Why Do Poverty and Inequality Exist? Reality Doesn't Charge for Having More. It Charges for Need Left Unmet.

It's 12:15 and you're in the school cafeteria with no lunch and no money.

At home the fridge is full. The food exists. It just isn't where you are.

At the next table, a kid throws away half a sandwich. You watch it go.

Two questions sit in that scene. Why are you hungry when there's food? And is the gap between you and the kid with the sandwich the problem?

Those are the two questions inside "Why do poverty and inequality exist?" Reality answers them separately.

The short answer

Reality's record charges for need left unmet. It doesn't charge for how much anyone holds.

Reality keeps a permanent record of every event, because the basic laws of physics never destroy information, so nothing in it is ever erased. Its entries are comparisons between the two ends of a relationship: a ratio, balanced at 1, never an amount. A comparison at balance costs nothing at any size. So a difference between what you hold and what the kid at the next table holds isn't, by that fact alone, a cost on the record. Having more costs nothing.

What the record does charge is a relationship out of balance. A person's need is one: what reaches them against what they require. Someone with 1 of the 4 units they need sits at 1/4, and the record charges 9/8. Someone with 3 of the 4 sits at 3/4, and it charges 1/24. The cost is one forced formula, given below, and it climbs steeply the further a person sits from enough. One more unit takes off 21 times as much cost for the first person as for the second, which is why, when someone gives a unit, reality's moral code sends it to the needier person first. One step under all of this isn't derived yet, and Step 2 says which.

Why is anyone short, then? Here are five ways, in two columns. In the storm's column no wrong is needed: there isn't enough, what there is sits somewhere else, or the good can't be divided. In the theft's column someone does wrong: they take, or they leave undone the help the code requires. A rising total can hide any of the five.

Here's the whole answer in seven steps. The rest of this post takes them one at a time, with the reason for each and a small example with the numbers worked through.

1. The record charges need left unmet, never the size of a holding. A balanced comparison costs nothing at any size, so a gap in what two people hold isn't a cost by itself. No law of how wealth distributes is derived.
2. An unmet need has an exact cost, steepest far from balance. 1 of 4 costs 9/8, 2 of 4 costs 1/4, 3 of 4 costs 1/24, and 4 of 4 costs 0.
3. Neediest first. The same unit takes off 21 times as much cost from the greater need, so the code sends it there. That's among acts both people write, and it never makes taking right.
4. Amounts matter in exactly two ways. They decide which acts are on the menu, and they fill the reserve that pays for repair.
5. Three ways to be short with no wrong needed. There isn't enough, it's somewhere else, or it can't be divided.
6. Two ways to be short because someone did wrong. Someone takes, or someone leaves undone the help the code requires.
7. Where one person's spare holdings can meet another's need, the code's act meets it. The rest ends only as production turns material into what people can use.

Why this matters: "poverty" and "inequality" get used as one word, and the record treats them as two things. A gap in holdings isn't charged. A need left unmet is, exactly, and the code says where help goes first and what never makes a taking right. That gives you a question to put to any case of someone short: did anyone do what the code forbids?

What this post stands on

Four starting claims, each with its reason.

The past still exists. Every event leaves a complete trace, and none is ever erased. The reason starts in known physics: the basic laws never destroy information. In quantum mechanics that's called unitarity. The present fixes the past exactly, and running the laws backward recovers every earlier state. The record has a rule of its own as well: it only grows. Each new entry is added with every earlier entry kept, and writing a new entry never alters an earlier one.¹ Part 1 tells the whole story of the record.

A relationship is a comparison with two ends, and each end keeps its own books. The smallest thing that can happen is one thing told apart from another. You're doing it right now, reading these letters: every measurement and every perception tells one thing from another. Telling two things apart takes information about both, so the record's unit is a relation between two ends. Call the record's entry for a relationship a bond. Its number is one end's amount divided by the other's: 1 when they match, and then the bond is level. Read from the other end, the number x becomes 1/x, and nothing changes. Each end keeps its own record of the bond in its own books and writes only there. A write is an end's entry in its own books. An act is a change written in the actor's books, or in both ends' books when two people act together. Nobody writes in another's books.

A bond has a cost, and the formula is forced. A level bond costs nothing. Any other number costs: J(x) = (x + 1/x)/2 - 1. Add the number to its flip (1 divided by the number), halve the sum, and subtract 1. For 2: 2 + 1/2 is 5/2, half of that is 5/4, and 5/4 minus 1 is 1/4. The cost has to be zero only when the two sides match, grow as they differ, and come out the same whichever side you put first. Add the rule for how the costs of combined comparisons add, and one calibration (how sharply the cost rises near level), and exactly one formula is left.² The cost measures imbalance. It isn't a payment to anyone. Each end of a bond carries all of its cost, and the record's own total counts each bond once. A person's burden is the cost of the bonds they're an end of.

There is one moral code, and it fits in a paragraph. An act is admissible when four things hold. It touches only bonds that exist now. Every record of every bond is true after it. An act may move a bond only when both of its ends write on it. And a bond ends only when one of its own ends ends it. Of the admissible acts, the code permits exactly those that leave the least total cost on the complete record, which counts every checkpoint still to come, and every other act is forbidden. Doing nothing is always admissible, so something is always permitted.³ The clauses are rules about acts, because acts are the only way a bond changes. Nothing moves a bond between acts: a bond changes only through something sent, and sending is an act.

The clauses come first and the cost second. Consent is a hard condition, not a price. Try a fine instead: charge extra for any push, an act that moves someone's bond without their write. No finite fine works, because the relief a push can buy has no ceiling. How Should We Live? puts numbers on it.

The route

Here's the route. Each step ends with a line on why the next one comes next.

Step 1: The record charges need left unmet, never the size of a holding

The record holds ratios, never amounts, so a balanced bond costs nothing at any size. A gap in what two people hold isn't, by that fact alone, a cost on the record. Having more costs nothing.

What a person holds is an amount. What the record carries for a relationship is the ratio between its two ends. The ratio of 4 to 4 is 1, and so is the ratio of 4,000,000 to 4,000,000. The cost reads the ratio, so it's 0 in both. What Is Money? works this out with two books, 5 against 5 and 5 million against 5 million.

So the record has no line for how much you have. It holds a ratio for each relationship, and the cost reads how far that ratio sits from 1. The gap between your lunch and the kid's isn't what the record charges, and a bigger lunch at the next table wouldn't be charged either. Why do holdings differ at all? Nothing in the cost pulls them toward equal: the record is indifferent to levels. No law of how wealth distributes among people is derived.

How we know. A comparison reads one thing: the ratio of its two terms. The same ratio comes out at every amount, and the cost reads only the ratio, so a bond at balance costs nothing at any size.³ The claim is exactly that size alone isn't charged.

Next, and why: if the record doesn't charge a level, what does it charge? Your hunger at 12:15, and Step 2 says how much.

Step 2: An unmet need has an exact cost, and the cost is steepest far from balance

What reaches a person, against what they require, is a bond. A need met exactly sits at level and costs nothing. A need left unmet sits below level, and the cost climbs as it falls.

Say you require 4 units of food a day. (The units are a drawing.) The bond's number is what reaches you divided by what you require.

Check two rows with the recipe. For 1/4, add its flip 4 to get 17/4, halve that to get 17/8, and subtract 1 to get 9/8. For 3/4, add its flip 4/3 to get 25/12, halve that to get 25/24, and subtract 1 to get 1/24. Then 9/8 minus 1/4 is 7/8.

Read down the last column. In 24ths, going from 1 unit to 2 takes off 21, going from 2 to 3 takes off 5, and going from 3 to 4 takes off 1. It's the same unit each time, and each does less than the one before. The cost has no top: it keeps climbing as what reaches you shrinks toward nothing. Near balance, it's nearly flat.

That answers the second question from the cafeteria. The gap isn't charged. The hunger is: the cost reads how far what reaches you sits below what you require, and it's steepest where you're furthest from enough. At 12:15 you're at the steep end of this curve.

That last step isn't derived yet: which physical comparison a need is. Everything above is exact for a comparison you supply, with what reaches a person against what they require as its ratio. Still to derive: that a person's need is a relation on the record with that ratio. The preprint lists it among the derivations still being finished (Section 10, item 11),³ and What Is Money? states the same step for Bob's two meals.

How we know. The cost is the forced J from the section above, so the arithmetic is exact.

Next, and why: the cost is steepest far from balance. So when there's one unit and two people short, where does it go?

Step 3: Neediest first

Least cost puts the greater need first: the same relief removes more cost from a bond the further it is from balance.

One unit of food, and two people who each require 4. Ana has 1 and Ben has 3, so Ana's bond is at 1/4 and Ben's at 3/4. A neighbor has a unit to spare: her own need is met without it. She can give it to Ana, to Ben, or to nobody. Each gift is an act she and the receiver both write, so each is admissible.

The neighbor's own need is met with or without the unit, so nothing on her side changes from row to row, and it drops out. Nothing moves a bond between acts, so if nothing more is sent, what the record holds right after the gift is what it holds at every checkpoint after it. Comparing the totals compares the whole record.

The gift to Ana leaves 7/24. The gift to Ben leaves 27/24, barely under the 28/24 of giving the unit to nobody. The code permits the admissible act that leaves the least cost, so the gift to Ana is permitted. The gift to Ben is forbidden, and so is giving the unit to nobody. Ana's unit takes off 21/24, which is 7/8. Ben's takes off 1/24. That's the 21 times.

This isn't special to these numbers. For every pair of needs and every amount of relief, the same relief toward balance removes more cost from the bond further from balance. The cost curve is a bowl, steep far from balance and flat near it. Nobody chose the order. It's the shape of the cost.

A good that divides. Say the neighbor has two units. One each leaves Ana at 1/2 and Ben at 1, which costs 1/4 + 0 = 1/4 on the record. Both to Ana leaves Ana and Ben at 3/4 each, which costs 1/24 + 1/24 = 1/12. So both go to Ana. They end equal, at 3/4 each, because they require the same amount. The code isn't equalizing holdings: it puts each unit where it takes off the most cost. When a good divides, exactly one split is permitted, and it fills the greater need first. Equal needs share a good that divides without loss equally. What Is Justice? works that out for two kids and a pot of soup.

A good that loses its effect when split. One coat, two people equally cold. Cut in half, it warms nobody. When splitting wastes a good, it goes whole to one, and which one is free. The two ways of giving the coat leave the same cost, so the code permits both, and giving it to nobody leaves more. The ticket in What Is Justice? is the same tie.

The scope. All of this is among acts both people write. A gift changes the giver's relationship and the receiver's, so both write it. Neediest first decides where a gift goes. It never makes taking right. A taking from someone who has more is a push: it moves an amount across the relationship between taker and payer without the payer's write, and the code forbids it. Having more costs nothing.

What it doesn't settle. This is need against need. A promise, a debt or a deal is a different kind of claim, written by two people, and which of two such claims comes first isn't derived yet. What Is Justice? says the same.

How we know. The judgment is the code's own, and the arithmetic is the recipe. The general statement follows from J's strict convexity: the curve flattens toward balance, so the same relief removes less cost near it. Given the need bond of Step 2, nobody chose this order.⁴

Next, and why: the unit had to exist, and the neighbor had to hold it. What decides that?

Step 4: Amounts matter in exactly two ways

Amounts decide which acts are on the menu, and they fill the reserve that pays for repair. Poverty is too little for both.

The menu. Giving a unit takes a unit. The menu is the set of acts the participants' holdings can pay for, so nobody can hand over a unit they don't hold. That's the first way an amount matters. That the record's menu is the set of acts holdings can fund isn't derived yet (the preprint's Section 10, item 11).³

The reserve. A reserve is what a person can spend on keeping going. The code works one case of what a reserve does. It's the code's worked case, with its own numbers, and every number below is the case's own.

Each person has a bond of their own: a number for how heavy their load is, level at 1. In the case, each week doubles a person's own bond, and the person puts it back to 1 by paying 1/4 from their reserve. That's the week's upkeep, and 1/4 is what a bond at 2 costs: J(2) = 1/4. A person with no reserve can't pay. Their bond stays where the week left it, and the next week doubles it again.⁵ Two neighbors face the same weeks. Cal has a reserve of 1, and Dee has none.

Check Dee's third week. For 8, add its flip 1/8 to get 65/8, halve that to get 65/16, and subtract 1 to get 49/16.

The same weeks, the same rule and the same starting level. Cal is level every week, and Dee's cost climbs. In the case, the only difference is the reserve. How Should We Live? runs the same doubling further.

This is the code's worked case, not a measurement of any town. The doubling is the case's own rule, and so is the price of putting a bond back. What the case shows is the second way an amount matters: a reserve is what pays for repair. Without one, the strain stays where it was left, and in the case the next week adds to it. Poverty is having too little for both: too little to put an act on the menu, and too little in reserve to pay for repair.

How we know. The preprint puts amounts in two places in the judgment, the energy an act needs and the reserve that pays for repair (Sections 1 and 3).³ The case's arithmetic is the recipe applied week by week.

Next, and why: now the two columns. Why is someone short?

Step 5: Three ways to be short with no wrong needed

Strain no person chose is suffering. Three things leave a person short with no wrong needed: there isn't enough, what there is sits somewhere else, and the good can't be divided.

Why Does Evil Exist? draws the line. Nothing in the record is authorless: every change to a bond comes from something sent. A storm is something sent that no person chose, and its strain is suffering. A wrong is an act a person chose. Call the shortages that need no wrong the storm's column, and the ones that are a wrong the theft's column. Step 6 takes the second.

1. There isn't enough. Shortage is a physical fact, and no rule removes it. Take the code's worked case from Step 4 again, with its own numbers. Each week costs each person 1/4. A meal costs the giver 1/4 in work and gives the receiver 1/2. Alice has a meal to make, and Bob needs it.

In the first panel Alice has 2 and Bob has 1/4. If she feeds him, they end the week at 3/2 and 1/2, and both are above zero. If she doesn't, Bob ends at zero. Feeding leaves less cost on the record than doing nothing, so not feeding breaks the code. In the second panel Alice has 1/2. If she feeds him, she ends the week at zero. If she doesn't, Bob does. No act keeps both above zero. That's a shortage, and no person chose it: whoever ends at zero is short because there isn't enough, whatever anyone does. The code still judges each act by the cost it leaves. What it can't do is make more. A promise doesn't either: an undertaking doesn't create the missing reserve, food or work.⁶

The general version holds in the code's care model. Keeping a chosen group going through every checkpoint takes a starting budget strictly above the least cost any history can have. When the budget isn't above it, every lawful history has someone who misses a checkpoint, and covering the checkpoints with promises leaves that failure on the record.⁷

2. What there is sits somewhere else. Back to the cafeteria. The fridge at home is full, and the total in your house doesn't feed you at 12:15. Whether a person keeps going depends on the food on hand at that person. It has to reach you, and you have to be able to take it in, and those are separate steps. A pooled total can't tell. Add up the food in a town and you get one number, and it's the same whether the food is spread across every kitchen or sits in one warehouse. So no rule that reads only the total can say who ate. That's the first question from the cafeteria: you're hungry because the food isn't where you are.

3. The good can't be divided. One coat, two people equally cold: it goes whole to one, and either way is permitted (Step 3). That's an unequal outcome with no wrong in it. One is warm and one isn't, and nobody did anything the code forbids. The need that goes unmet is still charged. The code has no better act.

How we know. Strain no person chose reads the same on the cost as strain a person chose, because a bond's cost depends on its number and nothing else. The shortage numbers are the book's, and the tie is Step 3's.

Next, and why: the other column: shortage that is a wrong.

Step 6: Two ways to be short because someone did wrong

Someone takes, or someone leaves undone the help the code requires. A taking moves an amount across a relationship without the payer's write, so it's a push and the clauses forbid it. The judgment forbids the omission.

4. Someone takes. A taking changes what reaches you, and you didn't write it. Your own record of that bond, which only you write, still gives the old number, so it's false. That's harm: a false entry in someone else's own record. An act may move a bond only when both of its ends write on it, so the clauses exclude it, and no good it does somewhere else changes that. Consent is a hard condition, not a price.

This is where neediest first stops. It decides where a gift goes. It never makes taking right, whoever has more: every transfer posts at both ends of the relationship between taker and payer, so a taking without the payer's write is a push, forbidden like any other.

The one gap is a relationship's own repair reserve: the clauses don't yet read changes to it, so a taking from it passes them with no write. Whether consent read through the amounts catches it is being derived.⁸ Why Does Evil Exist? works through a taking from what pays for repair.

5. Someone leaves undone what the code requires. The code requires you to help wherever an act both of you write lowers the cost, and then doing nothing is forbidden. No promise is needed: What Do We Owe Each Other? works the case of a stranger on the third floor who is owed a grocery trip. Nothing beyond the requirement is permitted either. A more generous act leaves more cost, and it's forbidden too.

Nothing physical stops the omission. The code judges acts. It makes no one do anything, so the forbidden act is as available as the permitted one. That's how a person can be short while someone who can help the code's way doesn't.

Does the code require the kid at the next table to hand over the half sandwich? Yes. The kid hands it over and you take it, so you both write it. It costs the kid nothing they need, since they were throwing it away, and it takes cost off your hunger at the steep end of the curve. The act lowers the cost, so the code requires it, and the bin is forbidden.

A rising total can hide any of the five. In the small economies of What Is Money?, a total rises while one person's share falls, and two plans with the same totals differ in whether a person's reserve stays above zero. No rule that reads only totals can tell. Even lowering the record's total cost can load someone who wrote nothing, and the code forbids that without their write. Those are constructed examples. They show what a total can do, not what it always does. So a report of the economy's total can't say who is short.

How we know. The clauses are the preprint's Section 2, the judgment and "Requirement and freedom" are its Section 3, and "The stranger is owed" is in its Section 8.³

Next, and why: if the code requires help wherever an act both people write lowers the cost, what does that do to poverty?

Step 7: Where one person's spare holdings can meet another's need, the code's act meets it

On the menu holdings can fund, the code permits exactly the acts that leave love's state of the bonds both ends write. So where one person's spare holdings can pay for an act, written by both of them, that meets another's need, leaving the need unmet is a forbidden omission, not a fact of nature. Beyond what holdings can meet, poverty ends only as production turns material into what people can use.

Love's act is the act the code permits: the admissible act of least cost. Love's state is the cheapest state the bonds can reach. Meet in the Middle builds it from scratch. On the menu the participants' holdings can fund, the code permits exactly the acts that leave love's state of the bonds both of whose ends write, and every permitted history from true books is at love's state from the first step on and raises no one's burden after.³

Here's the smallest case. Bob requires 2 meals, and 1 reaches him. His bond is at 1/2 and costs 1/4. Alice has a meal to spare, and she and Bob both write the gift. Now 2 reach him against the 2 he requires: level, cost 0. Each end carries a bond's whole cost, so both burdens fall from 1/4 to 0, Alice's too, although she gave up a meal.⁹ Why Do We Need Each Other? works through how a strained bond costs each of its ends all of it.

That's the code's act: one step, and nobody's burden rises. Where one person's spare holdings can pay for it, a need left unmet is an act left undone, and Step 6 says what the code does with that. It isn't a fact of nature.

Where no one's holdings can cover a need, no gift can meet it. What changes that is production, which changes what people can do without creating material. In the small economy of What Is Money?, Alice turns one raw unit and one unit of effort into two ready meals. A raw unit holds two meals' worth of material, so the material is the same before and after: nothing was created. What changed is what Alice can do. She can eat now, and she couldn't before.

How we know. The code's act is the preprint's Section 9. It holds on the menu holdings can fund, which is the open step of Step 4.³ Production that conserves material while raising what people can do is proved in the book's small economy.⁹

Next: what's still open, then the whole trip in one breath.

What's still open

The code is stated in full. These derivations are still being finished. The preprint's Section 10 lists the first two.

• Which physical comparison a need is. This is the one step the answer needs. For any comparison you supply, with what reaches a person against what they require as its ratio, Steps 2 and 3 are exact. Still to derive: that a person's need is a relation on the record with that ratio (Section 10, item 11).
• The menu of acts. That the record's menu is the set of acts the participants' holdings can fund, and that each act's writes are read off the record (item 11). Steps 4 and 7 rest on it.
• Competing claims. Which of two claims written by two people, a promise and a debt, say, comes first, and how a claim gets its authority.
• Takings from a relationship's own repair reserve. The clauses don't yet read changes to it, so a taking from it passes them with no write. Whether consent read through the amounts catches it is being derived.
• What a real person's reserve counts. The reserve case in Step 4 is the code's worked case, with its own numbers. Which physical quantity a real person's reserve is isn't derived.

The whole trip, in one breath

Reality keeps a permanent record whose unit is a bond between two ends, priced by one forced cost that reads a ratio and never an amount. So a balanced bond costs nothing at any size, and having more costs nothing. What the record charges is need left unmet, a bond below level, and the cost climbs steeply the further a person sits from enough: 1 of 4 costs 9/8, and 3 of 4 costs 1/24. The cost curve is a bowl, so the same unit takes off 21 times as much from the first, and the code sends a gift to the greater need first, among acts both people write. It never makes taking right. Amounts matter in two ways: they set the menu of acts, and they fill the reserve that pays for repair. Five ways to be short sort into two columns. In the storm's column no wrong is needed: there isn't enough, it's somewhere else, or the good can't be divided. In the theft's column someone does wrong: they take, or they leave undone the help the code requires. A rising total can hide any of them. Where one person's spare holdings can meet another's need, the code's act meets it in one step and raises no one's burden, and the rest ends only as production turns material into what people can use.

So, the cafeteria. You're hungry because the food isn't where you are, and a full fridge at home doesn't feed you at 12:15. The gap between your lunch and the kid's isn't what the record charges. Your hunger is. And the half sandwich doesn't belong in the bin. Handed over with the kid's write and yours, it's help the code requires, and when two kids are short, the same curve says who gets it: the one further from enough.

That's how reality is built: a record that reads how far you are from enough and never how much you hold, a cost shaped like a bowl, and a code that never makes taking right. Nobody voted on the order. The unit goes to the hungrier one because of the shape of the curve.