ONCE upon a time, before the fateful day when Clive Sinclair got his first tricycle, computers were rare. Huge mental cabinets filled with valves and filling large areas of university labs, they were designed and used by mathematicians.

It was confidently predicted that there would only ever be six computers in Britain because it would be impossible to train enough mathematicians to operate more. The mathematicians got quite excited by this, sensing a chance for a real job at last.

But sanity prevailed. Nowadays, any intrusion of mathematics into computing is viewed, quite rightly, with suspicion. On odd occasions a pure mathematician does chance across a computer; a progeny of just such a strange match is Whirligig.

Take the game screen. In the middle sits a comfortably familiar, if a little angular, 3D shaded spacecraft. Shame about the colours, but you can't have everything. But the area around the craft isn't yer ordinary hard interplanetary vacuum in which a thousand heroes have died, my goodness no. It's eigenspace. Come eigen?

Eigen is numberwallah jargon for among other things - solution. An eigensomething is a something which matches the conditions, so an eigenbus for East Ham is number 15.
An eigenspace has a number (from one to four billion), and a combination of stargates (links to other eigenspaces), missile, chaff and fuel depots and even the occasional perfect solid. Missiles and fuel are standard space game issue - except that if you fire a missile and there's no target they loop around and hit you - and chaff is an electronic fog that can confuse attacking ships.

You'll find a fuel store in an eigenspace which can be divided by 2 after you take 1 from it (so 5-1= 4, which divides by 2, so in 5 you'll find fuel), likewise missiles in sectors that can be divided by 3 after taking away 1, and chaff in sectors that do the same by 5. Perfect solids - of which there are just five - have to be collected; get the set and return to Earth's Golden Age. That's 1988, according to the book; a sobering thought.

All this wonderful numbercrunching means that, if you have a doctorate in integer mathematics, you can plot a course around the network of eigenspaces. If you don't, you're reduced to playing the game, and talking of course plots...
The only fun about is shooting at the ships which guard the solids. As some of these are invincible, you might have to run away.

This game is for retired professors who find spreadsheets just a little too exciting for the old ticker. Mediocre graphics - sprites dressed up as 3D solids with a light source - poor mouse control and frustrating screen changes, combined with hyperactive marching music, might put the rest of us off. Spend your twenty quid on Russell & Whitehead's Principia, it's much livelier.

Whirligig is the story of a ship with brains and a pilot with none. Point number 1: there are well over 4,000,000,000 so called eigenspaces which can be accessed via the old faithful stargates. Point 2: out of these eigenspaces you only need to visit five. In these five locations exist the perfect solids (a cube, a tetrahedron, a dodecahedron, an octahedron and a icosahedron) you need to complete this game.

The first game screen is a map which displays the various stargates, their routes and any other satellites in the eigenspace. There ensues a two minute wait while, presumably, the computer sets the area up. Then the game starts in earnest and the whole universe springs from the centre of the screen. At this point on the early eigenspaces it is a quick dash to the nearest stargate and the next eigenspace. But as you get to the higher spaces fuel starts to run out, and enemy craft attack and deplete your weapon supplies. Luckily base ships are to be found floating peaceably around certain areas of space. There are only three different base ships for the two types of weapons and fuel in certain eigenspaces so it can involve a lot of sidetracking before you can top your supplies up.

The solids are contained in spaces 6, 28, 496, 8128 and 33550336. Thankfully Firebird supply two possible routes to the last solid otherwise you could be left hanging around for a heck of long time.

Finding the first solid is no problem, the second is none too hard either but then the enemy ships start to become more devious and fly up from the bottom of the screen which means they spend half their time cleverly hidden by the ship's control panel should you have it raised. Sneaky.

To deal with the enemy you have four chaff pods and a number of heat seeking missiles.

The enemy 'spacers' are done out in very nice solid 3D like your craft only they tend to be a lot nippier and consequently ram your ship leaving a mass of engines, capsules and toilet rolls. One of the most impressive technical effects comes at the start and end of an area where the universe implodes or explodes depending on whether you are going in or out of space.

The control method really got me though. A continuous spin is induced by moving the mouse either left or right. Thrust is gained by moving the mouse forward and missiles are launched with a deft stroke of the mouse button. Grasping the little rodent in my left hand I promptly executed a series of dazzlng twists and turns that would make a no-legged elephant look overly graceful. After several hours of play my prowess with the control method enabled me to find the first stargate which I immediately rammed. Although it is fiddly the control method is well suited to the game, if it was any easier then alien bashing would be just an unnecessary waste of time. With the mouse it proves to be more of a challenge.

Whirligig could be subtitled Looking For A Needle In A Haystack Simulator, if there was more to do then I could have given a higher mark but with a total lack of real fun objective Whirligig stumbles, falls and lands smack on its nose.

Scientists have discovered a whole new network of universes. As each universe acted like a section of ordinary space, these areas were dubbed 'realspace' or 'Eigenspace'. Between them lie spacial warps, which are linked by gates to the Eigenspaces, rather like a funhouse maze. For this reason the network was dubbed the Whirligig.

Well, if you understood all that then it's probably time for a rest in your rubber room! What the game entails is a search through some 4,000,000,000 spacial spheres (aaargh! That's nine zeros!) to find the five tracts of Perfect Space wherein reside the Perfect Solids which yield the secret of time travel. With this, you can go back in the fourth dimension to a point in the cosmos untouched by squalid lifestyles and apocalyptic wars in space. Apparently, that point is on Earth in the year 1988.

Each level is chock-a-block with malevolent aliens who will stop at very little to get your craft disintegrating into the ether. Luckily, your Meson class fighter has two defence mechanisms - homing missiles and chaff pods which are a form of intelligent mine. Fire a missile when nothing is around, though, and it might just lock on to your own ship and blast you up the impulse engines!

Missiles, chaff and fuel are all in limited supply, so one trip through a packed Eigenspace can leave your reserves low, forcing you to restock at supply depots.

Guiding your ship through a stargate places you in gatespace through which you are transported to the next sector; the network of numbered Eigenspaces and stargates is based on certain rudimentary methematical relationships and formulae. The key to success is to use these to plot optimum routes to the five areas of Perfect Space, numbered 6, 28, 496, 8,128 and 33,550,336. Space Invaders was never like this!