Conditions for Patentability under Section 101

The Nature of Abstract Ideas

The Supreme Court has stated on numerous occasions that abstract ideas are not patentable. In order to understand what was originally understood by the term abstract idea, it is instructive to review the discussion of abstract general ideas in the works of the 18th century empiricist philosophers John Locke, George Berkeley and David Hume.

John Locke, in his Essay concerning Human Understanding discussed the natural of ideas. He classified ideas into various categories. These categories included simple ideas, which result from sense impressions, complex ideas, which are formed by aggregation from simple ideas, and abstract ideas. Abstract ideas are formed by a process of abstraction, which Locke described in Chapter 11 (Of Discerning, and other Operations of the Mind) of Book II (Of Ideas):

9. The use of words then being to stand as outward marks of our internal ideas, and those ideas being taken from particular things, if every particular idea that we take in should have a distinct name, names must be endless. To prevent this, the mind makes the particular ideas received from particular objects to become general; which is done by considering them as they are in the mind such appearances,—separate from all other existences, and the circumstances of real existence, as time, place, or any other concomitant ideas. This is called abstraction, whereby ideas taken from particular beings become general representatives of all of the same kind; and their names general names, applicable to whatever exists conformable to such abstract ideas. Such precise, naked appearances in the mind, without considering how, whence, or with what others they came there, the understanding lays up (with names commonly annexed to them) as the standards to rank real existences into sorts, as they agree with these patterns, and to denominate them accordingly. Thus the same colour being observed to-day in chalk or snow, which the mind yesterday received from milk, it considers that appearance alone, makes it a representative of all of that kind; and having given it the name whiteness, it by that sound signifies the same quality wheresoever to be imagined or met with; and thus universals, whether ideas or terms, are made.

(Locke, Essay concerning Human Understanding, II.11.9).

In the following Chapter, Chapter 12 (Of Complex Ideas) of Book II, Locke describes how the mind combines and creates new ideas:

1. We have hitherto considered those ideas, in the reception whereof the mind is only passive, which are those simple ones received from sensation and reflection before mentioned, whereof the mind cannot make one to itself, nor have any idea which does not wholly consist of them. But as the mind is wholly passive in the reception of all its simple ideas, so it exerts several acts of its own, whereby out of its simple ideas, as the materials and foundations of the rest, the others are framed. The acts of the mind, wherein it exerts its power over its simple ideas, are chiefly these three: (1) Combining several simple ideas into one compound one; and thus all complex ideas are made. (2) The second is bringing two ideas, whether simple or complex, together, and setting them by one another, so as to take a view of them at once, without uniting them into one; by which way it gets all its ideas of relations. (3) The third is separating them from all other ideas that accompany them in their real existence: this is called abstraction: and thus all its general ideas are made.

(Locke, Essay concerning Human Understanding, II.12.1).

The existence of abstract general ideas was disputed by George Berkeley and David Hume. Berkeley focussed his criticism on the following passage of the Essay concerning Human Understanding, to be found in Chapter 7 (Of Maxims) of Book IV (Of Knowledge and Opinion):

9. Because maxims or axioms are not the truths we first knew. First, That they are not the truths first known to the mind is evident to experience, as we have shown in another place. (Bk. I. chap. i.) Who perceives not that a child certainly knows that a stranger is not its mother; that its sucking-bottle is not the rod, long before he knows that “it is impossible for the same thing to be and not to be?” And how many truths are there about numbers, which it is obvious to observe that the mind is perfectly acquainted with, and fully convinced of, before it ever thought on these general maxims, to which mathematicians, in their arguings, do sometimes refer them? Whereof the reason is very plain: for that which makes the mind assent to such propositions, being nothing else but the perception it has of the agreement or disagreement of its ideas, according as it finds them affirmed or denied one of another in words it understands; and every idea being known to be what it is, and every two distinct ideas being known not to be the same; it must necessarily follow, that such self-evident truths must be first known which consist of ideas that are first in the mind. And the ideas first in the mind, it is evident, are those of particular things, from whence, by slow degrees, the understanding proceeds to some few general ones; which being taken from the ordinary and familiar objects of sense, are settled in the mind, with general names to them. Thus particular ideas are first received and distinguished, and so knowledge got about them; and next to them, the less general or specific, which are next to particular. For abstract ideas are not so obvious or easy to children, or the yet unexercised mind, as particular ones. If they seem so to grown men, it is only because by constant and familiar use they are made so. For, when we nicely reflect upon them, we shall find that general ideas are fictions and contrivances of the mind, that carry difficulty with them, and do not so easily offer themselves as we are apt to imagine. For example, does it not require some pains and skill to form the general idea of a triangle, (which is yet none of the most abstract, comprehensive, and difficult,) for it must be neither oblique nor rectangle, neither equilateral, equicrural, nor scalenon; but all and none of these at once. In effect, it is something imperfect, that cannot exist; an idea wherein some parts of several different and inconsistent ideas are put together. It is true, the mind, in this imperfect state, has need of such ideas, and makes all the haste to them it can, for the conveniency of communication and enlargement of knowledge; to both which it is naturally very much inclined. But yet one has reason to suspect such ideas are marks of our imperfection; at least, this is enough to show that the most abstract and general ideas are not those that the mind is first and most easily acquainted with, nor such as its earliest knowledge is conversant about.

(Locke, Essay concerning Human Understanding, IV.7.9).

George Berkeley, in A Treatise concerning the Principles of Human Knowledge, disputed the existence of such abstract ideas. He first summarizes Locke's account, in the Introduction, as follows:

7. It is agreed on all hands that the qualities or modes of things do never really exist each of them apart by itself, and separated from all others, but are mixed, as it were, and blended together, several in the same object. But, we are told, the mind being able to consider each quality singly, or abstracted from those other qualities with which it is united, does by that means frame to itself abstract ideas. For example, there is perceived by sight an object extended, coloured, and moved: this mixed or compound idea the mind resolving into its simple, constituent parts, and viewing each by itself, exclusive of the rest, does frame the abstract ideas of extension, colour, and motion. Not that it is possible for colour or motion to exist without extension; but only that the mind can frame to itself by abstraction the idea of colour exclusive of extension, and of motion exclusive of both colour and extension.

8. Again, the mind having observed that in the particular extensions perceived by sense there is something common and alike in all, and some other things peculiar, as this or that figure or magnitude, which distinguish them one from another; it considers apart or singles out by itself that which is common, making thereof a most abstract idea of extension, which is neither line, surface, nor solid, nor has any figure or magnitude, but is an idea entirely prescinded from all these. So likewise the mind, by leaving out of the particular colours perceived by sense that which distinguishes them one from another, and retaining that only which is common to all, makes an idea of colour in abstract which is neither red, nor blue, nor white, nor any other determinate colour. And, in like manner, by considering motion abstractedly not only from the body moved, but likewise from the figure it describes, and all particular directions and velocities, the abstract idea of motion is framed; which equally corresponds to all particular motions whatsoever that may be perceived by sense.

9. And as the mind frames to itself abstract ideas of qualities or modes, so does it, by the same precision or mental separation, attain abstract ideas of the more compounded beings which include several coexistent qualities. For example, the mind having observed that Peter, James, and John resemble each other in certain common agreements of shape and other qualities, leaves out of the complex or compounded idea it has of Peter, James, and any other particular man, that which is peculiar to each, retaining only what is common to all, and so makes an abstract idea wherein all the particulars equally partake—abstracting entirely from and cutting off all those circumstances and differences which might determine it to any particular existence. And after this manner it is said we come by the abstract idea of man, or, if you please, humanity, or human nature; wherein it is true there is included colour, because there is no man but has some colour, but then it can be neither white, nor black, nor any particular colour, because there is no one particular colour wherein all men partake. So likewise there is included stature, but then it is neither tall stature, nor low stature, nor yet middle stature, but something abstracted from all these. And so of the rest. Moreover, their being a great variety of other creatures that partake in some parts, but not all, of the complex idea of man, the mind, leaving out those parts which are peculiar to men, and retaining those only which are common to all the living creatures, frames the idea of animal, which abstracts not only from all particular men, but also all birds, beasts, fishes, and insects. The constituent parts of the abstract idea of animal are body, life, sense, and spontaneous motion. By body is meant body without any particular shape or figure, there being no one shape or figure common to all animals, without covering, either of hair, or feathers, or scales, &c., nor yet naked: hair, feathers, scales, and nakedness being the distinguishing properties of particular animals, and for that reason left out of the abstract idea. Upon the same account the spontaneous motion must be neither walking, nor flying, nor creeping; it is nevertheless a motion, but what that motion is it is not easy to conceive.

Berkeley then questions whether or not the mind can form abstract ideas:

10. Whether others have this wonderful faculty of abstracting their ideas, they best can tell: for myself, I find indeed I have a faculty of imagining, or representing to myself, the ideas of those particular things I have perceived, and of variously compounding and dividing them. I can imagine a man with two heads, or the upper parts of a man joined to the body of a horse. I can consider the hand, the eye, the nose, each by itself abstracted or separated from the rest of the body. But then whatever hand or eye I imagine, it must have some particular shape and colour. Likewise the idea of man that I frame to myself must be either of a white, or a black, or a tawny, a straight, or a crooked, a tall, or a low, or a middle-sized man. I cannot by any effort of thought conceive the abstract idea above described. And it is equally impossible for me to form the abstract idea of motion distinct from the body moving, and which is neither swift nor slow, curvilinear nor rectilinear; and the like may be said of all other abstract general ideas whatsoever. To be plain, I own myself able to abstract in one sense, as when I consider some particular parts or qualities separated from others, with which, though they are united in some object, yet it is possible they may really exist without them. But I deny that I can abstract from one another, or conceive separately, those qualities which it is impossible should exist so separated; or that I can frame a general notion, by abstracting from particulars in the manner aforesaid—which last are the two proper acceptations of abstraction. And there are grounds to think most men will acknowledge themselves to be in my case. The generality of men which are simple and illiterate never pretend to abstract notions. It is said they are difficult and not to be attained without pains and study; we may therefore reasonably conclude that, if such there be, they are confined only to the learned.

Berkeley subsequently considers what Locke had to say in another part of his Essay concerning the relationship between words, signs and ideas. Locke had written as follows:

6. How general words are made. The next thing to be considered is,—How general words come to be made. For, since all things that exist are only particulars, how come we by general terms; or where find we those general natures they are supposed to stand for? Words become general by being made the signs of general ideas: and ideas become general, by separating from them the circumstances of time and place, and any other ideas that may determine them to this or that particular existence. By this way of abstraction they are made capable of representing more individuals than one; each of which having in it a conformity to that abstract idea, is (as we call it) of that sort.

(Locke, Essay concerning Human Understanding, III.3.6).

Berkeley however, in the Introduction to The Principles of Human Knowledge, paragraph 11, argues as follows:

But it seems that a word becomes general by being made the sign, not of an abstract general idea, but of several particular ideas, any one of which it indifferently suggests to the mind. For example, when it is said “the change of motion is proportional to the impressed force,” or that “whatever has extension is divisible,” these propositions are to be understood of motion and extension in general; and nevertheless it will not follow that they suggest to my thoughts an idea of motion without a body moved, or any determinate direction and velocity, or that I must conceive an abstract general idea of extension, which is neither line, surface, nor solid, neither great nor small, black, white, nor red, nor of any other determinate colour. It is only implied that whatever particular motion I consider, whether it be swift or slow, perpendicular, horizontal, or oblique, or in whatever object, the axiom concerning it holds equally true. As does the other of every particular extension, it matters not whether line, surface, or solid, whether of this or that magnitude or figure.

Berkeley continues as follows:

12. By observing how ideas become general we may the better judge how words are made so. And here it is to be noted that I do not deny absolutely there are general ideas, but only that there are any abstract general ideas; for, in the passages we have quoted wherein there is mention of general ideas, it is always supposed that they are formed by abstraction, after the manner set forth in sections 8 and 9. Now, if we will annex a meaning to our words, and speak only of what we can conceive, I believe we shall acknowledge that an idea which, considered in itself, is particular, becomes general by being made to represent or stand for all other particular ideas of the same sort. To make this plain by an example, suppose a geometrician is demonstrating the method of cutting a line in two equal parts. He draws, for instance, a black line of an inch in length: this, which in itself is a particular line, is nevertheless with regard to its signification general, since, as it is there used, it represents all particular lines whatsoever; so that what is demonstrated of it is demonstrated of all lines, or, in other words, of a line in general. And, as that particular line becomes general by being made a sign, so the name “line,” which taken absolutely is particular, by being a sign is made general. And as the former owes its generality not to its being the sign of an abstract or general line, but of all particular right lines that may possibly exist, so the latter must be thought to derive its generality from the same cause, namely, the various particular lines which it indifferently denotes.

Berkeley then draws attention to Locke's assertion (Essay IV.7.9, quoted above) that “when we nicely reflect upon them, we shall find that general ideas are fictions and contrivances of the mind”, and then discusses at length the difficulties involved in forming the general idea of a triangle which is “neither oblique nor rectangle, neither equilateral, equicrural, nor scalenon, but all and none of these at once”. Berkeley then points out that the relationship between words and ideas corresponds to that between letters and quantities in (18th century) algebra:

19. But, to give a farther account how words came to produce the doctrine of abstract ideas, it must be observed that it is a received opinion that language has no other end but the communicating our ideas, and that every significant name stands for an idea. This being so, and it being withal certain that names which yet are not thought altogether insignificant do not always mark out particular conceivable ideas, it is straightway concluded that they stand for abstract notions. That there are many names in use amongst speculative men which do not always suggest to others determinate, particular ideas, or in truth anything at all, is what nobody will deny. And a little attention will discover that it is not necessary (even in the strictest reasonings) significant names which stand for ideas should, every time they are used, excite in the understanding the ideas they are made to stand for—in reading and discoursing, names being for the most part used as letters are in Algebra, in which, though a particular quantity be marked by each letter, yet to proceed right it is not requisite that in every step each letter suggest to your thoughts that particular quantity it was appointed to stand for.

David Hume devotes a section of A Treatise of Human Nature (also available here at www.davidhume.org) to the topic of abstract ideas. He argues (1.1.7) for the “impossibility of general ideas”, in support of Berkeley, observing that

Thirdly, it is a principle generally received in philosophy that everything in nature is individual, and that it is utterly absurd to suppose a triangle really existent, which has no precise proportion of sides and angles. If this therefore be absurd in fact and reality, it must also be absurd in idea; since nothing of which we can form a clear and distinct idea is absurd and impossible. But to form the idea of an object, and to form an idea simply, is the same thing; the reference of the idea to an object being an extraneous denomination, of which in itself it bears no mark or character. Now as it is impossible to form an idea of an object, that is possest of quantity and quality, and yet is possest of no precise degree of either; it follows that there is an equal impossibility of forming an idea, that is not limited and confined in both these particulars. Abstract ideas are therefore in themselves individual, however they may become general in their representation. The image in the mind is only that of a particular object, though the application of it in our reasoning be the same, as if it were universal.

Hume considers in depth, like Locke and Berkeley before him, the idea of a triangle. He concludes that

This then is the nature of our abstract ideas and general terms; and it is after this manner we account for the foregoing paradox, that some ideas are particular in their nature, but general in their representation. A particular idea becomes general by being annexed to a general term; that is, to a term, which from a customary conjunction has a relation to many other particular ideas, and readily recalls them in the imagination.

Having asserted this principple, Hume moves beyond consideration of triangles and geometrical figures:

The only difficulty, that can remain on this subject, must be with regard to that custom, which so readily recalls every particular idea, for which we may have occasion, and is excited by any word or sound, to which we commonly annex it. The most proper method, in my opinion, of giving a satisfactory explication of this act of the mind, is by producing other instances, which are analogous to it, and other principles, which facilitate its operation. To explain the ultimate causes of our mental actions is impossible. It is sufficient, if we can give any satisfactory account of them from experience and analogy.

First then I observe, that when we mention any great number, such as a thousand, the mind has generally no adequate idea of it, but only a power of producing such an idea, by its adequate idea of the decimals, under which the number is comprehended. This imperfection, however, in our ideas, is never felt in our reasonings; which seems to be an instance parallel to the present one of universal ideas.

Secondly, we have several instances of habits, which may be revived by one single word; as when a person, who has by rote any periods of a discourse, or any number of verses, will be put in remembrance of the whole, which he is at a loss to recollect, by that single word or expression, with which they begin.

Thirdly, I believe every one, who examines the situation of his mind in reasoning will agree with me, that we do not annex distinct and compleat ideas to every term we make use of, and that in talking of government, church, negotiation, conquest, we seldom spread out in our minds all the simple ideas, of which these complex ones are composed. It is however observable, that notwithstanding this imperfection we may avoid talking nonsense on these subjects, and may perceive any repugnance among the ideas, as well as if we had a fall comprehension of them. Thus if instead of saying, that in war the weaker have always recourse to negotiation, we should say, that they have always recourse to conquest, the custom, which we have acquired of attributing certain relations to ideas, still follows the words, and makes us immediately perceive the absurdity of that proposition; in the same manner as one particular idea may serve us in reasoning concerning other ideas, however different from it in several circumstances.

Fourthly, As the individuals are collected together, said placed under a general term with a view to that resemblance, which they bear to each other, this relation must facilitate their entrance in the imagination, and make them be suggested more readily upon occasion. And indeed if we consider the common progress of the thought, either in reflection or conversation, we shall find great reason to be satisfyed in this particular. Nothing is more admirable, than the readiness, with which the imagination suggests its ideas, and presents them at the very instant, in which they become necessary or useful. The fancy runs from one end of the universe to the other in collecting those ideas, which belong to any subject. One would think the whole intellectual world of ideas was at once subjected to our view, and that we did nothing but pick out such as were most proper for our purpose. There may not, however, be any present, beside those very ideas, that are thus collected by a kind of magical faculty in the soul, which, though it be always most perfect in the greatest geniuses, and is properly what we call a genius, is however inexplicable by the utmost efforts of human understanding.

Hume concludes the section of the Treatise of Human Nature concerned with abstract ideas by considering the impressions and ideas of a person presented with globes and cubes of white and black marble:

To remove this difficulty we must have recourse to the foregoing explication of abstract ideas. It is certain that the mind would never have dreamed of distinguishing a figure from the body figured, as being in reality neither distinguishable, nor different, nor separable; did it not observe, that even in this simplicity there might be contained many different resemblances and relations. Thus when a globe of white marble is presented, we receive only the impression of a white colour disposed in a certain form, nor are we able to separate and distinguish the colour from the form. But observing afterwards a globe of black marble and a cube of white, and comparing them with our former object, we find two separate resemblances, in what formerly seemed, and really is, perfectly inseparable. After a little more practice of this kind, we begin to distinguish the figure from the colour by a distinction of reason; that is, we consider the figure and colour together, since they are in effect the same and undistinguishable; but still view them in different aspects, according to the resemblances, of which they are susceptible. When we would consider only the figure of the globe of white marble, we form in reality an idea both of the figure and colour, but tacitly carry our eye to its resemblance with the globe of black marble: And in the same manner, when we would consider its colour only, we turn our view to its resemblance with the cube of white marble. By this means we accompany our ideas with a kind of reflection, of which custom renders us, in a great measure, insensible. A person, who desires us to consider the figure of a globe of white marble without thinking on its colour, desires an impossibility but his meaning is, that we should consider the figure and colour together, but still keep in our eye the resemblance to the globe of black marble, or that to any other globe of whatever colour or substance.

Thus for the purpose of construing the term abstract idea for legal purposes, it seems worth noting that ideas that are formed or experienced within the mind, and that many abstract ideas can be regarded as having been derived by a process of abstraction from more concrete ideas such as those arising from sense perception. Mathematical ideas pertaining to geometry and arithmetic that are derived from experience are considered to be abstract ideas. But Berkeley mentions humanity, human nature, body, life, sense and spontaneous motion as examples of ideas considered to be abstract ideas (The Principles of Human Knowledge, Introduction, Section 9, quoted above). And Hume also considers, in the portion of his treatise that deals with abstract ideas, the following ideas: government, church, negotiation and conquest. These examples convey some idea of the scope encompassed within the category of abstract ideas: if negotiation is considered to be an abstract idea, then business strategies like seeking a return on an investment, acting as a middleman, recovering the costs of providing services through the display of advertisements, hedging and escrow would by analogy also fall within the category of abstract ideas. If a church is an abstract idea, then by analogy so is an advertising agency, a financial institution or an exchange institution. And if conquest is an abstract idea, then so by analogy are promotion and advertising.

Consider the various ideas that might be conjured up by the word ‘church’. In some contexts this might refer to the one holy catholic and apostolic church. Some might associate this idea with the idea of the bride of Christ. For some, the idea might be associated with mental images of processions of red-robed cardinals accompanying a white-robed pope through ornate fresco-bedecked chapels in the Vatican. But the image of the cardinals in procession does not meaningfully suggest what is signified by the word used in that context. The idea formed in the mind when the word ‘church’ is used in this sense is an abstract idea.

Alternatively, the word ‘church’ might be used to refer to a specific building in the local community. It might occur in conversations in phrases such as “Turn left two blocks past the church.”. The word used in this sense might suggest various simple ideas: the visual image of the external appearance of the church; the image of the light streaming through the windows of the chancel at sunrise; the image of the light streaming through the rose window at the western end at sunset; the feel of the stonework of the church walls and pillars; the recollections of the hardness of the pews. The idea formed in the mind when the word is used in this sense is a complex idea formed by compounding many simple ideas, but it is not an abstract idea. Moreover the idea resembles but is distinct from the idea of a synagogue.

A corporation might regularly engage in sequences of structured financial transactions. They might note that, on numerous occasions, they incurred risk by engaging in financial transactions with certain parties, and chose to mitigate the risk to which they had exposed themselves by engaging in financial transactions with other parties to offset that risk. Reflecting on such business strategy might then lead, by abstraction, to the formation of an abstract idea, specifically the idea of hedging.

It should be noted that, whilst the philosophers Locke, Berkeley and Hume might differ as to the precise nature of abstract ideas and the manner in which they are formed in the mind, they are nevertheless in agreement concerning the subject matter of their disagreements. All three share a common understanding of the “metes and bounds” of the collection of ideas that are considered to be abstract ideas. Moreover it may be presumed that the term “abstract idea” came into common currency in the English-speaking communities as a result of people reading and reflecting on the writings of these philosophers.

Abstract Ideas in Mathematics

Many mathematical ideas arise directly through a process of abstraction that identifies properties and characteristics common to diverse objects of mathematical thought. For example the idea of a group in abstract algebra arises from contemplation of the common features of many well-known algebraic structures: subsets of the real or complex numbers that are closed under addition and subtraction, or under multiplication and division; properties arising out of the symmetries of geometrical objects such as triangles, squares, rectangles, cubes, tetrahedra and icosohedra; properties possessed by collections of permutations of finite sets. The lists of axioms that define the mathematical structures referred to by the terms group, ring, integral domain, field and vector space were chosen so as to encapsulate within themselves significant common properties of the more concrete mathematical structures that exhibit the characteristic structure of groups, rings, integral domains, fields or vector spaces. Also abstract simplicial complexes in homology theory capture characteristic combinatorial properties possessed by collections consisting of points, line segments, triangles, tetrahedra and their higher dimensional analogues that intersect each another in a suitably regular fashion so that, for example, where two distinct triangles intersect one another, they intersect along a common edge or at a single common vertex. Indeed, in the case of abstract simplicial complexes, the geometrical properties and visual appearances displayed by the concrete geometrical objects that correspond to points, line segments, triangles and tetrahedra in the real world are no longer present in their abstract counterparts which are defined in terms of collections of collections of elements taken from some list of symbols, where those symbols are themselves merely signs representing the vertices of the simplices of the corresponding geometrical complexes. Essentially all vestiges of geometrical and visual characteristics have been swept away in the process of abstraction that yields the mathematical concepts known as abstract simplicial complexes. Thus, when a simplicial complex made up out of geometrical simplices such as points, line segments, triangles and tetrahedra is considered as representing an abstract simplicial complex, the geometrical properties of the simplices that correspond to the visual properties of their real-world analogues have been ignored, just as the white and black colours of the marble objects described by David Hume (quoted above) were ignored when considering these objects as globes or cubes of marble, whereas the shapes of the pieces of marble were overlooked when considering these objects as pieces of black or white marble. Moreover two distinct geometrical simplicial complexes may indifferently represent the same abstract simplicial complex, provided that the simplices of one complex are in one-to-one correspondence with those of the other in a fashion that, whilst ignoring the sizes and shapes of those simplices, nevertheless respects both the dimensions of the simplicies and the incidence relationships between the simplices in each complex. Where such a one-to-one correspondence between respective simplices of two geometrical simplicial complexes establishes that the two geometrical simplicial complexes represent the same abstract simplicial complex, an equilaterial triangle in the first simplicial complex might, for example, correspond to a right-angled isosceles triangle in the second. However where a line segment is an edge of a triangle in the first complex, the corresponding line segment is an edge of the corresponding triangle in the second complex. Thus corresponding geometrical triangles in the two geometrical complexes correspond as instances of the abstract concept of a triangle, as discussed by John Locke (quoted above), though this abstract triangle could not consistently be said to be oblique, rectangle, equilateral, equicrural or scalenon.

The Supreme Court has held on many occasions that abstract ideas are patentable subject-matter under Section 101 of the statute (35 USC). But the mere fact that some ideas have been formed by some process of intellectual ‘abstraction’ from other more concrete ideas does not in itself supply a compelling reason for regarding such ideas as patentable. Rather it is that, in the case of ideas formed by abstraction from other ideas, the mental process of abstraction, whether performed consciously or unconsciously, has resulted in ideas that are pure intellectual concepts that only exist in the mind. “Phenomena of nature, though just discovered, mental processes, and abstract intellectual concepts are not patentable, as they are the basic tools of scientific and technological work.” Gottschalk v. Benson, 409 U.S. 63, 67, 93 S.Ct. 253, 34 L.Ed.2d 273 (1972). “A principle, in the abstract, is a fundamental truth; an original cause; a motive; these cannot be patented, as no one can claim in either of them an exclusive right.” Le Roy v. Tatham, 14 How. 156, 175.

Mathematical Ideas, Algorithms and Discoveries

The abstract intellectual creations of mathematicians include theorems, proofs and algorithms. An algorithm in mathematics defines the specification to determine a process for performing calculations or for solving particular problem. The Euclidean algorithm is an example of an algorithm for finding the greatest common divisor of two whole numbers. An analogous algorithm can be used to find a polynomial of highest degree dividing exactly two given polynomials. The simplex algorithm is an algorithm in the field of linear programming for finding the minimum value of a mathematical function on a set representable in mathematical terms as a geometric object in a multi-dimensional space. The Newton-Raphson method is a well-known algorithm for calculating numerically a value of a real variable at which some differentiable function has a value equal to zero. There are well-known procedures for solving equations that specify that some smooth function of several real variables takes on a given value

A branch of mathematics known as graph theory studies graphs that represent networks made up of vertices (or nodes) and edges. A graph in this context is an abstract idea. The real world presents many examples of networks: computer networks, telecommunications networks, social networks, etc. Nevertheless such networks connect entities, and, given any two entities within the network, the configuration of the network will determine whether or not those entities are directly connected. Abstracting from such situation, mathematicians arrive at the abstract idea of a graph, which is characterized in terms of finite collections of vertices and edges where, given any pair of distinct vertices, there exists at most one edge having those vertices as endpoints. Those edges may, in concrete situations represent cables connecting electronic devices, relationships between people, or links between web pages on the World-Wide Web. Solutions to problems expressible in the language of graph theory have many practical applications. For example scheduling problems often correspond to graph color problems whereby one seeks to assign a color to each vertex of a graph in such a way that adjacent vertices have distinct colors. When used to schedule lectures delivered at a university, the vertices might represent the lectures to be delivered in a given week, the edges might connect pairs of lectures that should be timetabled to ensure that a student can attend both lectures, and then the colors assigned to the vertices of the graph will represent the lecture times. One can formulate problems in the language of graph theory that are solvable for some graphs but not for others. One can ask how to characterize those graphs for which the problem in principle has a solution. One can then seek an efficient algorithm to solve the problem, for those graphs where the problem is known to have a solution. Such a problem is that of finding an Eulerian circuit within a connected graph. In 1735, the celebrated Swiss mathematician Leonhard Euler studied a recreational problem known as The Seven Bridges of Königsberg. The problem considered by the citizens of Königsberg was that of devising a route around their city returning to the starting point that would cross every bridge exactly once. Euler proved that no such route could exist, and determined the conditions under which similar problems would have a solution. This problem can be naturally expressed in the language of graph theory. A connected graph is a network of vertices and edges (with at most one edge directly connecting any two vertices) where there is a route joining any one vertex to any other. An Eulerian circuit is a circuit in such a graph that returns to its starting point after traversing every edge exactly once. One can ask whether or not such circuits exist in a given graph. It turns out that a connected graph has an Eulerian circuit if and only if, for each vertex of a graph, the number of edges incident on that vertex is an even number. Moreover, when the required condition is satisfied, one can devise an algorithm to determine a specification for such a circuit traversing every edge of the graph exactly once.

An essential point to note about such algorithms is that the set of rules that have to be followed to solve the problem algorithmically is often very straightforward, to the extent that those seeking to apply the algorithms can internalize the rules and procedures, and understand the reasons why the algorithm produces a solution to the problem. Moreover, if the size of a particular example is sufficiently small to permit calculation by hand, they can often follow the procedures with no more than pencil and paper to obtain the required solution algorithmically, without having to consult rulebooks to determine which step they have to perform at any given stage. The algorithm has therefore been internalized and has led to the formation of an abstract idea or abstract intellectual concept existing within the mind of the person performing the algorithm. And the steps of the algorithm will be the same, irrespective of the size of the particular configuration where the algorithm is being applied. Thus cryptological algorithms that determine public keys and private keys for secure cryptographic systems like RSA are based on results and algorithms in number theory developed in the 17th and 18th century if not before. Indeed the celebrated German mathematician Carl Friedrich Gauss commenced his celebrated treatise Disquisitionae arithmeticae (published 1801) with an systematic account of the theory of congruences that incorporated statements and proofs of theorems obtained by mathematicians such as Fermat and Euler that constitute the bedrock upon which modern cryptology has been founded. Moreover modern cryptology soon developed to employ many significant theorems in arithmetic and algebra developed by 19th century mathematicians in Germany and elsewhere. The security of modern cryptosystems designed on such principles relies on the fact that, where the keys are sufficiently large, massive computing resources are required to perform the calculations to crack the code in a relatively short period of time. To gain the security, the basic algorithms to determine the necessary cryptographic keys would be carried out on a digital computer. Nevertheless the rules and procedures for performing the calculation are rules that students at grade school or university could easily apply in situations where the numbers involved are much smaller. The concept of the algorithm is such that it can be comprehended by the human mind. What a computer-assisted implemention adds is the ability to carry out the computations in situations where it would be impossible to carry through the calculations by hand in a reasonable length of time.

The mental activity that involves the application of principles of classical logic (formalized and described in the principles of Propositional Calculus and Predicate Calculus) to the analysis and development of abstract intellectual concepts derived from collections, structures, quantities and geometrical figures is quintessentially mathematical. Any comprehensible algorithm that is formulated in terms of concepts that are intrinsically mathematical is a mathematical algorithm, and is itself an abstract intellectual concept. Indeed new ideas and concepts that are not generated by sense impressions are formed through reflection on other ideas within the mind. Where a complex idea is formed in the mind as a result of reflection of ideas that are themselves abstract intellectual concepts that are mathematical in nature, then that complex idea is itself a mathematical idea that is an abstract intellectual concept. Thus an algorithm whose design is formed in the mind through reflection on purely mathematical ideas is itself mathematical, and is in itself an abstract intellectual concept. In particular, a “procedure for solving a given type of mathematical problem” is a mathematical algorithm, and is thus an abstract intellectual concept (see Gottschalk v. Benson, 409 U.S. 67.

It is instructive to consider the history of a famous mathematical discovery. In the first half of the nineteenth century, mathematicians were familiar with the systems of real numbers (that can be represented by points on a line stretching to infinity in both directions), and complex numbers (that can be represented by points on a flat plain using the Argand diagram). Moreover the system of complex numbers can be regarded as a ‘two-dimensional algebra’ over the real numbers. One can use complex numbers to perform calculations relevant for plane geometry. The Irish mathematician William Rowan Hamilton (1805-1865) sought a corresponding three-dimensional algebra that would have corresponding uses when working in the geometry of three dimensions. For many years he sought such a three-dimensional algebra, admitting operations of addition, subtraction, multiplication and division, satisfying the Commutative and Distributive Laws, but without success. Then, in 1843, he was walking into Dublin along the towpath of a canal, when he had a flash of insight. He saw that he could construct a useful algebra, but it was a four-dimensional algebra over the real numbers which satisfied the Distributive Law but not the Commutative Law. He soon published his discovery. He referred to the elements of his four-dimensional algebra as quaternions. The system of quaternions shares another fundamental property in common with the systems or real and complex numbers: the operations of addition and multiplation satisfy the Associative Law. This law was identified and its significance recognized once Hamilton started exploring the properties of the quaternions he had discovered. The quaternions are useful: they provide efficient algorithms for computing the combined effect of several rotations about differing axes in three-dimensional space. The relationship between quaternions and rotations was worked out by Hamilton and, independently, by a young English mathematician, Arthur Cayley. The methods developed by Hamilton and Cayley subsequently proved important for spacecraft navigation, and for the programming of computer games.

In 1878, the German mathematician Georg Frobenius published a theorem that showed that the algebra of quaternions was the only algebra over the real numbers distinct from the systems of real and complex numbers, supporting operations of addition, subtraction, multiplication, and division by non-zero elements, that satisfies both the Distributive and Associative Laws familiar in grade school arithmetic and algebra. More precisely, any algebra with the required properties must be isomorphic to the algebra of quaternions. This means that there must be a one-to-one correspondence between quaternions and elements of the algebra under which sums, differences, products and quotients of quaternions correspond to sums, differences, products and quotients of elements of the algebra in question. Thus, once the problem for which Hamilton sought the solution had been fully formulated, the outcome was predetermined. In seeking a three-dimensional algebra with specified properties, Hamilton was attempting an impossible problem. When, after a number of years, he found a four-dimensional algebra, that lacked just one of the properties in question, he had succeeded in discovering the only possible solution to the reformulated problem consistent with the principles of logic.

Preemption

The respondents in Gottschalk v. Benson had devised a ‘data-processing method’ for converting binary-coded decimal numbers to numbers encoded as pure decimal numbers. The Supreme Court recognized that subject-matter concerned a computer program: “We have, however, made clear from the start that we deal with a program only for digital computers.” 409 U.S. 71. Nevertheless the Supreme Court held that the method was unpatentable, despite being a useful process. Moreover questions of novelty and nonobviousness were not taken into account in holding that the method was unpatentable: the Patent Office had rejected the remaining claims in the patent application without considering them for novelty and nonobviousness.

Now if one considers the problem on converting binary-coded decimal representations of whole numbers to pure binary representations of those numbers as a problem in mathematics, it soon becomes apparent that the problem is equivalent to that of evaluating the value p(x) of a polynomial when the argument x takes the value ten, in the particular case when all the coefficients of that polynomial are whole numbers between zero and nine, and then determining the binary representation of the resultant value. And the ‘data-processing method’ claimed in Claim 13 of the respondents' patent application is the method of evaluating that polynomial by Horner's method, in a context where the arithmetic is carried out in a system in which numbers are represented in binary arithmetic through strings of bits. Horner's Method is named after the English mathematician William George Horner (1786-1837), but it was familiar to Chinese mathematicians centuries earlier. Thus, had the patent issued to the respondents, Benson and Tabbot, anyone who programmed an algorithm to evaluate a polynomial on a standard digital computer using Horner's Method would almost certainly have infringed Claim 13 of the patent every time that a polynomial p(x) with whole number coefficients between zero and nine was evaluated with the argument x set equal to ten (see Gottschalk v. Benson, 409 U.S. 74).

One cannot sensibly ‘invent around’ Horner's method for evaluation of polynomials. Suppose that the polynomial p(x) is of degree 3. Then

p(x) = ax³ + bx² + cx + d

where a, b, c and d are the coefficients of the polynomial. The value p(x) of the polynomial for a given value x of the argument is evaluated using Horner's method as follows:

p(x) = ((ax + b) x + c) x + d.

This is clearly the optimal way to evaluate the value of the polynomial so as to minimize the number of computations required. In order to convert the number with decimal representation 1972 to pure binary, one would evaluate p(x) in binary arithmetic with a, b, c, d and x set equal to one, nine, seven, two and ten respectively. This should illustrate the extent of the “preemption” that would have resulted, had the Supreme Court affirmed the decision of the lower court in Gottschalk v. Benson and the patent had issued. As the Supreme Court pointed out, “if the judgment below [were] affirmed, the patent would wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself.” 409 U.S. 72.

In the patent application at issue in Parker v. Flook, Claim 1 (the independent claim) commenced as follows:

“1. A method for updating the value of at least one alarm limit on at least one process variable involved in a process comprising the catalytic chemical conversion of hydrocarbons wherein…” Parker v. Flook, 437 U.S. 596.

The rest of the claim described a purely mathematical algorithm for updating the alarm limit on that “process variable”. The algorithm is described in the Appendix to Opinion of the Court (Id, at 597--598). One fixes a value B₀, the “current alarm base” which should represent the normal value of the process variable. One also fixes a “predetermined alarm offset” K. The value of the ‘process variable’ should not normally exceed the value B₀ + K. One also chooses some predetermined quantity F between 0 and 1. The parameters B₀, K and F determine the corresponding updated alarm limit in accordance with Claim 1. Once the process of catalytic chemical conversion of hydrocarbons is underway, one determines, at some time t, the “present value” P(t) of the ‘process variable’ (denoted by PVL in the patent claim). The alarm limit is then updated to the value (1 - F) (B₀ + K) + F P(t). Any process comprising (i.e., involving) the “catalytic chemical conversion of hydrocarbons” which regularly updates at least one ‘alarm limit’ on at least one ‘process variable’ by this method would infringe Claim 1 of the patent.

In Bilski v. Kappos, the Supreme Court considered claims to a business method. The sole independent claim, Claim 1, claims, in general terms, a “a method for managing the consumption risk costs of a commodity sold by a commodity provider at a fixed price”, and sets out a series of steps that describe a method of hedging to reduce exposure the risk. Claim 2 limits the claim to a situation in which “transmission distributors” are distributing energy. Claim 3 further limits the claim to a situation in which the potential risks arise as a result of inclement weather. Claim 4 further limits the claim to a situation in which the fixed bill price is calculated by a specific mathematical formula:

F_i + (C_i + T_i + LD_i) × (α + β E(W_i)),

“Hedging is a fundamental economic practice long prevalent in our system of commerce and taught in any introductory finance class." 545 F.3d, at 1013 (Rader, J., dissenting).… “ The concept of hedging, described in claim 1 and reduced to a mathematical formula in claim 4, is an unpatentable abstract idea, just like the algorithms at issue in Benson and Flook. Allowing petitioners to patent risk hedging would pre-empt use of this approach in all fields, and would effectively grant a monopoly over an abstract idea.” Bilski v. Kappos, 130 S.Ct. 3231.

In Mayo v. Prometheus, the Supreme Court again revisited the issue of pre-emption. The case concerned a test to determine whether to adjust dosage of a medication in regular use. The patent owners had established a correlation between the toxicity of the dosage and the quantity of certain chemicals generated in the patent's bloodstream after administration of the medication. Thus blood tests would be carried out, and doctors would adjust dosage in the light of the results of those tests. The form of patent claim used was a patent on a method of administering the medication. The Federal Circuit had upheld the patent on the basis that administering the medication caused chemical reactions in the patient's bloodstream, and this was sufficient to show that the claim was not a claim to a law of nature, a natural phenomenon or an abstract idea. The Supreme Court reversed. The opinion discussed whether the scope of the laws of nature recited in the patent claim should have a bearing on patentability under Section 101:

“Second, Prometheus argues that, because the particular laws of nature that its patent claims embody are narrow and specific, the patents should be upheld. Thus, it encourages us to draw distinctions among laws of nature based on whether or not they will interfere significantly with innovation in other fields now or in the future.…

“But the underlying functional concern here is a relative one: how much future innovation is foreclosed relative to the contribution of the inventor.… A patent upon a narrow law of nature may not inhibit future research as seriously as would a patent upon Einstein's law of relativity, but the creative value of the discovery is also considerably smaller. And, as we have previously pointed out, even a narrow law of nature (such as the one before us) can inhibit future research.…” Mayo v. Prometheus, 132 S.Ct. 1303

“Courts and judges are not institutionally well suited to making the kinds of judgments needed to distinguish among different laws of nature. And so the cases have endorsed a bright-line prohibition against patenting laws of nature, mathematical formulas and the like, which serves as a somewhat more easily administered proxy for the underlying "building-block" concern.” Ibid.

The Supreme Court rejected the suggestion that virtually any step beyond a statement of a law of nature should be patentable:

“Third, the Government argues that virtually any step beyond a statement of a law of nature itself should transform an unpatentable law of nature into a potentially patentable application sufficient to satisfy § 101's demands.…

“This approach, however, would make the "law of nature" exception to § 101 patentability a dead letter. The approach is therefore not consistent with prior law. The relevant cases rest their holdings upon section 101, not later sections.” Ibid.

The Supreme Court concluded by deeming the claimed invention at issue in Mayo v. Prometheus to be unpatentable for essentially the same reasons that the Court, in Gottschalk v. Benson had deemed the invention at issue there to be unpatentable:

“For these reasons, we conclude that the patent claims at issue here effectively claim the underlying laws of nature themselves. The claims are consequently invalid. And the Federal Circuit's judgment is reversed.” Mayo v. Prometheus, 132 S.Ct. 1305.

It is thus well-established case law that any claimed invention that, though claimed as a process, nevertheless preempts a law of nature or an abstract idea is unpatentable, on the grounds that it effectively claims the law of nature or abstract idea itself.

Routine Applications of Laws of Nature and Abstract Ideas

In order to be patentable, a claimed invention or discovery must be new and useful, and must fall within one of the four categories of eligible subject-matter: processes; machines; manufactures; compositions of matter. It must satisfy all the relevant provisions of the statute. In particularly it must satisfy all the provisions of Section 102 regarding ‘novelty’, and must also satisfy the provisions of Section 103 regarding ‘nonobviousness’. Also the invention must be properly specified and claimed, in accordance with the provisions of Section 112, so that a person having ordinary skill in the art is enabled to make and use the invention.

However the conditions these sections do not encompass all the conditions that a purportedly new and useful invention must satisfy in order to qualify for protection under the statute. Laws of nature, natural phenomena and abstract ideas are not in themselves patentable. The applicable law was summarized by the Supreme Court in Mayo v. Prometheus, 132 S.Ct. 1293:

The Court has long held that this provision contains an important implicit exception. “[L]aws of nature, natural phenomena, and abstract ideas” are not patentable. Diamond v. Diehr, 450 U.S. 175, 185, 101 S.Ct. 1048, 67 L.Ed.2d 155 (1981); see also Bilski v. Kappos, 561 U.S. ___, ___, 130 S.Ct. 3218, 3233-3234, 177 L.Ed.2d 792 (2010);

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Routine Applications of Laws of Nature and Abstract Ideas

In order to be patentable, a claimed invention or discovery must be new and useful, and must fall within one of the four categories of eligible subject-matter: processes; machines; manufactures; compositions of matter. It must satisfy all the relevant provisions of the statute. In particularly it must satisfy all the provisions of Section 102 regarding ‘novelty’, and must also satisfy the provisions of Section 103 regarding ‘nonobviousness’. Also the invention must be properly specified and claimed, in accordance with the provisions of Section 112, so that a person having ordinary skill in the art is enabled to make and use the invention.

However the conditions these sections do not encompass all the conditions that a purportedly new and useful invention must satisfy in order to qualify for protection under the statute. Laws of nature, natural phenomena and abstract ideas are not in themselves patentable. The applicable law was summarized by the Supreme Court in Mayo v. Prometheus, 132 S.Ct. 1293:

The Court has long held that this provision contains an important implicit exception. “[L]aws of nature, natural phenomena, and abstract ideas” are not patentable. Diamond v. Diehr, 450 U.S. 175, 185, 101 S.Ct. 1048, 67 L.Ed.2d 155 (1981); see also Bilski v. Kappos, 561 U.S. ___, ___, 130 S.Ct. 3218, 3233-3234, 177 L.Ed.2d 792 (2010); Diamond v. Chakrabarty, 447 U.S. 303, 309, 100 S.Ct. 2204, 65 L.Ed.2d 144 (1980); Le Roy v. Tatham, 14 How. 156, 175, 14 L.Ed. 367 (1853); O'Reilly v. Morse, 15 How. 62, 112-120, 14 L.Ed. 601 (1854); cf. Neilson v. Harford, Webster's Patent Cases 295, 371 (1841) (English case discussing same). Thus, the Court has written that “a new mineral discovered in the earth or a new plant found in the wild is not patentable subject matter. Likewise, Einstein could not patent his celebrated law that E=mc2; nor could Newton have patented the law of gravity. Such discoveries are ‘manifestations of ... nature, free to all men and reserved exclusively to none.’” Chakrabarty, 447 U.S. 309, 100 S.Ct. 2204 (quoting Funk Brothers Seed Co. v. Kalo Inoculant Co., 333 U.S. 127, 130, 68 S.Ct. 440, 92 L.Ed. 588 (1948)).

“Phenomena of nature, though just discovered, mental processes, and abstract intellectual concepts are not patentable, as they are the basic tools of scientific and technological work.” Gottschalk v. Benson, 409 U.S. 63, 67, 93 S.Ct. 253, 34 L.Ed.2d 273 (1972). And monopolization of those tools through the grant of a patent might tend to impede innovation more than it would tend to promote it.

But closer examination of the opinions of the Supreme Court that deny patent-ineligibility to the subject-matter claimed in Funk Bros. v. Kalo, Gottschalk v. Benson, Parker v. Flook, and Mayo v. Prometheus demonstrates that the exclusion from patent-eligibility establed in this line of cases is not restricted to acts of contemplating laws of nature, natural phenomena and abstract ideas.

“Discovery of the fact that certain strains of each species of these bacteria can be mixed without harmful effect to the properties of either is a discovery of their qualities of non-inhibition. It is no more than the discovery of some of the handiwork of nature and hence is not patentable. The aggregation of select strains of the several species into one product is an application of that newly-discovered natural principle. But however ingenious the discovery of that natural principle may have been, the application of it is hardly more than an advance in the packaging of the inoculants.” Funk Bros. v. Kalo, 333 U.S. 131.

“We have, however, made clear from the start that we deal with a program only for digital computers.… What we come down to in a nutshell is the following.

“It is conceded that one may not patent an idea. But in practical effect that would be the result if the formula for converting BCD numerals to pure binary numerals were patented in this case. The mathematical formula involved here has no substantial practical application except in connection with a digital computer, which means that if the judgment below is affirmed, the patent would wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself.” Gottschalk v. Benson, 409 U.S. 71-72.

The question presented to the Supreme Court in Parker v. Flook was described by that court in the following terms:

“Respondent applied for a patent on a ‘Method for Updating Alarm Limits.’ The only novel feature of the method is a mathematical formula. In Gottschalk v. Benson, 409 U. S. 63, we held that the discovery of a novel and useful mathematical formula may not be patented. The question in this case is whether the identification of a limited category of useful, though conventional, post-solution applications of such a formula makes respondent's method eligible for patent protection.” Parker v. Flook, 437 U.S. 585.

The Court then pointed out that applications of an unpatentable principle do not necessarily meet the statutory requirements to qualify as a patentable process, even though they may be useful or be in themselves forms of activity:

“The notion that post-solution activity, no matter how conventional or obvious in itself, can transform an unpatentable principle into a patentable process exalts form over substance. A competent draftsman could attach some form of post-solution activity to almost any mathematical formula; the Pythagorean theorem would not have been patentable, or partially patentable, because a patent application contained a final step indicating that the formula, when solved, could be usefully applied to existing surveying techniques.” Parker v. Flook, 437 U.S. 590.

In Bilski v. Kappos, the Supreme Court considered the patentability of claims that were dependent on a unpatentable claim drawn to use of a simple mathematical formula for determining a price in a claimed business method, where the business method claim in turn was drawn to the abstract idea of hedging in business transactions, the Court considered the remaining claims. They found that these claims were obvious refinements and applications of the abstract method of the hedging method involving no more than well-understood, routine, conventional activity previously engaged in by those experienced in the use of statistical methods in modern business and finance:

“Petitioners' remaining claims are broad examples of how hedging can be used in commodities and energy markets. Flook established that limiting an abstract idea to one field of use or adding token postsolution components did not make the concept patentable. That is exactly what the remaining claims in petitioners' application do. These claims attempt to patent the use of the abstract idea of hedging risk in the energy market and then instruct the use of well-known random analysis techniques to help establish some of the inputs into the equation. Indeed, these claims add even less to the underlying abstract principle than the invention in Flook did, for the Flook invention was at least directed to the narrower domain of signaling dangers in operating a catalytic converter.” Bilski v. Kappos, 130 S.Ct. 3231.

Patentability of Computer-Assisted Inventions

Whilst the Supreme Court in Gottschalk v. Benson, Parker v. Flook and Mayo v. Prometheus deemed inventions that effectively preempted a mathematical method or a natural law to be unpatentable, the Supreme Court recognized in all those judgements that a novel and inventive application of a natural law or of an abstract idea might be patentable:

“It is said that the decision precludes a patent for any program servicing a computer. We do not so hold.” Gottschalk v. Benson 409 U.S. 71.

“Yet it is equally clear that a process is not unpatentable simply because it contains a law of nature or a mathematical algorithm. See Eibel Process Co. v. Minnesota & Ontario Paper Co., 261 U. S. 45; Tilghman v. Proctor, supra. For instance, in Mackay Radio & Telegraph Co. v. Radio Corp. of America, 306 U. S. 86, the applicant sought a patent on a directional antenna system in which the wire arrangement was determined by the logical application of a mathematical formula. Putting the question of patentability to one side as a preface to his analysis of the infringement issue, Mr. Justice Stone, writing for the Court, explained:

‘While a scientific truth, or the mathematical expression of it, is not patentable invention, a novel and useful structure created with the aid of knowledge of scientific truth may be.’ Id., at 94.”

Parker v. Flook, 437 U.S. 591.

“The Court has recognized, however, that too broad an interpretation of this exclusionary principle could eviscerate patent law. For all inventions at some level embody, use, reflect, rest upon, or apply laws of nature, natural phenomena, or abstract ideas.” Mayo v. Prometheus 132 S.Ct. 1293.

Nevertheless, obvious applications of a law of nature or an abstract idea are unlikely to be patentable: “[s]till, as the Court has also made clear, to transform an unpatentable law of nature into a patent-eligible application of such a law, one must do more than simply state the law of nature while adding the words ‘apply it.’” Mayo v. Prometheus 132 S.Ct. 1294.

In Diamond v. Diehr, the Supreme Court considered a case where the Commissioner of Patents had appealed a decision of a lower court reversing the rejection of a patent application made by the respondents. The curing process involved the use of a computer to monitor the temperature in the mold, and use this information to recalculate curing times using a simple mathematical equation known as the Arrhenius equation. The Arrhenius equation is an equation expressing the reaction rate of a chemical reaction as a function of the temperature. Specifically, the rate constant k of a chemical reaction is related to the absolute temperature T, the activation energy E_a and the Universal Gas Constant by an equation of the form k = A exp(-E_a/RT), where A is a constant. When employed in the rubber curing process, the cure time v would be inversely proportional to the reaction rate, and thus the equation could be reexpressed in the equivalent form log v = CZ + x, where C denotes the activation energy constant (unique to each batch), Z denotes the temperature of the mold at a specified position, and x is a constant depending on the geometry of the mold (see Diamond v. Diehr, 450 U.S. 179). Nevertheless, a preferred embodiment (disclosed in US patent 4344142) solves the equation numerically in the form v = exp(CZ + x) by expanding the exponential function on the right hand side as a Taylor series.

“Respondents claim that their process ensures the production of molded articles which are properly cured. Achieving the perfect cure depends upon several factors including the thickness of the article to be molded, the temperature of the molding process, and the amount of time that the article is allowed to remain in the press. It is possible using well-known time, temperature, and cure relationships to calculate by means of the Arrhenius equation when to open the press and remove the cured product. Nonetheless, according to the respondents, the industry has not been able to obtain uniformly accurate cures because the temperature of the molding press could not be precisely measured, thus making it difficult to do the necessary computations to determine cure time. Because the temperature inside the press has heretofore been viewed as an uncontrollable variable, the conventional industry practice has been to calculate the cure time as the shortest time in which all parts of the product will definitely be cured, assuming a reasonable amount of mold-opening time during loading and unloading. But the shortcoming of this practice is that operating with an uncontrollable variable inevitably led in some instances to overestimating the mold-opening time and overcuring the rubber, and in other instances to underestimating that time and undercuring the product.

“Respondents characterize their contribution to the art to reside in the process of constantly measuring the actual temperature inside the mold. These temperature measurements are then automatically fed into a computer which repeatedly recalculates the cure time by use of the Arrhenius equation. When the recalculated time equals the actual time that has elapsed since the press was closed, the computer signals a device to open the press. According to the respondents, the continuous measuring of the temperature inside the mold cavity, the feeding of this information to a digital computer which constantly recalculates the cure time, and the signaling by the computer to open the press, are all new in the art.” Diamond v. Diehr, 450 U.S. 177-179.

The Supreme Court, in Mayo v. Prometheus analysed its analysis of its previous holding in Diamond v. Diehr in the following terms:

“The Court pointed out that the basic mathematical equation, like a law of nature, was not patentable. But it found the overall process patentable because of the way the additional steps of the process integrated the equation into the process as a whole. Those steps included ‘installing rubber in a press, closing the mold, constantly determining the temperature of the mold, constantly recalculating the appropriate cure time through the use of the formula and a digital computer, and automatically opening the press at the proper time.’ Id., at 187, 101 S.Ct. 1048. It nowhere suggested that all these steps, or at least the combination of those steps, were in context obvious, already in use, or purely conventional. And so the patentees did not ‘seek to pre-empt the use of [the] equation,’ but sought ‘only to foreclose from others the use of that equation in conjunction with all of the other steps in their claimed process.’ Ibid. These other steps apparently added to the formula something that in terms of patent law's objectives had significance—they transformed the process into an inventive application of the formula.” Mayo v. Prometheus, 132 S.Ct. 1298-1299.

In other words, a “physical and chemical process for molding precision synthetic rubber products” (Diamond v. Diehr 450 U.S. 177) that involves using “a mold for precisely shaping the uncured material under heat and pressure and then curing the synthetic rubber in the mold“ (Ibid.) that would otherwise be considered to be a patentable ‘process’ does not cease to be patentable merely through the incorporation of a computing device that recalculates curing times by means of a simple equation that expresses in mathematical language a law of nature concerning chemical reactions. The mere incorporation of a computing device as a component in a machine, manufacture or process should not thereby deprive the claimed invention of patent protection, especially when the claimed invention is of a type “which ha[s] historically been eligible to receive the protection of our patent laws” (Id, at 184).

The opinion of the Supreme Court in Diamond v. Diehr was not unanimous, and Justice Stevens wrote a dissenting opinion in which he was joined by three other Supreme Court Justices. The opinion made it clear that their dissent was not based on the principle that computer-assisted inventions were not patentable. The dissenting judges were of the opinion that there was nothing novel in the claimed invention besides the computer-assisted process for calculating the curing time.

“As the Court reads the claims in the Diehr and Lutton patent application, the inventors' discovery is a method of constantly measuring the actual temperature inside a rubber molding press. As I read the claims, their discovery is an improved method of calculating the time that the mold should remain closed during the curing process. If the Court's reading of the claims were correct, I would agree that they disclose patentable subject matter. On the other hand, if the Court accepted my reading, I feel confident that the case would be decided differently.

“There are three reasons why I cannot accept the Court's conclusion that Diehr and Lutton claim to have discovered a new method of constantly measuring the temperature inside a mold. First, there is not a word in the patent application that suggests that there is anything unusual about the temperature-reading devices used in this process—or indeed that any particular species of temperature-reading device should be used in it. Second, since devices for constantly measuring actual temperatures—on a back porch, for example—have been familiar articles for quite some time, I find it difficult to believe that a patent application filed in 1975 was premised on the notion that a "process of constantly measuring the actual temperature" had just been discovered. Finally, the Patent and Trademark Office Board of Appeals expressly found that ‘the only difference between the conventional methods of operating a molding press and that claimed in [the] application rests in those steps of the claims which relate to the calculation incident to the solution of the mathematical problem or formula used to control the mold heater and the automatic opening of the press.’ This finding was not disturbed by the Court of Customs and Patent Appeals and is clearly correct.” Diamond v. Diehr, 450 US 206-208.

Thus it would appear that, for all the members of the Supreme Court, it was assessments of the specific nature, novelty and nonobviousness of the claimed invention and its contribution to the art that were the deciding factor when considering whether to affirm or reverse the decision of the lower court.

Machines and Manufactures

An artisan, working on a daily basis with machines or manufactures, may conceive of a useful machine or manufacture that either in itself resembles no machine or manufacture familiar to the artisan, or else possesses new or useful features that improve on the characteristics and capabilities of machines or manufactures known to the artisan. Such conceptions are inventive in nature. The artisan may then construct this machine or manufacture. Now the conception of such a machine or manufacture is not guaranteed protection under the Patent Statute. The purported invention may be new to the artisan, and may be an improvement over prior art known to the artisan. But the mere fact that the artisan's conception of the machine or manufacture was inventive in nature does not in itself entitle the artisan to a patent for the resulting machine or manufacture. Indeed the Committee Reports accompanying the 1952 Act observe that “[a] person may have ‘invented’ a machine or a manufacture, which may include anything under the sun that is made by man, but it is not necessarily patentable under section 101 unless the conditions of the title are fulfilled.” S. Rep. No. 1979, 82d Cong., 2d Sess., 5 (1952); H. R. Rep. No. 1923, 82d Cong., 2d Sess., 6 (1952). The conditions of the title (i.e., Title 35 of the United States Code) require in particular that the invention be novel with respect to the prior art (section 102) and that it not be obvious (section 103).

We suppose that obvious applications of laws of nature, natural phenomena and abstract ideas are unpatentable. We now consider whether a machine or manufacture of a traditional kind could plausibly be regarded as an obvious application of an abstract idea. The artisan has constructed her machine or manufacture. It is there before her. She can see it, touch it, hear it in operation, and smell it. The machine or manufacture before her is most definitely concrete and tangible. The idea of that specific machine is not an abstract idea as that term was defined by Locke. The idea of the specific machine or manufacture is a complex idea, compounded of many simple ideas, but the idea has not been formed by abstraction from those simple ideas. Thus it seems very unlikely that the claimed machine or manufacture could be unpatentable on the grounds of being an obvious application of an abstract idea.

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• Conditions for Patentability under Section 101 - Draft Continued! - Authored by: Anonymous on Sunday, March 24 2013 @ 06:05 PM EDT

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