Great art collections formed by individuals are generally highly specialised – French Impressionist paintings, English sporting pictures, early Chinese bronzes – or somewhat specialised – Classical antiquities, Old Master drawings, Islamic art. What is special about George Ortiz’s collection of antiquities and ethnographic art, part of which is currently on show at the Royal Academy, is its combination of quality and breadth.* Ortiz is not only like a decathlon winner; he is like an unheard-of phenomenon, a decathlon winner some of whose results are better than those of the winners of separate events.

His choice of objects, moreover, for all its eclecticism, clearly reflects a distinctive taste. The things that Ortiz brings together tend to become his own rather as the quotations absorbed into The Waste Land seem to become Eliot’s lines. Qualities Ortiz seems to relish are palpable geometry, refinement of modelling, a tender sensuousness, a meditative, benign atmosphere. He also seems to have a predilection for works on a small scale, which may reflect the common tendency in collectors to favour things in their own image (as God does): Ortiz is a small, alert, dapper man. His taste can be hinted at, perhaps, by a guess at what he might like to have samples of if he collected European painting. Cimabue? Masaccio? Giovanni di Paulo? Piero? Seurat?

The installation at the Royal Academy, for which Ortiz himself has been mainly responsible, is good. Most of the exhibits have to be in showcases, but these are invariably designed to leave plenty of space for the objects in them to breathe and therefore not die on us. We are not given the usual feeling that we are having a bath with our socks on.

Ortiz is admirably prepared to take chances in the way he puts things together. He often sets up a showcase with two objects in it on very contrasting scales – say, a life-sized head or a helmet and a thumb-sized figure – but always averts whimsy. Again, he often places objects in the open at an angle rather than square to the wall, but never so that they look like treasures in the wrong sort of drawing room.

There are some shortcomings in the installation, which are probably not due to him. The walls ought perhaps to have been light grey rather than white. The lighting is incomparably better than it has been in recent exhibitions at the Royal Academy involving objects – ‘The Age of Chivalry’, for example – but it’s a pity, with many of the small objects, that the sources of light were not closer to them. Judging from installation photographs, the exhibition looks less wonderful than it did when recently shown at the Hermitage in St Petersburg, because it was given more space there: at the Academy the Sumerian and Egyptian sections would have been even grander if they had not been cramped for space.

In any case, this installation by a private collector is far superior to the majority of installations of antiquities done by museum officials. It was Barnett Newman who said what every artist doubtless secretly feels, that he paints so that he’ll have something to look at. And it may be that a lot of collectors of antiquities are driven to collect them largely because they want to be able to look at them decently installed.

The exhibition begins with works from the Near East, including about twenty-five Sumerian pieces of the third millennium BC, some medium-sized, some small, some minuscule. Among several major works, including an alabaster bull-man (cat. 15), the most moving for me is a half-length figure in gypsum, 42 cm high, of a worshipper (cat. 1). It is a marvellous translation of a human stance into a luminous architectural structure, with no loss of its humanity – an architecture articulated with a beautiful clarity in the way in which in profile the set of the head rhymes with the set of the arms and from the front the horizontal bands in the beard rhyme with the interlaced fingers of the clasped hands, held away from the body to form a shape in space that seems charged with a mysterious spiritual force.

There is an overflow from this room into the Egyptian room which follows – notably a case with Babylonian objects of the second millennium BC that includes a number of tiny haematite weights representing within a centimetre’s span a baboon or a frog or a duck or a boar’s head (cat. 18) and a jar in rock crystal 9 cm high (cat. 17). They are pieces which exemplify the genius of Mediterranean art of that period for working hard, highly polished materials. And this is very relevant to the series of figures which dominate the Egyptian section.

They are Twelfth-Dynasty pieces from the reign of Amenemhat III (1843-1798 BC) in cast copper alloy. They are not only extremely rare but strange, inasmuch as Twelfth-Dynasty sculpture is so much about carving hard stone – granite, diorite and the like – in such a way that it yields up a human presence, just as Michelangelo’s art is about carving marble so that a human image emerges from the block. The bond between a certain kind of image and a certain kind of stone appears so inevitable that it’s quite disorientating to see that image embodied in forms which have been cast after having manifestly been modelled in a soft material. It is like hearing notes by Chopin performed, not on the expected percussive instrument, but on bowed stringed ones (we do, of course, have that experience when hearing Les Sylphides).

One of the outstanding pieces in this group is the kneeling figure of the king, 26 cm high (cat. 37), a superb example of how Twelfth-Dynasty sculpture conveys a sense of man in the face of the awesomeness of death. The other is the headless figure of a queen, robed, standing with one leg advanced, height 70 cm (cat. 35), in which the whole area from the waist to the knees is treated as one curved plane inflected with extreme subtlety to convey the vitality and the allure of the body beneath the dress.

Astonishing in a different way is the Eighteenth-Dynasty headless standing figure of a princess carved in serpentine, 48 cm high (cat. 39), dating from the reign of King Amenhotep III (1390-1353 BC). The astonishment is in finding so much vitality and strength in an Eighteenth-Dynasty work, as well as the expected sexy elegance. Only one or two pieces in the much acclaimed Amenhotep III exhibition, seen last year in Fort Worth and Paris, impressed me as much as this one. It has to do with the electric way in which the contrasts work between tightly incised areas of the carving and flowing, smooth areas, and with the perfection of its scale in relation to its energy.

To the right on entering the next room there is a large case with an assortment of small objects from the Greek world covering the sixth to the third millennia BC. Three Cyladic pieces include a vase of great quality (cat. 49) and an exquisite little object, purpose unknown, like an egg (cat. 47). There are no specimens of the familiar Cycladic idol: a pity; one would have liked to see Ortiz’s choice. But this showcase does provide typical, and very fine, examples of idols from Neolithic Thessaly. One of them especially is a marvel. It is a terracotta 5 cm high (cat. 44), a headless seated figure with both hands resting on one knee, a work that reconciles the creation of an ideally compact sculptural form, a dense parcel of abstract energy, with an acute realism in its recreation of a relaxed posture.

Nearby are two amazing European Bronze Age objects with a spiral form, an armlet in gold (cat. 70) and an armguard in bronze (cat. 71). Another case in the same room provides one of the scherzi of the exhibition, a series of small eighth-century Greek bronzes of horses in the Geometric style (cat. 76-8, 80); placed among them is a geometrically decorated pot of the pyxis type 18 cm high (cat. 75). We now begin to get among Ortiz’s famous collection of small Archaic and Classical Greek bronzes. My personal choices are a kore probably from Ionia (cat. 101), a warrior from Yemen (cat. 117), an Akonistes probably from Italy (cat. 192), a headless Kriophoros (cat. 140), and a hunter possibly depicting Alexander and ascribed to Lysippos or his circle (cat. 163); there is also a charming midfourth-century plate with a head in relief at its centre (cat. 157). Among the marbles of the period are a rather battered life-size head of a kore (cat. 125) and a headless, legless, draped figure, 43 cm high, in the Severe style (cat. 139).

We have been walking towards a splendid over-life-size marble head which might be the portrait of an exotic individual by Bernini (cat. 173). It turns out to date from the second or third century AD, probably to have come from the region of Peshawar and possibly to be a portrait of Prince Siddhartha, the first Buddha. A companion remarked that it made her think of a giant Indian movie poster (and she was not aware that Siddhartha was the subject of Bertolucci’s latest film). This set me thinking that another work in the same room, one of several Etruscan pieces, suggested an archetypal image from the Western – that of the rider who seems to have been born astride his horse. It is a damaged equestrian statue in volcanic stone, made in Vulci in the sixth century BC (cat. 191), a moving work, more rough-cast than most things in this collection. It is one of those works of art whose extreme poignancy is partly due to their being grand but dilapidated and thus both sad in mood and rich in connotation. Another allegedly Vulcian work, wonderful this time for its preciosity, is a pair of votive boots in terracotta, about 16 cm high (cat. 182).

There’s a pair of early Chinese bronze animal heads (cat. 209) and a mixed case of Animal Style bronzes (cat. 210-19) on the way to the next major section, the Roman, which includes two fine and sombre marble heads, that of a boy of around 100 AD (cat. 229), and that of a veiled woman of around 250 AD (cat. 239). Another marble head of a boy, of around 375 AD, probably from Constantinople and possibly a portrait of Gratian (cat. 246), is the work which touches me most in the Byzantine section.

It might have been a good idea to end the exhibition there rather than with an ethnographic room, even though this includes several remarkable objects. While the places as well as the times represented hitherto are very diverse, they are almost all around the Mediterranean and adjacent seas. The sudden shift to equatorial regions and the Southern hemisphere leaves a rather confusing aftertaste. But we might as well just be glad to have seen a few more exceptional pieces, above all an 18th-century Tahitian wooden stool (cat. 269) that is as beautiful as furniture can be.

Furthermore, their presence is a reminder of the admirable extreme eclecticism of 20th-century collecting. The openness of today’s art audience to a wider range of styles than has ever been simultaneously enjoyed before could obviously never have come about without the vast increase in the range of the investigations of archaeologists and ethnographers. But the key factor has been the opening of our eyes to the aesthetic qualities of objects that might have gone on being seen as having a merely documentary interest, and many of us – I do not say Ortiz – surely owe this to the impact, direct or indirect, of the ways in which Modernist art has profited from such objects: when I recognise the extraordinary greatness of Sumerian sculpture, this is certainly thanks to Picasso. It is always a major part of the purpose and value of living artists to make us see the work of dead ones in a new light. Western artists of this century have done this so comprehensively that we could say that there has never been a time when the art of the day has done so much for the art of the past.