Mental finger string, thinking out loud, in public, how vulnerable, embarrassing, but I do it all the time.
2012 11 15 I’m much better prepared to say what I mean clearly now: soon I hope, scratch meantime:
Zero is a juncture: between positive and negative. Any juncture has at least two sides. 0 = minimum2
The juncture between any two numbers is like a zero, has two sides at least.
I see this apply every day as I play any of the forms of solitaire in which you count cards down below the meta-line and up above it: when you switch from above to below or from below to above you’ll save a fumble if you remember to think below-juncture-above or above-juncture-below; otherwise you’re inviting BC / AD confusions.
We’re born, a year later family says we’re one year old. They don’t say you’re one when you’re born, they just say you’re born. You live a year, then they give you a number: “one.”
Jesus was born. Later on Christian priests called it “one.” They didn’t match “one” with when Jesus was one year old; they started counting from when he was born: calculating from their calculation of the first Christmas, accuracy difficult to impossible: but nothing is impossible or difficult when you just decide, in your ignorance, that you’re right: what priests, and people, are so good at.
Don’t get too upset, people weren’t too precise, or clear, about lots of things in former times, or today. Anyway, the above is of interest as a century ends, as a millennium ends: when does the Twenty-First Century start? Oh, criminy, we went through all that a dozen years ago. But of course everyone instantly forgot. Isaac Asimov had explained the problems, we didn’t follow the explanation. I’ll illustrate in the next draft, already been done by others as I say.
The Arabs, smart bastards sometimes, came up with a very clever invention to help out: they invented zero!
(I don’t know why they invented it: nevertheless, it applies here.)
Abu Dhabi Science Festival
When you’re born, you’re not one; you’re zero! (Never mind the nine months you’ve already spent gestating: we can feed ourselves one problem at a time. Regardless:) Now “one,” and “two,” and “three” can follow in rhythm.
I know all this, but still: I play my 7×7 form of solitaire: I deal, I reorganize, downward, by suit: then the suit can promote above the line: count ace to king above the line. Below the line they go king to ace — by suit; above it’s the opposite: by suit on both sides.
When I think I’ve got a suit licked, before I claim that the thirteen cards are complete, above the line, I count them, double check. I don’t want to claim a stack is good when there’s the deuce of clubs stuck among the suite of hearts: no, no: sit in the dunce corner.
Well, that’s all fine when I’ve got all thirteen, when I count them, when they check; but sometimes I’ll have ace to six above the line: now say I have a complete king to seven below the line: I pick up the suite to count: and frequently fumble for a few seconds. Something’s wrong, I’m counting wrong. Happens again and again.
For a few years now I’ve been convinced that it isn’t just that I’m getting old, going blind, going deaf, losing my other senses, getting stupid … All those things may be true, but I think there’s something else too: something inherent in counting (a mistake in how our culture counts, in our training), a mistake even Johnny von Neumann would have made before he retrained himself: zero is necessary but not instinctive. But in my present illustration, you’re not counting from zero, or one: you’re counting from seven! (What should be understood as “(… 6,) 7.”)
There’s always a concept I recommend, whether it’s zero or not: there’s the card which is a juncture here, and there’s a card, already accounted for, the card before that juncture. … In other words: the six card, if it’s remembered as a “zero” will permit the seven-to-king cards to be counted smoothly, swiftly, accurately.
So: zero is zero.
But also: think of “zero” as the number before the one you’re beginning with. There’s two to a juncture!
Make sense? I’ll maybe say it better once I’ve read it over and thought for another minute or two.
If what I’ve said, or tried to say, sounds obvious, then, you don’t get it, at all; or, I’m totally beyond the pale.
But here, I hope this helps:
Juncture comes minimally in pairs.
2012 09 17 OK, here’s maybe what I should have said (in cybernetic navigation you don’t have to hit bulls-eye the first attempt: you zero in on your target: miss closer and closer.) Our teachers, for centuries, were the priests, the ones who hadn’t counted from zero, who started from Christmas as “one.” We count:
We commence in a one-figure column and end in a two-figure column: 10: a zero comes up to show you how many times you’ve gone through the cycle: now you’re beginning a second cycle. But, in our habit, acquired in childhood, from teachers who don’t know what they’re doing, we don’t register the trespass.
Ah, but not computer people, not programmers. for decades now they’ve counted within the subset: they start counting at zero!
So: any geek can count either way, can easily switch back and forth: Now I’m counting like the culture, misleadingly; now I’m counting units, tens …
“Ten” is ambiguous: have you reached the last unit of the first set? or the first unit of the second set?
A mathematician may have been able to say that, accurately, in a few words; but I’m not a mathematician. I just try to figure things out, to explain oddities: like Asimov before me.
Him being older isn’t the only difference: he had an income!
(Him being a lady’s man isn’t the only similarity.)