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:
Fi + (Ci + Ti +
LDi)
× (α + β
E(Wi)),
wherein
Fi represents fixed
costs,
Ci repesents variable costs,
Ti represents long
distance transportation costs,
LDi represents local delivery
costs
and E(Wi) is an “estimated location-specific
weather
indicator in period i”, and where
α and β are constants.
Subsequent claims dependent
on Claim 4 cover situations where variables are
capped, or
are determined using standard statistical techniques.
The Supreme
Court determined that the claims were invalid,
as being drawn to a method of
hedging:
“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
The Court then offers a pragmatic justification for
upholding
a bright-line prohibition against patentablity of laws of
nature,
mathematical formulae and the like:
“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);[ Reply to This | Parent | # ]
|
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.
The
claimed subject matter in
Funk Bros. v. Kalo
was an inoculant for
agricultural use composed of strains of
root-nodule bacteria that were not
mutually inhibiting.
But as the Supreme Court explained in that
case:
“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.
The Supreme Court in
Gottschalk v. Benson held that
an
application of a unpatentable mathematical algorithm taking
the form for a
program for digital computers was itself patentable:
“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.
In
Mayo v. Prometheus,
the
Supreme Court deemed unpatentable claims drawn to
no more than well-understood,
routine, conventional activity
applying the law of nature at
issue.
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 Ea and the Universal Gas
Constant
by an equation of the form
k = A
exp(-Ea/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.
The respondents made a
case that their invention amounted to more
than an attempt to
claim a scientific truth, or the mathematical expression of
it:
“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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