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Commerce · III.02 · MMXXVI · daylight

La Bourse  /  Volume III  /  Nº III.02  /  Workbook — the student

WORKBOOK — THE STUDENT

Chapter III.02 · Energy as the Denominator

For the personal student. A term of practice, a term project, and a self-assessment. Everything here is done on your own life, your own bills and your own reading, because a denominator you have never checked by hand is a denominator you are trusting on somebody else's word.

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WHY THIS WORKBOOK IS DIFFERENT

Most of what you will be asked to do this term is not calculation. It is checking what a number was divided by — and that habit, once it is real, will serve you in every field you enter, not only this one.

The chapter makes one structural claim: energy is an excellent denominator and a poor numeraire. You are going to test that claim three ways on your own circumstances, and you are going to find that the interesting part is never the arithmetic. It is the boundary — what got counted, what did not, and who decided.

Three things to have before you start: a year of your own energy bills or a smart-meter export; a spreadsheet; and a notebook you are willing to write awkward sentences in.

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PART ONE — DISCOVERY

Days 1–30: find the denominators you already live inside

Exercise 1.1 — The five denominators (90 minutes)

Find five numbers in your own life that are ratios, and write out the denominator of each in full. Suggestions to start you off, though your own are better:

For each, write one sentence naming who chose the denominator and what they gained by choosing that one. This is the whole skill. Everything else this term is practice at it.

Exercise 1.2 — Your own energy account (one week)

Get twelve months of electricity and gas, in kilowatt-hours, not in currency. Most suppliers will export this; a smart meter will give you half-hourly data, which is much better. Build one table: month, kWh electricity, kWh gas, total kWh, total paid.

Now compute three things:

1. Your average price per kilowatt-hour, all in, including standing charges.
2. Your energy intensity: kWh per pound of your own total spending for the year. You have just computed, for yourself, the quantity the chapter reports for countries — and the world figure is 4.6 MJ per PPP dollar.
3. The ratio of your highest month to your lowest month.

Write the three numbers at the top of a page and leave the page open. You will add to it.

Exercise 1.3 — The appreciative conversation (45 minutes)

Find someone who manages energy for a living — a building manager, a facilities engineer, a farmer, a chef. Ask them this, in these words:

"When has paying attention to energy actually made something better here — not cheaper, better? What made that possible?"

Take notes on conditions, not outcomes. You are looking for the shape of a good case, because you will need one for the term project, and because the deficit question — what is wasteful here — reliably produces a shorter and less useful list than this one does.

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PART TWO — THE ARITHMETIC

Days 31–45: compute it yourself, twice

Exercise 2.1 — Exergy-weight your own consumption (2 hours)

Split your annual kilowatt-hours into two piles: those that end as work, light or electronics (weight 1.00) and those that end as low-grade heat — space heating, hot water (weight = the Carnot factor).

Use the chapter's table, with a 20 °C ambient:

Compute your exergy-weighted consumption. Worked, so you can check your method: a household using 60 percent electricity and 40 percent 80 °C heat, on 14.0 units, has 14.0 × (0.60 × 1.00 + 0.40 × 0.1699) = 9.35 units of exergy — the flat figure overstates by 49.71 percent.

Write one paragraph answering: which of my energy am I buying at a high grade and using at a low one? For most households the honest answer involves an electric immersion heater or a tumble dryer, and it is worth seeing on your own numbers rather than being told.

Exercise 2.2 — Find your own 409 (3 hours, needs half-hourly data)

If you have half-hourly consumption, get a year of wholesale day-ahead prices for your market — most system operators publish them free. Join the two series by hour and compute:

• The highest-priced hour in which you consumed anything.
• The ratio of that price to the annual average price.
• What proportion of your annual consumption fell in the most expensive 1 percent of hours.

For scale: in the ERCOT market the annual average real-time price was around $22 per MWh in 2020, and in February 2021 the price sat at the offer cap of $9,000 for roughly 96 hours — a factor of 409.1, with a floor of negative $251, so a span of $9,251 per MWh across one year in one market.

You will almost certainly find that a small share of your consumption sits in a large share of your cost. That asymmetry is the practical content of the whole chapter: the same joule is not the same thing at different hours.

Exercise 2.3 — Rebaseline a transformity (45 minutes)

Take any published transformity on Odum's 1996 basis and restate it on the 2016 baseline. The multiplier is 12.00 × 10²⁴ / 9.44 × 10²⁴ = 1.271.

Worked: 26,000 sej/J becomes 33,051 sej/J, a change of 27.12 percent.

Then do the part that matters. Take two transformities, compute their ratio on both baselines, and confirm it is unchanged: 26,000 / 39,800 = 0.6533, and 33,051 / 50,593 = 0.6533. Write one sentence explaining why, in your own words. If you can write that sentence you have understood the strongest criticism of emergy and its strongest defence, which most commentators manage only one of.

Exercise 2.4 — The consumption-based version of your own footprint (2 hours)

Run any reputable carbon calculator twice: once counting only what you burn directly, once counting what is embodied in what you buy. Record both.

For scale: 6.2 GtCO₂ was embodied in international trade in 2004 — 22.96 percent of global fossil emissions — and net transfers from developing to developed economies rose from 0.4 GtCO₂ in 1990 to 1.6 GtCO₂ in 2008, a factor of 4.00.

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PART THREE — DREAM AND DESIGN

Days 46–70: build the second column

Exercise 3.1 — Your own conversion table (90 minutes)

Write a one-page table, versioned and dated, giving the exergy weight you will use for every kind of energy in your account, and the ambient temperature you are weighting against. Sign it. Put a version number on it — v1.0 — and a date.

This is not ceremony. Odum's field learned at a cost of 1.271 on every published figure that an accounting convention which moves silently invalidates every historical series computed with it. Your own series will be worth something in three years only if you can say what convention produced it.

Exercise 3.2 — The two-column month (four weeks)

For one month, keep every purchase over a threshold you choose in two columns: what you paid, and the energy you can attribute to it. You will not be able to attribute most of it. That is the finding, and it is the same finding the national accounts have. Record what you could not attribute as a named gap, not as a zero — a missing answer and a zero are not the same fact.

At the end of the month, write half a page on: which column told you something the other did not?

Exercise 3.3 — The boundary argument (one seminar)

Pair with another student. One of you argues that the boundary of an embodied-energy account should be drawn narrowly — fuels only, verifiable, auditable. The other argues it should be drawn widely — environmental inputs and household labour included, as Costanza did in 1980.

Then swap and argue the other side. This is the Costanza–Huettner exchange, and it has not been settled since 1982, which is exactly why it is worth an hour of your time rather than a paragraph of somebody's conclusion.

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PART FOUR — DESTINY AND DELIGHT

Days 71–90: make it a habit, and notice it is pleasant

Exercise 4.1 — The standing check (five minutes, weekly, forever)

Once a week, take one number you encountered — in a lecture, a paper, a newspaper, a company report — and find its denominator. Write the number, the denominator, and who chose it. Three lines. Do it for eight weeks.

At the end of eight weeks read the page back. Most students find that at least two of the eight numbers were doing something quite different from what they appeared to be doing, and one of them was in a source they trusted completely.

Exercise 4.2 — The delight exercise (30 minutes)

Find the hour in your own data where the price was highest, and find out what you were doing. Then move it. Run the dishwasher, the washing machine, the charger at a different hour for two weeks and compute the difference.

It will be a small amount of money and that is not the point. The point is the feeling of having found a schedule inside a bill — of discovering that a thing you thought was a fixed cost was a timing decision nobody had made. That feeling is what this economics is actually like from the inside, and it is worth knowing early that it is enjoyable rather than austere.

Exercise 4.3 — Write the honest negative (one page)

Write one page arguing against the energy denominator, as strongly as you can, using the chapter's own numbers: the 15.7 times spread in exergy, the 11.54 times spread across an ocean in one month, the 409.1 times spread across hours. Do not soften it.

Then write one paragraph on what survives. If you cannot write the second paragraph, you have not yet understood the first.

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THE TERM PROJECT

One piece of work, carried the whole way

Build a two-column account of one real thing, for one year, and defend it.

Choose something with a boundary you can actually draw: a household, a department, a sports club, a small farm, a student union bar, a single building on your campus.

Deliver five things.

1. The conversion table, versioned, dated, with its ambient temperature.
2. Twelve months of data, in kilowatt-hours and in currency, side by side.
3. The exergy weighting, with the flat and weighted totals and the percentage between them.
4. The boundary statement — one page naming exactly what is inside, what is outside, and one thing you could not get and did not guess.
5. One decision the second column supports that the first column does not, with the number attached.

The fifth is the whole project. Four students in five produce a beautiful account that changes nothing. An account that does not end in a decision is a hobby with a spreadsheet, and finding the decision is the intellectual work.

Marking weights: boundary statement 30 percent, arithmetic 25 percent, the decision 25 percent, the conversion table 10 percent, presentation 10 percent. The boundary carries the most because it is where every real dispute in this field lives.

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SELF-ASSESSMENT

Score yourself honestly. This is not submitted.

The last row is the one that predicts everything else.

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CARRYING IT FORWARD

Three things to keep after the term ends.

The weekly denominator check. Five minutes. It will outlast every other habit on this list and it transfers to every subject you study.

Your own two-column account. Keep it running. Its value is entirely in comparison across time, which means it is worth almost nothing this year and a great deal in five — and that is the argument for starting it now rather than when it seems interesting.

The sentence about ratios. Rebaselining multiplies numerator and denominator alike, so ratios survive and absolutes do not. You will meet that structure in index numbers, in exchange rates, in psychometrics and in every adjusted-for-inflation series you ever read. Recognising it is a small piece of mathematical maturity that arrives early and stays.

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APPRECIATIVE QUESTIONS FOR YOUR SEMINAR

1. When has one of us found something real by checking what a number was divided by? What was it, and what tipped us off?
2. Which of the accounts we have built this term would still be useful in ten years, and what makes it durable?
3. If our department published an energy column beside every budget line, what is the first question we could answer that we cannot answer now?
4. What is the best argument against our own position, and who in this room makes it best?