The third girl made the cut not just because she was bright, but as some kind of reward for not going off the rails, or wearing gloves with her uniform for five days in a row, or something like that.

The nuns moved in mysterious ways.

They made me school vice captain for similar reasons. Not because I was a shining example of virtue, modesty and outstanding Christian values but, as one of the nuns later told me, to show other wild and noisy girls that they, too, could aspire to greatness - or at least the greatness that came with being number two in line when we walked into church for mass every so often, or being deputy to the school captain who was a shining example of virtue, modesty, etc.

Anyway, so my friend and I and the third girl fronted up to test our brains against kids from two other schools.

I remember quite a few things from that day. On the bus trip down to Sydney we stopped outside a used car yard where every car carried a sign with a few words describing it. I noted that one sign carried "imaculate" rather than immaculate.

I was captain of our team. The It's Academic format included spelling questions. I nearly laughed out loud when our very first question was to spell the word "immaculate".

I remember being so nervous that when I reached across the desk to pick up a glass of water my hand shook so hard that I dropped half down my front and onto my lap. My best friend responded as only the bestest of best friends can, by calling me an idiot. The girl who may have been at risk of going off the rails flashed a smile and we bonded from that point.

My strongest memory of that day was of the show’s end when teams were asked a series of rapid questions requiring one-word answers. Something in my brain clicked and I remember the almost out-of-body experience of watching myself answer question after question until the end.

It’s been downhill from then, of course.

From that peak in 1975 it’s been a smooth, and not unpleasant, ride to now when my brain takes over in another way. Someone asks me a question – like last week when my colleague Ian Kirkwood asked me a question for a video of that day’s evidence at the Royal Commission into Institutional Responses to Child Sexual Abuse – and the circuitry in my brain fires up, travels along a path for a fraction of a second, and comes to a dead halt.

The name of the man we’d been writing about for days was on the other side of that halt in the circuitry last week, and my brain gave me a blank. Nothing. Zero. Those miraculous neural pathways we’re told about were missing in action, and in their place was a brain full of thick custard.

Eventually, after a second or so, the custard cleared, a new neural pathway was formed and I remembered the man’s name without looking like too much of a twit. I put these episodes down to age, tiredness or whatever other excuse sounds reasonable at the time.

The facts and figures about our brains are astonishing to the point of being mind-numbing. The average person has about 100 billion nerve cells, or neurons, in his or her brain; then there’s the billions of nerve fibres known as axons and dendrites, and these neurons are connected by trillions of connections, or synapses. There are quotes tossed around saying the brain processes 400 billion bits of information per second – how we’re feeling, what we’re seeing, what we’re smelling, what others are doing, what’s the time, what’s that weird pain in my left toe, did I really just spend eight minutes watching a video of two kittens playing with a puppy and a roll of toilet paper? Keep counting until you reach 400 billion – every second.

But despite all that neural firepower millions of Americans still voted for Donald Trump, so there you go.

In recent years the term neuroplasticity – the brain’s ability to be re-modelled or re-wired in response to experiences over a lifetime – has dominated public talk about our most extraordinary organ. And you don’t have to look far to find credible research into how our new knowledge about the brain’s processes can be used to improve mental health.

I’m writing about the brain this week from a hospital room where my father Jim, 86, enters the final stage of his short battle with a cancer in his brain. He is sleeping the fitful sleep of a man whose body is shutting down. His pain is managed by drugs. His groans remind me that we may be in the same room, but my father has crossed to that time and space where I can’t go, yet.

A few minutes ago a nurse asked if he was in pain. He said no. I told her he would always say no if asked that question. If my father lost a limb and he was asked if he was in pain, he’d say no.

There were four or five of us in his room on Monday, talking in whispers while he appeared to sleep. I was holding his hand at the time. We were worried at the level of pain he might have been feeling when Dad suddenly volunteered, without opening his eyes: “I don’t think I’ve ever felt pain in my life.”

For a couple of minutes, while my sister filmed us talking, we reminded Dad – a brickie – of all the events in his life that might have caused him physical pain.

“What about when you put the star picket through your shin?” said my youngest brother. Dad conceded, eyes closed, that had hurt.

When he cut his palm open with a sharp knife? Yep, that hurt. Smashed his head, arms, legs and hands on building sites too many times to remember? Yep, those things probably hurt a bit, too, he said.

We laughed and he smiled, eyes still closed, until he said he needed to sleep.

Dad lived his life with thanks every day that he was alive. Now he’s slipping away, our father with the beautiful mind.