SEMIREGULARITY VIA DERIVED DEFORMATION THEORY ...

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SEMIREGULARITY VIA DERIVED DEFORMATION THEORY J.P.PRIDHAM Abstract. We realise Buchweitz and Flenner's semiregularity map (and hence a fortiori Bloch's semiregularity map) as the tangent of a morphism of derived moduli functors. An immediate consequence is that it annihilates all obstructions (not just curvilinear ones) globally. Introduction In [Blo], Bloch defined a semiregularity map τ : H1(Z,NZ/X) → Hp−1(X,Ωp−1X ) for every local complete intersection Z of codimension p in a compact complex manifold X, and showed that curvilinear obstructions lie in the kernel of τ .

• construction above satisfies
• rham cohomology
• smooth
• chern character
• perfx
• simplicial semirings
• dg−algk
• 2 dr
• dr
• functor
• map

Sujets

• Exposé
• Thomas
• Smooth
• Functor
• Cohomology
• Morphism

Informations

• Publié par: orzi
• Nombre de lectures: 13
• Langue: English

Extrait

ON BEING THE RIGHT SIZE

J. B. S. HALDANE

J. B. S. Haldane (1892-1964) was one of the supreme popularizers of
science, as well as a brilliant geneticist who helped found the modern theory
of evolution. This new selection of his popular scientific writing by one of
his former pupils includes some of his best-loved pieces, among them 'On
Being the Right Size', 'When I am Dead', 'The Origin of Life', 'What "Hot"
Means', and 'Cats'. Written, as Sir Peter Medawar says, 'in a style as
distinctive as Ernest Hemingway's and in some respects not unlike it',
Haldane's essays are still remarkable for their explanatory power and the
quality of their ideas.

A liberal individualist, Haldane was famous as a leading communist and
for his weekly articles in the Daily Worker, a number of which are to be
found here. After excelling in classics and mathematics at Oxford, he went
on to make his name in biochemistry and genetics. He admitted to rather
enjoying the First World War, but ended his life in India writing in defence
of non-violence. His colourful personal life, the importance of his
contributions to science, and the genius of his popular scientific writing all
bear witness to a most exceptional man.

John Maynard Smith is Professor of Biology in the University of Sussex.


INTRODUCTION

I first came across J. B. S. Haldane's essays when, as 1 schoolboy at Eton,
I found that he was the person my schoolmasters most hated. Feeling that
anyone they hated that much could not be all bad, I went to seek his books in
the school library. It is, I suppose, to my masters' credit that I found Possible
Worlds and other essays. The impact of those essays was such that, fifteen
years later, when I decided to have engineering and train as a biologist, I entered University College London, where Haldane was at that time a
professor, and became his student and later his colleague.

I can recall two things from that first reading of Haldane's essays. The
first, gained from the essay 'On Being the Right Size', which is reproduced
here, was the realization that there is a bridge between mathematics and
natural history; Haldane's own major contribution to science was in helping
to build that bridge. My second memory is of the intelligent barnacles in the
title essay, 'Possible Worlds', which distinguish between 'real' objects, which
they can reach with their arms, and 'visions', which they can see but not
reach, and of the philosophers belonging to the species Lepas urpims who
have devised a means of predicting whether (and if so, for whom) a vision
will turn into a real object, by performing abstruse calculations on the
directions in which the visions are perceived by different barnacles. I have
omitted 'Possible Worlds' from this collection, partly because it is rather
long, and partly because I hope to provoke readers to seek out that collection
for themselves.

As a scientist Haldane will be remembered for his contribution to the
theory of evolution. Today, Darwin's theory of natural selection and
Mendel's theory of genetics are so intimately joined together in 'neo-
Darwinism' that it is hard to imagine that, after the rediscovery of Mendel's
laws in 1900, the two theories were seen as rivals. Haldane, together with R.
A. Fisher and Sewell Wright, showed that they were compatible, and
developed the theory of population genetics which still underpins all serious
thinking about evolution. However, although it is not hard to identify
Haldane's major contribution to science, he is in other respects somewhat
difficult to classify. A liberal individualist, he was best known as a leading
communist and contributor of a weekly article to the Daily Worker. A
double first in classics and mathematics at Oxford, he made his name in
biochemistry and genetics. A captain in the Black Watch who admitted to
rather enjoying the First World War, he spent the end part of his life in India
writing in defence of non-violence.

These contradictions in his character and opinions only make him more
interesting to read. He was supreme as a popularizer of science, because he
saw connections that others missed. The present selection ranges from
articles intended for a scientific readership to others written for a daily
newspaper, the only constraint being that they should all be comprehensible
without any special technical knowledge. I have tried to cover the full range of his interests. Perhaps inevitably, essays on religious topics may be over-
represented. However, I do not think that this amounts to a distortion;
Haldane was at the same time fascinated and repelled by religious ideas. It is
characteristic of him that, when he settled in India after his retirement from
University College London, he should have made such a serious effort to
understand Hinduism.

It is also characteristic of him that he used popular articles to propose
original ideas; some examples are included here. 'The Origin of Life' is
perhaps the most important. The ideas presented here contributed
significantly to the fact that the topic is now one for experimental study and
not for philosophical speculation. The essay 'When I am Dead' makes the
claim (which I think he would have rejected later in life) that if mental
processes are physically determined, there is no reason to suppose that their
conclusions are correct, a claim which has since been elaborated by Karl
Popper. I discuss three other original ideas in the Appendix, 'Adumbrations',
in which I give brief quotations from Haldane’s writings, together with an
account of what has happened to the ideas since.

Haldane's views changed during his lifetime, although I think that his
views on practical and political matters changed more than his basic
philosophy. I have arranged the essays, at least approximately, in
chronological order, that changes in opinion are more readily recognized.
However, I must emphasize that my choice has been aimed at illustrating the
characteristic cast of Haldane's mind rather than at recording his political
history. The main feature of that history, of course, is that he joined the
communist party in the late thirties, and left it in the fifties. His political
views can be seen in the present volume in the set of articles from Science
and Everyday Life, A Banned Broadcast and other essays, and Science
Advances, all but one of which originally appeared in the Daily Worker.
They differ stylistically from the other essays in being aimed at a readership
with less formal education, and they contain a number of explicitly political
remarks, but I cannot see that they differ significantly in their attitude to
science. I do not think that anyone today is writing scientific articles for the
daily Press which approach these either in scientific content or entertainment
value. To illustrate their scientific content, the article 'Beyond Darwin'
contains a particularly clear account of Darwin's idea about the relationship,
between sexual dimorphism and polygyny, which has since become a
popular topic of research. I was amused to find that the same article contains
a false argument (about species which destroy their food supply and starve to death). I learnt the fallacy of such 'group-selectionist' arguments from
Haldane himself when I was his student.

In general, I do not think that Haldane's conversion to Marxism had much
effect on the way he saw biology, or on his views about how science ought
to be done. However, it does stem to have forced him to rethink his approach
to human genetics. Although highly critical of eugenic policies, as proposed
in Britain and applied in the United States, his early essays reveal a
somewhat hereditarian approach. I have here reprinted the first chapter from
Heredity and Politics, published in 1938, which presents a more
sophisticated discussion of the nature-nurture problem; it is a treatment
which many contemporary writers on the subject have still not understood.

After some hesitation, I have decided not to add footnotes explaining
particular references in the essays. Some of these will be unfamiliar to the
reader: indeed, some are so to me. The general sense of Haldane's argument
is so dear, however, that footnotes could do nothing to make it easier to
follow.

Rereading Haldane's essays has for me been an extraordinary pleasure,
which I hope you will share.

ON BEING THE RIGHT SIZE

THE most obvious differences between different animals are differences
of size, but for some reason the zoologists have paid singularly little
attention to them. In a large textbook of zoology before me I find no
indication that the eagle is larger than the sparrow, or the hippopotamus
bigger than the hare, though some grudging admissions are made in the case
of the mouse and the whale. But yet it is easy to show that a hare could not
be as large as a hippopotamus, or a while as small as a