Napoleonic & ECW wargaming, with a load of old Hooptedoodle on this & that


Showing posts with label Twaddle. Show all posts
Showing posts with label Twaddle. Show all posts

Friday, 15 May 2020

Hooptedoodle #364 - R-Nowt


I promised myself that I wouldn't upset anyone by airing my petty little thoughts on the global pandemic - after all, everyone is trying hard, doing their best, and some people are really performing absolute heroics in the public interest. And, of course, we have the top brains in the world concentrating on the problem, and surely we can be confident of the wisdom and the organising abilities of our elected leaders?

You may harbour some concerns about whether the leaders can actually hear the top brains, but I would hesitate to be unconstructive about the state of play.

Since I am starting to believe there is a very good chance that I may not survive this episode of world history, I'm beginning to lose touch with the reasons why I should keep quiet about it, but I shall avoid being rude about anyone in particular. This note is merely the musings of the sad little soul of an old mathematician, and I don't expect anyone to agree with me, nor be concerned about what I have to say - it's OK.

When something bad happens, reaction to it calls upon a lot of things. Some of these things will have needed some kind of investment of funds and effort before the event - preventative stuff. Identifying potential risks, putting in place rules and regulations to minimise the likelihood of a disaster; if we focus loosely on catastrophic building fires, as an obvious example, we might have implemented strict control of design and construction standards, of the safety of materials used, sufficiency of emergency exits and lighting, documented procedures for  using all these - and I mean maintained, tested procedures. We need to ensure that people who are at risk know what they need to do, or at the very least know where to find out quickly. There should be a good level of awareness of how to cope with an emergency, plenty of guidance information, and sufficient investment in rescue services and equipment is essential, obviously. The plans should be as complete as they can be, and should, if possible, be reviewed as part of the normal routine of making changes, and - if at all possible - they should be tested periodically. There's lots of this - far more than I can think of off the top of my head - things that have to be done in advance, just in case, procedures that have to be followed, if it happens, and trained, fully equipped rescuers who will turn up promptly and do the business in the regrettable circumstance of the bad thing happening.

All pretty obvious, really. I believe that in the UK we tend to concentrate on the end of the chain - we pride ourselves on our ability to perform well in an emergency, rather than in our talent for planning in advance to avoid problems happening at all, which is traditionally seen as rather unrewarding and maybe a bit negative. If the disaster comes, we film the heroes from the rescue services in action, we have a victory parade, we award medals, we may have a day of national mourning if we really have to. It's cheaper that way.

(1) it probably won't happen - let's hope not

(2) if it does, we'll make a huge splash about the heroics of the rescuers (quite rightly so, by the way - absolutely right on) - that's better politically and for uniting public support. The Daily Express loves that stuff.

(3) if there's a public enquiry afterwards, with a bit of luck we will no longer be in office to be held accountable or have to stump up with the money, or we may be able to spin it somehow to get off the hook

OK - that's all theory, and there's nothing particularly clever about it. That should be reassuring - we don't know for sure, of course, but we would certainly expect that things will be handled as well as possible by the people in charge.

I follow the daily bulletins in the UK media about the progress of our pandemic lockdown. It's been very harrowing, but thus far the course of action has been pretty much forced by events. We have been reacting - that's the bit we think we are good at. The next bit is going to be scaling the thing back, which will require decisions to get life going again, being careful not to have a new wave of infections as a result. This will take judgement - at which point my confidence in the leaders starts to leak - and, let's face it, we haven't done this before, so there is no manifesto to act out.


Like everyone else, I have to watch all this with as much hope as I can muster. A lot of faith seems now to be pinned on the Reproduction Number - R0, as it is termed, as an indicator. Sometimes, I find, mathematics can be reassuring - if you can measure something you can understand it - maybe even control it - so I spent a little time reading about this. Crudely speaking, as you will certainly know, it is a number which compares the number of new infections in a unit time with the number of people in the population who were already infected during the same interval. If you can get the value to less than unity, then that's good. We're not exactly sure what the consequences of R0 = 1 would be, but they would sure as hell be better than R0 = 10.

OK - it's not quite like this - we are considering rates of change here, so there is some calculus in there, and since we are considering variations in exponential growth functions there are a few natural logarithms too, but the spirit of the thing is that we have to divide one number by another, and try to get as small an answer as possible. This is obviously important, so I am paying attention.

The number on the top of this fraction - the new infections - is it known, then? How accurate is it?

Well, we only started widespread testing some weeks into the pandemic. We know about people who are in hospital, and we now know more about other categories - health workers, some other key workers, we are starting on residents and staff in care homes for the elderly (at this point I know more about the current situation in Scotland rather than the entire UK, but Scotland is normally the same as the rest of the country, maybe a few weeks behind). There are a whole pile of other people of whom we have no record at all:

* people who caught the virus and, as is very common, never knew - showed no symptoms at all, though they might well still be a source of infection to others
* people who became ill, and thought they might have Covid-19, but did not become sufficiently unwell to contact their doctor or go into hospital - they just quietly recovered, and thought they might have had it

The total of these two categories is certainly considerably larger than the people who have tested positive, so we have, at best, a measure of the size of the very small tip of an unknown iceberg.

Righto - what about the divisor, the number on the bottom of the fraction? - do we know how many people were already infected during the study period? Well no - of course we don't - given the tiny coverage provided by general testing, and the lack of understanding of how this virus behaves - how long are affected individuals infectious? - what is the true nature of the immunity which comes from recovery? We don't really know.

There are other details about what statistics we have on people who leave the infected population by either recovering or dying, but that is, once again, going to be a small number compared with people we can't identify and don't count. Let's not fuss about the details - the truth is that R0 is based on a mathematical function involving the comparison of one number we do not really know and another number which we also do not know. I do not find that comforting. We will be able to see if the number of people who die in hospital drops, and we can make some estimates of what has contributed to any change in that, but R0 looks like a dead duck to me, unless we know a whole lot more than we possibly can at present.

Overall, I'd be happier if someone would admit that R0 is no real help to us at the moment, and explain what else we can use. Next time the day's government spokesman makes a big deal about R0 dropping I shall be quietly confident that he is bluffing - there may be some number that he and his colleagues refer to as R0, but I don't believe it is anything which is of any real application to the public at large.

How about the entrails of a goat?





Wednesday, 6 May 2020

O Blog-ee O Blogg-er (Life Goes On)

This is just by way of a quick apology - I am having continuing problems with Blogger, and I wish to clear up any accidental breaches of etiquette.

Abergele Market, long ago - can you spot Desmond?
(1) A trifle to start with - the pictures which disappeared a few weeks ago have not come back, but it is reputed to be a known problem and Google are "working on it". If they come back, good - if they don't come back, I may replace the lost images. I may forget.

(2) There are certain bloggers who send comments to my blog and I don't get notified. I'm not sure why - it seems to be a regular feature of certain individuals - I keep an eye open for pending comments. If I've missed any, no offence intended.

(3) For some reason, I am only able to comment on some blogs if I use my own name, as per my Gmail account. If I have stopped commenting on your blog, it is not because I no longer love you, it is simply because I choose to use my MSFoy blog ID. Nothing sinister, it's just that if I use my real name I may get hassle from my ex-wife and the tax authorities of several Western nations. Also Max Foy's widow will be furious if she finds out he's dead.

(4) I can no longer follow any new blogs using my MSFoy ID - again, I am required to use my real name. This may be because my email provider is BTinternet - I've had occasional messages from Google that they cannot validate BT's mail server as having proper security certification - there was mention of some protocol or other (DMARC? - can't remember). Whatever, I'm not very interested.

I guess I have to be glad that it still works a bit. I am offered regular suggestions that I should try New Blogger, but I remember (with a shudder) similar pressures to move to Google+, and I am keeping my hand on my halfpenny.

I'd like to think this is the most boring post I've put here for a while - if you disagree, please don't bother to let me know.

Saturday, 25 April 2020

Hooptedoodle #361 - Home Physics Puzzle

This comes from a discussion I had with a friend on email - there is no trick to this, it is simply a bit of school physics, but I was surprised how much discussion it gave rise to. I thought I'd trot it out here - have a think about this...


A man who is working from home sets up an experiment with his children one afternoon, as part of their home-schooling. They like that kind of thing, apparently.

They place a boat in their (very small) swimming pool. The man climbs in, and takes on board a number of very large stones borrowed from the garden. When the ripples have stopped, his kids mark (very accurately) the water level on the side of the pool (not on the boat, on the pool side).

Once they have done this, the man very carefully drops all the stones over the side into the water. Again, when the ripples stop, the kids mark the water level on the pool side. We may assume that there is no loss of water through splashes, overflow, drainage, leakage or evaporation during the experiment, and that the kids can mark the level with unlimited precision.

OK then - when he dumps the stones overboard, does the water level in the pool

(1) rise

(2) fall

(3) stay the same

No prizes, obviously, just a bit of (supposed) fun. I won't publish any comments for a day or two, so as not to spoil the puzzle for anyone who cares - this will also allow me a couple of days before I have to reveal that there were no responses at all.

Splash!

Friday, 3 April 2020

Something for Self-Isolated Souls Aged from 12 years old to 150...

...and for those who claim to be working from home, and are interested in daft puzzles.

This all stems from my setting out some miniature soldiers on the attic floor yesterday (a procedure I found strangely stressful), and from a subsequent comment by Aly M, who empathised with my discomfort.

The challenge is - estimate how much HG Wells spent on his collection of toy soldiers!

Braw lads

I'd welcome thoughts and guesses on this - in terms both of UK prices in his day, and the modern equivalent. Let's set this in 1911-13 - that's a period between the publication of Floor Games and Little Wars. If it helps, there were 12 pence to the shilling in those days, 20 shillings to the pound. If you wish, you may calculate how many weeks it would have taken a typical agricultural labourer to earn the price of a toy soldier. Whatever. You have the whole of the World Wide Web as your playroom.

It would be useful to have a feel for Wells' rules and how he played his games, how big the forces involved might be, how many periods he played (or was it all just one vaguely "recent modern" period for him?), the contemporary prices of Wm Britains hollowcast figures, whether Wells might get a fancy discount for bulk (the more fanciful the ideas the better, here), where he got those famous firing cannons, and how much they cost - anything and everything that might be (even remotely) relevant will be welcome. Estimate for breakage-replacement if you wish. This is not an attempt to produce a lifetime sum, it's simply about the armies he had around 1911-13, and how much he spent on them. I assume that he bought his soldiers off the shelf, ready painted. To be honest, I'm not even sure what kind of soldiers he fielded, or what the "sides" were - illustrations I've seen look a bit like the Trooping of the Colours - not many trenches or light troops in woods - a lot of formal dress. All very correct and proper. This also applies to the players, of course.

Classic attic-floor view - note that this is an artist's impression, or is it an enhanced photograph?
Ignore his collection of scenery, I think, although if you wish to have a guess at that then please carry on. You should also ignore the cost of refreshments for his guests, though it would be instructive to consider what would have been appropriate. It might even give me some guidelines for a variation of the guest menu at Chateau Foy, when things resume, after the Armistice.

My entry point for this is that it's not something I know much about, either about the workings of Wells' rules nor the lore of the 54mm hollowcast soldier. A friend of mine, when challenged recently on how much he spends each year on his wargaming, proved that it is less than his wife spends on visits to the hairdresser (take notes if you wish). I'd be interested to have an estimate for how much HG committed to his rather niche hobby activities.

I haven't started on any of this yet, other than thinking vaguely what might be involved, but I did a little Wiki reading on HG, and was surprised to learn that he was certainly a bit off the wall for his day; a Fabian, a pacifist and something of a socialist visionary, he also had a very complicated marital life (if you are into that sort of research) - he'd have been better off sticking with the little soldiers if you ask me...

Wells working in the garden - now this is scary - imagine the feverish head-count at the end, and checking the grass-box next time the lawn is mowed
All suggestions welcome - the wilder and more far-fetched the better. If I get no responses at all I will have proved something (about myself, probably), but I'm happy to keep this topic open if there's any interest. I am certainly not an expert, so I hope to learn a bit here!


Thinking of soldiers on the floor, I remember that once, as a lad in short pants, I accidentally kneeled on some troops during one of my periodic battles (which would have included Zulus, WW2 US Marines, Foreign Legionnaires, Arab tribesmen, all sorts). I broke two Britains kneeling Highlanders - red jackets, white tropical helmets. This must obviously have been a single incident among many similar, but, apart from the early OCD evidence that I had these two identical figures next to each other, behind a flat metal Johilco hedge section, I recall that I was fascinated (though disappointed, naturally) at the time that they broke identically - they both lost the same leg - exactly the same fracture. This may have been the moment in my childhood when I decided that I wanted to grow up to be a madman.


This may be the moment when it all started to slide. It's also possible that the indentation is still in my kneecap, in which case I could maybe cast some replicas.

I'll check it out.

Sunday, 15 March 2020

Sieges: The Doofer and the Scale Paradox

It would be fatuous - probably even very irritating - to come up with some kind of useful personal spin-off from the current corona-virus situation, but it is a fact that, since quite a lot of things that I had planned to do are not going to be possible, then I am going to be forced to do something else instead. In the interests of preserving the tiny, ragged edges of what is left of my sanity I have an enforced opportunity to revisit things which have been shelved or passed over, and there will be any amount of time (if, of course, I am spared) to think about stuff.

Therefore it cannot be a complete coincidence that today's post returns to what used to be a tradition on this blog a few years ago - I shall begin with a lengthy digression. I, at least, will probably enjoy it, and it serves a useful secondary purpose in filtering out any unfortunate readers who arrived here by accident, and who are beginning to see what a huge mistake that was.


I always assumed that "a doofer" was just a saying used in my own family. My grandmother (the one from Preston) used the phrase to refer to any object whose real name she had forgotten, or simply didn't know. There was also a faint edge of intolerance in there - in my grandmother's world, which mostly was built around Dickens, Mozart, cats and Rich Tea biscuits, anything which had overtones of technology was an overhead - the sort of thing that some (common) technical person would know about. Thus, though the thing itself might be useful, the idea of actually understanding it was well beneath contempt. She had a doofer with which she lit the gas stove, and doofers which secured the stair carpet. Her life was filled with them.

Stove-lighting Doofer



Stair-carpet Doofers

Her brother, Alf, worked for many years in the tram (later bus) workshops at Edge Lane, Liverpool, and he also spoke of doofers. Originally, I believe, the term may come from the army - possibly WW1 - to describe something which was improvised, or fixed, or botched, and which would "do for now". [I checked my etymological dictionary, since that is the sort of thing for which I now have more time, and I see that the likely origins of doofer are pretty much as I thought, though the date is felt to be 1930s. That would surprise me if it were true, since Great Uncle Alf would never have adopted any phrase which appeared as late as the 1930s. Yes, this was a digression within a digression - we have nested digressions].


Gradually this evolved into a general term for something whose proper name you didn't know, and I am surprised at how widespread this became. It is bound to be out of fashion now, of course, but I recall that as my grandmother became older and more dotty there were more and more doofers around the place. In more recent years, my mother started calling almost everything "the thing-io"; it is a great comfort to be able to forget the real names of everyday objects - I can see this.

What were we talking about, again?

Oh yes - doofers. Well, you will be excited to read that I have taken delivery of a new doofer - it arrived on Saturday. I have been waiting for this doofer for nearly two years, and to be more accurate it is a prototype doofer.

Some time ago I commissioned the manufacture of some rather similar doofers for my medieval/ECW sieges. They worked well - they were, to be specific about it, firing platforms which could be stood behind fortress walls, to give standing room for guns or bodies of musketeers. I got my friend Michael at SLD to design and laser-cut them from MDF, enhanced a little with masonry-style engraving, and I made them up and painted and matt-varnished them, and they were good. They were doofers to help with problems arising from the eternal Scale Paradox in tabletop wargames (which, for reasons which I shall attempt to explain, reach their zenith in the arcane world of miniature sieges). At the time, I was also very surprised at the amount of criticism they generated.

Doofer to facilitate sieges on Medieval Walls - shades of "2001: Space Odyssey"?
And in action - a bit crude, but effective
The problem is, you see, that if you had attended a real medieval or Renaissance siege with your digital camera handy, you would not have seen any of my doofers in action. They are not part of the model-railway-style facsimile of a real siege, and quite a few readers reacted badly to this. I called them "gun platforms" or sometimes "buttresses", but really they were just add-on doofers to solve a problem arising from the Scale Paradox.

Before I get buried even further in this effort, let me insert a spoiler here, to explain that the new doofer I have received is a prototype of the same sort of device, but designed to work with Vauban-period walls. After adding the first-generation doofers to my ECW sieges, I realised that progress with my 18th-19th Century sieges would require the Mark II Siege Doofer. The walkways behind the parapets on my model Vauban walls are only 30mm wide, which is not nearly enough to mount a gun up there, without some form of extra support. I shall, I promise, come back to this after I have burbled on about the Scale Paradox for a bit. If you are still with me, you have my heartfelt admiration and gratitude.

My games usually take place on a hex-gridded table, which I have found helps greatly and keeps things simple. There is still an implied groundscale - my hexes are 7 inches across the flats, which is near enough 180mm. My default horizontal scale is (approx) 1mm = 1 yard/metre. This obviously varies for big battles scaled down, but that default is (approx) 200 paces = 1 hex, which is a useful round number.

I use 20mm or 1/72 scale soldiers, and for infantry and cavalry I use an age-old ratio of 3 figures = 100 men, so that my battalions normally have about 2 dozen men. The basing is designed to give frontages compatible with the 1/1000 groundscale, and it also tries to make the spacing of the miniature soldiers look about right for the kind of troops and the kind of warfare they represent. [Though please try to remember, Claude, that this is not the same as visual "realism" - a 24-man battalion is not at all realistic, however much the photos out of Charles Grant and Don Featherstone have come to shape our understanding].

Just to be awkward - another personal compromise - I have yet another scale on the go at the same time. My buildings are usually 15mm scale, which is about 1/100 - this is similar to the old TT model railway scale. The underscale buildings have a few advantages - they are cheaper, they have a smaller footprint, and they can be grouped into what seem to me to be more convincing villages. You can also, with time, get used to the look of the thing - the fact that a soldier would get stuck in the door of the church is a relatively unimportant matter when you are fighting Leipzig. I work on the assumption that a smallish village is marked by a representative cluster of slightly undersized houses - they are usually placed around the edges of a hex, so that a unit may be placed among them, and the houses themselves can be shunted about as necessary to make room for what is going on - the individual model buildings do not represent real individual buildings, and you can't take roofs off or put people inside. In the games I play, that is not necessary or useful. The important things about a village are its outline (and in a hex-based game that is an obvious concept, though non-hex players will still have a requirement to define the edges of the built-up area) and who is in it.

Anyway, you get the idea. On occasions I may choose to use 20mm-scale walls and hedges for my soldiers to stand behind, just for the look of the thing, but by and large this odd mish-mash of scales is now tried and tested and works well. Let's remind ourselves, that's

* 1/1000 horizontal scale, for ranges, moves, frontages, table layout.
* 1/72 (visual) vertical scale for the model soldiers - which is a given.
* 1/100  vertical scale for the buildings - which is simply a convenient compromise.

Now then. When we consider sieges this suddenly becomes more of a problem. The layout of a fort is not just a matter of appearance or convention - the lengths of the walls, the positioning and dimensions of the bastions and so on are set by rules which relate to the effective range of a musket (or whatever), and a representative model is no longer going to be fit for purpose unless it has about the right footprint. We now bump our noses quite firmly against the "look of the thing" problem - we can use 15mm buildings if we wish, but the big issue here is the Scale Paradox - our toy soldiers live in a world where a man is about 22mm tall, but the distances and the ground plan require a world where 1mm is 1 metre (or 2mm = 1 toise, if you insist). There - did you feel that bump on your nose? That's because the groundscale is one tenth of the visual scale. It always was, but it just became a problem.

For reasons which I really don't understand - I can only assume that the model designers had been through all this same reasoning before - the old Terrain Warehouse 15mm Vauban pieces that I use look OK with the soldiers, but the footprint of the various bits also makes sense in the groundscale I use. So it works in both senses (though obviously this must be a pretty silly-looking fort from the point of view of proportions, but it is silly in the same way as the soldiers themselves, so maybe that's what matters).

I've now reminded myself (again) that I don't really understand why this works, but it does. Further, it may not actually work at all - it might just be that I think it does. There you go - full circle - you set your games up to suit you, and I'll suit myself. That's probably where we came in. Before I finally put this note out of its misery, here's some photos of the new doofer. Since I am pleased that it is what I designed, that it works and is what I wanted, I shall get Michael to make me some more, and I'll make them up and store them away in the Sieges boxes. 

The new prototype Mk II Siege Doofer - assembled, painted and varnished
In position on the Terrain Warehouse 15mm scale Vauban wall

And here demonstrating how some big French guns may be deployed





Thursday, 12 March 2020

Hooptedoodle #357a - The Third World (contd)

Maybe this is a more general problem - here's the trailer for another of my very favourite films (if you've never seen this, I recommend it) - a French postal worker is traumatised by learning that he is to be transferred to Le Nord....


This movie, by the way, is the biggest laugh ever...

Wednesday, 11 March 2020

Hooptedoodle #357 - The Third World

A couple of days ago I was listening to BBC Radio 3 at breakfast time, as is my current routine; there is a show where listeners may text in suggestions for music selections. The host of the show (I suspect that on R3 they may still be "announcers") at one point said (announced?),

"I have received a text from Theresa, who is in Burnley, up there in Lancashire - Theresa would like to hear some Scarlatti..."

OK - no problem - there are probably a lot of people who don't know where Burnley is - or Lancashire, for that matter.

A few minutes later, the link was,

"I have a nice message from Tom, who is in Streatham, and today Tom is busy doing his accounts..."

She didn't say, "...Streatham, which is in South London...", presumably because everyone is expected to know where Streatham is. Funny that. It doesn't bother me in the slightest, but there is something a little retro about the episode. This is a national radio station, bear in mind. Faint echoes of Two-Way Family Favourites on Sundays on the BBC Light Programme, back in the 1960s. If Gunner Arkwright's family come from Rawtenstall, make sure that we mention that this is a long way from the Centre of Things - it's company policy.

There was no offence intended, obviously, but it is still an instinct on national radio - some gentle apology needed for reference to the Provinces (though, of course, there are a lot of new Tory MPs up there now, which must make a difference, you would think). Some reflected glory in demonstrating that the BBC is able to transmit to (and even has some kind of an audience in) the far-flung reaches of our Sceptred Isle.

Anyway, I had a laugh at it, and there is no harm done, but it reminded me of this clip, which I still find hilarious - apologies for the poor picture definition - best I could find.

Saturday, 29 February 2020

Hooptedoodle #356 - Another Wasted Opportunity

Last night I was clearing out the spam folder in one of my secondary email accounts, and I came across this message...


I see this dates from 2016 - goodness me! - just think, I may have missed out on a fortune. It just reinforces some recurring theme I haven't quite put my finger on yet, along the lines that big changes in our lives and fortunes might, at any moment, hinge on some unseen stroke of luck, or a message from a stranger.

By an astonishing coincidence, this spam folder contained quite a lot of messages like this - all from different people. A superstitious person might believe that this was more than mere chance. Do you think that, in some mystical way, I might be blessed? Since I would rather not dwell on the possibility of having missed out on several fortunes over a relatively short period, I am thinking that maybe I should treat this seriously, and consider resuming my research into developing a foolproof algorithm for predicting Lottery numbers.

I mean, it makes sense, doesn't it?

I do wonder what happened to that money, though - and it was a shame that the man's daughter was killed like that. And his wife. Tragic.

Why don't we all email Mr Daamba, and wish him all the best?

No...?

Tuesday, 18 February 2020

Rules - Turn Sequences

I've recently been working on some wargame rules of my own (yet again), and I seem to have developed a bee in my bonnet about building them around the turn sequence from the old WRG 1685-1845 rules, which in the past impressed me greatly. It is (or was, at the time I was impressed), unusual in that moving is the last thing you do, including the declaration of the first half of any charges to contact you wish to make. Thereafter, reaction to those charges, defensive retaliation, the completion of the charges and the actual melees take place in your opponent's turn.

I thought that was clever - I confess I never used the full rules as written, because I found them tricky to get the hang of, and there were far too many lists and reaction tests for my liking. Anyway, since the spark had now glowed again, I thought I should make a more serious job of understanding them properly, so that I could maybe use the turn structure in my new game - I have to say that the WRG's rules sometimes rely heavily on your spotting the subjunctive verb in Paragraph 417 to appreciate the full beauty of the logic. [Also, over the years I have skipped past "jezails" in the combat factor lists more times than I could estimate, and I still don't know what a jezail is.]

This, of course, is a jezail
Again, I have found this quite tricky. My new rules were suddenly full of morale tests that I hadn't wanted, there were coloured counters all over the place, to show where you were up to with keeping track of routing units, and, since the game would collapse in a heap if you did anything out of the correct order, I had written out the turn sequence as a checklist.

In a recent email exchange with a fellow bloggist - a game designer of some repute, let it be said - he offered the view that the turn sequence has to be capable of being carried in your head - if you need a chart then there may be something seriously wrong. He is right - I guess I knew this, but I needed someone else to say it.

Lightbulb.


I have - all right, regretfully - dropped the WRG bits, and my new game is looking slimmer and more like my idea of a recreation immediately.

What is capable of being carried in the head, of course, also depends heavily on how the old head is performing, and I am aware that the passing years have made me less patient in this area, but I prefer to think that I have become more fussy about how a game should be, rather than simply more stupid. Other opinions probably abound.


I was joking about this with another friend (I am showing off here, since this means I must have at least two friends), and we agreed that a wallchart for the turn sequence in chess would be

(1) White moves
(2) Black moves
(3) go to (1)

I could probably post that as a download on boardgamegeek - now there's fame.

Sunday, 9 February 2020

Hooptedoodle #354 - The Obstacle Course Game

This is rather a whimsical post - I wasn't sure whether to publish it. Maybe I'll delete it later.

Recently I've been corresponding with a friend about memories of childhood - especially about family get-togethers, in an age when it seemed everyone lived locally, and almost the entire family could be assembled from a small area. My friend and I had some laughs about social rituals, things that our families always did (and said, and sang), and about how the roles of various family members have changed. Since he and I come from different parts of the UK, it has been interesting to note the similarities and the regional differences.


Terraced street in Aigburth, some 10 years later than my tale
I got to thinking about the New Year parties at my grandparents' house, when I was a kid (that's my dad's parents, in Aigburth, South Liverpool). I think we only attended a few times, mostly because my dad would normally have fallen out with one or other of his siblings during the previous year!

The gatherings were large - a lot of people crammed into a small terraced house. They were good-hearted folk, in a tough, noisy sort of way. We must have been at that itchy post-war period when the working class had a bit more money, and everyone was becoming keen on what they saw as middle-class status symbols and values. It was all a bit competitive, and all of it was loud and in-your-face. My posh Auntie May had definitely "rose up", and she had married the boss/owner at her work, developed a new Hyacinth Bucket accent (see clip, below), sent her kids to private school and moved to the Wirral. In a strange, ambivalent way, the family were proud of her, yet envied her, and really hated it when she drove over for New Year in the new Vauxhall, even though they bragged about it when she wasn't there, and stood in the freezing cold to watch it drive away when she left.

Vauxhall Wyvern


At this time, everyone still had their feet and their roots in traditions that were, at the very least, Victorian. The family would come on various buses (only May had a car), some would walk, bearing biscuit tins filled with sandwiches, home baking, even bowls of trifle. When people arrived, all the big winter coats would be piled on the bed in the upstairs room at the front of the house (the smell of moth-balls was stifling), and everyone was issued with the regulation cup of tea to warm them up.

And, I guess, a good time was had by all. Occasional neighbours would appear (though the family was not noted for being very open to strangers), and eventually there were boyfriends of my various cousins (my cousins were legion, and they were all girls, now I think of it). If there were enough newcomers to the family throng, the inevitable party games in the kitchen after the tea-party would include a game called The Obstacle Course. I think my participation in this game came when I was about seven, after a number of years of non-attendance (politics). It was a game you could only play once, but when you could no longer take part you could be involved in the organisation and, of course, spectating.

Even by the prevailing standards, this was an unusually noisy game - it must have been audible a good way up the street. It was necessary to have a minimum number of first-time visitors to play - maybe 3 or 4. There was an element of initiation in it, to be sure. The family's taste in jokes and fun activities was always dominated by practical jokes, some humiliation, just a whiff of sadism, and giving a newcomer the opportunity to demonstrate that they were a "good sport", prepared to laugh at themselves - certainly to be laughed at by others. Maybe this was a test to see if they were going to fit in...

The Obstacle Course game required the identification of suitable (first-time) participants, and then my Uncle Harold and Cousin Joyce (who were the loudest of all) would take charge. The players would be led into the hall by Joyce, where they would be prepared for what was to follow, and while the course was set up. When everything was ready, they would all be admitted to the kitchen (living room), and would be shown an improvised obstacle course, which they had to memorise as best they could; then they would be taken out into the hallway again, and would be given some additional instruction on rules and so on. All the non-playing family members would be seated around the walls of the room - they would be the spectators, and later would vote for the best performer.

1950s clothes horse - we used to call ours a "maiden"
The course itself featured all sorts of household items, arranged in time-honoured constructions that you had to crawl under, step over, wriggle in-between - there was a horizontal broom handle, supported on boxes, to be stepped over without touching it, there were all sorts of cunning arrangements of sofa cushions, the wooden clothes horse, covered in rugs, a step-ladder, stacks of food tins - a lot of ingenuity came into play. And, of course, you would have to negotiate the course blindfolded, with plenty of instruction from Harold - and the spectators, obviously.

The participants (or "explorers" as they were termed) were solemnly blindfolded, and led into the room one at a time. Others went in ahead of me, and the noise was indescribable - the main object of the game was that everybody shouted at the same time - support, conflicting instructions, occasional sympathy, lots of banter. My turn came - I was completely blacked-out. I could hardly breathe, in fact.

The door closed behind me, and Harold said, "righto, Tony - come forward two steps - that's good - a little further - very good. Now, the first obstacle is you have to walk under the step-ladder without touching it, so stoop down a bit - right a bit - no not so much - good. Now edge forward slowly - good - a bit lower - right a bit more..."

And from the onlookers came a deafening uproar of "lower - not so low, turn left a bit - keep your elbows in" and so on.

After the step-ladder I was sweating profusely, but was pleased to have got past it. There was loud applause. Harold shouted, "OK - now you have to step over the bucket of water, so you need to turn left, where you are - righto - stop when I tell you - now - stop - two little steps forward - stop - now - you're going to have to turn sideways for this one..."

And so it went on. In spite of all the conflicting shouting from the sidelines, I did remarkably well, wriggling through sofa-cushion tunnels, tiptoeing through little mazes of tins, stepping over things, all without touching anything. At last, clear so far, I had to jump right across a little hearth-rug, without touching it. In a blaze of glory, I managed to do this. The applause was fantastic - I was as pleased as I could be. Then I was allowed to take off the blindfold, and I realised that the room had been completely cleared, apart from the spectator gallery around the walls. All my gyrations and extreme high-stepping and wriggling had been in an empty room. Of course I was embarrassed, but I got to join the audience and watch the last competitor in action, and I have to say it still seems to be one of the funniest things I have ever experienced. Cousin Pauline's new boyfriend, in his fashionable new shoes, keen to make a good impression, earnestly stretching his legs to impossible angles to avoid a broom-handle which was no longer there, all to the accompaniment of riotous approval.

Harold did a virtuoso performance as ring-master, no doubt. Fantastic noise, tears of laughter - it is sobering to realise that probably only about three or four of the people present are still alive - where did all that noise and camaraderie go? Of course, there are dozens of descendants, but they live in Australia, Singapore, Canada - even London. I have no idea at all about my extended family now - certainly it would be impossible to bus them all to my grannie's house - it might not even be possible to trace who they all are. Changed times.

I also remember that everyone that took part in the Obstacle Course that year got a prize. The bad news was that it was one of Auntie Laura's home-made rock cakes, left over from the festive tea, and quite rightly so, since anyone who had eaten one before would know to avoid them.


Saturday, 25 January 2020

Hooptedoodle #353 - Plastic Rot revisited

Topic 1 - Plastic Rot
 
There has always been plastic during my lifetime. 40-year-old kids' toys, Bic pen caps and trash out of Christmas crackers were the sort of things you found down the back of the sofa when you were looking for lost money, TV remotes, passport etc - I am sure that one day archaeologists will dig up a complete layer of plastic that defines our civilisation. Yet something has changed - about 10 years ago I bought  a small (but very handy) mp3 player which somehow deteriorated - it became sticky and disgusting, and eventually I threw it away. Over recent years, between us, my family have had loads of plastic hairbrushes, each of which lasted about a year before it became sticky and unuseable. I had a rather expensive pair of noise-cancelling headphones I bought in the USA - one day they turned sticky and then they broke. There have been other incidents - as it happens, all these items were black - a matt-finish material. A couple of cheapish travel alarms did this and (infuriatingly) the plastic parts of my current Pure pocket DAB radio are showing signs of doing the same thing - same problem - matt-black, rubbery plastic becomes sticky and unpleasant to touch.

 
Most serious of all, my wife's sunglasses - the ones she likes for driving - have started to go the same way. The frames are quite heavy - dark brown plastic - she bought them from Boots about 2 years ago for £60 or so. Sticky - if you wash them in soapy water it helps a little, but the stickiness comes back again.

What's going on here?

Have plastics changed? Are they now made from some cheaper or more environmentally friendly ingredients, which have a limited life? Are plastics now required to be biodegradable in some way?

I have always just assumed that plastic was forever - a belief which was shaken in the past by

(1) disintegrating 35-year-old Airfix soldiers - aargh!

It was the grey plastic ones that caused me grief
(2) a horrifying adventure with a vintage guitar I owned - this was a 1948 Gibson ES150 - the post-war version of the old Charlie Christian model. I got it cleaned up and restored, and it was a lovely old thing, but the original pick-guard (scratch plate) was made of bakelite - an ancient organic plastic made from resin and bone dust. This plate began to decompose, and it gave off fumes which would corrode steel (strings, for example) - it took me a while to work out what was happening, then I got a luthier to make me a replica plate out of modern plastic. Bakelite - occasionally I see antique radios or domestic items made of the stuff advertised for sale - don't touch them. Toxic.



Topic 2 - Jury Service Citation

Today got off to a bad start. I got a phone call about 9am from the care home where my mother lives. This is not likely to calm my nerves first thing in the morning, so I steeled myself for some bad news. In fact it was a fairly mundane call - my mum has been sent a citation to appear for jury service at the Edinburgh High Court in March. The home has obviously completed an Electoral Roll return for all their residents. They cannot deal with the citation themselves, since they have no power of attorney or authority to act on my mother's behalf, so would I please look after it.

Well yes, of course. The court office is closed over the weekend, but I'll contact them on Monday. It is famously difficult to get exempted jury duty, but anyone over 71 may choose to be excused. My mum is 94 now, and badly afflicted with dementia, so getting her excused should be straightforward. I fear that I may have to send a written request, which may require me first to submit the original documentation for my Power of Attorney, which is a hassle - mainly because of the eternal risk of the stuff getting lost in someone's in-basket. That sounds like an addition to Monday's do-list, so no worries there.

It also occurs to me that I could just ignore the citation, in which case we could have a brief moment of fame when they attempt to prosecute her for non-appearance (the Sunday Post would love such a story), or - better still - send her along to the court for jury service. That would be interesting.

No - on reflection, I'll phone up on Monday and see what we do next. Ho-hum.


Thursday, 9 January 2020

WSS Project - Figure Suppliers

Tonight I hope to finish off the current period of painting and re-basing, and then I'll spend a week or so trying to catch up on the small matter of flags. By tonight I should have completed a third and a fourth unit of cuirassiers for my 1702 Austrians. There's plenty more refurb work to be getting on with, but I'll take a bit of a break.

I cannot promise I have a completely firm idea of how these WSS armies may progress from this point, but there are a couple of basic principles I'd like to stick with if it's at all possible.

(1) The whole reason for buying these figures was that they provided an attractive shortcut into a period of which I have no experience. I intend to keep them "as-is" as far as possible - with just a modicum of touching-up where necessary. This is partly sheer laziness on my part (consciously so, since left to my own instincts I would have everything stripped back to start again, and I don't have the time or the energy for this) and partly a matter of respect - a wish to keep Eric's old soldiers in some recognisable form. It seems only right.

(2) I am determined (and if I succeed it will be the first time ever) to keep some idea of constant scale - I always tend to drift off into some kind of scale creep as I build armies, having convinced myself that 20mm = 25mm, or some such nonsense, and I always regret it later.

In pursuit of End (2), I have been checking out the availability of suitable extra figures. My units will be rather smaller than the original organisation, so - proportionately - I'll need extra command figures. The armies consist entirely of 1970s 20mm Les Higgins figures - and these are pretty small 20mm, too. I can get extra figures from Old John, including conversions and extensions to the original Higgins/PMD catalogue which he has produced, but in the interests of variety I have been looking to see what else will fit with them. After going through everything I could think of, the only makers I am left with are Irregular Miniatures (which are just a tad small, to be honest, but are OK if I mount them on Higgins horses), and Lancer Miniatures (which are OK for height, and have a bit of character about  them, but they are FAT, man - this is the Front Rank of the 20mm world).

On the Lancer front, I think they will probably be OK for isolated figures like staff groups (let us assume that the nobility were obese, then), and possibly odd cavalry command chaps, but generally they are less of a good match than I had hoped - also their horses are crude. I have to say that the cannons and carts look very nice - I'll probably make use of some of them.

A third unit of Austrian cuirassiers - these chaps are the regiment Jung-Darmstadt - the flag is in the pipeline; the odd man out is the trumpeter in the tricorne, who is an Irregular man on a Les Higgins horse. Yes, all right - he's a small man, but he's OK

This is the command base for the fourth regiment - Alt-Hannover. Once again, the flag is coming soon. The trumpeter is one of John's conversions of Les Higgins, the other two are Fat Lancers - not sure about them at all. They are quite nice, if you are into Noggin the Nog
Separate topic: I am disappointed to note I am having problems with metallic paints again. This is a recurrent theme for me - I have a long tradition of getting annoyed with metallic paints which won't cover, or don't shine, or lift when subjected to varnish, etc etc. I have the Foundry metallic paints, and have found them to be a bit feeble - I've tried all sorts of Vallejo and Tamiya and Revell and Testor paints. I used Citadel for a while - they were OK, though the pots went "off" rather quickly. For the last few years I've been using Humbrol acrylics - shades 11 (silver) and 16 (gold) - with no problems, apart from the hand-removing properties of the stupid little screw-top plastic pots. I have now replaced them with new Humbrol pots - different design, in the style of Foundry. The pots themselves are a lot better, but I fear that the paint recipe has been changed again. I spent a lot of time stirring, warming, swearing. The paint, I fear, is crap. I might as well apply yogurt to my soldiers. Thus I am back with my Foundry pots - they seem OK - maybe they've thickened up with being opened. I must revisit the Citadel range again - I have to admit that I don't really understand Citadel paints any more - nothing is just a pot of paint, it is a base colour, or a highlight colour, or some bloody thing or other. I must pay attention, and get some decent gold and silver paint in.

I was spoiled, decades ago - eons ago - by a brief flirtation with Rose Miniatures gold paint, which came as a jar of metallic powder and a jar of clear medium, into which you mixed the powder. It was fiddly, but it produced a magnificent finish - never seen anything as good since. Anyway - persevere.

Flag work starts tomorrow.

Thanks again to Old John, who has been heroically helpful with links and uniform sources, and to all others who have offered help and advice.    

Saturday, 4 January 2020

Hooptedoodle #352 - In Search of the White Stag


A few weeks ago I was recounting a daft old story for the benefit of the Contesse, and I enjoyed it greatly - though the Contesse did not say much about it, come to think of it.

I'll give a short version of the tale, mostly to fill out the post a bit.

The Original Tale

One Saturday morning in Spring, long ago, it seems I had something of a falling-out with my wife of the time - not an uncommon event, to be sure. On occasions like this, I sometimes used to go for a drive on my own, into the Highlands (I lived in Edinburgh at the time), to calm down. I can only add that traffic was lighter in those days - nowadays I would get stuck behind a caravan, and it would not calm me at all.

Citroen BX - this was so long ago that cars were monochrome
I remember the car I made this particular trip in - it was a Citroen BX - the second of three Citroens I owned. The reason I liked Citroens was that one of my sons used to get very travel-sick when he was a little boy, but he never got sick in a Citroen - something to do with the clever hydraulic suspension, which gave a ride like a hearse. The point is that this car dates the trip pretty accurately to 1988 or 1989.

Loch Lubnaig
On these trips I mostly used to head off towards Stirling - I was a big fan of the collection of vintage sports and racing cars at Doune - now all sold off and gone, alas - and I visited there regularly. On this occasion I headed north-west through Callander towards the Trossachs area. The A84 takes a twisty run along the shores of Loch Lubnaig - we may argue about where the Highlands really start, but this is good enough for me. It began to rain very heavily at this point, and when I got past the loch, as far as the village of Strathyre, I decided to stop for some lunch. There was a pub in the Main Street - I have always thought that Strathyre is a satisfyingly wild-sounding name anyway, so what could be better than to have a warming lunch in a Highland pub?

Strathyre Main Street (the A84) - looking south
I parked on the wide pavement outside, and went in. It was very dark. There was no-one in the bar. No log fire, nothing. As my eyes got used to the gloom, I observed that there were McEwan's tartan towel mats on the bar-top, such as I had not seen in use for maybe 10 or 15 years. I also noticed that I could smell the plumbing very distinctly. I assumed someone would appear soon, so I had a look at the old photos on the walls - grouse shoots from many years earlier, stuff like that, and I became aware that there was some evidence of life in the back room - so I knocked on a door and went in. Two locals in filthy overalls were playing pool - they seemed to have beers, so that was a good sign, I thought. When I entered they stopped playing immediately, stepped closer together, and approached me - quite aggressive - a bit like a phalanx. I backed off a pace or two.

"What are you wantin'?" asked one of them - I am ashamed to admit this, but the man had a glass eye, and I was so fixated by the idea that it must have given him problems playing pool that I was put rather off-balance. Also, alas, I wasn't quite sure if he was speaking to me.

"Er - I was looking for the landlord..."

"How? [Why?] Who are you, like?"

At this point I wasn't very sure, to be honest, but I explained that I was just a customer. The barman appeared in the room with us.

"This guy's looking for you," said Glass Eye. "He stopped us playing."

"What's the problem, then?" said the barman.

Fearing that this wasn't going very well, I went back into the bar with the barman, who took up the regulation position behind the taps.

"Are you wanting something?"

"I was wondering if I could perhaps get something to eat? Some lunch?"

"Lunch?" - perhaps I'd unwittingly suggested something indecent. "We've got crisps."

"You couldn't make me a sandwich or something? Any pies?" - as I said this, the word salmonella appeared like a subtitle.

"Crisps." The barman never blinked, I noticed.

"Erm - could I have a cup of coffee?"

"Nah - the machine's broken. I can sell you a beer..."

"What have you got on draught?" I peered into the darkness.

"You can see what we've got - the taps have signs on them, with the names of the beers."

"Oh yes - sorry - can I have a half-pint of Guinness?"

"It's off."

I was suddenly quite scared - I turned on my heel and ran out. I was delighted to get back into the rain and the fresh air. So much for my Highland idyll - I turned the car round and drove straight back to Edinburgh. At least when I argued with my first wife I knew what I was getting into.

I've always thought my Strathyre Lunch could have made the basis of a good mystery story - the stranger who disappeared. The man who was ritually murdered because he asked for lunch - the police never bothered to investigate, naturally.



Subsequently

After telling the story to the Contesse, the other day, I decided I would do some Internet poking-about, and see if the pub is still open. I forgot about the matter for a couple of days, but this morning I remembered, and I find that the pub - at least nowadays - is The White Stag. It looks quite nice, in fact - I'm sure it's been under new management for decades now. While I was surfing, I came across a bad review of the place on TripAdvisor - pretty spectacularly bad, in fact - and I came across a pretty heavy response from the current owner - I attach them here, in case you find them as entertaining as I did.



Maybe my mystery story is still a possibility - I'm sure the man with the glass eye would have sorted out any trouble-makers - I hope standards have not dropped since 1988.

Of course, we didn't have scope for giving bad reviews with such high visibility then - in those days you had to look people in the eye - real or fake - and deal with them. What an impoverished world it was, now I think about it.

Here's a bit of Jimmy Shand to provide some closing music - serves you all right. Have a good New Year anyway.

Friday, 15 November 2019

Hooptedoodle #350 - Strategy for Catching a Bus


This morning I was half-listening to the radio, and there was a phone-in discussion going on about people's private rituals - things they do every day as part of their lives, in that strange cross-over area where planning and commonsense checks start to shade into superstition and even obsession.

There were a lot of predictable items - one guy plays football in his local Sunday league - he always bends down to touch the grass as he walks on to the pitch - this is because his team once had an unexpected win in some competition or other, and since then he has come to believe that if he fails to touch the grass as he walks on then things might work out badly. In other words:

(1) it's become something he does on a regular basis

(2) it might do some good - OK, maybe unlikely, but it does no harm, so the safe bet might be to carry on doing it.

We probably all have a few of these wrinkles, though we might choose to claim that there is some rather more straightforward explanation. I always carry my penknife and a couple of guitar picks in my left-hand trouser pocket. I know where to find them, I can tell straight away if I've forgotten to pick them up from the tray on the bedroom chest of drawers - it's OK - it's a habit, but it's conscious organisation. You bet.

I knew a fellow years ago who played soccer to a decent amateur standard, and he always used to wear his "lucky" vest under his team jersey. He would claim that he was not superstitious, but panic would arise if he found his mother had this vest in the wash on match-day. The vest, by the way, was a total wreck, he had been wearing it since school. It was a relic.

When I was a kid, my dad, when he closed the front door, would tug the lock 10 times to check it was locked. If anything interrupted this procedure, he would start again. One morning (to my ecstatic, though secret, delight) he broke the lock. He would have maintained that he was checking the lock was secure, to keep his family and his possessions safe. Other opinions did exist.

Anyway, to the point. I was reminded this morning of a little conundrum that bothered me for years - not because it was a problem, but because it seemed there was an obvious need for some sort of simple strategy and - though you would think that such things were capable of numerical analysis, I never really managed to think it through.

Let's go back to the 1980s. At this time I lived in Morningside, a suburban district on the south side of Edinburgh, and I worked for a financial institution, whose offices were bang in the business centre - near St Andrew Square.


Each working day I would set off from home on my walk to the bus stop. It was about a mile to the bus stop - for the last half mile of this walk I had a straight view down to the main road ahead, crossing at right angles, where the buses I needed would pass from right to left.

These days the Edinburgh buses are a different proposition altogether - they have computer displays at each stop, which show you which buses, for which routes, are coming, and when they will be there. Everything is monitored. In the 1980s, the best I could do was to have a copy of the timetable on the notice board in the kitchen - I knew the times by heart, of course.

The problem was this last half-mile, during which I could see the bus route in the distance.  Now - a quick ponder on the nature of bus travel:

Suppose the buses ran every 15 minutes at this time of the day - officially, there might be a bus from my stop at 7:30am, 7:45am etc. Now, the traffic was heavy on working days, and the buses did not run on time - this was not any kind of symmetrical distribution - since the drivers got into trouble if they were early (because passengers would miss the bus), the buses would tend to be late. If I left home at 7:05, say, and it took me 20 minutes to walk to the stop, I would arrive five minutes before the 7:30 was due. Thus I might catch the previous bus, if it were running late, I might even, on rare occasions, be in time for the bus before that one, if it was very late indeed. Failing this, I should be in time for the published 7:30, though it could really turn up at any time after 7:30. The safest approach was to just assume that there was an irregular stream of buses, and that their arrival was pretty much random.

Right. So about 10 minutes after leaving the house I would get to the point on my walk where I could now see the buses passing, in the distance, and I would be able to see them from that point on. If a bus passed, I might be able to hazard a guess what official time that bus was supposed to have arrived, but it was not a particularly useful thing to think about during the final ten minutes' trek to the stop.

When I was still half a mile from the stop, if a bus passed, up ahead, then I would just shrug it off - it wasn't a bus I should have been on, the behaviour of subsequent buses was not affected in any predictable way. As I got nearer and nearer to the bus stop, this started to get more pressing; if a bus passed when I was, say, a hundred yards short of the stop then that would be a bit irritating, since a quick dash would have enabled me to catch that one. So the passage of buses at the end of the road became more important as I got nearer to the stop. Obviously, if a dash of a hundred yards would help, I could do this dash at any point during the walk, but that's not the instinct. What the dash might protect me from was not so much the risk of being late (since I should have plenty of time to get to work, and since getting earlier to the stop would simply put me into an unknown (earlier) bit of the sequence) - what I was protecting myself from was the frustration of having missed a bus when it was within my power to do something about it. This last bit is important.

Of course, I could just leave earlier, but that doesn't really change the unpredictability, or I could run the entire mile, which is not ideal if you are wearing a suit and office shoes, and maybe a top-coat, and maybe carrying a case - especially if you are going to spend a bus-ride jammed onto the lower deck - standing room only.

In practice, every day I would jog the last quarter mile - I felt better that way. Then, if I just missed a bus, I would feel that I had tried. I never jogged any previous quarter mile on the way there, because at that distance it doesn't seem like the correct thing to do.

None of this was ever really a problem - I can't recall ever being late for work. What bugged me was the suspicion that deciding to jog, every day, at the point where panic was beginning to set in felt a bit like dumb behaviour. There is a mathematical problem in which a man cuts diagonally across a square field, and a bull in the field charges at him from one of the other corners - it always heads straight towards him. The problem is to identify an equation for the path of the bull, and identify the limiting conditions, but the important, inescapable truth is that the bull is so damned stupid that it fails to realise it can catch the man by taking a short cut - taking a straight line to head him off rather than always just running directly at him.

I always had a feeling that I should have had an advantage over the bull, but it didn't feel like it.