Mental Model: Inversion

The technique of 'inversion' is the act of turning a problem around in reverse in order to discover insights that can’t be gained in other ways.

The great Charlie Munger describes it like this:

The way complex adaptive systems work and the way mental constructs work, problems frequently get easier and I would even say usually are easier to solve if you turn around in reverse.

In other words if you want to help India, the question you should ask is not “how can I help India?”, you think “what’s doing the worst damage in India? What would automatically do the worst damage and how do I avoid it?” You’d think they are logically the same thing, but they’re not.

Those of you who have mastered algebra know that inversion frequently will solve problems which nothing else will solve. And in life, unless you’re more gifted than Einstein, inversion will help you solve problems that you can’t solve in other ways.*

The following is a long example of inversion in practice. The paper was written by Lon Fuller, the legal philosopher. On the surface, this is a story about failure, however, this is not true. It's story about avoiding failure, and in turn, creating a better legal system. 

8 Ways to Fail to Make Law

Rex came to the throne filled with the zeal of a reformer. He considered that the greatest failure of his predecessors had been in the field of law. For generations the legal system had known nothing like a basic reform. Procedures of trial were cumbersome, the rules of law spoke in the archaic tongue of another age, justice was expensive, the judges were slovenly and sometimes corrupt. Rex was resolved to remedy all this and to make his name in history as a great lawgiver. It was his unhappy fate to fail in this ambition. Indeed, he failed spectacularly, since not only did he not succeed in introducing the needed reforms, but he never even succeeded in creating any law at all, good or bad. 

His first official act was, however; dramatic and propitious. Since he needed a clean slate on which to write, he announced to his subjects the immediate repeal of all existing law, of whatever kind. He then set about drafting a new code. Unfortunately, trained as a lonely prince, his education had been very defective. In particular he found himself incapable of making even the simplest generalisations. Though not lacking in confidence when it came to deciding specific controversies, the effort to give articulate reasons for any conclusion strained his capacities to the breaking point.

Becoming aware of his limitations. Rex gave up the project of a code and announced to his subjects that henceforth he would act as a judge in any disputes that might arise among them. In this way under the stimulus of a variety of cases he hoped that his latent powers of generalisation might develop, proceeding case by case, he would gradually work out a system of rules that could be incorporated in a code. Unfortunately the defects in his education were more deep-seated than he had supposed. The venture failed completely. After he had handed down literally hundreds of decisions neither he nor his subjects could detect in those decisions any pattern whatsoever. Such tentatives toward generalisation as were to be found in his opinions only compounded the confusion, for they gave false leads to his subjects and threw his own meager powers of judgment off balance in the decision of later cases.

After this fiasco Rex realised it was necessary to take a fresh start. His first move was to subscribe to a course of lessons in generalisation. With his intellectual powers thus fortified, he resumed the project of a code and, after many hours of solitary labor, succeeded in preparing a fairly lengthy document. He was still not confident, however, that he had fully overcome his previous defects. Accordingly, he announced to his subjects that he had written out a code and would henceforth be governed by it in deciding cases, but that for an indefinite future the contents of the code would remain an official state secret, known only to him and his scrivener. To Rex’s surprise this sensible plan was deeply resented by his subjects. They declared it was very unpleasant to have one's case decided by rules when there was no way of knowing what those rules were. Stunned by this rejection Rex undertook an earnest inventory of his personal strengths and weaknesses. He decided that life had taught him one clear lesson, namely, that it is easier to decide things with the aid of hindsight than it is to attempt to foresee and control the future. Not only did hindsight make it easier to decide cases, but—and this was of supreme importance to Rex—it made it easier to give reasons. Deciding to capitalise on this insight. Rex hit on the following plan. At the beginning of each calendar year he would decide all the controversies that had arisen among his subjects during the preceding year. He would accompany his decisions with a full statement of reasons. Naturally, the reasons thus given would be understood as not controlling decisions in future years, for that would be to defeat the whole purpose of the new arrangement, which was to gain the advantages of hindsight. Rex confidently announced the new plan to his subjects, observing that he was going to publish the full text of his judgments with the rules applied by him, thus meeting the chief objection to the old plan. Rex’s subjects received this announcement in silence, then quietly explained through their leaders that when they said they needed to know the rules, they meant they needed to know them in advance so they could act on them. Rex muttered something to the effect that they might have made that point a little clearer, but said he would see what could be done.

Rex now realised that there was no escape from a published code declaring the rules to be applied in future disputes. Continuing his lessons on generalisation, Rex worked diligently on a revised code, and finally announced that it would shortly be published. This announcement was received with universal gratification. The dismay of Rex’s subjects was all the more intense, therefore, when his code became available and it was discovered that it was truly a masterpiece of obscurity. Legal experts who studied it declared that there was not a single sentence in it that could be understood either by an ordinary citizen or by a trained lawyer. Indignation became general and soon a picket appeared before the royal palace carrying a sign that read, “How can anybody follow a rule that nobody can understand?”

The code was quickly withdrawn. Recognising for the first time that he needed assistance, Rex put a staff of experts to work on a revision. He instructed them to leave the substance untouched, but to clarify the expression throughout. The resulting code was a model of clarity, but as it was studied it became apparent that its new clarity had merely brought to light that it was honeycombed with contradictions. It was reliably reported that there was not a single provision in the code that was not nullified by another provision inconsistent with it. A picket again appeared before the royal residence carrying a sign that read, “This time the king made himself clear—in both directions."

Once again the code was withdrawn for revision. By now, however, Rex had lost his patience with his subjects and the negative attitude they seemed to adopt toward everything he tried to do for them. He decided to teach them a lesson and put an end to their carping. He instructed his experts to purge the code of contradictions, but at the same time to stiffen drastically every requirement contained in it and to add a long list of new crimes. Thus, where before the citizen summoned to the throne was given ten days in which to report, in the revision the time was cut to ten seconds. It was made a crime, punishable by ten years’ imprisonment, to cough, sneeze, hiccough, faint or fall down in the presence of the king. It was made treason not to understand, believe in and correctly profess the doctrine of evolutionary, democratic redemption.

When the new code was published a near revolution resulted. Leading citizens declared their intention to flout its provisions. Someone discovered in an ancient author a passage that seemed apt: “To command what cannot be done is not to make law; it is to unmake law, for a command that cannot be obeyed serves no end but confusion, fear and chaos.” Soon this passage was being quoted in a hundred petitions to the king.

The code was again withdrawn and a staff or experts charged with the task of revision. Rex’s instructions to the experts were that whenever they encountered ‘a rule requiring an impossibility, it should be revised to make compliance possible. It turned out that to accomplish this result every provisions in the code had to be substantially rewritten. The final result was, however, a triumph of draftsmanship.

It was clear, consistent with itself, and demanded nothing of the subject that did not lie easily within his powers. It was printed and distributed free of charge on every street corner. 

However, before the effective date for the new code had arrived, it was discovered that so much time had been spent in successive revisions of Rex‘s original draft, that the substance of the code had been seriously overtaken by events. Ever since Rex assumed the throne there had been a suspension of ordinary legal process and this had brought about important economic and institutional changes within the country. Accommodation to these altered conditions required many changes of substance in the law. Accordingly as soon as the new code became legally effective, it was subjected to a daily stream of amendments. Again popular discontent mounted; an anonymous pamphlet appeared on the streets carrying scurrilous cartoons of the king and a leading article with the little: “A law that changes every day is worse than no law at all.”

Within a short time this source of discontent began to cure itself as the pace of amendment gradually slackened. Before this had occurred to any noticeable degree, however, Rex announced an important decision. Reflecting on the misadventures of his reign, he concluded that much of the trouble lay in bad advice he had received from experts. He accordingly declared he was reassuming the judicial power in his own person. In this way he could directly control the application of the new code and insure his country against another crisis. He began to spend practically all of his time hearing and deciding cases arising under the new code.

As the king proceeded with this task, it seemed to bring to a belated blossoming his long dormant powers of generalisation. His opinions began, indeed, to reveal a confident and almost exuberant virtuosity as he deftly distinguished his own previous decisions, exposed the principles on which he acted, and laid down guidelines for the disposition of future controversies. For Rex’s subjects a new day seemed about to dawn when they could finally conform their conduct to a coherent body of rules.

This hope was, however, soon shattered. As the bound volumes of Rex's judgments became available and were subjected to closer study, his subjects were appalled to discover that there existed no discernible relation between those judgments and the code they purported to apply. Insofar as it found expression in the actual disposition of controversies, the new code might just as well not have existed at all. Yet in virtually every one of his decisions Rex declared and re-declared the code to be the basic law of his kingdom.

Leading citizens began to hold private meetings to discuss what measures, short of open revolt, could be taken to get the king away from the bench and back on the throne. While these discussions were going on Rex suddenly died old before his time and deeply disillusioned with his subjects.

The first act of his successor, Rex II. was to announce that he was taking the powers of government away from the lawyers and placing them in the hands of psychiatrists and experts in public relations. This way, he explained, people could be made happy without rules.

The Consequences of Failure:

Rex’s bungling career as a legislator and judge illustrates that the attempt to create and maintain a system of legal rules may miscarry is at least eight ways: there are in this enterprise, if you will, eight distinct routes to disaster. (1) The first and most obvious lies in a failure to achieve rules at all, so that every issue must be decided on an ad hoc basis. The other routes are: (2) the failure to publicise, or at least make available to the affected party, the rules he is expected to observe: (3) the abuse of retroactive legislation, which cannot in itself guide action, but undercuts the integrity of rules prospective in effect, since it puts them under the threat of retrospective change; (4) a failure to make rules understandable; (5) the enactment of contradictory rules or (6) rules that require conduct beyond the powers of the effective party; (7) introducing such frequent changes in the rules that the subject cannot orient his action by them; and finally, (8) the failure of congruence between the rules as announced and their actual administration.**

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Sources

*Poor Charlie's Almanack, pg 428

**Lloyd's Introduction to Jurisprudence by Michael D.A. Freeman, pg 138

Category: mathematics → algebra

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