If you approach the show with an art-historical eye, then the experience will merely be tiring. Kandinsky's career reads like a march through early 20th-century art movements: a couple of years as an Old Russian painter back home in Moscow; off to Munich in 1896 for a stint with the Jugendstil circle (Germany's answer to Art Nouveau); a brief flirtation with the Berlin Secessionists in 1902; the setting up of Der Blaue Reiter - a group with roughly Expressionist affiliations - with Franz Marc in 1911; a teaching post at the Bauhaus from 1922; and so on. And that is without Kandinsky's anecdotal invention of abstraction in or about 1913, supposed to have taken place when the painter saw one of his own pictures standing upside-down on an easel in his Munich studio and was struck by the strange beauty of its illegibility.
Even if you know nothing of all this, though, there is still clearly something exhausting going on in Kandinsky's work. The painter may have been a promiscuous joiner of movements, but the private ambitions of the pictures in this show strain against the house styles of Jugendstil and the Secession. The chronological hang allows us to see the development of Kandinsky's work as a series of explosions and subsequent implosions: a romantic colourism hurtles off into the vibrant forms of his early abstract pieces, which in turn regroup in the geometric style of his Bauhaus pictures, only to explode once more in the Small Worlds series of 1922. The spontaneity of watercolour painting - the show's main medium - matches the experimental feverishness of Kandinsky's mind, making this a more revealing show than an equivalent blockbuster of his oils might have been.
For all the stylistic big bangs in the exhibition, however, there is also a single agenda at work in Kandinsky's oeuvre. It is not entirely facile to view the evolution of his particular aesthetic as the triumph of the blob. There it is, even in early, folksy works like the Night pictures of 1903-1907, struggling to break free from the indignity of being merely part of the representation of something else - stars, flowers, patterns on a frock - to become a full-length portrait of itself. By 1913, the blob has tipped the balance, no longer appearing as a mere bit-player in works like Watercolour with Red Corners, but as a great red autonomous presence of its own. In 1921, it gets its first title role in Red Spot; by 1924, the blob has been geometricised by the rationalising mores of the Bauhaus into the circles of Floating. Twelve years later, Kandinsky's fondness for the form remained undiminished. "A red circle ... stands fast, holds its ground, is immersed in itself," wrote the painter, as though of an old friend. "Its radiance overcomes every obstacle and penetrates into the remotest corners ... A passionate `Here I am!' A circle is a living wonder."
To understand Kandinsky's unlikely tendresse for the blob (and for the lines, angles, squiggles and microbal shapes that fill his later works), it is helpful to think of the world - as he did - as being composed of a set of universal laws, or, in the artist's own phrase, "inner necessities". The laws governing art are of one with those that govern music, geography or physics. The job of the artist is thus to expose this universality by painting synaesthetically: that is to say, by finding a visual language which is able to express non-visual forces or sensations. titles like Light Weights and Hot (both of 1931) suggest these synaesthetic aspirations, as does that of Kandinsky's experimental play, The Yellow Sound (1909).
The problem with all of this, of course, is that it involves the portrayal of concepts which are invisible. How do you translate the idea of, say, weight into paint? Kandinsky's answer was to strip art back to its basics, seeing it as essentially composed of a series of conventional motifs - red blobs among them - assembled in varying configurations to represent the entire range of pictorial subjects: faces, lace, haystacks, whatever. Liberate these motifs from their surroundings - use a picture to paint a red blob rather than a red blob to paint a picture - and you will recreate them as signs, in much the same way as letters are used as the constituent signs of language, notes as those of music and algebraic symbols of mathematics.
If you want a crash course in this theory, make straight for Rows of Signs (1931) which proclaims Kandinsky's quasi-mystical role as the creator of a new universal language for 20th-century art, hieroglyphs for the modern man. This proclamation read, move on to the painter's synaesthetic masterwork, Pictures at an Exhibition: Scene XII, The Marketplace in Limoges (1928). As its title suggests, the work was intended as one of a series of sets for Mussorgsky's suite of the same name, itself a musical representation of a geographical place as represented in a painting. Kandinsky replaces the composer's synaesthetic transformation with one of his own, namely a map: the conventional visual symbol of place which Kandinsky reclaims for art by covering it with the constituent signs of art - three blobs of colour, one of them, naturally, red. (Painting representing music representing painting representing geography: you can see how it might all become a little wearying.) Off Balance (1929) meanwhile annexes the visual conventions of physics - lines for beams, triangles for fulcra - to represent its subject, while musical staves appear in pictures like Floating as indicators of Kandinsky's desire to create what might, at a later date, have been called a multi-media work. Another piece of symbolism in Floating - a stylised cross, also composed of straight lines and semi-circles - suggests the spirituality which Kandinsky clearly felt underlay his new synaesthetic language.
The trouble with a bald iconographic analysis of this kind, though, is that it makes Kandinsky's work sound like those innumerable Seventies poems about entropy: half-digested morsels of popular science with a dash of spirituality thrown in, the legalistic output of a man whose first career was as an academic lawyer.
So put all of the above to the back of your mind as you walk around the Royal Academy's excellent show. Reading the score of The Firebird won't necessarily make you love Stravinsky's music more, and Kandinsky likewise wanted his work to be felt rather than intellectualised. Let it wash over you instead as a great pictorial symphony, a fugue of colour, form and brilliance.
`Kandinsky': Royal Academy, W1 (0171 300 8000) to 4 July.