Three Directions ·
Why Isn’t It So?
First principles reasons up from the bottom. Analogy reasons across from where you stand. There is a third direction, down from the outcome. Run all three at once, and the places where they disagree are the diagnosis.
- ↓ Top down The axiom Why isn’t it so?
- → Level Analogy What is already working?
- ↑ Bottom up First principles What must be true?
Not three steps. Three lenses, held at the same time.
You are at the bar after close with the month’s numbers. Food cost is high again. Call it forty cents of every dollar. You already know what everyone will tell you, because you have heard it all before: shrink the portions, raise the prices, find a cheaper supplier.
Every one of those fixes takes something off the plate. None of them tells you what the forty cents is made of.
Two directions everyone knows
There are two famous ways to reason about a problem. The first is from first principles: dig down to what is fundamentally true and build back up. The second is by analogy: look across at how things are already done, by you or by others, and adjust a little. I wrote about both earlier this week, in The Name Is the Analogy and The Only Free Variable.
Put them on a vertical line and they are easy to tell apart. First principles works below today, at the floor. Analogy works at today’s level, looking sideways. That leaves a direction nobody names.
It comes from above.
The third direction: down from the outcome
Start with an outcome that most people would assume is true, and assume it. Not an ideal. Not a miracle. The ordinary healthy state. This restaurant is profitable. This person is well fed. Call it the axiom: you cannot prove it, but almost nobody would argue with it.
Then ask the only question the axiom allows. Why isn’t it so?
That question changes the job. You are no longer inventing a business. You are diagnosing one. A doctor does not ask the patient what a body should be. She holds the healthy body as given and reads the skin color, the posture and the weight as evidence of where this body departs from it. The symptoms only mean something against the norm. Remove the norm and a pale face is just a face.
Assuming the axiom does not make it so. It makes the gap readable. The fix is still work.
Bottom up asks what must be true. Level asks what already works. Top down asks why it isn’t so.
Figure 01
One line, three positions
- Above todayThe axiom. The ordinary outcome, held as true. Every gap below it reads as a symptom.
- TodayAnalogy. How things are done now, here and next door. It supplies the picture of what healthy looks like.
- Below todayFirst principles. What the thing is made of. It tells you whether a symptom is what its name says.
A word on the word
In the usual vocabulary an axiom sits at the bottom. It is the floor you reason up from, which is why people often use “axiomatic” as another name for first principles. Here it sits at the top. You do not reason from it. You reason toward it, and you read every gap as a symptom. It gets the same unquestioning status a mathematician gives an axiom. It just lives at the other end of the line.
The family it belongs to
The backward move is not new, and it should not pretend to be. Russell Ackoff told Bell Labs to design as if the phone system had been destroyed the night before, then close the gap between the ideal and the present. TRIZ starts from the Ideal Final Result. Toyota Kata has learners describe the target, then finish a sentence that begins “We can’t” and ends with “because.” Goldratt traced undesirable effects back to a core cause. Solution-focused therapists ask what would be different if a miracle happened overnight.
What the axiom adds is a starting point and a stance. The outcome is not the ideal, it is the ordinary state most people already assume. And reality carries the burden of explaining why it hasn’t arrived.
Not in order. At once.
The natural way to teach three methods is as steps: set the axiom, then compare, then dig. That is wrong, and the reason is the interesting part.
Each direction, alone, fails in a known way. The axiom alone turns stubborn: assume it hard enough and you stop reading the evidence. Analogy alone copies the neighbors, including their diseases. First principles alone is slow and has no idea where to dig. It can decompose everything, so it decomposes nothing in particular.
Run them in sequence and each one corrects the last after the damage is done. Run them at the same time and something better happens. They check each other as they go, and the places where they disagree become the findings. Agreement tells you nothing new. Disagreement is the diagnosis.
Figure 02
The same restaurant, three lenses at once
- Top down · The axiom
- “This restaurant is profitable.”
- Food cost is the symptom pulling hardest against it. That is where to look.
- Level · Analogy
- “What do places like this run?”
- Peers run a little lower. Forty cents is high, but not alarming.
- Bottom up · First principles
- “What is the forty cents made of?”
- The ingredient is a fraction of it. The rest is diesel, distribution, storage and a margin at every hand-off.
- Where they disagree
- Analogy says slightly high. First principles says structurally inflated. The gap between those two answers is the delivery stack, and every peer you benchmark against carries the same one.
That last line is the one a sequence would hide. If analogy runs first and alone, forty cents gets filed as “a bit high” and the investigation ends at portions and prices. Only when first principles runs beside it does the benchmark itself come under suspicion. Everyone you compare yourself to buys through the same chain, so the industry average is not a picture of health. It is a shared condition.
And the cures change. Smaller portions take something off the plate. Buying closer, consolidating orders and cutting a layer out of the chain take nothing off it at all.
Why this becomes practical now
A person cannot really do this. Attention is one thread. We hold one lens, then the next, and by the third we have half forgotten what the first one saw. That is why these methods were always taught in sequence. It was the only way a single mind could run them.
An AI does not have that limit. It can hold the axiom, the benchmark and the decomposition in one pass, and its most useful output is not an answer from any of them. It is the list of places where they disagree. The cost of running three directions in parallel has fallen to almost nothing. The scarce skill moves to the one thing the machine cannot supply: choosing the axiom.
The owner types one line. Assume this restaurant is profitable. Tell me why it isn’t.
What comes back is not a plan. It is three short columns and, underneath them, five places where they disagree, ranked by how much money sits in each gap. The first one is the delivery truck.
What I expect
“Why isn’t it so?” replaces “How do I?”
The how-question asks the machine to invent. The why-question asks it to diagnose, which it does far better, because diagnosis has a reference point. Owners who learn the second question will get better answers from the same tools.
The industry average loses its authority
Benchmarks were the backbone of reasoning by analogy. Once first principles runs beside them every time, an average will read as a shared condition, not a standard of health. “Normal for the industry” will start to sound like a symptom.
Line items get taken apart by default
Labels like food cost, overhead and cost of goods hide stacks. When decomposition is free, nobody will accept a category as an answer. The financial statement of the near future shows what each line is made of.
Disagreement becomes the deliverable
The most valuable report will not be a recommendation. It will be a map of where the three directions conflict, because that is where the money and the surprise live.
The axiom is the advanced skill
Analysis gets cheap. Choosing an outcome that is believable, specific and honest does not. The student who can state the right axiom in one sentence will outperform the one who can run every analysis.
This is how I want my advanced students to work. In Super Admin I asked them to take the seat of the one who carries the intention and remains the author. The axiom is that seat in its simplest form: one sentence about the outcome, held as true, with every lens pointed at the gap.
Two days ago I argued that the outcome is the only free variable a first-principles answer leaves you. This is the same idea seen from above. When I walked a restaurant’s food cost through all three directions at once, the finding that mattered, that most of the cost of food is not food, came from neither lens alone. It came from the space between them.
The ledger
- Already true
- Medicine has always worked this way: a presumed healthy norm, symptoms read against it, causes traced down to the bottom. Analogy and first principles are each well taught. An AI can already run all three in a single pass and report where they conflict.
- What has to happen
- People have to state axioms that are believable rather than aspirational, and ask for the disagreements instead of a single answer. The tools have to be used as diagnosticians, not as plan generators.
- Where I am probably wrong
- The axiom can be false. Some restaurants cannot be profitable on that corner at any realistic volume, and a method built on assuming the outcome invites people to defend it. My answer is that the diagnosis must be allowed to come back terminal. If first principles shows the axiom cannot hold, you change the axiom. If students skip that rule, this becomes a machine for stubbornness, and I will have taught the wrong thing.
Back at the bar. Same numbers. This time you don’t ask how to cut food cost. You assume the place is profitable and ask why it isn’t, from above, from beside and from below, all at once. The answer is not on the plate. It is on the truck.
Assume it is so. Then ask why it isn’t.
Background
- Russell L. Ackoff, Jason Magidson and Herbert J. Addison, Idealized Design, and the Bell Labs story
- Ellen Domb, Using the Ideal Final Result to Define the Problem to Be Solved, The TRIZ Journal
- Mike Rother, Toyota Kata, and Mark Rosenthal on the obstacle test
- Eliyahu Goldratt, the Current Reality Tree
- Steve de Shazer and Insoo Kim Berg, the miracle question
- John Rector, The Name Is the Analogy (First Principles, Part 1)
- John Rector, The Only Free Variable (First Principles, Part 2)
- John Rector, Super Admin: The Advanced Course in Personal AI