Although only a handful of the 700 or so British bulletin boards have
a major science theme, many more give access to the Fidonet Echomail science
conferences. These conferences – also known as areas or echoes – copy messages
automatically to a large group of participating bulletin boards. World Science,
for example, produces hundreds of messages a week, ranging from the theoretical
(cosmology and relativity), the controversial (creationism and crop circles)
to the puzzling (‘How would you separate a mixture of lead and copper ball-bearings?’).
The most ambitious British science bulletin board is Starbase One, which
the man who runs it, Nick Stevens, bills as ‘the biggest and best online
astronomy board around’. Starbase features local message areas called Astronomy
Chat, BAA Discovery News (with postings of observation schedules for current
astronomical events), Space Exploration, JAS News & Chat, CCD Cameras
and Astronomical Societies. There are also Fidonet European Astronomy, World
Astronomy and World Science conferences.

Of the 105 megabytes of files on Starbase, around two-thirds relate
to astro-nomy. These include programs for IBM-compatible, Amiga and Atari
ST personal computers, as well as bibliographies, catalogues, digitised
maps, GIF graphic images, and text. You can read text live using the board’s
database. It covers program reviews, a large body of information reproduced
from NASA’s own Spacelink BBS and answers to frequently asked questions.

Access to Starbase is free, but a subscription of £12 a year
brings extra privileges, such as use of a second, faster phone line, a printed
manual, more file areas, and access to astronomical images from Stevens’s
NASA collection of CD-ROMs.

Voyager, a smaller bulletin board based in Woking, also has an astronomical
theme. The man who runs it, Alex Macphee, has kept the file lists small
deliberately. He says Voyager’s main aim is to act as a messaging service
for scientific topics.

Voyager offers several news bulletin topics. These include a Signposts
area which gives brief characteristics of the planets for the month; abstracts
of the contents of Astronomy Now magazine; and NASA News. Like Starbase,
it subscribes to the Europe and World Astronomy echoes; World Science; Space;
and also the UK Science Echo.

Chemi-Call, in Dartford, acts as a forum for the exchange of information
relating to chemistry. It is also a lively general purpose bulletin board
with online games. You discuss chemistry in a specialist section called
The Laboratory, where ‘safety glasses must be worn’. Here you will find
information on the Royal Society of Chemistry, including membership details
and a programme of events. The Laboratory has mail areas for Chemistry
and Chemistry & Education, which is a discussion area, and a swap shop
for ideas and resources for teachers. A related file area contains IBM chemistry
programs, such as periodic tables, molecular modellers and databases.

The Academics BBS in Solihull hosts the Open University conference.
This international Echo for Open University students is used particularly
by those taking mathematical and computing courses, and Academics has
file areas for astronomy, chemistry/physics, electronics, and mathematics.

This board also takes the World Science, Astronomy and Space Echoes.
It offers useful detailed breakdowns on the origins of messages, so you
can trace a local bulletin board where you can join these discussion areas.

Of the fully commercial bulletin boards, one with a particularly strong
science content is CIX, which stands for Compulink Information Exchange
(Review, 19 October, 1991). This conferencing system has about 500 conferences,
including a lively science area, subdivided into General, Cats and Logs,
Dodgy, Latest, Pseudo and Water topics. Other practical science conferences
include Astronomy, Biology, Cosmo (‘Help me get into space, please’), Isle
(‘Can you increase your IQ or lifespan?’), Rheology, SF, Space and UFOs.
For the more mathematically-minded, there are two other sciences in computing
areas, covering topics such as Chaos, Life (the Cellular Automaton), Mathematics
and Statistics. CIX also has a gateway that allows subscribers to access
Usenet, providing more than a hundred specialised scientific newsgroups.
The CIX gateway, unfortunately, does not allow the specific text searches
and thread-following commands that you would find if you reached Usenet
through a Unix-based system, but it is much easier to use.

Registration to CIX costs £15, and it also charges for connection
time ( £2 an hour off peak, £3.10 peak).

Ray Girvan is a computer consultant.

* * *

Starbase One, Camberwell, modem speeds V21/22/22bis. Tel: 071 733 3992

Voyager, Woking, V21/22/22bis. Tel: 0483 751324

Chemi-Call, Dartford, all speeds to HST. Tel: 0322 278652

Academics, Solihull, V21/22/22bis. Tel: 021 705 2906

CIX, Surbiton, all speeds to HST. Tel: 081 399 5252

All these bulletin boards run 24 hours a day.

The first issue contains more than 500 entries, classified into 22 topics
including directories of shareware and commercial software, fractal books,
articles and publishers, and journals, newsletters and suppliers of fractal
merchandise. The entries supply useful descriptions and reviews of the products.
LIST allows key-word searches so it is easy to find an individual name in
a document. A further magazine section, Fractal Digest, will act as a forum
for discussion of fractal topics among subscribers. The publishers plan
quarterly updates to FRAC’Cetera, but will answer subscribers’ queries between
issues. Four issues cost Pounds sterling 12, or Pounds sterling 5 for
the pilot issue, which counts as part payment toward a full subscription.

For IBM PC users interested in drawing fractals, the Fractint program
stands out as definitive. It is the most powerful and versatile fractal
generator about – and all the more impressive for being public domain. It
has so many features, however, that the file containing the documentation
has grown to a cumbersome 350K. Although the latest Fractint 16 presents
this in a handy indexed form, readable from within the program, on-screen
manuals are not to everyone’s taste.

Fractint will gain a few more converts with the publication of Fractal
Creations, a printed manual that comes bundled with the program on 5.25-inch
disc. Together, they make an attractive and accessible commercial Fractint
package.

The book’s authors are two of the founder members of the Stone Soup
Group, the informal association of programmers responsible for Fractint.
The group’s name is an allusion to the folk tale in which a pedlar makes
soup from a stone by tricking villagers into progressively providing all
the ingredients – and this is more or less how Fractint evolved.

Programmer Bert Tyler provided the original fractal generator in 1988.
Subsequently, dozens of fractal enthusiasts have added to its functions,
collaborating via CompuServe’s Computer Art forum.

Fractal Creations begins with a primer on fractals, followed by a guided
tour to Fractint and lists of reference commands. The manual refers to the
special bundled version 15.11; this lacks the on-line documentation of version
16, but the differences are not otherwise significant.

There are about 60 fractal types in Fractint. Each has its own section
in the book, with a photograph, technical hints on areas worth exploring
and – very useful – appropriate warnings of long calculation times. The
majority are variants on Mandelbrot-type iteration of functions on the complex
plane, but the list also includes other fractal families such as Barnsley
IFS fractals, plasma clouds and chaotic attractor graphs.

For those who want to delve into the programming, there is a section
on user-defined functions and appendices on the fast C routines underlying
Fractint, video modes, the GIF graphics file standard and complex number
mathematics.

The book particularly emphasises Fractint’s functions for artistic post-processing
of its output. After saving an image in GIF format you can alter its colours,
map it to a sphere to make a ‘fractal planet’, overlay it on another image,
or convert it to 3D display. The latter option gives either separate full-colour
views, for later use as a stereo pair, or red-blue anaglyphs for viewing
on screen. The manual includes viewing glasses, and a colour poster with
examples.

Even with these novelties, Fractal Creations isn’t cheap for a paperback.
Nevertheless, for the depth of information and the further accessibility
it brings to Fractint, it is extremely good value. I recommend it highly
to any fractal fancier.

Ray Girvan is a freelance computer journalist.

First, though, you should be aware of Donald Knuth’s TeX system, popular
in the academic world. This is not a word processor but a typesetting language
that excels at mathematical work. It is in the public domain so you pay
only for the discs.

You insert TeX codes into plain ASCII text, and it then creates a ‘DVI’
(device independent) file, that you can preview or print on virtually any
computer. Although you can ‘draw’ with TeX, the ideal is that you specify
the document’s logical structure while TeX takes care of the aesthetics
and layout.

TeX is a low-level language; so most users work with a macro pack, such
as Leslie Lamport’s LaTeX. With these, TeX is certainly usable for everyday
work but not even enthusiasts call it friendly. However, it is so well established
that many scientific word processors use TeX-like commands.

One such is K-Talk’s Math-Edit equation editor. This outputs TIFF, PIX
or EPS files for export to word processors that can incorporate graphics.
Using its menus of symbols and functions, you build expressions on screen,
working logically from left to right and top to bottom. The program creates
the layout, which automatically adjusts itself around later amendments.

MathEdit also generates TeX or LaTeX output, so makes a convenient front
end for writing TeX mathematics. It is elegant and powerful. My only complaint
is that it cannot be used from inside a main program.

Design Science’s MathType is a similar equation builder for systems
running Microsoft Windows. You call it up while running a Windows word processor
or desktop publishing program, design the equation, then paste it into your
text using the Windows clipboard. Its handy pull-down menus of symbols make
it much superior in handling to MathEdit, but it needs a fast computer and
a laser printer. You can use MathType equations with nonWindows programs
if you have a PostScript printer.

A full word processor, EXP expands on MathType’s approach. For plain
text entry, EXP acts as a normal what-you-see-is-what-you-get (WYSIWYG)
program with the usual Alt and Ctrl combinations for basic editing. For
special symbols and controls, you press F1 to invoke a command line for
entering them by name.

The command syntax is similar to TeX, but EXP has also a pure TeX entry
mode for maths formulae. You also define macros for composite expressions.
Like MathEdit, it will resize symbols, such as radical signs if you edit
the contents.

EXP is polished and powerful, with a good range of fonts, and TIFF or
PCX graphics handling. However, it lacks pull-down menus and on-line help.
There is no alternative but to learn by heart the names of characters, macros
and codes. This makes it a difficult program for the beginner and occasional
user.

More tyically, scientific word processors use a graphics approach, where
you hand-build formulae from a menu of fixed graphic elements. ChiWriter
is probably the best-known product of this type (the ‘chi’ is a pun on the
name of its originator, Cay Horstmann).

The ChiWriter range is based on a core program with 14 fonts suitable
for mathematics and Western European languages. As extras, there are fonts
for chemistry, Russian and laser printers, and a one-way converter from
WordStar and WordPerfect (or all four as a Deluxe option). Beyond this,
you can add indexing, mailmerge, University of Groningen maths fonts and
a ChiWriter-to-TeX converter.

ChiWriter stands out for being easy to use. With the edit-as-you-read
tutorial file, you can be competent in an hour or less. The display is monochrome
but highly legible. ChiWriter also prints fast, using your printer’s own
fonts where possible.

Scientific word processing packages are available as shareware. Under
this system, a program’s suppliers freely circulate an evaluation version,
usually cut down or outdated. If you like this, you pay a registration fee
for an upgrade to the full version. Horstmann no longer supports a shareware
ChiWriter, but there are two others: Techwriter and Math Text.

Techwriter has been around several years. It uses colour codes to indicate
special characters. You obtain maths symbols with Alt-letter combinations;
these signal Techwriter to translate a normal character to one in your printer’s
alternate set. For instance, Alt and ) prints the fishhook symbol ‘J’ forming
part of an integral sign. The program files include user-definable translation
tables for various printers.

By today’s standards, Tech-writer is cumbersome, and the display confusing
if your overlay control codes with similar colours. But it is still an effective
program with clever print functions, such as superscript and subscript on
the same character, and delayed printing of a block to avoid splitting a
table or figure.

Math Text is similar to the basic ChiWriter. The shareware Math Text
comes as a Mini Edition with deliberate limitations: slow operation, an
8K limit on work files and neither file-to-file transfers nor disc macros.
Registration entitles you to the full version, plus a font editor, ASCII
converter and other utilities. Despite its limitations, the Mini form is
still a friendly program that looks likely to fill ChiWriter’s vacated niche
in the shareware scene.

Back in the commercial sphere, T3 is the largest and most expensive
of these programs. Fully WYSIWYG, it has 13 character sets, including cyrillic,
greek, chemistry and maths (40 fonts, counting size and style variants).
You access characters through 38 preset keyboards, eight of which may be
active, or you can dip into any font to pick a single character.

T3 allows unlimited macros, and macros may call up others. Indeed, its
rolling demonstrations are sequences of linked macros. It includes more
than a 1000 factory macros for maths, chemical structures and general control
changes.

This may all sound complex, but T3 is easy to learn and use. Its ‘shell’
documents reduce the bewildering range of choices by allowing you to load
in a single operation the appropriate layout, keyboard and font set. I can
only describe T3 as the Rolls-Royce of the scientific word processors.

Finally, one mainstream program caught my eye. Vuwriter began life at
the University of Manchester as a specialist editor for academic work. Although
its makers have since developed it into an excellent general word processor,
the new Vuwriter II also supports an optional pack of mathematical fonts.
These comprise roman and greek alphabets, plus three symbol groups.

Vuwriter allows accurate positioning of symbols using horizontal microspacing
and 14 vertical levels within a line. This fine control makes mathematical
work quite laborious, however, especially as there are no reference lists
on screen. Nor does the program include ready-made macros for complex constructions.
The print-out looks superb.

Overall, I found no ‘best’ program. Your choice will be dictated by
two main factors. First, are you more comfortable with TeX-like codes or
a library of symbols? Secondly, do you need typeset quality for your print
out or a less polished draft? Beyond that, the facilities are proportional
to price.

Ray Girvan is a software reviewer.

* * *

Apart from MathType, all these programs work on the standard IBM PC
XT or compatibles, and give good results on a 9-pin dot-matrix printer.
A laser printer is obviously essential for typeset output.

TeX: minimum system needed 512K RAM, EGA, hard disc (10 MB). Free but
about £20 for the discs, depending on configuration. Eigen PD Software,
PO Box 722, Swindon, Wiltshire SN₂ 6YB. Tel: 0793 611270. For
commercial TeX variants, contact the

MathEdit and ChiWriter suppliers. MathEdit: minimum system needed 512
RAM, EGA/Hercules, hard disc (1 MB). £150. Text Formatting Company,
Suffield Works, 1 Suffield Road, London N15 5JX. Tel: 081 802 4470

MathType: minimum system needed Windows 2.1, 640K RAM, EGA/Hercules,
mouse, 80286 processor, hard disc, laser printer. £199 + VAT. See
MathEdit

EXP: minimum system needed 384K RAM, CGA (but higher preferred),360
K. £221.50. Chapman and Hall, 11 New Fetter Lane, London EC4P 4EE
Tel: 071 865 0066

ChiWriter: minimum system needed 512K RAM, CGA, twin 360K floppies.
£109.95; deluxe £199.95 (further options extra). Scientific
Text Processing, 53 Westridge Road, Portswood, Southampton SO₂
1HN. Tel: 0703 557632.

Techwriter: minimum system needed 270K RAM, CGA colour. £1.45
( £20 to register). Premium Software, 24 Station Road, Barton Halsall,
Near Ormskirk, Lancashire L39 7JN. Tel: 0704 840569.

Math Text: minimum system needed 512K RAM, EGA/Hercules, 360K floppy.
£6 ( £199 for full version). PC-Serve, 1147 Greenford Road,
Greenford, Middlesex UB6 ODP. Tel: 081 864 2611.

T3: minimum system needed 640K RAM, EGA/Hercules, hard disc (6 MB).
£750 (site licences and educational discounts also available). Academic
users may download a T3 demo via JANET, the academic network. Scientific
Word, 62 Danes Road, Rusholme, Manchester M14 5JS. Tel: 061 256 2156.

Vuwriter II: minimum system needed 640K RAM, EGA/Hercules, hard disc
(1 MB). £350 ( £75 for extra language and scientific font packs).
Vuman Computer Systems, Enterprise House, Manchester Science Park, Lloyd
Street North, Manchester M15 4EN. Tel: 061 226 8311.

Recent work on the underlying mathematics makes it possible to control
and even shape some types of chaotic image. I tested three programs for
personal computers that harness these mathematical monsters for you to create
your own artwork.

Michael Barnsley’s program, The Desktop Fractal Design System, complements
his well-known book Fractals Everywhere, and is based on his fractal geometry
course at the Georgia Institute of Technology.

Barnsley pioneered the understanding of the common class of 2-dimensional
fractals generated on a plane from a starting ‘seed’ by the affine transformations
(scaling, shear, rotation and translation). In simple terms, his method
involves tiling a ‘window’ of the x-y plane with smaller transformed copies
of itself. By adjusting the transformation and position of the copies, you
can control the outcome to produce, say, Barnsley’s famous fractal imitation
of a spleenwort fern. Barnsley found that a simple set of six-digit numbers,
or IFS codes, defines this type of fractal.

He also invented the Chaos Game algorithm for building fractals from
a speckle of points produced by randomly operating its component transforms.

The heart of his program is a design screen simultaneously showing you
a fractal and its IFS codes. When you alter the generating rules, either
from a menu of transforms or by editing the IFS code, the program redraws
the fractal following the rules of the Chaos Game. So you gain a feel for
the relation between code and image.

You view stored fractals from the program’s library, which displays
a catalogue of miniature images; any can be chosen for enlargement. Further
sections contain interactive ‘maps’ of other types of fractals, including
Julia Sets, and information screens duplicating the content of the 40-page
handbook.

This program does show its age somewhat, not having advanced beyond
version 1.0, which works only in EGA mode and has somewhat clumsy ‘bounce
bar’ controls. However, I recommend it if you want a clear and practical
primer to help you to understand the mathematics behind IFS codes, affine
transformations, and the Chaos Game.

The art package Fractal Grafics is far less academic; its programmer,
Dick Oliver, describes his work as dedicated to placing new computing sciences
in the hands of the general user. Fractal Grafics is certainly quick and
easy to master, needs no mathematical knowledge, and takes little practice
before you can doodle in fractals.

As with Michael Barnsley’s program, Fractal Grafics is limited to fractals
made by geometric repeats derived from a starting shape. You begin with
a template, comprising a polygonal seed and up to 19 smaller copies related
to the seed by affine transformations. Fractal Grafics provides these transforms
as a simple toolkit for manipulating the template freehand with Microsoft
mouse or keyboard. There is a separate Adjust menu to give fine control
over the colour.

You display the fractal either by a Draw command, which approximates
it by overlaying successibe levels of polygons; or by Paint, which generates
it by Barnsley’s Chaos Game algorithm. You can then shift and alter the
template and draw further fractals on the same screen to build up ambitious
artwork. Unfortunately, Fractal Grafics will not produce hardcopy, but its
. PCX output files are widely compatible with paint packages.

If you need geometrical accuracy – hard to achieve freehand – Fractal
Grafics accepts templates as IFS codes. In theory, you can swap these with
The Desktop Fractal Design System, but the formats differ and need serious
editing.

Fractal Grafics’ codes do, however, export directly to the fast public
domain FRACTINT program, which comes with the package. FRACTINT also draws
a large range of other fractal types created by complex number operations,
including the Mandelbrot and Julia Sets. The package contains a third program,
JULIMAN, to generate these two as . PCX files.

Documentation consists of an on-line tutorial and a 60-page manual containing
chatty lessons and an excellent bibliography. The nearly 200 sample templates
range through famous historical fractals such as Koch’s Snowflake and Sierpinski’s
Triangle, fern and tree forms, and modern artwork such as fractal typefaces.

This is a compulsive program. To quote Michael Barnsley: ‘Fractal geometry
will make you see everything differently.’ After a few hours with this program,
you will find pot plants and trees take on a decidedly fractal look – be
warned.

Rudy Rucker’s CA Lab deals with a different class of mathematical graphics.
CA Lab is a toolkit for experimenting with cellular automata – pixel structures
which evolve by simple local rule deriving each generation from its precursor.

The product is a joint venture by Rudy Rucker, a science fiction writer,
and John Walker, who are employed respectively as ‘mathenaut’ and ‘virtual
programmer’ by the computer-aided design specialist Autodesk Inc. The Lab
comprises two parts: RC, Rucker’s fast low-resolution program, and CA, a
more analytical high-resolution version by Walker.

Both programs are control shells into which you can load and run a selection
of mathematical rules, with commands to view, edit and save the results
to disc.

The best-known cellular automaton, John Conway’s Life, settles rapidly
to dead or stable states. However, CA Lab also offers a range of newer and
more interesting rules for cellular automata. Some draw theorectical fractal
images. Others imitate biological systems; among these are Conway’s Life,
Brain, and the worm-like Langton automaton. Yet others simulate physical
situations that include the flow of heat, sublimation, dendrite growth,
and the unusual Zhabotinsky spiral chemical reaction.

CA Lab accepts Auto CAD drawings as input, and outputs to PostScript.
The manual suggests it as a commercial art tool; you could input artwork,
and modify it with special colour effects. I think the main justification
is aesthetic.

The images are strikingly beautiful, especially in high-resolution VGA.
On a PC XT, the screen updates every second or so; but on a fast PC, the
pattern evolve continuously, at the results are bizzare and compelling.
As with Fractal Grafics, it is disturbing to watch CA Lab for too long.

The Desktop Fractal Design System is supplied by Academic Press, Harcourt
Brace Jovanovich Limited, 24-28 Oval Road, London NW1 7DX. Tel: 071-485
7074. Price 29 Pounds + VAT. Minimum system: PC XT (but 286/386 recommended),
640K, EGA graphics, one floppy drive.

Fractal Grafics is available from: Cedar Software, R1 Box 5140, Morrisville,
Vermont 05661, USA. Tel: (802) 888 5275. Price: $79. Minimum system: PC
XT, 256K RAM (384K for VGA), CGA graphics, one floppy drive. Supports mouse
and maths co-processor.

Rudy Rucker’s CA Lab is supplied by Autodesk Limited, Cross Lanes, Guildford
GU1 1JJ. Tel: (0483) 303322. Price: 57.50 Pounds. Minimum system: PC T (but
286/386 highly recommended), 512K RAM, CGA graphics, one floppy drive.

Ray Girvan is a computer consultant.

Go is simple in concept. Two players place ‘stones’ alternately on the
intersections of a 19 x 19 grid, with the dual aim of walling off vacant
territory and capturing enemy stones. The stones stay where they are placed,
and are only removed if ‘dead’, that is surrounded and so captured. But
a complex philosophy and theory lie behind this simplicity. As Go tactics
are more akin to a real battle than the stylised moves of chess, Go sharpens
military strategy. Similarly, as players more often end with a stable ‘market
share’ of the territory, rather than an outright win, Go even relates to
business policy.

Go’s complexity also makes it a serious programming challenge. It has
about 100 ⁷⁰⁰ possible games, as opposed to chess’s 100 ¹²⁰,
and an order of magnitude more legal moves at any turn. This makes the tree-search
techniques used for computer chess unmanageable for Go. In 1972 the Japanese
Go Association declared that the game was unprogrammable.

Almost two decades later, artificial intelligence has begun to crack
the problem where numerical force has failed. Now, computer Go is a thriving
field: Go tournaments take place between machines; the Japanese research
consortium MITI works on the game as a test-bed for research in artificial
intelligence; and Ing Chang-Ki, a Taiwanese businessman, has offered a prize
of $1,300,000 for the first program to beat a human professional.

An offshoot of this work has produced commercial Go packages for personal
computers which make reliable opponents. Two programs stand out in this
field, Cosmos Go Partner and Nemesis Go Master.

Cosmos, published by Ishi Press International, is a no-frills package
that began life in machine Go tournaments. Suitable for the beginner, it
allows any odd-numbered board size from a practice 9 x 9 to the full 19
x 19, and any permutation of human and computer opponents. During a game,
you can ask Cosmos for a hint, or the reason for its last move, and call
up graphical displays of each player’s territory. Cosmos includes tutorial
and help screens, and you can save games for review either as compact archive
or readable ASCII files. It also has a library of joseki, or standard opening
sequences, and is packaged with The Way to Go, an introductory book by the
American Go Association.

Toyogo’s more sophisticated program, Nemesis, uses artificial intelligence
techniques to simulate human play. While working on Nemesis, the programmer
Bruce Wilcox devised his own heuristic Go theories to reach 6th dan (the
rating system rates players in level of skill), and is one of the top players
in the US. The Japanese Go Association also likes Nemesis enough to endorse
it.

The basic functions of Nemesis are similar to Cosmos, but its handy
pop-up menus make it more friendly. Go Junior is even friendlier – captured
stones frown, and winning stones smile!

Nemesis extras include: a game timer; move numbering; and screen editing,
either to produce Go diagrams or to edit the board to play a set piece.
Nemesis also lets you tweak more of the play variables, and rates its difficulty
levels in the conventional Japanese kyu.

You can buy the full Nemesis on its own, or as a deluxe package with
two add-ons, Joseki Genius (a study library of over 1000 joseki) and Tactical
Wizard. Tactical Wizard enables you to analyse moves to capture an enemy
group, or to save one of your own pieces or groups. You target a group,
and the program offers a series of play scenarios, so that you can pick
the correct starting moves. I like the Nemesis documentation, especially
the starter kit on Wilcox’s Instant Go theory, a lucid book.

Both programs play at advanced or beginner level. (Go skill is measured
on kyu and dan scales. A novice is 35 kyu, and can expect to advance to
10 kyu with a month or two’s serious practice. Above 1 kyu, the expert dan
scale ascends from 1 to 9.) By this reckoning, Nemesis at full strength
rates as 13 kyu; you can also set it to weaker levels from 35 kyu upward.
Cosmos is not kyu-rated, but the makers estimate it at between 12 and 15
kyu at skill level 30 (the usual tournament setting). Cosmos has beaten
Nemesis and appears slightly stronger, but Nemesis has the more human-like
play.

Go has a convenient handicapping system, where the weaker player begins
with stones already on the board. When you can regularly beat Cosmos or
Nemesis is an even game, you can increase the difficulty level by handicapping
yourself, so the programs’ usefulness does not end if you reach 10 kyu.
(This is a realistic goal, by the way.)

If you just want an absorbing computer game, there is little to choose
between Cosmos and Nemesis Go Junior. Cosmos has the slight edge in Britain,
as Ishi Press has a British outlet; Ishi also stocks Go books by Japanese
experts. However, you should consider Nemesis Deluxe if you intend to make
a serious study of Go tactics.

Both of these Go programs run on any personal computer with at least
512K RAM, on 360K floppy drive, and any graphics standard, including text-only.
A mouse is optional.

Nemesis is available from Toyogo, PO Box F, Kaneohe, Hawaii, Hl 96744,
USA. Tel: +1 (808) 254 1166. Go Master $79, Joseki Genius $49, Tactical
Wizard $59; and Nemesis Deluxe, which contains all three games, costs $169.

Cosmos is available from Far Communications, 5 Harcourt Estate, Kibworth,
Leicestershire LE8 ONE. It costs 31.95 Pounds plus VAT. Tel: 0533 796166.
In the US, Ishi Press International, 1400 North Shoreline Boulevard, Building
A-7, Mountain View, CA 94043, USA. Tel: +1 (415) 964 7294.

Ray Girvan play Go, and writes about computing.

A year ago I discovered Wordbench, which is far more suited to my work
as a technical writer. Developed in America by Franklin Smith and the Bank
Street College of Education, New York, Wordbench encourages a structured
approach to writing projects. As well as the writing, it also caters for
the planning, research, and other background tasks.

Wordbench has four main modules, which you use in turn: Outliner, Notetaker,
Writer and Print Manager. In Outliner, you first sketch out the sections
and subsections. Next you research your topic, using Notetaker to build
up a database of ‘cards’, each with a field defining its place in the outline.
Then you merge the notes and outline into a Writer document to polish before
printing via the Print Manager.

This approach may look frighteningly over-organised. It is, however,
very suitable for manuals, research papers and other technical works whose
structure is well-defined. The process is also more flexible than it sounds.

The word processor, Writer, has a range of specialist tools beyond the
usual word-count, thesaurus and spell-checker. There’s a matching-words
utility to check your work against a library of cliched, wordy, misused
or sexist phrases. The Viewer lets you browse and copy from other documents;
and ALT-I calls in a menu of special characters. This may not be as comprehensive
as scientific processors like Chi-Writer, but provides European accents,
lower-case Greek and basic mathematical symbols sufficient for most purposes.

For academic work, the Reference Tool allows you to create a separate
list of sources, for citing in the text, as footnotes or as a bibliography.
Its help facility, Reference Assistant, lists the Modern Language Association’s
guidelines for citing reference material from 80 types of source – everything
from academic dissertations to cartoons.

Modules called Brainstorm and Folder Manager complete the line-up. Brainstorm
(no relation to David Tebbutt’s well-known ideas processor) is a set of
novelty routines claimed to beat writer’s block. The Folder Manager handles
file housekeeping, macro definitions (‘short-cuts’), and customising.

I found the Folder Manager the only difficult area of Wordbench. For
the beginner, it has a large and confusing range of set-up options, though
few need altering in practice. Otherwise I encountered few problems beyond
the usual minor chore of updating the American spellings in the dictionary.

Incidentally, several people have mentioned to me a persistent rumour
that Wordbench will not export files in the ASCII format digestible by other
word processors. The mistake is understandable, as this important function
is extremely well-hidden. The final print option does allow ASCII output,
so there is no barrier to passing Wordbench work to a desk-top publishing
package for more sophisticated printing.

Wordbench is available from Addison-Wesley. Tel: 0734 794000. Pounds
sterling 140 + VAT for the IBM version.

Borland’s Eureka, although three years old, still stands up well if
you need a pure equation solver. It solves many systems of equations – linear,
nonlinear or transcendental – as well as handling polynomials, numerical
calculus solutions, and maximising and minimising functions.

Eureka is simple to use. You enter your equations via a text editor,
select Solve, and the result appears in the nearby Solution window. For
multiple solutions, you edit in new starting guesses or constraints, then
repeat.

Refinements include a Graph window; Verify, which plugs the answers
into the original equations; and reporting to screen file or printer. The
pull-down menus are clear and attractive and Eureka includes a good range
of worked examples, most of which are scientific.

My only serious criticism is over Eureka’s limited range of built-in
functions. For instance, Arc Tangent is the only inverse trigonometrical
function; you must define others in terms of it.

Formula/One, a new package available only from its American source,
expands the solver approach. It also includes more types of window: equation,
variable, units, tables, input and output lists, curve and regression analysis.

Ultimately, you may design an application sheet: a ‘live’ display customised
for, say, financial analysis. Formula/One has a strong business flavour,
and imports Lotus 1-2-3, Excel and dBASE files. Although it has more pure
mathematics functions than Eureka (it runs to inverse trig and Bessel functions),
Formula/One lacks matrices and complex numbers. The suppliers promise these
at the next upgrade.

For advanced use, Formula/One has commands to embed conditional branches
in the solving list. Although fine as a plain solver, its full potential
lies in application design and programming. This aspect needs time and effort
to master; it is a very powerful package, but far from easy.

The well-known MathCAD has a far more accessible scratchpad format that
allows you to do free-form mathematical work, laid out exactly as it would
be on paper. MathCAD’s primary use is for solving, plotting and ‘what-if’
calculations for science and engineering. As you can mix text with the algebra
and graphs, its worksheets also look good. The latest upgrade, version 2.5,
is notable for the expanded graphics facilities: 3-D plotting, drivers for
PostScript laser printers, and the ability to read in Hewlett-Packard graphics
files from CAD packages.

MathCAD has a professional slant, with a sophisticated range of functions
and good applied mathematics support. The authors, Mathsoft, supply specialist
add-on packs of models for electrical engineering, statistics, and advanced
mathematics.

Mathsoft and the technical publishers Addison-Wesley mar ket jointly
a MathCAD 2.0 Student Edition. This cut-down version shares most functions
of MathCAD proper, but limits the worksheet size severely, allowing only
10 simultaneous equations and 5 X 5 matrices. It also lacks the newer MathCAD’s
3-dimensional plotting.

The Student MathCAD is licensed strictly for education (the suppliers
provide product support only to registered tutors). Subject to these limitations,
it is still outstandingly good value.

A recent and exciting development has been the smart algebra package,
that not only crunches numbers, but also manipulates expressions in symbolic
form.

One product of this type is Derive: A Mathematical Assistant. Like MathCAD,
it displays and prints mathematical notation as it would be written, allowing
multiple screen windows for algebra and plotting (two-dimensional or wire-frame
three dimensional). You control it by pop-up menus.

The main algebra commands are Expand and Simplify. In the latter case,
Derive tries to recast an expression into the most compact form. This may
be completely automatic, or you may steer the derivation by your choice
of management settings.

Derive is suitable for A-level and first-year college mathematics. A
particular speciality is its analytical integration of most integrable classes
of function, and it also includes advanced vector calculus. The handling
of very large numbers – up to thousands of digits – is impressive too. It
is worth adding that Derive fits on just one 360K floppy; a sharp piece
of programming.

A British program of similar intent, Symbolator, is aimed at the educational
market. The author is Howard Phillips, Senior Lecturer in Computing and
Control at Huddersfield Poly technic, who describes it as an attempt to
bring mathematics back to the people.

Symbolator presents a command area where you manipulate an ‘object’
expression with a tool kit of several dozen ‘processes’. It accepts commands
more or less in English: factorise, integrate, trigtidy, graph and so on.
You can pass any result to a scrolling output window, whose contents may
be piped to file or printer for a permanent record.

Symbolator’s repertoire is similar to Derive, with the addition of Laplace
and z-transforms, and the numerical solution of differential equations.
The disc files include the manual, 17 lessons, and online help for each
process. A split screen lets you read a lesson while working.

Although rather less smart than Derive, Symbolator is more suitable
for education. Derive solves without explanation, so often teaches nothing
of how to derive a result yourself. When Symbolator fails at integration,
for instance, it will often prompt you to choose a substitution or algebraic
transformation to crack the integral, but it is up to you to decide how.

This list is by no means exhaustive, but a selection I have picked as
affordable, and usable on modest hardware. Formula/One needs a hard disc,
but the rest work acceptably on a basic IBM-compatible with floppy storage.
However, all packages will prove more satisfactory if speeded by a maths
coprocessor chip and a faster PC.

Eureka: The Solver, Borland International (UK) Ltd, 8 Pavilions, Ruscombe
Business Park, Twyford, Berkshire RG10 9NN. Tel: 0734 320022. Minimum system:
384K, DOS 2.0, one floppy drive.

Formula/One, Ocean Isle Software, Ocean Isle Square, Suite 3, Ocean
Isle Beach, NC 28459, US. Tel: +1 (919) 579 9945. Minimum system: 512K,
DOS 2.1, hard disc drive. It costs $295.

MathCAD 2.5, Adept Scientific Micro Systems Ltd, 6 Business Centre West,
Avenue One, Letchworth, Herts SG6 2HB. Tel: 0462 480055. Minimum system:
512K (640K recommended), DOS 2.0, twin floppies (hard disc recommended).
Pounds sterling 375 plus VAT. Application packs cost Pounds sterling 75
and VAT must be added.

MathCAD 2.0, Student Edition, Addison-Wesley Publishers Ltd, Finchampstead
Road, Wokingham, Berkshire RG11 2NZ. Tel: 0734 794000. Minimum system: 512K,
DOS 2.0, one floppy drive. Pounds sterling 24.95 plus VAT.

Derive, A Mathematical Assistant, System Science, 3-5 Cynthia Street,
London N1 9JF. Tel: 071-833 1022. Minimum system: 512K, MS-DOS 2.1, or later
version, one floppy drive. Pounds sterling 115 plus VAT.

Symbolator, H. Phillips Specialised Software, 3 Cliffe Ash, Golcar,
Huddersfield HD7 4PY. Tel: 0484 656225. Minimum system: Pounds sterling
39.50 for a single copy (Pounds sterling 97.50 site licence) and VAT must
be added.

Ray Girvan is a freelance computer journalist.