Most mornings, as I walk to the Underground, I pass a blue plaque honouring a generally forgotten man. Alan Turing earned himself a footnote in British history by cracking the Germans' wartime Enigma code at Bletchley Park.

Among computer scientists, his name rings carillons. A paper that Turing wrote in 1936, "On computable numbers with an application to the Entscheidungsproblem", laid the foundations of the entire post-industrial revolution.

Without Turing, there might have been no desktop PC, no Bill Gates, no internet. He ought, by any conceivable standard, to be recognised as one of the greatest men ever to inhale the smog of this city. If there is a vacant plinth at Trafalgar Square, Turing ought to be on it.

Yet such is the blurring of the notion of "greatness" that this acutest of British minds is commemorated only by a plaque on the wall of the Warwick Avenue maternity home where he was born. He died in 1954 of self-administered poisoning, while being hounded by police as a homosexual and putative security risk.

A terrible injustice? Turing is not alone. This March marks the tercentenary of the death of Robert Hooke, surveyor of the City of London after the Great Fire, crank inventor and propounder of Hooke's Law, which defines the physical causes of elasticity and is taught in schools to this day. There are not many men whose teachings endure 300 years, but Hooke is one of them.

Which makes it all the more disgraceful that not one portrait exists of this extraordinary man, let alone a public statue (apart from the Monument to the Great Fire, which he designed). Hooke was not, by most accounts, a nice man. Riddled with lice and cantankerous to a fault, he drove Isaac Newton to a nervous breakdown by disputing his theories, and irked Edmond Halley by producing a superior telescope.

Hooke was the terror of the Royal Society; nevertheless, to have denied him a portrait was mean. The British honours system has always been discriminatory, ennobling the elegant and shunning shambolic genius.

There is no precise measure of greatness, though science comes close. The Society that gathered Newton, Halley, Christopher Wren and the nit-picking Hooke around its hearth was indisputably a circle of genius, since each of these men transformed our understanding of the universe.

Ascribing greatness in art is trickier. Michelangelo did not need to be called "great" in his day because any Florentine fool could see that his marmoreal mastery of human form was unique. Similarly, Mozart and Beethoven were not awarded the adjective and Wagner's greatness was self-bestowed.

Greatness enters art in the 20th century as a by-product of mass media. Arturo Toscanini was the first conductor to be designated "great" when RCA imported him to America, with massive fanfare, as its network maestro.

The catalogue of his recordings created a canon of "great composers". The twin cults of great conductor and great composer have conspired ever since to stultify concert life in the US. At much the same time, the Great American Novel (a term alien to Henry James) came into common currency, and Hollywood, in an absurdity of excess, claimed greatness for movie stars.

Yet the adjective retained an ironic twist. Charles Chaplin, in The Great Dictator, poked holes in Hitler's image by ridiculing the pomposity of his assumption of greatness.

So what, exactly, do we mean by great? The distinction is easier to identify in the performing arts than scientists might credit. On the podium, for instance, three criteria set great conductors apart from the simply good. The great ones draw an individual sound from their orchestra, alter our perception of familiar works and, in exceptional cases, dominate a city or a nation. Toscanini ticked all three boxes, Furtwˆngler and Karajan the first two, Valery Gergiev the first, Simon Rattle just the third.

Anyone who has ever attended two orchestral concerts knows the line that divides the memorable from the pleasurable. The critical function, active even in the least sophisticated, identifies relative degrees of performance, the highest of which we call "great".

No one who saw Nureyev dance, Callas sing and Gielgud soliloquise would argue with that premise. Those artists were, in a word, great: both in comparison with their contemporaries and on an absolute level in performing history.

Greatness is by definition rare, and fast becoming rarer. Perhaps because so much of the art of interpretation is fakable on film, the magnetism of high performance has been dulled and mediocrity can pass, on first impression, for mastery, while genius is obscured by cheap gesture.

Since human nature abhors a vacuum, greatness gets bestowed on whoever catches the public eye. Ms Kylie Minogue has been named Greatest Living Australian. Not much competition, you might say, but what it is that Kylie does better than any other Aussie? The term "great" is a vital critical tool. It should not be wasted on a sprightly singer with a shapely butt.

But wasted it is. The dilution of greatness was given fatal acceleration by the BBC's widely derided Great Britons referendum, in which pop stars and politicians vied with a dead princess for a worthless title, ultimately won by a wartime leader. Three months on, the results are still discussed - testimony, says the BBC, of the educative importance of the exercise; aftershock, say the rest of us, of the erosion of critical distinction and the submission of mass society to the relentless sloganising of totalitarian media.

Winston Churchill is great, according to this process, not because he re-energised the English language and saved the nation, but because enough people still felt strongly enough to vote him above Princess Diana.

By eroding greatness, the BBC did not perform an act of populism. On the contrary, it blunted one of those tools that help ordinary people organise their world into bigger and smaller, more and less important, desirable and rejectable. Dull its edge, as the BBC did, and you hasten the dumbing of society, the loss of discrimination - ultimately the organisation of illinformed masses into ranting, programmed hordes.

There is still greatness around us, more than there is goodness. It may contradict political correctness to shout aloud that some artists are superior to others, but those of us who admire the human mind have a duty to use "great" sparingly and defend it from media depredation. The word is a laser beam of critical therapy.

Used properly, it can restore sight. Abused, it blinds us all.