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Cooperation: Three Ledgers, and One Flipped Table

BigCat · 2026-07 · Cross-Site Synthesis
"Why does cooperation exist?" has been answered seriously by at least four camps in this Hub, and they don't agree. Evolutionary biology says cooperation is genes looking after themselves. Game theory says it's an equilibrium forced out by repeated encounters. International relations says it's a fragile balance propped up by credible commitment.

The three answers sound wildly different, but underneath they perform the same move: they reduce apparently selfless altruism to a self-interest that balances the books—each just billing it in a different currency. Buddhism's bodhisattva path is the fourth answer, and it doesn't keep counting. It flips the table. This essay argues that the first three ledgers are secretly one ledger, that the fourth isn't on the table at all, and offers a checklist you can tick line by line the next time someone tells you "cooperation is really just self-interest in the end."

1. A question that backed Darwin into a corner

Skip the definitions for a moment and step into four rooms.

The first is a bat roost in South America. A vampire bat that fails to feed for one night starves—and a well-fed roost-mate will regurgitate blood to feed it, remembering who has fed it before. The second is the Western Front in 1915: entrenched soldiers deliberately fire wide at fixed hours and leave each other alone at lunch, on no one's orders. The third is the tightest years of the Cold War, when two states each able to erase the other from the map neither struck first. The fourth is Nālandā in the eighth century, where a monk takes a vow: to attain Buddhahood for the deliverance of all beings—and to seek nothing in return.

Set the four scenes side by side and you hit a question that once nearly overturned the theory of evolution. Darwin's logic was "survival of the fittest": the selfish individual should out-compete the one that takes a loss. So how did behavior that pays a cost to help others avoid being weeded out over billions of years? Worker bees don't breed, yet toil to raise another's offspring; a soldier throws himself on a grenade. The sheer existence of such acts is the deepest crack Darwin left behind.

Four camps have each patched that crack—and their patches are mutually incompatible. The point isn't who's right. It's that they aren't quite answering the same question, and that is exactly what this essay means to pry open.

2. Ledger one: billed to the genes

Biology's answer is the coldest: what looks like altruism is genes looking after themselves.

In 1964, W. D. Hamilton returned altruism to the genes with a single inequality:

rB > C

Here C is the reproductive cost to the altruist, B the reproductive benefit to the recipient, and r their relatedness—the probability that the recipient carries the very gene you carry. With full siblings and with your own children, r is 1/2; with cousins, 1/8. Whenever rB > C, a gene "for helping relatives" spreads into the next generation, because what it helps is a copy of itself. The geneticist Haldane's barroom quip—"I would lay down my life for two brothers or eight cousins"—is just the observation that 2×½ and 8×⅛ exactly balance your own single share. This doesn't mean animals do arithmetic; it means the genes that happen to help kin at just that ratio inevitably win over time. In the Hymenoptera, a peculiar genetics makes sisters related at r ≈ 0.75, higher than mother to daughter (0.5), so "forgo breeding and help mother raise more sisters" becomes the gene-level optimum—which is why eusociality evolved independently, again and again, in bees and ants. One line of algebra explains it.

The shift in viewpoint is the crux: the unit of selection drops from the organism to the gene, and the organism becomes a vehicle the gene builds to copy itself. Dawkins called this the "selfish gene"—but he insisted repeatedly that "selfish" is a metaphor for the gene, one realized precisely through genuine unselfishness at the level of the individual: maternal love, sibling devotion, the alarm call, are all genes looking after themselves. Beyond blood? In 1971 Robert Trivers added a second tier—reciprocal altruism: I help you today, betting you'll repay me later. As long as the two of you meet repeatedly, remember each other, and the cost of helping is less than the benefit received, a gene "for mutual aid" holds up. The blood-sharing vampire bat is the textbook case.

One more thing we'll need later. Dawkins borrowed Maynard Smith's evolutionarily stable strategy (ESS) to explain conflict: in the "Hawk-Dove" game, a population settles neither on all-out Hawks nor on all-yielding Doves, but on a mixed ratio—the point where no one can gain by unilaterally switching. Buried in it is a line worth keeping: evolution doesn't reach "best for the group"; it reaches the equilibrium where "no one can be exploited, so it holds." Don't ask what's best. Ask what's stable.

This ledger also carries an open controversy that has to be flagged. The "group selection" the gene's-eye view once thrashed has staged a comeback over the past two decades under the banner of "multilevel selection": whether an altruistic trait survives depends on which is larger, its within-group disadvantage or its between-group advantage. In 2010 Nowak, Tarnita, and E. O. Wilson published a Nature paper questioning the centrality of kin selection, drawing a rebuttal co-signed by well over a hundred evolutionary biologists; the dust hasn't settled. Note, though, that multilevel selection and the kin's-eye view are often mathematically inter-translatable—the same books, kept once "by group" and once "by gene"—so the fight is less about who's wrong than about which lens is more fundamental. We'll return to this in Section 5.

Sources → The full algebra of Hamilton's rule, naked mole-rats at r=0.81, the measured 3:1 ant investment ratio, and the Wilson-triggered war: Meta-Knowledge · Evolutionary Biology (Day 4) · the gene's-eye view, the cheater game of reciprocal altruism, ESS, and the naturalistic fallacy laid out in full: Deep Reading · The Selfish Gene (Read 2) · how kin cues get hijacked by "fictive kin" (shared language, a common flag): Mental Models · Evolutionary Psychology (Day 53) · kin detection and cheater detection as distinct mental modules: Psychology · Evolutionary Psychology (Day 32)

3. Ledger two: billed to repetition

Game theory swaps in a different currency. It says nothing about genes and asks one thing: will this game be played again?

Start from the famous crack—the Prisoner's Dilemma. Two players each choose cooperate or defect; whatever the other does, defection is the individually dominant move—yet mutual defection is worse for both than mutual cooperation. That is the Nash equilibrium's most subversive lesson: stable does not mean optimal. Mutual defection is the sole equilibrium and it is Pareto-inferior to mutual cooperation. Markets, teams, arms races can sit locked for years in a state everyone dislikes and no one dares leave first.

But put the same game in the dimension of time and the conclusion flips. The Folk Theorem proves that as long as the game repeats often enough and the players care enough about the future, almost any cooperative outcome above the minimum can be sustained as an equilibrium—even when the one-shot game's only equilibrium is defection. The decisive variable is the "shadow of the future": w, the probability of meeting again. When w is large enough, cooperation beats defection, because the short-run sweetness of defecting buys you the other side's permanent retaliation thereafter. This is why anonymous one-off deals breed fraud while long-lived communities sustain honesty on their own.

Around 1980 the political scientist Robert Axelrod ran a computer tournament of the repeated Prisoner's Dilemma, inviting game theorists worldwide to submit strategies. The winner was no intricate algorithm but a few lines submitted by the mathematician Anatol Rapoport: Tit-for-Tat—cooperate on move one, then copy the opponent's last move. It won twice, on four principles: be nice (never defect first), be retaliatory (answer defection at once), be forgiving (resume cooperation the moment the opponent does), and be clear (rules simple enough to read at a glance). It needs neither a nice opponent nor heavy computation; cooperation grows from structural incentive alone. Its one weakness is noise: a single misread can trap two Tit-for-Tat players in endless mutual retaliation—hence "Generous Tit-for-Tat," which cooperates with some probability even after a defection, building in a margin for error.

Cooperation can also break free of the circle of acquaintances. Indirect reciprocity doesn't require that you and I meet again; it rides on reputation: every act updates your reputation score, and bystanders decide from it whether to help you. Its condition is just as crisp—the probability q that others know your reputation must exceed cost-over-benefit (q > c/b). The more information flows, the better cooperation holds. This is the logic under rating systems: a stranger driving your ride-hail car has almost no incentive to cheat, because the rating wires every trip into a long-run reputation. And to sustain cooperation you need a dedicated detector—cognitive science finds the brain has a distinct cheater-detection module: nearly everyone flunks an abstract logic puzzle, yet accuracy jumps once it's recast as "who broke the deal, who's the cheat." Repetition, memory, reputation, catching cheats—four parts of this ledger.

None of this stays in the lab. "Political capital" inside an organization is its human edition: every time you unblock someone, every time you don't grab the credit, you deposit into a relationship account; when you need to push something across teams, you withdraw the sum of past deposits. Some distill the rule straight into Axelrod's advice—"don't be envious; don't be the first to defect; reciprocate both cooperation and defection; don't be too clever"—but it comes with a hard constraint: with someone who only withdraws and never deposits, cut off supply decisively. Don't be the sucker.

Sources → The Prisoner's Dilemma, Nash equilibrium, repeated games, and the four Tit-for-Tat principles, worked through point by point: Mental Models · Game & Cooperation (Day 28) · game-theory foundations, backward induction, credible commitment: Mental Models · Strategy (Day 4) · the Folk Theorem, Hawk-Dove ESS, mechanism design and the second-price auction: Meta-Knowledge · Game Theory (Day 11) · direct/indirect reciprocity, the q>c/b reputation condition, the Maghribi traders: Meta-Knowledge · The Evolution of Trust & Cooperation (Day 58) · political capital as a repeated game, Tit-for-Tat in organizations: Leadership · Office Politics (Day 6)

4. Ledger three: billed to credible commitment

Pull the camera out to relations between states and the currency changes again: credible commitment.

The ground of international politics is anarchy—no world police standing above the states. Domestic law is backed by police, courts, prisons; the international arena has none. So cooperation between states is, by birth, a Prisoner's Dilemma with no third-party enforcer. Worse, there is the security dilemma: even when both sides only want to protect themselves, one side's well-meaning defensive move reads in the other's eyes as an offensive signal, and the tension ratchets—no component wants the machine to blow, yet the machine slides toward the blast. That is the mechanism inside the Thucydides Trap.

Hobbes offered a solution back in the seventeenth century, and it is this dilemma's political-philosophy edition. Having lived through the English Civil War with order collapsing before his eyes, he argued: absent a common power to hold all in awe, people fall back into "the war of all against all"; the rational individual can only strike a covenant, ceding rights to an absolute sovereign—the Leviathan—to enforce peace. In today's terms: lacking a credible enforcement mechanism, rational self-interested individuals sink into a sub-optimal equilibrium of mutual defection; the Leviathan is the external enforcer that turns cooperation into a stable strategy. It is isomorphic to modern mechanism design and to blockchain's "consensus without trust"—rules and punishment substituted for reliance on goodwill.

But over states there is no Leviathan, so they must manufacture credible commitment themselves. Nuclear deterrence pushes the point to its limit. The strategist Bernard Brodie saw it in 1946: from now on the military's chief purpose is to avert wars, not win them. Deterrence rests not on "winning" but on convincing the adversary that "striking first carries unbearable cost"—which in the Cold War hardened into Mutual Assured Destruction: each side keeps a second-strike capability that can't be knocked out, so a first strike is suicide. Here lies a counterintuitive credibility paradox: at the actual moment of being hit, retaliation has no payoff left (everyone's already dead), so for deterrence to work you must make the adversary believe you'll carry out a retaliation with no rational payoff. The way to sustain it is precisely to reduce your own ability to renege—automate the response, pre-authorize it, publicly tie your hands. Cooperation (restraint) here is bought by cutting away your own options.

Rules do run without an enforcer, just on weaker machinery: reciprocity (I treat your POWs well only if you treat mine well), reputation, after-the-fact accountability. Far weaker than domestic enforcement, yet stacked together they suffice to make "keeping the rules" the rational choice most of the time—the force of a rule lies not in "cannot be broken" but in "breaking it costs." The same machine, seen in civilian life, is institutional trust: you get into a stranger's car not because you trust the person but because you trust the license, the insurance, the platform, the law. Money is its purest form—a slip of paper buys grain for one reason only, that "everyone believes everyone else will also accept it." Institutions outsource interpersonal trust to impersonal rules, and trust is scaled, for the first time, to millions of strangers. An earlier prototype: the eleventh-century Maghribi Jewish traders of the Mediterranean, who leaned almost not at all on law but on a tightly-informed coalition—an agent who cheated saw the news race across the network and was blacklisted by all. Research in institutional economics finds this pure-reputation mechanism no weaker in its grip than a formal court. The information network is itself the enforcer of the contract.

Sources → Just-war theory, nuclear deterrence and MAD, the credibility paradox, and the "no world police" enforcement problem of the laws of war: Civics & Geopolitics · The Rules of War and Peace (Day 13) · the Thucydides Trap, the security dilemma, complex interdependence: Civics & Geopolitics · Great-Power Rivalry (Day 10) · Hobbes's covenant as "the political-philosophy edition of the Prisoner's Dilemma," isomorphic to mechanism design: Philosophy · The Individual and Society (Day 15) · institutional trust, money as trust, the collapse conditions of cooperation: Meta-Knowledge · The Evolution of Trust & Cooperation (Day 58) · trust as a "costly signal": why volunteering the truth against your own interest builds trust fastest: Sales · Trust Is the Only Currency (Day 2)

5. The shared skeleton: the three ledgers are one

Set the three ledgers side by side and it's easy to see only the differences: one bills genes, one bills repetition, one bills commitment. But the differences are surface. Underneath is one skeleton, and it's worth making explicit—this is where the essay bears weight.

First, all three are structurally the same Prisoner's Dilemma. Kin selection, Hawk-Dove, the arms race, the tragedy of the commons, the security dilemma—strip the shells and they're that same payoff matrix: individual rationality shoves everyone toward a collective second-best, unless something re-ties the individual's fate to the collective's. The reason "why does cooperation exist?" is a live question in three disciplines at once is that all three face the same structural problem.

Second, the device each uses to break the dilemma is the same shape: convert the short-run gain from defecting into a long-run cost that reaches across the future. Only the hook doing the converting differs. Biology uses relatedness r: it routes the benefit, along the shared genes, back to a copy of "future you." Game theory uses the re-meeting probability w: it routes the benefit, along repeated interaction, back to the literal future you. International relations uses credible commitment: it makes "betrayal is certain to be punished" believable enough that the future cost presses down now. r, w, and credible commitment are one variable wearing three faces in three currencies—each answering "how long from now, and in what form, does the bill for betrayal come back to you?" That's why the controversy at the end of Section 2 takes the form it does: kin selection and multilevel selection are mathematically inter-translatable because they are two ways of keeping the same books.

This is no strained analogy but a real link you can cash in—which is exactly the cost that cross-disciplinary connection saves. A conclusion earned with sweat in one field can be carried straight into another. The variable w is written directly into BitTorrent's protocol: you upload to me and only then do I let you download, hard-coding Tit-for-Tat into the rules to suppress free-riding. Reputation's q > c/b is engineered into Uber's and Airbnb's two-way ratings, turning "a stranger" into "a party with a history." Blockchain hard-wires "cheat = permanently lose your stake" through staking-and-slashing, dragging anonymous nodes into a repeated game. And Hobbes's move grew into the entire discipline of mechanism design—the second-price auction makes "bid honestly" a dominant strategy precisely by resetting the payoff structure so that truth-telling pays best. A theorem proven in one room need not be re-proven in the next.

There's something equally valuable here: this ledger also tells you exactly how cooperation dies. Public-goods experiments find again and again that without punishment, cooperation decays toward zero; and collapse is often not a linear slide but a phase-transition avalanche—once the free-rider fraction crosses a threshold, the system flips all at once. The triggers are just the load-bearing variables in reverse: the group grows too large (individual impact diluted, anonymity rising), the shadow of the future shortens (the endgame nears), information turns noisy (a misread ignites a chain of retaliation), punishment goes missing. The "endgame effect" is especially insidious: merely knowing "this game will end" lets backward induction poison cooperation from the last round all the way back to the first. The lever for maintaining cooperation, then, is never a moral sermon—it's adjusting these parameters: lengthen the future, shrink the visible unit, make contribution legible, make free-riding cost.

6. Flipping the table: the fourth room isn't on this table

Now back to Nālandā. All three ledgers do the same thing—they reduce altruism to a self-interest that balances the books. The bodhisattva path doesn't keep counting. It flips the table.

The core judgment Śāntideva sets down in the eighth-century Bodhicaryāvatāra is this: all the joy in the world arises from wishing others well; all the suffering in the world arises from wishing only oneself well. Its practice is called "exchanging self and other"—trading places, seeing another's pain as your own; and the classic definition of bodhicitta is "the aspiration, for the sake of others, to full awakening." The crux is that it seeks nothing in return. The whole ingenuity of the first three ledgers rests on there being a bounded self as the beneficiary to whom the benefit ultimately flows back—whether that beneficiary is your genes, your future self, or your state. The bodhisattva path pulls out exactly this footing: to grasp at an independent "self" is itself the root of suffering; altruism is not an investment that eventually pays, but the path by which self-grasping dissolves and awakening is realized. The hard boundary between "self-benefit" and "other-benefit" melts—not "altruism is really self-interest," but a move that voids the self/other axis on which the whole bookkeeping runs. With no bounded self to be the beneficiary, who is the recipient in rB > C? Who is the "me" in "you'll repay this favor another day"? The books can't be kept.

Here one must be especially careful not to let the convergence come cheap. There is a tempting bridge: brain-imaging studies of compassion meditation (Tania Singer's and Richard Davidson's observations of long-term meditators) show that in seasoned practitioners, another's suffering activates not the pain network but positive-affect networks—"altruism yields joy" looks, at the neural level, as if confirmed. But to read this as "see, altruism really does make you happier, so it pays after all" is precisely to haul back in the table you just flipped. The bodhisattva's "seeking nothing in return" is a soteriological claim—its aim is to end suffering by dissolving self-grasping, not to describe a value-neutral mechanism; explaining it by "altruism makes you happy" translates the fourth room into the language of the first ledger, and the translation erases its entire point. The source page is careful here: it says empathy circuits are plastic and that altruism training can reshape the relevant brain regions—but it does not say "so the Buddha has been scientifically confirmed." That restraint has to be carried over intact.

Between the table and the ledger there is, in fact, an intriguing halfway state worth naming: Mozi's "impartial care" (jian ai). It asks you to weight another's welfare equally with your own in the moral calculus. In game-theoretic terms this is "utility interdependence"—once every player writes others' payoffs into their own utility function, the Prisoner's Dilemma dissolves on the spot. It looks a great deal like today's Effective Altruism and Peter Singer's "expanding circle." But note: impartial care is still keeping books; it has merely rewritten the weight coefficients on each person in the ledger. It hasn't flipped the table—only rearranged it. What flips the table is no-self: it changes not the weights but the premise of who the account holder is.

Sources → Śāntideva's Bodhicaryāvatāra, exchanging self and other, the classic "for the sake of others" definition of bodhicitta, and the brain-imaging corroboration of compassion meditation: Buddhism · The Bodhisattva Path (Day 11) · how "self-benefit and other-benefit are not two" dissolves the hard boundary between individual and other, set beside Hobbes and Durkheim: Philosophy · The Individual and Society (Day 15) · Mozi's impartial care as "utility interdependence," another way the Prisoner's Dilemma dissolves: Philosophy · Ethics and Virtue (Day 5)

7. The fracture: a checklist you can tick line by line

Taken this far, it turns into a handy tool. The next time you hear "cooperation is really just self-interest," or, the other way round, hear someone invoke evolution or game theory to bless a practice, run the five questions below line by line to place the claim in the right room—or decide it doesn't belong on this table at all.

1. Which currency is it billing in? Whom does the benefit ultimately flow back to—to the genes (is it talking relatedness, fictive kin, blood?), that's biology's ledger; to your own future self (repetition, reputation, meeting again?), that's game theory's; propped up by third-party-visible reputation or tied hands (enforcement, commitment, institutions?), that's the ledger of international relations and institutions. The three currencies don't mix: to call "the team is like a family" (borrowing fictive-kin r) a matter of "because we signed a contract" (resting on credible commitment) is to cross the books.

2. Is there a "shadow of the future" at all? All three ledgers depend on the cost of betrayal coming back to you later. So ask first: is this relationship repeated, or one-off, anonymous, near its endgame? If the shadow of the future is short—an endgame effect, a one-shot deal, an identity that can be reset at will—then what theory predicts is not cooperation but defection; don't expect morality to plug the gap. Conversely, to shore up cooperation the most effective lever is not slogans but lengthening that shadow: turn a one-off into an ongoing relationship, make reputation visible.

3. Does the claim need a bounded "self" as beneficiary? This is the watershed between the three ledgers and the fourth room. If it needs a beneficiary—genes, future self, or state—it's keeping books, belongs to one of the first three, and you can classify it with questions 1 and 2. If it doesn't, or even presupposes the dissolution of the self (the bodhisattva's seeking nothing in return), then it has flipped the table—don't jam it into "it's really self-interest," which isn't its language.

4. Translate it into "it's really a shrewd self-interest"—does the claim collapse? This operationalizes question 3. Rewrite the altruistic claim as "doing this benefits you in the long run": if it still holds afterward, with nothing lost, it was a self-interest ledger all along, and the translation is lossless (political capital, reciprocity, deterrence all pass). If the rewrite happens to erase its entire edge (reading the bodhisattva path as "altruism makes you happy, so it's worth it"), then you're stealing it with a cheap convergence—stop.

5. Is it describing "what is," or prescribing "what you ought to do"? The first three ledgers are all descriptive—they say how cooperation in fact arises, holds, and collapses. Not one of them tells you "therefore you ought to cooperate." If someone leaps from rB > C to "so favoring kin is right," or from Tit-for-Tat to "so you should return blow for blow," a value premise is missing in between—this is the naturalistic fallacy, and no ledger, however rigorous, can conjure an "ought." Reading "is" as "ought" is this table's most common abuse.

Why does cooperation exist? — the same Prisoner's Dilemma The device that breaks it is one shape: turn the short-run gain from defecting into a cost across the future Biology currency: relatedness r benefit flows to: gene copies rB > C · reciprocity · ESS Game theory currency: re-meeting prob. w benefit flows to: future self tit-for-tat · reputation q>c/b Int'l relations / institutions currency: credible commitment flows to: the hand-tied state Leviathan · MAD · inst. trust Three ledgers, one book: altruism = self-interest that balances, only the currency differs Cashable: BitTorrent hard-codes tit-for-tat, platforms engineer reputation, mechanism design descends from Hobbes Flipping the table: the fourth room isn't on this table Bodhisattva path · seeks nothing in return — not altruism reduced to self-interest, but the "self" beneficiary dissolved Beware cheap convergence: "altruism makes you happy, so it pays" = hauling the flipped table back in Five-question checklist (tick each) 1. Which currency? r / w / credible commitment — don't cross the books 2. Any "shadow of the future"? Short shadow → theory predicts defection, not cooperation 3. Does it need a bounded "self" beneficiary? No → it flipped the table; don't jam it in 4. Translate to "a shrewd self-interest" — collapses? → you're stealing it with cheap convergence 5. "Is" or "ought"? From rB>C to "favor kin" = the naturalistic fallacy reports a currency & number → real ledger, cashable mechanism clear, no number → metaphor / model  neither counts nor bills → flipped table, off the chart Syn 3 · Cooperation · BigCat's Learning Hub

8. When the account can be kept, and when not to keep it

After the teardown you owe a usage, or this essay is just another kind of rhetoric. Roughly three tiers.

When it reports a currency and a number, treat it as a real ledger and cash it freely. As long as a cooperation claim can name whether it's billing r, w, or credible commitment, and those quantities can be estimated in the concrete case—the frequency of repetition, the cost of exit, the probability that reputation is seen—it's a real account. The virtue of a real account is portability: you can write Tit-for-Tat into a protocol as BitTorrent does, engineer reputation as platforms do, set "truth-telling" as the dominant strategy as mechanism design does. What's proven in one field is used, as-is, in another.

When it names a clear mechanism but reports no number, treat it as a useful model, not a verdict. "The team goes all-in because it's like a family" names a mechanism—it borrows the kin circuit, synthesizing a "fictive-kin" r out of shared experience; but that r can't be quantified, and you can't report "this team's relatedness is 0.3." This tier is a good model: it reminds you what the loyalty is borrowing, and warns you of its dark side (cliques, nepotism, being hijacked by "we're all family" talk). Use it to see the structure, not to pass the sentence.

When it neither reports a number nor rests on any bookkeeping, it isn't on this table. The bodhisattva path is this tier—to force it into "it's really self-interest" is a category error, rhetoric or cheap convergence. The fastest way to spot it is question 4: does translating it into "a shrewd self-interest" erase it? If it does, what you face isn't an account kept in some unusual notation but a stance that refuses to keep accounts at all.

End on the line most easily stepped over. The first three ledgers speak, from beginning to end, of how cooperation arises—not of whether you ought to cooperate. The distinction isn't pedantry. At the close of The Selfish Gene Dawkins wrote the often-quoted line—"we, alone on earth, can rebel against the tyranny of the selfish replicators": the genes gave us brains, and brains can understand, foresee, and choose generosity; contraception, adoption, giving one's life for a stranger are all disobediences of the genes' "instructions." This theory describes how evolution works; it never legislates how we should live. However cleanly you keep the three ledgers, they won't add up to an "ought"—that step the bookkeeper has to take alone.