Laws of Form by G Spencer-Brown new English edition: At last this all-time classic has been
reset allowing more detailed explanations and fresh insight. There are seven appendices
doubling the size of the original book. This new edition of G Spencer-Browns all-time classic
comes with previously unreleased work on prime numbers as well as on the four-colour theorem.
Most exiting of all is the first ever proof of the famous Riemann hypothesis. To have in print
under your hands and before your own eyes what defied the best minds for a century and a half
is an experience not to be denied. Preface to the new English edition As is now well known
Laws of Form took ten years from its inception to its publication four years to write it and
six years of political intrigue to get it published. Typically of all unheralded best sellers
from relatively obscure authors it was turned down by six publishers including Mark Longman
who published my earlier work on probability. Even Sir Stanley Unwin refused to publish it
until his best author Bertrand Russell told him he must. This crucial recommendation was not
achieved without intrigue and required me (not unwillingly) to sleep with one of Russell's
granddaughters who asked me in the morning 'What exactly do you want from Bertie?' 'To
endorse what he said about the book when he first read it in typescript ' I told her. 'He never
will!' she exclaimed. 'You'll have to twist his arm you'll have to blackmail him. How can I
help?' The next few years were spent in vigorous arm-twisting and incessant blackmail from us
both. One of her threats was to invite me to Plas Penrhyn as her guest while Bertie and Edith
were away in London. This sent Bertie into a paroxysm of terror of what the neighbours might
think. He also had an irrational fear of spoiling his reputation as a mathematician which was
not good anyway by recommending a book that had not yet been tried by the critics. He seemed
totally unaware that any book he recommended however ridiculous would have no effect whatever
on this. When we finally got him cornered in my next visit to Plas Penrhyn he carefully
avoided mentioning the subject during the whole of my stay and I considered it too dangerous
to mention it myself. The next morning I was due to depart while Bertie and Edith were still in
bed and I thought I had failed miserably. But no! I missed my train because they had not
ordered me a taxi to the station which was their way of telling me that my visit was to be
prolonged by another day. The evening of this extra day came and still nothing was mentioned.
Ten o' clock bedtime arrived and I thought I had failed again when Bertie suddenly said
'What exactly do you want of me?' 'To endorse what you said about the book three years ago ' I
told him. 'You must remind me what it was ' he said. I produced a verbatim report of his
remarks neatly typed out and thrust it in his face. 'Are you sure this is all you want?' he
said. 'Don't you want me to write a detailed introduction to the work as I did for
Wittgenstein?' I told him that that would be very nice but that this was all I needed just
now. He contemplated the page of typescript for a moment and then a wicked gleam lit up his
face and he rubbed his hands. 'Supposing I don't?' he grinned. 'Then ' I heard myself saying
'it might delay the publication for a year or so but the book will still be published in the
end and you won't be associated with it.' 'Oh ' he said. 'I never thought of that. How would
you like me to sign it?' There is no stronger mathematical law than the law of complementarity.
A thing is defined by its complement i.e. by what it is not. And its complement is defined by
its uncomplement i.e. by the thing itself but this time thought of differently as having got
outside of itself to view itself as an object i.e. 'objectively' and then gone back into
itself to see itself as the subject of its object i.e. 'subjectively' again. Thus we are what
we see although what we see looks like (and is) what we are not. This incessant crossing of
the thing boundary to look at it from one side and then the other is called scrutiny which
as a small child was I told is not polite because by scrutinizing a person or thing we shall
notice uncomplimentary (same sound different word) qualities of the person or thing that it is
rude to mention or think about. At the age of three I discovered that most people from what
they told me could stop themselves from thinking these rude thoughts which is I suspect why
ordinary people do not usually do mathematics where you have to repeatedly cross and recross
the thing boundary. In fact Laws of Form is the book I wrote simply about doing just this and
nothing else. When the book finally came out in 1969 April 17 its effect was sensational. The
Whole Earth Catalog ordered 500 copies which was half the edition and other big dealers
followed suit. The first printing was sold out before it reached the shops and the publisher
had to order a hurried reprint to meet the demand. Nobody had seen anything like it. Here was
an upstart author explaining the mysteries of mathematics that the so-called greats of the
science in the last 8000 years (at least) had never noticed and in language that a child of
six could follow. Having achieved my life's ambition of composing and publishing a nearly
perfect work of literature by the age of 46 I was suddenly confronted by the problem of what
to do with the rest of my life. I knew and so did everybody else that I could never top this
achievement so with what significant purpose could I carry on? One thing I could and did do
was learn some mathematics. One of many reasons why the book is so famous is because I did not
know any math apart from school stuff when I began to write it. I had to teach myself and
with me my readers as I went along. In ten years I had learned enough to become a full
professor in the University of Maryland although I still thought I knew very little. Math is
almost impossible to master without personal tuition and I was lucky to strike up friendships
with D H Lehmer and J C P Miller both as it happened experts on Riemann's hypothesis in
which I had no interest whatever nor in analytic number theory in general. It was only on
being told by my former student James Flagg who is the best-informed scholar of mathematics in
the world that I had in effect proved Riemann's hypothesis in Appendix 7 and again in
Appendix 8 that persuaded me to think I had better learn something about it. I am an intensely
competitive person which comes from being repeatedly told by my mother that I would never be
any good. This forced me to spend my whole life attempting to prove her wrong. The tragedy of
it is that however brilliantly I performed it made no difference. Nothing I could do would
change her mind. I beat her at chess when I was four and all she did was refuse to play with
me ever again rather than admit that I was good. If you solve a famous unsolved problem by
mistake it doesn't count. You have to say 'I am going to solve this problem ' and then solve
it. So I had to spend another ten years learning analytic number theory which I hated in
order to secure and objectify what I had done and make it presentable. The result is so
fascinating that it made the effort seem almost worth while and the problem was so difficult
that solving it gave me nearly as much pleasure as writing Laws of Form. The world of analysis
is completely different from anywhere I had explored the science of continuous variation
rather than discontinuous jumping. And since Riemann's problem is solved by a marriage of the
two although the achievement of a solution cannot quite top what I did in Laws of Form it
runs it a close second if not an equal first. (0100 hrs 23 06 2007 Saturday)
