Here's Groklaw's response to the USPTO's request for suggested topics for discussion in the future by the Software Partnership. We just sent it to the USPTO today.
We are also publishing here on Groklaw a more detailed supplement on those four topics, explaining in depth why we propose them, with references, on the theme, "Using Semiotics to Identify Patent-Eligible Software". The supplement is referenced in the document sent, if they wish to read more in-depth arguments, based on interest level.
To help you find the document you are most interested in, here are links to each:
[Document Sent to the USPTO ]
[Supplement: Using Semiotics to Identify Patent-Eligible Software]
First, here's the document we sent to the USPTO, our list of the four proposed topics for discussion, after which you'll find the more detailed supplement.
Groklaw's Response to the USPTO on Topic 2:
Suggested Additional Topics for Future Discussion by the Software Partnership
In response to the USPTO's request for topics for future discussion by the Software Partnership, the technical community at Groklaw suggests the following four topics, in order of priority:
1: Is computer software properly patentable subject matter?
2: Are software patents helping or hurting innovation and the US economy?
3: How can software developers help the USPTO understand how computers actually work, so issued patents match technical realities, avoiding patents on functions that are obvious to those skilled in the art, as well as avoiding duplication of prior art?
4: What is an abstract idea in software and how do expressions of ideas differ from applications of ideas?
In order to explain why these topics could be fruitful, here are some brief thoughts in explanation. A more detailed explanation, with references, can be found here.
Suggested topic 1:
Is computer software properly patentable subject matter?
If software consists of two elements neither of which is patentable subject matter, can software itself be patentable subject matter?
Software consists of algorithms -- in other words mathematics -- and data, which is being manipulated by the algorithms. Mathematics is not patentable subject matter and neither is data. On what basis, then, is software patentable subject matter?
We would welcome a discussion on this topic, as it is a key issue to the developer community. Note that Groklaw has published a number of articles on this topic, which can all be found at here on Groklaw.
A particular point of interest is how the meaning of data influences the patentable subject matter analysis. Computers manipulate bits, and bits are electronic symbols which are used to convey meaning. In some patents, such as in Diamond v. Diehr's industrial process for curing rubber, what this meaning signifies is actually claimed clearly. In Diehr's case the rubber is cured. But in most pure software patents the meaning is merely referred to. Should this distinction influence whether the claim is patentable? We will return to this question in more detail, under the
headings of Suggested topic 3 and Suggested topic 4.
Suggested topic 2:
Are software patents helping or hurting innovation and hence the US economy?
It would be useful to hear from entrepreneurs on a wide scale on the effects software patents are having on their startups or business projects. Microsoft's Bill Gates himself has stated that if software patents had been allowed when he was starting his business, he would have been blocked.1 Is that happening to today's entrepreneurs? If software authors are unable to clear all rights to their own products because there is no practical way to do so, how can such a situation foster progress and innovation? Rather it seems to force developers, or the companies that hire them, to choose either to go ahead and develop innovative products with the certainty that if it is successful there will be infringement lawsuits or stop developing innovative products altogether.
Every firm with an internal IT department writes software. Every firm which maintains its own website writes software. There are roughly 634,000 firms in the United States with 20 or more employees and 1.7 million firms with 5 to 19 employees. A very large fraction of these firms write software. In an ideal world, all firms should verify all patents as they are issued to avoid infringement. This need to verify the relevance of all patents would necessarily be a constant, on-going activity. For one thing, corporate software must frequently be adapted to new needs and any new version may potentially infringe a patent not previously infringed. A study has concluded the task is practically impossible to accomplish.2
Even if a patent lawyer only needed to look at a patent for ten minutes, on average, to determine whether any part of a particular firm's software infringes, it would require roughly 2 million patent attorneys, working full-time, to compare every firm's products with every patent issued in a given year.
This is an impossibility, because there are only roughly 40,000 registered patent attorneys and patent agents in the US.
The above estimation covers just the work of keeping up with newly issued patents every year. Checking already issued patents would require even more attorneys.
Looking at the situation from yet another perspective, let us compare lines of code with sentences in a book. Each English sentence expresses an idea. Each combination of sentences expresses a more complex idea. Then more and more complex ideas are expressed in paragraphs, chapters etc. The total number of ideas from all works of authorship is extremely large. Imagine a hypothetical intellectual property regime where all such ideas are patentable. This would generate a large number of patents, with all authors having to check all the issued patents for potential infringement, with more patents issuing every year.
It is clearly impossible to promote innovation with such a system that is not practically functional, but that is the situation software developers face, one where they have no practical way to verify they own all rights to their own work. Such a system is guaranteed to harm the economy with monopolistic rent-seeking and unneeded litigation, which is what we are currently witnessing.
Suggested topic 3:
How can software developers help the USPTO understand how computers actually work, so issued patents match technical realities, avoiding patents on functions that are obvious to those skilled in the art, as well as avoiding duplication of prior art?
The current interpretation of patent law is riddled with what developers view as fundamentally erroneous conceptions of how computers work. Other than the current USPTO request for input, developers feel shut out of decisions, decisions made without their contributed knowledge and skill, yet considered legally binding precedent despite violating technical reality,
and yet the practitioners in the field
are the very ones who best understand what software is and how it does what it
Textbooks describe in detail what mathematical algorithms are, but case law doesn't seem to understand or to reference these sources. Instead, we see courts using standard dictionary definitions. These definitions are too succinct and incomplete, at best. The result is confusion about what algorithms are.
For an example, courts have made an unrealistic distinction between so-called mathematical algorithms and computer algorithms that purportedly are not mathematical. The field of computer science itself recognizes no such distinction, but the legal environment surrounding software patents ignores what mathematicians and computer scientists say about algorithms. Since the ensuing descent into surrealism directly
impacts the controversial question of when a computer-implemented
invention is directed to a patent-ineligible abstract idea, a serious
problem is caused, which could have been avoided by a deeper, more accurate technical understanding.
Second, it seems some, including some courts, believe the functions of software are performed through the physical properties of electrical circuits, incorrectly treating the computer as a device which operates solely through the laws of physics. This approach is factually and technically incorrect because not everything in software functions through the laws of physics. Indeed, bits in a computer are constructed and manipulated by the use of physical laws. However, bits are also symbols. They have meanings which are assigned by human beings. The meaning of bits is essential to performing the functions of software. The capability of bits to convey meaning is not a physical property of the computer.
Software developers don't write software by working with the physical properties of circuits. Developers define the meaning of data and implement operations of arithmetic and logic that apply to the meaning. They debug software by reading the meaning of the data stored in the computer and verifying whether the correct operations are performed. Again, the aspects of software related to meaning cannot be explained solely in terms of the physical properties of the computer.
This erroneous physical view of the computer is the basis of an oft-stated argument. Some have claimed that software alters the computer it runs on, thus creating a "new machine". (See
In re Bernhart, 57 C.C.P.A. 737, 417 F.2d 1395, 1399-1400, 163 USPQ 611, 615-16 (CCPA 1969) --"[I]f a machine is programmed in a certain new and unobvious way, it is physically different from the machine without that program; its memory elements are differently arranged.")
This belief is used to justify the view that software patents are actually a subcategory of hardware patents, making software patentable almost without restriction or restraint, in that all software runs on a computer. To demonstrate what is wrong with that argument at its very foundation, let's compare a printing press with a computer.
It is easy to see that the content of a book is not a machine part. The meaning of a book is not explained by the laws of physics applicable to a printing press. But the comparison of a computer and the printing press shows that there is no material difference in their handling of meaning. Any argument related to meaning which is applicable to a printing press is applicable to a computer and vice-versa.
Imagine a claim on a printing press configured to print a specific book, say Tolkien's The Lord of the Rings. This is a claim on a machine which operates according to the laws of physics. Printing is a physical process for laying ink on paper. It functions without the intervention of a human mind. But still this process involves the meaning of a book. Such a claim could only be infringed if the book has the recited meaning.
One could argue that a configured printing press is physically different from an unconfigured one. The configured printing press can print a specific book while the unconfigured one cannot. Books with different contents are different articles of manufacture. Differently configured printing presses perform different functions, because they make different articles of manufacture. Therefore, as this hypothetical argument goes, a printing press configured to print a specific book has become a specific machine which performs a
practical and useful task and, lo and behold, the result is a "new machine
test" for printing presses. However, the fact
that no one in the real world would accept a world in which a printing press
becomes a new machine every time it is set up to print a new book is quite sobering.
Or ought to be. Because this is the fallacious argument used to justify that a computer configured with software becomes a new machine.
Software patents are often written similarly to this analogy. Like a printing press, the computer operates according to the laws of physics. It functions mostly without the intervention of the human mind, although from time to time human input may be required. But the process of computing needs the meaning of the data to actually solve problems. The claim is infringed only if the data has the recited meaning.
The argument that a programmed computer is different from an unprogrammed one is exactly symmetric to the one we have just made about printing presses. There is a reason for this. The technologies are not that different. Further underscoring the similarity, a computer connected to a printer can be configured to print a book. And modern printing presses may be controlled by embedded computers.
There is no material difference between a configured printing press and a programmed computer in their handling of meaning. Users of a computer read the meaning of outputs. They also enter the inputs based on the meaning. When programming a computer, programmers must define the meaning of data. They implement algorithms which perform operations of arithmetic and logic on the meaning of this data. When debugging, programmers must inspect the internals of the computer to determine whether the correct operations are being performed. This requires reading the contents of computer memory and verifying it has the expected meaning. In other words, the act of making the invention depends on defining and reading the data stored in the computer. Software works only if the data has the correct meaning.
The output of a printing process is a book. Different books are distinguished by their contents. A typographer must define and verify the contents of the information to be printed to configure the printing press correctly. In other words, the act of making the invention depends on defining and reading the data stored in the printing press. A printing press works precisely because it prints the right contents. Printing makes a physical book which can be read and sold. Books with different contents are different books. A wrongly configured printing press prints the wrong book. Therefore the utility of the printing press doesn't depend just on the laws of physics. It also depends on the contents of the book.
Both machines work in part according to the laws of physics and in part through operations of meaning.
The courts have failed to acknowledge the role of meaning in software. Some errors result from the failure to take into consideration the descriptions of what is a mathematical algorithm in mathematical literature. Other errors result from explicitly and incorrectly denying the role of symbols and meaning in computers. And more errors result from the belief that computers operate solely through the physical properties of electrical circuits, in isolation from the meanings assigned by human beings.
Imagine now that every time a printing press prints a new book, you could patent that printing press as a new machine because it printed a new book. That is exactly what patent law does with software, purporting to create a new machine because new software running on the computer supposedly creates a new machine. And yet the computer can run any software at all that you can devise, just as a printing press can print any book you write. The computer can, in fact, run more than one program at the same time. Is it now two new machines? And if you remove one software program, now what is it? And when the computer is done with the job, it is still the
same old computer, just as when it is done with its job, the printing press
is still the same old
No one would allow a patent on a previously existing printing press just because it is now configured to print a new novel. Yet that is exactly what is allowed with software.
The consequence is a proliferation of patents on the expressions of ideas, on "doing so-and-so on a computer," and, even worse,
on the concept of "doing so-and-so on a computer" when the
procedure in question merely incorporates ideas and methods which may date back
centuries or even millenia.
Suggested topic 4:
What is an abstract idea in software and how do expressions of ideas differ from applications of ideas?
Abstract is not synonymous with vague or overly broad. A mathematical algorithm is narrowly defined with great precision, but still it is abstract.
Abstract is not the opposite of useful. The ordinary procedure for carrying an addition is a mathematical algorithm. It has a lot of practical uses in accounting, engineering and other disciplines. But still it is abstract. In particular it is designed to handle numbers arbitrarily large no matter whether we have the practical means of writing down all the digits. Besides, there are useful abstract ideas outside of mathematics. For example the contents of a reference manual, such as a dictionary, are both abstract and useful.
Mathematics is abstract in part because it studies infinite structures. For example, the series of natural numbers 0, 1, 2, ... cannot exist in the concrete universe, because it is infinite. Also, symbols in a mathematical sense are abstract entities distinct from the marks on paper or their electronic equivalent. For example, there are infinitely many decimals of pi even though there is no practical way to write them down. Infinity guarantees that mathematics is abstract. Therefore a definition of "abstract ideas" must acknowledge the abstractness of mathematics.
A proper understanding of the role of meaning is key to understanding when a claim is directed to a patent-ineligible abstract idea in software. Software patents don't claim abstract ideas directly. They claim them indirectly through the use of a physical device to represent them by means of bits. It would be easier to recognize claims on patent-ineligible abstract ideas if it were understood they take the form of claims on expressions of ideas as opposed to applications of ideas. The bits are symbols and the computation is a manipulation of the symbols. Expressions of ideas occur through this use of symbols.
This suggests a test similar to the printed matter doctrine. This test is best described using the concepts and vocabulary of a social science called semiotics. This science studies signs, or symbols, used to represent something else. We suggest it can be used to distinguish patent-eligibility in software.
Computers should be recognized to be what semioticians call sign-vehicles, physical devices which are used to represent signs. The sign itself is an abstraction represented by the sign-vehicle. Hence, sign-vehicles and signs are distinct entities.
Semiotics distinguishes between two types of meaning. There is the actual worldly thing denoted by the sign. This is called the referent. And there is the idea of that thing a human being would derive from reading the sign. This is called an interpretant. A sign usually conveys both types of meanings simultaneously. An example might be a painting representing a pipe. The painting itself is a sign-vehicle. People seeing this painting will think of a pipe. This thought is an interpretant. An actual pipe is a referent.
If nothing has been invented but thoughts in the mind of human beings, one should not be able to claim a sign-vehicle expressing these ideas as if it were an application of the ideas. But when the real thing denoted by the expression is claimed, we may have a patentable invention. In other words, one should be able to patent a particular pipe invention, but not the painting of that invented pipe.
These ideas lead to this test: A claim is directed to a patent-ineligible abstract idea when there are no nonobvious advances over the prior art outside of the interpretants. A claim is written to an application of the idea when the referent is claimed instead of merely referenced.
For example a mathematical calculation for curing rubber standing alone is not patentable under this test. It is just numbers letting a human think about how rubber should be cured. But when the actual rubber is cured the referent is recited and the overall process taken as a whole may be patentable.
This test is technology-neutral. It is applicable precisely when the claimed invention is a sign, or when it is a machine or process for making a sign. It applies whether the invention is software, hardware or some yet to be invented technology. This test works without having to define the boundary between what is software and what isn't.
The concepts of semiotics are quite simple and easy to define. They are related to the dichotomy between ideas and the specific expression of ideas in copyright law. Therefore this test for abstract ideas helps clarify the line between what should be protected with copyrights and what belongs to patent law. The expressions of interpretants may be protected by copyrights and the corresponding referents may be protected by patents.
This test will correctly identify abstract mathematical ideas. Mathematics is, among other things, a written language. It has a syntax and a meaning which are defined in textbooks on topics such as mathematical logic. Algorithms are features of this language. They are procedures for manipulating symbols.3 They solve problems because they implement operations of arithmetic and logic on the meaning of the symbols. Algorithms are also procedures which are suitable for machine implementation. Computer programs may solve a problem only if it is amenable to an algorithmic solution. In this sense, all software executes a mathematical algorithm.
Mathematical language refers to abstract mathematical entities such as numbers, geometric shapes, etc. We assimilate this abstract meaning with interpretants. Mathematical language may also be used to describe things in the concrete world, for instance using laws of physics. The corresponding referents are applications of mathematics. Mathematical algorithms and other types of mathematical subject matter are a subcategory of interpretants. And things in the concrete world modeled using mathematical language are a subcategory of referents. Hence the proposed test will properly distinguish between the expression of a mathematical idea from an application of the same idea. Claims of applications are to be accepted, while claims on expressions should be rejected.
"Challenges and Strategy" (16 May 1991). Gates exact words were:
"If people had understood how patents would be granted when most of today's ideas were
invented, and had taken out patents, the industry would be at a complete standstill
Also found at http://bat8.inria.fr/~lang/reperes/
2 See Mulligan, Christina and Lee, Timothy B., Scaling the Patent System (March 6,
2012). NYU Annual Survey of American Law, Forthcoming. Available at SSRN:
The quoted paragraph is at pages 16-17.
3 Stoltenberg-Hansen, Viggo, Lindström, Ingrid, Griffor, Edward R.
Mathematical Theory of Domains, Cambridge University Press, 1994, page 224; Boolos George S.,
Burgess, John P., Jeffrey, Richard C., Computability and Logic, Fifth Edition, Cambridge University
Press, 2007, page 23.
Here is the supplement. Because it is published locally and referenced in the above document sent, we can continue to perfect it, so if you see anything you'd like to suggest be improved, please do so in your comments. Thank you to everyone who already helped to draft this supplement. We've added a table of contents, with links to the various sections.
Supplement: Using Semiotics to
Identify Patent-Eligible Software
The patent system should distinguish between the expression
of an abstract idea and an application of an idea. Currently,
with respect to software, it does not do so. Patents issue where
expressions of ideas are mistaken for applications, due to not
properly defining when a claim is directed to patent-ineligible
As a result, in the field of software, innovation is not being
promoted as intended by patent law.
Organization of the Supplement
The purpose of this supplement is to support the suggested topics for
future discussion by the Software Partnership sent to the USPTO by
Groklaw. The supplement is divided into four sections:
A. Fundamentals of Computers, Software and Mathematics
The topics we proposed in our response to the USPTO's request for
topics for future discussion, above, correspond to the following
sections in this supplement, as follows:
B. Technical Errors in Legal Arguments about Software and Patents
C. What is an Abstract Idea in Software and How Do Expressions of
Ideas Differ From Applications of Ideas.
D. The Negative Effect on Innovation of Patents Granted on the
Expressions of Abstract Ideas.
Suggested topic 1: Is computer software properly
patentable subject matter?
Topic 1 is supported by all sections of the
supplement, but particularly in Sections A, B and C. The goal is to
explain the importance of distinguishing between expressions of ideas
and their application, which in turn should help determine if a claim
involving software should be patentable.
Section A demonstrates that computers are machines for
manipulating symbols, symbols which have meanings. It also defines
some terms, like the vocabulary and concepts of semiotics, and
explains some principles of computer science such as:
what is a mathematical algorithm;
(2) how mathematics and
algorithms relate to symbols and meaning;
(3) how computers use
(4) what is the stored program architecture.
Collectively these principles explain what the role of expressions
and meaning are in computer science.
The main theme underlying section B is that computers don't
perform their functions solely through their physical properties. They
also depend on semantical properties as is explained in section A.
The legal view of software found in case law contradicts these
technical realities, and that is causing difficulties.
Suggested topic 2: Are software patents hurting
innovation and hence the US economy?
Topic 2 is discussed in section D.
We document how patents on the expressions of ideas in software break
the assumptions underlying the operation of the patent system in three
ways: (1) the patent system does not work effectively as a property
system in that there is no way for software authors to clear all
rights to their own properties; (2) disclosure isn't working as
intended, because it is ineffective for inventors, and patents are
legally dangerous for developers to read; (3) the standard
cost/benefit analysis motivating patents thus has broken down when it
comes to software patents.
Suggested topic 3:
How can software developers help the courts and the USPTO
understand how computers actually work so judges' decisions will match
Topic 3 is discussed throughout, in that this is our
attempt to explain the technology so as to help bring patent law and
technical reality into sync. Section A explains some principles of
computer science while Section B identifies technical errors noted in
legal rulings and suggests how the errors can be corrected.
Suggested topic 4: What is an abstract idea in
software and how do expressions of ideas differ from applications of
Topic 4 is discussed in section C.
We argue that when the referent of symbols is not claimed, their
meaning is just a thought in the human mind. There should be no
patents on thoughts in the mind. The meaning of symbols must be given
no patentable weight unless the referent itself is
Table of Contents
A Fundamentals of Computers, Software and Mathematical Principles.
A.1 Semiotics defines the concepts and vocabulary necessary to understand issues of meaning.
A.2 Mathematics is a written language based on logic; algorithms are procedures for manipulating symbols in this language.
A.3 Mathematicians have defined their requirements for a procedure to be accepted as a mathematical algorithm.
A.4 Algorithms are machine-implementable because they rely only on syntax to be executed, but they solve problems because they implement operations of arithmetic and logic on the meaning of the data.
A.5 All computations carried out by a stored program computer are mathematical computations carried out according to a universal mathematical algorithm.
B Some Errors of Facts Found in Arguments About Software and Patents
B.1 The proper understanding of the term "mathematical algorithm" is the one given by mathematicians.
B.2 The vast majority of algorithms can be carried out in practice for smaller inputs and are impractical for larger inputs.
B.3 The printed matter doctrine should be strictly applied to computations.
B.4 The language used in the disclosure and claims in software patents rely on an inversion of the normal semantical relationships between symbols and their meaning.
B.5 In a stored program computer, the functions of software are performed through a combination of defining the meaning of data and giving input to an already implemented algorithm.
1 The naive understanding of computer programming ignores the role of the meaning of data.
2 Main memory is a moving part of a computer. A physical change to a moving part of a machine doesn't make a structurally different machine. It is merely the action of the process by which the machine operates.
3 The mere act of storing data in memory does not implement functionality. This only happens when the data is given as input to an algorithm. This remains true when the data is instructions for a program.
4 All data may be used to implement functionality when given as input to an algorithm. This capability is not limited to instructions.
B.6 The meaning of data distinguishes an algorithm from an application of the physical properties of a machine.
C What Is an Abstract Idea in Software and How Expressions of Ideas Differ From Applications of Ideas.
C.1 Mathematical algorithms are abstract ideas.
C.2 Semiotics is the proper approach to define what is an abstract idea in software.
C.3 This description of abstract ideas is technology neutral and it doesn't require us to determine whether the algorithm is 'mathematical'.
C.4 There is no alternative to this description of abstract ideas.
D The Effect on Innovation of Patent Rights Granted on the Expressions of Abstract Ideas.
D.1 Clearing all patents rights on expressions of ideas is practically impossible.
D.2 Litigation risks are a particular burden to community-based software development.
D.3 In the computer programming art, patents provide low quality disclosure which is legally dangerous for a programmer to read.
D.4 The normal costs/benefits analysis of patents is not applicable to software.
* * * * * * * * * * *
A. Fundamentals of Computers, Software and
Let's begin by defining some important terms and summarizing
some fundamental facts about computers, software, and the underlying
A.1. Semiotics defines the concepts and vocabulary
necessary to understand issues of meaning.
In the social science of semiotics,
a thing that stands for something else is called a sign.
Books and computers when associated with their meanings are examples
of signs. Semiotics defines the concepts and vocabulary we need to
properly analyze meaning. We present here the basic concepts which
will be used in the rest of this response. It's important to
understand semiotics if one wishes to understand how computers and
A sign in the Peircean
tradition has three elements. The physical object used to
represent the sign is called a sign-vehicle. The entity in the
world which is denoted by the sign is called the referent. The
idea a human being would form of the meaning of the sign is called an
interpretant. This triadic view of a sign is traditionally
represented as a triangle.
We may use the famous painting The Treachery of Images as an illustration of these
notions. This painting represents a pipe with the legend "Ceci n'est
pas une pipe" which means "This is not a pipe" in French. The point is
that a painting of a pipe is a representation of a pipe. It is not the
pipe itself. In this example, the painting is the sign-vehicle, the
actual pipe is the referent, and the idea of a pipe in the human mind
is the interpretant.
We have a sign when there is a convention on how to associate
the sign-vehicle with its meaning. A sign exists when something
stands for something else to somebody who gets what the meaning is
from the sign. In the case of the painting this convention is the
practice of associating a visual representation of something with what
Please note the sign-vehicle is only an
element of a sign. It is not the whole sign. The three elements must
be brought together in order to have a sign. A human interpreter with
the knowledge of the convention will mentally assemble the three
elements and "make the sign" by associating the sign-vehicle with its
meaning. This is a cognitive process of the human mind called
semiosis. In particular,
books and computers when taken as physical objects independently of
their meanings are sign-vehicles. They are not the whole signs because
semantical elements are not physical parts of books and computers.
These sign-vehicles are turned into signs by semiosis when a human
interpreter reads meanings into them.
the concepts in a letter to William James:
creates something in the Mind of the Interpreter, which something, in
that it has been so created by the sign, has been, in a mediate and
relative way, also created by the Object of the Sign, although the
Object is essentially other than the Sign. And this creature of the
sign is called the Interpretant. It is created by the Sign; but not by
the Sign quÃ¢ member of whichever of the Universes it belongs to; but
it has been created by the Sign in its capacity of bearing the
determination by the Object. It is created in a Mind (how far this
mind must be real we shall see).
All that part of the understanding of the Sign which the Interpreting
Mind has needed collateral observation for is outside the
I do not mean by "collateral observation" acquaintance with the system
of signs. What is so gathered is not COLLATERAL. It is on the contrary
the prerequisite for getting any idea signified by the sign. But by
collateral observation, I mean previous acquaintance with what the
sign denotes. Thus if the Sign be the sentence 'Hamlet was mad,' to
understand what this means one must know that men are sometimes in
that strange state; one must have seen madmen or read about them; and
it will be all the better if one specifically knows (and need not be
driven to presume) what Shakespeare's notion of insanity was. All that
is collateral observation and is no part of the Interpretant. But to
put together the different subjects as the sign represents them as
related - that is the main of the Interpretant-forming.
Take as an example of a Sign a genre painting. There is usually a lot
in such a picture which can only be understood by virtue of
acquaintance with customs. The style of the dresses for example, is no
part of the significance, i.e. the deliverance, of the painting. It
only tells what the subject of it is. Subject and Object are the same
thing except for trifling distinctions. [---] But that which the
writer aimed to point out to you, presuming you to have all the
requisite collateral information, that is to say just the quality of
the sympathetic element of the situation, generally a very familiar
one - a something you probably never did so clearly realize before -
that is the Interpretant of the Sign, - its 'significance.'"
A.2. Mathematics is a written language based on logic;
algorithms are procedures for manipulating symbols in this
Mathematics is a written language. We can find the definition of its
syntax and semantics in textbooks on the foundations of mathematics,
logic.1 There is more
to mathematics than the language. Mathematical entities like numbers
and geometrical figures are also mathematics. But for the purpose of
this discussion it is the linguistic aspect that matters most.
Concepts such as formulas, equations and
algorithms are part of this mathematical language.
A mathematical formula is text written with symbols in
this mathematical language. It is the equivalent of a sentence in
English. An equation is a special kind of formula which asserts
that two mathematical expressions refer to the same value.
The famous equation E=mc2 is an
example of such a mathematical formula. The meaning of this formula is
a law of nature, actually a law of physics. It is a statement
relating the mass of an object at rest with how much energy there is
in this object. This shows how mathematical language may be used to
describe the real world.
The formula implies a procedure to compute the energy when the
mass is known. Here it is:
Multiply the speed of light c by itself to obtain
its square c2.
Multiply the mass m by the value of
c2 obtained in step 1.
The result of step 2 is the energy E.
This kind of procedure is known in mathematics as an
algorithm. The formula is not the algorithm. The
procedure is the algorithm. Someone with sufficient skills in
mathematics will know the algorithm simply by looking at the formula.
This is why it is often sufficient to state a formula when we want to
state an algorithm.
The task of carrying out the algorithm is called a
computation. When carrying out the algorithm with pencil and
paper, we have to write mathematical symbols, mostly digits
representing numbers but also other symbols such as the decimal point.
These writings too are parts of mathematical language. In the example,
the meaning of the writings are numbers representing the speed of
light, its square, the mass, and the energy of an object.
A function is not an algorithm.
Mathematicians distinguish between a function and an algorithm.
Hartley Rogers explains:2
(emphasis in the original):
It is, of course, important to distinguish between the
notion of algorithm, i.e., procedure, and the notion of
function computable by algorithm, i.e., mapping yielded by
procedure. The same function may have several different algorithms.
A mathematical function is a correspondence between one or more
input values and a corresponding output value. For example, the
function of doubling a number associates 1 with 2, 2 with 4, 3 with 6
etc. Nonnumerical functions also exist.
A function is not a process. There is no requirement that the
function must be computed in a specific manner. All methods of
computation which produce the same output from the same input compute
the same function.
Despite the similarly sounding words, a software
function is not the same thing as a mathematical function.
The functions of software are what the program do in terms of the
real world applications, like banking, engineering etc. A mathematical
function is defined in terms of mathematical entities.
Regardless of the difference, the two concepts are closely related.
If we look at the underlying principles of mathematics which are at
the foundations of computer science, all computations are carried out
with mathematical entities like numbers and boolean values.
The functions of software are described with
The methods used to perform the functions of software are implemented
using mathematical algorithms.
The language of mathematics is based on logic
There is a close connection between logic and mathematics.
Theorems are proven by means of deductions where the formulas and
expressions in mathematical language are organized according to the
rules of logic. Most mathematical truths are established in this
The relationship between mathematics and logic is explained by
Haskell Curry as follows:4 (emphasis in the original, footnote
The first sense is that intended when we say that
"logic is the analysis and criticism of thought." We observe that we
reason, in the sense that we draw conclusions from our data; that
sometimes these conclusions are correct, sometimes not; and that
sometimes these errors are explained by the fact that some of our data
were mistaken, but not always; and gradually we become aware that
reasonings conducted according to certain norms can be depended on if
the data are correct. The study of these norms, or principles of valid
reasoning, has always been regarded as a branch of philosophy. In
order to distinguish logic in this sense from other senses introduced
later, we shall call it philosophical logic.
Mathematical logic is also part of the mathematical
underpinnings of computer science.5
In the study of philosophical logic it has been found fruitful
to use mathematical methods, i.e., to construct mathematical systems
having some connection therewith. What such system is, and the nature
of the connection, are question which will concern us later. The
systems so created are naturally a proper subject for study in
themselves, and it is customary to apply the term 'logic' to such a
study. Logic in this sense is a branch of mathematics. To distinguish
it from other senses, it will be called mathematical logic.
[A]lthough the distinction between the different senses of
'logic' has been stressed here as a means of clarifying our thinking,
it would be a mistake to suppose that philosophical and mathematical
logic are completely separate subjects. Actually, there is unity
between them. mathematical logic, as has been said, is fruitful as a
means of studying philosophical logic. Any sharp line between the two
aspects would be arbitrary.
Finally, mathematical logic has a peculiar relation to the rest
of mathematics. For mathematics is a deductive science, at least in
the sense that a concept of rigorous proof is fundamental to all parts
of it. The question of what constitutes a rigorous proof is a logical
question in the sense of the preceding discussion. The question
therefore falls within the province of logic; since it is relevant to
mathematics, it is expedient to consider it in mathematical logic.
Thus the task of explaining the nature of mathematical rigor falls to
mathematical logic, and indeed may be regarded as its most essential
problem. We understand this task as including the explanation of
mathematical truth and the nature of mathematics generally. We express
this by saying that mathematical logic includes the study of the
foundations of mathematics.
To summarize the main points, mathematics is a written
language. It has a syntax and a semantics. It is used to establish
theorems by means of logical proofs. Formulas and equations are
expressions in this language. Computations and algorithms are elements
of this language which are used to solve problems.
A.3. Mathematicians have defined their requirements for
a procedure to be accepted as a mathematical
If we seek a definition in the sense of a short dictionary-like
description of an algorithm, we won't find one which is universally
accepted. But if we read textbooks of computation theory and
mathematical logic we find full text descriptions of what it takes for
a procedure to be a mathematical algorithm. These descriptions vary in
their choice of words, and some authors mention aspects others omit.
It is best to read a few of them to obtain a complete picture.
A.4. Algorithms are machine-implementable because they rely
only on syntax to be executed, but they solve problems because they
implement operations of arithmetic and logic on the meaning of the
Here is a collection of the requirements for a procedure to be
an algorithm mentioned by one or another of the authors cited in the
Procedures to actually solve a category of problems
An algorithm is a procedure intended to actually solve a
category of problems. It takes one of more inputs describing the
specific problem and it produces the corresponding solution. This
means the procedure is meant to be carried out, at least in principle
if not in practice. If it is followed without error it will produce
the correct answer. Stoltenberg-Hansen, Lindström and Griffor
explain:7 (emphasis in
An algorithm for a class K of problems is a
method or procedure which can be described in a finite way (a finite
set of instructions) and which can be followed by someone or something
to yield a computation solving each problem in K.
Mathematicians sometimes call algorithms "effective procedures"
to emphasize their ability to actually find a solution.
This concept is broadly defined in intuitive terms because it is
intended to be open-ended. Researchers constantly discover new ways of
defining and carrying out procedures able to actually solve problems.
Their notion of algorithm isn't strictly defined because they don't
want to exclude from the concept these future discoveries. When they
need mathematical rigor, mathematicians study specific models of
computations like Turing machines, recursive functions, or
Manipulation of symbols
All algorithms are ultimately procedures for manipulating
symbols. Stoltenberg-Hansen, Lindström and Griffor explain:8 (emphasis in the original):
It is reasonable to assume, by the intended meaning of
an algorithm explained above, that each problem in K should be a
concrete or finite object. We say that an object is finite if
it can be specified using finitely many symbols in some formal
For a mathematician the two concepts of arithmetic and symbolic
computations are equivalent.
Boolos, Burgess and Jeffrey explain one aspect of this
equivalence by pointing out that ultimately numbers must be
represented by means of symbols when doing arithmetic
in the original, link added):
When we are given as argument a number n or
pair of numbers (m, n), what we in fact are directly
given is a
numeral for n or an ordered pair of
numerals for m and n. Likewise, if the value of
the function we are trying to compute is a number, what our
computations in fact end with is a numeral for that number.
Now in the course of human history a great many systems of numeration
have been developed, from the primitive monadic or tally
notation, in which the number n is represented by a sequence of
n strokes, through systems like Roman numerals, in which
bunches of five, ten, fifty, one-hundred, and so forth strokes are
abbreviated by special symbols, to the Hindu-Arabic or
decimal notation in common use today.
Conversely, the same authors explain that symbols may be
represented as numbers. Then symbolic computations may be defined in
terms of arithmetical calculations:10 (emphasis in the original, link added):
A necessary preliminary to applying our work on
computability, which pertained to functions on natural numbers, to
logic, where the object of study are expressions of a formal language,
is to code expressions by numbers. Such a coding of expressions is
called a Gödel
numbering. One can then go on to code finite sequences of
expressions and still more complicated objects.
This may sound like a chicken and egg problem. Which is defined
first? The manipulation of symbols or the manipulation of numbers?
Actually it is impossible to manipulate numbers directly without first
representing them as symbols of some sort. Even when a computation is
defined as an operation of arithmetic it is ultimately a manipulation
An algorithm must be described with a finite number of
symbols.11 It is not
possible to learn and execute a procedure whose description is
infinite. This requirement may seem obvious, but much of mathematics
is about infinite structures, like the set of natural numbers or the
decimal expansion of pi.
The steps must be defined precisely so we know exactly how to
execute them. Boolos, Burgess and Jeffrey describe this requirement as
The instruction must be completely definite and
explicit. They should tell you at each step what to do, not tell you
to go ask someone else what to do, or to figure out for yourself what
to do: the instructions should require no external source of
information, and should require no ingenuity to execute, so that one
might hope to automate the process of applying the rules, and have it
performed by some mechanical device.
A procedure doesn't solve a problem unless and until it is
actually executed. The requirements of finite description and precise
definition are meant to instruct exactly how the procedure should be
This requirement of actual execution has a consequence. An
algorithm imposes a burden on the computing agent that executes it.
The steps must be actually carried out, and the symbols must be
actually written. This burden is called computational
complexity. It is measured by the number of steps which must be
executed and by the amount of writing space required to write the
symbols. This burden typically vary according to the size of the
inputs. When the number of symbols in the inputs is larger, the number
of steps and the storage space required to read and process the inputs
will also increase.
Independence from physical limitations
Mathematicians assume the agent executing the algorithm has
unlimited time to carry out the computation and unlimited space to
write symbols while computing. The goal is to separate the
mathematical properties of the algorithm from the physical resources
available to compute. Boolos, Burgess and Jeffrey describe this
requirement as follows14 (emphasis in the original)"
There remains the fact that for all but a finite
number of values of n, it will be infeasible in practice for
any human being, or any mechanical device, actually to carry out the
computation: in principle it could be completed in a finite amount of
time if we stayed in good health so long, or the machine stayed in
working order so long; but in practice we will die, or the machine
will collapse, long before the process is complete. (There is also a
worry about finding enough space to store the intermediate results of
the computation, and even a worry about finding enough matter to use
in writing down these results: there is only a finite amount of paper
in the world, so you'd have to writer [sic] smaller and smaller
without limit; to get an infinite number of symbols down on paper,
eventually you'd be trying to write on molecules, on atoms, on
electrons.) But our present study will ignore these practical
limitations, and work with an idealized notion of computability that
goes beyond what actual people or actual machines can be sure of
doing. Our eventual goal will be to prove that certain functions are
not computable, even if practical limitations on time,
speed and amount of material could somehow be overcome, and for this
purpose the essential requirement is that our notion of computability
not be too narrow.
It is understood that an algorithm will be carried out in practice
by a computing agent with finite amount of time and writing space,
therefore the computation can only be done for a "finite number of
values of n" as Boolos et al. put it. This doesn't mean the
calculation isn't done according to the algorithm. It means that the
algorithm is carried out only to the extent that sufficient resources
are available. When the resources are exhausted, the calculation stops
prematurely, and the answer is not reached.
For example consider the ordinary pencil and paper procedure of
arithmetic for adding numbers. It is designed to produce the correct
answer no matter how many digits are required to write the numbers. If
the numbers have one trillion digits it may not be realistic to expect
a live human to complete the task. Mathematicians still regard this
procedure as a mathematically correct algorithm for addition. They
consider that finding a computer powerful enough to carry out the task
until completion is a separate issue from finding a mathematically
The purpose of this abstraction is to study the mathematical
properties of the computation in itself, independently from the
limitations of the computing agent. For example mathematicians want to
know when a function cannot be computed at all regardless of the
physical resources available. And they want to be confident that the
algorithm produces the correct solution to the problem for all inputs.
This procedure gives us a mathematical guarantee that an increase of
the capabilities of the hardware will increase the range of computations
which are practical without introducing errors because the algorithm
is not limited to the capabilities of the current hardware.
This requirement is controversial.15 In some flavors of 'algorithm' it is
People who expect the algorithm to actually produce the answer
demand that there is a point in time where the answer is available.
This means there must be a finite number of steps after which the
procedure is completed and the answer is available. But there are
useful computational procedures which cannot meet this requirement.
Stoltenberg-Hansen, Lindström and Griffor explain16 (emphasis in the original):
The requirement that an algorithm should solve each
problem in a class K is actually a requirement on the class
K (to be algorithmically decidable) rather than on the concept
of an algorithm. Indeed the notion of an algorithm is partial
by its very nature. Regarding an algorithm as a finite set of
instructions, there is certainly no a priori reason to expect the
computation, obtained from applying the algorithm to a particular
problem, to terminate.
An example is a procedure for computing the decimals of pi. This
calculation can never be carried out to the end, because there are
infinitely many decimals. On the other hand it can compute the
decimals of pi to an arbitrary degree of precision, if we have the
patience to carry it out long enough.
The main mathematical models of computation17 have the ability to define
both algorithms which terminate and computational procedures which
This requirement is controversial.18 In some flavors of 'algorithm' it is
Some people expect the requirement of precise definition to
imply that every step be deterministic, with no random element. But
there are useful computational procedures that involve probabilistic
steps, that is some steps have an outcome randomly selected from a
predefined set of possibilities. This is called a randomized algorithm.
It is well-known that a randomized algorithm can be transformed
into a deterministic algorithm when a source of random numbers is
available as an input. Then the random element is moved out of the
calculation to the source of input. The calculation itself is
deterministic relative to the input. Alternatively, pseudo-random number generators may be used to simulate
nondeterminism by deterministic means.
The requirement of precise definition permits the machine execution
of algorithms. See the preceding quote of Boolos et al. An alternative
statement of this requirement is given by Stephen Kleene as
A.5. All computations carried out by a stored program computer
are mathematical computations carried out according to a universal
In performing the steps we have only to follow the
instructions mechanically, like robots; no insight or ingenuity or
intervention is required of us.
If the meanings of the symbols are ambiguous it is impossible
to execute the algorithm in this manner. Resolving the ambiguity is an
intervention that requires insight or ingenuity. This requirement
would not be met. On the other hand if the symbols are unambiguous,
for purposes of executing an algorithm mechanically, like robots,
their meanings are superfluous. For example, when evaluating a single
bit there is no need for the step of noticing the symbol means the
boolean value true when we already know the symbol is the
numeral 1 because this numeral always means true in boolean
For the sake of comparison, here is an example of a procedure
which is not an algorithm: Interim Examination
Instructions For Evaluating Subject Matter Eligibility Under 35 U.S.C.
§ 101 (PDF). Legal procedures such as this one require the human
to consider the meaning of the information and then inject additional
information based on his experience, knowledge, and convictions to
reach a decision. They require insight and ingenuity to be
executed, and for this reason they are not mathematical
A consequence of this requirement is that the algorithm
operates only on the syntax of the mathematical language. It
doesn't operate on the meaning. This point has been noticed by
Richard Epstein and Walter Carnielli20, where they describe a series of models of
computations used to define classes of algorithms:21
What all of these formalizations have in common is
that they are all purely syntactical despite the often anthropomorphic
descriptions. They are methods for pushing symbols around.
Human beings may be taught procedures to process data based on
their meanings. Computers can't. They must be programmed to execute
algorithms. This is a prerequisite for writing a machine-executable
program. If the procedure is not an algorithm, it is not possible to
program a computer for it.
But then what is the role of meaning? It defines the problem
and its solution. There is a whole body of computation theory which
analyzes computation from the point of view of syntactic manipulations
of symbols. But this literature is limited in the study of which
problems are solved by these algorithms. For that we need the meaning.
The art of the programmer is to find an algorithm which
corresponds to operations of arithmetic and logic that solve the
As a first step the programmer must define how the data
elements will be representing symbolically, with bits.22 This task is referred to
with phrases such as: defining a data model, defining data structures
and defining data formats. This task amounts to defining how to
represent the problem and its solution in a suitable language of
symbols. Then, as a second step, the programmer must find an algorithm
operating on this data that will produce the correct outputs. This
means the programmer must find a way to manipulate the symbols without
referring to their meanings and still reach the correct answer. If the
programmer fails to find such a procedure he cannot write a
The connection between logic and data is key. Well-chosen
logical inferences can solve practical problems. They can be turned
into algorithms using data types. Consider the following series of
"Abraham Lincoln" is a character string.
"Abraham Lincoln" is the name of a human being.
"Abraham Lincoln" is the name of a politician.
"Abraham Lincoln" is the name of a president of the United
States of America.
Each line is attaching a data type to the character string
"Abraham Lincoln". Most computer languages are only concerned with the
data type in line 1. This is all they need to generate executable
code. But logicians have been interested in more elaborate forms of
data typing. Each of the statements mentions a valid data type in this
Logicians have noticed that data types correspond to what they call
"predicates" which are templates to form propositions that are either
true or false. For example "is the name of a president
of the USA" is a predicate. If you apply it to "Abraham Lincoln" you
are stating the (true) proposition that "Abraham Lincoln" is the name
of a president of the USA. And if you attach the same predicate to
"Albert Einstein" you get a similar but false proposition.
When writing a program, programmers must first define their
data. They don't just define the syntactic representation in terms of
bits. They also define what the data will mean. A logician would say
they define the logical data types, the predicates which are
associated with the data. These predicates are documented in the
specifications of the software, in comments included in the source
code or in the names they give to the program variables. This
knowledge is essential in understanding a program.
However these predicates are not used for generating
machine-executable instructions. The predicates are not used by the
computer for the manipulation of the symbols. During execution the
predicates are implicit. They are defined by a convention the reader
must know in order to be able to read the symbols correctly. They are
for human understanding and verification that the program indeed does
what it is intended to do.23 And they are also for the user of the
program as he needs to understand the meanings of the inputs and
outputs in order to use the program properly.
Data types in this extended logical sense relate to algorithms
in the following way. If you expect the data to be of some type, then
the data is implicitly stating a proposition. You can tell which
proposition by applying the predicate to the data. If you expect a
quantity of hammers in your inventory and the data you get is 6, then
you implicitly have a statement that you currently have 6 hammers in
stock. All data is implicitly the statement of a proposition
corresponding to its logical type.
When the algorithm processes the data, it implicitly carries
out logical inferences on the corresponding propositions, because a
correctly working program must always produce data of the correct
type. For example if you ask a program for the birth date of Theodore
Roosevelt, and the program returns October 27, 1858, it implicitly
states that this is the birth date of Theodore Roosevelt -- because
this is the proposition corresponding to the expected data type. The
definition of correctness for a program is that it produces a
logically correct answer. Programmers are well aware of this
correspondence between predicates, data and correctness. They use it
to design, understand and verify their programs.
There is a whole body of theory on how algorithms correspond to
logic based on logical data types. The Curry-Howard correspondence is part of this
theory. It works like a translation, similar to translating between
Russian and Chinese, except that the translation is between two
mathematical languages. If the algorithm is expressed in the language
of λ-calculus, then the Curry-Howard correspondence translates the
algorithm into a proof of mathematical logic expressed in the language
of predicate calculus. The translation works also in the other
direction. Proofs of mathematical logic may likewise be translated
into algorithms. In this sense, an algorithm is really another
expression for rules of logic. The difference is a matter of form and
As an alternative, when the algorithm is written in an
imperative language instead of λ-calculus, it may be assigned a
logical semantics using
Poernomo, Crossley and Wirsing argue that Hoare logic is what the
Curry-Howard correspondence becomes when it is adapted to imperative
To summarize the main points, algorithms are machine-executable
because their execution depends only on syntax with no need for a
human to interpret their meaning. But they solve problems because the
symbols have meanings.
Mathematicians have discovered that some algorithms have a universal
property. They can compute all possible computable functions provided
they are given some corresponding input called a program. Universal
algorithms make it possible to build general purpose computers. When
we have a machine able to compute a universal algorithm, we can make
it compute any function of our choosing by supplying it with the
corresponding data. This is the difference between making a machine
dedicated to carrying out a single algorithm and software.
When a general purpose computer is built in this manner, every
program ends up being executed by the universal algorithm. Therefore
every computation is a mathematical computation according to a
mathematical algorithm. This phenomenon is often referred to by the
slogan "software is mathematics". This has been discussed
in numerous articles on Groklaw, if you wish to delve into the subject
in more detail.
Several universal algorithms are known. Here is a selection of
the main ones.
There is SLD
resolution which is used in the logic programming paradigm and languages such as
Prolog. SLD resolution is
a universal algorithm which applies rules of logic to the data.25
various implementations of
normal order β-reduction
are used.26 These
universal algorithms are used in languages derived from
cycles are the preferred universal algorithms for imperative programming which is the most widely
used programming paradigm. Instruction cycles have both hardware and
software implementations. A hardware implementation results in the
stored program computer architecture which is the
dominant way of making general purpose programmable computers.
Software implementations often take the form of virtual machines or bytecode
The universal Turing machine plays an important role
in the theoretical foundations of computer science. It played a role
in the birth of computation theory. It has also been the inspiration behind the
invention of the stored program computer. Unlike the previously
mentioned universal algorithm, it is not used for actual computer
When a universal algorithm is implemented in software, the
computer needs to be programmed twice. The first program uses the
native instructions of the computer to implement the universal
algorithm in software. The second program is the data given to
the software universal algorithm.
The instruction cycle works as follows, assuming a hardware
implementation in a stored program computer.27
The CPU reads an instruction from main memory.
The CPU decodes the bits of the instruction.
The CPU executes the operation corresponding to the bits of the
If required, the CPU writes the result of the instruction in main memory.
The CPU finds out the location in main memory where the next
instruction is located.
The CPU goes back to step 1 for the next iteration of the cycle.
As you can see, the instruction cycle executes the instructions
one after another in a sequential manner. In substance the instruction
cycle is a recipe to "read the instructions and do as they say". This
instruction doesn't execute anything. It is data read and acted upon
by the CPU.28
Not all universal algorithms use instructions as their input as
the instruction cycle does. It is incorrect to assume every computer
program is made of instructions, because some programming languages
target universal algorithms that don't use instructions as their
B. Some Errors of Facts Found in Arguments
About Software and Patents
This section enumerates a few errors of facts that have
poisoned the discussion of software and patents.
These errors have had a cumulative effect. They solidify the erroneous
notion that the functions of software are performed solely through the
physical properties of electrical circuits. Each error either
disregards or denies the role of symbols and their meaning in computer
programming. Then, the cumulative effect is that the expression of an
abstract idea is conflated with the application of an idea. As a
result, patents on the expressions of abstract ideas have been
granted improperly, because they have been mistaken for the
applications of these ideas.
B.1. The proper understanding of the term "mathematical
algorithm" is the one given by mathematicians.
Historically the courts have had problem understanding the term
"mathematical algorithm". For example the Federal Circuit stated in
AT&T Corporation vs Excel Communications:
Courts have used the terms "mathematical algorithm,"
"mathematical formula," and "mathematical equation," to describe types
of nonstatutory mathematical subject matter without explaining whether
the terms are interchangeable or different. Even assuming the words
connote the same concept, there is considerable question as to exactly
what the concept encompasses.
Also see in
The difficulty is that there is no clear agreement as
to what is a "mathematical algorithm", which makes rather dicey the
determination of whether the claim as a whole is no more than that.
The courts' difficulties lie
in the definitions used. Referring to the correct textbooks of
mathematics would clear up their confusion. Let's look at some of
their attempts to define algorithms using such sources as ordinary
v. Benson the Supreme Court described the term algorithm like
A procedure for solving a given type of mathematical
problem is known as an "algorithm."
This is not an altogether wrong one-sentence summary, but it is too
concise to be a complete definition. The details of the mathematically
correct notion cannot be known if this sentence alone is used as the
sole source of information.
Touch Technologies, Inc. v. Dell, Inc. the Federal Circuit
explained their understanding:
The usage "algorithm" in computer systems has broad
meaning, for it encompasses "in essence a series of instructions for
the computer to follow," In
re Waldbaum, 59 CCPA 940, 457 F.2d 997, 998 (1972), whether in
mathematical formula, or a word description of the procedure to be
implemented by a suitably programmed computer. The definition in
Webster's New Collegiate Dictionary (1976) is quoted in In
re Freeman, 573 F.2d 1237, 1245 (CCPA 1978): "a step-by-step
procedure for solving a problem or accomplishing some end." In
Freeman the court referred to "the term `algorithm' as a term
of art in its broad sense, i.e., to identify a step-by-step procedure
for accomplishing a given result." The court observed that "[t]he
preferred definition of `algorithm' in the computer art is: `A fixed
step-by-step procedure for accomplishing a given result; usually a
simplified procedure for solving a complex problem, also a full
statement of a finite number of steps.' C. Sippl & C. Sippl, Computer
Dictionary and Handbook (1972)." Id. at 1246.
In particular the court in In
re Freeman decided that these definitions of this term are
more or less synonymous with process. Consequently the courts have
tried to narrow down the understanding of mathematical algorithm to a
subcategory of algorithms that the courts would deem "mathematical".
Because every process may be characterized as "a
step-by-step procedure * * * for accomplishing some end," a refusal to
recognize that Benson was concerned only with
mathematical algorithms leads to the absurd view that the Court
was reading the word "process" out of the statute.
This is exactly where the problem occurs. The definitions the courts
have used provide no insight into what makes an algorithm
mathematical. As a result, the courts don't have the information they
need to distinguish a mathematical algorithm from a process in the
Mathematicians have told us what a mathematical algorithm is.
The courts should use this information. Then they would know what an
algorithm is in the mathematical sense of the term.
An algorithm is a procedure for manipulating
symbols which meet the additional requirements we have given
above.29 We can ensure
an algorithm is "mathematical" by verifying it meets the requirements
It happens that the computations carried out by a computer
always meet these requirements. Saying "software is
mathematics" is to refer to this correct conclusion. We may reach that
conclusion in several ways. For the purposes of this response, it
suffices to mention three of them.
First, we may just compare the manipulation of bits in a
computer with the requirements of mathematics to see that there is a
match. An algorithm is a procedure that solves a problem through the
mechanical execution of a manipulation of symbols. A programmer must
find a way to solve the problem exclusively by syntactic means,
without having the machine refer to the semantic. This obligation is
what ensures the algorithm always meets the requirements of
mathematicians for an algorithm to be a mathematical algorithm.
Second, observe that software is always data given as
input to a universal algorithm. Given that the universal algorithm is
mathematical, then the computation must be the execution of a
Third, use a programming language approach. We may ask
whether the claimed method is implementable in the Concurrent ML extension of the programming
language Standard ML. The official definition of the
language specifies in mathematical terms which algorithms must be
executed when a program is executed. Concurrent ML extends this
specification to input/output routines and various concurrent
programming constructs. A program written in this language is
guaranteed to correspond to a mathematical algorithm given by the
definition of the language.30
The patent eligibility of a computer-implemented invention
hinges on whether the claim is directed at an application of the
mathematical algorithm as opposed to the algorithm itself. A logical
conclusion of "software is mathematics" in the sense above is that any
threshold test of whether a mathematical algorithm is present in the
invention is always passed when software is used. Attempts to
distinguish computer algorithms that are 'mathematical' from those
which are not run contrary to the principles of computer science. Then
the section 101 analysis must proceed to whether the claim is directed
to a patent-eligible application of the algorithm as opposed to the
patent-ineligible abstract idea. A proposal for doing this will be
presented in section C below.
B.2. The vast majority of algorithms can be carried out in
practice for smaller inputs and are impractical for larger
B.3. The printed matter doctrine should be strictly applied
Mathematicians know that algorithms must be executed in practice in
order to actually solve problems. A procedure which can't be actually
carried out won't solve anything. But still they have made a conscious
decision to ignore the practical limitations of the computing agent in
their criteria for accepting a procedure as an algorithm.31 This is in direct conflict
with a frequently stated legal argument. Some people argue that
whether or not the computation can be implemented in practice is one
of the distinguishing factors between abstract mathematics and an
application of mathematics.32 In one version of this argument it is
argued that if the algorithm is hard to implement in practice then
this is evidence that it is not an abstract idea.
The problem with this argument is that the burden of carrying
out the steps of an algorithm increases with the quantity of data
present in the input. There are few exceptions, but typical algorithms
require at least to read their inputs. Then logically, if the size of
the inputs increases, more work is required to read them. Then the
input must be processed, and again the amount of work increases with
the quantity of data to be processed. All typical algorithms are
practical to use for a small enough size of inputs. And all typical
algorithms are impractical when the size of the data grows over a
certain limit. Therefore all typical algorithms will both pass and
fail the "can be implemented in practice" test depending on the size
of the input. That makes such a "test" useless.
In particular all ordinary arithmetic calculations may be
either practical or impractical depending on how many decimals are
required to write the numbers. Doubling the number pi with a precision
of one trillion decimals is not something a human doing pencil and
paper calculations can achieve in his lifetime. A computer can do it,
but there is no limit to infinity. If we increase the number of
decimals to a high enough value, the calculation is impractical on the
fastest computers. This statement will remain true no matter how
powerful our computer may be, because their capacity will always be
This is the point of the abstraction mathematicians have made.
By ignoring the practical limitations, they separate the mathematical
properties of the algorithm from the capabilities of the computing
agent. A test of whether the method may be carried out in practice is
not a test for what a mathematical algorithm actually is.
We may compare algorithms with legal arguments. Courts enforce
limits on the number of pages a brief may have and on the duration of
oral arguments. Lawyers must find concise arguments that fall within
these limits. This is not inventing a smaller stack of paper covered
with ink or a faster process for emitting sounds in a courtroom. The
argument remains an abstract idea even though concision makes it fit
within physical limits.
Computations are mathematical, written utterances because they
are procedures for writing symbols. When a better algorithm is found,
the utterances are more concise. This is still a mathematical
algorithm. The comparison with a legal argument is applicable because
according to the Curry-Howard correspondence, an algorithm is an
expression of logic.33
An algorithm solves problems precisely because it uses sound
principles of logic and arithmetic to derive the
What happens when the only new and nonobvious advances over the prior
art are in the meaning of the symbols? There is the printed matter
doctrine. That is explained in this
article by Kevin Emerson Collins, Semiotics 101: Taking the
Printed Matter Doctrine Seriously (footnotes
B.4. The language used in the disclosure and claims in
software patents rely on an inversion of the normal semantical
relationships between symbols and their meaning.
The contemporary printed matter doctrine
restricts the products of human ingenuity that can be patented under
section 101 of the Patent Act. Roughly stated, it dictates that
"information recorded in [a] substrate or medium" is not eligible for
patent protection--regardless of how nonobvious and useful it is--if the
advance over the prior art resides in the "content of the
information." For example, the printed matter doctrine prevents an
inventor from claiming a diagram or text explaining how to perform a
technological procedure. A technical diagram is an artifact of human
ingenuity that satisfies the major statutory requirements for patent
protection. Among its attributes, it can be both useful--it helps a
technologist to perform the procedure more quickly, reliably, and
precisely--and nonobvious--a person having ordinary skill in the art may
not have been motivated to make the diagram before the inventor's
discovery. However, the printed matter doctrine prevents a patent
claiming this type of diagram from issuing. Similarly, the printed
matter doctrine prevents an inventor from claiming an old machine with
new labels, regardless of the nonobviousness of what the labels mean
and the utility of the relabeled machine to society. The advance over
the prior art is understood to reside not in the mechanics of the
machine, but rather in the content of the information conveyed by the
It is well-understood that stories of hobbits traveling in faraway
countries are not physical elements of books or printing processes.
The contents of the book cannot be used to distinguish the invention
over the prior art.
On the other hand, there seems to be no one applying the
printed matter doctrine to computations carried out by computers
at all, let alone strictly in other contexts. This is a problem. The
meaning of data is not a computer part. A patent should not issue
when only the meaning of data distinguishes the invention from a
prior art machine or process.
Let me illustrate why. Please take a pocket calculator. Now
use it to compute 12+26. The result should be 38. Now give some
non-mathematical meanings to the numbers. For example, say they are
apples. Use the calculator to compute 12 apples + 26 apples. The
result should be 38 apples. Do you see a difference in the calculator
circuit? Here is the riddle. What kind of non-mathematical meanings
must be given to the numbers to make a patent-eligible difference in
the calculator circuit? Answer: no non-mathematical meaning can do
This example carries over to programming. There is no
difference in the computer structure between an instruction to add
12+26 and an instruction to add 12 apples + 26 apples. There is no
difference in a computer structure between doing a calculation for the
sake of knowing the numerical answer and doing a calculation because
the numbers mean something in the real world.
There are two issues there. First, if meaning doesn't make a
difference in the computer structure, then we can't argue a new
specific machine is made on that basis alone. Second, the difference
between a pure mathematical calculation and an application of
mathematics is the meaning given to numbers and other mathematical
entities in the real world.
When the innovation lies strictly in the meaning, with no
physical difference in the machine, then there is no patentable
invention. At the very least the invention cannot be a machine or the
operating process of a machine. We need a way to recognize these
Here is another way to make the same point. Consider if there
were such a claim as this:
A [computer / printing press] comprising a printing
device and a microprocessor configured to use the printing device to
print the story of hobbits traveling in faraway countries to destroy
an evil anvil.
The words in brackets indicate a choice. This hypothetical claim is
written for a computer or a printing press. A computer may be
connected to a printer. A printing press may have an embedded
microprocessor to control it. Even if we assume that destroying an
anvil instead of a ring is a new and nonobvious improvement over
Tolkien's The Lord of the Rings, such a claim should still be
invalid whether we are discussing a printing press or a computer.
We may argue that a configured printing press is different from
an unconfigured printing press. Different books are different articles
of manufacture. The marks of ink on paper will not be arranged in the
same manner. Therefore printing presses configured for different books
will perform different functions because they don't manufacture the
same article. This means a printing press configured to print a book
is a different machine than a printing press without the
configuration. One may print the stated book while the other can't.
Also, the configured printing press is physically different from the
unconfigured one because some of its elements are differently
This argument repeats the typical justifications of the
doctrine that programming a computer makes a machine different from
the unprogrammed computer. The correspondence is complete when we
consider that a printing press may be controlled by an embedded
programmed microprocessor and a computer may be connected to a
printer. There are no factual difference that justify patenting
a configured computer on the basis of the "new machine" doctrine
and not a configured printing press. The relationship with hardware
configuration is the same.
Let's compare the printing process with computing. Printing is
a physical process which is performed through the physical properties
of ink and paper. This process functions automatically without the
intervention of a human mind. The specific book being printed is
determined by data previously given as input to the printing
In a stored program computer, the computation is carried out by
executing the instruction cycle. This instruction cycle is a physical
process which is performed through the physical properties of an
electrical circuit. This process functions automatically without the
intervention of a human mind. The specific calculation is determined
by data given as input to the instruction cycle.
There is no factual difference which would justify applying the
printed matter doctrine to a printing process but not to the
instruction cycle. The relationship between the meaning of symbols and
the machine is exactly the same in both cases.
The Federal Circuit guidance given in In
re Lowry is unhelpful:
The printed matter cases "dealt with claims defining
as the invention certain novel arrangements of printed lines or
characters, useful and intelligible only to the human mind." In
re Bernhart, 417 F.2d 1395, 1399, 163 USPQ 611, 615 (CCPA
1969). The printed matter cases have no factual relevance where "the
invention as defined by the claims requires that the
information be processed not by the mind but by a machine, the
computer." Id. (emphasis in original).
It is hard to see how this guidance can work. Technically, it
makes no sense. Take the printing press.
A claim on a
configured printing press
requires that the information be processed not by a
human mind but by a machine, the printing press. The issue of meaning
arises whether or not the human mind is an element of the process.
Software is much more likely to require the use of a human mind
than a printing press. Many computer programs are interacting with
their users, providing outputs, and requiring inputs. In these
circumstances part of the data processing is done by a human mind,
because human decisions are involved.
On the other hand a printing press replicates the printed matter
in an entirely automatic manner.
This is not the only flaw in
Authors write books using word processors. Books exist in
electronic form and printing devices are controlled by computers.
characters are machine-readable through
optical character recognition (OCR)
has been designed for the express purpose of processing text,
and it can process the result of an OCR scan.
The preceding paragraph assumes that "intelligible to a machine"
means the ability to recognize the characters and process their
syntax. If "intelligible" means the faculty to relate the syntax with
meaning, computers absolutely don't do that.34 This is precisely why programmers must use
algorithms to solve problems.35
The Lowry test for the applicability of the printed
matter doctrine is arbitrary and illogical. It is not consistent with
The error discussed in this section occurs when this inversion
of the normal semantical relationship is not acknowledged. This leads
to a contradictory reading of Supreme Court precedent on Section 101
subject matter patentability. But if the inversion is taken into
account, it is easy to see that Supreme Court precedent is consistent.
B.5. In a stored program computer, the functions of software
are performed through a combination of defining the meaning of data
and giving input to an already implemented
Let's use ink and paper as an analogy. The marks of ink
represent letters, and the letters form words which have meanings. So
the normal semantical relationship goes from the physical substrate,
the ink, to the symbol, the letter. And then it goes from the letters
to the words, from the words to the sentences, and ultimately to the
meaning of the sentences.
This observation is applicable to the mathematical foundations
of computing. Mathematics is a written language. The semantical
relationships follow the normal progression, from ink to the symbols,
from the symbols to the syntax of mathematical language, and then to
the mathematical entities like numbers which are denoted by the
symbols. Then there is an additional relationship between math and
whatever in the universe is described by means of math.
This applies to algorithms too. An algorithm is a mathematical
procedure to solve problems, like the ordinary pencil and paper
arithmetical calculations we learned in school. When computing, the
computer writes symbols that have the same semantical relationships.
An algorithm is a procedure for writing and rewriting the symbols
until we arrive at a solution of the problem.
We find in computers the same semantical progression, except
that the symbols are not written on paper. Computers use electrical,
magnetic, and optical phenomena to represent bits. The bits are
symbols representing boolean values and numbers. Finally the numbers
means whatever in the universe is described by the numbers. The
computations are manipulations of the bits according to some
algorithm. This is part of the mathematical foundations of computer
Sometimes we may invert this semantical relationship. For
example we may enter a bookstore and ask for the book where hobbits
travel in faraway countries where live elves and orcs trying to
destroy an evil ring. The store keeper will likely bring a copy of
Tolkien's The Lord of the Rings. We described the physical book
by referring to its contents. Instead of using the book to tell the
novel, we used an outline of the novel to refer to the book.
This inversion of the semantical relationship occurs in software
patents. The functions of the software are disclosed and claimed. This
language is written in terms of the meaning of the data. If the
patent is on a payroll system, the functions of the software will be
described in terms of employees, wages and deductions, for example.
The expectation is that a skilled programmer will be able to write the
software from this disclosure. Also, the claim is presumed to describe
a new machine, which is the programmed computer. The claimed invention
is either this machine or some machine process such as transistors
turning on and off while carrying out the functions of the software.
This is describing the physical device in terms of its meaning,
exactly like the physical book may be described by an outline of the
This point is related to the distinction between the expression
of an abstract idea and an application of an idea. A mathematical idea
is written using symbols. This is an expression of the idea in a sense
close to copyright law. But mathematics may be used to describe
something else, like a rocket in flight or the finances of a
corporation. This is the application of mathematics. We can see these
concepts are related to mathematical language. In semiotics terms, the
expression of the idea is a sign-vehicle and the application is a
A mathematical calculation involving pure numbers like 12+36=48
is not distinguishable from an applied calculation like 12 apples + 36
apples = 48 apples unless we consider the meaning of the numbers. In
this example, the meaning is counts of apples. Therefore the
difference between pure abstract mathematics and applied mathematics
is in the meaning.
The same mathematical expression may or may not have a meaning
outside of mathematics depending on context. It can be both pure
mathematics or applied mathematics depending on what the meaning is.
The same is true of algorithms. The same algorithm can be used for
both pure mathematics and applied mathematics, depending on the intent
of its user. This supports the notion that an expression of a
mathematical idea is a sign-vehicle, and its application is a
We may represent the inversion of semantical relationships in a picture:
This inversion is not a problem, as long as everyone understands
and acknowledges this is what is going on. The translation between the
two views is straightforward, and everybody will understand each
Problems occur when people are oblivious to the normal
semantical relationships and only consider the legal view. Then they
argue the computer is described by mathematics in a manner analogous
to a description of the physical universe according to the laws of
physics. Then they will treat the programmed computer as an
application instead of an expression of mathematics. This conflation
is indicated in the diagram above.
This argument is found explicitly in In
[A]ll machines function according to laws of physics
which can be mathematically set forth if known. We cannot deny patents
on machines merely because their novelty may be explained in terms of
such laws if we are to obey the mandate of Congress that a machine is
subject matter for a patent.
A device described according to the laws of physics is the meaning
of the mathematical language. It is not the language itself. But the
computation as carried out by the computer is the actual manipulation
of symbols representing numbers. They are the digital counterpart of
pencil and paper calculations. This is illustrated in the picture
This picture shows that the laws of physics follow normal
semantical relationships: from symbols to math and from math to the
described device. But a patent goes the other way around, because the
programmed computer is where the symbols are stored and manipulated.
The Bernhart law of physics argument is valid when applied to a
device described according to the laws of physics. But when it is
applied to a software patent claim, this difference must be taken into
account and the argument should not apply.
Let's use a payroll system as an example. The algorithm is
described in terms of calculations about hours worked, hourly rates
and deductions. None of that is machine parts. A payroll algorithm is
not a mathematical description of the computer. It is a description of
the calculations which are applicable to payrolls. We can use this as
a description of the programmed computer only when we invert the
semantical relationship and use the functions of the software as a
description of what the computer must do with the bits. This is not
like the laws of physics.
If we took the laws-of-physics argument seriously, there is no
arithmetic calculation which is abstract mathematics. The logic goes
like this. All mathematical formulas may be used as a mathematical
description of a programmed computer for doing the corresponding
calculations. To paraphrase the court in Bernhart, we cannot
deny patents on machines merely because their novelty may be explained
in terms of such formulas if we are to obey the mandate of Congress
that a machine is subject matter for a patent.
When we disregard the inversion of the semantical relationship,
an application of mathematics is incorrectly conflated with a written
expression in the language of mathematics. Or in the terms of of
semiotics, the sign-vehicle is conflated with the referent. This leads
to a contradictory reading to the Supreme Court precedent in Gottschalk
Parker v. Flook and
Diamond v. Diehr. The factual
difference between Diehr and the other two cases is that in
Diehr the referent is claimed, but it is not claimed in the
other two cases. The only basis we have to find that there is an
application of mathematics in Diehr but not in Benson
and Flook is that the referent is claimed. This is consistent
with the view that an application of mathematics is a referent, while
an expression of a mathematical idea is a sign-vehicle. But if we
don't distinguish the expression from the application, we cannot
distinguish Benson and Flook from Diehr , and the
three cases are contradictory.
A contradictory reading of these cases cannot be correct.
Therefore the proper interpretation of these cases should be that an
application of a mathematical algorithm is a referent and not a
sign-vehicle. This is also the conclusion which is reached when the
proper semantical relationships are taken into consideration when we
analyze how algorithms perform their functions.
The error highlighted in this section is a common misunderstanding
of the operating principles of a computer. The courts have ruled that
programming a computer is the act configuring a general purpose
computer into a specific machine for performing the functions of the
software. This is the legal doctrine that programming a computer makes
a machine different from the unprogrammed computer. This view is
technically incorrect, because the functions of software are not
implemented in this manner. The consequence of this error is that
patents are granted on machines, when no machine has been
B.6. The meaning of data distinguishes an algorithm from
an application of the physical properties of a
There are two main arguments supporting this doctrine: the
new-function argument and the change-to-the-machine-structure
According to the new-function argument, the configured circuit
can perform a function that the circuit without the configuration is
not capable of performing. Therefore the configured circuit is a
different circuit from the one without the configuration.
The change to the machine structure argument has been stated in
In re Bernhart
: "[I]f a machine is programmed in a certain
new and unobvious way, it is physically different from the machine
without that program; its memory elements are differently
These two arguments follow from a naive and technically
incorrect understanding of computer programming. In this
understanding, the functions of software are implemented by storing
the instructions of the program in main memory. Then, according to
this understanding, the structure of the general purpose computer is
changed and it becomes a specific machine able to perform the
functions of software. This view is incorrect, because the functions
of software are not related to the machine structure in this
Some old general-purpose computers like the
ancient ENIAC were programmed by
physically rewiring the computer using a plug board. This kind of
programming makes a particular circuit for each program. This is an
obsolete design. Most modern general-purpose computers are built
according to the stored program computer architecture. They are not
programmed with plug boards or equivalent devices. These computers are
programmed through a combination of two techniques: (a) defining the
meaning of data, and (b) giving some input to an already implemented
algorithm which could be either the instruction cycle or some other
algorithm implemented in software. It is the second technique which
distinguishes modern computer programming from programming an ENIAC.
These two techniques, taken alone or in combination, do not
configure the computer to make a new, specific machine. They leave the
structure of the machine unchanged.
The naive understanding of programing departs from the
technically correct view in four ways.
The naive understanding of computer programming ignores the
role of the meaning of data.
Main memory is a moving part of a computer. A physical change
to a moving part of a machine doesn't make a structurally different
machine. It is merely the action of the process by which the machine
The mere act of storing data in memory does not implement
functionality. This only happens when the data is given as input to an
algorithm. This remains true when the data is instructions for a
All data may be used to implement functionality when given as
input to an algorithm. This capability is not limited to instructions.
We illustrate these issues using a multiplication algorithm as
an example. We assume the algorithm is implemented as a dedicated
digital circuit for the sake of making clear what is the relationship
between functionality and the underlying hardware. Then the
explanation will also apply to the hypothetical specific machine which
is created when a computer is programmed.
Our hypothetical circuit performs a series of multiplications.
It takes as input a series of number, like 2, 5, 7, 12, 43, and
multiplies them by some predefined number. The circuit is
configured by recording this predefined number in a hardware
register.37 If the
number in the register is 2, then the circuit will double the sample
series above to produce the result 4, 10, 14, 24, 86.
Let's call this circuit a multiplying circuit. Then we
may write a series of claims:
A multiplying circuit comprising an arithmetic unit and a
register configured to double a plurality of numbers.
A multiplying circuit comprising an arithmetic unit and a
register configured to triple a plurality of numbers.
The multiplying circuit of claim 1 where the numbers are counts
The multiplying circuit of claim 2 where the numbers are counts
A multiplying circuit comprising an arithmetic unit and a
register configured to quadruple a plurality of counts of peppercorns.
The claims are directed to a hardware implementation of the
algorithm. However the details of the hardware are purposefully left
out of the claims. As they are written, they may as well read on the
specific machine that results, according to patent law, from the
programming of a general purpose computer. This ambiguity is intended
for educational purposes. It builds an easy to understand
correspondence between the operation of the hardware and the action of
the algorithm. Any argument about the hardware circuit obviously
transposes to the equivalent software implementation.
Claims 1 and 2 illustrate the meaning of the phrase "configured
to" when it is applied to a circuit for executing an algorithm. In
claim 1 the function is doubling. In claim 2 the function is
functions are implemented by storing a number in the circuit register.
For claim 1 this number is 2. The number is 3 for claim 2. Configuring
circuits for performing some functions is the act of storing one or
more numbers in a memory element. In the case of the multiplying
circuit only one number is needed and the memory element is a
register. In the case of a stored program computer we store long
series of numbers in the computer main memory. Often the numbers
represent instructions to be executed by the instruction cycle, but
this is not always the case. Often other numbers are used as inputs to
other algorithms. For example, this would occur in a software
implementation of claims 1 and 2.
1. The naive understanding of computer programming ignores
the role of the meaning of data.
Claims 3 and 4 show how the meaning of data relates to
functionality. Claim 3 doubles counts of apples instead of doubling
plain numbers as in claim 1. And claim 4 triples counts of oranges
instead of tripling counts of plain numbers as in claim 2. The
difference is strictly in the meaning of numbers. The physical
configuration of the machine is unchanged when compared to claims 1
and 2. This method of implementing functionality is a pure operation
There is no way to argue that defining the meaning of data
makes a circuit different from the circuit without the meaning. We
cannot argue there is a change to the machine structure, because no
change at all is made to the machine. Arguing the circuit must be
different because it performs a new function is nonsensical.
This point alone suffices to refute the doctrine that
programing a computer makes a different machine. The reason is that
the meaning of the numbers is not a machine part. The sole operation
of giving some non-mathematical meaning to numbers can never make a
machine different from the one where the numbers don't have this
In claim 5 the two programming techniques are used in
combination. A number is configured in the register as input to the
multiplying algorithm, and simultaneously we define the numbers to be
counts of peppercorns. Programs for general-purpose computers use this
same combination of techniques. The meaning of data is defined, and
numbers are stored in main memory and given as input to
The contribution of the count of peppercorns to the circuit
structure is nil. This is defining the meaning of the numbers like in
claims 3 and 4. This claim doesn't recite a circuit different from a
circuit configured to quadruple plain numbers. This same point is
applicable to a stored-program computer. Reciting the meaning of the
data does not direct a claim to a computer different from one that
manipulates plain numbers, because meaning is not a machine
If someone were to insist on salvaging the doctrine from this
argument, he might try to remove the meaning of data from the
definition of the functionality and claim a specific machine for
performing whatever remains of the function. This attempt would fail
for two reasons. First, for all practical purposes it would eviscerate
the doctrine. Software is useless unless the data has meaning, and
utility is a requirement for patentability. Second, once the meaning
is removed, the resulting function is a manipulation of plain numbers.
Then the claim should be invalid because the mathematical algorithm
A patentable application of mathematics must actually use the
referent. Merely referring to it is not sufficient, because then there
is no contribution of the referent to the invention structure when
compared to an identical manipulation of pure numbers.
2. Main memory is a moving part of a computer. A physical
change to a moving part of a machine doesn't make a structurally
different machine. It is merely the action of the process by which
the machine operates.
Do the changes to the memory elements resulting from
programming the computer suffice to make machine different from the
unprogrammed computer? The answer is that no such machine is made,
because memory elements are moving parts of the circuit. They can be
changed billions of times per second.39 Clearly a different machine isn't made
every time one of these changes occur. To rule otherwise yields the
absurd result that no machine can perform a computation until the end
because it always become a different machine every time a memory
element is altered.
Storing information in memory never makes a structural change
to the computer. This action is always part of the execution of the
electrical process by which the computer operates.40 Regardless of how a computer
is programmed this electrical process is always the execution of the
3. The mere act of storing data in memory does not implement
functionality. This only happens when the data is given as input to an
algorithm. This remains true when the data is instructions for a
If someone were to insist that programming a computer makes a
different machine from the unprogrammed computer, he has to argue that
he can somehow distinguish some memory changes that make a different
machine from other changes that don't.41 This argument is not defensible because
the technology doesn't work in this manner.
Looking at claims 1 and 2 again, there is no physical
difference between a number used to configure a multiplying circuit
and a number used for another purpose. The bits representing the
number are identical in both cases. The difference is in what is done
with the number after it has been stored. If we transpose this logic
to a stored-program computer, there is no physical difference between
numbers in memory which are instructions to the microprocessor and
numbers which are used for another purpose. Again the bits
representing numbers are identical. The difference is in what is done
with the numbers afterwards.
There are programs which use instructions as ordinary numeric
data without executing them. Examples are programs which compute
checksums or hash functions to verify that the file containing
the instructions has not been tampered with. When instructions are
stored in memory for this purpose the functionality is not imparted to
the computer. The instructions will result into functionality only
when they are given as input to the instruction cycle.
The changes in the memory elements do not impart functionality
to a computer. The act of giving the data as input to an already
implemented algorithm imparts the functionality. This is why we can't
distinguish memory changes that make a structurally different machine
from those that don't. The difference is in how the data is
used and not in which data is used or what happens to the
4. All data may be used to implement functionality when given
as input to an algorithm. This capability is not limited to
The naive view of computers asserts that because the
instructions have a special meaning to the hardware, they impart
functionality while other data without such special meaning will not.
This is not how its works. Instructions are series of numbers given as
input to an algorithm implemented in hardware which is the instruction
cycle.42 But this is
only one of several algorithms programmers may use for this
can and do implement functionality with data which is not instructions
recognizable by the hardware.
As a general rule every algorithm that accepts multiple
parameters can be used to produce more functions by partially
specifying one of its parameters in the manner illustrated by claims 1
and 2. Any type of data can be used as an input as long as the chosen
algorithm can process it.
The range of functions which can be so specified will vary
depending on the capabilities of the algorithm. Some algorithms are
especially prone to be used in this manner. The extreme case is the
various universal algorithms mentioned in section A.5 supra.
Each of these algorithms can compute all functions which are
computable. But non-universal algorithms can also be used, although
they are more limited in the range of what they can compute. For
example algorithms for pattern matching using regular
expressions can be used for a wide range of text processing
functions. And algorithms for reading and writing data in a database
can be used for a wide range of storage and retrieval functions.
Please note how some of these algorithms accept as input data which is
not instructions to the hardware.
The main memory of the computer is always a moving part of the
device regardless of which type of information is stored and how it is
Changing the contents of main memory never makes a structurally
different machine. In addition defining the meaning of data makes no
changes whatsoever to the computer. The doctrine that programming a
computer makes a machine different from the unprogrammmed computer
corresponds to a naive and incorrect view of how functionality relates
to the underlying hardware. The effect of this doctrine is to
incorrectly extend the patentability of machines to claims where the
actual invention is clearly not a machine.
The Court of Customs and Patents Appeals once said (in
There is nothing abstract about the claimed invention.
It comprises physical structure, including storage devices and
electrical components uniquely configured to perform specified
functions through the physical properties of electrical circuits to
achieve controlled results.
The functions of software are not always performed through the
physical properties of an electrical circuit. Software relies on the
meaning of data, and this is not a machine part. And most importantly,
when data has no meaning, an algorithm doesn't solve its problem.
It is possible to view the computer as a machine that functions
according to the laws of physics. It may be argued that the computer
will function without a human mind watching the meaning of the bits
inside the computer. The same may be said of a printing press. In most
software patents, what is claimed is not the sole operation of the
machine according to the laws of physics. Semantical elements are
claimed. They are needed to infringe. This distinguishes the invention
from a claim on a machine operating according to the laws of
In sections B.1 through B.5, five independent errors of fact
have been identified. All five errors can be argued separately, and
they should all be corrected.
To make matters worse, the role of meaning is not acknowledged.
This sixth error seems to be a recurring theme underlying several of
the previous five errors. This is a major problem because meaning is
the very thing that makes computers useful. As a result, the subject
matter of the invention is often mistaken for something physical, when
nothing physical has actually been invented.
The effect of the errors is cumulative. They prevent the patent
system from understanding the difference between an abstract
mathematical idea and the application of this idea.
C. What Is an Abstract Idea in Software and How
Do Expressions of Ideas Differ From Applications of Ideas?
This section argues that semiotics is the proper approach to
defining what an abstract idea is in computer programming. Some
alternative approaches are examined and rejected. This section also
includes an examination of why mathematical subject matter is abstract
and why the semiotics approach will correctly identify this type of
C.1. Mathematical algorithms are abstract
It is understood in case law that mathematical algorithms are a
subcategory of abstract ideas. We explain in this section how the
principles of mathematics justify this view.
C.2. Semiotics is the proper approach to define what is
an abstract idea in software.
An algorithm is often abstract because it is designed to handle
a potentially infinite range of inputs. This is the case of all
arithmetic operations because there is no limit to how many digits a
number may have. This is also the case of many nonnumerical
algorithms, such as searching text, which are designed to work on
arbitrarily large text. Planet Earth is not vast enough to make
concrete implementations of "infinite". Data of arbitrarily large size
An algorithm is abstract because it is a procedure defined in
terms that ignore the limitations of time and space of its practical
implementation. It is designed to produce the correct answer for all
size of inputs whether or not the resources to handle this input are
An algorithm is a procedure for manipulating symbols. We note
that a symbol is an abstract entity that is different from a mark of
ink on paper or an electric charge in a capacitor.46 The same algorithm may be
implemented with a diversity of technologies where the same symbol has
different physical representations. The algorithm is abstract, because
it is a manipulation of the abstract symbol. It is not a physical
process for manipulating the physical representations.
An algorithm is abstract because its utility depends on
meaning. The meaning of symbols is not a machine part. It is not a
physical element of the machine.
Algorithms are analogous to novels, legal briefs and other
forms of text. They have to be represented physically, and yet they
are abstract. Software patents often contain claims directed to the
physical representations as long as they convey the recited meaning.
These claims are charades. They are attempts to preempt the underlying
abstract ideas by claiming the physical means that are used to express
them on the basis of their meanings.
The question arises of how do we distinguish a claim on an
abstract idea such as a mathematical calculation from a claim on an
application of the idea. We argue that the proper way to answer this
question is to use the concepts and vocabulary of semiotics,47 as in the picture below.
C.3. This description of abstract ideas is technology
neutral and it doesn't require us to determine whether the algorithm
We rely on the notion that mathematics is a language and a
computation is a written expression of this language. The symbols must
be written somehow, often with pencil and paper, but also by
electronic means in a computer. The computation itself is a
manipulation of symbols in this language. The symbols represent
various mathematical entities like numbers and boolean values. If
mathematics is used for a practical application, these abstract
mathematical entities model something in the physical reality.
In semiotics terms, the computer is a sign-vehicle, a physical
device used to represent the sign. Whatever physical reality is
referred to by the data is a referent. In between the abstract
mathematical ideas are interpretants. They are thoughts in the mind of
the programmer, or in the mind of the user of the computer.
There is room to argue whether a number is a thought in the
mind of humans, or something that exists in an abstract mathematical
universe. This is a controversial topic in the
philosophy of mathematics. A
similar question may be raised with such concepts as commodity
hedging. The law shouldn't be concerned with this debate. Either way
the mathematical entities are abstract and not patentable. Regardless of
the outcome of such debate it should be acceptable to treat such
abstract entities as interpretants for legal purposes because they do not
exist as physical objects in the real world.
Semiotics makes two important distinctions. First the physical
devices such as computers are sign-vehicles. They are not signs. The
meaning is a part of the sign but it is not part of the sign-vehicle.
The meaning of data is not part of the computer. This distiction reflects
the point previously made that meaning is not a physical property of
The other distinction is that there are different types of meanings.
Interpretants are thought in the human mind. They are abstract ideas.
Referents are concrete entities in the real world. They are not abstract
and they may be patentable inventions. Suppose we have a claim involving a
sign, like a programmed computer associated with the meaning of the data.
Which type of meaning is recited is helpful information when trying to find
out whether this claim is directed to a patnent-ineligible abstract idea.
The Supreme Court in Diamond
v. Diehr said (footnote omitted, bold added):
We recognize, of course, that when a claim recites a
mathematical formula (or scientific principle or phenomenon of
nature), an inquiry must be made into whether the claim is seeking
patent protection for that formula in the abstract. A mathematical
formula as such is not accorded the protection of our patent laws, Gottschalk v. Benson, 409 U. S. 63 (1972), and
this principle cannot be circumvented by attempting to limit the use
of the formula to a particular technological environment. Parker v. Flook, 437 U. S. 584 (1978). Similarly,
insignificant postsolution activity will not transform an unpatentable
principle into a patentable process. Ibid. To hold otherwise
would allow a competent draftsman to evade the recognized limitations
on the type of subject matter eligible for patent protection. On the
other hand, when a claim containing a mathematical formula implements
or applies that formula in a structure or process which, when
considered as a whole, is performing a function which the patent laws
were designed to protect (e. g., transforming or reducing
an article to a different state or thing), then the claim satisfies
the requirements of § 101.
Please refer to the part in bold. We argue that this kind of
structure or process must be a referent. It cannot be a
sign-vehicle such as a programmed computer because it is a
representation of the mathematical language itself. A sign-vehicle is
not an application of the language. To hold otherwise would allow one
to claim mathematical subject matter, because an expression in the
language must always have some form of physical structure. Whenever
the claim is directed to a sign-vehicle an inquiry must be made
into whether the only nonobvious advances over the prior art are
interpretants. If this is the case the claim is directed to the
abstract meaning of the mathematical language.
Mathematics is mentioned in this discussion in part because
algorithms are the only type of procedures computers are capable of
executing48 and in part
because a mathematical algorithm exception has been created by Supreme
Court precedent. But the semiotics approach is applicable to all
manipulations of symbols, whether or not they are mathematical.
Therefore, if this approach is adopted, the issue of whether or not a
mathematical algorithm is involved can be eschewed.
C.4. There is no alternative to this description of
This semiotics approach is not limited to software. It is
applicable in all circumstances where a sign is involved. It doesn't
matter if the sign is a stored program computer or some other
technology like a dedicated circuit. The issue of meaning is handled
in the same manner.
These circumstances are advantageous. There is no need to
design some special test on what is 'mathematical' or what is
'software'. Also the notions of semiotics are not that hard to
understand, and they require no deep knowledge of mathematics or
computer science. This leads to a test for abstract ideas which is
workable for judges and juries with little or no mathematical and
technology background. This test is also consistent with the
established printed matter case law.49 It helps draw a logical boundary between
copyright and patent law because it distinguishes the expression of an
idea from the application of the idea.
Previous attempts to test for "abstract ideas" in software have
failed. All these attempts have disregarded the issue of meaning. No
test will succeed until the role of meaning is taken into
consideration. The problem is that every expression of an idea must
have a physical representation. Then it is easy to give a claim
preempting an abstract idea a façade of concreteness by directing it
to a sign-vehicle defined by its meaning. It is impossible to analyze
the subject matter of this type of claims unless it is recognized that
they are sign-vehicles and they have meanings.
Abstract is not synonymous with "vague or overly broad".
Mathematical subject matter such as algorithms is abstract, but it is
narrowly and precisely defined.50
Abstract is not the opposite of "useful". The contents of a
reference manual or a dictionary is useful, but it is an interpretant
which is an abstract idea. Also the ordinary pencil and paper
procedures for arithmetic calculations are abstract mathematical
algorithms, and they have practical uses in accounting, engineering
and many other disciplines.
Tests based on whether the invention is practically difficult
to implement don't work, because most mathematical algorithms are
practical to implement when the size of the input is small enough and
practically impossible to implement when the size of the input is
The Federal Circuit has tried for years to find a definition of
what makes an idea abstract. They report that they have failed.
Inc. v. GraphOn Corp.:
When it comes to explaining what is to be understood
by "abstract ideas" in terms that are something less than abstract,
courts have been less successful. The effort has become particularly
problematic in recent times when applied to that class of claimed
inventions loosely described as business method patents. If
indeterminacy of the law governing patents was a problem in the past,
it surely is becoming an even greater problem now, as the current
Bank International v. Alice Corporation PTY. LTD.:
In an attempt to explain what an abstract idea is (or is not)
we tried the "machine or transformation" formula--the Supreme Court
was not impressed. Bilski, 130
S.Ct. at 3226-27. We have since acknowledged that the concept lacks of
a concrete definition: "this court also will not presume to define
`abstract' beyond the recognition that this disqualifying
characteristic should exhibit itself so manifestly as to override the
broad statutory categories of eligible subject matterâ€¦ ." Research Corp. Techs., Inc.
v. Microsoft Corp., 627 F.3d 859, 868 (Fed.Cir.2010).
Our opinions spend page after page revisiting our cases and
those of the Supreme Court, and still we continue to disagree
vigorously over what is or is not patentable subject matter. See,
e.g., Dealertrack, Inc. v. Huber, ___ F.3d ___ (Fed. Cir.2012)
(Plager, J., dissenting-in-part); Classen Immunotherapies, Inc. v. Biogen IDEC, 659
F.3d 1057 (Fed.Cir.2011) (Moore, J., dissenting); Ass'n for Molecular Pathology, 653 F.3d
1329 (Fed.Cir. 2011) (concurring opinion by Moore, J., dissenting
opinion by Bryson, J.); see also In re Ferguson, 558 F.3d 1359 (Fed.Cir.
2009) (Newman, J., concurring).
This effort to descriptively cabin § 101 jurisprudence is
reminiscent of the oenologists trying to describe a new wine. They
have an abundance of adjectives--earthy, fruity, grassy, nutty, tart,
woody, to name just a few--but picking and choosing in a given
circumstance which ones apply and in what combination depends less on
the assumed content of the words than on the taste of the tongue
The abstractness of the "abstract ideas" test to
patent eligibility has become a serious problem, leading to great
uncertainty and to the devaluing of inventions of practical utility
and economic potential. See Donald S. Chisum, Weeds and
Seeds in the Supreme Court's Business Method Patent Decision: New
Directions for Regulating Patent Scope, 15 Lewis & Clark L. Rev.
11, 14 (2011) ("Because of the vagueness of the concepts of an `idea'
and `abstract,'â€¦ the Section 101 abstract idea preemption inquiry can
lead to subjectively-derived, arbitrary and unpredictable results.
This uncertainty does substantial harm to the effective operation of
the patent system."). In Bilski, the Supreme Court offered some
guidance by observing that "[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."
Bilski II, 130 S. Ct. at 3230 (quoting
Le Roy v. Tatham, 55 U.S. (14 How.) 156, 175
(1852). This court has also attempted to define "abstract ideas,"
explaining that "abstract ideas constitute disembodied concepts or
truths which are not `useful' from a practical standpoint standing
alone, i.e., they are not `useful' until reduced to some practical
application." Alappat, 33 F.3d
at 1542 n.18 (Fed. Cir. 1994). More recently, this court explained
that the "disqualifying characteristic" of abstractness must exhibit
itself "manifestly" "to override the broad statutory categories of
patent eligible subject matter." Research Corp., 627 F.3d at 868.
Notwithstanding these well-intentioned efforts and the great volume of
pages in the Federal Reporters treating the abstract ideas exception,
the dividing line between inventions that are directed to patent
ineligible abstract ideas and those that are not remains elusive. "Put
simply, the problem is that no one understands what makes an idea
`abstract.'" Mark A. Lemley et al., Life After Bilski, 63 Stan.
L. Rev. 1315, 1316 (2011).
In section B, supra, we have identified that the source of
these problems is the refusal to acknowledge the role of symbols and
their meaning in computer programming. There is a failure to consider
what an algorithm is in mathematics.52 Had this notion been considered, the role
of symbols and meaning would have been apparent. Then there is a
failure to recognize the similarities between the computer instruction
cycle and a printing process.53 This recognition too would have made
apparent the role of symbols and their meaning. There is also the
failure to acknowledge that the language of a typical software patent
inverts the normal semantical relationships between a sign-vehicle and
the referent. This failure yields an inconsistent reading of the
Supreme Court precedents of Benson, Flook and
Diehr.54 It also
leads to the incorrect conclusion that the functions of software are
performed exclusively through the physical properties of electrical
conclusion is cemented by the doctrine that programming a computer
makes a machine structurally different from the unprogrammed computer.
The cure is to acknowledge the linguistic aspects of
mathematics and take into account that a computer is a sign-vehicle.
It is a device for manipulating bits, and bits are symbols with
meanings. Then the proper definition of abstract ideas becomes
D. The Effect on Innovation of Patent Rights
Granted on the Expressions of Abstract Ideas.
Software patents don't promote innovation because they can't.
The burden imposed on job-creating software authors is large. They
cannot possibly clear all rights to their own products. The
consequences are deleterious. Not only can software authors not be
secure in their own property, but they can't use the disclosure from
patents for fear of being liable for treble damages. In addition, the
normal costs/benefits analysis of patents is not applicable to
software development. None of the factors that normally allow patents
to promote innovation function according to theory in the computer
programming art. Therefore there is no reason to believe software
patents promote innovation.
D.1. Clearing all patents rights on
expressions of ideas is practically impossible.
Let's imagine a regime where proprietary rights may be granted to
each particular idea. In this imaginary regime, the author of a book,
any book, would be required to secure the rights to each idea he is
using. Each sentence expresses an idea which may be owned by someone.
Each combination of sentences makes a more complex idea. The author is
expected to check each of these ideas, determine whether it is in the
public domain or if it is owned by someone, and in the latter case
secure the rights to the idea or remove it from his work.
2. Litigation risks are a particular burden to
community-based software development.
It is not realistic to expect authors to comply with this
requirement because it is overly burdensome. The rights cannot be
cleared, because the number of ideas in a book is just too great to
check them all. Authors would have to choose between not writing or
risking a lawsuit. This regime would hinder the creation of new
works of authorship, because it would put all the authors who choose
to keep writing at perpetual risk of infringement.
This is exactly the kind of regime patent law imposes on
computer programmers. Case law doesn't recognize that a computation is
the expression of an idea, exactly like English sentences in a book.
This is technically wrong. Programs are useful because data has
meaning. They solve problems because the computation implements
operations of logic through a syntactic manipulation of
Software is written in the form of lines of code. The source
code is a copyrightable expression, and it is not patented. But source
code corresponds to a computation. Because the computation is a
manipulation of symbols it is also an expression of an idea. Patents
rights are granted to this expression, and this is where the problem
Each line of code is roughly similar to a sentence in English
in that each expresses an idea. Like sentences, lines of code are
grouped to make more complex ideas. But under the current case law
every single one of these ideas is specifying a physical process which
is performed through the physical properties of an electrical circuit.
Each of these processes may be the subject matter of a patent. Typical
software has between thousands and millions of lines of code. The
number of ideas which may potentially infringe on someone's patent is
Mark Lemley quantifies the numbers of patents which may be
applicable to a software product57:
Because computer products tend to involve complex,
multi-component technology, any given product is potentially subject
to a large number of patents. A few examples: 3G wireless technology
was subject to more than 7000 claimed "essential" patents as of 2004;
the number is doubtless much higher now.72 WiFi is subject
to hundreds and probably thousands of claimed essential
patents.73 And the problem is even worse than these numbers
suggest, since both 3G wireless technology and WiFi are not themselves
products but merely components that must be integrated into a final
product. Some industry experts have estimated that 250,000 patents go
into a modern smartphone.74 Even nominally open-source
technologies may turn out to be subject to hundreds or thousands of
patents.75 The result is what Carl Shapiro has called a
"patent thicket"-- a complex of overlapping patent rights that simply
involves too many rights to cut through.76
Christina Mulligan and Timothy B. Lee have observed58 the burden of compliance
with patents depends primarily on two numbers: the number of patents
which may be potentially infringed and the numbers of firms which
write software. Both numbers are large. Over 40,000 software patents
are granted every year in the US. Also every firm having an internal
IT department develops software. It is common even for small
enterprises to own a web site. Each of these firms may potentially
infringe on some software patent, and in an ideal world each of them
must check all applicable patents for possible infringement. The size
of the task is staggering:59
 For discussion and sources, see Mark A. Lemley & Carl
Shapiro, Patent Holdup and Royalty Stacking, 85 Tex. L.
Rev. 1991 (2007). Information on patents essential to 3G wireless
technology is collected at http://www.3gpp2.org/, though that
includes only patent disclosed to that group.
 Ed Sutherland, WiMax, 802.11n Renew Patent
Debate (Apr. 7, 2005),
 See http://googleblog.blogspot.com/2011/08/when-patents-attack-android.html
(statement of David Drummond, Chief Legal Officer at Google).
 Id. (discussing patents that threaten the
open-source Android operating system). Microsoft, Nokia, Apple and
others have all filed suit against makers of Android phones, part of a
crazy tangle of litigation.
 Carl Shapiro, Navigating the Patent Thicket: Cross
Licenses, Patent Pools, and Standard-Setting, in 1 Innovation
Policy and the Economy 119 (Adam Jaffe et al. eds., 2000). See
also Michael Heller & Rebecca S. Eisenberg, Can Patents Deter
Innovation? The Anticommons in Biomedical Research, 280
Sci. 698 (1998).
Even if a patent lawyer only needed to look at a
patent for 10 minutes, on average, to determine whether any
part of a particular firm's software infringed it, it would require
roughly 2 million patent attorneys, working full-time, to compare
every firm's products with every patent issued in a given year.
This calculation covers just the work of keeping up with the newly
issued patents every year. Checking already issued patents is not
This result is justified by simple arithmetic. The assumptions
are 40,000 patents issued per year, 600,000 firms that actively write
software, and each attorney is capable of working approximately 2000
billable hours per year. Then the math is straightforward: 40,000
patents*600,000 firms*(10 minutes per patent-firm pair)/(2000*60
minutes per attorney)=2 million attorneys.
These assumptions are admittedly speculative. It doesn't
matter. There are only roughly 40,000 registered patent attorneys and
patent agents in the US. Even if we alter the assumptions by a large
margin the patent bar clearly doesn't have enough members to perform
Even if we consider only the work required within a single
organization, this is still an overly burdensome task. Mulligan and
Lee examine a simple hypothetical scenario where 30,000 firms making
widgets own one patent each for a total of 30,000 patents. Then they
inquire how much work it is for each participant to evaluate whether
they infringe on the remaining 29,999 patents:60
Each of the 30,000 firms would need to hire a patent
attorney to examine 29,999 other patents, which takes 1 hour per
patent, so attorneys would spend a total of 30,000 * 29,999 * 1 hour =
899,970,000 hours. Assuming a typical attorney bills 2000 hours of
work per year, each firm would need just shy of 15 attorneys to
examine 29,999 patents.
This analysis assumes each firm wants to complete the work in
exactly a year. It also assumes that lawyers can determine whether a
given patent is infringed. This is not always the case. It is
notorious that this kind of analysis is not dependable.61
The analysis also assumes software firms can wait until the
analysis is done before releasing their products in the marketplace.
This is usually not the case. There is a strong first-mover advantage
in the software industry. Delays may jeopardize the commercial success
of the product. Releasing the software before the patent search is
completed may lead to a finding of willful infringement and treble
damages. A company may be better off not to search for patents at all
than release a product before the search is completed.
Also, patent compliance is not a one-time event. Software is
constantly being modified. Products are constantly being upgraded. It
is commonplace to release so-called "beta-tests", that is unfinished
versions of the product for the purpose of testing. After one or more
such testing releases an official version is produced. Then various
bug fixes are released. Some of them are security fixes and must
imperatively be released immediately because any delay leaves the
customers at risk. Eventually upgrades to new versions are developed.
Each release may potentially introduce a patent-infringing change. In
an ideal world, legal analysis must be constantly done to keep the
software non-infringing on a timely basis.
The cumulative effect of all these constraints ensures that
clearing all rights to one's own product is a practically impossible
task. This is not a problem that can be solved with faster, better
search engines for patents and prior art. Even with perfect
information on all the applicable patents and all relevant prior art,
the sheer number of patents and the frequency with which they must be
verified are too great. The burden is mostly a function of
If software authors wish to be active participants in the
marketplace, they have no choice but to ignore patents and operate at
the risk of infringing. The only alternative is to stop writing
software. Mark Lemley describes this situation thus62 (footnotes omitted):
This is a particular problem for semiconductor,
telecommunications, and software companies, which must aggregate
hundreds or thousands of different components to make an integrated
product. Each of those components may be patented, some by many
different people. The threat that any one of those patent owners can
obtain an injunction shutting down the entire integrated product
allows them to extort settlements well in excess of the value of their
patent. The patent damages rules similarly permit excessive
recoveries, such as the recent $1.5 billion jury verdict against
Microsoft for infringing one of many patents covering just one of many
features of an add-on to the Microsoft Windows product. Patent law
permits these product manufacturers to be found to be "willful"
infringers liable for treble damages and attorneys' fees, even if they
were unaware of the patent or even the patent owner at the time they
began selling the product. And even if the manufacturer can avoid any
of these risks by invalidating or proving noninfringement of each of
these patents, doing so will cost millions of dollars per case in
legal fees. Given these problems, it's a wonder companies make
products in patent-intensive industries at all.
Mulligan and Lee further explain63 (footnotes omitted):
And yet make products they do. Both my own experience and what
limited empirical evidence there is suggest that companies do not seem
much deterred from making products by the threat of all this patent
litigation. Intel continues to make microprocessors, Cisco routers,
and Microsoft operating system software, even though they collectively
face nearly 100 patent-infringement lawsuits at a time and receive
hundreds more threats of suit each year. Companies continue to do
research on gene therapy, and even make "gene chips" that incorporate
thousands of patented genes, despite the fact that a significant
fraction of those genes are patented. Universities and academic
researchers continue to engage in experimentation with patented
inventions despite the now clear rule that they are not immune from
liability for doing so. John Walsh's study suggests that threats of
patent infringement are not in fact responsible for deterring much, if
What's going on here? The answer, I think, is straightforward,
if surprising: both researchers and companies in component industries
simply ignore patents. Virtually everyone does it.
To get a perspective on how strange this might seem to an
outsider to the patent system--or even to an outsider to the component
industries in which this behavior is common--compare it to the world
of real property. If I want to build a house, I'd better be darn sure
that I own the land on which the house is built. In fact, it would be
foolhardy to begin construction before I owned the rights to the land,
in the hopes that I would be able to obtain the rights later. Nor
would a prospective homebuilder put up with significant uncertainty
about the boundaries of the land on which she was building. People
don't often build houses that might or might not be on their land,
hoping that they would ultimately win any property dispute. And even
if a few people were so reckless as to want to do one of these things,
banks won't fund construction without certainty in the form of a title
insurance search report indicating that the builder unambiguously owns
all the rights she needs.
The tendency to implicitly assume that economic actors
are omniscient is a common pitfall of theoretical social science. By
definition, the theorist knows everything there is to be known about
the stylized model he has invented. Theorists often implicitly assume
that economic actors automatically have the information they need to
make decisions. Indeed, this may be essential to building a tractable
model of the world. But the failure to ponder the feasibility of
acquiring and using information can lead to flawed conclusions.
This situation is not fostering innovation. It imposes an
unreasonable burden on job-creating businesses that sell actual
products. The only businesses who can be sure of owning all software
patent rights to their products are those which don't make actual
software and prefer to sell and license patents. This situation
promotes monopolistic licensing rents and litigation.
The contemporary patent debate suffers from just this blind
spot. Each patent is a demand that the world refrain from practicing a
claimed art without the patent holder's permission. Potential
infringers can only comply with this demand if they are aware of the
patent's existence. On a blackboard or in the pages of a law review
article, it's easy to implicitly assume that everyone knows about
But the real world isn't so simple. To avoid infringement, a
firm must expend resources to learn about potentially relevant
patents. Typically this means hiring patent lawyers to conduct patent
searches, which may or may not be affordable or effective. In this
paper, we'll call the costs of such information-gathering activities
the patent system's "discovery costs." One criterion for a well-
functioning patent system-- or any system of property-like rights-- is
that discovery costs should be low enough that it's economically
feasible for firms to obtain the information they need to comply with
Thinking explicitly about discovery costs is a powerful tool
for understanding the dysfunctions of the patent system. As we will
see, discovery costs are relatively low in pharmaceuticals and other
chemical industries. As a consequence, the patent system serves these
industries relatively well. In contrast, discovery costs in the
software industry are so high that most firms don't even try to avoid
infringement. Unsurprisingly, software is a major contributor to the
recent spike in patent litigation.
Sharing ideas among a group of people is a very effective way to
develop software. Several models of organizations have been invented
for this purpose.
3. In the computer programming art, patents provide low
quality disclosure which is legally dangerous for a programmer to
One possible model is the free and open source model.64 People agree on a copyright
license and share source code.65 Everyone can download, run, debug and
improve the programs. The improvements are contributed back to the
community. Very innovative and commercially important software is
developed in this manner.66
Another model is the definition of communication protocols by
the IETF. The formal definition of the process is centered around
specification documents called RFCs (Request for Comments).67 But in practice the source
code for reference implementation is also frequently shared.68 All the core protocols of
the Internet have been invented and standardized in this manner.
The problem of patents for these groups is the same as for
anyone else. They can't verify they don't infringe someone else's
patents. These groups can agree among themselves on whatever agreement
they need to share the rights and function as a group. But they can
verify they won't infringe on the rights of outside parties. They must
take the risk and find out the hard way if someone will sue. Either
that or they don't write the software.
This problem may be more acute for these groups than it is for
proprietary vendors, because these development models don't permit
pinpointing any specific date when the code is released. Every
contribution from every member must be shared publicly the very moment
it is made, if the group is to function as a group. Since members may
contribute something any time they please, new code is constantly
being published. Public repositories such as
github are used for this purpose. Hence,
there is no publication event before which it could make sense to
perform a legal review of the code.
This situation is hindering innovation. These collaborative
groups have invented very influential technologies. The working
methods of these groups are themselves innovative. The legal risks
imposed on these groups by software patents are real. On the other
hand the benefits are non-existent. Their goal is to develop software,
disclose their inventions and share them with the world. They do this
without the incentive of exclusive rights, and they don't hide
anything as trade secrets. And they can't opt-out of the patent
system, because they can't opt-out of inadvertently infringing on
someone else's patent and being sued.
For a programmer, reading patents is legally dangerous. He risks
becoming liable for treble damages for willful infringement. There is
no hope to mitigate this risk by clearing all the patent rights to the
software for the reasons explained above. The only effective
mitigation strategy is not to read patents. But then disclosure is
ineffective because it is intended precisely to be read by the
developers. Patent law cannot promote innovation according to its
theory unless the disclosure is read by the practitioners of the
4. The normal costs/benefits analysis of patents is not
applicable to software.
Many Groklaw members report that their employers forbid their
developers from reading patents because the legal risks are high and
there are no benefits. This phenomenon has been reported by Mark
Lemley as well69
[B]oth researchers and companies in component
industries simply ignore patents. Virtually everyone does it. They do
it at all stages of endeavor. Companies and lawyers tell engineers not
to read patents in starting their research, lest their knowledge of
the patent disadvantage the company by making it a willful infringer.
Walsh et al., similarly find that much of the reason university
researchers are not deterred by patents is that they never learn of
the patent in the first place. When their research leads to an
invention, their patent lawyers commonly don't conduct a search for
prior patents before seeking their own protection in the Patent and
Trademark Office (PTO). Nor do they conduct a search before launching
their own product. Rather, they wait and see if any patent owner
claims that the new product infringes their patent.
Software patents are not only ignored as a property system. They
are also ignored as a source of knowledge.
For programmer the preferred form of disclosure is the source
code of a well written working program. If the license allows the
programmer to modify the program and distribute the modifications it
is even better. Communities of developers in FOSS projects do this on
a routine basis.
Software patents do not require the disclosure of source code.
Please see Fonar
Corporation v. General Electric Corporation:
As a general rule, where software constitutes part of
a best mode of carrying out an invention, description of such a best
mode is satisfied by a disclosure of the functions of the software.
This is because, normally, writing code for such software is within
the skill of the art, not requiring undue experimentation, once its
functions have been disclosed. It is well established that what is
within the skill of the art need not be disclosed to satisfy the best
mode requirement as long as that mode is described. Stating the
functions of the best mode software satisfies that description test.
We have so held previously and we so hold today. Thus, flow charts or
source code listings are not a requirement for adequately disclosing
the functions of software.
See also Northern
Telecom v. Datapoint Corporation:
The computer language is not a conjuration of some
black art, it is simply a highly structured language â€¦ . The
conversion of a complete thought (as expressed in English and
mathematics, i.e. the known input, the desired output, the
mathematical expressions needed and the methods of using those
expressions) into a language a machine understands is necessarily a
mere clerical function to a skilled programmer.
From the perspective of a programmer, these cases eviscerate the
usefulness of disclosure. The functions of most software inventions
can be defined after a few brainstorming sessions. Turning these
functions into a working implementation is still a lot of hard work.
When only the functions are known, the programmer is still required to
do the bulk of this work. But this obligation does not follow from the
disclosure, which is commonly available from FOSS projects.
The functions of existing software can usually be seen just by
watching the program in action. Developers may watch over the shoulder
of a user, or they may inspect the computer internals with debugging
tools. Disclosing the functions of software without source doesn't
disclose any trade secret.
The ineffectiveness of disclosure has been noted by some patent
scholars. For example Benjamin Roin states70 (footnotes omitted):
If the Supreme Court is correct that "the ultimate
goal" of patent law is to facilitate the disclosure of information
that would otherwise be kept secret, then our patent system appears to
be in trouble. A number of empirical studies suggest that patent
disclosures play an insignificant role in promoting R&D spillovers.
This is partially a reflection of the basic economics of patenting,
where companies typically patent only those inventions that are
disclosed to the public through other channels. It also reflects the
numerous alternative sources of information available to inventors.
Both of these issues are largely inherent in the patent system.
Until these issues are fixed, there is no point for a programmer to
read patents. He takes a huge legal risk, and most of the time he
doesn't learn anything that wouldn't otherwise be known to him without
Many of the other problems discussed in this Note are more
amenable to repair, assuming the courts and policymakers genuinely
wish to improve the disclosure value of patents. The Federal Circuit's
willful infringement rules, for example, encourage innovators to
protect themselves from treble damages by remaining "willfully
ignorant" of the patents in their field. Many commentators have
recommended abolishing the willfulness rules entirely, although the
Federal Circuit appears wedded to the doctrine. Similarly,
commentators have suggested that Congress remove the remaining
loopholes in the publication rules for patent applications, which
currently allow some of the most time-sensitive innovations to be both
patented and withheld from the public. In industries where patent
applications are thought to disclose too little knowledge, courts
might require more detailed information about how to enable the
claimed invention. In the software industry, for example, there might
be a strong case for requiring patent applicants to disclose the
source code of their program.
The usual costs/benefits analysis is based on the patent quid pro
quo. The inventor is granted exclusive rights for a limited period of
time in exchange of the disclosure of his invention. Then, according
to theory, society benefits from the invention when the exclusive
rights expire. But during this time period, the patentee may recoup
his investment. This incentive to innovate is viewed as more
advantageous for society than forcing the inventor to protect his
invention with trade secrets.
The table below summarizes this analysis of the costs and
benefits of patents.
Benefits to Society
Costs to Society
Promotes progress of useful arts by rewarding inventors
Grant of exclusive rights to the invention for limited time
Supports the economy by encouraging innovation
Administrative costs (we need a patent office)
Disclosure of what would otherwise be trade secrets
Legal costs such as liability for infringement and
patent defense strategies
But in the case of software this analysis is not applicable.
There are strong incentives to innovate other than patents. Software
is protected by copyrights. Software authors have a strong first-mover
Community-based development like FOSS amounts to free R&D to
organizations who know how to keep a good relationship with a
community. Also community-based development inherently provides
The table below shows how the costs and benefits of patents are
applicable to software. This table is very different from the previous
Benefits to Society
Costs to Society
Promotes progress of software by rewarding inventors
above and beyond the rewards already provided by copyrights, first
mover advantage and community contribution to FOSS projects
Grant of exclusive rights to the invention for limited time
Supports the economy by encouraging innovation above
and beyond the rewards already provided by copyrights, first mover
advantage and community contribution to FOSS projects
Administrative costs (we need a patent office)
Disclosure of what would otherwise be trade secrets
above and beyond disclosure inherent to the release of source code by
FOSS projects, but only to the extent readers don't fear being liable
to treble damages for willful infringement
Legal costs such as liability for infringement and
patent defense strategies
Software authors are unable to clear the rights to
their own programs, because it is not practically feasible to do
Harm to collaborative development such as FOSS limiting
its positive contribution to progress, the economy, and to disclosure
of source code
Exclusive rights granted to the expressions of abstract
ideas impinge on individual free speech rights
We cannot presume software patents are promoting innovation
according to the normal costs/benefits analysis, because this analysis
is seen therefor not applicable to software. There is no reason to
believe an analysis which takes all relevant factors into
consideration will show a positive contribution to society. In
particular the inability of software authors to clear the rights to
their own products strongly suggests that the costs far outweigh the
The fundamental problem of the patentability of software is
that the Federal Circuit (and the CCPA before them) believes that the
functions of software are performed through the physical properties of
This belief leads to the natural conclusion that software is an
electrical process and software patents are not different from
hardware patents. But programmers are not configuring circuits to take
advantage of their physical properties. They are defining the meaning
of organizations of data. They implement operations of arithmetic and
logic which are applicable to this data based on its meaning.73 The legal view of software
is based on a faulty understanding of computer programming.
The functions of software are performed through a combination
of defining the meaning of data and giving input to an already
implemented algorithm. Meaning is not a physical property of a
circuit.74 Giving input
to an algorithm is not configuring a machine structure.75 The consequence of the
beliefs of the Federal Circuit is to treat as hardware patents what is
actually patents on a certain category of expressions of ideas.
This treatment of software patents does not promote innovation
because it cannot. Software patents do not actually practice any of
the the principles of patent law that theoretically lead to
innovation. The patent system cannot function as a property system for
software because it is impossible for authors of software to be secure
in their own property. Patent disclosure is not being read in practice
because there is no reason for software authors to do so and plenty of
reasons not to. In addition, the usual costs/benefits analysis of
patents is not applicable. The incentive of patents to innovators
overlaps with copyrights, FOSS, and first-mover advantage, but their
full costs and risks still accrue to the developers and to society as
Software patents harm innovation because they encourage
monopolistic rents and litigation.
The cure is simple -- the courts should just admit the facts
are as they are and apply the law accordingly. They should recognize
that computations are expressions of ideas and stop conflating them
with applications of ideas.
Not applying this cure will allow the problem to persist. This
problem cannot be solved by improving the quality of prior art
discovery and analysis. It cannot be solved by curtailing vague or
overly broad claims. These improvements are welcome, but they don't go
to the point of solving the actual problem. We need to stop allowing
patents on the meaning of symbols when they are dressed up as patents
An approach based on semiotics would be a better interpretation
of the law.76 This
approach has the advantage of being neutral relative to technology. It
is applicable whenever the claim recites a sign. Anything can be a
sign if it is used as a sign. Therefore this approach is not limited
to software. It is applicable (and limited) to whenever there is an
issue of whether the subject matter of a claim is related to the
meaning of a sign.
The semiotics approach avoids terms like "abstract idea" which
are hard to define. It doesn't depend on whether the subject matter is
mathematical or related to software. It relies on the well understood
distinction between an expression and its meaning. It relies on the
well understood notion that thoughts in the human mind are abstract
ideas. It builds on established principles of law. It relies on the
linguistic aspects of mathematics to define a clear boundary between
abstract mathematical ideas and their applications which is consistent
with Supreme Court precedents.77
There is no need to ask Congress to change the law. It is
sufficient for the courts to acknowledge facts and interpret existing
Under this approach claims reciting software will be patentable
when they claim a referent which is a patent-eligible invention. An
industrial process for curing rubber such as the one in Diehr
is patent-eligible. Inventions like remote surgery systems and
anti-lock brake systems are patent-eligible when the referent is
actually claimed and not merely referenced. Only claims directed to
the expression of abstract ideas will be rejected. This is conforming
with the theory that innovation is promoted by patents on the
application of ideas but not by patents on the ideas themselves.
Examples of such textbooks are:
Haskell B., Foundations of Mathematical Logic, Dover
Publications, 1977, Revised and corrected reprint from McGraw Hill
Book Company, Inc. 1963
Delong, Howard. A Profile of Mathematical Logic.
Addison-Wesley Publishing Company. 1970. I use the September 1971
second printing. Reprints of this book are available from Dover
Richard L., Carnielli, Walter
A., Computability Computable Functions, Logic and the
Foundations of Mathematics, Wadsworth & Brooks/Cole, 1989, pages
Stephen Cole, Introduction to Metamathematics, D. Van
Nostrand Company, 1952. I use the 2009 reprint by Ishi Press
Kleene, Stephen Cole, Mathematical Logic, John Wiley &
Sons, Inc. New York, 1967, reprint from Dover Publications 2002. pages
2 See Rogers,
Hartley Jr, Theory of Recursive Functions and Effective
Computability, The MIT Press, 1987 pp. 1-2
3 See for instance textbooks
on denotational semantics for one method of writing such descriptions.
An example of such textbook is Stoy, Joseph E., Denotational
Semantics: The Scott-Strachey Approach to Programming Language
Theory, MIT Press, First Paperback Edition
4 See Curry supra,
5 See Ben-Ari,
Mordechai, Mathematical Logic for Computer Science, Second
Edition, Springer-Verlag, 2001, for a textbook on mathematical
logic as it is applied to computer science.
6 Here are a few places where
such descriptions may be found:
George S., Burgess,
John P., Jeffrey, Richard
C., Computability and Logic, Fifth Edition, Cambridge
University Press, 2007, page 23-25.
Richard L., Carnielli, Walter
A., Computability Computable Functions, Logic and the
Foundations of Mathematics, Wadsworth & Brooks/Cole, 1989, pages
Stephen Cole, Mathematical Logic, John Wiley & Sons, Inc.
New York, 1967, reprint from Dover Publications 2002. pages
Abstract Computing Machines, A Lambda Calculus Perspective
, Springer-Verlag Berlin Heidelberg 2005, pages 11-14.
Minsky, Marvin L.,
Computation, Finite and Infinite Machines
, Prentice-Hall, 1967, pages 103-111
Viggo, Lindström, Ingrid, Griffor, Edward R.,
Mathematical Theory of Domains, Cambridge University
Press, 1994, pages 224-225.
7 See Stoltenberg-Hansen et
al., supra, page 224.
8 See Stoltenberg-Hansen et
al., supra, page 224.
9 See Boolos et al.,
supra, page 23.
10 See Boolos et al.,
supra, page 187.
11 See Epstein et al.,
supra, pages 65-66, quoting from Hermes, Enumerability,
Decidability, Computability. 2nd ed., Springer Verlag 1969. "[W]e
must be able to express the instructions for the execution of the
process in a finitely long text." See also Stoltenberg-Hansen,
Lindström and Griffor, supra, page 224. "[An algorithm] is a
method or procedure which can be described in a finite way (a finite
set of instructions)"
12 See Boolos et al.,
supra, pages 23.
13 See Stoltenberg-Hansen,
Lindström and Griffor, supra, page 224. "[An algorithm] can be
followed by someone or something to yield a computation solving each
problem in [a class of problems]."
14 See Boolos et al.,
supra, pages 23-24.
15 See Kluge, supra,
16 See Stoltenberg-Hansen
et al., supra, page 225.
17 This is Turing machines,
general recursive functions and λ-calculus.
18 See Kluge, supra,
19 See Kleene,
supra, page 223.
20 See Epstein et al.,
supra, page 70.
21 A model of computation is a class of syntactic
manipulations of symbols defined in terms of the permissible
operations. Examples of models of computations are Turing-machines,
λ-calculus and general recursive functions.
22 For a discussion of how
problems are represented syntactically using symbols, see Greenlaw, Raymond, Hoover, H. James,
Fundamentals of the Theory of Computation, Principles and
Practice, Morgan Kaufmann Publishers, 1998, Chapter 2.
23 This is used during
debugging. Programmers verify programs work as intended by reading the
data stored in the computer memory. They interpret this information
according to its logical data type to determine if the program
implements the operations of arithmetic and logic that solves the
24 See Poernomo, Iman Hafiz,
Martin, Adapting Proofs-as-Program, The Curry-Howard
Protocol, Springer 2005. This thesis is presented in chapters 4, 5
25 See Ben-Ari,
supra, chapter 7 and 8 for a discussion of SLD-resolution.
for a book dedicated to several implementations of normal order
-reduction. It should be noted that normal order
-reduction is a universal algorithm which modifies its program
as the computation progresses. It cannot be assumed the program is
always unchanged by the computation as is usually (but not always) the
norm in imperative programming.
27 This is a simplified
explanation for readability. Here is how Hamacher, V. Carl, Vranesic, Zvonko G.,
Zaky. Safwat G.,
describes the hardware implementation of an instruction cycle. See
Computer organization, Fifth Edition, McGraw-Hill Inc. 2002 p.
43 (emphasis in the original)
Let us consider how this program is executed. The processor contains
a register called the program counter (PC) which holds the
address of the instruction to be executed next. To begin executing a
program, the address of its first instruction (i in our
example) must be placed into the PC. Then, the processor control
circuits use the information in the PC to fetch and execute
instructions, one at a time, in the order of increasing addresses.
This is called straight-line sequencing. During the execution
of each instruction, the PC is incremented by 4 to point to the next
instruction. Thus, after the Move instruction at location i + 8
is executed the PC contains the value i + 12 which is the
address of the first instruction of the next program segment.
Executing a given instruction is a two-phase procedure. In the
first phase, called instruction fetch, the instruction is
fetched from the memory location whose address is in the PC. This
instruction is placed in the instruction register (IR) of the
processor. At the start of the second phase, called instruction
execute, the instruction in IR is examined to determine which
operation to be performed. The specified operation is then performed
by the processor. This often involve fetching operands from the memory
or from processor registers, performing an arithmetic or logic
operation, and storing the result in the destination location. At some
point during this two-phase procedure, the contents of the PC are
advanced to point at the next instruction. When the execute phase of
an instruction is completed, the PC contains the address of the next
instruction, and a new instruction fetch phase can begin.
28 A suitable
analogy may be travel directions. These instructions don't drive the
car. They are input given to the driver.
29 See section A.3,
supra. Section A.2 explains the relationship between
algorithms, formulas and equations. These two sections explain the
mathematical meaning of all terms which have troubled the Federal
Circuit in AT&T Corporation.
30 See Milner,
Robin, Tofte, Mads, Harper, Robert, MacQueen, David,
The Definition of Standard ML (Revised) , The MIT Press, 1997,
for the official definition of the Standard ML language. See also Reppy, John H.,
Concurrent Programming in ML, Cambridge University Press, First
published 1999, Digitally printed version (with corrections) 2007,
appendix B, for the official definition of the Concurrent ML
31 See section A.3 supra.
Corporation vs Retail Decisions, Inc. sounds like a possible
example of this argument. They write "That purely mental processes can
be unpatentable, even when performed by a computer, was precisely the
holding of the Supreme Court in Gottschalk v. Benson." And then
they continue writing, "This is entirely unlike cases where, as a
practical matter, the use of a computer is required to perform the
claimed method." Benson is the case which established the
mathematical algorithm exception. To the extent that ordinary logic is
applicable here, one may conclude the Federal Circuit in
Cybersource said the mathematical algorithm exception is not
applicable when the use of a computer is required as a practical
matter to perform the claimed method. Mathematicians have deliberately
decided to ignore this kind of distinction when they defined their
notion of algorithm.
33 See section A.4 supra.
34 This is unless we count
artificial intelligence programs such as IBM's
Watson as being able to relate the syntax of human language with
its meaning. No matter how we look at this issue, there is no factual
difference between a printing press and a computer instruction cycle.
If we consider computers as unable to understand meaning they are no
better than printing presses. But if they are able to understand
meaning printed information is not intelligible only by a human being.
Either way the guidance offered by Lowry doesn't apply to the
35 See section A.4 supra
36 An alternative version
of the change to the machine structure argument has been stated in
WMS Gaming vs International Game technology:
The instructions of the software program that carry
out the algorithm electrically change the general purpose computer by
creating electrical paths within the device. These electrical paths
create a special purpose machine for carrying out the particular
This alternative explanation is immediately refuted because it is
manifestly false. A stored program computer is programmed by storing
the instructions in main memory. This action doesn't create electrical
paths, because main memory doesn't work in this manner. Main memory is
a component that merely records information. On modern DRAM technology this information is electric
charges stored in capacitors. No transistors are opened and closed to
create electric paths in the microprocessor when these electric
charges are stored.
[Footnote 3]: A microprocessor contains a myriad of
interconnected transistors that operate as electronic switches.
See Neil Randall, Dissecting the Heart of Your Computer,
PC Magazine, June 9, 1998, at 254-55. The instructions of the software
program cause the switches to either open or close. See id. The
opening and closing of the interconnected switches creates electrical
paths in the microprocessor that cause it to perform the desired
function of the instructions that carry out the algorithm. See
Programs are not stored in the microprocessor mentioned in the
footnote because this component is not main memory. The activity of
the transistors turning on and off in the microprocessor is the
execution of the program. Programming a computer and executing
a program are two separate actions. It is an error to conflate them as
the court do in WMS Gaming.
The instructions that could be executed by a microprocessor are
very elementary. A complete algorithm typically requires a large
number of these rudimentary instructions. Complete programs require
thousands or even millions of instructions. On the other hand a
microprocessor typically executes the instructions one by one. In some
microprocessors gains of speed are achieved by executing a very small
quantity of instructions in parallel when it is feasible to do so.
Microprocessors execute large number of instructions by executing on
them in successive cycles, one (or a few) instruction(s) per cycle.
The transistors turning on and off are the execution of this small
number of instructions and different electrical paths are created in
each cycle. No electric paths for carrying out a particular algorithm
is created because the number of instructions which are executed in a
single cycle is too small.
See section A.5 supra for a
discussion of theinstruction cycle.
37 In mathematics this
partial application of the parameters of a mathematical function is
38 These function are not
special cases of multiplication. We can double a number by adding it
with itself. This shows that doubling is a concept independent from
multiplication because we can implement it without multiplying.
Similarly we can triple a number by adding it with itself twice.
Adding the number with itself three times quadruple the number.
39 In some cases the
configuration can be made permanent by storing it in memory types such
as ROM that can't be overwritten. However typical software patents are
not limited to this type of memory. They will read on implementations
using the more commonly used writable memory.
40 Remember that it is not
possible to define this process in terms of the meaning of the data.
41 Without such an argument
his position would immediately be refuted by the observation that main
memory changes up to billions of times per second.
42 Let's consider, for
example, what happens when we store instructions for a x86 CPU on a
SPARC workstation. The SPARC uses a different instruction
set than the x86. A program for a x86 computer does not normally
run on a SPARC workstation. But a SPARC can execute the Bochs program which is a
software version of the x86 instruction cycle. If this program is used
the x86 program will run on a SPARC. This shows that instructions by
themselves are just a series of numbers in memory. They don't impart
functionality unless and until they are given as input to an algorithm
which is the instruction cycle.
43 Please remember that
several programing languages use a software universal algorithm. They
don't directly use the computer native instruction cycle. See section A.5 supra.
44 The extreme case occurs
with self-modifying programs. In a stored-program computer, all data
in memory may be modified as the program is executed. Programmers may
arrange their programs so that they are modified in memory as they are
executed. Then the alleged "machine configuration" doesn't stay in
place long enough to perform all the steps that are necessary to
infringe on the patent claim. A simple way to achieve this result is
to use a programming language with relies on a variant of normal order
β-reduction as its universal algorithm. (See section A.5
supra.) This particular category of universal algorithms
constantly modifies its program as it executes. This is done
automatically by the language run-time system without any action of
the part of the programmer other than his decision to program in this
45 But remember that an
algorithm is also meant to be executed in practice. Practical
implementations functions only to the extent there are sufficient
resources and are therefore limited to sufficiently small sizes of
inputs. See section B.2 supra.
46 An example of a symbol
is a letter in the common Latin alphabet. A letter may be a mark of in
on paper, a carving in stone, the shape of a neon sign, an arrangement
of pixels on the screen. A letter come in different shapes depending
on typefaces. These are different physical objects separate from the
abstraction called a letter. This concept of 'symbol' as an
abstraction separate from its representation is explicitly
acknowledged in mathematical logic and computation theory. See for
instance Curry, supra, pages 15-16:
In the theory presented here, one may conceive such
assumptions as entering in certain abstractions. The first of these is
involved in the use of such terms as 'symbol' and 'expression'; these
denote, not individual marks on paper or the blackboard--which are
called inscriptions--but classes of such inscriptions which are
"equiform." Thus the same expressions may have several "occurrences."
47 See section A.1. The approach
suggested here has been proposed in Collins, Kevin Emerson,
Semiotics 101: Taking the Printed Matter Doctrine Seriously
(February 28, 2009). Indiana Law Journal, Vol. 85, p. 1379, 2010.
Available at SSRN: http://ssrn.com/abstract=1351066.
We don't agree with everything Collins says, because he did not
recognize the errors we have mentioned in section B. We believe that
once these errors are corrected his approach is correct.
48 See section A.4 supra.
49 This is the thesis of
Kevin Emerson Collins in his article quoted supra.
50 See the criteria of
"precise definition" for the mathematical notion of algorithm in
section A.3 supra.
51 See section B.2 supra.
52 See section B.1 and
53 See section B.3 supra.
54 See section B.4, supra.
55 See section B.5 and
56 See section A.4, supra.
57 See Lemley, Mark A.,
Software Patents and the Return of Functional Claiming (July 25,
2012). Stanford Public Law Working Paper No. 2117302. Available at
or http://dx.doi.org/10.2139/ssrn.2117302 pages 24-25.
58 See Mulligan, Christina
and Lee, Timothy B., Scaling the Patent System (March 6, 2012). NYU
Annual Survey of American Law, Forthcoming. Available at SSRN: http://ssrn.com/abstract_id=2016968.
59 See Mulligan and Lee,
supra, pp. 16-17
60 See Mulligan and Lee,
supra, p. 7.
61 See Mulligan and Lee,
supra, p. 6.
In the real world, lawyers frequently cannot state for
certain whether a given activity actually infringes a particular
patent. In this paper, we will largely set this issue to the side and
assume counterfactually that lawyers can always determine whether a
particular activity infringes a particular patent in a reasonable
amount of time. For further reading on the challenges of claim
construction and determining the scope of patents, see Jeanne Fromer,
Claiming Intellectual Property, 76 U. CHI. L. REV. 719 (2009),
Michael Risch, The Failure of Public Notice in Patent
Prosecution, 21 HARV. J. L. & TECH. 179 (2007); Christopher A.
Cotropia, Patent Claim Interpretation Methodologies and their Claim
Scope Paradigms, 47 WM. & MARY L. REV 49 (2005); Christopher A.
Cotropia, Patent Claim Interpretation and Information Costs, 9
LEWIS & CLARK L. REV. 57 (2005).
62 See Lemley, Mark A., Ignoring
Patents (July 3, 2007). Stanford Public Law Working Paper No. 999961;
Michigan State Law Review, Vol. 2008, No. 19, 2008. Available at SSRN:
or http://dx.doi.org/10.2139/ssrn.999961 pages 19-21.
63 See Mulligan and Lee,
supra, pp 2-4.
64 A description of what
is free software is maintained by the Free Software Foundation.
The Open Source Initiative maintains the definition of open source
65 The Free Software
Foundation maintains a list of
licenses which are accepted for free software development. The
Open Source Initiative also maintains their list of licenses
for open source software.
66 The most famous example is the
Linux operating system kernel. It
is at the core of several operating systems such as GNU/Linux and
Android. We may also mention the Perl and Python programming languages, the Coq proof assistant, web browsers such
and also the Apache web server.
This list far from exhaustive.
67 See RFC 2026 for the current version of
the RFC development process. RFC 2555 is an historic account describing how the
RFC process has been used to invent and disclose the core Internet
68 An example of a
reference implementation is found in RFC 1321 Appendix A.
Reference implementations may also be incorporated by reference. For
example RFC 5905
includes the reference "This document includes material from [ref9],
which contains flow charts and equations unsuited for RFC format.
There is much additional information in [ref7], including an extensive
technical analysis and performance assessment of the protocol and
algorithms in this document. The reference implementation is available
at www.ntp.org." This same RFC 5905
also includes a skeleton program with code segments in appendix A.
69 See Lemley, Mark A.,
Ignoring Patents (July 3, 2007). Stanford Public Law Working
Paper No. 999961; Michigan State Law Review, Vol. 2008, No. 19, 2008.
Available at SSRN:
70 Benjamin Roin, Note,
The Disclosure Function of the Patent System (Or Lack
Thereof), 118 HARV. L. REV. 2007 (2005) (noting that the patent
system doesn't achieve this disclosure goal). Available at: http://hlr.rubystudio.com/issues/118/april05/Note_3857.php
71 Eric Goldman explains
this first mover advantage in term of the soft life-cycle of software.
Eric, Fixing Software Patents (January 1, 2013). Forbes
Tertium Quid Blog, November 28, December 11 and December 12, 2012;
Santa Clara Univ. Legal Studies Research Paper No. 01-13, available at
SSRN at http://ssrn.com/abstract=2199180
Software innovators can recoup some of their R&D
investments from the de facto marketplace exclusivity associated with
being the first mover. An example: assume that a particular software
innovation has a two-year commercial lifecycle and it takes
competitors 6 months to bring a matching product to market. In a
situation like this, the first mover gets 1/4 of the maximum useful
exclusivity period simply by being first to market. In some
situations, the exclusivity period provided by the first mover
advantage is more than enough to motivate software R&D without any
72 See section B generally,
especially the quote from In re Noll in section B.6,
73 See section A.2 and A.4,
74 See section B generally,
especially sections B.3,
75 See section B.5, supra.
76 This is the approach we
have described in section C.2,
77 See section B.4, supra.