Edwin Abbott Abbott

Born: 20 December 1838 in Marylebone, Middlesex, England
Died: 12 October 1926 in Hampstead, London, England

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Edwin Abbott Abbott's parents were Jane Abbott and Edwin Abbott. His mother Jane was a first cousin of his father, so both had the name of Abbott which explains Edwin Abbott Abbott having 'Abbott' as both a surname and a middle name. Edwin Abbott was headmaster of the Philological School at Marylebone.

Abbott was educated at the City of London School which had gained a fine reputation under Dr G F W Mortimer who was headmaster throughout the years during which he studied there. Following a fine school education, Abbott entered St John's College, Cambridge, in 1857. After an outstanding academic career as an undergraduate he was the Senior Classics medallist in 1861 and was elected to a fellowship at his college in the following year. In the same year he was ordained a deacon and in 1863 he became a priest. At this time College fellows were not allowed to marry so, when Abbott wished to marry Mary Elizabeth Rangeley from Unstone, Derbyshire, in 1863, he had to resign the fellowship. Edwin and Mary had one son and one daughter.

After leaving Cambridge, Abbott taught at King Edward's School, Birmingham, and then at Clifton College. In 1865 he was appointed as headmaster of the City of London School on the retirement of his former headmaster Dr Mortimer. It was a post which Abbott held for 24 years until he retired in 1889. Of course Abbott was relatively young when he retired being only 50 years old. He did not retire to give up work, rather he enjoyed writing and retired so that he could devote more time to his literary efforts. Before looking at some of the books which he published, we should first say a little about his fine qualities as a teacher and as a headmaster which saw the already excellent City of London School reach even higher standards during his years in charge [1]:-

His greatness as an educator derived partly from his organization of new methods of instruction, partly from his initiation of many innovations in the school curriculum, and partly from what can only be called his genius for teaching. Having a reverence for physical science not often found among the classical scholars of his day, he made an elementary knowledge of chemistry compulsory throughout the upper school.
He made many innovations to the curriculum taught at the school in addition to the sciences referred to in the above quote, and he transmitted his own enthusiasm for literature, both English literature and classical literature, to pupils at the school.

As a scholar, Abbott was very broad writing excellent works on a wide variety of topics. He published Shakespearean Grammar (1870), English Lessons for English People (1871) and How to Write Clearly (1872). He was a leading expert on Francis Bacon, published Bacon and Essex (1877) and wrote an introduction to Bacon's Essays (1886). Some of his works on textual criticism contain excellent statistical analyses, for example Johannine Vocabulary (1905) and Johannine Grammar (1906). Among numerous religious writings we mention Philochristus (1878), Onesimus: Memoirs of a Disciple of Paul (1882), and Silanus the Christian (1906).

Of course we have not yet mentioned his most famous work, and certainly the one which merits his inclusion in this archive. This was Flatland: a romance of many dimensions (1884) which Abbott wrote under the pseudonym of A Square. The book has seen many editions, the sixth edition of 1953 being reprinted by Princeton University Press in 1991 with an introduction by Thomas Banchoff. Flatland is an account of the adventures of A Square in Lineland and Spaceland. In it Abbott tries to popularise the notion of multidimensional geometry but the book is also a clever satire on the social, moral, and religious values of the period. Here is Abbott's introduction to Flatland:-

I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space. Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows - only hard with luminous edges - and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said "my universe": but now my mind has been opened to higher views of things.

In such a country, you will perceive at once that it is impossible that there should be anything of what you call a "solid" kind; but I dare say you will suppose that we could at least distinguish by sight the Triangles, Squares, and other figures, moving about as I have described them. On the contrary, we could see nothing of the kind, not at least so as to distinguish one figure from another. Nothing was visible, nor could be visible, to us, except Straight Lines; and the necessity of this I will speedily demonstrate. Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle. But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.

In Abbott's Flatland, the more sides you have then the higher is your class. Workers are equilateral triangles, the author himself is A Square, a person of middle class, while the highest classes are the circles who are priests. The Flatland world is visited by a sphere which A Square sees at first as a dot which grows into a disk, then shrinks again to a dot and vanishes. The sphere opens his eyes to the possibility of a third dimension, and he suggests to the sphere that he might live in a world with four or more dimensions, but the sphere makes fun of this suggestion. When A Square tells his fellow Flatlanders about the third dimension they ridicule him, and eventually he is put in prision where he writes the book.

It is worth noting that this remarkable piece of writing by Abbott predated by many years Einstein's four dimensional world of relativity. Abbott wrote a Preface which contains the following:-

It is true that we have really in Flatland a Third unrecognised Dimension called 'height,' just as it also is true that you have really in Spaceland a Fourth unrecognised Dimension, called by no name at present, but which I will call 'extra-height.' But we can no more take cognisance of our 'height' than you can of your 'extra-height.' ...

Suppose a person of the Fourth Dimension, condescending to visit you, were to say, 'Whenever you open your eyes, you see a Plane (which is of Two Dimensions) and you infer a Solid (which is of Three); but in reality you also see (though you do not recognise) a Fourth Dimension, which is not colour nor brightness nor anything of the kind, but a true Dimension, although I cannot point out to you its direction, nor can you possibly measure it.' What would you say to such a visitor? Would not you have him locked up? Well, that is my fate: and it is as natural for us Flatlanders to lock up a Square for preaching the Third Dimension, as it is for you Spacelanders to lock up a Cube for preaching the Fourth. Alas, how strong a family likeness runs through blind and persecuting humanity in all Dimensions! Points, Lines, Squares, Cubes, Extra-Cubes - we are all liable to the same errors, all alike the Slavers of our respective Dimensional prejudices ...

More recently, in 2002, an annotated version [2] of Flatland has been produced with an introduction and notes by Ian Stewart who gives extensive discussion of mathematical topics related to passages in Abbott's text.

Abbott is described in [1] as follows:-

In spite of a frail and delicate physique, Abbott could keep discipline without effort. He was an impressive preacher: in the pulpit he was a bold and original exponent of advanced broad church doctrines.
Abbott died of influenza at his home, Wellside, Well Walk in Hampstead, and was buried in Hampstead cemetery.

Article by: J J O'Connor and E F Robertson

List of References (6 books/articles)

A Quotation

A Poster of Edwin Abbott Abbott

Mathematicians born in the same country

Additional Material in MacTutor

  1. Preface to the Second Edition of Flatland
  2. Obituary: The Times

Other Web sites
  1. Google books
  2. MathSciNet Author profile

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JOC/EFR February 2005
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