Old Papers (and maths!) (by alaric)

This weekend, I've been going through old papers and dealing with them. This involves sorting them into three categories:

1. To be shredded and turned into logs with our log maker
2. To be filed in the cabinet (with many subcategories corresponding to the files therein), and sorted by date where applicable
3. Demanding some action (which, for now, means putting them into my in-tray, rather than disrupting the activity in progress)

The magnitude and importance of this task is not to be underestimated - when we moved here I had a new baby, a very sick wife, and two jobs to deal with; unpacking and properly setting up my office never really happened, as opposed to setting up a desk and digging through boxes to find the things I needed to get started. So my once-pristine filing system was never quite established, and my "to file" tray grew fat with paperwork I needed to put somewhere. There was slow progress, of course; but then two years later the house flooded, so we had to rush a lot of furniture and stuff from downstairs up into the office, then pack a lot of stuff up and send it into storage while the house was repaired... and we weren't living in the house for nearly a full year, so more often than not I was working on my laptop from wherever I could get an Internet connection. Once again, my paperwork was in disarray.

But, three years on, we're finally catching up. I've gone through my filing cabinet and re-filed the mish-mash therein, then gone through my to-file tray and the various piles of papers dotted around the place, and dealt with them all. "To shred" has been by far the biggest category; as I write, Sarah is sitting feeding sheet after sheet into the shredder. And I've found a bunch of interestings that need further action.

For one of them in particular, the action is to write it up. Many years ago, I bought and read a book on statistics in order to refresh my memory, as I was working on a system for analysing the actions of large numbers of people. Now, I didn't enjoy statistics much when I was doing A-level maths, and reading the book reminded me why: I find the random-variable notation unnecessarily vague and confusing, and the various other notations used in statistics seem inconsistent to me.

I recall reading this book on a long bus journey (the bus from Tottenham Court Road to Gallows Corner in Romford, to be precise), and deciding to take matters into my own hand, and designing m own notation for statistics based on set theory. I like set theory and find it sensible and logical, so this was an obvious choice. I wrote my notation down on a sheet of paper, tucked it into the book, and took it home.

Many years later, I found the sheet of paper inside the book, and put it in my TODO pile, as I needed to take a second look at it and do something with it. This never happened. Until now.

So without further ado, here's the content of the sheet. It still needs more thinking about, but if I write it up into the computer now, this is more likely to happen than waiting for me to encounter this bit of paper again.

Let L be a multiset of real numbers.

• SUM(L) = sum of x, where x is an element of L.
• |L| = the number of elements in L.
• L(n) where 1 <= n <= |L| = nth largest element of L
• MIN(L) = L(1)
• MAX(L) = L(|L|)
• MEDIAN(L) = L(|L| / 2) if |L| is odd, (L(floor(|L| / 2)) + L(ceil(|L| / 2)))/2 otherwise
• SUM^2(L) = sum of x^2, where x is an element of L
• VAR(L) = SUM^2(L) - (SUM(L))^2 etc.
• L ~ D iff L is distributed as per D (D is a distribution as per normal stats notation)
• SRn(L) is a multiset of all possible sets of n random samples from L with replacement
• SWn(L) is a multiset of all possible sets of n random samples from L without replacement

Let L be a multiset of records (named tuples) of real numbers (a,b,c,...)

• La is a multiset of just the as
• Lab is a multiset of the products, a*b
• sigma(L) f(a,b,c) is the sum of f(a,b,c) across all the elements in L
• pi(L) f(a,b,c) is the product
• L ~ (D1, D2, ...) iff. La ~ D1 and Lb ~ D2 and so on
• cov(a,b)(L) = sigma(L) ab - M(La)*M(Lb)

...and there it ends!

Convince Alaric to let the Drs Put him under the Chop (by sarah)

Alaric has a... well nipple on the back of his head, the size of which only became apparent when we chopped off all his hair to try and deal with a dandruff problem. The dandruff problem turned out to be interesting as well but more on that later!

This lump on the back of his head has a distinctive look and I found a couple of smaller ones on him (one of which I had accidently mangled with a razor 🙁 ). The Dr says it's a variation on a wart but isn't that contagous but that it should be removed - doesn't have to be but should be. It will really need a scalpel taken to it as it is too large and fleshy to be frozen off and it simple wouldn't get it all.

Any way - due to the horror on Alaric's face the DR said he could think about it - I think it should be removed - help me convince him

You can’t get the staff these days! (by alaric)

We've got houseguests over, and we left them at home while we went for a walk in the countryside.

However, when I got home, I found they'd decided to go to Tesco many hours previously, and had gone off leaving:

• Jean's rabbit outside in his run
• The shed unlocked
• The front door of the house wide open

When asked why, they said "Oh, Barbara (the next door neighbour, my aunt) was around"...

Had it not occurred to them that Barbara might decide to go out herself, and is not supposed to be responsible for locking up our home? Or that Barbara might not actually take it upon herself to guard our open doors from passing opportunists, and sit watching, but might have her own things to do?

sigh

Adrian Brown and The Cheap Car Trade Centre (by alaric)

Earlier this year, Sarah and I spent my bonus pay on a second-hand car from The Cheap Car Trade Centre in Gloucester.

Sadly, they neglected to buy it a tax disc before I picked it up, so I couldn't drive it (other than the quick trip) home for a couple of weeks while the papers went through to make me the registered keeper. However, even on the trip home, the engine started to overheat, and the engine started to run badly; as the car had been stationary for a while, and had been almost entirely out of fuel, I was suspicious but it might have just been sludge from the fuel tank washing into the engine; I looked into the cooling system and found a syphon tube had become disconnected, so the engine could blow out excess coolant into the reservoir when the pressure was high, but could not suck coolant back in. Sure enough, although the reservoir was full, the cooling system was very low, so I flushed it out and filled it up after replacing the syphon hose.

All was well for a few days, but then it started overheating again. I was dropping Sarah off in Cheltenham at the time, so I stayed in the car park to let it cool down before heading home; however, it quickly overheated again, and again, and started to emit white smoke from the exhaust, and steam from under the bonnet. I pulled in another car park, and rang the RAC, who came and told me the head gasket was leaking badly.

So I rang the warranty company, who said that head gasket failure wasn't covered. So I rang The Cheap Car Trade Centre and explained the problem, but they disavowed any responsibility, so I informed them that the Sale of Goods Act made them responsible for the goods they sell being fit for the advertised purpose, which includes a reasonable life expectancy, even if they are second-hand; and this car was sold to me as "ready to drive". They told me I'd have to take them to court in that case.

So I sent them the required two warning letters, then tried to take them to court. This was hampered somewhat by them refusing to say who owned the business, which is an obligation under the Business Names Act, so I rang Gloucester Trading Standards, who pointed me at:

Office of Fair Trading Investigation into The Cheap Car Trade Centre

Which led to:

Formal Undertaking against Adrian Brown, Sole Director, Adrian Brown Limited

So Adrian Brown was the man behind the business, using his limited company, Adrian Brown Ltd, company number 04831719, which is registered as being at The Cheap Car Trade Centre's premises.

A look on the Companies House web site reveals:

REGISTERED OFFICE CHANGED ON 16/09/09 FROM: SUNNYLEA ASH LANE DOWN HATHERLEY GLOUCESTER GL2 9PS

...that's five days after his "formal undertaking" with the OFT. I suspect he changed it from his home address to his premises to divert unwanted attention at home. However, Companies House remembers all. I wonder if he still lives there. I would discourage my loyal readers from jumping to the conclusion that he does and inundating the address with junk mail or any other forms of harassment, in case he doesn't.

Anyway, knowing who to sue, I proceeded to activate the county court system.

They answered my claim with a defence (stating that it must have been me driving the car while overheating that broke the head gasket), so I was waiting for a date for the hearing when I received my last letter to them returned unopened, with "THE LTD CO THAT TRADED AS 'THE CHEAP CAR TRADE CTR' HAS CEASED TRADING AND IS INSOLVENT WITH NO ASSETS, AND HAS VACATED 333 BRISTOL RD GLOUCESTER".

I got back in touch with the Trading Standards folks, who said that they knew the company was closing, but that this action was suspended as there were county court cases in progress, so my case would probably still proceed, even though I might never be able to extract any money if the company was truly insolvent.

However, I'm still going to try. Limited companies protect their shareholders and directors by limiting their liability; the company is sued, not the people. But there's a limit to the limit. If a director can be shown to have acted fraudulently or incompetently, then they can be personally liable.

It looks like I won't get my money back, which will leave us carless until I get another bonus or something - but I'm hoping that, perhaps, the courts might find Adrian Brown personally liable. Given the involvement of the Office of Fair Trading and Trading Standards, it would appear that I'm not alone in having suffered from his business practices (the OFT judgement explicitly mentions him attempting to avoid the Sale of Goods and Business Names acts).

After all, I have little choice but to pursue this - I am scraping by with buses (which run once an hour, and don't run at all after about 5pm), being bankrupted by taxis, and begging lifts from people. This is seriously hampering my ability to live my life.

A large rabbit run (by alaric)

Today, I made a run for Jean's rabbit, Blacky. He has a hutch, but rabbit hutches are far too small for rabbits to spend all day in; we'd been letting him run around the house (which requires constant watching, so can only happen for an hour or so), or letting him enjoy the slightly larger possibilities of a large cage with the bottom removed pegged down on the lawn, but we knew it wasn't nearly enough for him; he was always wanting to get out, and when he's in the house, he enthusiastically runs the entire length of downstairs.

So, I built him a run, with some help from Jean (he's her rabbit, after all, but there's only so much use a four-year-old is in this kind of project). Two metres and ten centimetres long, a metre and five centimetres wide, and fifty centimetres high; made out of a wooden frame with rabbit mesh, and a liftable solid door at one end, which also provides some fixed shade.

I relish the chance to do something with my hands, as I usually don't get time to, and end up spending all of my time at a computer. And Blacky certainly seemed happy; he was running around it at high speed, occasionally bounding into the air and spinning round, which is what rabbits do when they're happy. Note the motion blur:

That's not all, though; we've also bought him a lead, so we'll be able to safely take him for walks along the drive.