The local education authority adviser, a former head and a big woman, came over to me during the tea break. Had I noticed anything about all the people in the teachers' centre? Something they nearly all had in common?
It was a training day for headteachers, asking them to look with favour upon members of staff who wished to share jobs. So they all had a certain "not bloody likely" expression. And most of them looked as if they would like to fold the facilitator up in her own flipchart.
"Irascibility?" I suggested.
No, she said. Height.
Ah, yes. Now she'd mentioned it, I was indeed surrounded by a men a lot taller than me (I'm 5ft 8in) and only two of the women were noticeably shorter.
Not that there were many women.
"Alpha male, that's really what you have to be if you want to be a head. In the secondary phase, at least. It's what impresses governors.
"And if you have to be a woman, you'd better be an alpha female, unless you're in primary. Thirty-five years in teaching, five years with the LEA, what have I seen? A lot of tall men getting to the top."
It was an East Anglian authority, so I suggested it might be Viking inbreeding. It was more to do, she said, with gorillas than with Vikings.
"It's the leader of the pack thing. This lot get up in the morning and thump their chests."
Is it true? Well no one keeps records, but everyone says it's true. Height impresses people. Take the experience of Phil Revell, teacher-turned-journalist. "In my second school," he says, "I found myself being interviewed by a huge bloke. This head was heavily into cod psychology. Interviewees were offered a low-slung chair which gave a good view of the great man's knees. When he stood up to shake hands it was as though the lights had been switched off.
"As a 5ft 4in sprog, I didn't meet this guy's idea of what an authoritative teacher ought to look like, but I scraped through on the back of my weekend rugby. Scrum halves were just about acceptable, although he'd have preferred a second row."
Well, perhaps it's a good thing that the boss is tall. On the open day for his potential secondary school, my 11-year-old son was awestruck when the head, at least a second row if not a tower block, shook his hand. It wasn't the status, just the stature. "He's very big, Mr B, isn't he? How big do you think he is? What size feet do you think he has?"
No behaviour management issues with that future Year 7, I would think.
After all, faced with a pierced and growling 15-year-old, a top gorilla has a lot more chance of facing him down than a 5ft 2in woman waving an equal opportunities form. Doesn't he?
Not always, says Phil.
"A few years later the same head appointed a science teacher who became universally known as Lurch. This poor bloke towered over the kids, but they ran rings round him. Senior staff had to be retimetabled to teach near his room so that they could step next door to quell the inevitable riots."
Peter Greaves, who teaches at Dovelands primary school in Leicester and is a columnist for TES Teacher magazine, says children at least have more sense than to be impressed by mere size. "A classroom assistant caught up with me in the staffroom to tell me that as I walked past, one of the pupils she had been working with said, 'He looks dead fierce, but he's really nice.'
"At 5ft 10in and certainly underheight for my weight, I could never imagine being described as fierce. I've worked with some Basil Fawlty types in my time and they sometimes look fierce, but what I do know is this, authority that comes from any physical attribute - be it height, size, gender, age or fashion - disappears the moment the children perceive the talk doesn't match the walk."
So can you buck the law of the jungle? The prize doesn't always go to the tall guy. Ask John Kerry. (Although, if you look at earlier presidential elections you'll see it nearly always does and poor old Michael Dukakis who stood against George Bush Snr in 1988 suffered not only from inch deprivation: his other handicap was trouser-shoe separation, which made it hard for people to take him seriously.) They say interview panels make up their mind about you in the first 30 seconds or so. So the first hurdle is getting your headship. Then you can test the tall-equals-competence-plus-respect theory. Be encouraged by the short success stories you can find. The high-profile head of a south coast public school is small and remarkably dynamic: the pupils call him the pocket rocket. No one could overlook him.
Then there's Kenny Frederick, 5ft 4in and principal of George Green's secondary school on the Isle of Dogs in east London, not an easy beat for a head.
If you're long on ambition and short on inches, you can still succeed, she believes. "Size is not the issue. Good leadership cannot be measured in feet and inches. It is actions that count," she says in mock indignation.
"Seriously, I think it may be an issue for men rather than women and may be more about their self-image and stereotypes. The stereotype is that small men are more aggressive and pushy because of their lack of height and tall men more laid back.
"I have had two trainee heads working alongside me. One was very tall (6ft 7in) and one medium (5ft 9in). Both were very good and both are now heads.
The only advantage was that the very tall one could open the windows in my office without standing on a chair."Lofty ideals, page 2