Some extracts from the judgement to summarise what happened (sorry
it's still long, but the judgement is 22 pages). Short comments in
line, overall comments below.

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23. This case is by no means unique as an example of a computer
implemented invention in which the word “computer” is conspicuous by
its absence from the patent claims. I am quite certain that one
reason for this is a desire by applicants to try and play down the
fact that their inventions are really based almost entirely on
computer software. It fools no-one and in some cases makes things
more complicated than they need to be.

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Patents Act:
s1(2) It is hereby declared that the following (among other things)
are not inventions for the purposes of this Act, that is to say,
anything which consists of—
[...]
(c) a scheme, rule or method for performing a mental act, playing a
game, or doing business, or a program for a computer;
(d) the presentation of information;
but the foregoing provision shall prevent anything from being treated
as an invention for the purposes of this Act only to the extent that a
patent or application for a patent relates to that thing as such.

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30. The difficulties in this area arise mostly in relation to
inventions which involve the use of computers. All the Court of
Appeal cases (from Merrill Lynch to Symbian) are about inventions
implemented in software. The simple problem is that computer programs
(as such) are excluded by s1(2)(c) (c.f. EPC Art 52(2)(c) and 52(3)) .
Whether it was so clear in the past however, one thing is clear
today. An invention which makes a contribution to the art which is
technical in nature (to echo Kitchin J’s words in Crawford) is
patentable even if it is implemented entirely on a computer and even
if the way it works is entirely as a result of a computer program
operating on that computer. The outcome of the Symbian case proves
that.

31. [quotes Symbian]: 50. The fact that “the boundary line between
what is and what is not a technical [contribution]” is imprecise (as
Nicholls LJ said in Gale, and as was echoed by Aldous LJ in Fujitsu)
may be attributable to three causes, which are not mutually exclusive.
First, national tribunals and the Board may still be at an
intermediate stage of working out and identifying the precise location
of that line; secondly, the problem may be inherent and never wholly
satisfactorily soluble; thirdly, there are competing views based on
different philosophies (the “open source movement represents one
extreme, that of companies such as the present applicant, the other).
The uncertainty is well demonstrated by the elusiveness of the meaning
of “technical”, the change of attitude manifested in the more recent
decisions of the Board, the contrasting outcomes in Vicom and Fujitsu,
and indeed the possible reconsideration of the correct view of
computer program patents in the United States (see Professor John
Duffy: Death of Google's Patents? Patently-O Patent Law Blog, July
21st, 2008).

32. Thus when confronted by an invention which is implemented in
computer software, the mere fact that it works that way does not
normally answer the question of patentability. The question is
decided by considering what task it is that the program (or the
programmed computer) actually performs. A computer programmed to
perform a task which makes a contribution to the art which is
technical in nature, is a patentable invention and may be claimed as
such. Indeed (see Astron Clinica [2008] RPC 14) in those
circumstances the patentee is perfectly entitled to claim the computer
program itself.

33. If the task the system performs itself falls within the excluded
matter and there is no more to it, then the invention is not
patentable (see Symbian paragraph 53 above). Clear examples are from
the cases involving computers programmed to operate a method of doing
business, such as a securities trading system or a method of setting
up a company (Merrill Lynch and Macrossan). Inventions of that kind
are held not to be patentable but it is important to see why. They
are more than just a computer program as such. For example, they self
evidently perform a task which has real world consequences. As Fox LJ
said in Merrill Lynch (p569 at line 27), a data processing system
operating to produce a novel technical result would normally be
patentable. However that is not the end of the analysis. He
continued: “however it cannot be patentable if the result itself is a
prohibited item” (i.e. a method of doing business). When the result
or task is itself a prohibited item, the application fails.

34. The reasoning in Merrill Lynch means that the computer implemented
invention claimed there would not have been excluded from
patentability if it were not for the combined effect of two exclusions
in s1(2) - computer programs and (in that case) business methods. The
cases in which patents have been refused almost always involve the
interplay between at least two exclusions.

38. "when the task carried out by the computer program is not itself
something within the excluded categories then it is likely that the
technical contribution has been revealed and thus the invention is
patentable."
[nb: would this not cover Folding@Home; Journeyplanner, etc?]

63. In my judgment the correct scope of the mental act exclusion is a
narrow one. Its purpose is to make sure that patent claims cannot be
performed by purely mental means and that is all. The exclusion will
not apply if there are appropriate non-mental limitations in the
claim. [would this be as little as storing to a hard disk?]

70. Approached on the correct, narrow basis, the mental act exclusion
is irrelevant in this case. The claimed method cannot be performed by
purely mental means and that is the end of the matter. Put another
way, the contribution is a computer implemented method and as such
cannot fall within the mental act exclusion.
[OMFG. There you have it. Take ordinary, everyday mental step, call it
X. For example, deciding whether to stand up or sit down, depending on
whether there is a chair close behind you. Now the Patent Office
cannot raise that specific objection (mental process) against any
computer implemented X]

72. [...] Although obviously some mathematics is involved, the
contribution is not solely a mathematical method (on top of being a
computer program) because the data on which the mathematics is
performed has been specified in the claim in such a way as to
represent something concrete (a drill bit design etc.). That is an
important difference between the position in Gale [algo for
efficiently calculating square roots] and the position here.
[One Click Ordering, here we come]

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Basically programs which do one of the other excluded things (business
method, doing maths, performing mental act, or presenting information,
for example) are out, and others can be in. And performing mental act
can no longer count towards a second strike, because he rules out the
'wide' view that it means "anything _capable_ of being done mentally"
but instead it means "anything _the patent says is done_ mentally".
Add software, and you're high and dry.

This might be case law as it is laid down (or is Birss QC just
limiting patentability rejections to slam-dunkable cases? i.e. "we
don't know what software per se is, therefore let's only activate that
rejection when we can also reject the invention on other exclusionary
grounds!"), but it seems inconsistent with the letter of the law.

Is the software exclusion worth anything at all, if it's only active
when another exclusion also is?
That makes even less sense when you read that the listed exclusions
are only 'amongst other things'.

It then further beggars belief that this patent stands even though it
is an invention designed to speed up mental acts, doing mathematics
and presenting mathematical information - in other words arguably just
such a slam dunk.

The most horrible thing about this judgement, I find, is that it
clearly allows Halliburton to sue anyone using computer simulations of
drills penetrating earth when the aim is to make better drill bits.
But because the patent doesn't actually say that - dismissed by Birss
QC as 'poor drafting', something that is potentially entirely resident
on a computer (for example, making drill bit designs that are never
actually manufactured, but merely protected under a different area of
intellectual proterty, Registered Designs), allows Halliburton to
merely run this program day and night to generate new designs to
monopolise using IP, and block anyone else from doing the same using
the patent!