Very slow

In my various meanderings about the properties of jigsaws on 1st November I listed a property 4: four pieces meet at every vertex.

I am now rather cross that despite being in possession of the relevant information - in this case about how the cutting dies for the cardboard jigsaws that I solve are made - I completely failed to observe that there was a symmetry issue here. A sort of senior moment.

Cutting dies are made out of (say) 1cm strips of bendy steel with a sharp upper edge. In essence, the die maker lays parallel strips on the base board, sharp edge up and running from top to bottom, maybe an inch apart. The strips will include all kinds of wiggles reflecting the prongs and holes of the intended jigsaw, but we are talking of continuous strips. The strips are then fixed down.

The die maker then fills in in the other direction, but this time instead of a small number of long strips we have a large number of short strips of steel, one for each piece. And while the die maker may choose to line all these left-to-right strips up, as if they were a single, continuous strip, he does not have to. The short strips may be always aligned (in which case the jigsaw will have property 4), mostly aligned, sometimes aligned or more or less never aligned.

With the result that pieces are always aligned vertically but may not be aligned horizontally. Or vice-versa in the case that the die maker does it all the other way around. In the illustration, A is always aligned vertically with B, but may or may not be aligned horizontally with C.

So the puzzle has orientation. Top to bottom is different to left to right, a difference which can be exploited in solution.

PS: it would be interesting to see such a die. How do they fix the strips to the base board firmly enough to stand perhaps hundreds of cuttings? And how do you get steel which is hard enough to hold the necessary edge while being soft enough to be bent into the necessary shapes? The die has to hold the edge as I do not see how one could sharpen a completed die. Would it be worth taking one to pieces to sharpen it - then put it back together again?

Jigbooks

I reviewed some properties of jigsaws on 1st November and now notice a book about same, a book which, I might say, takes no interest whatsoever in the formal properties of these fascinating puzzles.

So far, my second book about jigsaws, the first being the memoir by Margaret Drabble, noticed in the other place on June 14th amongst other dates. A quite different sort of book this one, a book written with all the love and care of someone - Tom Tyler - who has spent a good part of his adult life in and around jigsaws, rather than that of someone, albeit a gifted amateur, who has come rather late to the craft.

The first interesting point about this book is that its purchase, from Amazon, was the first occasion on which I noticed that the Amazon price was not the best price on the street. On this occasion, we learned from a leaflet accompanying the Saturday DT that an outfit called Postcript would have supplied the book for something like half the price that Amazon required. To be fair, Postscript (http://www.psbooks.co.uk/) do seem to rather specialise in this sort of coffee table book for the discerning buyer. The sort of books which one suspects were made to be remaindered, with some obscure shop in some obscure town serving to offer them at what is described at the proper price and from which very few purchases are ever made. It would not even need to be open very often or for very long to comply with the laws of the land concerning sale price labeling.

But the main point is that the book has done what I wanted. I have learned something of the history of jigsaws, something of their manufacture and something of the worlds of jigsawyers and jigsaw collectors. A regular cornucopia of jigfacts.

I have, for example, been conditioned by having restricted myself, in large part, to machine pressed jigsaws, with the way in which the cutting dies are made (by hand) accounting for much of the regularity that I was talking about on the 1st. Saw cut jigsaws are much freer in their composition, also rather prone to the inclusion of whimsies which I find a little irritating. I like the regularity of the machine pressed puzzles. On the other hand, it would be interesting to see how hard I would find it to switch to the hand cuts. Would the whole pace & nature of the game change? Would one enjoy the various traps and pratfalls which the enterprising hand cutter had worked into your puzzle, traps and pratfalls which make cunning and subtle use of the subject image? Certainly, some of those illustrated in this book look as if they would be very difficult to solve. It would not do to be in a hurry or to be competitive.

Then I think that it would be fun to visit a jigsaw factory. But maybe that would take a bit of organizing. Maybe it would be easier to visit a jigsaw museum. So I ask Mr. Google about jigsaw museums to find that there are plenty of museums offering online jigsaws of their exhibits (see, for example http://www.liverpoolmuseums.org.uk. Clearly my notion of using jigsaws as an art educational aid is not very original at all) but none where the jigsaws are the exhibits. One would have thought that there would be such a thing somewhere. The sort of thing you might come across in Brading (on the Isle of Wight), or Yarmouth or Blackpool. I shall try to remember to keep looking.

The book goes on to explain that there is now a computer controlled contraption which enables one to cut a wooden jigsaw using high pressure water jets - the same sort of thing I presume which dental hygienists like to attack one's mouth with. Hopefully this will mean that one will be able to commission a jigsaw of more or less any image one likes, of more or less any degree of difficulty - without the expense of a hand cut. If one had a companion machine that could apply a digital image in a suitable way to a sheet of plywood one would be away. And I would hope that such a companion machine would be available, art shops having been able to transfer images to hardboard - thus avoiding the need for the glass which reflects - for thirty years or more. It may even be that the imaged boards that they produce are already of jigsaw quality, that is to say that the image will stand up to and survive the cutting process.

In the meanwhile, there are plenty of people out there who make their living cutting puzzles to order. So I shall spend a happy breakfast hour dreaming about the image that I shall have turned into a puzzle for some upcoming birthday. Shall I go for a photograph or a painting? Shall it be a landscape? Shall I tour the National Gallery to select a suitable image? In the case where the artist has fussed about the frame - Holman Hunt, for example, was apt to - would it be appropriate to include the frame in the image?

And so one might go on.

Remember, remember, the 5th of November...

Certain amount of firework activity hereabouts, activity which has been running pretty much steady but not large since Halloween.

Which brings to mind the idea, probably more fantasy than reality, than when I was a child one celebrated Guy Fawkes Night on Guy Fawkes Night, whatever day of the week that it happened to fall on. And one did not, small boys with bangers and urchins doing penny for the guy aside (some of these guys were quite elaborate in those days, well worth their penny), celebrate it on other days. I don't suppose this can be quite right as I do not suppose one would have celebrated on a Sunday, but I do believe there is some truth in it. Also that one detracts from the mystery of the event if one allows it move around at the whim of people who like to keep things nice and tidy.

That apart, I find that I do not remember all that much about childish Guy Fawkes. We lived on what was then a newish housing estate and the plot next to our house had been kept vacant against the possibility of the builder getting his paws on the field behind. A vacant plot which contained the odd sections of trunk of an elm tree which had been pulled down and which we used for the purposes of fireworks, generally with two or three other families. I do remember that the eating aspect of fireworks was more important to me than the fireworks aspect. While for my mother, sparklers were the thing, writing messages with sparklers. Marsh mellows on sticks were fun but not particularly nice to eat. Sausages were much better and I vaguely think that we might have wrapped potatoes in foil and cooked them in the ashes. This being in the days when we bought potatoes from the market on a Saturday from a chap who actually grew the things - and who did not bother to wash the earth off as thoroughly as is the custom nowadays. I wonder if we did twists and dampers and scouting things like that - a well made twist with well made jam being a fine thing on a cold evening? And that, is about the extent of my associations with Guy Fawkes. Maybe some more will come to me overnight.

We celebrated today in a slightly different way, taking our first meal out of the new era, selecting our local Wetherspoons for the purpose. Not too crowded, food served quickly and good facilities. On this occasion two steak and kidney puddings for £6.49. Chips not that great, but a very decent meal for the money; maybe even better value than McDonalds. Certainly easier to eat, as I find McDonalds a bit full of sticky yellow goo for rapid consumption. (The last time must have been when stranded at a filling station on the outskirts of Cardiff, maybe ten years ago).

Followed up by the first bit of DIY of the new era, a bit occasioned by the pull ring of my shiny new box file from Staples falling out. Generally speaking I find Staples stuff OK and as we have one in walking distance, I use it. Must have spent a fair bit on genuine HP ink there over the years, never having gotten around to using fake. But this pull ring just pulled out, rather than pulling the admittedly full box file out of its hole. On inspection, I find that the thing was only held onto the cardboard of the box by a rather feeble rivet. Poke around in the cold & gathering gloom in the garage to find that I do indeed have suitable nut, washer and bolt to replace the rivet. Drill out the hole in the pull ring and away we go. Pull ring now firmly attached. The only worry is that there are two box files and I am not at all sure that I am going to be able to manage the same nut, washer and bolt combination to do the same job on the other one. The trouble with just keeping a great heap of such things loose in a box: one can nearly always find one of what one wants, but finding two the same is generally quite challenging. That requires a visit to Screwfix.

Aide memoire

In reporting my recent perusal of 'Black Beauty' in the other place (October 24th), I mentioned what I had learned to be the obnoxious practice of forcing horses to hold their heads up with gadgets called bearing reins.

Since then I have been trying to work out whether the various horses which figure in the various costume dramas we watch here  - Sherlock Holmes, Poirot, Barchester Towers and their like - have been fitted with these things. The horses do seem to hold their heads up but they are never in the right position for long enough to check for a bearing rein. I suppose I am going to have to resort to the pause button - a zoom button being too much to hope for on our bottom of the range DVD player. Or do the various replay sites on the internet have such a thing?

The point being that this seems to be an excellent issue to stir up the costume drama world with. It may well be that the clerics of places such as Barchester did indeed insist on their horses being fitted with bearing reins but is it fit that in recreating such places for our evening edification, we should recreate this particular iniquity? It all all very well making actors smoke on the job (I observe in passing that a lot of Trollope's characters smoke a lot of cigars); they are consenting human beings. They can chose not to play the game. But this is certainly not the case for dumb animals.

Maybe I could interest the Badger Brigade in the issue? Give them something to bite on in the slack season before the cull gets under way again?

Maybe it would be worth campaigning to get the Board of Governors of the BBC to issue a code of conduct controlling the use of bearing reins in productions which they commission - an outright ban being perhaps a little millenarian at this time?

PS: with thanks to Mr. Google for the illustration. Does anyone know where it comes from?

Mediffairs

I share my pearls of wisdom on two matters.

The first concerns a drug which, for present purposes, may be called poppyparazodamiene, 30 portions of which were issued to me for use as required during my recent visit to hospital. As it turned out, I was fairly needy and was getting through my supply fairly quickly. So I started to worry about what would happen if I ran out? I had no idea how long the need would persist for but the prospect of being very needy was not pleasant. Now it is not the sort of thing that you are going to be able to get over the counter at Boots. Or at Lloyds for that matter. So I apply to my GP who kindly arranges for me to be given a further 100 portions and there is now nothing to worry about.

But being of a worrying disposition I manage to come up with something. My need is showing signs of abating and it is possible that I will not need any of the additional supply. But my understanding is that, in this event, I cannot usefully return the stuff to the pharmacist. His instructions are to send all returned medicines to the incinerator and I can see that in the great scheme of things it might not be worth his time to try and sort out the stuff which can safely be reused from that which cannot. So my worry is, supposing this stuff is expensive? Maybe even very expensive - I don't happen to think that it is, but it is always possible.

And my question is, given that we need to manage the potion bill for the nation at large, where should the price of the stuff bite? Is it enough that the GP, who is or is about to become the budget holder, worries about this, and if he decides that the potion costs a lot relative to the transaction cost of a prescription, he can always prescribe in smaller volumes? Is it right that I should be worrying about the costs of potions when I should be worrying about getting better?

My answer, is that it would not hurt for prescriptions to carry a price ticket. Those who do not care what they spend in this way will not be hurt and those who do care will be able to do so. This is, of course, quite different from asking people to pay at the point of delivery. Hopefully we have, in large part, got away from that and will not return, bullingdons permitting.

My second concerns the possibility of getting lost in the system and I spent my quality waking up time this morning thinking about I how would reduce this possibility.

Step 1, get the IT department to buy some decent work flow software. It seems quite likely that there is something available on the shelf, perhaps a spin off from all the billions poured into healthy IT by the Blair Brown team. The outfit called Filenet (mentioned in the other place on 20th October) used to sell the sort of thing that is needed.

Step 2, divide the hospital up into teams, with team leader roughly equating to consultant.

Step 3, make a rule that when anyone is admitted to the hospital for more than a passing visit, they are assigned to a team. That person is then the responsibility of that team and it us up to the team leader to make sure that the work, that is to say the patients, flow (systems of this sort not called work flow for nothing) through the system in an orderly way.

Software of this sort is very good at keeping teams up to scratch. At making sure, for example, that observations are made and recorded (in which connection, see 25th September). At raising exception reports. At escalating problems to senior management. Generally making sure that the flows are orderly.

Step 4, make rules for transferring someone from one team to another. Maybe another team at another location - this last apt to be slightly tricky as it is too much to hope for that the other location will be operating the same work flow software. Some sort of protocol which requires a positive acceptance from the receiving team before the donor team can sign off.

Step 5, make rules about who is allowed to do what to which records. So a member of team A is not, for example, allowed to tamper with key details of a patient assigned to team B.

Step 6, add some bits and pieces to do team maintenance. For team members and team leaders to come and go. Sometimes one can deal with this by talking of roles rather than people.

Over a liquid lunch, a work flow salesman might get quite enthusiastic. Use the system for controlling the management of patients in quite a detailed way. So for example, a request by doctor A to nurse B do procedure C on patient D might be expressed as a work flow. An item, rather like an email, which arrives in the nurse's in box. Authority, documentation, everything he or she needs to get on and do the job. And make the record afterwards.

In other process or transaction orientated industries all this is bog standard stuff. Been around for years. But has it percolated to the health world yet? All this being prompted by reports in the DT which suggest that it has not percolated as far as North Devon.

DT stuff

I share two items from yesterday's DT, one amusing, one annoying.

The first is the obituary of a scholarship boy from what was Southern Rhodesia, who made his way to the University of York where he got his first degree, then to London where he got his doctorate. Presumably a pampered and personable advertisement for our so enlightened management policies in East Africa. I think there were quite a few of them knocking around our universities at that time, shortly before I arrived on the scene. He then swanned around the groves of African Academe for a bit before winding up as a spokesman for Mugabe. In the process he seems to have forgotten whatever he may have learned about civics during his stay in England, aiding and abetting the unpleasant goings on in what had become the Zimbabwe of the end of the millennium, perhaps going the whole hog as he was not really trusted by the old fighters, of whom he was not really one. They probably thought that he was pampered and worse rather than pampered and personable. He died on the farm that he had managed to winkle out of all of this, having been gored by a grumpy bull.

The second is the front page lead about the use of the Liverpool Care Pathway in the NHS, a pathway which the DT seems to have a pathological aversion to. It is always finding opportunities to have a pop at it, insinuating that it is pretty much the creeping euthanasia of decent readers by the faceless bureaucrats of the NHS. No recognition that I have spotted that having a properly documented and supported process to help us die might be a very good thing. For us, for our relatives and for our carers. A process which puts the whole business on a much better footing than the lottery that it tends to be at present.

The DT was helped along in its popping on this occasion by the deployment of the Pathway being incentivised by all kinds of performance indicators, indicators which can look a little crass in this context. But who is to blame for all the indicators? Answer: the management consultants and privatisers for whom the DT has done so much to empower and enrich.

Sadly, another case of irresponsible coverage of important matters by a widely read newspaper which claims to be serious. Claims to be respectable fading. The good news is that, as far as I have been able to see, none of the other national newspapers are picking up on the story. Maybe it really is just a private pathology of the DT; a smelly eddy in the media pond, a smelly eddy without great significance.

Jigthoughts

In the other place, at the start of series 1, I gave some thought to classifying the pieces of a jigsaw according to their shape and to the way that they fitted together, but without regard to colour, finish, pattern or material or to their number. I think it is time to give this matter some more thoughts.

We restrict ourselves to two dimensional, one-sided jigsaws which are flat and which are of circular, square or rectangular shape.

We restrict ourselves to jigsaws the pieces of which are essentially quadrilaterals. We specifically exclude the jigsaws which might be made on the basis of a triangle or a hexagon rather than a square. Never come across either, which seems odd, so maybe there is some catch which has not yet reached me.

We consider just the interior pieces. Boundary pieces are subject to boundary conditions, rather different to those of the interior.

Property 1. A jigsaw has property 1 if the pieces may be considered to be making up a rectangular array of so many rows and so many columns, with exactly one piece at each position of the array. Circular puzzles might exhibit a rotary or polar version of this property, although I do not recall one which does; circular puzzles generally being cut more freely than rectangular ones. But nor do I recall a circular puzzle in which the pieces have been cut on a rectangular grid superimposed on the circle; the cut is always at least vaguely polar, with the result that the center of a circle is a singularity which is not shared with rectangles.

Property 2. A jigsaw has property 2 if each piece may be considered to have four sides and for each side to carry either a hole or a prong. With holes being of a shape to hold a corresponding prong, so it should not be possible to slide one piece into position against another; the prong has to be lifted into the hole not pushed. Prongs and holes usually having this not pushing property; the only puzzle which I can remember which systematically failed this test was the foreign puzzle noticed in the other place on 12th April.

Property 3. A jigsaw has property 3 if each piece has a prong-hole-prong-hole configuration. No exotics like prong-prong-hole-hole or hole-hole-hole-hole. The addition of proportion of exotics generally makes a puzzle easier to solve.

Property 4. A jigsaw has property 4 if exactly four pieces meet at every vertex. One makes fewer mistakes with a jigsaw with this property - but on the other hand the interest is fewer too.

Property 5. A jigsaw has property 5 if all the pieces are of a size. The area of the largest is not more than (say) two times the area of the smallest.

Property 6. A jigsaw has property 6 if there is exactly one solution to the puzzle.

Property 7. A jigsaw has property 7 if any one piece fits exactly one position in the jigsaw, without regard to the image. A stronger version of property 6.

Property 8. Property 8 is a combination of property 1 and property 2, with the added qualification that each piece is roughly rectangular and sensibly placed in its position. It's center of gravity is not far from the center of the position. The four prongs and holes are roughly cardinally pointed cruciform with respect to the center of gravity. Variation is permitted, but of a modest and demure variety; no extravagance or whimsy.

Rectangular puzzles from charity shops are generally fairly well behaved with regard to these properties.

The next step is to consider the extent that these properties are independent, one from another. Can a jigsaw have property A while not having property B?