Ripples in Flatland

A link to a youtube video of Carl Sagan using Flatland as a demonstration model for describing higher dimensional space was posted last week by Fortean blog The Daily Grail. This fits snugly into the stream of twentieth century responses to Abbott’s book that exploits its pedagogical intent and Sagan’s lesson demonstrates just how effective Flatland is as a teaching tool.

TDG’s take on the video, that Sagan is engaging with anomalous phenomena, also reflects the cultural work that the fourth dimension did in the late nineteenth and early twentieth centuries by providing an explanation for purported seance phenomena or clairvoyance.

Also interesting is this video at Dwell demonstrating a 1980  fine-press edition of Flatland in an aluminium case and bound accordion-style. It’s a groovee object and no mistaking.

I’m giving a paper at the Utopian Spaces conference in Oxford on 18th September (abstract to follow). It combines some ideas from a paper I gave in Belfast last year with some new research into how British Theosophists engaged with Hinton’s work and what they did with the fourth dimension: the utopian elements are all Hinton’s doing but without them, I don’t think that the fourth dimension would have been as attractive to Theosophy. The plan is to go for the full powerpoint whizzbang, not least because I missed having the visual crutch at the Angles conference a few months back.

The Angles conference was inspiring and intimidating in equal measure. There were a number of fantastic papers – Tim Livsey’s reading of Poplar Town Hall and Marco Bohr on Japanese post-bubble photography are just two that come to mind immediately – and I felt that I might have been preaching to the converted with a defence of interdisciplinarity, not to mention coming across as something of a postgraduate fanboy of last year’s hot theory. A crime doubtless more serious than both of these, given the invariably amiable and forgiving crowds gathered at Birkbeck-based conferences, was not taking a glass of water to the podium: cue dry-mouthed gum-licking. You live and learn.

Rucker on Boole-Stott / Hinton’s bigamy

Rudy Rucker has onlined the intro to his edited collection of Hinton’s work here. After first encountering Hinton in Iain Sinclair’s White Chappell, Scarlet Tracings, this was the piece of writing that really got me hooked. It’s a real boon to have it online, so respect to the man like Rudy.

He’s linked to it as part of a post on Alicia Boole Stott, Hinton’s sister-in-law, and included a letter from Thomas Banchoff, who did some research into the Hinton family. Coming to Hinton some twenty years after Banchoff and being based in London I’ve been fortunate enough to be able to access a number of resources that give a clearer picture of the events surrounding his conviction for bigamy. I’ll dig out the newspaper clippings at some point, and scan these, but for now, the following is from a draft of some biographical background research I did that isn’t going to be in my thesis, but may be of interest. I tried to piece together exactly what happened chronologically and to bed it into the social context: i.e. who were the witnesses and documenters of the events and how did they know each other. I apologise for the patchy and incomplete referencing: this was just a draft and my research had headed off in different directions. If anyone who reads it has queries about any specific sources, please drop me a line and I’ll dig them out.

In addition to the below, it is worth clarifying that Mrs Nettleship was indeed Adaline, Howard’s sister. She was married to John Nettleship, brother of Richard Lewis Nettleship, a tutor at Balliol, Hinton’s Oxford College, and quondam headboy of Uppingham College. My guess would be that Richard recommended Howard for the Uppingham job, and that Howard introduced his sister to Richard’s brother, but it looks as if the Nettleship family and Hinton family were friends from the same non-conformist Oxford circles for a couple of generations.

Anyway, here’s the text:

THE CONVICTION FOR BIGAMY OF CHARLES HOWARD HINTON

In 1879 a young Henry Havelock Ellis returned to England from Australia with a burning interest in the ideas of English philosopher and aural surgeon, James Hinton. James Hinton’s writing, focused on domestic life, was outside of mainstream philosophical and cultural thought, and radical in its advocation of polygamous relationships, freer relations between the sexes, and the benefits of female nudity. For the progressive Ellis, here was a bold and outspoken thinker, and he wrote to Ellice Hopkins, the author of a biography of Hinton, stating as much.

James Hinton had been dead for four years by the time of Ellis’s arrival in England, but Hopkins forwarded the letter to Hinton’s widow, Margaret, nee Haddon. Mrs Hinton invited Ellis to dinner at her house in High Barnet on January 6^th, 1880. Also present were Miss Caroline Haddon, Mrs Hinton’s sister, and Charles Howard Hinton, her son. Ellis made notes of the conversation that evening in his journal, later used by his wife Edith for her study of James Hinton, A Sketch, published shortly after Howard’s death in 1909.

Ellis’s interest in James Hinton, and particularly unpublished manuscripts mentioned by Hopkins in her book, was welcomed by the Hinton family and access to the work was granted. Both parties were keen that the work should be published, and Ellis’s energy and enthusiasm was clearly a godsend.  Several projects were proposed including a collaboration between Howard and Ellis.

Ellis became very close to the Hintons, as he spent a great deal of time staying in the family home working on the James Hinton manuscripts, or visiting Howard and his family in Uppingham. He later wrote in his autobiography:  ‘I was soon on friendly terms with the whole family, who took me into their inner circle and interested themselves in all my affairs. In later years Mrs Hinton told my future wife that in some respects I much resembled Hinton, adding, however, some remark to the effect that such resemblance was no recommendation as a husband.’[1]

In 1883 Ellis met the South African novelist Olive Schreiner, having corresponded with her following the publication of her book The Story of an African Farm. The relationship between the two blossomed rapidly and they corresponded frequently and profusely. This correspondence, held in archive at the Harry Ransom Humanities Research Centre at the University of Texas, and published in an invaluable scholarly edition by Yaffa Claire Draznin, includes much remarkable detail about Charles Howard Hinton and his private life.

Early in the relationship between Ellis and Schreiner questions were raised about the unconventional nature of the Hinton domestic environment, which was evidently a much gossipped-about subject. In September 1884 Olive had heard rumours about James Hinton putting into practice some of his more progressive theories, which she put to Ellis. He responded thus:

I don’t know anything about Hinton’s daughter Ada being undressed with her father and brother. I don’t quite know that I could ask. It is quite possible. The nakedness of women is a point he insists on a great deal. He puts it rather one-sidedly; he doesn’t say much about men going naked. Whether he took that for granted or whether he thought they weren’t worth seeing, or whether he considered that women were not so much in the need of the moral and aesthetic influence of nakedness, I don’t know.[2]

In December 1884 Ellis wrote to Schreiner referring, for the first time, to their shared knowledge of Charles Howard Hinton’s extra-marital affair with a woman known to them as Maude Weldon. Remarkably, this affair was known also to others in Howard’s immediate family: ‘Miss Haddon knows about Miss Weldon; says she doesn’t quite take Howard’s view, & feels, too, the difficulties for the children.’[3]

Over the course of 1885 both Ellis and Schreiner corresponded with Miss Weldon and visited her in Brighton. The emergent picture of the extra-marital relationship is one of instability, and an instability to which both Schreiner and Ellis were close witness. ‘Just got this from Brighton’, Ellis wrote to Schreiner on 20^th January of that year, enclosing Maude’s letter to him. ‘It surprises me a little; I didn’t know she was religious like that. I’m not quite certain if ‘My King’ means Jesus or Howard. It’s a bit mixed.’[4]

In April Ellis actually visited Brighton with Hinton. His letter to Schreiner on this occasion, noting Howard’s intellectual concern with higher space, suggests that a strain was beginning to set in to the affair:

He came to me yesterday – plunged into a favourite question of his – “space-relations” – walking eagerly up & down. But I knew he had something more definite than that to talk about & by and bye he plunged into it with a good deal of confusion and hesitation. Olive, why is it people want to trust me so much & tell me things they don’t tell anyone else.[5]

By June this instability had evidently become a schism between Howard and his mistress, as Schreiner wrote to Ellis, drawing an analogy between their relationship and that of Howard and Maude: ‘Mrs Weldon gave the love to Hinton that you want, & now she talks of revenge.’[6]

At this point the Ellis-Schreiner correspondence becomes mute on the matter. Most likely the split between Howard and Maude had meant that their paths did not cross, and Schreiner, due to illness, spent much of 1886 living in two different nunneries. Discussion of the legacy left by James Hinton, however, flourished in different groupings.

In 1884 both Ellis and Schreiner had become members of the Men and Women’s Club, co-founded by the scientist Karl Pearson so that both men and women could meet to discuss freely the relations of the sexes. In early 1885 Pearson had invited Miss Haddon to speak about James Hinton’s philosophy, and the discussion of Hinton’s thinking within the club had prompted action on behalf of a number of its members who had, it emerged, violently different opinions of the man. The subsequent campaign against ‘Hintonianism’ revealed some uncomfortable truths.

Firstly Emma Brooke, on the posthumous publication of Hinton’s Serving Others, a pamphlet put out by Miss Haddon with Ellis’s assistance, wrote to both Ellis and Karl Pearson to describe how, as a young girl, she had found herself staying in the company of James Hinton for a weekend. Hinton had made a series of advances towards her, at one stage hoping to entice her away from company and attempting to encourage her to ‘serve his needs’. She had rebuffed him, but was appalled at the continued currency of his ideas, having witnessed at first-hand how he practically applied them. By the end of the year, numerous witnesses to similar behaviour had emerged. A letter from E.M. Walters to Olive Schreiner attested to the strength of feeling:

One acquaintance of mine used to have her hand kissed & worshipped by him when she went to him as a patient. “What a long hand!” with a fond gaze at it.

I often heard of this kind of ’service’ to ‘other’s needs’, & his spiritual-wife theories, but I never knew anyone whom he had gone farther with than to seduction of the mind [...]

How any woman, & especially his wife and sister-in-law can believe such a wretch, passes my understanding. You know I am not squeamish – you know I am not bound by any social proprieties – I always rebelled against the word ‘duty’ & I can admire love often when society would condemn it – but Hinton excites the intensest loathing in my mind. Far better to be a bold and boastful seducer than a sneak spinning webs of fine moral reasoning to catch his victims.

You know he was the son of a dissenting minister – that explains much.[7]

These rumours compounded the facts already public. At the time of James Hinton’s death, he had been living with his wife, Miss Haddon, a spinster called Agnes Jones, and Mary Boole, the widow of the mathematician George Boole, who had taken up a job as his secretary when the Committee of Education decided her no longer fit to run a boarding house for students at Queen’s College, London, and had terminated her lease. Of these he had shared physical relations with his wife, Miss Haddon and Mary Boole, while Agnes Jones had evidently been keen on the idea. To his circle he was known as ‘The Wizard’. Mrs Hinton had told Ellis that James had once remarked to her: ‘Christ was the saviour of Men but I am the saviour of Women and I don’t envy him a bit.’[8]

This unconventional domestic environment now took on a more sinister appearance, as anecdote and hearsay described James Hinton as a sexual predator. His philosophical writing was dismissed as the self-serving justification of a lecher. Miss Haddon was no longer invited to give papers but was forced to defend herself in a series of letters to Karl Pearson, Elisabeth Cobb and other members of the Men and Women’s Club. It was against this background that Howard’s bigamy came to light.

On 27^th September Olive Schreiner left the nunnery in Harrow at which she had been living for the past three months and moved in with Mrs Hinton at 35 Acacia Road in St John’s Wood. By the 9^th October she had moved to lodgings on Blandford Square. On 11^th October she wrote to Pearson: “I had two trying visitors today (trying because one wishes to help but hasn’t the means) [...] The other woman this afternoon is one whose son has seduced a woman & had two children by her; now his wife has found it out. Both she & the other woman are in such a wretched mental condition that one does not know which to pity the most [...] This is one of the most painful cases I have seen. I will tell you about it some day [sic]. The poor old mother was walking up and down my bedroom crying and wringing her hands long after it was time for me to start, so I must with my head full of many things to the club.’[9]

We can roughly date the emergence of the truth of Howard’s affair and identify those who knew: Miss Haddon, Ellis and Schreiner, but not Mrs Hinton. And while we cannot know how Mary Hinton came to discover Howard’s infidelity, we can perhaps speculate as to what might have catalysed one of Howard’s confidants into telling her. In September 1886 Mary was four months pregnant with their fourth child.

Over the course of the next five days the situation unravelled. On 13^th October Charles Howard Hinton presented himself to Edward Thring, the headmaster at Uppingham. ‘What a piteous and strange thing,’ Thring wrote in his diary. ‘Hinton came in with his wife and his sister (I understand) to say he had committed bigamy and that they had persuaded him to give himself up to justice.’[10]

The following day Charles and Mary reported to Bow Street police station. Charles confessed to the acting inspector that he had married a woman at the Registry Office in Bow Street in January 1883, having already been married to his wife, Mary Everest Boole, the daughter of his father’s quondam secretary, in April 1880, shortly before taking up his post as assistant science master at Uppingham.

Howard had evidently hoped to protect Maude. The Times recorded that ‘he had married another woman, whose name he did not remember.’ Mary reportedly ‘said she did not wish to prosecute, and prisoner had only given himself up as a matter of conscience as they did not wish to have a secret in the house.’[11] Charles was nevertheless remanded as the police sought Maude, whose maiden name they now knew as Florence, having recovered the certificate of their illegal marriage.

The following day the case was seen by a magistrate, Sir James Ingham. Charles was defended by Mr A.J. Ashton. Maude had been located and was called as a witness in court. It was confirmed that Howard had married her under the name of John Weldon, giving the occupation of electrical engineer, on 19^th January 1883. Her testimony, as reported in The Chronicle, detailed events and for the first time, the truth of the affair, that there were children involved, became known to a broader public:

When she married him she knew he had been married before and that his other wife was then alive. She lived with him about a week after they were married in Argyll-square, King’s-cross [sic]. He went back to live with his former wife and witness went away. Since that time until very lately they had been intimate. She had twins eight months after she was married. It was to give a colour of legitimacy to any children who might be born that she married and not in any way to injure the prisoner’s wife. She first proposed that they should marry.

Asked if she thought she was doing wrong, Maude replied that she did not. She stated that she loved him. On being asked to sign her name to her deposition, the woman known to the Hinton circle as Maude Weldon asked: ‘What is my name?’

The story was reported widely, covered by all three major London papers on the 15^th and 16^th October and as far afield as Birmingham, Worcester and Liverpool over the succeeding week. Charles was released and the trial was set for the session beginning October 25^th at The Old Bailey.

The scale of the trauma for all involved is apparent from the letters Olive Schreiner wrote during this period. On 16^th October she wrote to Karl Pearson:

As I write Mrs Nettleship has come in to ask me to get Mrs Weldon to come and take a room near this till the trial, so that I can look after her. They are afraid she may run away or kill herself & then Howard will they think kill himself. He really loves this woman, he doesn’t care a stroke for his wife as compared to her [...] You don’t know how terrible it was in the court yesterday. That poor woman would have been there utterly alone if I had not been there with her: all the others were together; she seemed such an outcast.[12]

On the same day she wrote more briefly to Ellis of the same matter: ‘Terrible day at the Old Baley [sic]. You know my brain has given way.’[13] Draznin reads some difficulty between Ellis and Schreiner during this time, evidenced by Ellis’s destruction of sections of his correspondence with Schreiner: ‘Considering that Ellis knew both parties extremely well and was, in fact, Howard Hinton’s confidant in this illicit love affair, the fact that all relevant letters are now gone suggests (as OS does) that his role was not a very admirable one, since he neither visited nor gave even written support.’[14]

Charles’s openness towards his friends regarding his affair with Maude was now beginning to emerge through other sources. On October 17^th Edward Thring recorded in his diary: ‘A letter from Mrs Hinton to Mrs David. She knew nothing of her husband’s infidelity till about a week before she made him confess. Mrs Nettleship knew it from the beginning almost. This is fearful. Altogether it is the strangest tragedy I ever heard of.’[15]

The Hinton family closed ranks. Olive Schreiner wrote to Karl Pearson on Monday October 18^th, 1886: ‘The Hinton affair gets worse and worse. They are now trying to prove that the children are not his but another man’s. Perhaps they are right. Life seems to have been to me like a grim face with a smile of despair on it since I came to town.’[16]

By the time of the trial, the last heard before the Recorder on 27^th October, The Hintons had mobilised what resources they oculd in defence of Howard. The solicitor acting on behalf of Hinton, Mr Bexley, read out glowing letters of recommendation of Howard’s good character from Edward Thring and Benjamin Jowett, the Master of Balliol. Sir Thomas Chambers, presiding, noted that the details of the case were so painful that they should not be made public. Howard was found guilty and sentenced to three days in Pentonville jail, which he would not have to serve due to the time he had already spent in prison on remand since being arrested on 25th.[17]

Alerted by the newspaper reports and Schreiner’s letters to Pearson, the members of the Men and Women’s Club were  disappointed to discover the extent to which the trial had been ‘managed’, thanks to the auspices of Geoffrey Lewis, a friend of Hinton’s sister. Ralph Thicknesse, attending on their behalf, noted that Maclure, the solicitor for the prosecution, ‘was a school or college friend of the prisoner at Balliol or Cheltenham’.[18]

For those members of the club who had felt betrayed to discover the unpleasant truth about James Hinton, the fact that clear evidence of the danger of his teachings was to be suppressed was difficult to stomach. Elisabeth Cobb, particularly, struggled to conceal her feelings in her letters to Pearson, writing on November 2nd: ‘One hardly feels as if it was fair, it seems as if it would have been better if James Hinton’s name had come in, & people who think about him, had understood more. And yet one can hardly wish that more cruel pain would have fallen on those who perhaps are innocent.’[19]

According to Ellis’s biographer Phyllis Grosskurth, ‘subsequent events are very confusing. Howard Hinton tried unsuccessfully to find work lecturing on four-dimensional space, about which he seemed, like his father in his way, to be an obsessional.’[20] Elisabeth Cobb wrote to Pearson: ‘All the family [...] have to join together to support this man & wife & all the children, in their utter material ruin. He is trying to get mathematical pupils.’[21]

Throughout all this, the absence of Howard Hinton’s own voice is noticeable. In a later letter Elisabeth Cobb wrote to Pearson that Miss Haddon was insisting that Howard was concerned that his crime should not be misinterpreted:

“Poor Howard was never for a moment misled into thinking he had been acting according to his father’s theories, & it is one of his bitterest thoughts now that he may have been the means of deferring the time when his father’s ethical doctrine should be accepted.” & again “he cannot believe that any readers of his father would make the mistake of in any way associating his errors with his father’s teaching.”

Miss Haddon’s protestation did little to convince Cobb or Pearson. Olive Schreiner, despite her friendship and loyalty, was also completely opposed to Hintonianism, describing it as a ‘terrible deadly theory’ and ‘a blight’.  A Hintonian rearguard action was always doomed to failure faced with such a damning crime. Howard’s conviction was the silver bullet for the anti-Hinton lobby, the final evidence that James Hinton’s philosophy was more dangerous than muddleheaded.

We are afforded a single account of Howard’s thoughts, contained in a letter to his publisher, William Swann Sonnenschein, one of only two that survive, written on 22^nd February 1887 at 31 Acacia Road , nine days after the birth of his fourth son Sebastian and as he prepared to leave the country to work for a mission in Japan. So revealing of Howard’s thought processes and his philosophy is it that it bears citing here in full.

I think I may take the liberty of writing pretty freely with you as from the conversation I have had with you will I think understand my position. In the essays which you have already had of mine there lies not merely chance and occasional thoughts but the most serious ones which I have had and they form if I may say so the necessary train of reasoning by which a mind must pass from materialism to a different form of belief – if it proceeds in a purely scientific way not accepting any form of historical “revelation”.

What I have come to see is that in the mere facts of the material world there is an evident and clear proof of a higher existence than that which we are conscious of in our ordinary bodily life. And it is, I believe, in the prosecution of this line of thought that the access to science of those truths which are apprehended of the religious consciousness will be found. However much or little these may seem in the reflections of others, they have been of vital importance to me – and the effect has been thus far simply ruinous – for I found myself in a false position – and the first & absolute condition of any true life as I understand it now lies in absolute openness. I have had to give up everything and go through disgrace such as rarely falls to anyone’s lot – and have to put up with misconception on every side. But still although I have lost all outward things I have got on the right basis of life. In the book which you have got of mine lie the steps of my reasoning. And I cannot help believing that at the present time when there are so many who like myself base all their belief on the evidence of the senses and refuse to admit anything supernatural, the process of thought which has led me to see that in materialism itself and through it there is a truer and higher idealism than can be got by turning from matter, may be of interest and perhaps of use.

If therefore you are inclined to help me in this subject I should be glad to have the book brought out as soon as possible.

If you think the present juncture is unfavourable for publication I should be much obliged if you would return me the M.S.S.

Believe me

Sonnenschein’s reply was the most personal he would offer to his author in a professional correspondence that spanned a decade:

I fear I am too much of an ordinary-minded individual to fully enter into your thoughts. I consider your speculations, so far as I have examined them, of much interest; but it appears to me that their application to every-day practice is fraught with much risk of error, not to speak of so mean a thing as danger. I should want a greater confidence in the sureness of my own mental strength before I ventured on so hazardous a line of action as such [illegible] ever feel inclined to judge others by the standards of my own timidity: I can only wonder at others’ confidence in themselves, & sometimes enjoy it.

What of Maude Weldon and her children by Hinton?  Of all those who suffered from the scandal, Maude would surely have faced the most difficulty as the young mother of two illegitimate children. We know she remained in London immediately after the trial. On 29th October Olive Schreiner visited her and wrote to Karl Pearson: ‘I have just returned from the city (11 PM) where I have been to see Mrs Weldon who is lying alone & ill in a miserable little public house near the Old Bailey.’[22]

Thereafter, Schreiner makes no mention of Maude in her correspondence. Almost a week later, on the 2^nd of November, Elisabeth Cobb wrote to Pearson that Olive was unwell but was seeing Mrs Weldon ‘constantly’: ‘I hardly know how but she [OS] has taken the guardianship of this unhappy Mrs Weldon on herself.’[23]

The correspondence between Ellis and Schreiner is incomplete for the period after the trial but a curious footnote is to be found in the papers of Ellis.

In 1935, having read of the award of an OBE to a Howard Hinton of Sydney, Australia, in the New Year’s honours list, Ellis made enquiries through friends in Australia and wrote to the man in question. No doubt his friends had reported that this Howard Hinton had grown up in London and moved to Australia as a child, for Ellis ventured: ‘I now address you in [illegible] that you may be my old friend’s son. If so I knew your mother about the time of your birth and was acquainted with all the circumstances.’[26]

The man was not and could not have been Howard Hinton’s son, having been born in 1867 to Thomas Hinton and Mary Howard. The fact that Ellis thought he might be, however, and his allusion to ‘the circumstances’ suggests very powerfully that Ellis suspected this man to be Hinton’s illegitimate son. Ellis, after all, knew the legitimate Hinton children and having stayed with them in Uppingham would certainly have known their names: George, Eric, William and Sebastian. He was in contact with Sebastian as late as 1913, four years after Charles Howard Hinton’s death, when Edith Ellis dined with him in Washington DC.

Phyllis Grosskurth has speculated that Ellis had acted as the midwife at the birth of Maude’s twins. Her evidence for this claim is, firstly, that Ellis specialised in midwifery and, secondly, that Elisabeth Cobb wrote the following line to Pearson referring to Olive Schreiner’s friendship with Maude: ‘She had been to see her, thro’ Mr Ellis who as a doctor attended her, some time ago before she even knew she (Mrs W) had anything to do with H.H.’[27]

In the same letter, Elisabeth Cobb also wrote to Karl Pearson: ‘OS is wondering if she can help Mrs W away to work at the Cape.’ Schreiner was wondering aloud about how to help Maude Weldon shortly before all mention of her disappeared from correspondence. Her letters to Ellis of this period were incompletely destroyed at her request and some fifty years later Ellis wrote to a stranger in Sydney, hinting at knowledge of the ‘circumstances’ surrounding his birth. My own speculation is that Schreiner did indeed act upon her instinct to help Maude Weldon and her twins to leave the country and that Ellis, friend to them both, was her sole confidant in the matter and subsequently destroyed all correspondence relating to it. Ellis certainly seemed to think it possible that he was writing in 1935 to Hinton’s illegitimate son in Australia.[28]

---

[1] Ellis, My Life, 142.

[2] Draznin, 116.

[3] Draznin, 276. For the purposes of brevity and clarity I shall hereafter refer to Charles Howard Hinton by the Christian name Howard, by which he was known to his family and friends.

[4] Draznin, 291.

[5] Draznin, 337.

[6] Draznin, 361. Draznin, who has seen the further correspondence of Schreiner archived at the HRHRC, notes that this remark ‘may also refer specifically to a promise Howard Hinton gave to Mrs Weldon to seek a divorce from his wife, which he has now reneged upon.’ I have been unable to locate any primary material referring to such a promise so cannot comment upon its veracity and can only assume it is mentioned elsewhere in Schreiner’s letters.

[7] EM Walters to Olive Schreiner, Pearson papers. There is an irony to this last line, in that Karl Pearson, perhaps the most morally indignant member of the Men and Women’s Club, was also from a family of dissenters.

[8] Havelock Ellis papers, British Library.

[9] Karl Pearson papers, UCL.

[10] Edward Thring diaries, Uppingham School. Only the first and last of Thring’s diaries survive, the remainder having been destroyed by Thring’s biographer Parkin. The final diary begins in October 1886, a trying time for the headmaster.

[11] The Times, October 15^th 1886.

[12] Pearson papers, UCL.

[13] Draznin, 422.

[14] Draznin, 9.

[15] Thring diaries, Uppingham School.

[16] Pearson papers, UCL.

[17] In the same session of the Old Bailey, eight cases of bigamy were tried. Sentences ranged from three days to two years with hard labour. Hinton’s was the shortest sentence.

[18] Karl Pearson papers, UCL.

[19] Karl Pearson Papers, UCL.

[20] Phyllis Grosskurth, Havelock Ellis: A Biography, 102.

[21] Karl Pearson papers, UCL.

[22] Karl Pearson papers, UCL.

[23] Karl Pearson papers, UCL.

[24] Draznin, 9.

[25] Draznin, 423.

[26] Havelock Ellis papers, British Library.

[27] Karl Pearson papers, UCL.

[28] I note the difficulty in tracking Maude due to the ambiguity over her name after the trial. That Ellis might have assumed that an illegitimate son assumed the name of the father who abandoned him is reasonable in light of this.

Angles conference

All has been silent here for a couple of months for two reasons. The final push towards publishing a new issue of 19 always takes up more time than expected, so April was pretty much flat out on that, leaving little time for blogging. I think the resulting issue, the last in the current dreamweaver-built html format before a switch to an all-singing, all-dancing redesigned OpenJournal version, has been worth it. That’s here.

My own research has been focused on chasing down the influence of Francis Galton on Flatland. It’s been very fruitful and I’m trying to pull it all together into an essay that might be suitable for submission for publication, so until that’s all done I won’t know exactly which bits I’ll be free to put up here, but as soon as I do I’ll post them up.

This has been a real eye-opener, particularly reading Galton, who I was only aware of by reputation, and as the father of eugenics, that rep aint so clever. Attempting to periodise his work, to think in nineteenth century terms when dealing with phrases such as ‘the prognathous brow of the Irishman’, is tricky, especially when 21st century liberal vibes throw up great clouds of cotton-wool in front of my vision. It’s essentially a filleting job, because disproved and prejudicial statements, risible methodology and intense social conservatism rub shoulders with influential psychological experiments and radical approaches to the application of statistical methodologies.

And writing of methodology, I’m giving a paper at the Angles conference on cultural history at Birkbeck on 20th June. Given that I’m calling Fairyland a cultural history it seemed as if it would be pretty remiss not to put in a proposal, and it’s a useful stage to think again about my methodology, as I’ve allowed the material to direct me so far. In essence, the paper will describe this process and the sources that have suggested the way I’m now working. It’s much more personal than the other papers I’ve given, and I’m slightly nervous that it will seem unscholarly in comparison to other papers on the day, but I should feel at home with the material and some of it will be drawn from rough drafts of my introduction.

Anyway, here’s the abstract:

Unintended hybridity: the case of higher space

Through initial encounters with the concept of the fourth dimension in twentieth century literature and secondary writing on Modern art, my research has led me rapidly into a period – the nineteenth century – and disciplines – mathematics, history of science and psychology – in which I was inexperienced and with which I felt varying degrees of comfort. The subject under consideration nevertheless dictated an engagement with these fields.

This paper gives an overview of two approaches to the idea of interdisciplinary research that have informed my work on higher space (and provided some level of comfort). Drawing on Michel Serres’s conversations with Bruno Latour, it situates Serres on interdisciplinarity. Using Roger Luckhurst’s cultural history The Invention of Telepathy, it highlights a blueprint approach to how such interdisciplinary research might be pursued, embarking from a literary historical or cultural theoretical background.

Examining the link between the two, the work of Bruno Latour, and focusing on Latour’s involvement in the SOKAL affair, it addresses continuing doubts over the practice of interdisciplinary modes of research. In so doing it seeks to find a justification for allowing the diktats of the subject under consideration to overcome the risks inherent in the untrained transgression of disciplinary boundaries.

Flatland criticism…

An overview of the secondary literature on Flatland should correctly begin with the various notices and reviews of the period. A number of these are admirably collected and posted by Thomas Banchoff here, so rather than commenting, I’ll allow the reviewers of the period to speak for themselves. The breadth of the publications in which notices were published demonstrates the immediate reach of the book, and the second flurry of reviews follows the publication of the third edition with a foreword by William Garnett, in 1926.

Despite the fact that it remained in print pretty much throughout the 20th century, the only writing on Flatland to be found in the middle of the century was Banesh Hoffman’s 1952 intro to the Dover edition, which has been reproduced several times since. In laudatory mode, Hoffmann situates the text in scientific history as a pre-relativity work: ‘In these days space-time and the fourth dimension are household words. But Flatland, with its vivid picture of one and two and three and more dimensions, was not conceived in the era of relativity. It was written some seventy years ago, when Einstein was a mere child and the idea of space-time lay almost a quarter of a century in the future.’ He describes it as ‘no trifling tale of science fiction. Its aim is to instruct, and it is written with subtle artistry.’

David W. Davies took a more literary historical approach in 1978, penning a brief biography of Abbott and citing the reviewers of the day and Abbott’s own article from The Contemporary Review in 1890, ‘Illusion in Religion’, to contextualise Flatland. Noting also Abbott’s engagement with Bacon and Cardinal Newman, Davies’s short intro is surely the wellspring for more recent criticism. Significantly, Davies closed by comparing Abbott’s application of ‘a mathematical way of thinking to literature’ to that of the OULIPO writer Harry Matthews, concluding: ‘Mathew’s permutations are for fun, and as the Boston Advertiser reviewer noted, that is the purpose of Flatland.’

Interest really began to increase in the 1980s, and I’d suggest a couple of reasons for this: the impending centenary of publication in 1884 and the advent of computing that could facilitate the rendering of four-dimensional images. This surge of interest was led by SF writers, publishers and the critics who had begun to found a scholarly response to the genre. So in 1982 Isaac Asimov contributed as dry an introduction as one might expect from the hardest of hard SF writers, praising Flatland as an essentially educational text, while Ray Bradbury’s 1983 introduction responded in far softer terms to the satirical intent of the novel. Rudy Rucker, meanwhile, commented on and responded to dimensional work by both Abbott and Hinton extensively in his fiction and non-fiction writing of this period, and will receive closer attention in a future post. For now I want to look at Bradbury’s response, which is rare in Flatland criticism by paying particular attention to the literary qualities of the work and taking considerable joy in them. It’s worth quoting a sizeable chunk of this:

Why has the book remained so popular for almost a hundred years? Because, like Mark Twain, Professor Abbott must have thought: I refuse to be serious about a serious subject. Churches brim with seriousness and snoozers snooze. Scientific conferences of one denomination or another drone on through endless and ungoiden afternoons and one chooses the catnap as against suicide. The only medicine is high spirits and good humor. Professor Abbott has both in tonic proportions. I cannot help feeling that those who shared his home with him while he was flattening his concepts to fit his pen must have heard quick bursts of laughter from his den when it suddenly struck him to write, for instance, those sections on ’feeling’ as a means of identification amongst the Flatlanders. There are serene and marvelous sexual under-and-overtones here perhaps more for us in this neo-barbarian age, than for those who inhabited the three-plus-one dimensions of 1884. Abbott, in other words, is able to play himself and win. Given the measurements of Flatland he moves out intuitively and with huge delight to ’feel’ his own creations, sum them up in shapes, and report back to us. We go with him, because it is not often we have such a guest, in our living room, so full of mathematical logic leaning into fun that we are quite content to shut our mouths and score his game.

The same year witnessed the publication of the first scholarly genre pre-history of science fiction by Darko Suvin. The progressive strain in Flatland was central to Suvin’s elevation of the text to lofty status within his pantheon of Victorian Science Fiction. For Suvin, Flatland is categorised as a ‘sophisticated alternative history’. He’s highly approving of ‘the first concrete account of a plebeian rebellion in UK SF’ (372) (despite its failure, which he doesn’t mention) and describes Abbott’s abstraction as ‘not unworthy of the fertile analytical abstractions of Darwin and Bacon (of whom he knew) or indeed of Marx (of whom he did not know).’ (370)

Roger Luckhurst’s dismissal of Suvin’s definition of SF as a literature of ‘cognitive estrangement’ – on the grounds that this definition is so ideologically conditioned that it fails to account for important texts that don’t conform to a Marxist perspective, and here’s a list of such texts by the man himself – should be noted, but need not concern us unduly here, because Flatland gets the thumbs up from Suvin and is therefore given considerable attention. (In Luckhurst’s account, mechanisation defines the genre of SF, which clearly excludes Flatland, and here it’s hard to disagree. As any fule no, Flatland is in fact math-fi, so perhaps we shouldn’t get too hung up on generic definitions.)

Suvin makes one particularly useful observation which I would like to stet, writing: ‘Cleverly adapting Carroll’s and Verne’s strategy of subsuming but transcending the juvenile reader, Abbott’s is in truth “A Romance of Many Dimensions”; in its thoroughgoing democratism, it is addressed to the best minds in the new reading public, issuing from the newly introduced obligatory primary schooling.’ (373) As has been noted numerous times subsequently (Jameson, Stableford, Luckhurst, among others), the idea that a new generation of lower middle class readers had been produced by the primary system by the 1880s has been pretty much put to bed, but let’s not lose the first part of Suvin’s point, that Flatland works for both younger and older readers. Secondary criticism since Suvin has tended to ignore this younger readership.

Such criticism has been more concerned with contextualising Flatland in the broader cultural field. In 1986 Rosemary Jann argued that ‘as part of Abbott’s wider commentary in the role of imagination in cognition, Flatland alludes to contemporary debate over the role of hypothesis in scientific discovery and the relationship between material proof and religious faith’ (473). For Jann, Flatland is a paean for ‘the progressive force of the imagination’ (486), and negotiates a middle way through inductive science, responding to debates over the unseen in the natural world, and dogmatic faith, allowing for a less absolute faith in the literal truth of the written scriptures.

Jann’s work informed Jonathan Smith, writing a decade later, in his chapter ‘Euclid Honourably Shelved’, which offers a Baconian reading of Abbott. Suvin’s comment (above) on Abbott being aware of Bacon doesn’t really do justice to the relationship: Abbott published two books on Bacon, and Smith charts the trajectory of his modulating opinion. In so doing he positions Flatland among the contemporary arguments for and against non-Euclidean geometry, working deftly with the detail of the primary material. Smith’s overview of secondary writing on Flatland is worth quoting:

When not treated as a joke, Flatland has tended to be approached in ways that divorce it from its cultural position in the debate over non-Euclideanism and its implications. Historically, literary critics have treated it as an early example of science fiction and fantasy, while scientists and mathematicians have used it as a clever way to introduce their students to concepts of dimensionality and non-Euclideanism. It has only been recently that the book has been brought back to the center of the study of Victorian culture, and it will be to further that movement that I approach the novel here. (191)

The party most guilty of treating Flatland as a joke in Smith’s account was Bertrand Russell, who addressed ‘metageometry’ in his Essay on the Foundations of Geometry, published in 1897 and based on his PhD thesis. It’s not strictly accurate, however, to say that Russell treated Flatland as a joke: he actually wrote that Abbott used the dimensional analogy as a joke, and this seemingly subtle difference is quite significant, I think.

Shortly after the publication of his book on Bacon in 1996, Smith contributed to an essay co-written with Berkove and Baker that responded to Rosemary Jann’s reading of Flatland’s ending as ambivalent by highlighting what the authors argued was an implied criticism of the theology of Cardinal Newman. Most interestingly for me, Smith et al. draw out from Flatland not an analogical inspiration, but rather an extended critique of misapplied analogy, of which they argue that Abbott believed Newman was guilty. They draw attention to English for English Readers, a textbook Abbott compiled with his friend J.R. Seeley, and its sections on analogy. English was aimed at the improving native reader and writer of English – the schoolboy – and its lessons on analogy, and the parent category of induction, are clear.

Analogy meaning Likeness. – Analogy meant originally an Equality of Ratios, or Proportion. It is sometimes, however, loosely used to represent not so much proportion, as the similarity and regularity of natural phenomena. (265) So far as it is an argument at all, [it] comes under the head of Induction. Otherwise it is not an argument, but a metaphorical illustration of an argument. (273)

What’s more, induction itself is unsound:

The Induction that proceeds from enumeration of instances to a general statement about a class [...] is evidently an insecure method of proof [...] It is based upon the principle of uniformity in nature, “what has been is and will be” [...] Induction is always incomplete [...] Thus all statements that result from merely enumerative induction are temporary and liable to correction. They may therefore be called provisional. (262-263)

Smith et al therefore turn Jann’s conclusion on its head: ‘Flatland is a cautionary tale about the dangers of the imagination when wrongly applied.’ (129-130)

Most recently K.G. Valente has done some serious digging and found an essay published in the City of London School Magazine in 1877 dealing with higher dimensioned space. Please click through the scans below to read ‘A New Phbilosophy’ for yourself.

It’s a striking find for a number of reasons: like Flatland it presents a humorous response to very recent writing on n-dimensions; it was published anonymously in the magazine of the school at which Abbott was headmaster during his tenure; and it also essays the sketching of a parodic belief system based on the reductio ad absurdum of the dimensional analogy. Is it Flatland in utero? It’s certainly a fantastic piece of writing for a schoolboy audience, ably demonstrating the euphoric headlong rush into error through rigid application of a woolly logic, eerily similar to that upon which Zollner was just embarking in Leipzig.

Valente wisely refrains from pointing the finger directly at Abbott (and how frustrating it must be not to be able to stand it up!) Of course, it could have been Abbott who authored the piece, but it could just as easily have been William Garnett, the headboy at City of London in Abbott’s third year as headmaster, who had by 1877 begun work as Clerk Maxwell’s assistant and would go on to be his biographer (Garnett would have been just as well versed in the contemporary discussions of n-dimensioned space taking place in The Academy, Nature, Mind and at the BAAS: Clerk-Maxwell alluded to it in his verse on a number of occasions in this period). Or it could simply be the work of an unusually bright pupil at City of London. We’re unlikely ever to know.

While I would follow Valente in leaving the question of authorship tantalisingly open (the beauty of blogging – I can have my cake and eat it by adding my own wild speculations before retreating rapidly!), I wouldn’t necessarily subscribe to his reasoning. Valente writes that

even with such satirical potential there is one element of the piece that would not be subjected to [Abbott’s] ridicule. Recall that the author identified serious limitations that materialism represented regarding religious contemplation; this is a conviction Abbott would not wish to mock. Although Jann noted ambivalent elements in Flatland (488), testimonials by students and peers strongly suggest that Abbott’s intellectual integrity made it difficult for him to condone ambiguity. Consequently, attributing “A New Philosophy” to him would require the problematic approbation of contradictory ideological juxtapositions as well as an explanation for their amelioration by 1884. (66)

But ‘A New Philosophy’ is monomaniacal. I can’t help but feel that while Valente acknowledges that ‘A New Philosophy’ is a humourous piece, he reads it with too straight a face, and as I’ve suggested two pars back, I think it’s intended as a piece of absurdist reasoning and is parodic to its bones: it could certainly contain ‘ideological juxtapositions’ to Abbott’s stated beliefs without entertaining any ambiguity. I also believe it has a specific satirical target in its sights, and, once again, I plan to develop that idea in a later post.

The trajectory of current criticism on Flatland, then, follows Smith’s aim to bring the text back to the ‘center of the study of Victorian culture’. While this shift in emphasis has produced some inspiring work and has rescued Flatland from ghettoisation as a sci-fi precursor text, it also, by bedding it so thoroughly into the contexts of religious or scholarly discussion of significance in this period, risks obscuring the anomalous nature of the text and the very source of its popularity. Not only was Flatland the only fiction published by the prolific Abbott in a thirty-year writing career, but it is also, like ‘A New Philosophy’, less than serious.

I’m likewise suspicious when the secondary criticism positions Flatland as an element in some kind of smooth-surfaced theological project on the part of Abbott. I think it’s important, particularly when attempting to recreate the ‘cultural position’ of the text, to hold in mind William Garnett’s description, in his preface to the third edition, of the book as a ‘jeu d’esprit’, and the comments of earlier respondents like Bradbury and Davies: Abbott was having fun with this book, and writing for a broader audience than that he habitually addressed. Russell recognised this, as did contemporary reviewers. There are certainly consistencies with his theological writings, as one would expect, but we must remember that what we are reading is not a manifesto (in the case of Flatland, at least: a manifesto is exactly what ‘A New Philosophy’ is, and a very good a priori spoof of the form it is too.)

Of course, to argue for a reading of Flatland responsive to its humourous intent is to create a rod for my own back – is satire necessarily actually funny? can intent be assumed? – but what I’m really advocating is the recuperation of elements of earlier criticism rather than the dismissal of fresher discoveries. It goes without saying that I think Smith’s work in contextualising Flatland in discussion of non-Euclideanism was entirely necessary; it’s important, too, to hold in mind Abbott’s position on miracles and the imagination; I’m particularly persuaded by the argument that Flatland critiques rigid and literalised analogical reasoning; and I’m totally thrilled by ‘A New Philosophy’. None of this stops Flatland being an amusing book written with a schoolboy audience in mind: this is a crucial point when it comes to the spread of the concepts of higher space. It’s important that we don’t ‘divorce it from its cultural position’ as a funny and popular book. And I also think it’s overstating the case to think of Flatland as an integrated part of a theological project when it is enmeshed in a complex matrix of contemporary social and cultural concerns and responsive to such a broad range of ideas as Galton’s eugenics, ‘plebeian rebellion’, geometrical pedagogy and the education of women.

So that’s a fairly breezy overview, which has doubtless missed some significant contributions, but it’s a reasonable launch-pad for some consideration of thee text itself, which I always seem to be threatening without ever actually doing…

Hinton photos

In the absence of a written post last week (immersion in secondary literature on Flatland has really just identified much further reading and not produced much in the way of original material), some archival Hinton imagery.

The first is a family photograph taken at the studio of K Yoshida in Kanazawa ca 1890 (the image is undated but the youngest child Sebastian, born in 1887, looks about three.) The original print is held in archive in the papers of Howard Everest Hinton at the University of Bristol. The second is just a closeup of Charles and the final one is the court document relating to Hinton’s conviction for bigamy at the Old Bailey in 1886.

The family of Charles Howard Hinton, ca. 1890

Close-up on Charles

Hinton’s conviction for bigamy in 1886

The dimensional romance continued…

While on the subject of publishing contexts at the end of 1884, and before edging further into Flatland and dealing with content…

It has become customary to connect Flatland to the work of Charles Howard Hinton, and the connections between Edwin Abbott and the author of Scientific Romances have been explored in some detail by a number of writers (Banchoff, Stewart, Valente). Developing the case made by Banchoff in 1990, that ‘Hinton lies at the centre of a web of intellectual, mathematical and social influences’, Ian Stewart argues that ‘the similarities between Hinton’s 1880 article [‘What is the Fourth Dimension?’] and Flatland are far too great to be coincidence’ and that ‘the circumstantial evidence that they probably did meet – or that, at the very least, Abbott was strongly influenced by Hinton’s ideas – is considerable’.

Extrapolating the publishing history of Hinton’s work clarifies one such connection. Hinton’s ‘What is the Fourth Dimension?’ had, as noted, been first published in 1880, but to a very limited audience; indeed, to an audience so scant that it failed to sustain The University Magazine, the ailing journal in whose last number the essay appeared (originally the monthly Dublin University Magazine, The University Magazine had been renamed in 1878, and reduced frequency of publication from monthly to quarterly from June 1880, before finally closing at the end of 1880. Hinton’s mother-in-law Mary Boole had been a frequent contributor).

By the end of 1880 Charles Howard Hinton was working as assistant science master at Uppingham College (one of the connections made by Banchoff: Abbott’s lifelong friend Howard Candler, to whom Flatland was dedicated, was mathematics master at the same school). He was not a novice to publishing, having edited a collection of his father’s work, Chapters on the Art of Thinking and Other Essays, published by C.K. Paul & co in 1879, but ‘What is the Fourth Dimension?’ was his first published work under his own name.

It was reprinted in slightly expanded form in 1883 in the magazine of Cheltenham Ladies College, where the author had worked as assistant master from 1877 to 1880. Once again, it is safe to assume that the school magazine had a limited audience, although precise figures are not available. Stewart’s speculation that Edwin Abbott’s acquaintance with the headmistress Dorothea Buss in the 1880s was another potential point of contact between Abbott and Hinton seems more tenuous than the Candler link. What is clear from both the titles in which Hinton’s essay first appeared – a magazine hoping to appeal to a core student readership, and the magazine of a school – is that its author considered it a pedagogical piece. An instructional essay for students it is likely to have remained were it not for Abbott’s book.

The timing, format and re-editing of Hinton’s essay for publication by Swan Sonnenschein in November 1884 suggests very powerfully a commercial response to Flatland, whose first edition of 1,000 copies had been sold within a month of publication. What is the Fourth Dimension? (italics will henceforth be used to distinguish between the pamphlet and the collected essay) came hot on the heels of Abbott’s book as a part-issue, a format suggestive of a rapid publishing response: as the entry for ‘Serials and the Nineteenth Century Publishing Industry’ in the Dictionary of Nineteenth-century Journalism notes: ‘The principle motivations underlying the rise of serial publications were speed and economy.’ (Brake, Demoor eds, 2009: 567) There is also considerable evidence in the archives of Swan Sonnenschein that Hinton did not yet have enough completed work for a book.

Should there be any doubt concerning the opportunistic nature of the 1884 re-publication of Hinton’s essay on its third go round the block, its new title and subtitle surely settle them. It has been suggested by Rudy Rucker that the subtitle Ghosts Explained was added by the canny publisher, aware of the Zöllnerian hypothesis and its currency in spiritualist groupings. But surely the title of the series, Scientific Romances, is even more suggestive of commercial expediency? Hinton’s first ‘romance’, after all, was not even fiction, but a pedagogical exposition answering its own question in terms that only began to hint at the visionary hue of the psychological metaphysics that would follow. Stylistically, it owed more to the popular science writing of Tyndall than it did to Stevenson, but the content was evidently particularly amicable towards Flatland and the market was demonstrably keen on dimensional romances in November 1884.

It seems highly likely, then, that the chosen designation of ‘romance’ would have identified Hinton’s work to the readership to whom it was most likely to appeal: recalling Stevenson’s definitional account, a young (?), masculine, domestic (British) readership. The subject matter of geometry would further limit the audience to those educated in mathematics.

Darko Suvin’s obsessive historical materialist categorisations of the readerships of early SF precursor texts are interesting here, not because I would like to categorise Hinton’s work in such a way, but because in identifying a social proximity between the authors of proto-SF, scientific non-fiction and the readers of both, outside of mainstream circuits, he speaks directly to the textual hybridity of Hinton’s work: ‘Indications from the textual system point to one of those groups comprising mostly upper-middle and middle class males with special interest in politics, religion and public affairs in general. This is a circuit very close, perhaps even identical, to that of the bourgeois nonfiction reading – which would explain the intertextual closeness to SF of such nonfiction genres as the social blueprint, the political tract, the predictive essay, even the semi-religious apocalypse.’ (Suvin, 1983: 403)

This also, however, creates an interesting tension. I find myself wanting to argue that savvy publishing nouse helped to make the fourth dimension a subject of discussion in social groupings beyond specialist mathematicians and spiritualists.  If the readerships of texts such as Flatland and What is the Fourth Dimension? are as socially narrow as Suvin suggests, however, do they really introduce the arcania of higher space to a broader audience? I think the answer to that question probably lies, in part, elsewhere: it’s what these texts do with the subject, as well as to whom they tell it, that catalyses interest.

Finally, a word or two on that canny publisher, William Swan Sonnenschein. Sonnenschein built his list in the early years (ca. 1878-1882) around books for children, educational texts or theoretical work concerning education policy. There was also a focus on German language translations, such as Grimm’s Teutonic Myths. Both arose naturally from the publisher’s family background: his father was a German-born mathematics teacher. Although Sonnenschein described himself as a liberal, he was closely connected socially to a number of Fabians and socialists, publishing both the first English translation of Marx’s Capital and George Bernard Shaw’s Unsocial Socialist in 1887. (Stepniak, exiled Russian revolutionary, was apparently often to be encountered taking tea chez Sonnenschein).

The Swan Sonnenschein list also always included philosophy, and the publisher was a member of the first Ethical Society in the late 1880s. Commissioned to write a history of the firm’s precursors by George Allen and Unwin in the 1950s, the historian F. A. Mumby wrote: ‘Throughout his life Swan Sonnenschein was a remarkable blend of other-worldliness and business acumen; a man of wide erudition whose interests were quickly roused by the simplest human problems’. Combining education, mathematics, philosophy and literature, Swan Sonnenschein was a highly appropriate home for the esoteric and hybrid work of Hinton.

So, some further lines of research worth pursuing with regard to dimensional romance: its roots in pedagogy and a progressive, broadly socialist, political subtext. Onwards and upwards. Or, as Flatland has it, Upward, not Northward.

Flatland illustrations

Some initial thoughts on Flatland. So, to begin at the beginning with the title page…

Many dimensions

Strange that this has occasioned so little critical comment. Iain Stewart’s excellent annotated edition of the text locates the Shakepearean quotes (Hamlet, Act I Scene v, the appearance of the ghost, and Titus Andronicus, Act III Scene i), both of which are fairly obviously puns and perhaps only tangentially connected to their context. I’m intrigued by the illustration – is it a map? – of a nebulous mass, perhaps fog, perhaps clouds.

It might well be a map. Flatland, ‘a Romance of Many Dimensions’, was published in October 1884. As such it arrived not terribly long into the ‘romantic revival’ of the 1880s, inaugurated, according to most accounts, the previous year, with Robert Louis Stevenson’s Treasure Island. Before that, in the launch issue of Longman’s Magazine in November 1882, Stevenson had given a theoretical outline of his fictional practice with ‘A Gossip on Romance’, advocating a robust, masculine, adventuring, fiction delivering a ‘kaleidoscopic dance of images’ and recalling books read in the ‘bright troubled period of boyhood’. Stevenson’s advocacy of romance has subsequently been read in opposition to Henry James’s championing of the interiorized, feminine and despicably foreign (!) realist novel.

This brief sketch is sufficient for now to give an idea of one aspect of the context into which Flatland arrived: while the descriptive term romance had been used in the title of many earlier nineteenth century novels, and even proto-SF novels – Edward Maitland’s An Historical Romance of the Future (1873) being an (the only?) example of the latter – when Abbott subtitled his book a ‘romance’, he connected it to a very current trend in fiction publishing. There was good reason for so doing: Treasure Island had been a bestseller. The inclusion on the title page of Flatland of a map would have underlined the connection to Treasure Island in particular.

Treasure Island

So is it fog, or is it clouds? The text contains fog – common, apparently, in the temperate regions of Flatland – but the closing illustration repeats the nebulous illustration with more Shakespeare, this time from Prospero’s speech in The Tempest, Act IV, Scene i:

You do look, my son, in a moved sort,

As if you were dismay’d: be cheerful, sir.

Our revels now are ended. These our actors,

As I foretold you, were all spirits, and

Are melted into air, into thin air:

And, like the baseless fabric of this vision,

The cloud-capp’d towers, the gorgeous palaces,

The solemn temples, the great globe itself,

Yea, all which it inherit, shall dissolve,

And, like this insubstantial pageant faded,

Leave not a rack behind. We are such stuff

As dreams are made on; and our little life

Is rounded with a sleep.

The baseless fabric of vision

Thin air, then, and clouds. And I’d suggest that the classical scholar Abbott may also have had in mind an earlier passage of satire, from Aristophanes’ The Birds. In the following exchange the tyrannical Pithetaerus passes judgement on the geometer Meton in his attempt to enter Cloudcuckooland:

(Enter METON, With surveying instruments.)

METON: I have come to you…

PITHETAERUS (interrupting): Yet another pest! What have you come to do? What’s your plan? What’s the purpose of your journey? Why these splendid buskins?

METON: I want to survey the plains of the air for you and to parcel them into lots.

PITHETAERUS: In the name of the gods, who are you?

METON: Who am I? Meton, known throughout Greece and at Colonus.

PITHETAERUS: What are these things?

METON: Tools for measuring the air. In truth, the spaces in the air have precisely the form of a furnace. With this bent ruler I draw a line from top to bottom; from one of its points I describe a circle with the compass. Do you understand?

PITHETAERUS: Not in the least.

METON: With the straight ruler I set to work to inscribe a square within this circle; in its centre will be the market-place, into which all the straight streets will lead, converging to this centre like a star, which, although only orbicular, sends forth its rays in a straight line from all sides.

PITHETAERUS: A regular Thales!

Tools for measuring the air, indeed! This prompts a number of lines of thought. A bone of contention in discussions over higher space concerned its imaginary as opposed to its empirical nature. As an algebraic and then a geometric theory – in other words, as a mathematical construct – higher space remained comfortably ideal. With interventions from physics and Zollner’s catastrophic/catalytic misreading of four-dimensional space, the waters became muddied – or perhaps better to write that the airs became fogged. Was physical space actually four-dimensional?

Higher space existed in the interstices between the ideal and the empirical, as did the emergent sciences of mind, in which perception of space was a primary site of conflict. Abbott’s cloud, then, is thought, imagination, the higher space of mind in which the higher space of geometry existed, an analogue noted by William Spottiswoode in his 1878 address to the BAAS: ‘Or once more, when space already filled with material substances is mentally peopled with immaterial beings, may not the imagination be regarded as having added a new element to the capacity of space, a fourth dimension of which there is no evidence in experimental fact?’

As for Pithetaerus’s remark on Thales, this suggest routing discussions through Michel Serres, whose two essays on the origins of geometry consider the case of Thales and the discovery of mathematical analogy. But I believe that would justify another post entirely and this one already needs more work!

A Tangled Tale: knots, matter and magic in the 1870s

[text of a paper given at the WiP conference at Birkbeck on 7 February 2009 - slides to be inserted as images at a later date]

KNOTS, MATTER AND MAGIC

In early 1878 Johnann Karl Friedrich Zöllner, professor of astrophysics at the University of Leipzig, published in The Quarterly Journal of Science, edited by the British chemist and spiritualist William Crookes, an account of an experiment he had undertaken with the spirit medium Henry Slade.

‘On Space of Four Dimensions’ argued that the human conception of space as three-dimensional was based upon experience and that as soon as experience appeared to contradict this conception we would be forced to revise our theories of space. Pausing briefly to appeal to the work of the mathematician Bernhard Riemann, whose paper ‘Concerning the Hypotheses Upon Which Geometry is Founded’ had become a posthumous cornerstone of the recently emerged non-Euclidean geometry, Zöllner went on to describe manipulations of a cord of string.

Confined to a plane, or two dimensions, a knot could be conceived as a simple twisting of the cord. Without access to the third dimension, this twisting or crossing could not be undone except by cutting the cord or passing it back through itself; with access to a third dimension, a simple rotation of the cord would suffice to undo the loop. This loop was the two dimensional equivalent of a knot and so extending space to three dimensions, and placing a three-dimensional knot in the cord, Zöllner argued that access to a fourth dimension of space would, by analogy, allow the knot to be undone without cutting the cord or passing it back through itself. Here, Zöllner was précising an 1874 paper by the young projective geometer Felix Klein, to whom I shall return later.

Zöllner continued his argument by borrowing highly selectively from the work of the mathematician Carl Friedrich Gauss and his own philosophical touchstone, Immanuel Kant. He quoted from Kant to demonstrate that because a space of four dimensions could be conceived, it would ‘probably’ exist, and likewise immaterial beings of the spiritual world.

His groundwork established, Zöllner proceeded to the core of his argument:

If a single cord has its ends tied together and sealed, an intelligent being, having the power voluntarily to produce on this cord four-dimensional bendings and movements, must be able, without loosening the seal, to tie one or more knots in this endless cord. Now, this experiment has been successfully made within the space of a few minutes in Leipzig, on the 17th December 1877, at 11 o’clock AM, in the presence of Mr. Henry Slade, the American.

Zöllner’s friend, and fellow witness, Gustave Theodor Fechner, was also convinced of the experiment’s success, describing it in his diaries as ‘above suspicion’. The spiritualist community in Germany and England was elated, and the triumph was trumpeted throughout its journals, and reported uncritically in the Daily Telegraph. Within a week British spiritualists, including T.L Nichols and the medium William Eglinton, claimed to have reproduced Zöllner’s ‘splendid manifestation’. At the heart of the longed-for scientific proof of the existence of both spirits and the fourth dimension, lay the not-so-humble knot.

The repercussions of Zöllner’s experiment echoed for some time. It became a highly contested episode in the history of Psychic Research and is still cited in spiritualist literature as evidence of scientific plausibility of the spiritual hypothesis. Scientific border policing and counter-currents of legitimisation and deligitimisation typical of hybrid scientisms surrounded accounts of Zöllner’s experiment. Evidence suggestive of its illegitimacy lay buried within Zöllner’s own accounts of his work, which stretch to over 4000 pages in the original German. I am grateful, therefore, to Eleanor Sidgwick, wife of Henry, one of the founders of the Society for Psychical Research, for undertaking the work of sifting through these papers in 1886. Mrs Sidgwick reported to the Society:

That Professor Zöllner did not always perceive and avoid important sources of possible error may, I think, be inferred from his writings. For instance, in describing the séance on December 17th, 1877, wherein he obtained four knots in a string of which the ends were tied and sealed together, he omits to mention that the experiment had been tried and failed before. We learn that this was so, accidentally, as it were, from his mentioning it in another place and in another connection, where he tells us that it was a long time before the spirits understood what kind of knot was required of them, and that before they did so he obtained knots, but not such as he wanted – knots, I infer, which could be made by ordinary beings without undoing the string.

Putting to one side for now the scientific legitimacy of Zöllner’s work, I want to focus on his interest in the knot. I want to untie its threads and trace them back, asking how the knot became proof of something so fantastic as fourth dimensional intelligence. In so doing, one theoretical touchstone has presented itself in an irresistible fashion. In Pandora’s Hope, the French sociologist Bruno Latour explores scientific concepts through metaphors of knots in networks. Latour argues against the idea of ‘pure’ science, seeing bound together in the knots of scientific concepts the heterogeneous processes on which they depend, processes he lists as ‘instruments, colleagues, allies, public’ and the knot itself. Indeed an equation is the perfect knot, so many different elements so tightly bound into one expression.

Latour’s way of thinking is particularly useful in approaching what might immediately be recognised as a hybrid, scientistic concept: he has used a historicist approach to the history of science to re-examine lost or abandoned theories. In this instance, as will become apparent, we’re examining disqualified theories on both sides of the argument. Furthermore, Latour’s insistence on the permeability of the object-subject relationship, on the significance of the non-human in science, is clearly appropriate to the technological object of the knot itself, the dense structure doing so much work at the heart of this account.

If you’ll permit me to really stretch Latour’s metaphor, I propose to pick out three strands from this particular knot: magic, matter and higher space.

The first strand of the splice follows the history of spiritualist performance and its shadow play in stage conjuring. For both mediums and conjurors, the knot was a tool and the tying of knots an essential skill. The Spiritualist Davenport Brothers who exhibited to their audience purported spiritual manifestations occurring inside a cabinet, such as the playing of instruments, were bound by ropes before being shut into their box. Their bindings were proof to their audience that these manifestations could not be performed by the brothers themselves but must be created by the spirits they summoned.

When the Davenports performed in Cheltenham in 1864, a young man called John Nevil Maskelyne interrupted their performance to announce that he knew how it was done. Two months later Maskelyne and his partner Cooke gave a performance with their own spirit cabinet. Special attention was given to their bindings, knotted by a sailor, with additional ropes tied and sealed with wax by other members of the audience. Maskelyne and Cooke nevertheless reproduced the manifestations the Davenports had earlier claimed to be due to spirits, launching a stage conjuring career that continued well into the 20th century.

Maskelyne was not alone in mastering the knot tricks of spiritualist performers. In France, Jean Robert-Houdin, who had already successfully reproduced various aspects of the performances of the medium Daniel Home, announced upon witnessing the Davenport’s act in 1865 that ‘the article wherein lay all the deception was the rope.’ Houdin explained that along with various tricks of misdirection and contortion, the type of rope used, and specifically, the type of knot tied, allowed the brothers to free themselves from their bindings. Papers published in English translation posthumously in 1880 give illustration of the type of slip-knot, or cat’s paw, Houdin believed to have been used. The first book length guide to magical knots written by Harry Houdini in 1923 was seeded in this sketch.

In the context of spiritualism, then, the knot was part of the armoury of the conjuror, both professed and occluded. In this context it was an ambiguous object, capable of manipulation and being manipulated, the focal point of both confidence and doubt: highly unstable, in other words. Illusory.

Before I move on to matters more scientific, it is important to note that Maskelyne was a witness for the prosecution at the trial of Henry Slade in London in 1875, a highly publicised and sporadically farcical event at which the biologist Edwin Ray Lankester and his friend Herbert Donkin attempted to prove that they had caught the slate-writing medium in the act of concealing a pre-prepared slate during a seance. Lankester’s aim had been to discredit spiritualism, which had been leant considerable scientific legitimacy by the publicised interest of several leading scientists, not least William Crookes. So Maskelyne and Slade had encountered each other across a courtroom before Zöllner and Slade met.

The second strand of the splice. In a roughly synchronous timeframe, the knot was also coming under close scrutiny from the physicists William Thomson and Peter Guthrie Tait. In his 1867 paper given before the Royal Society of Edinburgh, ‘On Vortex Atoms’, Thomson proposed that atoms were vortex rings, that matter was a mode of motion in space. He demonstrated diagrams and models of various knotted or knitted vortex atoms, and while I don’t have an image of the models that accompanied that talk, this sketch from his notebook gives some idea of what he envisaged in terms of knotted or knittedness. Thomson wrote:

two ring atoms linked together or one knotted in any manner with its ends meeting, constitute a system which, however it may be altered in shape, can never deviate from its own peculiarity of multiple continuity, it being impossible for the matter in any line of vortex motion to go through the line of any other matter in such motion or any other part of its own line.

Thomson had been in part inspired by a demonstration of smoke rings by his colleague Peter Guthrie Tait, and Tait in turn took his lead from Thomson. If atoms were knots, Tait reasoned, then further research into knots was required. Tait’s first realization, now known to anyone who’s ever attempted to untangle fairy lights or headphone cords, was that some objects appearing to be knots, are in fact merely tangles, and can be unraveled by pulling. These he termed trivial knots, or unknots. Tait tabulated true knots according to the number of their crossings and presented his research to the Royal Society of Edinburgh in 1876, instigating the branch of mathematics now known as knot theory.

Mathematical knots, then, in distinction to magical knots, were closed. The putative cords in which they were tied had no ends. They were unambiguous; indeed, they distinguished between true knottedness and unknottedness. They were unbreakable in their own space. And they were – possibly – the very bedrock of matter.

The third strand of the splice. By the time Tait’s work was published later that year, he had received notice from Felix Christian Klein, whose name you might recall in connection with Zöllner. Klein, a young projective geometer working with geometries allowing for dimensions greater than three, had made, in Tait’s words, ‘the very singular discovery that in space of four dimensions there cannot be knots.’

In Klein’s own description he had demonstrated that: ‘the presence of a knot can be considered an essential (i.e., invariant under deformations) property of a closed curve only if one is restricted to move in three-dimensional space; in four-dimensional space a closed curve can be unknotted by deformation.’ In other words knots, or closed space curves, could be untied by deformation, or movements that did not involve cutting the knot or passing the cord through itself, in space of four dimensions.

In the mid-1870s Klein had also informed Zöllner of his research. According to Klein: ‘Zoellner took up my remark with an enthusiasm that was unintelligible to me. He thought he had a means of experimentally proving the “existence of the fourth dimension”’.

Zöllner, in fact, had previously engaged with both the fourth dimension and Thomson and Tait. In his 1872 book Uber die Natur der Cometen, Zöllner had launched a highly personal, unscientific attack against various British physicists including Thomson and Tait, and their German friend and translator Helmholtz. His vituperative comments occasioned a front page editorial in Nature describing the ‘numberless sources of amusement which the work affords’ and letters of apology from Helmholtz in which he imputed charges of insanity against Zöllner.

And so, back to the beginning of my presentation, six years later, when the same scientist published work dealing with spiritualism and knots, what was the response in the British scientific press? Understandably, it was too much for Tait, who seized the opportunity of an amateur’s dabbling in the field of knots to belatedly retaliate. Tait’s review of Zöllner’s work in Nature in 1878 is a hatchet job of the first order, best summed up by the extravagant typography of his response to the knot experiment:

He has held the two ends of a cord (sealed together) in his hands while trefoil knots, genuine, IRREDUCIBLE TREFOIL KNOTS, of which he gives us a picture, were developed upon it!

For Tait, who had glimpsed the vastness of the mathematics of knots, the simple trefoil knot, the very first knot on his table, was evidently not very impressive. And this was several years before he had the advantage of Mrs Sidgwick’s close readings of Zöllner’s experimental accounts. What Tait would have made of the trivial knots previously produced under Slade’s aegis, we can only guess.

CONCLUSION

So what does this tangled tale reveal?

My own research is focused on higher space, the fourth dimension in which Zöllner’s knots were supposedly created. I see Zöllner’s intervention as crucially transformative for higher space. Not only did his work put the fourth dimension on the front page of daily newspapers, for the first and possibly the final time, but it inflected all subsequent understanding of this already difficult concept. Unravelling the knots in his cord reveals some of the resources drawn together in this moment and subsequently internalised in the cultural fourth dimension. The conjuring context of the knot is particularly important, and often obscured by its shadow brother, spiritualism. The fourth dimension is magical, but a crucial element of this magic is the performed, dramatised, fictive magic of the stage conjuror, as opposed to the theorised, scientistic magic of the occult.

Zöllner’s knots are also demonstrative of the hybrid construction of higher space and higher spatial theories and objects, drawing together geometry, scientific rivalries, national politics, occult belief systems: this is typically Latourian. Latour’s critique of a hard and fast division between reality and language is informative when we consider the knot. Latour argues that: ‘We never detect the rupture between things and signs and we never face the imposition of arbitrary and discrete signs on shapeless and continuous matter.’

This resonates particularly acutely with regard to the seductive idea of the atom as a knot, an idea in which Thomson and Tait tied word and world so tightly.

Before closing, I believe my abstract promised visual demonstration of how the knots were produced in the cord. And I think if we look here [attempt at sub-Tommy Cooper magic trick]

There is no more appropriate summary to this set of stories than that provided by the most aloof and brilliant of Victorian physicists. James Clerk Maxwell had long chuckled from the sidelines at his friend Tait’s obsession with knots, channelling his mockery through a favourite form: humourous verse. The very last poem Clerk-Maxwell wrote before his death combined an informed overview of spatial theories enjoying currency at the time with a critique of Tait’s own pet theory of Continuity, an attempt to reach a compromise between religious faith and physical science, dependent upon the concept of the infinite as a stand-in for the Godhead, and outlined in two books co-written with Balfour Stewart, The Unseen Universe and its sequel, Paradoxical Philosophy.
Clerk Maxwell, no mean parodist, pastiched Prometheus Unbound thus:

My soul’s an amphicheiral knot
Upon a liquid vortex wrought
By Intellect in the Unseen residing,
While thou dost like a convict sit
With marlinspike untwisting it
Only to find my knottiness abiding,
Since all the tools for my untying
In four-dimensioned space are lying,
Where playful fancy intersperses
Whole avenues of universes,
Where Klein and Clifford fill the void
With one unbounded, finite homoloid,
Whereby the infinite is hopelessly destroyed.

Introduction

I’m now over a year into my research, and having covered what, for a humanities researcher, is hopefully the hardest stretch, the geometrical origins of the concept of higher-dimensioned space, it seems like an opportune time to start putting some of my own research online (although probably not the maths stuff until I’ve redrafted it many more times and had real mathematicians read it over). I’m beginning to re-engage with more comfortable territory – the perennially popular Flatland and the work of the more obscure, but no less cultish, Charles Howard Hinton, the remarkable figure whose writing first drew me into this field – so there may be interest from beyond my immediate family (and to be honest, that often flags, and who can rightly blame them for that?).

I suppose some initial comments on the working title would be useful. ‘The Fairyland of Geometry’ is a phrase owing to the American mathematician Simon Newcomb (see how easily the patterns of Victorian prose take hold?) Newcomb first used it in 1897 in an address to the American Mathematical Society, but evidently liked it so much he used it again for a popular article on higher space in Harper’s Magazine five years later. I like it, too, because it covers the necessary ground between pure maths and fantastic fiction, pausing for heavy breath in the mystical graveyard of the occult.

And I guess, since Newcomb uses the term hyperspace, I should explain why I use higher space. It’s partly a transatlantic thing, but also for reasons of consistency: higher space was Hinton’s preferred coinage; hyperspace was first used by G.B. Halsted in the American Journal of Mathematics in 1878 (although he was using the term pro-space not long before); Bertrand Russell’s An essay on the foundations of geometry (1897) preferred the term meta-space; and an occultist account of fourth dimensional clairvoyance from 1893 delighted in the title Throughth. Evidently higher space is prepositionally challenging: this is something I’ll certainly be returning to at greater length, so suffice to say I lean towards higher space not least for its relative clarity.

And finally the dates: not as arbitrary as they may at first seem. This is Hinton’s lifespan, and not only is it impossible to imagine a study like this without Hinton, it’s also a handy period container for most of what I want to do: to trace the transformations of the concepts of higher space from their origins in analytic geometry to their various manifestations in esoteric/occult texts, science fiction and popular culture, working up to and into the more thoroughly researched area of Modernism’s fourth dimensions and pulling short a good few years before Einstein muddies the water with relativity, damn his crazy eyes. And hair.