This page is in author alphabetical order: Graham Cairns-Smith - Marcus Chown - Richard Dawkins - Daniel Dennett - J E Gordon - Douglas Hofstadter - Hofstadter and Dennett - Julian Jaynes - John McLeish - Roger Penrose - Steven Pinker - John Searle - Stuart Sutherland - D'Arcy Wentworth Thompson - David Wells
This is a delightful book - only just over one hundred pages, and interspersed with Sherlock Holmes quotations in the manner of an unfolding detective story. He starts with a brief introduction to the problem, and mentions some of the "solutions" often found on loopy websites, but rightly considers these sterile. Chapter 1 closes with the following quotation, from The Hound of the Baskervilles, chapter 3:
"Of course, if Dr. Mortimer's surmise should be correct, and we are dealing with forces outside the ordinary laws of Nature, there is an end of our investigation. But we are bound to exhaust all other hypotheses before falling back upon this one."
Then he plunges into a description of the basic nuts and bolts of life: the DNA-RNA replicating machine, the coded messages, the folding proteins. I suppose he is only skimming the surface of biochemistry, but I found the exposure to the details very stimulating. (Surely no-one can come out of this thinking biochemistry is simple!) But while people with a lot of time and patience have been able to piece together so many of the mechanisms, these all start with the basic large molecule replicating machinery already in place. How could this ever have been bootstrapped, he asks? Chapter 10, "Crystals," introduces his candidate, an entirely different, utterly low-tech replication mechanism that could have built the scaffolding for subsequent organic evolution. In the last third of the book, he gives us plenty of support ideas, but is quite clear that this remains a hypothesis - the book closes not with a Verdict, but with the eponymous Seven Clues. Fascinating.
This is a wonderful book. It deals with beginnings - the beginning of the universe, and the beginning of scientific thought. What is everything made of? Just indefinitely divisible "stuff", or are there ultimate building blocks like Lego bricks? The elusive figure of Democritus in ancient Greece was the first to answer this question, giving us the word we still use: atomos or "uncuttable". Democritus gave arguments to suggest why matter should be atomic, but this remained entirely hypothetical until experimental science got underway almost 2000 years after him. So the story leaps to the time of Newton, who not only hypothesised, but also tested his ideas, and produced (among other things) his laws of motion. It was Daniel Bernoulli who thought through the implications of seeing a gas as a collection of particles like billiard balls, in constant motion, and saw that it fitted reality. From there on, a stream of thinkers gradually pieced together the story of the basic stuff the world is made of.
The Englishman John Dalton can perhaps lay claim to being the "father of chemistry." He saw the implication of the fact that substances taking part in a chemical reaction do so in fixed ratios - that individual atoms were combining in discrete ratios. Thus if hydrogen and oxygen combine in the ratio 1:8 by weight, he guessed one oxygen atom, weighing eight times as much, combined with one hydrogen atom. He was wrong in detail (everyone now knows water is H2O), but correct in his intuition that mathematics was the key to unravelling nature's secrets. Over and over again, mathematical patterns turned out to be the key: Mendeleev saw the cyclic pattern in the elements which had been identified so far, and successfully predicted the elements that would fill in the gaps. Of course, behind this was the unfolding realisation that atoms are not the ultimate building blocks, but are made of elementary particles. Chown's historical treatment makes it clear just how many loose ends there were: in this particular case, while most elements have atomic weights close to integral multiples of the atomic weight of hydrogen, chlorine sat obstinately at just 35-and-a-half. But inexorably, the gaps were closed, and models of the atom emerged. And as the secrets of things too small to be seen were teased out, we began to learn about things too far away to be seen, neatly spoiling the prediction of Auguste Comte, the French philosopher, in 1835: "Never, by any means, shall we be able to study the chemical composition or mineralogical structure of the stars." The primary tool in this latter process was the spectral lines discovered by Fraunhoffer in the early 1800s, though it was only in 1859 that Kirchoff and Bunsen found that these lines identified elements which were either absorbing or emitting specific frequencies. Without waiting for a quantum theory description of why this should be so, the two surged ahead identifying previously unknown elements. The most spectacular of these, of course, was helium, which was found in the sun (helios in Greek) before it was isolated on earth.
So by the early 20th century, and slightly over half-way through the book, the first understanding of the internal structure of atoms was taking shape. The remainder - Part 3, "The Magic Furnace" - tackles the much harder question: how is it that the universe contains an interesting mix of different elements? After all, it would seem simplest if there were just protons, or hydrogen atoms, but then we wouldn't be here. Measurements of the masses of different atoms showed that they were not exact whole-number multiples, as one would expect if elementary particles behaved like billiard balls. In particular, hydrogen was almost 1% heavier than it "ought" to be, and it was Francis Aston who eventually realised that was because the extra mass of four separated hydrogen atoms (protons) compared with a helium nucleus was converted to energy when they combined, whether in the sun or in a H-bomb. Painstakingly, a diagram emerged, showing the different elements on a "roller coaster" graph, with high energies at both the light end (hydrogen) and the heavy end (the radioactive elements), with a minimum at iron. This made it relatively easy to see that the elements up to iron could be made from hydrogen, but there were still many many obstacles before the whole story could be told of how the heavier elements are made in the interior of a star, then blasted into space in a supernova explosion.
I'm skimming, over the last part of the book in particular, because it's not easy stuff. Chown is not frightened to include numbers and reasoning (though there is no actual mathematics), yet I think does an extremely good job of keeping up the pace of the historical narrative, as we meet the many and varied characters who worked all this out. And the book is not daunting - he has packed the story into 220 pages, plus a helpful glossary.
There is a subtext: this was part of the Great Mathematical Adventure, that goes all the way back to Pythagoras and his walk past the blacksmith. See "Music by numbers" and Jamie James' book "The Music of the Spheres" in particular. There is also a fascinating (and famous) essay by Eugene Wigner, written in 1960, whose title sums it up: "The unreasonable effectiveness of mathematics".
It just so happens that a friend of mine translated the Japanese version. It's a nice edition, with a number of additional diagrams, and photographs of many of the personalities scattered throughout.
Bokura wa hoshi no kakera (translated by Hiroshi Itokawa) - Amazon Japan
A seminal advocacy of Darwinian evolution as the answer to the question "Where did we come from?" I read it more than ten years ago, before the Internet, and before I had any comprehension of how widespread is a total misunderstanding of the mechanism of evolution, helped along by a variety of straw-clutchers and agenda-bearers and now their loopy websites.
Dawkins starts from the well-known story of William Paley's exposition of the "Argument from design" in 1802, in which he contemplates stumbling over a watch on a heath. Paley deduces that "the watch must have had a maker," by which he of course means a personifiable deity. Dawkins spends the next three hundred pages pointing out that this just doesn't follow, since we understand that there is a non-personifiable - that is, blind - mechanism for doing the same thing. But not quite in the same way: for this blind watchmaker, design just has to be good enough to survive, and there is no going back to sort out early design decisions that leave us with lumbago and eyes that are wired backwards.
In a book as lucid as this, only a professional misinterpreter could fail to follow his argument. Unfortunately, this is probably the only field in which professional misinterpreters are really active: but read it for yourself, and you should be able to pull most of their arguments to bits in no time.
The picture above is of the US edition, with the subtitle "Why the Evidence of Evolution Reveals a Universe Without Design." It's not surprising, perhaps, that this has to be spelled out for an American audience.
Dennett, Daniel: "Darwin's Dangerous Idea" pub. Simon & Schuster, 1995, 590pp, ISBN 0-684-82471-X
Highly recommended: see my review
Dennett, Daniel: "Consciousness Explained", pub. Little Brown and Co., 1992
I read this some time ago, and unfortunately my copy is still on loan to somebody, but here's a very quick summary. Dennett's basic thesis is a denial of the "Cartesian theatre", the notion that inside the head, everything is played out on a virtual stage, which might be viewed by the homunculus that is "me". I found it very readable (as Dennett always is), and persuasive - but be warned that Francis Crick thinks Dennett is "overpersuaded by his own eloquence" (not a bad thing to be criticised for). At least one of Dennett's specific predictions, about the way in which the eye/brain "fills in" a blind spot has, I believe, been refuted by experiment, but of course it's a token of the down-to-earth nature of much of what he says that it is capable of refutation.
Dennett, Daniel: "Kinds of Minds - Toward an understanding of consciousness", pub. Basic Books 1996, 240pp
Tempting to say "Dennett, more of the same". As always he's attacking any of the "absolutes", ideas that the difference between a human mind and that of, say, a dog is unbreachable. Good stuff, and a much more manageable size than Darwin's Dangerous Idea for instance.
These books cover the two aspects of making things: the materials you use, and the way you put the bits together. There is a certain degree of overlap, and I think you could happily read the two in either order. Gordon writes in an immensely approachable style, a bit port-and-cigars-British perhaps, full of memorable examples of ships breaking in two, and why not oiling a grandfather clock makes it last longer. He is not afraid to write equations, but most of them are fairly simple.
"Materials" introduces us first to stresses and strains, elastic behaviour, and Hooke's law. Then he dives into the molecular basis of material strength, and the reason why practical materials (such as sheet steel) fall miserably short of the theoretical value. The problem turns out to be cracks. He opens Chapter 5, "Crack-stopping, or how to be tough," by commenting on the unreliability of Pliny the Elder's "Natural History", and then writes (in italics):
The worst sin in an engineering material is not lack of strength or lack of stiffness, desirable as these properties are, but lack of toughness, that is to say, lack of resistance to the propagation of cracks.
Much of the rest of this book concerns itself with this issue of toughness, and there is a wealth of down-to-earth information on practical materials such as masonry or plywood, in addition to the metals.
"Structures" brings more tales of cracks in beams, boats, and bridges, but he also touches on some "Growth and Form" themes: the engineering basis on which some animals are constructed. In particular, he shows us the two most basic ways of making a rigid structure: either building on a space-frame, or using a monocoque. The latter is the principle on which modern cars are made, with essentially a single body piece in the form of a shell - the sort of construction plants have always used. Gordon keeps this entertaining, with lots of anecdotes, and personal opinions: "Greek roofs can only be described as intellectually squalid," he says.
At Amazon.com (USA) in particular, look out for a special deal on the two books together. (I can't get a direct link to work, unfortunately.)
A huge tome, full of wonderful stuff. He does tend to be lengthy about things, so some people love him, while others hate him. Get it and see what you think.
His selection of the three heros of the title is interesting. Kurt Gödel was the mathematician who published a famous paper in 1931 ("On Formally Undecidable Propositions") that demolished the idea of building a complete axiomatic basis for mathematics, as proposed by Hilbert in his set of Big Problems at the beginning of the twentieth century, and most enthusiastically pursued by Bertrand Russell and Alfred North Whitehead. The basic "trick" which it used to do this is the Strange Loop (Hofstadter's term), the contradictory self-reference typified by the old chestnut "This statement is false." The book is a discovery of similar patterns in J. S. Bach's music and M. C. Escher's drawings.
Of course it also features many other personalities - Fermat, Turing, Ramanujan, and Magritte to name but a few - and some gruesome puns and multilingual wordplay. He has a thing about "ants" in particular, and we meet "Fermant's last fugue"- "Aunt Hillary" - "Di of Antus" - and "Lierre de Fourmi", whose discovery of the following somehow ends up called "Johant Sebastiant's Well-Tested Conjecture":
na + nb = nc has no solutions in integers for n > 2.
Actually the above is "Fermat's last theorem upside down". I have also seen a claim that the subtext of the book is an assertion of Goldbach's conjecture about prime numbers. Well, together with Douglas Hofstadter, his coeditor of "The Mind's Eye" Daniel Dennett, J S Bach, and the Goldberg variations, it is certainly easy to end up very confused - as I did. Here's just one more joke: from the bibliography, and curiously close to the bone.
Gebstadter, Egbert B.: "Copper, Silver, Gold: an Indestructible Metallic Alloy." Perth: Acidic Books*, 1979. A formidable hodge-podge, turgid and confused - yet remarkably similar to the present work. Professor Gebstadter's Shandean digressions include some excellent examples of indirect self-reference. Of particular interest is a reference in its well-annotated bibliography to an isomorphic, but imaginary, book.
Douglas Hofstadter & Daniel Dennett: "The Mind's I, Fantasies and reflections on self and soul", Basic Books, 1981, 500pp
A compendium of seminal articles, by authors as varied as Borges, Turing, Dawkins, Searle, Smullyan, and Nagel, plus some articles by the editors, and their comments on all of the other authors. A must-have, because even if you disagree violently with DH and DD, you can get much of the stuff you need to argue with from this one book.
Here's an interesting site with more related reviews, that lists the complete contents.
Jaynes, Julian: "The Origin of Consciousness in the Breakdown of the Bicameral Mind" pub. Houghton Mifflin, date unclear (copyright 1976, 1990, but preface dated 1982!) ISBN 0-395-56352-6 paperback 500pp. $17
Recommended: see my review
Amazon.com (USA) -
Amazon Japan (Popup help)
McLeish, John: "Number" pub. Ballantine Books, 1991; I got my copy from Strand for $7.
"An odd number, one feels."
Penrose, Roger: "The Emperor's New Mind" pub. Oxford University Press, 1989
Wonderful book, though I'm one of many people who think he's basically wrong, which is why this is sometimes referred to as "The Emperor's Old Hat". Some comments here
Roger Penrose: "Shadows of the Mind" pub. Oxford University Press, 1994
"Son of beyond the valley of the return of the Emperor's Old Hat, part II." Haven't actually read it yet: he claims to have patched up some of the objections to ENM, and there's even more quantum physics and other Hard Stuff than in "Part I".
Excellent: won the somethingorother science prize, I forget exactly when. Pinker is a linguist in the Chomskyan tradition, and this is his exposition of Chomsky's linguistics for the general reader. But it is also much more - a broad introduction to the whole sweep of modern ideas about language. Pinker is a skilled writer, and the book is full of witty examples.
Pinker, Steven: "How the Mind Works" pub. in USA by W. W. Norton, 1997 (also in Penguin paperback), 650pp
Eminently readable as always, Pinker gives a rundown on evolutionary psychology. Starts with uncontroversial (good) stuff about perception, and goes on to explain, well almost everything. He includes some good jokes, too, and here's just one: Lady Astor said to Winston Churchill, "If you were my husband, I'd put poison in your tea." He replied, "If you were my wife, I'd drink it."
Perhaps he tries to explain too much: here's my demolition job on his attempt to account for the pentatonic scale: Music by numbers.
Searle, John: "The Mystery of Consciousness", pub. New York Review of Books, 1997
Rather like Daniel Dennett, John Searle keeps churning out stuff aiming at the same basic idea, but of course they are on opposite sides. I find Searle profoundly unconvincing: yes, he starts ok - "When you pinch your arm it hurts, and the pain is real" - but basically he just pumps this intuition that there's a "thing" there called "the pain", and explains nothing at all.
As always, in this book he trots out the notorious (and totally bogus) "Chinese room" fable: Imagine you have a program which passes the Turing test in Chinese, and implement it with slips of paper in drawers with instructions on, with John Searle mindlessly following the instructions and shuffling the slips around, his friend Chang operating the (manual) air-conditioning. You're supposed to believe that because Chang understands Chinese, but Searle doesn't, and Chang is only a punkah-wallah, this means that no digital computer can "understand" Chinese. On the other hand, presumably if Chang and Searle swapped jobs, then Chang's understanding would somehow affect the program operation, even though it would be unchanged. Or perhaps the air-conditioning would "understand" Chinese. I don't know, but it all seems very silly.
Apart from the basic wonkiness of his thesis, Searle is quite readable, and sometimes there is no substitute for the horse's mouth. And the exchanges with Daniel Dennett and David Chalmers reprinted in this book make lively reading.
See also: Do qualia exist?
A very wide-ranging survey of irrational aspects of human behaviour. As John Allen Paulos eloquently puts it in one of the 'blurbs', "One of the most appealing aspects of this book is that its grand pronouncements are few and its specific illustrations plentiful..."
It seems extraordinary that this book keeps going out of print - last year the US edition was out of print - now the UK one is. Hmm - perhaps an excellent topic for conspiracy theorists?
After an introductory chapter on philosophy - ultimate causes, and that sort of thing - he begins as he intends to continue, with no hesitation about writing down equations. He deals first with the basic ideas of dimensions and scaling: Why do elephants have such thick legs in proportion to those of grasshoppers? Because weight scales with the third power of linear size, and the supporting strength of a bone scales with only the second power of its linear dimension (i.e. the cross-sectional area). At the other end of the scale, the form of cells and unicellular organisms can largely ignore gravity: here simple rules of geometry kick in to govern the shapes that objects form. He has a memorable section on gnomons, self-similar shapes typified by mollusc shells and curly rams' horns; as in so many cases, apparenty unrelated items are in fact only mathematical variants on a theme.
That is an extremely cursory skim over the themes of this book. So many things fell into place once I had read it, that I consider it the single most essential book in my "Top Ten" list.
After original publication in 1917, D'Arcy Thompson expanded the content in the second edition (1942). Then John Tyler Bonner produced the abridged version (only 330 pages) in 1992, the version I read, though for complicated reasons I now have the second edition.
Read the BBS posting I made back in 1995: "More paper formats"
Wells, David: "The Penguin Dictionary of Curious and Interesting Numbers" pub. Penguin, 1986, 230pp (Revised ed. ISBN 0-14-026149-4)
This delightful book turned out to be the first of a successful series. In one way it is clearly the most interesting, since it really is a dictionary of numbers in, well, numerical order. But there is also a small alphabetical index, in case you forget the smallest Carmichael number, and a few useful tables of primes and things.
Just as it's interesting to look at the thumb index marks on the edge of an A-Z dictionary, to see how it matches one's intuitions about the commonest letters, here we can examine the distribution of numbers in the dictionary. He starts with several pages each on "-1 and i" (our only excursion on the complex plane) and "0", then starts on positive numbers. And only a few pages brings us to 1 - how odd that there are more interesting very large numbers than very small ones! Then mostly integers, but we stop at each of the obvious small and famous irrationals - the square root of two, the golden ratio, e, pi. Some numbers get a lot more attention than others, and there are some mundane - almost useful - snippets among the arcana, such as 22 being the maximum number of pieces into which you can cut a pancake with six straight cuts. We're already half-way through the book at 35, and decimal fractions are becoming rare, but there's a pastiche numerology entry for 512.73, which is the Dewey Decimal classification for "Number theory: analytic." The accolade of "among the most famous of all numbers" goes to 1729, Hardy's taxicab, which Ramanujan instantly pointed out is the smallest number to be represented as the sum of two cubes in two different ways (123 + 13 = 103 + 93 = 1729). The largest number written out in full decimal notation has 45 digits (and it's prime):
I must note one oddity (of a type I collect). The binary system, he says, was invented by Leibniz, but "referred to in a Chinese book which supposedly dates from about 3000 BC." Hmm. Claims of Chinese books of fantastic antiquity are common on the web (try a search for "ginkgo China 2800 bc") but totally implausible. For example, according to the chapter on Chinese in Geoffrey Sampson's Writing Systems, there are only fragmentary relics of Chinese writing back to about 2000 BC.
It's also curious that (apart from the generic -1) there are no negative numbers offered as interesting in their own right. OK: here's a candidate property of -5. For integers a and b, -5 is the only non-square integer value of the ratio (a2+b2)/(1+a*b). Here's the sci.math newsgroup thread about it.
Disclaimer: David Wells is an old friend - we played go in London in the 1970s. Note also that mine is the original edition - before it was revised in 1997.
Wells, David: "The Penguin Dictionary of Curious and Interesting Geometry" pub. Penguin, 1991, 280pp; ISBN 0-14-011813-6
Ah, but sadly in alphabetical order! Of course there is a good reason for this: geometrical objects and problems can't be neatly fitted into any linear order. Only a software lookup system could let me find the proof involving "pairs of tangents" + "circles" + "collinear". (It turns out to be called "Monge's theorem": here's my proof.)
But anyway, this is a wonderful book to dip into. It is a slightly larger format than the others in the series, and must have more than 500 good-sized illustrations. This does make it hard to flip to a page you found in the index without stopping at several others on the way. There are some classical-looking results, but many of the topics are "recreational maths", with some attractive tiling ideas in particular. This might be the book to convince your children that maths is fun!
Wells, David: "The Penguin Book of Curious and Interesting Puzzles" pub. Penguin, 1992, 380pp; ISBN 0-14-014875-2
I'm glad they didn't try to call this a "dictionary" because is isn't, but it's more than just a grab-bag collection. He protests in the introduction that it is not a history of puzzles, but nonetheless starts with the world's oldest puzzle, and works through the Egyptians, Babylonians, and Greeks, through Arabic, Indian, and Chinese puzzles, various medievals, then the most famous puzzlers of all: Sam Loyd from Philadelphia and Henry Ernest Dudeney from Sussex. Many of the puzzles are basically mathematical, though many are not, and there are also a few trick questions. The solutions form almost exactly the second half of the book, and are interspersed with historical snippets just as the puzzles themselves are.
Wells, David: "The Guinness Book of Brian Teasers" pub. Guinness, 1993, 130pp; ISBN 0-85112-592-1
Oh dear, this looks like a hack job, David. I've tried to give as much care to writing the title as the publishers gave to proof-reading: missing figures, wrong figures, and simple misprints. Well, that's probably beyond the author's control in a book like this, but then I found a horror.
It's the old chestnut about pulling backwards on the pedal of a bicycle when it is at the bottom. Which way does the bicycle and/or pedal go? Here's the answer we're given:
If Jennifer pulled backwards on the pedal, the pedal would move backwards, relative to the bicycle, but the bicycle would move forwards relative to the ground and it would move forwards faster than the pedal moved backwards. Therefore, on balance, the pedal would go forwards, although Jennifer pulled it backwards.
At last! No more fossil fuels! No more nuclear waste! Energy can be extracted from bicycle wheels, for free! If you have something which when pushed comes back towards you, simply push it with a spring, supported by a solid block. The bicycle obligingly compresses the spring for you - and the stiffer you make the spring, the harder the bicycle will push. Then you use the energy stored in the spring to power an electrical generator. Of course, you can also use a specially manufactured bicycle directly for jobs like crushing concrete blocks.
Why is this nonsense? Because if you exert a (constant) force (otherwise known as pressing), and move forward a certain distance, the energy you have put into the system is the force multiplied by the distance you move forward. If you push, but actually move back, then you are extracting energy, and you can obviously do this if there is some energy source providing the push against you. It is true that in an extremely low-geared bicycle, it would be possible to pull the pedal back so that the bicycle went forward, but this is not what happens with an ordinary bicycle.
Above I've quoted the first paragraph of the answer. The second points out that when you ride a bicycle, you are pushing the bottom pedal back with respect to the bicycle; this is of course true, but entirely irrelevant. The last paragraph invites us: "Get on your bike and try it!" But the problem wasn't about getting on the bike, it was about standing on the ground, and pushing the pedal backwards: just to check my own sanity I just went outside and tried, with the expected results.
I bought this from the Good Book Guide, thinking that the author would be sufficient to guarantee it. When I wrote and complained, they said (basically) that their reviewer couldn't see anything wrong. Hmm, perhaps mercifully, it seems to be out of print.
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