First principles · Perception and price
Ten Dollars Is Ten Dollars
You feel a saving as a share of the price, so money hides inside big totals where no one feels it. A delegate counts dollars, not shares. The hiding place does not close. It moves to the purchases you still make by hand.
felt change ≈ log( new ÷ old )
A body reads a change against what it is already holding. A ledger reads the difference.
To a delegate the bars read $5, $5 and $1,400.
You drive twenty-five minutes across town because the same lamp is twelve dollars cheaper there, and you feel clever the whole way home. At four o’clock, in a small office at the dealership, the finance manager adds a fourteen-hundred-dollar protection package to a thirty-eight-thousand-dollar car, and you sign without looking up.
Weights in the hand
In 1834 a physiologist in Leipzig, Ernst Weber, asked people to hold two weights and say which was heavier. He found that the smallest difference a person can notice is not a fixed amount. It is a fixed fraction of what they are already holding. Add a little to a light weight and the hand notices. Add the same little to a heavy one and it does not. Gustav Fechner turned this into a law in 1860: what we feel grows with the logarithm of the stimulus, not with the stimulus itself.
It holds for brightness, loudness, pressure and length. It holds for money too. In 1981 Amos Tversky and Daniel Kahneman asked people whether they would drive twenty minutes to save five dollars. On a fifteen-dollar calculator most said yes. On a hundred-and-twenty-five-dollar calculator most said no. The five dollars was the same. The thing it was measured against was not.
This is not a flaw to be trained out. It is structural. A nervous system has to work from starlight to noon and from a whisper to a jet. A sense that counted in fixed steps would be swamped at one end and blind at the other. The only reading that works across that range is a ratio. A body that sensed differences instead of fractions would not survive a sunny day.
My own framework is built on the same log. Surprise is the logarithm of what happened over what was expected (P4), and the log is not a choice. As I wrote in What Is a Logarithm, a mind that adds has to read a world that multiplies this way. The framework even names this as one of the places it can be shown wrong: equal ratios should feel equal, at any size.
The ratio is the right reading for a body. It is the wrong reading for a bank account, because money adds.
That gap is where a great deal of money lives. Whatever is attached to a large purchase rides on the large number and is felt against it. The extended warranty at the register. The fees on a closing statement. The upgrade at the gate. The “only nine dollars more a month” on a car payment. The commission quoted as a small percent of a house, which for many families is among the largest fees they ever pay and the one they argue about least. None of this needs anyone to lie. It needs only that the buyer is holding something heavy when the extra weight is added.
A reader with nothing in its hand
Now change one input: who reads the price. A delegate going through your purchases is not holding the car while it reads the add-on. It does not read the add-on against the total. It adds. Fourteen hundred dollars on a car is fourteen hundred dollars, exactly as heavy as fourteen hundred dollars on a lamp.
The obvious consequence is that the delegate finds the money first where you felt it least: inside the biggest numbers in your year. The house, the car, the insurance renewal, the retirement account fee, the medical bill. That is where a ratio sense hides the most, so that is where a difference sense finds the most.
The second consequence runs the other way. The delegate will tell you not to drive across town for the lamp. Twelve dollars against fifty minutes of your Saturday is a poor trade, and the delegate has no thrill of the bargain to weigh against it. The thrift you were proud of turns out to have been aimed at the small numbers, where the ratio made savings feel large.
The third consequence is the one most people will miss. The money does not stop hiding. It moves. A seller who earned on the add-on attached to a big purchase loses that margin once a delegate reads the contract. The margin goes looking for a place where a person still decides by feel, with no delegate between the hand and the till: the small, fast, in-person purchase. The tip screen. The snack at the gate. The in-app upgrade at eleven at night. Ratio blindness used to hide money inside big totals. With delegates reading the big totals, the hiding place becomes the moment.
This is new beside Surprise Has a Noise Floor, which was about changes delivered in steps too small to feel. That piece took the floor of the ratio. This one takes its other edge: how the same sense makes large extras feel small, and what happens when a reader without that sense joins you at the desk.
Your phone shows two lines before you leave the house. “Skip the lamp trip: it saves $12 and costs 50 minutes. The car offer has a $1,400 package and a rate half a point above your credit union. I’ve asked them to take both off. Difference: about $3,100.” You buy the lamp on the way to the dealership, at full price, and do not mind.
Five predictions
- The biggest household savings will come from the biggest purchases. The delegates people come to trust first will be the ones that read closing statements, car contracts, insurance renewals and fee schedules. The money they find will dwarf anything coupons ever saved, and people will be startled at where it was.
- Add-ons at the big moment shrink, and sticker prices rise to meet them. When “only nine dollars more a month” stops working on the buyer’s delegate, sellers will move the margin into the headline price. All-in pricing becomes the norm wherever delegates do the shopping, and the base price of a car or a flight looks worse while the total looks better.
- Percent fees get restated in dollars. Fees quoted as a small share of a large number will be shown to buyers as a dollar figure by default. Fee structures built on the share, from commissions to annual percentage charges on savings, will be questioned first and hardest.
- The hiding place moves to the purchase you make by hand. Margin will flow toward small, frequent, in-person and late-night purchases where no delegate stands between you and the screen. Expect more of the price of ordinary life to sit at the counter and in the tap, and expect delegates to start asking to see those too.
- Thrift becomes a hobby. Driving across town for the cheaper lamp will become something people do for pleasure, like fishing, not for money. The households that save the most will be the ones that hand over the big documents, not the ones that clip coupons.
Where I stand
I hand recurring work to my AI and do not look at it again. I also built a framework on the logarithm, so I am not about to call my own nervous system foolish for using one. It is doing what a body has to do. The point is to stop asking it to do a ledger’s job. If I were giving a delegate its first job with money, it would not be finding a cheaper lamp. It would be reading the documents where the numbers are so large that my feelings go quiet, and telling me in plain dollars what was added while I was holding the heavy thing.
The claim ledger
- Already true
- Weber’s fraction has been found again in sense after sense for nearly two hundred years, and the calculator result has been repeated many times. Add-ons sold at the moment of a large purchase are a standard part of selling cars, homes and travel. Delegates that read long documents are already in use.
- What has to happen
- People have to let a delegate see the big documents before they sign, and the delegate has to work for the buyer, not be paid by the seller to look away. That second condition is the subject of Who Gets Paid for Your Indifference?
- Where I am probably wrong
- The delegate can read the difference and still not move the hand. If people see “$3,100” on the screen, feel it against a thirty-eight-thousand-dollar car, and sign anyway, the ratio wins and the money stays hidden in plain sight. I am also wrong if sellers simply bury the extras in terms too tangled for delegates to price, or if the delegates people use are paid by the sellers.
Back to the small office
The pen is over the line. The fourteen hundred dollars sits on the page next to a much bigger number, and next to it, it looks like nothing. It is exactly as heavy as it was this morning, when twelve dollars was worth a drive across town. It is more than a hundred times that.
It was never small. It was only standing next to something big.
Background
- Ernst Heinrich Weber, De Tactu, 1834.
- Gustav Theodor Fechner, Elemente der Psychophysik, 1860.
- Amos Tversky and Daniel Kahneman, “The Framing of Decisions and the Psychology of Choice,” Science, 1981.
- Richard Thaler, “Mental Accounting and Consumer Choice,” Marketing Science, 1985.
- John Rector, What Is a Logarithm; Surprise Has a Noise Floor; Who Gets Paid for Your Indifference?
Spine v1.72 · Primitives: P4 · Results: no numbered result is invoked · Registers: DOCTRINE (the reading as a logarithm of a ratio), REPORTED (Weber, Fechner, and the calculator study, sources above). The predictions, and the claim that the margin moves to purchases made by hand, are this piece’s own; the falsifier is in the ledger.
Part of John Rector’s first-principles writing. Start with The Immutable Past, then read What Is a Logarithm and Surprise Has a Noise Floor.