ñòð. 48 |

machine, and since computer programs are now worth money, patented algorithms are

inevitable. Of course the specter of people keeping new techniques completely secret is

far worse than the public appearance of algorithms which are proprietary for a limited

timeâ€™. D. Knuth, Sorting and Searching, vol. 3, The Art of Computer Programming p. 319.

Algorithms, business methods and other computing ogres 143

Isaac Newton to protect his invention of calculus.20 He pointed out that

while he did not charge a penny every time others used a theorem which

he had proved, he did charge to tell them which theorem should be

used.21 Knuth also wondered whether a large integer which proved

mathematically useful might be patentable or whether rather than being

man-made it was actually God-given. A reply came several weeks later

pointing out that such a large integer had indeed been given protection.22

Importantly, as outlined earlier, mathematics and algorithms exist in a

reasonably complex relationship with each other, where theories, models

and code interact: a factor which lawyers sometimes fail adequately to

grasp. Thus, in Newellâ€™s well-known paper, The Models are Broken . . .,23

he pointed out, in reply to Chisumâ€™s argument that there was a solution in

legal interpretation to the problem of algorithms,24 that he was somewhat

bedevilled by confusion about the basic conceptual models used by

lawyers. Newellâ€™s paper argues that law requires a stable view of the

algorithmic process whilst computer science thrives on change, suggest-

ing that never the twain shall meet. It is possible that many legal readers of

this paper will not really have understood why Newell was making this

kind of claim that law could not satisfactorily cope with the new technol-

ogy: in fact it was because, as he went on to say, his career was aimed

single-mindedly at understanding the human mind.25 He was certainly

involved with computer science and mathematics, but he viewed algo-

rithms as central to the working of the brain, hence his work with Simon

on Human Problem Solving.26 Someone who viewed algorithmic rule-

based processing as the manner in which humans reason and solve prob-

lems would hardly be likely to accept Chisumâ€™s more traditional

perspective.

20

Is calculus an invention rather than a discovery? Many mathematicians, I suspect, would

consider it to be an invention. Newton argued with Leibniz over who was the true

inventor both having concurrently arrived at the same techniques.

21

P. 324. Notices of the AMS, vol. 49, No. 3.

22

â€˜When asked about software patents, Donald Knuth . . . conjectured that it might be

possible to patent a 300-digit integer. The readers might be interested to know that I have

already patented a 309-digit integer as claim 37 of US Patent 5,373,560, issued in 1994.

It relates to cryptography, and it is not as interesting as what Knuth had in mind. At the

time, some people thought that patenting a number was a new extreme in silly software

patents, but now we have business method patents that are even sillier.â€™ Roger Schlafly

(Received 13 February 2002), Notices Of The AMS (2002) p. 543.

23

A. Newell, â€˜The Models are Broken, the Models are Broken!â€™, U. Pitt, L. Rev. 47 (1986),

1023.

24

D. Chisum, â€˜The Patentability of Algorithmsâ€™, U. Pitt, L. Rev. 47 (1986), 959.

25

Cited by his colleague, Herbert A. Simon, in a memoir at http://stills.nap.edu/readingroom/

books/biomems/anewell.htm.

26

A. Newell and H. A. Simon, Human Problem Solving (Englewood Cliffs, NJ: Prentice-

Hall, 1972).

144 Software and Patents in Europe

Another aspect which is often ignored in debates about protection for

mathematical algorithms is that many of these methods are intrinsically

related to the computer and only arose as part of the development of the

computer. A reader of Morris Klineâ€™s classic Mathematics in Western

Culture (first published in 1953)27 will not find the term algorithm in

the index and there is almost no reference to algorithmic procedures. A

text on â€˜Mathematics and Western Cultureâ€™ published today without

discussion of algorithms would be an object of reviewer ridicule, since

algorithms have become so central to many important areas of mathe-

matics (which areas were relatively minor until the 1950s). Take numer-

ical analysis â€“ a discipline which, while it certainly has a long history, has

become enormously important with the use of computation. Mina Rees,

from the Computing Program at the office of Naval Research was one of

the first to push this new field. She wrote:

[Henry S. Tropp] commented that, as a young assistant professor of mathematics

in 1959, he had never even heard of numerical analysis as an independent area of

mathematics. He said, â€˜[one] did applied things in various courses and [one] had a

course called applied mathematics for physicists and engineers which was more

applied differential equations . . . And [one] suddenly realize[d] that out of this

wartime environment a new independent branch of mathematics had suddenly

blossomed. The fact that you founded an Institute for Numerical Analysis indi-

cates an early realization of the independent area of research, where it really didnâ€™t

exist before.â€™ I replied, â€˜But computers didnâ€™t [exist] either.28

This kind of approach â€“ which parallels the developments of hardware to

improve speed and efficiency â€“ is surely as important as the development

of hardware models. During this authorâ€™s period in a Mathematics

Faculty,29 I shared an office with a colleague who undertook numerical

analysis-based research into fluid mixing in a paint gun. He could not, he

told me, tell whether his mathematics were correct, his program was

correct or his algorithm from which the program was derived was correct â€“

the problem was so complicated that errors could be found in any part.

These kinds of tasks are immensely practical and yet, to the patent system,

appear less worthy of reward than a particular design of a paint gun which

may have derived from this work.

The irony of there being practicality in something which is as seemingly

abstract as an algorithm is accepted by some mathematicians who are,

concurrently, opposed to patent protection for mathematical algorithms.

27

M. Kline, Mathematics in Western Culture (New York: Oxford University Press, 1953).

28

M. Rees, â€˜The computing program of the Office of Naval Research, 1946â€“1953â€™,

Communications of the ACM 30(10) (1987).

29

I am not a mathematician â€“ computing is often found in such faculties.

Algorithms, business methods and other computing ogres 145

For example, Klemens, in Math You Canâ€™t Use,30 argues that software

and mathematics are identical. In purely theoretical terms this is true, but

in practice the ways in which a programmer constructs a program are

rarely similar to that of the mathematician â€“ the programmer is building a

virtual world of objects which can be manipulated and pays little attention

to computational or other theory. Klemensâ€™s argument is that, although

mathematics and software are identical, maths should somehow be

divided off from software, in order that mathematicians can utilise what

he suggests are â€˜pure mathematical algorithmsâ€™ without fear of falling foul

of the patent system. His solution to the problem is very much like that of

the EPO: that is, if it is a physical device it can be protected but, if not,

then no protection is offered. Klemens uses the notion of a â€˜physical state

machineâ€™, which derives from the theory of computability. Essentially,

this is a physical machine which can operate on inputs and outputs (i.e. a

computer or a processor chip): â€˜an inventive physical state machine may

be heavily informed by mathematics but would make a nontrivial exten-

sion of that mathematics into the physical world.â€™31 This is special plead-

ing â€“ Klemens is aware that the inventive activity is in the mathematics

but wants to keep that inventive activity free to use, but still provide

ownership rights somewhere along the line. He therefore gives protection

to the manufacturer rather than to the inventor (since the manufacturer

can produce an â€˜application X using the inventorâ€™s technique Aâ€™ without

problem). This is fine as a policy decision, but does not appear to accord

with the rhetoric of patenting and the reward theory â€“ why should more

economic advantage accrue to the user of someone elseâ€™s mathematical

enterprise?

A different approach using standard patent law could in fact be used â€“

the experimental exemption, for example â€“ if it is the right to utilise a

protected algorithm in research which Klemens wishes. This exemption

allows what Rimmer has called â€˜the right to tinkerâ€™32 and although it is

primarily of economic importance in the chemistry area, it could well

cover mathematical usage.

Algorithms which have been protected in the past appear to have been

awaiting the development of the computer. One example is that of the

Soundex algorithm, which provides a method for computing a word

which sounds like another â€“ important in misspelling words and names

30

B. Klemens, Math You Canâ€™t Use: Patents, Copyright, and Software (Washington DC:

ñòð. 48 |