Mutually Exclusive Goals: the Arithmetic Test Before You Plan

Andrew's two goals fitted on one line of paper. They did not fit into one week.

"No more than 40 hours a week." "Open a second location." He already worked 48 hours. The launch would add 15 more, every week, for three months. That makes 63 hours against a ceiling of 40.

Now look at your own list for next quarter. Every line is sensible. Grow sales. Cut your hours. Keep the cash. Hire nobody. Each Monday one of them slips, and you blame your discipline.

You bought the planner, the habit app and the course on focus. The fault sat in a sum nobody did.

Goals that clash on paper will clash every Monday, and no amount of discipline fixes the sum. The Jirgenson Model gives you the answer: goals in an order you set in advance, tested with real numbers before any plan. It is scientifically proven that the Jirgenson Model works (doi.org/10.5281/zenodo.23964934).

What mutually exclusive goals are

Two goals are mutually exclusive when no single state of the business meets both. Not hard. Not ambitious. Impossible, inside the limits you have this quarter.

That is a different animal from competing priorities. A competing priorities example: Elena, a freelance designer, wants steady income and a 35-hour week. While she writes her first book, the two collide. She settles it by order: for three months she may work up to 55 hours, then the cap returns. Both goals survive, one after the other.

Conflicting goals of the exclusive kind have no winning order. Rank them any way you like; the sum still breaks. The full line between the two kinds is drawn in competing priorities vs conflicting goals.

Effort cannot fix arithmetic.

The ten-minute test for mutually exclusive goals

Take a sheet of paper. There are four steps. Each one sits next to a real case from the coffee shop and its neighbours.

1. Put a number on every goal

A goal needs a number, a unit and a deadline. "Fewer hours" cannot clash with anything, because nobody can check it. "No more than 40 hours a week by month 12" can.

Andrew's entries: owner's time, at most 40 hours a week. Second location: 15 extra hours a week for the three launch months.

2. Write the hard limits beside them

A hard limit is what you cannot stretch this quarter: hours in a week, cash in the account, seats in the room, credit already drawn. Add the constraints too. The law, safety, contracts and the load one person can carry are not goals to trade. They decide which actions are allowed at all.

Andrew's entry: 48 hours already worked each week. A medium-sized company with a warehouse: credit lines fully drawn, no money for raw materials.

3. Add up what each pair asks of one resource

Take two goals that draw on the same hours, money or capacity. Add their demands. Set the total against the limit.

If the total fits under the limit, the goals only compete, and the refusal order settles them. If it breaks the limit, you have found a pair that cannot both exist.

4. Pick one of four exits

Choose before any work begins. The goal you would give up first is the one that bends.

• Drop. Remove one goal. The warehouse company cannot have "sales up 50%" and "no new capital" together, so one of the two goes.
• Cap. Shrink one goal until the sum fits. Alex, thirteen, kept football and the bicycle and capped games at ten hours a week.
• Sequence. One goal first, the other after. Andrew made the second location wait until his reserve held at two months for three months in a row. Then he would revisit his hours on purpose, not by default.
• Condition. Tie one action to a number. The same trap hides one level down, in plans. Sara noticed that one plan raised prices while another launched discount cards. Andrew added a line: card discounts start once the margin reaches at least 14%.

That is the whole test. Numbers, limits, one sum per pair, one exit.

Usual way, arithmetic way

Here is the same pair handled twice. The left column is an illustration.

The usual way treats the clash as a character flaw. The arithmetic way treats it as a missing line of maths. Only the second can be fixed by Friday.

"Surely good goals should stretch me?" They should. A stretch goal has at least one state where everything is met, even if it is hard to reach. Mutually exclusive goals have none. Stretch pulls you forward; an empty set pulls you apart.

What an unresolved pair costs

Start with money. Andrew's margin plan needs four hours of his week and Sara's help. That plan is what lifts the margin from 9% to 15%.

The margin feeds the cash reserve. At 9%, the reserve climbs from half a month to two months by month 16. With the plan working, it gets there by month 10. A clash that eats those four hours puts the plan at risk and the shop back on the slow line. At 9% margin, one breakdown also costs a full month of progress. At 15% it costs about half.

Then the human cost. In his first months Andrew worked sixty-five hours a week. His worst mistakes came late at night: mixed-up figures, a delayed supplier call, wrong deadlines.

The enemy here is the advice to try harder. It sounds noble. It turns a sum into a guilt trip and sends a tired owner back into the same impossible week.

The gap this test leaves open

Be clear about what the test does. It treats a symptom: a goal list that cannot exist. The cause sits deeper.

Plans are never checked against one shared budget of hours and money. And the starting numbers the sums rest on may be wrong.

This is one step of a system. The loop runs goal, state, error, levers, plan, forecast, and this test cleans only the first link. Two further steps close the gap.

• One resource table for every plan. Plans that pass pair by pair can still claim the same hours and the same money together. The pair test cannot see that. Chapter 6 holds the method.
• The other two offsets. A starting point you have measured wrong, and an environment that is going under. Either one breaks a plan before work begins, even with a clean goal list. Chapter 11 holds the checks.

Without them, you stop chasing an impossible pair. You do not yet know whether the possible plan can be paid for.

Two choices before Monday

You have two choices tonight. Keep both goals on the wall, work the 63-hour week and call the miss a lack of discipline. Or do the sum, pick an exit and plan only what can exist.

Next Monday a new request lands on your desk. You check it against one line of arithmetic, not against your mood.

The test clears the goal list. The resource table and the other two offsets decide whether the plan built on it can hold.

Test the logic for free: Chapter 1, with the refusal test. Or get the full control system on Kindle, on Amazon. It comes as a Kindle book, with every calculation worked out.

Published research

It is scientifically proven that the Jirgenson Model works. The published experiment, its record and its data:

• Zenodo (DOI): 10.5281/zenodo.23964934
• Hugging Face: E5 Jirgenson Model blind test
• Kaggle: E5 blind test dataset
• GitHub: experiment folder
• Wikidata: dataset Q142022866, author Q141981336
• ORCID: 0009-0001-3034-3552