Why you should never be a referee

There are many reasons why you should never be a referee, but the reason I’ve never become a referee is fear of being cooked if I make a decision the home side don’t like. That’s right, cooked. I’m about to do the maths for those of you who don’t believe me.

The average man weighs about 70 kg. Now I reckon the average ref weighs less than this, but we’ll count that as slack.

On a cloudless day (the ideal kind for a football match) the earths surface receives approximately 942 Js-1m-2. More when the earth is closer to the sun, and less when it’s further away.

Now the human body consists mainly of water, which has a specific heat capacity of 4.2×103Jkg-1oC-1. This is generous, as the human body would probably be easier to heat than 70kgs of water.

So the amount of heat energy required to raise a mans body temperature by 35 degrees (way more than we need – to kill we only really need about 10 degrees) all the way through is 70 x 4.2×103x35 which is 10290000 Joules.

Now lets say we give the home side audience reflective programs that fold out to be about a half metre square. If we allow that they are going to be tilted at on average 30 degrees to the vertical in order to focus them then the area of sunlight they are each catching is the width * (the height * sin 30), which works out at 0.125m2 each.

Now there’s the matter of time. That is, how long will it take for the ref to work out whats going on and come up with a strategy to counteract it? Well, on the roads, they allow 2 seconds thinking time, but I think that refs are a little stupider than average folk so I reckon about 3 seconds.

Over 3 seconds, we only need 10290000 / (942 * 3 * 0.125) people focussing these programmes on the ref for three seconds to raise his whole body temperature by 35 degrees. That’s only 29129.5 people. Well, lets call it 30,000 people.

Wembley stadium can hold over 126,000 people (according to Britannica), and its not even the biggest stadium by a long shot. So a home side in Wembley is going to be well over 30,000 people. Even if only half of the home side (say three quarters of capacity – 94,000 people) are organised to do this, and only three quarters of them got it right, you’d still kill the ref with a bit left over.

So a survival tip in case you are ever compelled to referee a football match – ensure it’s on a cloudy day, or be blatently biased in favour of the home side.

I got the idea for this node from a short story by Arthur C Clarke, called A Slight Case of Sunstroke. Also, c.f. Archimedes mirrors and the rtmark demonstrations at Genoa which got the italian police to classify mirrors as weapons.

This post was originally posted on everything2.com under the username delfick.

Dog Incompleteness

This is the story of how I discovered that not every dog has his day.

I got a fantastic pair of dogs the other day, they’re always having pups, but the most amazing thing is that I’ve trained them to give birth to whatever kind of dog I specify. So I go to them one day, and I say “I want a dog born on the 22nd of February with 14 teeth and black hair and blue eyes, and sure enough, the dog is born.

Well I got to thinking about all the things I could do with this amazing dog breeding trick, and I thought about collecting the full set. It took me a bit, but eventually I realised that there was a never ending list of properties and abilities of dogs. I mean, there’s “propensity to chase cats” for example, but there’s also “psychic dogs”, and then theres “propensity to chase dogs that chase cats” and “propensity to chase dogs that chase dogs that chase cats” and so on. Or theres “dogs that can do only the 2 times table in their heads” or “dogs that can do only the 3 times table in their heads” and so on. So I began to realise that if you gave me any list of properties of dogs, I’d always be able to think of ones you’d missed.

Well, that put paid to the idea of collecting the full set, which was a disappointment, as you can imagine.

One day a man from the Pedigree office came round, and he said to me “You’ve got a large number of dogs that haven’t been named, if you want them registered, you’ve got to have them named”, so I went to work, and named all the dogs that I’d had born, quite a big task by then. I mean, you start ok with Rex, Bowser, Gnasher etc, but after the hundredth or so you start having to tax your creativity.

A couple of days later, I was thinking, and I realised that it’d be handy if I just worked out all the names of all the potential dogs that could be born, so I didn’t have to think up new names. Even if I used a meaningless string of letters or numbers, at least they’d have a name, and it’d keep the Pedigree office happy. Although there’s a never ending list of possible dogs, theres also a never ending list of possible names, so there should be no problem right?

So, I got a piece of paper, and down one side, I listed the names that I’d come up with in alphabetic order, and down the other side I listed the properties of the dogs. I was only able to make a start on each of those lists, but I figured that once I had a system, it’d be obvious how to continue it.

It went kinda like this

```
Name  | Psychic	| Eats Cats | does 2xTable | does 3xTable…
Rex1	No	    No		No	        No
Rex2	Yes	    No		No	        No
Rex3	No	    Yes		No	        No
Rex4	Yes	    Yes		No	        No
…
```

Wed Aug 29 2001 at 22:40:48
Well everything was fine until one day the Pedigree office turned up and complained about a dog that I’d had born with no name. I said “Look, it can’t have, cus I listed all the names out, and it’s all done”. The officer showed me the list and he said “Look, sir, this dog you’ve got, well it’s not called the first name, cos it’s different from Rex1 in that it’s Psychic, it’s different from Rex2 in that it eats cats, it’s different from Rex3 in that it can do the 2x table….”. And he went on. I saw what had happened in an instant. The dog born had the opposite characteristic to the first named dog in the first property, and to the second named dog in the second property, and to the third named dog in the third property, etc. Even if I listed the names forever, There’d still be at least one dog with no name.

I slowly came to realise something big, wonderful, and profound. We can never fully describe all the dogs that might exist.

First published on everything2.com under the name delFick

Halting dog problem

Here is the story of how I discovered that if you believe in psychic dogs, you must be barking.

Ok, I’ve got a bunch of dogs that bark. Now these dogs aren’t just any dogs, oh no, they’re pretty clever. So, I’ve got a dog (rex) that barks at cats, and a dog (gnasher) that barks at fish, and a dog (fido) that barks at black things, a dog (pig) that barks at white things and some others. But am I happy? No. I want more!

One day, I start playing with a mirror. Most of the dogs look in the mirror and aren’t even remotely interested, but my dog that barks at black things (fido) happens to be black, so when he looks in a mirror, he goes off on one. Some of the other dogs bark at themselves in the mirror as well.

Unfortunately, my mirror is one of those full length ones on the front of a wardrobe, so whenever I want to play with the mirror and the dogs I have to carry the whole wardrobe downstairs (the dogs aren’t allowed upstairs).

So, I think for sometime, and I come up with a plan. I spend months training an amazing psychic dog (meg), which barks if it sees a dog that will bark at itself. This makes it a bit easier, as I don’t need to cart the wardrobe around anymore, meg barks at fido, but not at gnasher, so I can take meg around with me instead of going to all that furniture movement effort.

One day, just for fun, I retrain Meg to bark at the opposite of what she used to bark at. This is fairly easy – she’s pretty intelligent. Now, she barks at dogs that won’t bark at themselves in a mirror. She barks at gnasher now but not at fido anymore.

So everything was fine, until one day, in contravention of the rules, Meg went upstairs and looked in the mirror…

First published on everything2 (hence the linking style) under the name delfick, with the title “Halting Dog Problem”