A New Definition of Right and Wrong Through Entropy

Most of what we used to call right was really a matter of conformity.

In mathematics, an answer is right if it conforms to known axioms and rules of calculation. In physics, a conclusion is right if it agrees with established theory and experiment. A person's conduct is usually called right when it conforms to the laws, morals, customs and role expectations of the time.

Under this system, right and wrong measure degree of fit. The closer an action is to the accepted standard, the more correct it appears. The farther it departs, the more likely it is to be judged wrong.

This definition once worked very well. Rules compress experience that humanity acquired at great cost, so each person does not have to repeat every failure from the beginning. But the limit is becoming harder to ignore. A norm can address the problems that existed when the norm arose. It cannot exhaust the possibilities that come later.

When technology, social structure and human relationships change quickly, we repeatedly face actions for which no ready answer exists. Old rules may also conflict. What is right within one tradition may be wrong within another. What counted as responsibility in one era may become an obstruction in the next.

The new era therefore needs more than additional rules. It needs a higher principle by which the rules themselves can be judged.

I want to propose one:

A decision is wrong if it pushes the system it affects toward greater entropy. It is right if it pushes that system toward lower entropy.

The key is no longer the similarity between an action and an inherited norm. It is the direction in which the action moves a local system relative to the path that system would otherwise have taken.

Entropy reduction here is a marginal idea. It does not require entropy after the action to be lower than entropy before it. It compares two trajectories, one in which the action is taken and another in which it is not. If acting leaves the local system with less entropy than it would otherwise have reached, the action points toward entropy reduction. A right decision is not a guarantee of a right outcome. It is the choice that, given the information available at the time, is more likely to produce this local reduction.

What do I mean by entropy?

I do not mean thermodynamic entropy in a simple literal sense, nor do I mean visible mess. A room full of scattered books may look untidy while remaining stable and useful. A perfectly uniform organization may look orderly while fear has filled it with invisible disorder because no one dares to tell the truth.

Information theory gives us a direct way to express the difference. Let X be the complete state of a system, and let Y = g(X) be the conduct or order visible from outside. Since Y is only a surface projection of X:

H(X) = H(Y) + H(X | Y)

Forcing everyone to behave alike may reduce the visible H(Y) while increasing hidden conflict, uncertainty and fragility in H(X | Y). Stronger visible order therefore does not imply a reduction in effective entropy:

greater visible order does not imply lower S_eff

Entropy reduction does not mean making a system neater, more uniform or easier to control. A system with a real capacity to reduce entropy may retain considerable difference, freedom and change at the surface, because those differences provide information, feedback and the ability to adapt.

By entropy I mean effective entropy within a system: avoidable uncertainty, functional mismatch, irreversible damage, and disorder transferred to other people, other places or the future.

A simplified definition is:

S_eff(X) = alpha U(X) + beta F(X) + gamma I(X) + delta E(X)

Here:

U(X) is avoidable uncertainty within the system.

F(X) is functional mismatch among its parts.

I(X) is the irreversibility of damage, which can also be understood as the cost of recovery.

E(X) is disorder exported beyond the system boundary, meaning externalities.

alpha, beta, gamma and delta are weights chosen for the problem at hand.

Uncertainty can be represented with information entropy. If a system may occupy n states and, given current information, we assign probability p_i to state i, then:

H(X | I) = - sum from i = 1 to n of p_i ln p_i

Let H_min(X) be the background uncertainty that cannot be removed under present conditions. The avoidable part is:

U(X | I) = max{0, H(X | I) - H_min(X)}

The quantity that matters is not everything we do not know. It is the uncertainty that better information, cooperation or design could have reduced, but that the actor needlessly increased.

I am not claiming that a single physical equation has proved every moral phenomenon. I am giving entropy increase and reduction an operational definition that can be debated, challenged and revised. S_eff is an effective quantity obtained by projecting a local system onto the variables relevant to the decision. Its mathematical structure begins by defining the local system, then comparing the trajectories created by different choices.

For an action a, let a_0 be the control case in which the action is not taken. After time T, its expected entropy change can first be written as:

Delta S_eff(a; a_0, T) = E[S_eff(X_T^a) - S_eff(X_T^a0) | I_0]

X is the state of the selected local system. Costs exported beyond its boundary are brought back through the externality term. This definition compares two future trajectories, not merely the state before and after an action. The following three conditions can therefore all be true:

E[S_eff(X_T^a) - S_eff(X_0)] > 0

E[S_eff(X_T^a0) - S_eff(X_0)] > 0

Delta S_eff(a; a_0, T) < 0

The first two say that entropy may end up higher than it is now whether we act or do nothing. The third says that entropy after the action is still lower than the level the default path would have reached. That third, marginal sense is the heart of entropy reduction in this new account of right and wrong.

If an action keeps producing effects along the way, the whole time path must be included:

Delta S(a; a_0) = E[integral from 0 to T of w(t)(S_eff(X_t^a) - S_eff(X_t^a0)) dt | I_0]

T is the period under consideration. w(t) weights different moments. I_0 is the information available when the decision was made.

The simplest right and wrong function is then:

R(a) = - Delta S(a; a_0)

If R(a) > 0, the decision is right.

If R(a) < 0, the decision is wrong.

If R(a) = 0, the evidence is insufficient or the decision is neutral at the chosen scale.

In real life, every feasible option may involve loss. Right then means choosing the option with the smallest marginal entropy increase, or the greatest local contribution to entropy reduction:

a* = arg min over a in A of Delta S(a)

This is why a correct decision in the real world may look imperfect and may still end in disorder and loss. It is correct not because it guaranteed a world without entropy increase, but because it reduced a larger disorder that would otherwise have occurred.

Right and wrong become judgments about marginal direction, not obedience to a norm

This view does not begin by asking, "What did people do before?" It asks, "Compared with not doing this, does my action reduce disorder, or does it accelerate, postpone or relocate it?"

A person may lie to escape an immediate crisis. The tension falls for the moment, but the future costs of trust, verification and repair all rise. Entropy has not been reduced. It has been postponed.

A company may squeeze employees, waste resources or manipulate data to produce an attractive quarterly report. It may reduce uncertainty in one financial metric while increasing organizational fragility, employee turnover, loss of trust and external cost. It has not created order. It has created an entropy-increasing system hidden by the report.

A manager may silence everyone until visible conflict disappears. The system then loses its ability to find errors and correct itself. That is not entropy reduction. It trades visible neatness for invisible fragility.

Some actions, by contrast, look disorderly in the short term. Discussion reveals disagreement. Creation breaks old forms. Experiments fail. Admitting a problem interrupts the peace. Yet if these actions improve information, adaptability and self-repair, they may reduce entropy over a longer horizon.

Entropy reduction is not the elimination of change, nor is it the reduction of the world to sameness. Real entropy reduction allows a system to retain difference, choice and freedom while achieving better coordination, less useless friction and a stronger ability to recover.

Local entropy reduction, however, cannot become an excuse to draw the system boundary wherever it is convenient. Living and social systems use energy, information and cooperation to build local structure. If one local system maintains itself only by exporting greater entropy to other people, the environment or the future, its achievement is counterfeit. The local system is where the action happens. It is not where responsibility ends.

Four questions must come first

"Entropy reduction is right" sounds simple. Applying it to the world requires at least four answers.

First, where is the system boundary?

If I throw my rubbish into someone else's room, my room becomes cleaner, but no genuine entropy reduction has occurred. When we draw the boundary around ourselves alone, entropy transfer can easily masquerade as reduction.

Second, what is the time horizon?

Today's convenience may become tomorrow's heavy debt. Avoiding conflict now may accumulate a larger conflict later. Different horizons may yield different conclusions, so any claim about entropy change must state its period.

Third, what is the counterfactual?

We cannot ask only whether an action has costs. We must also ask what happens if it is not taken. In disaster, illness and crisis, even the best choice may involve loss. Right and wrong cannot be judged apart from the feasible alternatives.

Fourth, are we judging before or after the event?

A decision may be reasonable on all information available at the time, then produce a bad result because of an unforeseeable event. If we judge decisions by luck alone, we mistake rationality for gambling.

Before the event, we should examine the expected marginal entropy change relative to the default path. After the event, we should examine the entropy change that actually occurred. The first judges whether the decision pointed toward entropy reduction at the time. The second tests and revises our model of the world. One bad outcome does not automatically make a reasonable ex ante decision wrong. We should reassess it only when the result shows that the actor ignored information that was already obtainable. Direction and guarantee must remain separate.

This framework does not end value disputes. It makes them visible

The definition of effective entropy plainly contains value choices. Where should the boundary be drawn? How long is long term? How should uncertainty, mismatch, irreversible damage and externalities be weighted?

Writing an equation does not make these questions disappear. That is precisely the point. The framework refuses to disguise a value judgment as a self-evident rule. It forces the boundary, horizon, weights and costs onto the table.

Older accounts of right and wrong often conceal these weights inside tradition and then present tradition as the only answer. An entropy account does not guarantee agreement. It does make the location of disagreement easier to see.

Why call this a deeper mathematical definition?

For me, the central purpose of this view is to pass through the surface names supplied by sociology, ethics and historical custom, then return to a more basic question: which system trajectory did an action change?

Once the system boundary Omega, time horizon T, local state X, control action a_0 and information I_0 are fixed, the form of the judgment can be compressed into a sign:

sgn R(a) = - sgn E[S_eff(X_T^a) - S_eff(X_T^a0) | I_0]

If the action makes effective entropy lower than the counterfactual path, R is positive. If it makes it higher, R is negative.

Ethics, law and custom can then be understood as interfaces that human societies developed to reduce local entropy. Do not deceive, because deception raises verification costs across an information system. Keep promises, because trust lowers uncertainty in cooperation. Respect autonomy, because a person deprived of information, choice and feedback cannot function as a healthy decision node within a system.

Old norms do not disappear

This definition does not require us to discard every inherited rule. Many reliable norms are themselves entropy-reducing solutions distilled from repeated historical episodes of entropy increase.

Their value, however, no longer comes from the bare fact that they are norms. It comes from the fact that they reduced entropy under comparable conditions. When the environment changes, the boundary changes, or the old rule begins producing greater entropy, we have reason to revise it.

A norm moves from final judge to historical prior.

From "Did I conform?" to "Which trajectory did I advance?"

Older accounts make it easy to treat responsibility as procedural compliance. If the steps, role and cited rule were correct, the outcome can appear to belong to someone else.

The entropy definition moves attention from "Did I conform?" to "Compared with another possibility, where did I push the system?"

It is a dynamic view of right and wrong. It does not demand that the world provide every answer in advance. It asks the actor to observe feedback, revise the model, widen the boundary and remain alert to costs pushed out of sight.

It is also harder to fake. A person can quote the right words, occupy the right role and follow the right procedure while still increasing uncertainty, division, injury and consequences that no one can repair. Procedural correctness does not prove that the action points in the right direction. By the same token, one unlucky result does not automatically invalidate a decision that pointed toward entropy reduction on the information then available.

My definition for the new era can finally be condensed into two sentences:

Right does not mean resembling what was right in the past. It means leaving a local system with less disorder, mismatch and irreversible damage than its original trajectory would have produced.

Wrong does not mean departing from an old answer. It means accelerating avoidable entropy increase, or turning today's convenience into entropy that other people, other systems or the future must bear.

The old idea of correctness was conformity to an answer.

The new idea is to keep choosing the direction of local entropy reduction.