The Scandal of the Forward Pass

Living in Australia, as I now do, it is quite difficult to watch the Six Nations, but snatches are available on YouTube, and of course I can look at the news. One of the features of the news is complaints about what are said to be forward passes, which are not allowed in rugby. It turns out to be rather interesting. In particular, there seems to be a significant divergence between (1) the Laws, and (2) what passes for the Laws in the interests of common sense and the good of the game. Let us start with the former, and at the beginning.

Like practically every other good game, rugby was invented in England in the latter part of the 19th century, and the “Laws of Football” as they were called by the Rugby Football Union were published in 1871. Unsurprisingly, there was a rule prohibiting passing forward by hand. It was in the following terms, stating what was allowed rather than what was not allowed:

26. Throwing back. – It is lawful for any player who has the ball to throw it back toward his own goal, or pass it back to any player of his own side, who is at the time behind him in accordance with the rules of on side.

It is immediately apparent that there are two permissible moves. A player may throw the ball back towards his own goal. Or he can pass it back. If the latter, there are two criteria here. It is lawful to “pass it back to any player of his own side”. But the second part indicates a further constraint: the receiving player has to be “behind him” and on side.

Both of these criteria are somewhat uncertain. As to the first criterion, what does “back” mean in the phrase “pass it back”? Does it mean, picking up the first sentence, “towards his own goal”? That is possible, but it would lead to absurdity. Suppose a player, standing in front of his own goal on his own 25 yard line (as it then) passes the pool to a stationary teammate near the right-most touchline standing a yard short of the at 25 yard line. That would not be a pass towards his own goal, because the pass is away from his own goal, not toward it. And so a more natural reading would be that “back” here is to be judged by reference to the goal lines, rather than the goal. It leaves the absurdity that it would still be unlawful for a player to throw the ball in that very direction without any intention of making a pass. But hey. There are wrinkles.

Pounding Along

I had to go for a medical examination today, in order to keep my driving licence. It is because I have a motorbike licence apparently. I no longer have a motorbike, And to be honest, I barely need a motorbike, since for most of my trips either the dog wants to come, or my darling Louise, or I need shopping which will not conveniently fit in a motorcycle pannier.

Anyway, I had to do all sorts of cognitive tests. What was the day of the week? Count back from 100 in 7’s. Trace out a path in a maze on a piece of paper. And finally, write sentence in a box on piece of paper, and explain what it means.  I wrote

Quadratic equations – Double Solutions, Imaginary Solutions and Just Plain Wrong

Sometimes I find myself lying awake at night, thinking about stuff. Last night, I was kept awake by the realisation that I had forgotten how to solve quadratic equations, which is something which would have been routine for me as a schoolboy.

The quadratic equation is something in this form:

ax² + bx + c = 0  

You get told what a, b and c are, and you have to work out what x is. So I looked it up to remind myself of the formula. It is thus:

x = [-b ± √(b² − 4ac)] / (2a)  

It all came flooding back. The bit inside the square root is known as the discriminant. If it is positive, then there are two possible answers. If it is 0, then there is just one answer. If it is negative, then you get imaginary solutions – i.e. in the weird territory to which the door is the square root of -1.[1]  

SuperGrok gave me some examples, thus: