Shannon, Entropy and Guardian Crosswords...

As part of the Fifteensquared discussion of a Crossword by Brummie in the Guardian last Wednesday, this thread started:-

Dr. Whatson says:

February 27, 2019 at 3:15 am

There’s something about Brummie you folks may find interesting.  His puzzles have the most helpful crossers of all setters here.   This is following the notion that the more unusual the letter (e.g. Z, J) the more helpful it is as a crosser, the more common (e.g. E, T) the less helpful.  I won’t go into details, but you can calculate the helpfulness via entropy, and his numbers are statistically significantly higher than the average.  At the other end of the spectrum is Chifonie, with Pan nipping at his heels.  Nobody else stands out. I don’t imagine this is intentional on any of their parts, but rather a side-effect of their grid-filling methods/software.

How is this useful?  Probably not much, except if you’re stuck on a Brummie, maybe that crosser is a B or a C.

thezed says:

February 27, 2019 at 1:23 pm

.....

Dr. Whatson @1 – re entropy, the first time I came across comments on this was in Claude Shannon (engineer, inventor of a juggling robot and, more famously, the man who invented information and communication theory, giving us Shannon’s Law) who discussed information contained in language in terms of its entropy. In his seminal paper “A Mathematical Theory of Communication” (free link) on page 15 he even briefly detours into the necessary redundancy in a language in order to be able to make crosswords possible. English is well-suited it turns out. He goes into more detail on language, but not on crosswords, in his “Prediction and Entropy of Printed English” (here). I’ve not read a biography recently so do not know if he was a cruciverbalist on top of his other talents, but I’ve always treasured that little detour in one of the most important papers of the 20th century.

Well, crikey, I thought.

On the South Bank of the Thames, in the Cold Spring Sunshine

After a visit to Tate Modern, which surprisingly wasn't irredeemably awful (they've reorganised their stuff since I was last there, so that it makes a little more sense, including putting some of the things I don't hate in the same spaces - like a gallery on 'Realisms' which chimes with Christine Lindey's course on The Alternative Tradition, a little), I came out into the Spring sunshine to see these two  chaps eating fire and juggling:

Which was quite fun. 

I then did something I rarely do: the tide was out, so I went down to the beach; the real South Bank of the Thames, if you will.

The Shard seems small and unimportant from this angle, compared with the expanse of the River and the rest of London.  And there is a wealth of stuff down at water level you don't see from up on the embankment.

And of course, the River itself is closer.

...while the bridges are... up there.

The red piers from the old, 1864 Blackfriars Bridge are especially impressive from the waterline.

While the Millennium Footbridge (no longer so bouncy) was very busy on the day...

And finally, just like almost every other cultural barn in London in the last ten years, Tate Modern is getting a new bit built...

Poem of the Week

Juggling Jerry
George Meredith

Pitch here the tent, while the old horse grazes:
By the old hedge-side we'll halt a stage.
It's nigh my last above the daisies:
My next leaf'll be man's blank page.
Yes, my old girl! and it's no use crying:
Juggler, constable, king, must bow.
One that outjuggles all's been spying
Long to have me, and he has me now.

We've travelled times to this old common:
Often we've hung our pots in the gorse.
We've had a stirring life, old woman!
You, and I, and the old grey horse.
Races, and fairs, and royal occasions,
Found us coming to their call:
Now they'll miss us at our stations:
There's a Juggler outjuggles all!

Up goes the lark, as if all were jolly!
Over the duck-pond the willow shakes.
Easy to think that grieving's folly,
When the hand's firm as driven stakes!
Ay, when we're strong, and braced, and manful,
Life's a sweet fiddle: but we're a batch
Born to become the Great Juggler's han'ful:
Balls he shies up, and is safe to catch.

Here's where the lads of the village cricket:
I was a lad not wide from here:
Couldn't I whip off the bale from the wicket?
Like an old world those days appear!
Donkey, sheep, geese, and thatch'd ale-house—I know them!
They are old friends of my halts, and seem,
Somehow, as if kind thanks I owe them:
Juggling don't hinder the heart's esteem.

Juggling's no sin, for we must have victual:
Nature allows us to bait for the fool.
Holding one's own makes us juggle no little;
But, to increase it, hard juggling's the rule.
You that are sneering at my profession,
Haven't you juggled a vast amount?
There's the Prime Minister, in one Session,
Juggles more games than my sins'll count.

I've murdered insects with mock thunder:
Conscience, for that, in men don't quail.
I've made bread from the bump of wonder:
That's my business, and there's my tale.
Fashion and rank all praised the professor:
Ay! and I've had my smile from the Queen:
Bravo, Jerry! she meant: God bless her!
Ain't this a sermon on that scene?

I've studied men from my topsy-turvy
Close, and, I reckon, rather true.
Some are fine fellows: some, right scurvy:
Most, a dash between the two.
But it's a woman, old girl, that makes me
Think more kindly of the race:
And it's a woman, old girl, that shakes me
When the Great Juggler I must face.

We two were married, due and legal:
Honest we've lived since we've been one.
Lord! I could then jump like an eagle:
You danced bright as a bit o' the sun.
Birds in a May-bush we were! right merry!
All night we kiss'd, we juggled all day.
Joy was the heart of Juggling Jerry!
Now from his old girl he's juggled away.

It's past parsons to console us:
No, nor no doctor fetch for me:
I can die without my bolus;
Two of a trade, lass, never agree!
Parson and Doctor!—don't they love rarely
Fighting the devil in other men's fields!
Stand up yourself and match him fairly:
Then see how the rascal yields!

I, lass, have lived no gipsy, flaunting
Finery while his poor helpmate grubs:
Coin I've stored, and you won't be wanting:
You shan't beg from the troughs and tubs.
Nobly you've stuck to me, though in his kitchen
Many a Marquis would hail you Cook!
Palaces you could have ruled and grown rich in,
But your old Jerry you never forsook.

Hand up the chirper! ripe ale winks in it;
Let's have comfort and be at peace.
Once a stout draught made me light as a linnet.
Cheer up! the Lord must have his lease.
May be—for none see in that black hollow—
It's just a place where we're held in pawn,
And, when the Great Juggler makes as to swallow,
It's just the sword-trick—I ain't quite gone!

Yonder came smells of the gorse, so nutty,
Gold-like and warm: it's the prime of May.
Better than mortar, brick and putty
Is God's house on a blowing day.
Lean me more up the mound; now I feel it:
All the old heath-smells! Ain't it strange?
There's the world laughing, as if to conceal it,
But He's by us, juggling the change.

I mind it well, by the sea-beach lying,
Once—it's long gone—when two gulls we beheld,
Which, as the moon got up, were flying
Down a big wave that sparked and swell'd.
Crack, went a gun: one fell: the second
Wheeled round him twice, and was off for new luck:
There in the dark her white wing beckon'd:—
Drop me a kiss—I'm the bird dead-struck!

Siteswap BBC 2

... and then we listened to the actual broadcast of More or Less on BBC Radio 4 which discussed juggling notation. 

Super.

Siteswap on the Beeb

Eldest has just posted me this link about Siteswap from the BBC, from a day or so ago. 

Pretty good huh?

It finally helps me understand the notation - which as I said many years ago, I never really got.

Camden

To Camden Market for some shopping.  We took a few minutes in a smashing vegetarian cafe looking over Regents' canal and Camden Lock.

It was a hot June Saturday morning, but the market was still very busy.

One of the things I like about the market is the decorated shop fronts:

But we were heading for a more modestly appointed emporium, in search of diablos (diabli?).  I've laxed wyrical elsewhere about the amazing time you can have in Oddballs, so I won't repeat it here.  Suffice it to say that it lived up to expectations and exceeded them... Go there at once, you'll have a great time.

Notation

Man is a language-making animal.

This statment is not just meant to assert in some tautologous way that she uses language to communicate. Indeed, it usually intends the coining of new words, such as street slang or specialist jargon. It is also true, however, that people do invent complete new languages – and not solely in the way that Tolkien did. Languages communicate, and any time we find a wholly new and complete way to convey an experience, practise or activity, we arguably create a new language - albeit one in which only certain things can be said.

One of my recent purchases from Oddballs was an ‘Encyclopaedia of Ball Juggling’ (Charlie Dancey, 2005). As is often the case in publications about juggling, this is full of cartoons, jokey exhortations and personal opinions. (It does however try for a measure of comprehensiveness).

Flicking though the book in the shop, I discovered the new world of juggling notation. In essence, it’s a language, as I suggest is any comprehensive system of descriptive notation. This one is used to describe what a juggling trick involves. I was fascinated by the diagrams and numbers, and the detailed explanations.

So I bought the book.

The book is careful to say that few if any people can learn a manoeuvre from a notation, but that it can be useful to explain the sequence of moves that make it up. The notation is a systematic communication of precisely what is involved.

Whatever.

I now find myself deep in the world of Ladder Notation, Siteswap, Causal Diagrams and the mighty Mills’ Mess State Transition Diagram (MMSTD):-


Each of these solutions tries to get across something of the character of a trick from its own perspective. None of them seem easy to understand or to use – I have to work through the examples very slowly, mumbling under my breath. And with my tongue stuck out.

(As an aside, I suspect there may be a similarity with those notations used to describe dance steps. I have a memory of a children’s story – Blyton or Crompton? – where the hero suspects the new visitor in the village is a spy when they come across his ballet notation. They assume it is a secret code. That is certainly how Siteswap feels sometimes).

I’m fascinated by these systems, and would love to use them. However, possibly because there seem to be a fair number of mathematician jugglers, the notations do seem quite subtle to grasp. I'm struggling at the moment.

Thankfully, I can revert to all of the little cartoons of jugglers doing specific tricks in the book. I feel more at home with them and they do seem to know what they are doing. And nowadays there are lots of really helpful videos and DVDs. And finally, software is becoming available that connects the friendly diagrams and the notation together. So that's all right. It just doesn't seem to stop me dropping stuff...

More than Most...

So today we went to Oddballs (est 25 years!) in Camden Market. This is a shop to visit and to spend a long time in. Not because it is very, very large (it isn't), nor because it carries a huge range of stock (it isn't bad, but that isn't the point).

No, the reason for staying a while is that the staff are exactly what you used to get from the BR International Booking staff at Victoria station when trying to book an open return railway ticket to Vienna via Cologne (pre-privatisation and pre-Tunnel).

In other words, knowledgeable, helpful specialists who are deeply interested in their subjects and in your wants. At Victoria in those Halcyon days, a somewhat portly man in his thirties carefully leafed through multiple International Railway timetables and complex fares manuals, (real books, not Web sites), making notes on a pad with a stub of pencil and occasionally looking up to ask me for detailed clarification on difficult points regarding my desired journey. He thoughtfully offered choices to help me reduce the overall ticket price, and advised me (from his personal knowledge) on the platform layout at Cologne station so that my changes would be easier. This is all true, it really happened, and not that long ago (1989/1990), and it was wonderful. Today, following the nasty Tory demolition of the railway system in the UK (which I think we can all agree has resulted in an unsightly, disorganised and loathsome mess of a service and inter-alia created a new, mean-spirited language that diminishes those who choose to use the railway, changing us from passengers to customers and promoting the cheap shoddy term 'train station') , the same travel problems have no easy solution (although to be honest, the Man in Seat 61 isn't a bad try at offering something a bit more limited on the InterWeb).

Deep breath.

What I was going to say is that a visit to Oddballs is joyful, because of the staff. Today we witnessed one of the chaps on duty spend about half an hour with a Dutch family whose son wanted a new yo-yo - and that, if you don't know about these things, is a complex and difficult decision. The boy showed what tricks he could do and there followed a complicated Dutch - English conversation (given the topic, let's say it was in Danglais), with illustrative tricks being demonstrated with the various different yo-yo technologies by the shop assistant. At the end, with the relevant yo-yos being selected for purchase, the conversation moved on to additional equipment and adaptations; when the assistant could not quite work out how the chuck worked on one machine, he took the trouble to ring up someone who knew more about it on his mobile. Meanwhile, the other assistant spent considerable time (well over 20 minutes) coaching on how to perform tricks using two diablos at a time (diablii?), on the same string. Both of these exemplars discussed different equipment with other customers as they continued, and the yo-yoist stopped briefly at one point to show me some nice Henry's Thuds - and just as a side illustration he performed a five-ball cascade. Marvellous. We must have spent an hour in there and I was entranced. Oh, and we did of course spend a fair amount of money in the shop as a result. Just don't tell the Tories about it.

There is a further point, of course. Both examples suggest that online shopping - e-commerce - is unlikely to be able to offer the full, fun experience of a physical visit to certain shops. Those quirky bookshops with (hopefully) serendipitous filing systems, and those markets where you can smell the carrots, cheeses or tomatoes before you buy. Not to mention those places where you can also smell the books... Oddballs has a very good Web site - with lots of demonstration videos and Flash movies - but it is nothing like the real visit.

But as the railways have proven, this doesn't mean that these wonders will survive. And they certainly won't if we don't get out and use them. So the message is: get out there and enjoy the show.

(The title of this post comes from the name of a now-defunct juggling shop that I used to frequent, called More Balls than Most. Like Oddballs, and BR International Enquiries, a visit was a real treat. But it is no longer there. Again - don't let this happen to a joy near you).