Haute Lumière

Commerce · VII.10 · MMXXVI · daylight

La Bourse  /  Volume VII  /  Nº VII.10  /  Workbook — the student

WORKBOOK — THE STUDENT

Chapter VII.10 · The Cosmological Frame

For the person studying this alone, or in a seminar, with no organisation to change yet. This is the chapter where you stop taking numbers on trust — from this book or from anybody else — and the habit you build here is the one you will use for the rest of your working life.

---

WHY THIS WORKBOOK IS DIFFERENT

Every other workbook in this edition asks you to find something inside an organisation and cost it. This one asks you to do something narrower and, in the long run, more useful: verify a published claim from first principles, using constants anyone can look up, and then find the place where the claim stops being load-bearing.

That is the whole skill. A chapter about the cosmos is the ideal training ground for it, because there is no proprietary data, no confidentiality, no access problem and no excuse. Three constants, a flux, a reflectivity and a calculator reproduce the planetary energy budget exactly. If you can do that, you can check anything, and you will never again be in the position of believing a large number because it was in a serious-looking book.

You will also learn the harder half: knowing when a correct argument does not apply. This chapter's own honest negative is that nothing in it should change an allocation this century. Holding a true thing and a limit on its use at the same time is the distinguishing mark of a serious mind, and it is trainable.

---

PART ONE — DISCOVERY

Find the frame already working around you

Exercise 1.1 — The sky audit (60 minutes, one clear night and one clear morning)

Go outside on a clear night with nothing over your head, and again before dawn. Record, in a notebook:

• Air temperature, from any source.
• Whether there is dew or frost on a car roof, a bench, a bicycle saddle, or a patch of grass — and whether there is any on surfaces that sit under a tree, an eave, a balcony or a bridge.

You are looking for the boundary. Surfaces with an unobstructed view of the sky will be wet or frosted; surfaces a metre away with something above them will often be dry. That line on the ground is the atmospheric window, drawn in dew. It is the same mechanism that made ice in Iran and Bengal for centuries and the same mechanism the 2014 Raman paper industrialised, and you have now seen it with your own eyes rather than read about it.

Write one paragraph on what you saw, including the surfaces where you expected the effect and did not find it. The exceptions are the interesting part.

Exercise 1.2 — Four cases, four eras (90 minutes)

The chapter names four things already working: the Persian yakhchāl, the CERES-plus-Argo planetary account, the Montreal Protocol, and passive daytime radiative cooling. For each, write three lines:

1. What was the mechanism, physically?
2. What made it work — what condition had to be present?
3. What is the closest thing to it in your own field?

Then answer one question in writing: which of the four is most likely to be cited wrongly by someone arguing for something else? Say why. Learning to spot the case that will be misused is half of learning to use it.

---

PART TWO — THE ARITHMETIC

Do not take one number of this chapter on trust

Exercise 2.1 — Reproduce the planetary budget (2 hours, by hand)

Open lib/verify/VII_10.py, read it, then close it and compute these independently — on paper, in a spreadsheet, in whatever language you use.

1. Intercepted power. Total solar irradiance 1,361 W/m², Earth mean radius 6,371,000 metres. Compute π r² and multiply. Confirm 173,549 TW.
2. Absorbed power. Bond albedo 0.294. Confirm 122,526 TW.
3. Absorbed per square metre. Confirm 340.25 W/m² at the top of the atmosphere and 240.2 W/m² absorbed.
4. Effective radiating temperature. Invert Stefan-Boltzmann with σ = 5.670374419e-8. Confirm 255.1 K, which is -18.0 C.
5. The entropy ratio. 5,772 / 255.1. Confirm 22.6.
6. The absolute export. (4/3) × P × (1/255.1 − 1/5,772). Confirm 6.12 × 10^14 W/K, and then do it again without the four-thirds and confirm 4.59 × 10^14. Write down which convention you used and why the ratio did not change.

Exercise 2.2 — The three denominators (45 minutes)

Compute humanity's 19.6 TW as a share of each of:

• the absorbed solar flux, 122,526 TW — confirm 0.0160 percent;
• global net primary production, 129 TW — confirm 15.2 percent;
• Earth's energy imbalance, 459 TW — and state the ratio the other way round, 23.4 times.

Now write a single paragraph using all three, in which you are honest about all of them at once. This is the hardest paragraph in the workbook. Most writing on this subject picks the denominator that supports the conclusion it already had. Notice how strong the pull is.

Exercise 2.3 — Landauer, and the assumption that carries the answer (60 minutes)

1. Compute k_B T ln 2 at 300 K. Confirm 2.87 zJ.
2. From 72.7 GFLOP/W, compute energy per FLOP. Confirm 1.3755e-11 J.
3. Now assume 1,000 bit operations per FLOP and compute the headroom above the Landauer floor. Confirm 4,791,104 times — 6.68 orders of magnitude, 22.2 halvings.
4. Redo step 3 with 100 and with 10,000. Write down the three answers for the horizon at Koomey's 2.6 years per halving. One of them is 58 years.

Then answer: which number in this calculation is a measurement and which is a judgement? A reader who cannot tell them apart in someone else's work cannot be trusted with their own.

Exercise 2.4 — The waste-heat table, built yourself (45 minutes)

Using dT/T = (1/4)(dP/P) about 255.1 K:

1. Confirm that today's 19.6 TW produces 0.010 K.
2. Confirm that 1,921 TW produces one whole kelvin.
3. Build the horizon table for growth rates of one, two and three percent to each of 1,921 TW, 10,000 TW and 122,526 TW. Confirm 231 years at two percent to the first threshold and 441 to the last.
4. Then compute the horizon at 0.7 percent — output growth of 2.0 percent minus intensity improvement of 1.3. Confirm 657 years.

Write one sentence saying which of those four rows is a fact about physics and which is a fact about economics. They are not the same kind of claim and the chapter's whole argument rests on keeping them apart.

---

PART THREE — DREAM AND DESIGN

Build the apparatus you will use for thirty years

Exercise 3.1 — Your own intensity series (start now, keep for a term)

The only term in the cosmological budget that anyone moves is the denominator — value produced per unit of energy. Build the personal analogue and keep it weekly for twelve weeks:

Choose outputs you can count without lying: pages of drafted text, problems solved, kilometres run, circuits built, pieces practised. Count attention, not time at the desk. Do not change anything for the first four weeks; you are establishing a baseline, and the chapter is emphatic that an unagreed baseline is a future dispute even when the only party to the dispute is you.

At twelve weeks, compute your own improvement rate. Compare it to the world's 1.3 percent a year. You will almost certainly beat it, which tells you something true: aggregate intensity improvement is slow because it is an average over everything, including everything nobody is working on.

Exercise 3.2 — The refusal exercise (90 minutes, in writing)

Write two documents about the same proposal — anything you would like to see happen, at any scale.

Document A. Make the case using the cosmological frame. Entropy, the sink, the two-hundred-and-thirty-one-year threshold, the Kardashev ladder. Make it as compelling as you can.

Document B. Make the case for the identical proposal using only figures with a horizon inside five years.

Now give both to somebody who has not read this chapter and ask which one they would act on. Then write a paragraph about what you learned, and keep it. The temptation to reach for the large frame when the small one is doing the work is the single most common failure of the educated, and this is the cheapest lesson in it you will ever get.

Exercise 3.3 — Measure a real surface (one afternoon, about the cost of a meal)

An inexpensive infrared thermometer is enough. On a clear day, point it at:

• the open sky at the zenith,
• the sky at about thirty degrees above the horizon,
• a cloud,
• a wall in shade,
• a car roof in the open.

The zenith sky will read far colder than the air, the low sky warmer than the zenith, and the cloud close to air temperature. You have just measured the atmospheric window, its angular dependence and its closure by cloud, with a handheld device. Write down the four readings and the air temperature.

Then estimate, roughly, the cooling power of a surface facing that sky using σ(T_surface⁴ − T_sky⁴) and compare it to the chapter's 40 W/m². Being within a factor of two is a success; being able to say why you were out is a larger one.

---

PART FOUR — DESTINY AND DELIGHT

Make it hold, and enjoy it

Exercise 4.1 — The two-hundred-year sentence (30 minutes)

Write one sentence that will still be checkable in two hundred years, about anything you know. Then write what you would have to do this month for that sentence to be findable — a deposit, a record, a published number, a file in a place that outlives a laptop.

This is the chapter's durability argument applied to you. Stefan-Boltzmann will not be revised; almost nothing else you write will survive. Choose the one thing deliberately rather than letting the surviving fragment be chosen at random.

Exercise 4.2 — Delight (one night, no writing)

Go out on the next clear night, and this time look up knowing what you are looking at: a hole in the atmosphere, some five micrometres wide in wavelength, opening onto a reservoir at three kelvin, through which the planet is at that moment shedding 6.12 × 10^14 watts per kelvin of accumulated disorder — and every ordered thing beneath it, including the particular arrangement of you, is being paid for out of that flow.

Do not take notes. The chapter earns its Delight movement honestly and so should you.

---

THE TERM PROJECT

One piece of work, carried the whole way

Build a verified figure, and publish it.

Choose one widely quoted number about energy, climate, computation or resources that you have seen repeated without a source — the sort of figure that appears in three articles with three slightly different values.

1. Find its origin. Trace it back to a primary source: a paper, a dataset, an agency publication. Most such figures dissolve at this step, and that dissolution is itself the finding.
2. Recompute it. From inputs, with units, showing every intermediate term.
3. State what you could not verify. Explicitly, as a list. A survey that hides its gaps is an advertisement.
4. State what moves the answer. Which input carries the result, and how far the result travels if that input is wrong by a factor of ten. This chapter does it for the bit-operations-per-FLOP factor; do it for yours.
5. Write the honest negative. Name the decision your figure does not bear on, and say so as plainly as the chapter says it about itself.
6. Publish it — a repository, a page, a blog, a seminar handout — with the computation attached and reproducible.

Length is not the point; reproducibility is. A two-page note whose arithmetic anybody can run is worth more than a thirty-page essay nobody can check, and it is the thing you can show somebody in ten years.

---

SELF-ASSESSMENT

Mark each honestly. This is for you.

---

CARRYING IT FORWARD

Three habits are worth taking out of this chapter, and none of them is about the cosmos.

Recompute before you repeat. Any figure you pass on becomes yours. The arithmetic in this chapter takes an afternoon and immunises you permanently against a whole class of confident nonsense.

Name the denominator. Almost every argument about scale is an argument about what to divide by, conducted by people who have not said what they are dividing by. Say yours first and the conversation improves immediately.

Hold the true thing and its limit together. This chapter is right about the planet and wrong to be used in a business case, and both halves are stated on the same page. Learn to write that way and people will trust the parts where you do claim something.

---

APPRECIATIVE QUESTIONS FOR YOUR SEMINAR

1. Which number in this chapter did you most want to be true before you checked it, and what did checking it feel like?
2. When has a very large frame genuinely changed what someone in this room did? What made that instance different from the ones that changed nothing?
3. What would it take for this seminar to produce one verified figure a term that other people could rely on — and who would have to keep it?