Mr Williamson sits on his sofa at home in Tauranga, in New Zealand's North Island, trying to watch the television, circa 1993.
"Dad," says a three year-old boy, holding a cricket bat as usual.
"Yes, son. What is it?"
"Please bowl to me, dad."
"Alright, Kane, give me the ball." The boy has a twin brother, Logan, who is not really interested in cricket, and three elder sisters, but they do not play at all. So it has to be Mr Williamson who lobs a soft ball which the child prodigy carefully hits around the living-room.
Around the world three other boys of almost the same age are likewise programming the synapses of their brains to pick up the trajectory and pace of a ball quicker than their contemporaries. The boy in Sheffield is called Joe, the one in Delhi called Virat, the one in Sydney called Steve. One of these four, in 18 months from now, will probably be crowned the world's best batsman in succession to AB de Villiers.
Virat Kohli is aged 29, Steve Smith 28, a bit further down the track as batsmen and Test captains than Joe Root and Kane Williamson, who are 27. Williamson could be rated the outsider, partly because he bats at number three while the others prefer the softer option of four. But this race is no sprint; and Williamson is the calmest of the four personalities, perhaps partly because he lives in a country where cricket plays third fiddle to rugby, so he faces fewer media and public pressures than the other three. He is also the only New Zealander ever to have a Test average of 50 so he already has a proven technique when the ball moves sideways. Playing on flatter pitches, Smith averages 62 in Tests and Kohli 53, the same as Root.
Kane's father had played club cricket with his brothers around Taupo before becoming a sales rep of office products and moving to Tauranga in the Bay of Plenty. The family home had a garden and driveway on which he could bowl to Kane, and over the back wall was his primary school (Steve Smith had a cricket ground behind his home in Sydney). One problem: no cricket pitch.
"I had my little miniature bat and probably drove my dad nuts," Kane said in the modest, self-effacing manner that has never changed. "He'd sit there and watch telly, watching the news or something, and he'd be throwing me the ball and I'd hit the ball back on the full so he didn't have to move off the couch. And the ball in the sock in the car-port - it's just what you enjoy doing when you're really young, spending hours in little competitions with myself. And there was a stump and a golf ball - I drilled a hole through the ball and tied a string through it. Then I broke one of my grandad's golf clubs so I had a golf shaft to bat with.
"I was fortunate our house backed on to a primary school. Dad and a couple of other guys fund-raised and put in cricket nets and an artificial cricket pitch - there hadn't been one before - and that was brilliant. There were a lot of cricket teams at primary school level then and the game was thriving. We'd just go through the gate and walked down to the nets across a field. I always enjoyed watching Sachin Tendulkar and Ricky Ponting but I really liked watching Jacques Kallis as well. In the backyard me and my mate would pick teams and Kallis was always a popular pick because you could bowl fast and bat at three or four."
He was soon churning out centuries - exactly how many, nobody knows. "I wouldn't have a clue," Williamson said. "All I remember is that at the school, if you got a hundred, you used to get a voucher for a sports shop but the principal never followed through with it. A few of the guys got them but I never got any. He's a good guy though."
That is because Williamson qualified for a voucher almost every time he batted. David Johnston, whom Williamson credits with being his main batting coach in Tauranga, confirms it.
"I do remember a rep tournament (under 13) when he scored four hundreds in five innings including one batting at seven after the batting order was changed around to give others a bat," Johnston said.
"Through his teenage years he scored a multitude of runs and centuries, all completed with the same calmness and skill he continues to display at international level - and most importantly the same humility and respect for the game and those involved in it including the opposition, officials and volunteers who run this wonderful game. He was a tremendous youngster and is now equally a fantastic young man."
A more rounded upbringing - not specialising in cricket so early as his three rivals - may have contributed to Williamson's level-headedness. "In winter time I played soccer or football, and basketball, and rugby as a first five for the intermediate Bay of Plenty team. I had a great time at college, which in New Zealand is 13 to 18, and I really enjoyed my economics because it kind of made sense to me. I took pride in my school work."
What drives him? "I do like to train and improve," Williamson said. Johnston agreed: "Kane's always competing with himself, not others."
"But the older you get, you start to realise the importance of having time away from the game and putting it in other areas of your life," Williamson went on. "I really enjoy surfing - there's no phone, no contact, you just get away from things, and when you get a nice wave it's such a good feeling." Surfboarding is similar to batting - you fall off, very publicly, and have to get back on.
When India tour this summer, it will be Kohli's turn to present his case that he can cope with a moving ball in England, after averaging 13 in 2014; in the Ashes of 2019 it will be Smith's turn. Williamson meanwhile, though only 27, will set the New Zealand record for most Test centuries if and when he moves ahead of Martin Crowe and Ross Taylor - and a century in what is likely to be a low-scoring Test in Auckland is liable to be a match-winner. Not so much jockeying for position, he is quietly moving up on the outside rail.