A rule promulgated by an agency that is subject to the Administrative Procedure Act is invalid unless the agency first issues a public notice of proposed rulemaking, describing the substance of the proposed rule, and gives the public an opportunity to submit written comments; and if after receiving the comments it decides to promulgate the rule it must set forth the basis and purpose of the rule in a public statement. 5- U.S.C. §§ 553(b), (c). These procedural requirements do not apply, however, to “interpretative rules, general statements of policy, or rules of agency organization, procedure, or practice.” 5 U.S.C. § 553(b)(A). Distinguishing between a “legislative” rule, to which the notice and comment provisions of the Act apply, and an interpretive rule, to which these provisions do not apply, is often very difficult — and often very important to regulated firms, the public, and the agency. Notice and comment rulemaking is time-consuming, facilitates the marshaling of opposition to a proposed rule, and may result in the creation of a very long record that may in turn provide a basis for a judicial challenge to the rule if the agency decides to promulgate it. There are no formalities attendant upon the promulgation of an interpretive rule, but this is tolerable because such a rule is “only” an interpretation. Every governmental agency that enforces a less than crystalline statute must interpret the statute, and it does the public a favor if it announces the interpretation in advance of enforcement, whether the announcement takes the form of a rule or of a policy statement, which the Administrative Procedure Act assimilates to an interpretive rule. It would be no favor to the public to discourage the announcement of agencies’ interpretations by burdening the interpretive process with cumbersome formalities.
The question presented by this appeal from an order of the Department of Agriculture is whether a rule for the secure containment of animals, a rule promulgated by the Department under the Animal Welfare Act, 7 U.S.C. §§ 2131 et seq., without compliance with the notice and comment requirements of the Administrative Procedure Act, is nevertheless valid because it is merely an interpretive rule. Enacted in 1966, the Animal Welfare Act, as its title implies, is primarily designed to assure the humane treatment of animals. The Act requires the licensing of dealers (with obvious exceptions, for example retail pet stores) and exhibitors, and authorizes the Department to impose sanctions on licensees who violate either the statute itself or the rules promulgated by the Department under the authority of 7 U.S.C. § 2151, which authorizes the Secretary of Agriculture “to promulgate such rules, regulations, and orders as he may deem necessary in order to effectuate the purposes of [the Act].” The Act provides guidance to the exercise of this rulemaking authority by requiring the Department to formulate standards “to govern the humane handling, care, treatment, and transportation of animals by dealers,” and these standards must include minimum requirements “for handling, housing, feeding, watering, sanitation,” etc. 7 U.S.C. § 2143(a).
The Department has employed the notice and comment procedure to promulgate a regulation, the validity of which is not questioned, that is entitled “structural strength” and that provides that “the facility [housing the animals] must be constructed of such *168material and of such strength as appropriate for the animals involved. The indoor and outdoor housing facilities shall be structurally sound and shall be maintained in good repair to protect the animals from injury and to contain the animals.” 9 C.F.R. § 3.125(a).
Enter the petitioner, Patrick Hoctor, who in 1982 began dealing in exotic animals on his farm outside of Terre Haute. In a 25-acre compound he raised a variety of animals including “Big Cats” — a typical inventory included three lions, two tigers, seven ligers (a liger is a cross between a male lion and a female tiger, and is thus to be distinguished from a tigon), six cougars, and two snow leopards. The animals were in pens (“primary enclosures” in the jargon of the administration of the Animal Welfare Act). The area in which the pens were located was surrounded by a fence (“containment fence”). In addition, Hoctor erected a fence around the entire compound (“perimeter fence”). At the suggestion of a veterinarian employed by the Agriculture Department who was assigned to inspect the facility when Hoctor started his animal dealership in 1982, Hoctor made the perimeter fence six feet high.
The following year the Department issued an internal memorandum addressed to its force of inspectors in which it said that all “dangerous animals,” defined as including, among members of the cat family, lions, tigers, and leopards, must be inside a perimeter fence at least eight feet high. This provision is the so-called interpretive rule, interpreting the housing regulation quoted above. An agency has, of course, the power, indeed the inescapable duty, to interpret its own legislative rules, such as the housing standard, just as it has the power and duty to interpret a statute that it enforces. Stinson v. United States, 508 U.S. 36, 42-46, 113 S.Ct. 1913, 1918-19, 123 L.Ed.2d 598 (1993).
On several occasions beginning in 1990, Hoctor was cited by a Department of Agriculture inspector for violating 9 C.F.R. § 3.125(a), the housing standard, by failing to have an eight-foot perimeter fence. Eventually the Department sanctioned Hoctor for this and other alleged violations, and he has sought judicial review limited, however, to the perimeter fence. He is a small dealer and it would cost him many thousands of dollars to replace his six-foot-high fence with an eight-foot-high fence. Indeed, we were told at argument that pending the resolution of his dispute over the fence he has discontinued dealing in Big Cats. The parties agree that unless the rule requiring a perimeter fence at least eight feet high is a valid interpretive rule, the sanction for violating it was improper.
We may assume, though we need not decide, that the Department of Agriculture has the statutory authority to require dealers in dangerous animals to enclose their compounds with eight-foot-high fences. The fence is a backup fail-safe device, since the animals are kept in pens, cages, or other enclosures within the compound, in an area that is itself fenced, rather than being free to roam throughout the compound. Since animals sometimes break out or are carelessly let out of their pens, a fail-safe device seems highly appropriate, to say the least. Two lions once got out of their pen on Hoctor’s property, and he had to shoot them. Yet, when he did so, they were still within the containment fence. The Department’s regulations do not require a containment fence, and it is unclear to us why, if that fence was adequate — and we are given no reason to suppose it was not — Hoctor should have had to put up an additional fence, let alone one eight-feet high. But we lay any doubts on this score to one side. And we may also assume that the containment of dangerous animals is a proper concern of the Department in the enforcement of the Animal Welfare Act, even though the purpose of the Act is to protect animals from people rather than people from animals. Even Big Cats are not safe outside their compounds, and with a lawyer’s ingenuity the Department’s able counsel reminded us at argument that if one of those Cats mauled or threatened a human being, the Cat might get into serious trouble and thus it is necessary to protect human beings from Big Cats in order to protect the Cats from human beings, which is the important thing under the Act. In fact Hoctor had shot the two lions because they were dangerously close to one of his employees. Since tort liability for injury caused by a wild *169animal is strict, Burns v. Gleason, 819 F.2d 555 (5th Cir.1987); Behrens v. Bertram Mills Circus Ltd., [1957] 2 Q.B. 1; W. Page Keeton et al., Prosser and Keeton on the Law of Torts § 76, p. 542 (5th ed. 1984), the common law, at least, is solicitous for the protection of the citizens of Terre Haute against escapees from Hoetor’s menagerie even if the Animal Welfare Act is not. The internal memorandum also justifies the eight-foot requirement as a means of protecting the animals from animal predators, though one might have supposed the Big Cats able to protect themselves against the native Indiana fauna.
Another issue that we need not resolve besides the issue of the statutory authority for the challenged rule is whether the Department might have cited Hoctor for having a perimeter fence that was in fact, considering the number and type of his animals, the topography of the compound, the design and structure of the protective enclosures and the containment fence, the proximity of highways or inhabited areas, and the design of the perimeter fence itself, too low to be safe, as distinct from merely being lower than eight feet. No regulation is targeted on the problem of containment other than 9 C.F.R. § 3.125, which seems to be concerned with the strength of enclosures rather than their height. But maybe there is some implicit statutory duty of containment that Hoctor might have been thought to have violated even if there were no rule requiring an eight-foot-high perimeter fence.
We need not decide. The only ground on which the Department defends sanctioning Hoctor for not having a high enough fence is that requiring an eight-foot-high perimeter fence for dangerous animals is an interpretation of the Department’s own structural-strength regulation, and “provided an agency’s interpretation of its own regulations does nOfNib'l^te the Constitution or a federal statute, it must be given ‘controlling weight unless it is plainly erroneous or inconsistent with the regulation.’ ” Stinson v. United States, supra, 508 U.S. at 44-46, 113 S.Ct. at 1919. The “provided” clause does not announce a demanding standard of judicial review, although the absence of any reference in the housing regulation to fences or height must give us pause. The regulation appears only to require that pens and other animal housing be sturdy enough in design and construction, and sufficiently well maintained, to prevent the animals from breaking through the enclosure — not that any enclosure, whether a pen or a perimeter fence, be high enough to prevent the animals from escaping by jumping over the enclosure. The Department’s counsel made the wonderful lawyer’s argument that the eight-foot rule is consistent with the regulation because a fence lower than eight feet has zero structural strength between its height (here six feet) and the eight-foot required minimum. The two feet by which Hoctor’s fence fell short could not have contained a groundhog, let alone a liger, since it was empty space.
Our doubts about the scope of the regulation that the eight-foot rule is said to be “interpreting” might seem irrelevant, since even if a rule requiring an eight-foot perimeter fence could not be based on the regulation, it could be based on the statute itself, which in requiring the Department to establish minimum standards for the housing of animals presumably authorizes it to promulgate standards for secure containment. But if the eight-foot rule were deemed one of those minimum standards that the Department is required by statute to create, it could not possibly be thought an interpretive rule. For what would it be interpreting? When Congress authorizes an agency to create standards, it is delegating legislative authority, rather than itself setting forth a standard which the agency might then particularize through interpretation. Put differently, when a statute does not impose a duty on the persons subject to it but instead authorizes (or requires — it makes no difference) an agency to impose a duty, the formulation of that duty becomes á legislative task entrusted to the agency. Provided that a rule promulgated pursuant to such a delegation is intended to bind, and not merely to be a tentative statement of the agency’s view, which would make it just a policy statement, and not a rule at all, the rule would be the clearest possible example of a legislative rule, as to which the notice and comment procedure not followed here is mandatory, as dis*170tinct from an interpretive rule; for there would be nothing to interpret. American Mining Congress v. Mine Safety & Health Administration, 995 F.2d 1106, 1109 (D.C.Cir.1993); Robert A. Anthony, “ ‘Interpretive’ Rules, ‘Legislative’ Rules and ‘Spurious’ Rules: Lifting the Smog,” 8 Admin. L.J. of Am. Univ. 1 (1994). That is why the Department must argue that its eight-foot rule is an interpretation of the structural-strength regulation-itself a standard, and therefore interpretable, in order to avoid reversal.
Even if, despite the doubts that we expressed earlier, the eight-foot rule is consistent with, even in some sense authorized by, the structural-strength regulation, it would not necessarily follow that it is an interpretive rule. It is that only if it can be derived from the regulation by a process reasonably described as interpretation. Metropolitan School District v. Davila, 969 F.2d 485, 490 (7th Cir.1992). Supposing that the regulation imposes a general duty of secure containment, the question is, then, Can a requirement that the duty be implemented by erecting an eight-foot-high perimeter fence be thought an interpretation of that general duty?
“Interpretation” in the narrow sense is the ascertainment of meaning. It is obvious that eight feet is not part of the meaning of secure containment. But “interpretation” is often used in a much broader sense. A process of “interpretation” has transformed the Constitution into a body of law undreamt of by the framers. To skeptics the Miranda rule is as remote from the text of the Fifth Amendment as the eight-foot rule is from the text of 9 C.F.R. § 3.125(a). But our task in this case is not to plumb the mysteries of legal theory; it is merely to give effect to a distinction that the Administrative Procedure Act makes, and we can do this by referring to the purpose of the distinction. The purpose is to separate the cases in which notice and comment rulemaking is required from the cases in which it is not required. As we noted at the outset, unless a statute or regulation is of crystalline transparency, the agency enforcing it cannot avoid interpreting it, and the agency would be stymied in its enforcement duties if every time it brought a case on a new theory it had to pause for a bout, possibly lasting several years, of notice and comment rulemaking. Besides being unavoidably continuous, statutory interpretation normally proceeds without the aid of elaborate factual inquiries. When it is an executive or administrative agency that is doing the interpreting it brings to the task a greater knowledge of the regulated activity than the judicial or legislative branches have, and this knowledge is to some extent a substitute for formal fact-gathering.
At the other extreme from what might be called normal or routine interpretation is the making of reasonable but arbitrary (not in the “arbitrary or capricious” sense) rules that are consistent with the statute or regulation under which the rules are promulgated but not derived from it, because they represent an arbitrary choice among methods of implementation. A rule that turns on a number is likely to be arbitrary in this sense. There is no way to reason to an eight-foot perimeter-fence rule as opposed to a seven- and-a-half foot fence or a nine-foot fence or a ten-foot fence. None of these candidates for a rule is uniquely appropriate to, and in that sense derivable from, the duty of secure containment. This point becomes even clearer if we note that the eight-foot rule actually has another component — the fence must be at least three feet from any animal's pen. "Why three feet? Why not four? Or two?
The reason courts refuse to create statutes of limitations is precisely the difficulty of reasoning to a number by the methods of reasoning used by courts. Hemmings v. Barian, 822 F.2d 688, 689 (7th Cir.1987). One cannot extract from the concept of a tort that a tort suit should be barred unless brought within one, or two, or three, or five years. The choice is arbitrary and courts are uncomfortable with making arbitrary choices. They see this as a legislative function. Legislators have the democratic legitimacy to make choices among value judgments, choices based on hunch or guesswork or even the toss of a coin, and other arbitrary choices. When agencies base rules on arbitrary choices they are legislating, and so these rules are legislative or substantive and *171require notice and comment rulemaking, a procedure that is analogous to the procedure employed by legislatures in making statutes. The notice of proposed rulemaking corresponds to the bill and the reception of written comments to the hearing on the bill.
The common sense of requiring notice and comment rulemaking for legislative rules is well illustrated by the facts of this case. There is no process of cloistered, appellate-court type reasoning by which the Department of Agriculture could have excogitated the eight-foot rule from the structural-strength regulation. The rule is arbitrary in the sense that it could well be different without significant impairment of any regulatory purpose. But this does not make the rule a matter of indifference to the people subject to it. There are thousands of animal dealers, and some unknown fraction of these face the prospect of having to tear down their existing fences and build new, higher ones at great cost. The concerns of these dealers are legitimate and since, as we are stressing, the rule could well be otherwise, the agency was obliged to listen to them before settling on a final rule and to provide some justification for that rule, though not so tight or logical a justification as a court would be expected to offer for a new judge-made rule. Notice and comment is the procedure by which the persons affected by legislative rules are enabled to communicate their concerns in a comprehensive and systematic fashion to the legislating agency. The Department’s lawyer speculated that if the notice and comment route had been followed in this case the Department would have received thousands of comments. The greater the public interest in a rule, the greater reason to allow the public to participate in its formation.
We are not saying that an interpretive rule can never have a numerical component. See, e.g., American Mining Congress v. Mine Safety & Health Administration, supra, 995 F.2d at 1108, 1113; St. Mary’s Hospital v. Blue Cross & Blue Shield Ass’n., 788 F.2d 888, 889-91 (2d Cir.1986). There is merely an empirical relation between interpretation and generality on the one hand, and legislation and specificity on the other. Especially in scientific and other technical areas, where quantitative criteria are common, a rule that translates a general norm into a number may be justifiable as interpretation. The mine safety agency in the American Mining case could refer to established medical criteria, expressed in terms of numerical evaluations of x-rays, for diagnosing black-lung disease. 995 F.2d at 1112-13. Even in a nontechnical area the use of a number as a rale of thumb to guide the application of a general norm will often be legitimately interpretive. Had the Department of Agriculture said in the internal memorandum that it could not imagine a case in which a perimeter fence for dangerous animals that was lower than eight feet would provide secure containment, and would therefore presume, subject to rebuttal, that a lower fence was insecure, it would have been on stronger ground. For it would have been tying the rule to the animating standard, that of secure containment, rather than making it stand free of the standard, self-contained, unbending, arbitrary. To switch metaphors, the “flatter” a rule is, the harder it is to conceive of it as merely spelling out what is in some sense latent in a statute or regulation, and the eight-foot rule in its present form is as flat as they come. At argument the Department’s lawyer tried to loosen up the rale, implying that the Department might have bent it if Hoetor proposed to dig a moat or to electrify his six-foot fence. But an agency’s lawyer is not authorized to amend its rales in order to make them more palatable to the reviewing court.
The Department’s position might seem further undermined by the fact that it has used the notice and comment procedure to promulgate rules prescribing perimeter fences for dogs and monkeys. 9 C.F.R. §§ 3.6(e)(2)(ii), 3.77(f). Why it proceeded differently for dangerous animals is unexplained. But we attach no weight to the Department’s inconsistency, not only because it would be unwise to penalize the Department for having at least partially complied with the requirements of the Administrative Procedure Act, but also because there is nothing in the Act to forbid an agency to use the notice and comment procedure in cases in *172which it is not required to do so. We are mindful that the court in United States v. Picciotto, 875 F.2d 345, 348 (D.C.Cir.1989), thought that the fact that an agency had used notice and comment rulemaking in a setting similar to the case before the court was evidence that the agency “intended” to promulgate a legislative rule in that case, only without bothering with notice and comment. The inference is strained, and in any event we think the agency’s “intent,” though a frequently cited factor, is rather a makeweight. What the agency intends is to promulgate a rule. It is for the courts to say whether it is the kind of rule that is valid only if promulgated after notice and comment. It is that kind of rule if, as in the present ease, it cannot be derived by'interpretation. The order under review, based as it was on a rule that is invalid because not promulgated in accordance with the required procedure, is therefore
VACATED.