
    Application of Chiranjib K. SARKAR.
    Appeal No. 78-554.
    United States Court of Customs and Patent Appeals.
    Dec. 7, 1978.
    Rehearing Denied Jan. 25, 1979.
    Geoffrey R. Myers, William D. Hall, Hall & Myers, Potomac, Md., attorneys of record, for appellant.
    Joseph F. Nakamura, Washington, D. C., for the Commissioner of Patents, Jere W. Sears, Washington, D. C., of counsel.
    Before MARKEY, Chief Judge, RICH, BALDWIN and MILLER, Judges, and FORD, Judge.
    
      
       The Honorable Morgan Ford, Judge, U. S. Customs Court, sitting by designation.
    
   MARKEY, Chief Judge.

Appeal from the decision of the Patent and Trademark Office (PTO) Board of Appeals (board), affirming the rejection, under 35 U.S.C. § 101, of claims 1-39, all of the claims in application serial No. 445,765, filed February 25, 1974, and entitled “Methods of Open Channel Analysis and Control.” We affirm.

The Invention

The subject matter of Sarkar’s invention is a technique for mathematically modeling an open channel, e. g., a natural stream or artificial waterway. Sarkar says his method of constructing a mathematical model is capable of accurately providing the flow parameters of a river over a period of time, even though it (1) contains obstructions such as dams or bridges, tributaries, and by-passes, (2) experiences flooding, (3) has lateral inflow, (4) has actual inflow at its upstream end, and (5) empties into a tidal body. The ability to account for additional complexities is said to comprise the principal advance over 'more idealized models in the prior art.

The claims take two forms. The first includes claims 1-13, of which claim 1 is representative:

1. A method of constructing a mathematical model of at least a portion of an open channel segmented into at least one reach and in which there is spatially varied unsteady flow and including the existence of at least one gravity wave during a given period of time comprising:
(a) measuring the cross-sectional dimensions of the channel at a specifically chosen, predetermined number of locations usable for schematizing said dimensions into a rectangularized cross-section for each regularly spaced but arbitrarily chosen distance Ax along the length of the channel irrespective of the chosen value of the interval of time At;
[steps (b)-(h)]. .

Step (b) recites the mathematical equations used to define the open channel flow. Steps (c)-(g) recite additional data-gathering steps, and step (h) recites the method of solving the flow equations using the collected data of steps (a) and (c)-(g).

The second form includes claims 14-39, reciting construction activity with the mathematical model of claims 1-13. Claim 14 is representative:

14. A method of locating an obstruction in an open channel to affect flow in a predetermined manner comprising:
a) obtaining the dimensions of said obstruction which affect the parameters of flow;
b) constructing a mathematical model of at least that portion of the open channel in which said obstruction is to be located in accordance with the method of claim 1 using those dimensions obtained in step (a) above;
c) adjusting the location of said obstruction within said mathematical model until the desired effect upon flow is obtained in said model; and thereafter
d) constructing said obstruction within the actual open channel at the specified adjusted location indicated by the mathematical model.

The Board

The board rejected all claims solely because it considered them as not being directed to a “process” within the meaning of 35 U.S.C. § 101. There were two distinct rationales for the § 101 rejection. The first concerned the interpretation and significance of step (a) of claim 1. The second concerned the significance of “post-solution activity” steps.

Respecting step (a) of claim 1, Sarkar sought to meet the examiner’s rejection based upon Gottschalk v. Benson, 409 U.S. 63, 93 S.Ct. 253, 34 L.Ed.2d 273, 175 USPQ 673 (1972), as interpreted in In re Christensen, 478 F.2d 1392, 178 USPQ 35 (CCPA 1973), with an argument that step (a), i. e., measuring the channel dimensions at arbitrarily chosen distance intervals Ax along the length of the channel, irrespective of the chosen value of time interval At, is a novel, nonobvious physical step, taking claims 1-13 outside the holdings of Benson and Christensen. In response, the board said step (a) was old, as indicated by Otter and Day, Tidal Flow Computations, The Engineer, January 29, 1960, at 177-82 (Otter). As the board stated,

The nature of the results of the calculations, that is, stable or oscillatory, is not set out in the claims at bar and we think that the general .commentary in Otter, for example page 181, column 3, first paragraph,[] is indicative of the fact that values for Ax and At have been selected in arbitrary fashion in the past even though such selection may take on non-arbitrary characteristics in order to achieve stable results.

The board, therefore, considered step (a) as nothing more than one of “the old and necessary antecedent steps of establishing values for the variables in the equation,” citing In re Christensen, supra at 1394, 178 USPQ at 37. The board concluded that the claims at issue would preempt all meaningful use of the formulas recited therein.

Concerning claims 14-39 and the' significance of “ppst-solution activity,” like building a bridge or dam, the board concluded:

While it is true that the final step in each of these claims makes reference to the mathematical result achieved by performing the prior recited steps, we consider the connection to be so tenuous that the several steps recited in each claim when considered as a whole do not constitute a proper method under the statute.

That the claimed invention was as a whole new, useful, and nonobvious, is nowhere challenged.

Issue

The broad issue under the statute is whether the processes of claims 1-39 constitute statutory subject matter under 35 U.S.C. § 101. The specific issue, occasioned by the presence of a mathematical algorithm, is whether measuring step (a) establishes that the claimed invention as a whole is not the algorithm but an application thereof.

OPINION

Section 101, the threshold provision of the patent statute, enumerates categories of inventions possibly subject to patenting and includes any process and any improvement thereof. Given the fundamental purposes of the patent law to encourage inventions, their disclosure, and their commercialization, Congress employed broad language in enumerating the types of inventions coming within the statute. Judicial exclusion of an invention from the “any process” provision by Congress, and its consequent relegation to the caves of secrecy (as here), must be approached with great care lest the intent of Congress and the constitutionally stated purpose it has implemented be thwarted. The in camera procedure invoked herein has underlined appellant’s determination not to disclose the invention absent the quid pro quo of a patent.

Congress cannot be expected to foresee, or to annually amend Title 35 to incorporate, every future breakthrough onto entirely new technological terrain. The Constitution granted Congress the power to “promote * * * progress * * *,” not the power to foretell its direction. Congress was granted authority not prescience.

Further, the patent system encourages disclosure of technological breakthroughs. It deals largely with disclosure of the unforeseen, the obviously foreseeable being rejected, 35 U.S.C. § 103. Hence, to limit “any process” to familiar or predicted arts would be to stifle much technology at its birth.

Though every set of steps, of whatever nature, may properly be labeled a “process,” § 101 (“Whoever invents”) limits the patent system to invented processes. Sets of steps conducted entirely by nature are not subject to patenting; they are not invented by man. Sets of steps occurring only in the mind have not been made subject to patenting because mental processes are but disembodied thoughts, whereas inventions which Congress is constitutionally empowered to make patentable are tangible embodiments of ideas in the useful, or technological, arts. See In re Waldbaum, 457 F.2d 997, 1003, 59 Cust. & Pat.App. 940, 173 USPQ 430, 434 (1972) (commenting on the synonymity of useful arts and technological arts).

Mathematical exercises, or methods of calculation, are within the myriad of mental processes of which the human mind is capable. Though they may be represented by written formulae, symbols, equations, or “algorithms,” mathematical exercises remain disembodied. They may not, therefore, cross the threshold of § 101. On the other hand, the mere presence of a mathematical exercise, as a step or steps in a process involving nonmathematical steps, should not slam the door of the Patent and Trademark Office upon an applicant seeking eventual disclosure of that process. To hold otherwise would be to ignore the intent and purpose expressed (“any process”) by Congress in § 101.

Thus a series of steps is a “process” within § 101 unless it falls within a judicially determined category of nonstatutory subject matter exceptions.

The advent of computer technology, with its accompanying computer programs, requires neither abandonment nor revision of the foregoing considerations. It requires merely their careful application. In making that application, each invention must be evaluated as claimed; yet semantogenic considerations preclude a determination based solely on words appearing in the claims. In the final analysis under § 101, the claimed invention, as a whole, must be evaluated for what it is.

Sarkar’s claims recite a mathematical “algorithm.” See Benson, supra, 409 U.S. at 65, 93 S.Ct. 253, 175 USPQ at 674; In re Freeman, 573 F.2d 1237, 1245-46, 197 USPQ 464, 471 (CCPA 1978). Although not disclosed in this opinion, mathematical equations expressed in algebraic form, and a technique for solving them are recited in each claim. In an effort on this appeal to establish that his claimed invention as a whole is not merely a mathematical exercise, but a process in which mathematics is but a part, Sarkar makes three arguments, all related to measuring step (a).

First, in an effort to show his invention to be other than a mathematical exercise, Sarkar contends that his claims would not preempt the mathematical algorithms, because prior mathematical models and solution techniques suffered the disadvantage that channel dimensions could not be measured at arbitrarily chosen distance intervals Ax irrespective of time interval At, /. e., the values of Ax and At had to satisfy the Courant condition:

A* <_ _Ax_
M + c

Sarkar says his formulae and algorithms could be freely used without infringement by simply so choosing Ax and At as to satisfy the prior art Courant condition.

That contention does not comport with the language of the claims. Step (a) says only that Ax is selected arbitrarily relative to At. It thus covers those situations where, though chosen arbitrarily, the values of Ax and At do satisfy the Courant condition. Sarkar’s argument that “arbitrarily chosen” is a term of art explained in his specification, and that it should be read as precluding satisfaction of the Courant condition, is without merit. The specification says the relationship between Ax and At need not satisfy the Courant condition. It does not, as Sarkar would have us read it, say the relationship must not do so. In sum, we agree with the solicitor’s position that step (a) does not preclude coincidental satisfaction of the Courant condition. Hence Sarkar’s first argument, that his claims do not preempt the algorithm because they do not encompass satisfaction of the Courant condition, must fail.

Sarkar’s second contention is that measuring step (a) is not just an old and necessary antecedent step of establishing values for the variables in the formulae recited in the claims.

In In re Christensen, supra 478 F.2d at 1394, 178 USPQ at 37-38, (emphasis added) this court stated:

Given that the method of solving a mathematical equation may not be the subject of patent protection, it follows that the addition of the old and necessary antecedent steps of establishing values for the variables in the equation cannot convert the unpatentable method to patentable subject matter.

Accord, In re Chatfield, 545 F.2d 152, 158, 191 USPQ 730, 736 (CCPA 1976). The reason for so holding is clear. No mathematical equation can be used, as a practical matter, without establishing and substituting values for the variables expressed therein. Substitution of values dictated by the formula has thus been viewed as a form of mathematical step. If the steps of gathering and substituting values were alone sufficient, every mathematical equation, formula, or algorithm having any practical use would be per se subject to patenting as a “process” under § 101. Consideration of whether the substitution of specific values is enough to convert the disembodied ideas present in the formula into an embodiment of those ideas, or into an application of the formula, is foreclosed by the current state of the law. See note 9 supra.

Though Sarkar admits that arbitrary selection of Ax and At was used in the prior art, he says that is not determinative, because prior algorithms were unstable when used with arbitrarily chosen Ax and At, contending essentially that earlier arbitrary selection was inoperative. We-decline the underlying invitation to treat the mathematical properties of Sarkar’s algorithm as divorced from the algorithm itself. Whether arbitrary selection is operative or inoperative is a function, respectively, of the stable nature of Sarkar’s algorithm and the oscillatory nature of prior algorithms. Indeed, Sarkar’s second contention supports the view that his invention as a whole is his new and stable algorithm. There exists, in any event, no basis for treating data-gathering step (a) differently from the data-gathering steps in Christensen.

Thirdly, Sarkar asserts that step (a) is novel (because his algorithm makes it operative) and nonobvious. Sarkar says that makes his invention an “inventive application” of the algorithm, citing this from the majority opinion in Parker v. Flook, supra note 9, at 2528, 198 USPQ at 199:

Even though a phenomenon of nature or mathematical formula may be well known, an inventive application of the principle may be patented. Conversely, the discovery of such a phenomenon cannot support a patent unless there is some other inventive concept in its application.[]

Beyond the irrelevance of novelty and nonobviousness considerations to determinations under § 101, Sarkar’s difficulty is that step (a), to the extent that it be considered novel, derives such “novelty” solely from the algorithm itself.

Sarkar’s claimed invention as a whole consists of a mathematical exercise, wherein a new formula is provided, formula-dictated values are gathered and substituted for the variables- in that formula, and the calculations required by the formula are made. Sarkar’s offer to disclose his process by patenting must, in the present state of the law, be declined.

Conclusion

The decision of the board, rejecting claims 1-39 as not directed to a “process” within the meaning of 35 U.S.C. § 101, is affirmed.

AFFIRMED. 
      
      . Quotation of steps (b)-(h) would reveal material retained as a trade secret. The Court granted Sarkar’s Motion for In Camera Proceedings and To Seal the Record under Rule 5.13(g) of this court. In re Sarkar, 575 F.2d 870, 197 USPQ 788 (CCPA 1978). Though the issues are of sufficient interest to merit publication, explication of our rationale does not require discussion of the technical details of Sarkar’s invention.
     
      
      . A rejection of all claims under 35 U.S.C. § 112, second paragraph, was withdrawn in the examiner’s answer.
     
      
      . 35 U.S.C. § 101 provides:
      Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
      35 U.S.C. § 100(b) provides:
      The term “process” means process, art or method, and includes a new usé of a known process, machine, manufacture, composition or matter, or material.
     
      
      . Otter, page 181, column 3, first paragraph, states in pertinent part:
      A point of very considerable practical importance in connection with any computer programme for a second order partial differential equation is the ratio of the time interval to the distance interval. In an earlier programme on a somewhat different organizational basis it was found that considerable numerical oscillations took place in the figures for level and velocity and it was not at first appreciated why this should be so. * * Whilst a general solution for the stability of any given equation is not completely known it seems clear in this case that, provided Ax/ At is greater than the celerity of the wave * * for the highest level in the river, the calculations are stable.
     
      
      . The examiner’s final rejection reveals no rejection based on either § 102 or § 103. The board did, however, cite the Otter reference as evidence that step (a) was old.
     
      
      . From the oral argument, we conclude that Sarkar no longer relies upon bridge or dam construction as post-solution activity steps effective to bring his process within § 101. It is unnecessary, therefore, to address that question or to consider claims 14-39 differently from claims 1-13.
     
      
      . The growth of technological progress is slowed, not only by judicial restriction to familiar areas, but by myopia. A bishop condemned the sinful prediction that man might one day fly. The speaker was Bishop Milton Wright, father of Orville and Wilbur. Golden Anniversary Observance of Man’s First Successful Powered Flight, H.R. Doc. No. 480, 83d Cong., 2d Sess. 17 (1954). The New York Times excoriated Professor Langley for wasting money on gravity-doomed attempts to fly, in an editorial published seven days before the historic flight at Kitty Hawk. N. Y. Times, Dec. 10, 1903, at 2.
     
      
      . The Patent and Trademark Office has nothing to do with regulating use of technology. The Government is adequately supplied with numerous other agencies able and eager to perform that function.
     
      
      . Applying the guidance of Benson, supra, and Parker v. Flook, 437 U.S. 584, 98 S.Ct. 2522, 57 L.Ed.2d 451, 198 USPQ 193 (1978), insofar as guidance may be gleaned from the opinions in those cases and applied to the facts before us.
     
      
      . But not for its patentability. Considerations of novelty and nonobviousness have no place in evaluations under § 101 as to whether an invention is within the categories of possibly patentable inventions. Those considerations arise, as the statute makes plain, under §§ 102 and 103, respectively. See Nickola v. Peterson, 580 F.2d 898, 906-07, 198 USPQ 385, 395-96 (CA6 1978). Cognitive dissonance arises from references to “novelty,” or to “patentability,” in reviewing a rejection under § 101. If the subject matter as claimed is subject to patenting, i. e., if it falls within § 101, it must then be examined for compliance with §§ 102 and 103. Absent such examination (or admissions), no record basis exists for determination or discussion of novelty, nonobviousness, or ultimate patentability.
      This court is required to consider appeals from the PTO on the record there made. 35 U.S.C. § 144. It is not at liberty to consider issues never raised below. Nor will it assume de novo the function of an examiner who has declined, in reliance upon §' 101, to conduct an examination for patentability under §§ 102 and 103.
      In the present case, the record reflects an apparent examination for novelty of some kind, the board having relied on the reference to Otter. The board’s consideration of what is old or new in Sarkar’s invention, in applying § 101 thereto, tends only to obfuscate the law.
      A § 101 determination is concerned (setting aside utility) only with whether the claimed invention is within the categories there broadly enumerated. Since the 1952 Patent Act, and especially since Graham v. John Deere Co., 383 U.S. 1, 86 S.Ct. 684, 15 L.Ed. 545 (1966), it has been clear that a § 101 determination in no way involves consideration of the existence of “invention,” if it ever did. The words “Whoever invents” in § 101 are used in the sense of “whoever originates,” patentability of the thing originated being dependent, as § 101 states, on its meeting the “requirements of this title.”
     
      
      . See note 1 supra.
      
     
      
      . Sarkar contends that the board’s decision was based upon isolation of step (a) as the presumed “point of novelty,” not on consideration of the claimed invention as a whole. That analysis would have been improper:
      [Respondent relies on opinions by the Court of Customs and Patent Appeals which reject the notion “that a claim may be dissected, the claim components searched in the prior art, and, if the only component found novel is outside the statutory classes of invention, the claim may be rejected under 35 U.S.C. § 101.” Application of Chatfield, 545 F.2d 152, 158 (Cust. & Pat.App. 1976).
      
      16 Section 103, by its own terms, requires that a determination of obviousness be made by considering “the subject matter as a whole.” 35 U.S.C. § 103. Although this does not necessarily require that analysis of what is patentable subject matter under § 101 proceed on the same basis, we agree that it should.
      
        Parker v. Flook, supra note 9, at _, 98 S.Ct. at 2527, 198 USPQ at 199.
      Unlike earlier cases, in which the board characterized the formula or algorithm as the only “point of novelty,” the instant claims recite the algorithm in steps other than step (a). The board’s analysis of the significance of step (a), and appellant’s emphasis on that step, manifest a careful analysis of the claims to determine whether the invention as a whole resides in the algorithm or in its application.
     
      
      . v = mean velocity across a channel cross-section.
      c = celerity of the wave = (gy)
      wherein g = acceleration due to gravity
      y = depth of flow with respect to channel bottom as datum.
     
      
      . Sarkar contends in his reply brief and at oral argument that the solicitor’s position on this issue is wholly new, the examiner and the board having agreed with appellant’s interpretation of the breadth of step (a). But the board cannot be viewed as so interpreting “arbitrarily chosen,” while holding that “the instant claims preempt all meaningful use of the formulas and algorithms recited.” Moreover, appellant introduced this issue in his main brief.
     
      
      . Whether there may be other grounds for holding that the present claims do not preempt the algorithms has not been argued. That question is not, therefore, before us.
     
      
      . Sarkar asserts that the PTO agreed with that view. At oral argument the solicitor did not disavow the views of the examiner and the board, but said it makes little if any difference, citing Parker v. Flook, supra note 9. The suggested interpretation of Flook is overbroad.
     
      
      . Patent law is statutory. Hence, the word “inventive” must be read as meaning “novel and nonobvious.” 35 U.S.C. §§ 102, 103.
     
      
      . If step (a) had been novel and nonobvious, that circumstance would not alone have changed the result here. Concerning the particular antecedent data-gathering steps in In re Richman, 563 F.2d 1026, 1030, 195 USPQ 340, 343 (CCPA 1977), this court stated:
      In the present case too, notwithstanding that the antecedent steps are novel and unobvious, they merely determine values for the variables used in the mathematical formulae used in making the calculations. Thus, such antecedent steps do not suffice to render the claimed methods, considered as a whole, statutory subject matter.
      The antecedent steps in Richman were dictated by the mathematical formulae. The same is true of Sarkar’s step (a).
      Whether a data gathering step not dictated by a formula may exist, whether it would enable a claim to pass muster under § 101, and whether it would render patentable the claimed process including that step, if the claimed process is examined and found novel and nonobvious under §§ 102 and 103, are questions not before us.
     