The walk from Newcastle railway station to the river goes from the high, crescent-shaped vaults of the train-shed down steep streets bending their way under the tall arches that carry roads and railway lines as far as the Tyne bridges – a whole sampler of span design. There are concrete beams, two kinds of truss, a suspension arch (like a miniature Sydney Harbour Bridge) and finally the elegant and ingenious Millennium Bridge: imagine a pair of wishbones joined at the tips. The bridge’s walkway is curved, so that when it swings up to make a navigable passage and the arch above it swings down level with it, the pair of them form a barrel vault, its surface defined by the horizontal cables joining them.

This delightful plaything leads to the Baltic, once a flour mill, now four floors of gallery space. The new bridge is not essentially practical, but the flour mill was part of the city’s solid commercial past. So how to stop it looking uncomfortable when dressed for its new function? The architectural solution was to keep it in work clothes: the staircases are in industrial-looking steel, the galleries are big, plain spaces.

‘Domain Field’ by Anthony Gormley

The glazed lift shafts look out over the river. A few hundred yards downstream, a new music centre is rising. Its ballooning curves have not been determined by the old rules of thumb and, seen from the river, they echo imperfectly the simpler curves of the bridges. It used to be the case that looking elegant was a good indicator of structural soundness; but now computers have so expanded the number of possible shapes that instinct fails as to which structures are sound. If you want a 20-storey building that looks like Donald Duck, a lotus flower or a piece of crumpled paper, a computer helps with calculations, working drawings, templates and so on. In the new music centre the pre and post-industrial won’t have to accommodate each other.

In the Baltic – as in Tate Modern – no mask of decoration obscures the load-bearing function of the walls. The exhibition spaces are notably successful. Most of them at the moment are given over to work by the sculptor Antony Gormley – the exhibition runs until 25 August. His impersonal aesthetic suits them. What you see, floor by floor, are, first, two huge, rusted fruit-like pieces suspended by substantial cables from the ceiling; then, on the next floor up, in a large, rather dimly lit gallery, concrete boxes topped by smaller concrete boxes set out according to a loosely rectangular grid – block-like heads balanced on block-like bodies, figures suggestive of the Chinese Emperor’s terracotta army. This is Allotment II. In the uppermost, top-lit gallery, the sepulchral gives way to the sprightly. Shadows of clouds pass over the floor and hundreds of life-size figures stand about, each a mesh of bright metal rods a few inches long. You pick your way between them. Allotment II was a parade ground; Domain Field is a playground.

The function of Newcastle’s new bridge and converted mill is to give pleasure to the visitors they carry or house. A crowd gathers to watch the bridge do its thing, waiting for the warning hooter as they might once have listened for the midday gun. If you have read in the papers about what Gormley has done, you cross the bridge to the Baltic for the first time in a curious and expectant mood – as though you were hoping to see a flypast or a marathon go by. You are as much engaged by the tasks Gormley has set himself and the processes he has used to generate his sculptures – the concrete and welded figures and the hanging fruit – as by the things themselves. They are the result of computer programs, conceptual ‘what if’ games made serious by being taken seriously. In making his moves, Gormley resembles Christo, particularly the Christo who made the fence that ran for twenty miles across the Californian landscape: negotiating agreements for it to cross people’s land was part of the work, the collaboration that resulted being as impressive as the structure itself.

The dimensions of the concrete blocks in Allotment II match sets of measurements taken from the citizens of Malmö – height, head size, size and position of ear, height of anus from the ground and so on. They were processed according to an algorithm that determines the dimensions of the blocks and of the rectangular holes which have been cut in them. They are precise, highly abstracted accounts of individuals: so abstract that it makes no sense to come and look at all of them one by one as you would portraits. Once you have taken in the details of any one figure – the way the angled holes cut into the boxes (they may remind you of the windows in Le Corbusier’s Ronchamp chapel); the threaded boss in the top of the top box (which could be there to fix a hook to make it easier to move); the serial numbers stamped on each body-box (which are unsettling) – and once you have seen that these elements repeat, and have taken in that there are differences (creosote-like splashes on a few pieces, for example, resembling the accidental-on-purpose decoration of tea-ceremony pots), you are at your ease. Not too much is expected of you. You are a spectator. Purposefully achieved purposelessness, a thing done for its own mildly mysterious sake – justified in part by the relationship between artist, place and people set up during the process of making.

Domain Field was made to a different program. Hundreds of people from Newcastle-Gateshead answered a call for subjects, and casts were made from their bodies in the gallery (the processes involved could be watched by the public). The casts were then cut open and used as templates; the assemblages of welded rods are three-dimensional sketches of individuals in zigzags of bright white metal. When real people wander among these presences, whose individuality has been suppressed by their reduction to spillikins (all the attributes of surface – smoothness as well as wrinkles; freckles and creases as well as colour and blushes – are gone), the effect is easy and pleasing. There is no Pygmalion effect here, no marble Venus to compare with real girls wandering through the forest of welded steel.

In Gormley’s work, you don’t get telling changes in proportion (no Giacometti-like attenuation). You do get things scaled up (the Angel of the North), but more often scale is a matter of big numbers, not big things. You don’t get many, if any, jokes (no Koons-like games), or shock or irony (as in the Chapman brothers or Hirst). You do get a neat, impersonal finish (but not perfection), such as you could ask of a good amateur carpenter or welder. The figures are individuals, yet it is the whole that is particular, and the whole that you take in. Deprived of particularities, you are encouraged to think quietly about our collective personality.

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