The Man Who Killed Pythagoras – and other tales

Pythagoras, indicating the tricky diagonal

I’ve recently been involved in a number of Real Life issues which have left me very little time for any hobby-related activities, but I have managed to spend the odd moment reading other people’s rules, and scribbling and pondering ideas – some of them very old ideas, it has to be said.

I have banged on about hexagons and their pros and cons at great length in the past, and am confident that I don’t have very much more to say on the matter – you would think...

In one of my odd moments, the other day, I was recalling a series of debates that I had with a few friends – a very long time ago now – in which we considered gridded miniatures games and their advantages, but which mostly served as an excuse to drink beer. We agreed, very early in our discussions, that the most innocent comment any of us had made on the topic to date was credited to our resident optimist, Alan Low, and it went along the lines of:

“It is much easier to consider the merits of hexes if you can rise above all the prejudices and sacred cows which they seem to upset.”

Yes, Alan, we said – but you can’t really separate these things – the problem is that the biggest single disadvantage of hexes is that people hate them. Whether that is justifiable or even fair is beside the point – if HG Wells had been pictured with hexagons scribed on his floor then no-one would worry about it. As things stand, hexes are an affront to everything which is cherished in miniatures gaming. Worst of all, they are associated with BOARD GAMES, which are the greatest affront of all. We are, after all, talking of orthodox religion here.

We also agreed that the only acceptable plea we might make on their behalf was that Joe Morschauser was famous for gridded games – though I believe that at the time Joe was regarded as less Old School than he is now. His game was generally seen as a harmless eccentricity, and not proper wargaming.

Morschauser, of course, used squares. Squares are easy to draw, and have an ancient precedent in the chessboard, but for wargames they have some inherent snags, the very largest of which is Pythagoras. Orthogonal moves of 1 square are fine, but a diagonal move of 1 square is 1.4142135 (etc etc) times as far. Some games get round this by prohibiting diagonal moves or combats – somehow, units which are adjacent to each other along a diagonal cannot see each other – or, as in the De Gre/Sweet game, the square root of two is taken to be a rather more convenient 1.5. That certainly helps.

A to B is easily seen to be 4 hexes

Hexes are not easy to draw at all – even with an accurate template, you can get a gradual drift with accumulated small errors, so it is necessary when marking out a hex table to have copious guidelines and preliminary sketchings. They do have the advantage of six-fold symmetry, and they get rid of Pythagoras, but many gamers object to the fact that they distort straight lines. You can either lay out your hexes so that there are straight columns going across the table (like my own hex-based games) – in which case your units may advance in a straightforward manner (literally), but do not line up side by side very neatly – or you may have the straight columns running sideways across the table (like Commands & Colors) – in which case you may form exemplary lines of battle, but your units advance in a rather odd zig-zag.

In fact both these issues can be solved visually at a stroke by having the hexes a good bit larger than the units, so that you can place the units off-centre and smooth out the battle lines and the marches.

We rambled around this subject through many beers, enjoying the scenery but not really deciding anything, and then one Sunday morning Pat Timmins rang me and announced:

“I may have just killed Pythagoras.”

Pat had been applying square vinyl tiles to his kitchen floor – in a very bold combination of navy blue and white. His wife objected to the basic chequer-board configuration because, she said, it “gave her the buzzings” and seemed likely to promote epilepsy. He had tried various alternatives, and at one point experimented with alternate rows offset by half a tile, like this:

He realised that such an arrangement on a wargames table would allow movement in six directions, and was in fact a sort of hexagonal arrangement without the hexagons. Judging distances, for example A to B in the illustration, was not quite as intuitive as with hexes, but was still possible with a bit of methodology (I reckon AB is 5 squares distant).

We were unreasonably enthusiastic about this – perhaps we could pass off our offset squares (or “squexes”, as Pat called them) as a sort of logical descendant of Morschauser’s game, and overcome some prejudices. The next non-development was that someone suggested that the squares should not be squares but rectangles with sides in the proportions of √3 to 2, which would even up the six-fold symmetry so that it was a proper 60 degrees all round. It made the table layout closer to natural hexes, but made the board look even more distorted – at this point, we actually preferred normal hexagons, which put us back where we started. So we eventually decided that squexes had had their brief moment, and resigned ourselves to being outcasts in the wargaming fraternity with our conventional hexes.

Glinski's game - note the 3 bishops

Also on the topic of hexes, I invented hexagonal chess in about 1970. My excitement was tempered more than somewhat when I discovered that there were already in existence a number of varieties of hexagonal chess, and that my own new game had been previously invented by a man named Glinski. This was useful, since it allowed me to drop the idea and move on to dabble with something else. I expanded Glinski’s game into a 3-sided version. There are 3-sided chess games now, but mine used a board with a full hexagonal grid (most of the available games now use distorted squares) – the board was a little larger than the normal (normal?) Glinski board, and the 3 sets of pieces set up in alternate corners.

It looked spectacular, but it didn’t work very well. Early experiments revealed that a game of this type for 3 players brings some interesting problems. The first is order of turns – if red plays white into check then white has to respond immediately, which reverses the turn cycle if it was in fact black’s move next.

More fundamentally troubling is the very nature of 3-player strategy. It is very difficult to have a game in which each of the players is attacking both of the others – it makes more sense to have two gang up on the third, and then double-cross each other at the end, which gets you into all sorts of negotiation, time-outs for diplomacy and other stuff which we decided it was simpler to just ban. No chat, we said – no sign language, no secret notes left in the bathroom. This left us with a game in which the only possible recommended strategy was a passive opening - allow the other two players to attack each other and weaken each other. If all 3 players adopt the same strategy, of course, you get a very strange non-game. You may feel free to draw your own parallels from history on any or all of these.

A very smart looking 3-sided chess set - mine was different from this,
since it used the Glinski layout of pieces, and  the playing board was
a rather larger version of Glinski's

So we gave that one up as well, though we did briefly consider 3-sided soccer on a triangular pitch, but abandoned that very quickly, not least because we could not agree how the offside rule would work. We did, however, think that the winner might be the team which conceded the smallest number of goals.

How very silly.    

Alien Life Form

What are you doing in my garden?

The wet summer last year and the generally odd weather so far this year have had a marked effect on our garden. The most obvious excuse we can offer in our own defence is that there has been reduced opportunity to get out there and do something about it, but the damp has produced changes in the lawn, a lot of moss, almost uncontrollable weed growth and these things, as seen in the photo. The biggest is about 6 inches tall, but they have appeared very quickly, so no-one knows how large they might grow if left to get on with it.

We had a large tree cut down a couple of years ago, and I suspect that these are the result of the root system starting to rot away. Anyway, there's a lot of them (the tree roots, of course, will be under most of the garden) and I've never seen them before.

I don't think we'll be eating them. It's unnerving when your garden turns into a science project. Damp and decay - theme of the month.

VwQ – Plus Point – Simple Treatment of Casualties

A running commentary on my growing collection of fixes and tweaks for the Victory without Quarter rules for ECW/30YW games may give the wrong overall impression of my opinion of them, so I thought I might offer a very brief moment of applause for a change, to balance things up.

In my previous post I made vague reference to a “list of likes and dislikes”, by which I judge wargames rules as they come along. One thing I am not fond of, my friends, is any form of separate, hand-written record of casualties – especially of the early WRG variety, where it is necessary to record losses as the fractional parts of a figure – i.e. in actual men. The great big chart tells you that 14 figures throwing bits of muck into the wind on a Thursday have disabled one twentieth of a figure. Result! - amend your roster sheet - where is it? - is that it over there? - no, on the bookcase, under your reading glasses?

Keep adding the bits up and – if you live long enough – in time this will accumulate to a complete figure, and you can remove him, and start to tally the fractions all over again. We shouldn’t make fun of this – it was (and may again become) the state of the art, but you can really see why WRG replaced it with the much preferable arrangement where a roll of 4 or a 5 might kill one figure (H) and a 6 might kill two (HH - YES!). Much more like the thing. More like a game, rather than a book-keeping exercise.

I do not care for anything which detracts from the immediacy of the wargame, or which takes the eye and the attention away from the action on the tabletop. I also very much dislike pieces of paper which clutter up the battlefield – why do we fight with miniatures if it is not for the spectacle? My late friend Alan Gallacher used to impose a spot fine of 1 non-staff figure – to be chosen by the opponent, for every offending piece of litter on the battlefield – you may regard this as extreme, but a good-humoured application of this house rule made a great difference once everyone got the hang of it. And litter, by the way, included reference sheets and rulers as well as plastic cups, beer mats, mobile phones and so on.

All this means that I really like the Victory without Quarter arrangement for calculating and tracking losses. A unit attacking another unit causes a number of “hits”, and 3 is the magic number. For every complete 3 hits caused in a single attack, the target is given one casualty marker, which they cart around with them thereafter. Any odd hits left over are ignored, insignificant, forgotten about and not carried forward. Which means that, quite often in VwQ, a sincere and wholeheartedly delivered attack may gain only one or two hits – nice try, but no marker. Perhaps next time? There is also a special rule for artillery - any hits by artillery, even if insignificant in the sense of not gaining a marker, will frighten the recipients sufficiently to require a morale check. Nasty stuff, artillery.

When the number of casualty markers for a unit becomes equal to the number of bases, the unit is eliminated. We do not care whether they are all dead, or disarmed or simply discouraged – they are no longer with us.

Just the sort of uncomplicated arrangement I like.

...so you lose eleven-twentieths of your bishop...

Topic B

On a completely different tack, I had a gentle rebuke from my new car yesterday. I am still getting the hang of what it will do. I recall that my relationship with my old truck was similar when it was new - I accumulated so many mental notes to sit down with the owner's manual and look up things that puzzled me that eventually I just did it, and I learned a lot. This was quite a good approach, I think, though "approach" might imply more formality than was really the case. If there had been any underlying reasoning - which I doubt - it might have included the following themes:

(1) Owner manuals are not the sort of thing you read right through for entertainment. Brain-death will certainly follow.

(2) The manual will often refer to a whole range of models, plus variants, and thus tends to be a bit on the generic side - after you have read the 25 pages on the optional in-car entertainment system you find that you don't actually have it.

(3) These cars are invented by clever people - they must be pretty intuitive to drive, right?

(4) ...right?

(5) Real men do not read instructions before they act. In the noble tradition of (I think) Bugs Bunny, it is not actually necessary to learn how to land your aeroplane until after you have taken off.

(6) Etc.

And so, encouraged by my previous success with this so-called approach, I have gone about things in the same way this time. I've had the new vehicle for some 4 months now, and I still don't know why the heater will suddenly blow hot air at me when the outside temperature is 25 deg C, or what that weird orange dashboard light that looks like a pineapple means, or why quite a lot of people flash their headlights at me at night. Must check that, I keep saying to myself.

One of the reasons I behave like this, I am beginning to suspect, is fear. A primitive, superstitious fear of something which is cleverer than I am, and which - unlike me - is getting cleverer every day. The new buggy is the first one I have owned which will automatically switch on lights or wipers when it thinks you need them. It's quite fun, actually - feels like something of a luxury - but my initial reaction, before I became accustomed to the idea and forgot about it, was to wonder what particular problem this was solving. It is not difficult to switch on your own lights, as I recall, though on occasions you might forget to do so. Is the sensor which now makes the decision on my behalf just one more thing to go wrong? What if I get used to having my lights look after themselves and one day drive a vehicle which doesn't do this? Ultimately, am I more or less of a potential danger on the road? Hmmm.

I'm still a bit dubious about cleverness for its own sake. I embrace the ancient urban legends about an automatic emergency brake which, allegedly, was fitted to Mercedes' E-Class, and would occasionally decide arbitrarily that someone was having an emergency when in fact he was driving at 110 kph along the autobahn, chatting to his wife about the neighbours' new gazebo. And then there was the nameless experimental audio system which was designed to turn up the volume when it sensed that the background noise in the car had increased, which - again, reputedly - in some of its early versions became dangerously confused when passengers began to shout to make themselves heard above the music, and cranked the level even higher...

Yesterday my car played a joke on me. I believe it has recognised my basic insecurity. As I was driving home from visiting my mother, enjoying a rare moment of fine weather, it suddenly began making a chiming noise at me - very like the noise you might sometimes hear at an old-fashioned railway crossing when the gates are closed. No warning lights, no apparent problems, just this noise - and, since these things are built by clever people, you just know that this is not likely to be good news. Has the oil pressure zeroed? Has something awful happened to the hydraulics? Has the lambda probe (or some other dread gizmo) gone faulty, and the engine is about to shut down to protect itself? How much is this going to cost? Does the warranty cover labour charges? Is there, in fact, a train coming?

I got home without incident, though with further intermittent chimes, and was sitting in the car, worrying about it, when my wife arrived. She knew instantly what the problem was - her Volkswagen does the same thing. The car had sensed the parcel I had placed on the passenger seat, and when I went around corners it complained that this passenger it had identified was not wearing a seat-belt.

So that's all right then - but it might have given me some visual clue, you would think. The point is made - I shall show more respect in future. It is watching me.

What?

   

Degrees of Abstraction

Proper Old School - the early pioneers were all different sizes, as you see

One of the characteristics of Old School wargaming, as we grew up with it, was that everything appeared on the table. You want skirmishers? – no problem – there they are (mind you, the rules don’t work too well for them, and it takes so much time to manoeuvre them that we normally ignore/forget them after Bound 4). You want a honking great model of La Haye Sainte on the battlefield? – there it is (yes – agreed – it takes up the same space as the city of Brussels on the tabletop, but just look at it, and you can get an entire Division in the farmyard, too).

As we all got more and more enthusiastic about reflecting every known (or suspected) aspect of warfare in the game (mostly Napoleonic in my case, and the words National Characteristics still cause me to shudder), so we found it harder and harder to finish any of our games. Speaking for myself, my growing interest in looking for new approaches and greater pragmatism came from my frustration at finding that the widely accepted, latest forms of my hobby didn’t actually work very well. I remember being embarrassingly close to tears trying to get to grips with the latest version of Halsall & Roth’s rules (as used in the national championships – I only bought the very best...). I realised that this was no longer fun – at least not to me. I became very interested in the reasons why board war games seemed to work better, without people coming to blows, or taking their troops home in disgust.

Many years later, after my wargaming sabbatical, I got myself involved with more modern rulesets, and a lot of what I read made a whole lot of sense. Dr Mustafa said that in a big wargame it was impracticable to fuss about with skirmishers, for example – it was a distraction, something which in any case would be beneath the attention of an army commander. In his Grande Armée rules, the idea was that, surrounding the main columns and other formations on the tabletop, there were invisible little clouds of light troops, scrapping away. They were abstracted – a new word for me in this context then – and only existed by implication. They appeared as adjustments in combat calculations, and as “SK” numbers associated with the parent units. This seemed a more businesslike approach, though I did have a few slight traditionalist pangs. Just a minute – I actually enjoy fiddling with skirmishers – and what about all those lovely voltigeurs and people I’ve painted and cherished? What are they going to do? There does seem to be a slight tension here – if we agree that a particular style of skirmishing was an important characteristic of the Napoleonic Era – something, in fact, which served to make it different from the Seven Years War – is it OK to remove Napoleonic skirmishers from the miniature battlefield?

Hmmm. This wasn’t as easy as I’d hoped.

Out of all the reading, scribbling and reconciling necessary compromises, I came to terms with the fact that I probably needed at least two sets of rules for each period. One was for big battles, where the emphasis was on speed of movement, simple-but-robust mechanisms and games which were capable of being played to a conclusion in a sensible amount of time. The other would be for smaller fights, where it was required to consider a more detailed level of tactical behaviour, where forming lines and wheeling and deploying skirmish troops were still appropriate, and even necessary.

My decision to start dallying with the English Civil War – something over a year ago – required a whole new dose of considering available rules. After a lot of reading and soliciting of advice, I plumped for Victory without Quarter as my main rules. The game scale and general philosophy fitted well with the list of personal likes and dislikes which I had built up over the years. Having reached the point of actually playing some games, I now find I have the familiar two-level situation – I have a home-brewed adaptation of Commands & Colors to handle the bigger battles, and I have VwQ for the smaller stuff – my proposed provincial, North-country ECW campaigns will certainly throw up games for which C&C is too blunt a tool, and for which it becomes necessary to worry about which direction units are facing, how they are formed up, the advantages of march columns on roads, the exact point in a charge where the defenders got off a volley and all that.

My relationship with VwQ is still evolving. The only time I have used the rules in anger (grrrr!) was when I visited Old John in North Wales last year. We found that the game was fun, but there were some chunks missing (dragoons didn’t work properly, no advantage for a flank or rear attack, no explanation of how artillery should be treated in a melee, for a start). Concentrating on positives, I spent some time adding extensions to the rules – suggestions came from various sources, including Harry Pearson, even some ideas from Clarence Harrison himself (the originator) - and I have reached a fairly robust version for playtesting.

The one area which still bothers me about this game is Activation. Broadly speaking, the game uses cards to activate units – there is a card for each, and there is also a card for each commander at brigade level or higher. Drawing an officer’s card allows orders to be given to any of his subordinate units which are within shouting distance, which allows some decent progress to be made when moving troops about. Last year, Old John and I found that – as often as not – drawing a card for a single unit would produce no effect at all, certainly no movement, since advancing a single unit without the rest of its brigade was usually not a great idea. I’m still tinkering with this, which remains the one weak spot. I have even given thought to having cards only for brigades and higher formations – single unit cards being dropped. John and I had certainly deduced that any group of units which was expected to move anywhere had to be provided with an on-table brigadier.

I hope I’m not anywhere close to going back to the research phase. VwQ is designed to support the smaller type of game which I expect to feature a lot in my campaigns – my commitment to these rules, albeit expanded and tweaked, is such that I have based my troops to suit (which is not a problem – whatever rules I use can handle these bases) and have even produced (and now tested, honest, Clive...) a computer-managed version to facilitate solo play. Maybe copious provision of generals is the answer, maybe the single-unit activation cards are a bad idea, but – whatever the answer might be – I have a faintly worrying recollection of our game in Wales, during which there were lengthy periods when some parts of the armies were left stranded by the original card drawing system.

Hooptedoodle #87 - Let him who is without sin cast the first stone

Because of family and health-related issues which I have no intention of describing in this blog, there has been precious little wargaming or hobby stuff going on around here of late, so I do not have much to write about that is relevant.

This last week, though, I’ve been a bit taken aback by what I perceive as the breathtaking hypocrisy of our dear chums at Auntie BBC. I’m not exactly sure of the latest details, but there is (or has been) some further inquest going on into the tragic suicide of the unfortunate nurse who was tricked into giving confidential information on the Duchess of Cambridge’s medical condition, as a result of a so-called “prank” hoax telephone call from some Australian DJs.

This week, the BBC was full of self-righteous horror in a radio item about the inquest – as usual, assuming the role of guardian of public decency – as usual, referring to “the media” as though somehow they were talking about someone other than themselves.

Morons - and scapegoats

Just a minute, there. This particular BBC licence-payer wishes to point out a couple of things:

1. I cannot receive Australian radio – if knowledge of the prank had been restricted to listeners to the station in question then very few of us in Britain would ever have heard about it.

2. The nurse, as I understand it, is believed to have killed herself because she could not live with the humiliation or the public ridicule which followed from her having been duped and having compromised the Duchess’s privacy. No-one could reasonably have anticipated such an extreme reaction, however brutally stupid or unkind the prank might have been. It makes no difference – tragically, she killed herself.

3. As I recall, I heard about the matter in the same way as all other UK residents – I heard it on UK radio – “just fancy that – someone has been tricked into answering questions about the D of C – isn’t that shocking? – here’s some edited highlights of the phone conversation...”

4. I know nothing at all about it, of course, but I suggest that the degree of humiliation and ridicule was directly related to the extent of the media coverage the incident got in the UK. In all the sanctimonious clap-trap I have heard on this topic – and there has been plenty of it – I have never once heard anyone from the British press or the BBC express the slightest concern that they themselves had more to do with the catastrophic publicity - and thus the nurse’s death - than did the imbeciles who perpetrated the original practical joke.

Hooptedoodle #86 – The World Is Getting Faster

This is not a rant. I state this right here, up front, so that I can refer back to it if I forget.

A gentleman on the radio this morning was waxing positive about how technology has speeded everything up, and how much better our lives are as a result. He may be correct. If he was on the radio, then it’s bound to be true, isn’t it?

I have expressed concerns here before about the risks to mental health and society if the entire population has too much information, most of it distorted by marketing and vested interests, too little imagination and judgement to make use of that information, and a compulsion to multitask between trivial, inconsequential, purely transactional exchanges. That was beginning to sound a bit rantish, so I’ll stop that paragraph.

The world according to my desktop is not getting faster. It is continuing to slow down. As I have mentioned before, I live out in the countryside, and my broadband is slow. This means that most of the cyber world is now specifically designed not to work properly for people like me. The charming little lady illustrated here is someone I see a great deal of. Since my internet provider is BT (British Telecom), and since they are sort of poor relations within the Yahoo edifice, I am unable to open any page in my email service until I have been provided with an advert for an American charity – they even have 800 toll-free numbers, which of course are meaningless outside the US. I can’t switch this feature off, and the ads take on average about 22.46 seconds a time to retrieve from some remote server. Every single mail item, every index page – everything – has to wait for an ad which I’ve seen before and is of no relevance. You can see that would begin to grate after a while.

As I type my mail, the browser is constantly jamming the buffer, trying to check what I am saying, so that it can target advertising at me which is relevant to what I’m writing about. I constantly have to retype bits where it got stuck, or where it dropped characters while it was distracted. I’ve started using WordPad to type my bigger mails, and pasting them into the browser – I hope the text interpreter gets very serious indigestion as a result of not being able to chew its food properly.

As I type anything into the input field for a search engine, the poor thing has a brave attempt to predict what I’m going to type, but always gets it wrong, since the time taken to realise that I am typing in the search field and call HQ results in its losing the 2^nd to 5^th characters – so its predictions are not worth the effort. Not helpful.

Well, I’m fighting back. We realised that, despite everything, my wife’s new laptop works much faster than my desktop does when it’s online, so we deduce that more modern designs cope better with all this friction and superfluous junk. I shall buy a new desktop machine next week, and set about the (estimated) 3 month project of transferring software and documents from the old one. I shall, however, keep the old computer – it is still of a high spec, although it is coming up for 7 years old now, and the processor and video components are fast and efficient, if left to themselves and not constantly interrupted.

I intend to strip back the old machine – remove Internet access, take off the virus checker – XP will no longer be supported very soon so a static OS should be OK. I shall remove everything I don’t need to be on it. Goodbye Google Toolbar. Goodbye RealPlayer. Goodbye DropBox. Goodbye Spotify. I shall use it for typing, and utility jobs like writing CDs, graphic and photographic work and desktop publishing. When I need to move files between the machines, I shall use USB memory sticks. The computers will share a printer, but it will be hard-wired so that there is no need for WiFi.

I can sense the beginnings of a smile playing around the corners of my mouth. With luck, my future sightings of the little Unicef girl will be instantaneous, since my new computer will be designed to cope with her as part of the mail service.

The broadband will still be slow, though.

Maybe it won’t work any better.

Hmmm. 

The Thunderer

The general in this picture has appeared here before, and there was some helpful discussion of how I could use him. Generals on foot have always been a problem for me, since I find it unlikely that even infantry generals would have led their men into action on Shanks's pony.

As a result of suggestions made, I resolved to get him a held horse to add a little potential mobility, and I have finally done it. You can't rush these things, of course.

This is Sir Nathaniel Aspinall, known to his men as The Thunderer, and occasionally God's Trumpet - I sincerely hope this was because of his very loud voice. A noted lay preacher, and sometime Member of Parliament for Bury, in the Hundred of Salford, Sir Nathaniel was unusually well qualified to be a general of foot, since he had served some years of his youth as a professional soldier in Germany in the Wars of Religion.

He is here seen with his horse, Herod, and a horse-holder who was formerly in the artillery. Hinton Hunts to a man - or horse.

This sets a useful precedent - I'm quite pleased with Sir Nat (this is about as close to a diorama as you get in my armies), and will follow a similar grouping style with other suitable Staff castings which I have.