. + This is D-009 arriving at its conclusion. The mirrorlet swarm was already Tower's body language; now it is also its lungs and its weather. There is no autonomic layer underneath. **If Tower's attention ever lapses, the rain stops.** @@ -567,6 +587,7 @@ Costs, for scale against a 54.3 TW budget: |---|---|---| | Earth-like rainfall, 1,000 mm/yr | **12.2 TW** | **22.4 %** — Earth spends the same fraction | | Recirculating all runoff (1,792 m³/s) against 500 m | 8.8 GW | 0.016 % | +| The far cap window's loss to space (§1.9.6) | 0.65–1.9 TW | 1–4 % | #### 1.9.5 Rivers are a closed, pumped circulation @@ -598,6 +619,71 @@ Two consequences of the sealed hull: Lifting is also slightly cheaper than on Earth, since gravity falls off with height: 1 % cheaper at 1 km, 5 % at 5 km, 25 % at 25 km. +#### 1.9.6 The far end is cold, and Tower keeps it so + +*Worked out with the author, 2026-09-28; D-090.* + +**The window is a radiator.** Glass is opaque to thermal infrared, so the far cap's +single glazing does not let the world's heat out as light — it absorbs it, and its outer +face radiates it to space at 3 K. A pane 0.1–1 m thick loses **80–250 W/m²**, and over +the cap's 7,854 km² that is **0.65–1.9 TW**, 1–4 % of the beam. Air cooled against the +glass is denser and slides down the cap, which on a cap means radially outward to the +rim, and it spreads sunward over the Deepward Sea as a **cold wind off the window**, +roughly 5–15 m/s. Nothing Tower does makes this; it is what a cold wall does. The ice at +the foot of the cap is where the physics was going anyway. + +**Tower keeps that end of the world dim, and lets it freeze in bands.** Sunward to cap: + +| z (km) | Band | By day | By night | +|---|---|---|---| +| 496–512 | **open water** | grey sea at about freezing, with sea smoke where the cold wind crosses it | dark | +| 512–525 | **pack ice** | floes made at the fast ice's edge, carried sunward by the wind, melting where they meet open water | dark | +| 525–540 | **fast ice** | dusk — the rod's glow and nothing aimed | night; the sun goes out overhead at dusk | +| 540 | **the window** | white frost with a scatter of clear panes | stars through the clear panes | + +- **The dark is dusk by day, not darkness.** The rod's own glow cannot be aimed away + (§1.3.2) and runs on past the sun to the cap (D-079), so the fast ice gets tens of W/m² + by day — a permanent overcast dusk — and real night only by night. The sun still goes + all the way to the cap (§1.3.4), so once a day it goes out directly over the ice, and + the moon sets out from the same place. +- **The fast ice holds.** The window wind pushes on it with about 1,500 N per metre of + cliff; 3 m of ice frozen to the cap holds some 3 MN. **Tower has no tides** — its moon + is light (§1.3.5) — so the thing that breaks Earth's fast ice out is absent. Storm swell + is the threat to it, and the Deepward Sea is on the weather plan. +- **The whole sea is ice-cold, not only the ice.** With no Coriolis in the plane of the + floor (§1.9.1), a 1 K difference in the water drives an exchange of about 0.45 m/s, + cold out along the bottom and warm in over the top. That mixes the sea's 44 km to within + about a kelvin, so the open water sits at freezing. It is a polar sea, grey and foggy, + and its coast has fog where the land's air comes down onto it. **No sea in Tower can + be frozen in one corner** — only whole or not at all. +- **The window's bill is paid by the air.** If the sea paid the 0.65–1.9 TW, the open + water would need daylight on it, 140–400 W/m². Instead the weather runs one overturning + cell: warm air from the lit lands comes deepward aloft to the glass, cools, sinks, and + goes back sunward along the surface as the window wind. The sea pays only what that + wind takes from the open water, which is also how fast ice is made — so **Tower sets + the ice edge by how hard it runs the cell**. +- **Tower turns the hull down under the sea** (§1.9.4). If the floor went on drawing its + share, the sea would be cooled from beneath and freeze on its bed first, and no light + would keep any of it open. The far end takes about 2 TW of Tower's 5 TW of heat control. + +**The window frosts, and Tower clears it one pane at a time.** Cold glass collects frost +on its inner face — very roughly millimetres a day, enough to whiten a pane in days — so +left alone the far cap would go white and the stars would go. Tower heats one pane at a +time from its frame: melting a pane's frost is about 6 × 10¹² J, a few minutes at tens of +GW, and the meltwater runs down the cap onto the ice. + +- **One pane per turn of the world**, every 7 min 29 s. The window has **282 panes** + (216 whole triangles and 66 cut by the rim, D-078), so a loop takes **35.1 hours** — + not a whole number of days, so the clearing drifts against day and night. +- **Shuffled, and reshuffled every loop.** A fixed order could be learned by anyone who + watched long enough; a fresh one each loop cannot. Each loop's order is drawn from the + world's seed and the loop's number, so which panes are clear at any moment can be + worked out without the history, the same in the app and in the book. +- A pane's gap between clearings runs from almost nothing to almost two loops, so the + frost on it ranges from clean glass to thick white. The window reads as a white lattice + with a scatter of black, starry triangles, perhaps one in ten; how long a pane stays + clear rests on the frost rate, which is rough to a factor of ten. + ### 1.10 Slat orientation — RESOLVED: none Axial strips versus rings was weighed at length (D-016) and answered by removing @@ -623,7 +709,7 @@ along the axis**, which is the natural grain of an engineered climate (§1.9.4): | 214–430 km | **Greatwood** | forest belt: about three billion trees, with meadows Tower left open in it (D-071) | | 248–402 km | **The Deep** | 154 × 32 km sea, long down the axis and narrow around | | 270 km | **The Capital / The Spindle** | axial midpoint; 20 km across, its spinward edge on The Deep's shore (D-070) | -| 496–540 km | **The Deepward Sea** | ring ocean at the foot of the far cap | +| 496–540 km | **The Deepward Sea** | ring ocean at the foot of the far cap: open water to 512 km, pack ice to 525, dim fast ice to the cap (§1.9.6, D-090) | | 110–480 km | **The Axial Line** | railway down the length of the world, through The Narrows (D-086) | | 140 km | **The Uplands Ring** | railway round the world across the Uplands (D-086) | @@ -714,6 +800,10 @@ there; water runs down to the rim and pools. **Both ring oceans exist whether an planned them or not**, each with a 314 km shoreline and a 50 km cliff standing behind it. The only windows in the world are at their feet (§1.4). +They are not the same sea. The far cap's window is a cold wall, so **the Deepward Sea is +a polar one** — ice-cold throughout, and frozen in bands toward the cap (§1.9.6). The sun +cap is double-glazed and does none of this, so the Sunward Sea stays temperate. + #### Skiing, because it is a different sport here Level motion feels no Coriolis (§1.9.1) but a descending skier has radial velocity, @@ -1268,3 +1358,6 @@ Things decided to be worth coming back to, not scheduled. - **The moon's light** (D-088). It is drawn as fed by Tower lifting the banked beam, so the rod is the same either side of it; the sun instead takes its share from the rod and leaves it dimmer past it (D-079). Canon could have the moon do the same, or settle why it does not. +- **Drawing the far end** (D-090). The Deepward Sea's ice bands and the far cap's frost + and pane clearing are canon but not drawn. The world file has no kind for sea ice yet, + and the panes need the seeded shuffle of §1.9.6.