How we are duped by the wrapper, how we mistake the veneer for the structure underneath.

Alastair Cook's appearance is guileless, his speech polite, his behaviour dignified. Too nice? Check the record. He is the toughest cricketer England have produced for decades.

Yesterday in making 153 not out under intense scrutiny and pressure, he once again underlined his pre-eminent gift: responding to a crisis by entering a state of extended and productive concentration.

There are many widespread misconceptions about concentration. It is not so much a wilful and assertive state of mind ("I am going to concentrate hard now") as a state of freedom that flows from the absence of irrelevant thought ("There is nothing extraneous in my mind, no impediments in the road ahead").

Anyone who achieves mastery of a craft, art or profession has by definition also learned to master concentration. They may still suffer anxiety and concern in prospect and retrospect ("Will my work be good enough?", "Was my work good enough?"). But in the act itself, when the script is still being written, they must achieve a state of clarity.

That's why when you meet a brilliant performer - whatever the field - they almost always have an air of calmness and simplicity. When the game is on, their mind is free and uncluttered.

"Steve Waugh defined "toughness" as emotional stability and psychological consistency rather than outward displays of "spiritedness". A batsman with a clear mind amid chaos is displaying mental toughness"

Cook's calmness is preternatural. I watched him carefully yesterday and on Saturday, studying his manner and habits between balls. The gentle walk out to square leg after each ball; the brushing away of stray dust on the pitch; the nonchalant way of standing at the non-striker's end, legs crossed, one hand on hip; the twiddle of the bat in his hands as the bowler turns, looking down at his bat for the first stride or two, then up towards the bowler. All were totally consistent, unruffled by the changing facts of the scoreboard or the corresponding level of anxiety within English cricket.

Whether Cook was watching Ian Bell edge behind as the ball swung in the anxious morning session, or if he was a contented spectator as Ben Stokes smashed England into a dominant position - neither circumstance made any difference to him. He was the same player throughout. His tempo and body language found perfect equilibrium.

It serves as a good metaphor for Cook the man as well as Cook the player. Very seldom is he knocked off kilter or thrown off balance. People have certainly tried. Consider the context of Cook's innings. Yesterday the Sunday papers suggested that Cook was batting to save his captaincy. (Not true, incidentally, as Andrew Strauss has said Cook will captain in the Ashes, but the temptation to turn genuine drama into a phony last-chance saloon often proves irresistible.) In the short term, the fortnight before the Test was dominated by the Kevin Pietersen saga, whipped up once again into full fury. In the medium term, English cricket has endured a state of near permanent crisis for months - at the top of the English game, Cook's captaincy is almost the only aspect of continuity. Widen the focus to take in the last 18 months. Cook has suffered an Ashes whitewash and then, in the summer of 2014, near universal calls for his removal as captain. All bruising, they were experiences that would have crushed many players. Captaincy exhausts and depletes almost everyone in the end. It shows no sign of hobbling Cook yet.

It has long been obvious that Alastair Cook is the finest concentrator to play for England in the modern era. He is also among the most psychologically resilient. Only now do I realise that those two facts are intimately connected. Indeed, watching Cook over the past weeks has reinforced a link I've struggled to notice before: mental strength, whatever the sphere, relies on the art of concentration.

Blue skies ahead? Alastair Cook savours victory Getty Images

Concentration (the ability to filter out unnecessary noise) leads to clarity, and clarity preserves mental reserves. Quite simply, you don't waste precious focus on things that don't matter.

When I played with Steve Waugh for Kent in 2002, we had several conversations about his mental approach. One recurrent theme was that Waugh defined "toughness" as emotional stability and psychological consistency rather than outward displays of "spiritedness" or meaningless emotion. A batsman with a clear mind, no matter what is going on around him, is displaying mental toughness. The toughest players win more of those scraps, the battles that happen inside their own minds.

Waugh called it mental toughness because sport is adversarial. But that state of flow and focus has much in common with the writer who can see past the mess in his study and follow the story in his head; with the painter sketching a portrait on a noisy train; with the surgeon who tunes out the sense of panic around him when an operation is going wrong and sees only the path ahead. Concentration is not about seeing more. It is about seeing less.

Pressure, in fact, brings out the best in Cook. In the third innings of Tests, when England face a first-innings deficit, he averages 66.

Just as well. Given the nature of the Test season ahead (Australia, Pakistan, South Africa) there will be many more days when Cook will need to do what he does best: to forget the blurry frustrations in the middle distance and watch the ball onto the middle of the bat.