Throughout the ages people have sensed the existence of a benevolent force intervening from time to time in their lives as if to offer them help and protection - or to chasten them. The good fairy of folklore and the guardian angel of Christian tradition belong in this category. Socrates said that he had heeded the voice of his ‘daemon’ all his life, and it had never let him down. Churchill sometimes had ‘a strong feeling’; he told an audience of miners during the Second World War, ‘that some guiding hand has interfered’.
In The Unknown Guest Brian Inglis explores the historical and present-day evidence of the force. In perhaps its most familiar guise it operates as the ‘muse’ for writers and artists. And many of us have felt that chance and luck can’t explain away hunches, premonitions, meaningful coincidences and extra-sensory perceptions. Brian Inglis concludes that we don’t know enough to be sure about the source of these promptings but the evidence is impressive enough to be worth examining afresh.
About the author
Brian Inglis (31 July 1916 – 11 February 1993) was an Irish journalist, historian and television presenter. He was born in Dublin, Ireland, and retained an interest in Irish history and politics. He was best known to people in Britain as the presenter of All Our Yesterdays, a television review of events exactly 25 years previously, as seen in newsreels, newspaper articles etc. He also presented the weekly review of newspapers known as What the Papers Say. He joined the staff of The Spectator in 1954, and became editor in 1959, soon afterwards hiring the young Bernard Levin to write for the magazine. He continued as editor until 1962. He also had interests in the paranormal, and alternatives to institutionalised medicine. Inglis’ friend and colleague Bill Grundy died on 9 February 1993. Inglis had just finished writing Grundy’s obituary when he, too, died.
Perhaps the strongest evidence that mathematical abilities cannot be accounted for in conventional terms has been provided not by famous scientists, but by children; in particular some child prodigies who have been able to show that they can make abstruse calculations in a flash. How? Commentators have had to fall back on ‘intuition’ - ‘Whatever that may mean,’ as Sir Oliver Lodge ruefully remarked.
Myers listed some of the more celebrated prodigies, ranging from Ampere at one end of the alphabet to Richard Whately, later to be archbishop of Dublin, at the other. Of the two, in this context, Whately is the more interesting because whereas Ampere’s ability remained with him throughout his life, Whately’s lasted only for three years. It began to show itself when he was five or six.
“I soon got to do the most difficult sums, always in my head, for I knew nothing of figures beyond numeration. I did these sums much quicker than anyone could upon paper, and I never remember committing the smallest error. When I went to school, at which time the passion wore off, I was a perfect dunce at ciphering, and have continued so ever since”.
This coming and going of the faculty is quite common. According to Franz Gall, a ‘Mr Van R’ of Utica showed a similar faculty at the age of six and not merely lost it at eight, but had no idea how he had performed the calculations. Professor Safford, another mathematical prodigy, retained the faculty for long enough to establish himself as a mathematician, eventually becoming a professor of astronomy; yet by that time he could calculate no better than the next man.
Some prodigies have been highly intelligent; others have been accounted stupid in all respects, other than calculating; some have not been able to calculate in the ordinary sense at all”. ‘We know that Dase (perhaps the most successful of all these prodigies) was singularly devoid of mathematical grasp,’ Myers observed.
On one occasion Petersen tried in vain for six weeks to get the first elements of mathematics into his head. He could not be made to have the least idea of a Proposition in Euclid. Of any language but his own he could never master a word! Yet Dase received a grant from the Academy of Sciences at Hamburg on the recommendation of Gauss for mathematical work; and actually in twelve years made tables of factors and prime numbers for the seventh and nearly the whole of the eighth million-a task which probably few men could have accomplished without mechanical aid in an ordinary lifetime. He may thus be ranked as the only man who has ever done valuable service to mathematics without being able to cross the ass’s bridge.
How are such feats achieved? According to Wellesley Pole, a Fellow of the Royal Society, the prodigy G. P. Bidder (who later became a QC) ‘had an almost miraculous power of seeing, as it were, intuitively what factors would divide any larger number, not a prime’. Given the number 17,86r, ‘he would instantly remark it was 337 X 53’. He could not, he said, explain how he did this; ‘it seemed a natural instinct to him.’
At the height of the positivists’ domination of science, there could be only one explanation. When in 1837 the ten-year-old Vito Mangiamele, a shepherd’s son with no formal training in mathematics, was tested by the French scientist Dominique Arago and his colleagues of the Academy of Sciences, the boy took only a minute to work out in his head that the cube root of 3, 796,416 was 156. The committee members, unable to deny that Vito could perform such calculations, decided it could only be fraud. His instructors, they claimed, must have found a way to keep the method they had taught a secret.
This would not do for Myers. Dase and the others, he felt, were the output of ‘some unseen world in which the multiplication table is, so to speak, in the air’. Oliver Lodge thought prodigies represented ‘some form of possession’. Conventional psychology has no more plausible answer, nor is likely to find one until old mechanist shackles are finally thrown off.
How difficult it will be to throw them off has been illustrated by Oliver Sacks in his paper ‘The Twins’. They differed from the infant prodigies in that they were adults, but from the age of seven they had been in institutions, ‘variously diagnosed as autistic, psychotic or severely retarded’. At the time he meets them at the age of twenty-six, they are a sort of grotesque Tweedledum and Tweedledee, indistinguishable mirror-images, identical in face, in body movements, in personality, in mind, identical, too, in their stigmata of brain and tissue damage. They are undersized, with disturbing disproportions in heads and hands, high- arched palates, high-arched feet, monotonous squeaky voices, a variety of peculiar tics and mannerisms, and a very high degenerative myopia.
Confronted with ordinary simple mathematical problems, the twins do ‘as badly as their IQs of sixty might lead one to think’. They cannot add or subtract without making mistakes, and they cannot even understand the meaning of multiplication and division. Yet, the twins say, ‘Give us a date any time in the last or next 40,000 years.’ You give them a date, and almost instantly, they tell you what day of the week it would be. ‘Another date!’ they cry, and the performance is repeated. They will also tell you the date of Easter during the same period of 8o, ooo years.
This was in 1966. The explanation which has since found most favour among scientists who have studied the twins, put forward in Steven Smith’s The Great Mental Calculators (1983), is that they use algorithms - a kind of mathematical shorthand. Sacks is too polite to dismiss this as the nonsense it manifestly is; if the twins could not do simple sums, algorithms would not have helped them. In any case, they could not readily be used to date past Easters, or other feats which the twins found simple. The hypothesis, Sacks suggests mildly, is ‘a misapprehension’; the reality must be ‘far stranger, far more complex, far less explicable’. The mistake which had been made was to regard them simply as subjects for trials and experiments; ‘one must lay aside the urge to limit and test, and get to know the twins,’ he decided. Then, ‘one finds there is something exceedingly mysterious at work, powers and depths of a perhaps fundamental sort, which I have not been able to solve in the eighteen years that I have known them.’
How do they do their ‘calculations’? ‘If you ask them how they can hold so much in their minds - a 300-digit figure or the trillion events of four decades- they say, very simply, “We see it.” And “seeing” - “visualising” - of extraordinary intensity, limitless range and perfect fidelity seems to be the key.’ Sacks has no doubt that the twins have available to them ‘a prodigious panorama, a sort of landscape’, and also the ability to ‘see’ and retrieve anything that lies in it. Seeking to explain the process, he turns to art for an analogy: the twins, he believes, have ‘not just a strange “faculty”, but a sensibility, a harmonic sensibility, perhaps allied to that of music’.
But Sacks’s advice has gone unheeded. Now, twenty years after first meeting the twins, he expresses exasperation- again mildly - at the fact that as soon as the ‘algorithms’ explanation was presented, wretchedly inadequate though it was, scientists felt there was no longer any need to bother with the twins. Eventually they were split up ‘for their own good’ to terminate their ‘unhealthy’ communication and to make them fit to lead socially acceptable lives- doing menial jobs under supervision. In the process they ‘seem to have lost their strange numerical power, and with this the chief joy and sense of their lives. But this is considered a small price to pay, no doubt, for their having become quasi-independent and “socially acceptable”.
This has not been the first time, and will not be the last, when science has grasped at a straw to spare the orthodox from the embarrassment of contemplating ESP as a possible alternative. Even Sacks himself, though his descriptions of the twins point inexorably to some form of extra-sensory communication between them, does not care to contemplate that possibility. He cites the algorithm notion as if it had thrown some useful light on the problem, rather than obscured it. Yet his account, and theirs, of the way they performed as prodigies could readily be put into a textbook of parapsychology.
Publisher: White Crow Books
Published April 2018