🚀 go-pugleaf

This is a transcript of an essay that I have submitted to a local
competition. It is concerned with the assertion by some authors
(Read as: Gemignani and Chisum) that there is some clarity to be
gained by extending patentable subject matter to mathematical
algorithms.
The file is a latex (sub-)file, but nothing of great interest
was included. If anyone wants the references I can put a ps file
of the essay up for ftp somewhere.

Brendan

(the title was something along the lines of:
Extending Patentable Subject Matter to Algorithms - The Question
of Clarity)

*** begin included file:

Case law in the \us\ on mathematical algorithms has begun to settle. 
Fundamental principles have been agreed on by the courts, at
least to some extent. Some commentators are unsatisfied with the position. 
They argue that the present law is neither clear enough nor adequately
founded on precedent. Suggestions are also made that more protection is
required to encourage the development of the computer software industry.
Consequently it is suggested that the current law should be extended in 
order to alleviate these difficulties. With the last two justifications
for extension we do not concern ourselves. Rather, we focus on the first:
that by extending patent protection for algorithms more clarity will be
introduced into the law. By considering a subset of algorithms, mathematical
formulae, we argue that any gains to be made in clarity of admissible
subject matter will be lost when it comes to determining infringement
of that matter. We conclude that such an extension does not therefore
serve its stated purpose in this respect. Our discussion begins with 
an overview of the law in this area.

In 1972 the Supreme Court of the United States decided that mathematical
algorithms were not statutory subject matter within the meaning of their
patent statute.\footnote{\bensonref.} Since then American courts have seen a
diversity of patents directed toward sequences of mathematical steps.
The Federal Patent Court of that country, in a series of decisions\footnote{
\freemanref, \walterref, \abeleref.} devised a test for patentability of 
mathematical algorithms which the Australian Patent Office has 
adopted.\footnote{\guidelinesref, cited in \ibmbref, 37436.} 
This test, the Freeman-Walter test, requires
that such an algorithm be implemented in a manner which defines 
structural relationships between physical elements in the claim.\footnote{
\walterref, 407, \ryenref.} 
In addition to that, the Supreme Court in \diehr\ \footnote{\diehrref.}
sanctioned the use of a mathematical algorithm in an otherwise
statutory claim. 

In 1959 the High Court of Australia interpreted the meaning of s 6 of the
\statmon\ to have a very broad scope - it's basis being in
the production of some material advantage, something economically 
useful.\footnote{\nrdcref, 275.} More recently, in December of last year, 
the Federal Court ruled that an improved curve image was a commercially
useful effect\footnote{\ibmref.} although it declined to say that 
mathematical algorithms or principles are patentable per se. 
 
The decisions of the Courts, both in Australia, and the United States
have been keen to ensure that patent protection does not extend
to ``scientific principles'' or mathematical algorithms per se.\footnote{\ibmref, 423, \diehrref, 7.} 
There have consequently been a number of
attempts to straddle the line between the pure and the applied.\footnote{
e.g. the applications of Dale Flook \flookref, and Hiroyuki Iwahashi \iwahashiref.} 
The Courts have been hard put to devise an adequate 
definition of ``mathematical algorithm''.\footnote{
\gemignaniref, 327.}
How is a mathematical 
algorithm different in kind to another sort of process? Will 
``means for'' performing an algorithm also be excluded? What is a 
physical element in the \walter\ sense? These are difficult questions
and the Courts have not always given consistent answers, resulting
in no small amount of judicial confusion. The dissent in 
\diehr\footnote{\diehrref\ at 22.} 
did not believe that the judgment of the majority 
in that case was sufficient to relieve that confusion. Several
commentators have since called for a widening of 35 USC 101 to
include within its ambit mathematical algorithms.\footnote{
\gemignaniref, \chisumref, \dunnerref.}

In reply to views such as those of Chisum have been the papers of
Professors Samuelson,\footnote{\samuelsonref} and Newell.\footnote{\newellref} Professor
Newell's paper immediately followed that of Professor Chisum in 
the University of Pittsburgh Law Review. Its pith and marrow
was that there was little certainty to be gained by expanding
patent protection to algorithms, and it is upon this aspect  
which we would like to focus. 

The scope of meaning of ``mathematical algorithm'' has yet to 
be setted. One thing universally presumed to be within its 
bounds is a formula of some sort.\footnote{\christensenref, 38, per 
Rich J., \flookref, 195.} Any 
formula can be viewed as an algorithm by breaking it into its
component operations and observing precedence of the operations.
For example the function:\footnote{Here, * denotes multiplication, 
$2*3 = 6$.}
\begin {equation}
        f(z) = 2 * \cos (z) + z
        \label {fex}
\end {equation}

can be expressed as an algorithm by:

An algorithm for calculating a value of $f(z)$, given a value for
the variable $z$, consisting of the steps: calculating the value 
of the cosine of $z$, multiplying that value by $2$, to give a new
value, and adding the original value of $z$ to said new value.

We are not concerned with whether the algorithm is new or non-obvious,
we shall assume this to be the case. 
The first thing that we note is 
that a number is absent of any meaning unless it is tied to some 
physical situation. The number $1$, for example, means nothing, unless
we are explicitly told about the representation which has been 
adopted. If we know that when the light is off a certain meter 
will read `$1$' and `$0$' when the light is on, then we have a 
context to interpret the meter reading. The `$1$' and `$0$' on 
the dials themselves have no direct representation.\footnote{This
would also be true if the meter read ``on'' and ``off'' because
we would also have to know that the meter correlated properly
with the state of the light. In the example given, $0$ was deliberately
and counter-intuitively related to the light being {\ul on}.}

This is also true of a function. A meter can be seen to be the
same as a function - the meter gets information about the state
of the light, and outputs a result, $0$ or $1$ based on that
information. If $z$ represents the state of the light, we have
the function:
\begin {equation}
        f(z) \eql \left\{ \begin{array}{ll}
			0 & \mbox{ if $z$ is on.} \\
			1 & \mbox{ if $z$ is off.}
			\end{array}
		\right.
\end {equation}

Legal tests aside, if we presume that
a valid patent had been issued for $f(z)$,
would we want to hold that the function
\begin {equation}
        g(z) \eql \left\{ \begin{array}{ll}
			0 & \mbox{ if $z$ is {\ul off}.} \\
			1 & \mbox{ if $z$ is {\ul on}.}
        		\end{array}
		\right.
\end {equation}
infringes the issued patent? The functions are clearly different,
they give different results, based on the same 
information. If $g(z)$ infringes the patented function we must
be protecting more than just the function itself. If it doesn't
then all a competitor has to do to evade infringement is to 
change his interpretation of the data. If we want a bell to 
ring when the light is on, the patentee will cause the bell 
to ring if $f(z)$ is $0$, the competitor if $g(z)$ is $1$.
The bell will ring at the same times for both of them, but
via ostensibly different means.

Perhaps a more striking example might be taken directly from 
the \diehr\ case itself. In that case, a temperature was 
frequently read, the value put into a function, and when
that function equalled zero, a mould for rubber was opened.
The equation reads:\footnote{\diehrref, 5, note 11}
\begin {equation}
        f(z) = \ln v = cz + x
        \label {diehreqn}
\end {equation}
where both $c$ and $x$ are constants, $\ln v$ is the natural
log of the cure time, and $z$ is the temperature of the mold. 

\diehr\ is an American decision, so presumably the measurements
were taken in degrees Farenheit. What of the competitor who uses
a device that reads in Celcius, and uses the equation:
\begin {equation}
        g(z_{1}) = \ln v = c\Bigl(\frac{9}{5}(z_{1}) \splus 32\Bigr) 
				\splus x
        \label {celciuseqn}
\end {equation}
where $c$ and $x$ take the same values as in the equation 
above, $z_{1}$ is the temperature read in Celcius, with the 
process otherwise identical to that in {\it Diehr}.
Both these moulds will open at the same time, does the 
competitor infringe?
The functions which determine when they will be opened,
and the apparatus used to read the temperature of the mould
are fundamentally different - or are they?

Let us put two temperature readers into the competitor's
mould, the first reading in Farenheit ($z$), the second 
in Celcius ($z_{1}$). We take the Celcius reading and start
to calculate $g$ with it. Moving from left to right, 
and evaluating brackets first we find that $\frac{9}{5}(z_{1})
\splus 32$ is precisely equal to $z$! Our function now looks
like:
\begin {equation}
        g(z_{1}) = \ln v = cz \splus x
\end {equation}

In choosing a {\ul representation}, or an {\ul interpretation}
for the data we find that the two functions are in some
sense similar. In fact, the functions themselves are all but
meaningless without the interpretation. 

It is very tempting to think that since $g(z_{1})$ is a 
contrivance derived from $f(z)$, that $g(z_{1})$ should
be held to infringe. However, this contrivance is only 
detectable {\ul because of the physical context}. If we
{\ul forget that $z$ and $z_{1}$ stand for temperatures},
would a patent for the function:
\begin {equation}
        f_{1}(z) \eq z
\end {equation}
be infringed by the function:
\begin {equation}
        g_{1}(z) = \frac{9}{5}(z) \splus 32?
\end {equation}

What about
\begin {equation}
        g_{2}(\zeta) \eq \frac{9}{5}(\zeta) \splus 32
\end {equation}
or
\begin {equation}
        g_{3}(\zeta) \eq \frac{\zeta^{2}}{17} \sminus 17 ?
\end {equation}

If the first two, why not the third? If the third, why?

In the first function we have transformed the function 
$f_{1}$ by reference to something we know about the
physical world; Farenheit $\eq$ $\frac{9}{5}$ Celcius
$\splus 32$. In the second, we have simply substituted
the symbol $\zeta$ for $z$, what of the third? It seems
totally random.\footnote{
According to MIT folklore 17 is 
the least random number, see {\it The Jargon File}, Version 2.9.6,
16 August 1991 (electronic copy; published by MIT Press as 
{\it The New Hacker's Dictionary}), entry ``random numbers''.
}
Yet there would be nothing stopping an electrical engineer
>from changing his or her meter to read off numbers in a 
strange representation - that is, the numbers are 
{\ul only significant when interpreted}. Beside convenience,
there is no reason why anyone must use Imperial (Farenheit), 
or S.I. (Celcius) units. Indeed, there is 
nothing stopping someone from devising a whole new system
of units for themselves! Consequently, if it were held 
that $g_{3}(\zeta)$ infringed $f_{1}(\zeta)$ or even 
$g_{1}(z)$, or $g_{2}(\zeta)$ then we would be forced
to conclude that practically any function $g_{4}(\zeta)$
would infringe $f_{1}(z)$, no matter how different $g_{4}(\zeta)$
may appear on its face.\footnote{There will be technical problems
if $g_{4}(\zeta)$ is pathological, but this is not to the 
point.} That is, only one patent for a formula should be
valid at any one time. If we don't, then it is not possible
to enforce the patent claimed for $f_{1}$ as anyone may 
evade it by implementing a different, but equivalent function 
-adopting a different interpretation of the data.

More strongly, it is not going to be sufficient to deal wholly with 
the words and symbols of a formula per se. That is, we cannot rely on 
the form in which the formula is expressed, we have to look also to 
the way that formula relates to the physical world. It is not possible
to divorce the form from the context in any real sense. 
Thus allowing patents to issue on mathematical formulae will 
reduce confusion for those who seek to patent them, but vastly 
increase it for all in infringement actions. Competitors will not
know what things they may do without infringing an issued patent.
Similarly, the patent holder will be in an unclear position as to 
the circumstances in which he or she may bring an action. 

One may speculate that the \us\ court foresaw these difficulties
in {\it Walter}, when they
added the ``relations between physical elements'' clarification to 
the {\it Freeman} test. Heed should be taken of the {\it Walter}
modification when claims are drawn up. The further removed the claims
are from the tangible, the more vulnerable they will be. If at
all possible, formulae should be used to relate obviously physical
elements in an obviously physical manner. The claim in {\it Diehr}
provides a good example: a rubber mould can be touched and moved,
opening a mould is a distinctly physical action.  If such 
elements of the claim are scarce, then the claim should be framed 
to produce human-sensible output: a curve on a screen as in the 
{\it IBM} claim, for example, or, by logical extension, some 
visual representation of the results. 

Therefore, although extension of patentable subject matter to 
cover mathematical algorithms per se will clarify the patent
acquisition step, only those with some physical part in their
claim will be secure in the validity of their claim, and in 
their knowledge of when infringement actions can be brought. 
An extension therefore serves only to substitute the problem
for an equally difficult one. We therefore suggest that the 
{\it Freeman-Walter} test be embraced without extension.

*** end included file.

Comments?

---
Brendan Scott, Australian National University.
brendan@gauss.anu.edu.au
Strictly no reproduction for commercial purposes.