"From the Closed World to the Infinite Universe" by Alexandre Koyre

This is from the 'Easy Reading Series' of Forgotten Books: it is relatively easy to read but the format which fails to easily distinguish between extensive quotations and the author's gloss makes it much more difficult to read than it should be.

Koyre is concerned with the change of world view which occurred about the same time as the Copernican revolution.

He starts with the arguments of Nicholas of Cusa who "denies the finitude of the world and its enclosure by the walls of the heavenly spheres" (p 8) although he won't go so far as to assert the infinity of space, only that the universe is 'interminate', "it is boundless and not terminated by an outside shell" (p 8) but also that it "utterly lacks precision and strict determination" (p 8) so it can never reach the limit; he reaches this conclusion by using his doctrine of '"learned ignorance" (p 8) "the intellectual act ... which transcends discursive, rational thought". He illustrated this by pointing out that an infinitely large circle has straight sides (the curved side at any point will coincide with its tangent) and an infinitely small circle will also have straight sides (the side will correspond to its radius) and that therefore the big infinite and the little infinite are the same.

Unfortunately Koyre does not really explain 'learned ignorance'; I had to find Wikipedia to tell me: "docta ignorantia means that since mankind can not grasp the infinity of a deity through rational knowledge, the limits of science need to be passed by means of speculation. This mode of inquiry blurs the borders between science and ignorantia. In other words, both reason and a supra-rational understanding are needed to understand God. This leads to the coincidentia oppositorum, a union of opposites, a doctrine common in mystic beliefs from the Middle Ages."  https://en.wikipedia.org/wiki/De_Docta_Ignorantia

Next he talks about a poetic philosopher named Palingenius who uses the Principle of Plenitude (again unexplained but which is the idea that God is so brilliant that all possible forms of creation are available in the world) to deny "the finitude of God's creation" (p 21).

Koyre continues to Copernicus which he says "undermined the very foundations of the traditional cosmic world-order with its hierarchical structure and qualitative opposition of the celestial realm of immutable being to the terrestrial or sublunar region of change and decay." (p 23) He points out that "the immediate effect of the Copernican revolution was to  spread scepticism and bewilderment" (pp 23 - 24) Perhaps the most convincing Copernican argument was the fact that it would take much more effort to make the large sphere of the fixed stars rotate than the much smaller Earth.

There is also a chapter on Giordano Bruno, who asserted the infinity of the heliocentric Universe and was burnt at the stake. But he wasn't that modern or perhaps he was, he asserted that since the senses were flawed and could be fooled the intellect was primary.

Then, via Galileo, comes Descartes who starts with the idea of God and therefore starts with infinity and derives the finite from the idea of the infinite. Typically weird. You start to understand where the other French philosophes have got it from.

We next get several chapters on Henry Moore, a Neo-Platonist who disputed with Descartes and taught Newton and therefore a fascinating and often overlooked philosopher of nascent science. He pointed out the daftness of Descartes endeavour to avoid the void because nothing can come of nothing as Lear might have said. |Moore suggests that the primary property of matter is not its extension but its impenetrability; he asks how "can a purely spiritual soul ... which, according to Descartes, has no extension whatever, be joined to a purely material body, that is to say something which is solely and only extension?" By exposing the contradictions inherent in the ramshackle Cartesian system which endeavours to solve scientific problems through the appeal to a wholly biased intellect, Moore laid the foundations for Newtonian science. And for infinity. Because Descartes believed that the Universe was bounded. But Moore asked: "Could Descartes not tell what would happen ... if somebody sitting at the extremity of the world pushed his sword through them limiting wall? On the one hand, indeed, this would seem easy, as there would be nothing to resist it; on the other, impossible, as there would be no place where it could be pushed." (p 89)

Moore, Koyre tells us, was a syncretist who tried to synthesise the new discoveries with the occult, magical and hermetic traditions nut nevertheless "succeeding in grasping the fundamental principle of the new ontology, the infinitization of space." (p 93) And such dabbling in weird stuff was necessary to develop the theory of, for example, gravity. This has a challenging principle of action at a distance. "Gravity cannot be explained by pure mechanics" (p 98) Koyre points out.

And so from Moore to Newton and, in particular, his letters to Mr Richard Bentley in which he states that "the cause of gravity is what I do not pretend to know"; nevertheless Newton realises that he can analyse its effects without knowing its causes. (p 131).

This is an interesting book but it would be an easier read if (a) some of the Latin tags were translated (I managed to work out most of them but I was taught Latin forty five years ago) and (b) if Koyre explained some of the things he mentions such as the Principle of Plenitude.

May 2017, 200 pages

"Science in a Free Society" by Paul Feyerabend

Feyerabend's thesis is that rationalism has too firm a grip on society and that the best medicine is a little anarchy.

He defines rationalism as "a secularized form of the belief in the power of the word of God." (p 20) which believes itself to be "'objective' and tradition-independent" but he suggests that although modern society bases itself on science "as uncritically as one once accepted the cosmology of bishops." (p 74) it is just another tradition fighting for itself in a world of alternative traditions. No tradition, he asserts, can judge another tradition because the values and beliefs of each tradition are different; this is a form of Kuhn's incommensurability thesis. You can't even damn a tradition on the basis that it is internally contradictory. Contradictions are not necessarily signs of a weak argument. The idea "that we do not live in a paradoxical world" so that our "knowledge must be self-consistent ... loses it authority the moment that we find that there are facts whose only adequate description is inconsistent and that inconsistent theories may be fruitful."

OK. These are serious issues. We have to acknowledge that science is 'just' another tradition and that it is difficult to make an objective judgement about whether as a tradition is is one of the best. But Feyerabend then appears to assert that this difficulty therefore means that anything ought to go.

He asserts that "a free society is a society in which all traditions are given equal rights, equal access to education and other positions of power." (p 30). Thus Hopi creation myths should be taught alongside the Big Bang Theory, astrology with astronomy, homeopathy with scientific medicine (he doesn't like scientific medicine!). Thus far he is relativist; he is also anarchist is the sense that "rules have their limit" (p 32) though he probably doesn't go on to assert that "all rules and standards are worthless and should be given up." (p 32). 

He appears to advocate the Socratic view that everything should be examined (although he places a significant restriction on the ability to examine if we can only examine any one tradition from inside). But Feyerabend does not appear to examine his basic assumption which seems to be that we 'should' live in a 'free' and 'democratic' society. 

Because if he is right that a 'free' society must give all traditions equal rights then it would follow that a 'free' society must give "equal rights, equal access to education and other positions of power" to 'traditions' such as racism and Nazism and Aztec human sacrifice. I don't think I want to live in such a society.

The second half of the book is dedicated to vitriolic attacks on those who have dared to criticise him, suggesting that he has been misunderstood. He seems hurt by the violence of the reaction to what he thinks are reasoned views but the section in which these protestations are made is entitled "Conversations with illiterates" which doesn't sound either friendly or reasoned. 

Some interesting points but the overall conclusions seem ridiculous. September 2016; 217 pages

"Consilience" by Edward O Wilson

This far-ranging and brilliantly written book pleads the cause that science should be united with the social sciences, and the humanities, and the arts, and even ethics and religion, on the basis of the scientific method. The thesis is that biology, which accepts that is is linked to chemistry and physics, is the basis for psychology through the evolution by natural selection within the human brain of epigenetic rules, and that scientific psychology is (or should be) the basis for sociology, anthropology and economics. Wilson is predominantly a socio-biologist and presents compelling evidence for his point of view. This book thus complements, supports and is supported by Steven Pinker's brilliant book The Blank Slate.

He starts by celebrating the power of science:  "The idea of the unity of science ... has been tested in acid baths of experiment and logic and enjoyed repeated vindication. It has suffered no decisive defeats. At least not yet." (p 3). To those who fear the 'mad scientist', variously mythologised as Frankenstein, the forbidden apple from the tree of knowledge in the garden of Eden, and Icarus, the ultimate in hubris, Wilson responds: "Let us see how high we can fly before the sun melts the wax in our wings." (p 5)

He believes that the romantics led the reaction against the Enlightenment ideal of consilience, the unit of knowledge, when  Rousseau "invented the deadly abstraction of the 'general will' ... the rule of justice agreed upon by assemblies of free people whose interest is only to serve the welfare of the society and of each person in it ... Those who do not conform to the general will ... are deviants subject to necessary force by the assembly. There is no other way to achieve a truly egalitarian democracy." (p 14) but he points out that  "The Enlightenment ... was less a determined swift river than a lacework of deltaic streams working their way along twisted channels" (p 21) and reminds us that "What counts most in the long haul of history is seminality, not sentiment." (p 22) "Reductionism, given its unbroken strong of successes ... may seem today the obvious best way to have constructed knowledge of the physical world." (p 31) "The cutting edge of science is reductionism ... It is the research strategy employed to find points of entry into otherwise impenetrably complex systems." (p 58) The present situation is one in which the "natural sciences have expanded to reach the borders of the social sciences and humanities" (p 71)

Wilson is at one with Dennett is his claims that "Mind is a stream of conscious and subconscious experience. It is at root the coded representation of sensory impressions and the memory and imaginations of sensory impressions." (p 119) and that "Consciousness consists of the parallel processing of" networks of neurons. These "create scenarios that flow back and forth through time. The scenarios are a virtual reality." (p 120) He thus denies the Cartesian theatre: "Who or what within the brain monitors all this activity? No one. Nothing. The scenarios are not seen by some other part of the brain. They just are. ... There is no single stream of consciousness in which all information is brought together by an executive ego. There are instead multiple streams of activity, some of which contribute momentarily to conscious thought and then phase out. ... The mind is a self-organizing republic of scenarios that individually germinate, grow, evolve, disappear, and occasionally linger to spawn additional thought and physical activity." (p 120)

I think therefore I am? Wilson questions the identity of the Self, seeing it as an actor improvising: "The self, an actor in a perpetually changing drama, lacks full command of its actions." (p 131) Free will is an illusion: "We make decisions for reasons we can sense only vaguely, and seldom if ever understand fully. Ignorance of this kind is conceived by the conscious mind as uncertainty to be resolved; hence freedom of choice is ensured. An omniscient mind with total commitment to pure reason and fixed goals would lack free will." (p 131): this implies that an omniscient God could not have free will; this is a fascinating theological restriction on God that I need to think about.

He revisits the nature-nurture debate, accepting that culture affects us but claiming that culture is an amalgam of the evolution of epigenetic rules which are prescribed by genes. "We know that virtually all of human behaviour is transmitted by culture. We also know that biology has an important effect on the origin of culture and its transmission. The question remaining is how biology and culture interact." (p 138) "Culture is reconstructed each generation collectively in the minds of individuals ... culture can grow indefinitely large ... But the fundamental biasing influence of the epigenetic rules, being genetic and ineradicable, stays constant." (p 139). This creates an unchangeable human nature. He has a great example showing how nature and nurture interact in the arrowleaf plant which has arrowhead leaves on land, lily-pad leaves in shallow water, grass-like ribbon leaves in deep water. Similarly, humans genetically predisposed to be fat can be thin with a significant dieting regime and "Later-borns, who identify least with the roles and beliefs of their parents, tend to become more innovative and accepting of political and scientific revolutions than do first-borns. As a result they have, on average, contributed more than first-borns have to cultural change throughout history." (p 152)

Culture itself evolves and Wilson suggests that this is because cultural evolution can facilitate survival faster than genetic evolution, thus enabling faster adaptation to environmental change and potentially explaining the success of our species. "The more successful epigenetic rules have spread through the population along with the genes that prescribe the rules. As a consequence the human species has evolved genetically by natural selection in behaviour. ... Certain cultural norms also survive and reproduce better than competing norms ... Culture allows a rapid adjustment to changes in the environment through finely tuned adaptations." (p 140) Culture exists in other species: "Wild chimps regularly invent and use tools. And the particular kinds of artifacts they invent, just as in human culture, are often limited to local populations." (p 145). 

He casts a new light on rationality itself! "I suggest that rational choice is the casting about among alternative mental scenarios to hit upon the ones which, in a given context, satisfy the strongest epigenetic rules." (p 199) But epigenetic rules ("rules of thumb that allow organisms to find rapid solutions to problems encountered in the environment") (p 213) are "typically emotion driven" (p 214) so "Rational calculation is based on surges of competing emotions." (p 227)#

He is fascinating on a wide range of topics including pre-verbal communication which is probably "our primate heritage" and includes:

• "a male pheromone concentrated in perspiration and fresh urine. Perceived variously as musk or sandalwood, it changes sexual attraction and warmth of mood during social contacts." (p 174)
• Touching: strangers: arms only; other parts of body for more familiar acquaintances; more familiarity with opposite sex (p 174)
• "Dilation of the pupils": greater in women (p 174)
• "Pushing the tongue out and spitting are aggressive displays of rejection; flicking the tongue around the lips is a social invitation, used most commonly during flirtation" (p 174)
• Close eyes & wrinkle nose: rejection (p 174)
• "Opening the mouth while pulling down the corners of the mouth to expose the lower teeth is to threaten with contempt." (p 175)

"The optimum sexual instinct of men ... is to be assertive and ruttish, while that of women is to be coy and selective. Men are expected to be more drawn than women to pornography and prostitution. And in courtship, men are expected to stress exclusive sexual access and guarantees of paternity, while women consistently emphasize commitment of resources and material security." (p 187)

The theory of the family: "The basic assumption is evolution by natural selection" (p 214)
"Families are basically unstable, but the least so in those controlling high-quality resources. Dynasties ... arise in territories permanently rich in resources." (p 215)
"The closer the genetic relationships of the family members .. the higher the degree of cooperation." (p 215)
"The closer the genetic relationship of the family members, the lower the frequency of sexual conflict." (p 215)
"Breeding males invest less in offspring when paternity is uncertain. If the family consists of a single conjugal pair, and one of the parents is lost, the opposite-sex offspring compete with the surviving parent for breeder status. When the father dies, for example, a still fecund mother is likely to enter into conflict with a son over the status of a mate he may newly acquire, and a son is likely to discourage his mother from establishing a new sexual relationship." (p 215)
"Stepfamilies are less stable than biologically intact families." (p 215)
"Reproduction within a family ... is increasingly shared when there is an improvement in the alternative option for subordinate members to disperse and start families of their own. Such forbearance is greatest of all when the members are genetically very close and when the cooperating individuals are siblings rather than parents and offspring." (p 215)

Economists tend to use "folk psychology" (p 223) Their "principle of rational choice" assumes "narrow self-interest" but people are also "variously altruistic, loyal, spiteful, and masochistic." (p 224)

"The arts are not solely shaped by errant genius out of historical circumstances and idiosyncratic personal experience. The roots of that inspiration date back in deep history to the genetic origins of the human brain, and are permanent." (p 242)

"Either ethical precepts, such as justice and human rights, are independent of human experience or else they are human inventions." (p 265) But if ethical rules "increased the survival and reproductive success of those who conformed" then epigenetic ethical rules could have evolved. (p 275)

"Rarely do you see an argument that opens with the simple statement: This is my starting point and it could be wrong." (p 268)

Pascal's wager: I might as well believe: if I am right I get eternity in heaven, if I am wrong I lose nothing. This could be turned around: "If fear and hope and reason dictate that you must accept the faith, do so, but treat this world as if there is none other." (p 274)

The naturalistic fallacy (to go from is to ought) is itself a fallacy: "To translate is into ought makes sense if we attend to the objective meaning of ethical precepts ... they are no more than principles of the social contract hardened into rules and dictates, the behavioral codes that members of a society fervently wish others to follow and are willing to accept themselves for the common good." (p 278)

"One hunter considers breaking away from the others to look for an antelope on his own. If successful he will gain a large quantity of meat and hide ... But he knows from experience that his chances of success alone are very low ... In addition ... he will suffer animosity from the others for lessening their own prospects." (p 281) therefore those humans who cooperate have greater reproductive success and cooperation evolves. Therefore the prisoner's dilemma can be solved if "Honor does exist among thieves" (p 281)

"I found it hard to accept that our deepest beliefs were set in stone by agricultural societies of the eastern Mediterranean more than two thousand years ago." (p 4)

At then end he offers two warnings. 

First: we are destroying our environment. "At best an environmental bottleneck is coming in the twenty-first century." (p 320) "Economic miracles ... occur most often when countries consume not only their own material resources, including oil, timber, water, and agricultural produce, but those of other countries as well." (p 325) Life is becoming increasingly fragile:
"The more knowledge people acquire, the more they are able to increase their numbers and to alter the environment, whereupon the more they need new knowledge just to stay alive." (p 302)
"Greed demands an explanation." (p 302)

Secondly, we are about to become in charge of our own evolution.
"Homo sapiens, the first truly free species, is about to decommission natural selection, the force that made us. ... Soon we must look deep within ourselves and decide what we wish to become. Our childhood having ended, we will hear the true voice of Mephistopheles." (p 309)

This is an amazing book. July 2016; 333 pages 

"Against Method" by Paul Feyerabend

Feyerabend is a firebrand, an iconoclast, whose purpose is to demolish any theory that seeks to systematise the processes of scientific discovery. He starts with the statement that "anarchism, while perhaps not the most attractive political philosophy, is certainly excellent medicine for epistemology, and for the philosophy of science" (p 1). The history of science is "complex, chaotic, full of mistakes, and entertaining." (p 3) And he continues to challenge throughout the book. Don't be misled by the italics, which he peppers with the abandon of a Caribbean chef. This is not the work of an obsessed dilettante. He is thoroughly immersed in the history of science and proceeds to provide extensive evidence from the Copernican revolution.

Although it is a little worrying, given his tendency to make broad-brush statements such as "There is not a single interesting theory that agrees with all the known facts in its domain" (p 14; my emphasis), that the evidence he cites comes exclusively from the Copernican revolution (with a little bit added in about Newton but he rarely strays into biology or chemistry or even quantum physics).

His essential thesis is that scientists are mavericks who don't assess theories in terms of the facts they can explain (and certainly, despite Popperianism, don't reject theories because they are falsified by inconvenient facts). Nor do scientists neatly construct methodologies. Indeed, in Feyerabend's eyes, the process of scientific discovery is an essentially ad hoc muddle of methodological innovation, new philosophical insights and perspectives, and facts. In order for science to make progress it is necessary, from time to time, to flout the rules of scientific methodology. (p 7) "Inventing theories and contemplating them in a relaxed and 'artistic' fashion, scientists often make moves that are forbidden by methodological rules." (p 150)

This is an interesting book and contains many insights into the work of Galileo in particular. He can get carried away: "his natural sense of humour and not the inbred and always rather nasty kind of jocularity one finds in specialized professions" combines yet another of his italicisings with the naturalistic fallacy with a sweeping generalisation ('always') and bitchiness. But on the whole it is well written, with reams of footnotes (some pages have more footnote than text) and tons of well-argued evidence.

I often do not read the Appendices of books. Hence, having reached Appendix One, I put the book down and wrote the blog post above. Then, for some reason, I took the book back up and discovered that there were five more chapters after Appendix One (including, interspersed, Appendix Two). And a Post Script. That really is it. So below is the rest of the blog post.

The remaining chapters investigate the processes involved when two inconsistent ideas interact, which is where he differs from Thomas Kuhn who his classic Structure of Scientific Revolutions has suggested that paradigms can be so different as to be incommensurable with no possibility of interaction. Feyerabend believes that "Incommensurability depends on covert classifications." (p 171) and he defines "Covert classifications are sensed rather than comprehended." (p 170) This means that when, for example,an iconoclastic young Turk in, say, theatre despairs of the theatre of his time and, by searching outside the box, promotes a revolution in drama, his new revolutionary school can and does interact with the old school which may "lead to a slight modification of the original practice, it may eliminate it, it may result in a tradition that barely resembles either of the interacting elements." (p 224) This is a very common-sense view.

But his overall argument, summed up in his title Against Method, is that "all rules have their limits" although "I do not argue that we should proceed without rules and standards" (p 242). He uses a nice analogy which will even work in the sat nav era: "The wanderer uses the map to find his way but he also corrects it as he proceeds ... Using the map no matter what will soon get him into trouble. But it is better to have maps than to proceed without them." (p 233)

But one of the reasons why a single uniform method should not be imposed is that we are always seeking to explore hitherto unmapped regions. "We don't know the region, we cannot say what will work in it." Fair point, although one suspects that the human reaction will be to try to apply whatever has worked so far.

He's right of course. Scientists don't follow their own rules. Who does? Exploration must always involve a great deal of making-it-up-as-you-go-along. We should not try to discern, still less impose, a single Method on research. That is just common sense. But Feyerabend's gift for communication sometimes makes him seem more like a prophet than a philosopher, more of an iconoclast than an academic, and ever so slightly a crank. When he seems to suggest that physics as a way of discovering the universe is not as good as mysticism, it is easy to see why his opponents should accuse him of an 'anything goes' platform when actually his 'anarchy' is merely a plea against totalitarianism.

June 2016; 287 pages

"Patterns of Discovery" by Norwood Russell Hanson

Hanson starts by undermining claims the science is objective by showing that visual illusions prove that "seeing is a 'theory-laden' undertaking" (p 19): two biologists looking at the same slide might disagree as to whether they are seeing an artefact of the staining process or an organelle. He then claims that this undermines the hypothetico-deductive model of science as popularised by (for example) Karl Popper in Conjectures and Refutations. At the same time he disagrees that the creation of a hypothesis is some sort of magical act of creativity:

"The initial suggestion of an hypothesis is very often a reasonable affair. It is not so often affected by intuition, insight, hunches, or other imponderables as biographers or scientists suggest." (p 71)

Unfortunately he seems to be light on the evidence for this point. I would offer the mass of evidence accumulated by Lowes in The Road to Xanadu when explaining the sources of inspiration for Coleridge when writing the Rime of the Ancient Mariner.

He then talks of different types of explanation laying particular stress on the 'abduction' or 'retroduction' of Peirce which Hanson suggests is the same as Aristotle's 'apagogy'.

He also points out that: "some events need less explaining than others" (p 95); as good a justification for Ockam's Razor as I have seen.

He shows how the laws of physics may start out as "empirical generalizations" but they can "graduate to being 'functionally a priori'" (p 98) in the same way that a legal judgement in one case can become a precedent for another.

He suggests that a theory is "an intelligible, systematic, conceptual pattern for the observed data. The value of this pattern lies in its capacity to unite phenomena which, without the theory, are either surprising, anomalies, or wholly unnoticed." (p 121)

In a moment that was stunningly exciting for me he showed why all electrons must be identical: Born showed that the electric field strength inside an electron must rise to a singularity and since only one kind of singularity is possible therefore all electrons must be the same. (p 135)

This short book was an immensely readable (and quaintly old-fashioned, it was written in 1965 and has endearing mannerisms like referring to Heisenberg as "Professor" Heisenberg) journey through a mall portion of the philosophy of science and deserves to be better known. May 2016; 158 pages

"Conjectures and Refutations" by Karl Popper

This is a classic work of philosophy in which Popper explains his Criterion of Falsifiability to separate Science from Non-Science. Why, he asks, is Einstein's work so different from that of, for example, Marx or Adler. The answer he gives is that Einstein makes precise predictions which can be tested whereas Marx and Adler offer vaguer forecasts. For example, the General Theory of Relativity proposed that light would be bent by a gravitational field and that therefore we would be able to see stars during a solar eclipse that were behind the sun, invisible unless light bent. If the stars could not be seen, Einstein would be wrong. In other words, Einstein's theory was easy to refute (and, to add spice, it would be refuted if light travelled in straight lines as everyone had hitherto believed). But Eddington photographed the eclipse and Einstein was acclaimed. On the other hand, Adler's theories are often so vague that they can predict either of two opposite occurrences. As for Marxism, it made some precise predictions which were falsified but the theories were then adapted so the theories fitted the facts. In Popper's view, such theory-elasticity in non-Scientific.

Popper believes that Science proceeds thus: a scientist makes a hypothesis, testable predictions are generated, these are then tested and, if they are found to be false, the hypothesis is discredited and a new one dreamed up. The more falsifiable the predictions, the sooner they can be refuted and the quicker Science can progress.

Many people have criticised Popper's views. He says nothing about how the hypotheses are generated in the first place. He does not give sufficient weight to how observations are made in the context of theories so that what is observed may be inaccurate or spurious. He fails to acknowledge sufficiently that most theories have refuting observations but these are usually treated as anomalies, the theory is still believed in spite of them, unless and un til the 'time has come' for the theory to be refuted. And he fails to account for the fact that Science might be unable to proceed if refutations were too easily able to displace a theory.

In my mind Science progresses like the sandpiles of Per Bak. The anomalies add to the theory like grains of sand add to the pile. Normally there are a few trickles down the pile as the theory adjusts itself. But sometimes, unpredictably, a grain of sand starts an avalanche and the theory is refuted and another one steps in to take its place. And the process starts all over again.

And Science would not be possible if the grains slipped too easily (perpetual avalanches would result in paradigm overload - perhaps this is the problem with the social sciences) or hardly ever slipped resulting in knowledge becoming fossilised a bit like scholasticism in the middle ages (though James Hannam might disagree with me).

Per Bak is the author of How Nature Works, a brilliant book about the phenomenon of self-organised criticality in the context of a wide range of complex systems including an ecosystem. Read it!

James Hannam is the author of God's Philosophers, an equally brilliant book about the growth of scientific knowledge in the middle ages.

April 2016; 415 pages

"What is this thing called science?" by A F Chalmers

This is an extremely readable account of the history and philosophy of science. He explains some difficult ideas with brilliant clarity.

He talks about the problem of induction, expressed by Bertrand Russell as the problem the turkey faces when, following daily examples, he induces that he is always fed at 9AM ... until he discovers he is wrong on Christmas Eve. Furthermore, since what you see depends on what you expect, in some sense theory comes before observation; Chalmers illustrates this rather neatly with an example about junior doctors learning to see what the weird marks on X-rays actually mean.

He then discusses Popperian ideas about falsificationism at length and shows the weaknesses of this theory.

He then looks at alternative accounts of the historical development of Physics from the point of view of Lakatos, Kuhn and Feyerabend.

For me, the most important moments came when he was talking about concept networks. He argues that "the Newtonian concept of mass" is more precise than "the concept of democracy" (pp 77 - 78) because "the concept plays a specific, well-defined role in a precise, structured theory." (p 78). "If this suggested close connection, between precision of a term or statement and the role played by that term or statement in a theory, is valid, then the need for coherently structured theories follows fairly directly from it." (p 78). For example, a dictionary definition requires one to understand many other words. He also quotes Feyerabend as asserting the importance to Copernicus of the "internal connectedness" of the parts of his system. (p 103)

This of course links to the idea that Kuhn viewed "normal science as a puzzle-solving activity" (p 92) and, putting coherence above correspondence, stated that "puzzles that resist solution are seen as anomalies rather than as falsifications of the paradigm." (p 92)

But Chalmers also provides a justification which I can use for my choice of Grounded Theory as a methodology for exploring liminality: "Precise experimentation can only be carried out if one has a precise theory capable of yielding predictions in the form of precise observation statements." (p 79) and since Galileo was creating a new paradigm "it need not be surprising that his efforts involved thought experiemtns, analogies and illustrative metaphors rather than detailed experimentation." (p 79)

This is a well written and readable account of the history of physics though perhaps a little out of date with the latest ideas.

April 2016; 170 pages

"Big Bang" by Simon Singh

This is a delightful and fascinating history of cosmology up to and slightly after the near-universal (pun not intended) acceptance of the Big Bang theory of the creation of the Universe. Having taught Physics for 33 years I knew most of the Science and understood the arguments but there were still aspects I had not fully appreciated. These were carefully explained and I am confident that this book would be accessible to the general reader. Singh also explained the philosophical issues and weighed up the various arguments carefully so that their merits and demerits could be easily compared. But the icing on the cake was his affectionate portrayal of the very human astronomers and cosmologists who contributed to (or fought against) our present understanding.

There were so many characters. Here are just a few:

• Fritz Zwicky, for example, was famously rude. His favourite insult was to call you a 'spherical bastard' because,just like a sphere, he thought you were a bastard whichever way he looked at you. 
• Lord Rosse owned an estate in Ireland and gave up astronomy to look after his tenants during the Irish Potato Famine; he built a huge telescope on his lands but was rather foiled by the fact that there are two sorts of weather in Ireland: raining and about to rain. 
• Walter Baade, a German emigre in USA during the Second World War experienced similar frustrations when the authorities decided that, as an enemy alien, he should be confined to his house between sunset and sunrise despite working on the Mount Wilson optical telescope. 
• George Gamow, a practical joker, who had to defect from the USSR; his first attempt involved trying to canoe across the Black Sea which he had to give up after two days. 
• Fred Hoyle, the proponent of the Steady State Theory, who shot himself in the foot not once but twice: first when he developed the theory for nucleosynthesis which removed a significant problem for the Big Bang theory and secondly during a radio broadcast when he scornfully referred to what was then called the dynamic evolving model as a Big Bang, thus creating a catchy name to popularise the idea.

The book ends with a short epilogue in which the continuing issues facing cosmology are outlined. Why is the expansion of the Universe apparently accelerating? What is the mysterious dark energy that might explain this? Why are the six numbers that govern the Universe so perfectly aligned that humans can exist? Does this mean that we are just one bubble in a multiverse? And most of all, of course: What happened before the Big Bang?

A thought-porvoking book that takes you for a ride through the mysteries of the Universe and yet explains them so well that you understand some reallt difficult science.

April 2015; 493 pages

Other books by this author:

• Fermat's Last Theorem: I have not yet read this
• The Code Book: I very much enjoyed this history of cryptography
• The Simpsons and Their Mathematical Secrets: a fun book about Maths which I have reviewed in this blog

"The Structure of Scientific Revolutions" by Thomas Kuhn

I first read this book, which was published in 1962, when I was studying the History and Philosophy of Science at Cambridge in 1987-8. It was a revolutionary thesis. This is the third edition (1996) which adds a postscript to respond to some of the issues that its original publication raised.

Science, Kuhn suggests, does not make steady progress closer and closer to the truth. Rather, it is oscillates between a 'normal' phase during which scientists solve problems and a 'revolutionary' phase when scientific certainties are thrown out of the window and a radically different understanding is born.

He calls the framework within which normal science is done a 'paradigm' and the revolution a 'paradigm shift'. There are many similarities between the way science develops during a paradigm shift and the way students learn if we assume the 'threshold concepts' theory of learning.

For example, In the 1880s physicists were complacently expecting that soon their classical models would be able to explain all that needed to be explained. They were refining them and making them a little more accurate. There were a few clouds on the horizon. Maxwell's equations suggested that light was an electromagnetic wave but no one could detect the 'aether', the postulated medium through which the e-m waves must ripple. The 'ultra-violet catastrophe' was the theoretical model of the atom which predicted that when you heated something up it should glow purple before it glowed red and at some stage it would radiate infinite amounts of energy in the ultra-violet part of the spectrum. And the photo-electric effect was an experiment which suggested that the energy of the electrons emitted from a surface when light was shone on it was not linked to the brightness of the incoming light. But these were blips and no-one seriously doubted that classical physics would soon be able to solve these problems.

In fact the failure to detect the aether was explained once Einstein had discovered his theory of Special Relativity with its bizarre claims that the speed of light was the fastest possible speed, the simultaneity was relative, that time slowed down as you got faster and that mass and energy were inter-convertible. The ultra-violet catastrophe gave rise to the weird world of Quantum Physics and the photoelectric effect was the key evidence for wave-particle duality which shortly led to de Broglie's claims that particles could behave like waves.

In some ways this makes Science a little like the pile of sand as explained in the book Ubiquity. As grain after grain is added to the pile it becomes more and more unstable. Sometimes there are slight slips; at other times there are near-catastrophic landslides.  Or science is like the punctuated equilibrium model of evolution as described in John Gribbin's brilliant Deep Simplicity. Most of the time evolution just contributes a little variation which make organisms marginally better adapted to their evolutionary niches. But when there is a major ecological catastrophe, evolution goes wild to fill the new ecological niches that have been created.

Kuhn writes with elegance and power. This is a very convincing thesis that had a major impact on the history and the philosophy of Science.

March 2015; 210 pages