Archive for February, 2012

‘Alice’s Adventures in Wonderland’

The book was first published by Macmillan, London, in 1865. It consisted of 192 pages of text (35000 words) and was supplemented by 42 engravings, by John Tenniel. The author was ‘Lewis Carroll’.

The first print run was of 2000 copies. This, however, was held back because John Tenniel was concerned about the print quality. And so a new edition was prepared, and accepted; this was released in December 1865, but carried an 1866 publication date. The author, in fact, allowed that first print run to be sold to the New York publishing house, Appleton.

This suggests the book was published on both sides of the Atlantic almost simultaneously.

The book has never been out of print.

That is one version of the tale, another is:

‘Alice’s Adventures Under Ground’

This story goes that in 1862 Charles Dodgson, along with Reverend Robinson Duckworth, was on a rowing trip up the River Thames from Oxford. Their passengers were three young girls, daughters of the Vice-Chancellor of Oxford, Doctor Henry George Liddell. These three girls were Lorina, aged 13, Alice, aged 10, and Edith, aged 8. As can be imagined the girls were finding the five mile journey up-river a little tedious, and so Charles Dodgson extemporised a wonder story for them. Alice, after whom the heroine of the piece was named, implored Mr Dodgson to write it down for her. Which he eventually did.

In November 1864 he presented her with a handwritten text of the story, complete with his own drawings and illustrations. This was an 18000 word piece called ‘Alice’s Adventures Under Ground.’. Many parts of the story were based on ‘situations and buildings in Oxford and at Christ Church’. The rabbit hole, itself, is said to be an interpretation of the aspect of the stairs ‘in the back of the college’s main hall.’

As can be deduced from the text the tale takes place on May 4th. This is a significant date, because it was the date of Alice Liddell’s birthday.

About a year later Dodgson, using the pseudonym ‘Lewis Carroll’, and with engravings by John Tenniel, published an expanded version of the story, now entitled ‘Alice’s Adventures in Wonderland’.


There has been much speculation about the nature of Dodgson’s relationships with little girls, Alice included. One version is that Dodgson’s sexual nature was not fully developed; as such he could take pleasure in the company of young girls, even if he avoided young boys as much as possible (it has been suggested that the Duchess’ baby was a boy, and his turning into a pig, quite appropriate). There was no hint of impropriety with any of the daughters of the Vice-Chancellor; or any of his other ‘friends’. He himself admitted elsewhere that Alice Liddell was indeed his favourite; he spent as much time in her company as he could. He seems to have been allowed access to the company of the three sisters, and Alice, over a long period. There would surely have been repercussions if there had been impropriety. One certainly hopes so, anyway; though it is not always the case.

What is known from the Liddell Diaries (‘The Annotated Alice’) is that Alice’s mother argued for more distance between them. She was wary of the romantic feelings Dodgson seemed to be developing for her middle daughter; it was not just the age difference, but also Dodgson was considered to be of lower social status.

We talk of social class now, but when we come across the proliferation of levels and sublevels in examples like this, and the rigidity with which they were adhered to it can get a little scary. Consider a Dickens novel: everyone is rigidly held to their social position; there can be no movement above a small elevation from that level, but plenty below it.

The grown-up Alice had a serious romance with Prince Leopold. This was suppressed on the recommendation of Queen Victoria, almost wholly because she was a ‘commoner’. She went on to marry however, had children of her own; one of whom she named… Leopold. And guess what? One of Prince Leopold’s daughters when he married… Alice.

And then there is the issue of the photographs. Naked young girls. Admittedly none were salacious, sexually posed – just their nakedness. Or shall we say nudity? The former implies salaciousness, whereas the latter posits the possibility of naturism with all its entreaties to innocence, health, a balanced attitude. We in our time are not in a position to see these issues clearly.

Alice in Numberland


There is a big discrepancy between the two versions of the book; something like a 17000 word discrepancy. This consisted of some of the major adventures and images that we now most take for granted as the heart and soul of the book being added to the expanded version of the tale: the Cheshire Cat, the Baby and the Duchess, the Caterpillar with the hookah pipe, and even the Mad Hatter’s Tea Party.

Dodgson’s wit and playfulness in the book is all to do with the laws of geometry, perspective, quantity… in other words, he was playing with logic.

Was John Tenniel not above a moment or two of wit? The engraving of The Mad Hatter does look suspiciously like a caricature of the young philosopher and logician Bertrand Russell – who unfortunately had not been born by this time. ‘Philosopher’ though is probably the best clue. Martin Gardener in ’The Annotated Alice’ gives many answers to who might be caricatured here. A good follow up to the Bertrand Russell joke is that he, along with fellow philosophs G E Moore, and J M E McTaggart became known as ‘the Mad Tea Party of Trinity’. And also Russell’s major work, his ‘Principia’, was an attempt to reconcile logic with mathematics; that it failed only further explores what it is that differs, and thereby the further possibilities of both.


In 1984 Helena Pycior, University of Wisconsin-Milwaukee, noticed a definite resemblance between the book’s trial of the Knave of Hearts, and the logic puzzles and assumptions of a book of Victorian algebra.

Why should this surprise us? After all teaching mathematics at Oxford was Dodgson’s profession: he was a Victorian mathematician.

He published many books and pamphlets in his life time; I remember trying to read his book on Symbolic Logic a short time ago. How shall I say it: it… needs some clarification. As one commentator has suggested, there are at least two Dodgsons, one is witty and plays with logic and fantastic images with a deft hand, another plods through his subject matter with little flair, but dedicated pedantry. Obviously I had got one of the latter.


Then in 2009 Melanie Bayley published an article in The New Scientist magazine (16th December 2009, Issue 2739 – back copies still available, but only just) that explored other parts of the book in the light of the emergence of the new mathematics that was taking root in Oxford at the time he wrote the book.

Dodgson, she claimed, was one of the old school; he was a Euclidean, above all else. And so when non-Euclidean mathematics became the rage, when imaginary numbers caught young mathematician’s imaginations, Dodgson reacted.  He is at his best when he reacts against something, it has been claimed, because then his mind dances around his subject with a glee that is missing at other times.

If we look at his playing with proportion in the episode in the rabbit hole, we see something of the argument from this angle. In this scene Alice’s height varies from 9 feet, to 3 inches. She quite rightly finds this very perplexing. The ‘Drink Me’ and ‘Eat Me’ are agents of change. Later, the caterpillar says she needs to keep her “temper”. ‘Temper’ here, Bayley argues, is the technical term for “the proportion in which qualities are mingled”. Yes, another of those opaque mathematical phrases; the argument is to keep one’s sense of one’s body in proportion, no matter what one’s size. In Euclidean geometry absolute magnitude does not matter, what does matter is keeping one’s ratios constant.

Dodgson’s wit not only sets up visual puns on mathematical theses, but also uses verbal references to theses, as with the term ‘temper’ in the above example. Another verbal example is in the use of the term algebra itself. It is an Arabic-derived word from a truncated phrase, which means ‘restoration and reduction’. This, of course, is exactly what happens to Alice in the rabbit hole, and when eating different sides of the mushroom.

The episode of the Duchess and the Baby (that turns into a pig), Bayley argues, is an excellent example of Dodgson as his satirical best. Here he subjects the French mathematician Jean-Victor Poncelet’s working on projective geometry, to the rhetorical scourge of reductio ad absurdum: using the man’s own arguments to produce a ridiculous conclusion. It does not invalidate the argument, but the fun overtakes the sense, and so wins the day.

What is being attacked here, Bayley writes, is Poncelet’s theory of continuity: does a figure stay the same when projected onto a different surface? Poncelet writes: “Let a figure be conceived to undergo a certain continuous variation, and let some general property concerning it be granted as true, so long as the variation is confined within certain limits; then the same property will belong to all the successive stages of the figure.” A baby should remain a baby, no matter where it is. But Poncelet was writing about mathematical figures; Dodgson applied the theory outside of its domain, and his distrust of the theory became evident.

The Mad-Hatter’s Tea Party, Bayley suggests, explores the work of Irish mathematician William Rowan Hamilton (died 1865). Hamilton discovered quaternions (published 1843). Quaternions ‘belong to a number system based on four terms – one for each dimension of space’. And so, at the tea party, we have the Mad Hatter, the March Hare, and the Dormouse. The other dimension that was missing was Time. Hence we have the scenes about the stopped watch being oiled with butter. The consequence of the loss of Time is that the tea-party (T-party?) can never end, that when cups etc are used up they all just move around the table to the next places. Bayley writes: ‘the rotations around the table is reminiscent of Hamilton’s early attempts to calculate motion, which was limited to rotations in a plane before he added time to the mix.’

I was hoping by this point to have some kind of grasp of quaternian maths in order to understand and further elucidate this. But, alas, like most of arithmetic it remains inert to me, a dead dog.


There are no dead dogs in Wonderland.

Tutors and children love this book for different reasons. Tutors for its playing with logical possibilities – the bases of all our knowledge and reason are in use here. Not only is the book a fascinating read, but it also has sound academic qualifications. Children love it because it allows them wonderful images and imaginings. They become increasingly aware of its sound superstructure in thinking-processes as they grow: as their learning in methods of knowledge-acquirement increases, and their interaction with the world and how it is ordered increases. It is a book that grows along with them.

Do I expect too much of children, here? I would hate to expect too little: I have been there and it is more destructive than expecting too much. Much is known subconsciously; the hard work is to drag out into the light what we actually know, to recognise it, and to own it.

The follow-up book, ‘Alice Through the Looking-Glass’ (published 1871) was equally successful. This later book includes such standards as the episodes with Tweedledee and Tweedledum, Humpty Dumpty, and the tale of the Jabberwock. This book constructs a contrary world to that of the previous book. It begins in the dark of a November evening indoors, as the other in the bright of a May morning outdoors. The central images are those of the chess game, as the previous book was of cards. This book plays with time, whereas the previous played with spatial dimensions. This latter book has a suppressed chapter, The Wasp and the Wig, which has been subsequently rediscovered, and in some new editions reincorporated.

Both books continue to tease, perplex and fascinate all ages. And yet they are not subversive. They appeal both to traditionalists, and to explorers equally.

It started off, we were told/ it was suggested we Do Not use mobile phones in hospitals – because they can affect the sensitive equipment in use there.

Sounds so reasonable – frequencies, wavelengths; constant monitoring equipment etc etc.

Then everywhere – I am talking here about the acme of informed representation, in films and on tv – we see phones in use on hospitals again. I think I even remember one of the fictional representatives of the medical profession assuring the user that it perfectly ok to use them.

It was just an ill-informed scare story – you know, the sort the liberal/libertarian wusses flap about along with their PC rubbish.

And then, well, my wife was hospital visiting and having time on her hands: hospitals – all waiting, little of the seeing-to – got chatting to a nurse.

And the latest directive from medical counsels is that


they Can interfere with ECG, EEG, even Pace-Makers.

I have not seen any reports of any problems – but then, I do not read Medical journals; nor do I read a wide swatch of newspapers. How would I know?

Maybe it is even thought  ‘convenient’, by interested parties, to play it down.

If so it cannot be long before we start to read/read reports in this field.

As for me I think I’d choose to err on the side of caution.