I figured I ought to blog this book at some point, and today I decided to take out the time to do it. This is the second book by Darwin I’ve read – for blog content dealing with Darwin’s book The Voyage of the Beagle, see these posts. The two books are somewhat different; Beagle is sort of a travel book written by a scientist who decided to write down his observations during his travels, whereas Origin is a sort of popular-science research treatise – for more details on Beagle, see the posts linked above. If you plan on reading both the way I did I think you should aim to read them in the order they are written.
I did not rate the book on goodreads because I could not think of a fair way to rate the book; it’s a unique and very important contribution to the history of science, but how do you weigh the other dimensions? I decided not to try. Some of the people reviewing the book on goodreads call the book ‘dry’ or ‘dense’, but I’d say that I found the book quite easy to read compared to quite a few of the other books I’ve been reading this year and it doesn’t actually take that long to read; thus I read a quite substantial proportion of the book during a one day trip to Copenhagen and back. The book can be read by most literate people living in the 21st century – you do not need to know any evolutionary biology to read this book – but that said, how you read the book will to some extent depend upon how much you know about the topics about which Darwin theorizes in his book. I had a conversation with my brother about the book a short while after I’d read it, and I recall noting during that conversation that in my opinion one would probably get more out of reading this book if one has at least some knowledge of geology (for example some knowledge about the history of the theory of continental drift – this book was written long before the theory of plate tectonics was developed), paleontology, Mendel’s laws/genetics/the modern synthesis and modern evolutionary thought, ecology and ethology, etc. Whether or not you actually do ‘get more out of the book’ if you already know some stuff about the topics about which Darwin speaks is perhaps an open question, but I think a case can certainly be made that someone who already knows a bit about evolution and related topics will read this book in a different manner than will someone who knows very little about these topics. I should perhaps in this context point out to people new to this blog that even though I hardly consider myself an expert on these sorts of topics, I have nevertheless read quite a bit of stuff about those things in the past – books like this, this, this, this, this, this, this, this, this, this, this, this, this, this, and this one – so I was reading the book perhaps mainly from the vantage point of someone at least somewhat familiar both with many of the basic ideas and with a lot of the refinements of these ideas that people have added to the science of biology since Darwin’s time. One of the things my knowledge of modern biology and related topics had not prepared me for was how moronic some of the ideas of Darwin’s critics were at the time and how stupid some of the implicit alternatives were, and this is actually part of the fun of reading this book; there was a lot of stuff back then which even many of the people presumably held in high regard really had no clue about, and even outrageously idiotic ideas were seemingly taken quite seriously by people involved in the debate. I assume that biologists still to this day have to spend quite a bit of time and effort dealing with ignorant idiots (see also this), but back in Darwin’s day these people were presumably to a much greater extent taken seriously even among people in the scientific community, if indeed they were not themselves part of the scientific community.
Darwin was not right about everything and there’s a lot of stuff that modern biologists know which he had no idea about, so naturally some mistaken ideas made their way into Origin as well; for example the idea of the inheritance of acquired characteristics (Lamarckian inheritance) occasionally pops up and is implicitly defended in the book as a credible complement to natural selection, as also noted in Oliver Francis’ afterword to the book. On a general note it seems that Darwin did a better job convincing people about the importance of the concept of evolution than he did convincing people that the relevant mechanism behind evolution was natural selection; at least that’s what’s argued in wiki’s featured article on the history of evolutionary thought (to which I have linked before here on the blog).
Darwin emphasizes more than once in the book that evolution is a very slow process which takes a lot of time (for example: “I do believe that natural selection will always act very slowly, often only at long intervals of time, and generally on only a very few of the inhabitants of the same region at the same time”, p.123), and arguably this is also something about which he is part right/part wrong because the speed with which natural selection ‘makes itself felt’ depends upon a variety of factors, and it can be really quite fast in some contexts (see e.g. this and some of the topics covered in books like this one); though you can appreciate why he held the views he did on that topic.
A big problem confronted by Darwin was that he didn’t know how genes work, so in a sense the whole topic of the ‘mechanics of the whole thing’ – the ‘nuts and bolts’ – was more or less a black box to him (I have included a few quotes which indirectly relate to this problem in my coverage of the book below; as can be inferred from those quotes Darwin wasn’t completely clueless, but he might have benefited greatly from a chat with Gregor Mendel…) – in a way a really interesting thing about the book is how plausible the theory of natural selection is made out to be despite this blatantly obvious (at least to the modern reader) problem. Darwin was incidentally well aware there was a problem; just 6 pages into the first chapter of the book he observes frankly that: “The laws governing inheritance are quite unknown”. Some of the quotes below, e.g. on reciprocal crosses, illustrate that he was sort of scratching the surface, but in the book he never does more than that.
Below I have added some quotes from the book.
“Certainly no clear line of demarcation has as yet been drawn between species and sub-species […]; or, again, between sub-species and well-marked varieties, or between lesser varieties and individual differences. These differences blend into each other in an insensible series; and a series impresses the mind with the idea of an actual passage. […] I look at individual differences, though of small interest to the systematist, as of high importance […], as being the first step towards such slight varieties as are barely thought worth recording in works on natural history. And I look at varieties which are in any degree more distinct and permanent, as steps leading to more strongly marked and more permanent varieties; and at these latter, as leading to sub-species, and to species. […] I attribute the passage of a variety, from a state in which it differs very slightly from its parent to one in which it differs more, to the action of natural selection in accumulating […] differences of structure in certain definite directions. Hence I believe a well-marked variety may be justly called an incipient species […] I look at the term species as one arbitrarily given, for the sake of convenience, to a set of individuals closely resembling each other, and that it does not essentially differ from the term variety, which is given to less distinct and more fluctuating forms. The term variety, again, in comparison with mere individual differences, is also applied arbitrarily, and for mere convenience’ sake. […] the species of large genera present a strong analogy with varieties. And we can clearly understand these analogies, if species have once existed as varieties, and have thus originated: whereas, these analogies are utterly inexplicable if each species has been independently created.”
“Owing to [the] struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, in its infinitely complex relations to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring. The offspring, also, will thus have a better chance of surviving, for, of the many individuals of any species which are periodically born, but a small number can survive. I have called this principle, by which each slight variation, if useful, is preserved, by the term of Natural Selection, in order to mark its relation to man’s power of selection. We have seen that man by selection can certainly produce great results, and can adapt organic beings to his own uses, through the accumulation of slight but useful variations, given to him by the hand of Nature. But Natural Selection, as we shall hereafter see, is a power incessantly ready for action, and is as immeasurably superior to man’s feeble efforts, as the works of Nature are to those of Art. […] In looking at Nature, it is most necessary to keep the foregoing considerations always in mind – never to forget that every single organic being around us may be said to be striving to the utmost to increase in numbers; that each lives by a struggle at some period of its life; that heavy destruction inevitably falls either on the young or old, during each generation or at recurrent intervals. Lighten any check, mitigate the destruction ever so little, and the number of the species will almost instantaneously increase to any amount. The face of Nature may be compared to a yielding surface, with ten thousand sharp wedges packed close together and driven inwards by incessant blows, sometimes one wedge being struck, and then another with greater force. […] A corollary of the highest importance may be deduced from the foregoing remarks, namely, that the structure of every organic being is related, in the most essential yet often hidden manner, to that of all other organic beings, with which it comes into competition for food or residence, or from which it has to escape, or on which it preys.”
“Under nature, the slightest difference of structure or constitution may well turn the nicely-balanced scale in the struggle for life, and so be preserved. How fleeting are the wishes and efforts of man! how short his time! And consequently how poor will his products be, compared with those accumulated by nature during whole geological periods. […] It may be said that natural selection is daily and hourly scrutinising, throughout the world, every variation, even the slightest; rejecting that which is bad, preserving and adding up all that is good; silently and insensibly working, whenever and wherever opportunity offers, at the improvement of each organic being in relation to its organic and inorganic conditions of life. We see nothing of these slow changes in progress, until the hand of time has marked the long lapses of ages, and then so imperfect is our view into long past geological ages, that we only see that the forms of life are now different from what they formerly were.”
“I have collected so large a body of facts, showing, in accordance with the almost universal belief of breeders, that with animals and plants a cross between different varieties, or between individuals of the same variety but of another strain, gives vigour and fertility to the offspring; and on the other hand, that close interbreeding diminishes vigour and fertility; that these facts alone incline me to believe that it is a general law of nature (utterly ignorant though we be of the meaning of the law) that no organic being self-fertilises itself for an eternity of generations; but that a cross with another individual is occasionally perhaps at very long intervals — indispensable. […] in many organic beings, a cross between two individuals is an obvious necessity for each birth; in many others it occurs perhaps only at long intervals; but in none, as I suspect, can self-fertilisation go on for perpetuity.”
“as new species in the course of time are formed through natural selection, others will become rarer and rarer, and finally extinct. The forms which stand in closest competition with those undergoing modification and improvement, will naturally suffer most. […] Whatever the cause may be of each slight difference in the offspring from their parents – and a cause for each must exist – it is the steady accumulation, through natural selection, of such differences, when beneficial to the individual, which gives rise to all the more important modifications of structure, by which the innumerable beings on the face of this earth are enabled to struggle with each other, and the best adapted to survive.”
“Natural selection, as has just been remarked, leads to divergence of character and to much extinction of the less improved and intermediate forms of life. On these principles, I believe, the nature of the affinities of all organic beings may be explained. It is a truly wonderful fact – the wonder of which we are apt to overlook from familiarity – that all animals and all plants throughout all time and space should be related to each other in group subordinate to group, in the manner which we everywhere behold – namely, varieties of the same species most closely related together, species of the same genus less closely and unequally related together, forming sections and sub-genera, species of distinct genera much less closely related, and genera related in different degrees, forming sub-families, families, orders, sub-classes, and classes. The several subordinate groups in any class cannot be ranked in a single file, but seem rather to be clustered round points, and these round other points, and so on in almost endless cycles. On the view that each species has been independently created, I can see no explanation of this great fact in the classification of all organic beings; but, to the best of my judgment, it is explained through inheritance and the complex action of natural selection, entailing extinction and divergence of character […] The affinities of all the beings of the same class have sometimes been represented by a great tree. I believe this simile largely speaks the truth. The green and budding twigs may represent existing species; and those produced during each former year may represent the long succession of extinct species. At each period of growth all the growing twigs have tried to branch out on all sides, and to overtop and kill the surrounding twigs and branches, in the same manner as species and groups of species have tried to overmaster other species in the great battle for life. The limbs divided into great branches, and these into lesser and lesser branches, were themselves once, when the tree was small, budding twigs; and this connexion of the former and present buds by ramifying branches may well represent the classification of all extinct and living species in groups subordinate to groups. Of the many twigs which flourished when the tree was a mere bush, only two or three, now grown into great branches, yet survive and bear all the other branches; so with the species which lived during long-past geological periods, very few now have living and modified descendants. From the first growth of the tree, many a limb and branch has decayed and dropped off; and these lost branches of various sizes may represent those whole orders, families, and genera which have now no living representatives, and which are known to us only from having been found in a fossil state. As we here and there see a thin straggling branch springing from a fork low down in a tree, and which by some chance has been favoured and is still alive on its summit, so we occasionally see an animal like the Ornithorhynchus or Lepidosiren, which in some small degree connects by its affinities two large branches of life, and which has apparently been saved from fatal competition by having inhabited a protected station. As buds give rise by growth to fresh buds, and these, if vigorous, branch out and overtop on all sides many a feebler branch, so by generation I believe it has been with the great Tree of Life, which fills with its dead and broken branches the crust of the earth, and covers the surface with its ever branching and beautiful ramifications.”
“No one has been able to point out what kind, or what amount, of difference in any recognisable character is sufficient to prevent two species crossing. It can be shown that plants most widely different in habit and general appearance, and having strongly marked differences in every part of the flower, even in the pollen, in the fruit, and in the cotyledons, can be crossed. […] By a reciprocal cross between two species, I mean the case, for instance, of a stallion-horse being first crossed with a female-ass, and then a male-ass with a mare: these two species may then be said to have been reciprocally crossed. There is often the widest possible difference in the facility of making reciprocal crosses. Such cases are highly important, for they prove that the capacity in any two species to cross is often completely independent of their systematic affinity, or of any recognisable difference in their whole organisation. On the other hand, these cases clearly show that the capacity for crossing is connected with constitutional differences imperceptible by us, and confined to the reproductive system. […] fertility in the hybrid is independent of its external resemblance to either pure parent. […] The foregoing rules and facts […] appear to me clearly to indicate that the sterility both of first crosses and of hybrids is simply incidental or dependent on unknown differences, chiefly in the reproductive systems, of the species which are crossed. […] Laying aside the question of fertility and sterility, in all other respects there seems to be a general and close similarity in the offspring of crossed species, and of crossed varieties. If we look at species as having been specially created, and at varieties as having been produced by secondary laws, this similarity would be an astonishing fact. But it harmonizes perfectly with the view that there is no essential distinction between species and varieties. […] the facts briefly given in this chapter do not seem to me opposed to, but even rather to support the view, that there is no fundamental distinction between species and varieties.”
“Believing, from reasons before alluded to, that our continents have long remained in nearly the same relative position, though subjected to large, but partial oscillations of level, I am strongly inclined to…” (…’probably get some things wrong…’, US)
“In considering the distribution of organic beings over the face of the globe, the first great fact which strikes us is, that neither the similarity nor the dissimilarity of the inhabitants of various regions can be accounted for by their climatal and other physical conditions. Of late, almost every author who has studied the subject has come to this conclusion. […] A second great fact which strikes us in our general review is, that barriers of any kind, or obstacles to free migration, are related in a close and important manner to the differences between the productions of various regions. […] A third great fact, partly included in the foregoing statements, is the affinity of the productions of the same continent or sea, though the species themselves are distinct at different points and stations. It is a law of the widest generality, and every continent offers innumerable instances. Nevertheless the naturalist in travelling, for instance, from north to south never fails to be struck by the manner in which successive groups of beings, specifically distinct, yet clearly related, replace each other. […] We see in these facts some deep organic bond, prevailing throughout space and time, over the same areas of land and water, and independent of their physical conditions. The naturalist must feel little curiosity, who is not led to inquire what this bond is. This bond, on my theory, is simply inheritance […] The dissimilarity of the inhabitants of different regions may be attributed to modification through natural selection, and in a quite subordinate degree to the direct influence of different physical conditions. The degree of dissimilarity will depend on the migration of the more dominant forms of life from one region into another having been effected with more or less ease, at periods more or less remote; on the nature and number of the former immigrants; and on their action and reaction, in their mutual struggles for life; the relation of organism to organism being, as I have already often remarked, the most important of all relations. Thus the high importance of barriers comes into play by checking migration; as does time for the slow process of modification through natural selection. […] On this principle of inheritance with modification, we can understand how it is that sections of genera, whole genera, and even families are confined to the same areas, as is so commonly and notoriously the case.”
“the natural system is founded on descent with modification […] and […] all true classification is genealogical; […] community of descent is the hidden bond which naturalists have been unconsciously seeking, […] not some unknown plan or creation, or the enunciation of general propositions, and the mere putting together and separating objects more or less alike.”
This is a book full of quotes on the topic of mathematics. As is always the case for books full of quotations, most of the quotes in this book aren’t very good, but occasionally you come across a quote or two that enable you to justify reading on. I’ll likely include some of the good/interesting quotes in the book in future ‘quotes’ posts. Below I’ve added some sample quotes from the book. I’ve read roughly three-fifths of the book so far and I’m currently hovering around a two-star rating on goodreads.
“Since authors seldom, if ever, say what they mean, the following glossary is offered to neophytes in mathematical research to help them understand the language that surrounds the formulas …
ANALOGUE. This is an a. of: I have to have some excuse for publishing it.
APPLICATIONS. This is of interest in a.: I have to have some excuse for publishing it.
COMPLETE. The proof is now c.: I can’t finish it. […]
DIFFICULT. This problem is d.: I don’t know the answer. (Cf. Trivial)
GENERALITY. Without loss of g.: I have done an easy special case. […]
INTERESTING. X’s paper is I.: I don’t understand it.
KNOWN. This is a k. result but I reproduce the proof for convenience of the reader: My paper isn’t long enough. […]
NEW. This was proved by X but the following n. proof may present points of interest: I can’t understand X.
NOTATION. To simplify the n.: It is too much trouble to change now.
OBSERVED. It will be o. that: I hope you have not noticed that.
OBVIOUS. It is o.: I can’t prove it.
READER. The details may be left to the r.: I can’t do it. […]
STRAIGHTFORWARD. By a s. computation: I lost my notes.
TRIVIAL. This problem is t.: I know the answer (Cf. Difficult).
WELL-KNOWN. The result is w.: I can’t find the reference.” (Pétard, H. [Pondiczery, E.S.]).
Here are a few quotes similar to the ones above, provided by a different, unknown source:
“BRIEFLY: I’m running out of time, so I’ll just write and talk faster. […]
HE’S ONE OF THE GREAT LIVING MATHEMATICIANS: He’s written 5 papers and I’ve read 2 of them. […]
I’VE HEARD SO MUCH ABOUT YOU: Stalling a minute may give me time to recall who you are. […]
QUANTIFY: I can’t find anything wrong with your proof except that it won’t work if x is a moon of Jupiter (popular in applied math courses). […]
SKETCH OF A PROOF: I couldn’t verify all the details, so I’ll break it down into the parts I couldn’t prove.
YOUR TALK WAS VERY INTERESTING: I can’t think of anything to say about your talk.” (‘Unknown’)
“Mathematics is neither a description of nature nor an explanation of its operation; it is not concerned with physical motion or with the metaphysical generation of quantities. It is merely the symbolic logic of possible relations, and as such is concerned with neither approximate nor absolute truth, but only with hypothetical truth. That is, mathematics determines which conclusions will follow logically from given premises. The conjunction of mathematics and philosophy, or of mathematics and science is frequently of great service in suggesting new problems and points of view.” (Carl Boyer)
“It’s the nature of mathematics to pose more problems than it can solve.” (Ivars Peterson)
“the social scientist who lacks a mathematical mind and regards a mathematical formula as a magic recipe, rather than as the formulation of a supposition, does not hold forth much promise. A mathematical formula is never more than a precise statement. It must not be made into a Procrustean bed […] The chief merit of mathematization is that it compels us to become conscious of what we are assuming.” (Bertrand de Jouvenel)
“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” (Albert Einstein)
“[Mathematics] includes much that will neither hurt one who does not know it nor help one who does.” (J. B. Mencke)
“Pure mathematics consists entirely of asseverations to the extent that, if such and such a proposition is true of anything, then such and such another proposition is true of anything. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true … If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” (Bertrand Russell)
“Mathematical rigor is like clothing; in its style it ought to suit the occasion, and it diminishes comfort and restricts freedom of movement if it is either too loose or too tight.” (G. F. Simmons).
“at a great distance from its empirical source, or after much “abstract” inbreeding, a mathematical subject is in danger of degeneration. At the inception the style is usually classical; when it shows signs of becoming baroque, then the danger signal is up … In any event, whenever this stage is reached, the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas.” (John von Neumann)
I could theoretically write a lot of posts about this handbook, but I’m probably not going to do that. As I’ve mentioned before I own a physical copy of this book, and blogging physical books is a pain in the neck compared to blogging e-books – this is one of the main reasons why I’m only now starting to blog the book, despite having finished it some time ago.
The book is a 600+ pages long handbook (752 pages if you include glossary, index etc.), and it has 16 chapters on various topics. Though I’m far from sure, I’d estimate that I spent something like 50 hours on the book altogether so far – 3 hours per chapter on average – and that’s just for ‘reading the pages’, so to speak; if I do decide to blog this book in any amount of detail, the amount of time spent on the material in there will go up quite a bit.
So what’s the book about – what is ‘cognitive psychology’? Here are a few remarks on these topics from the preface and the first chapter:
“the leading contemporary approach to human cognition involves studying the brain as well as behaviour. We have used the term “cognitive psychology” in the title of this book to refer to this approach, which forms the basis for our coverage of human cognition. Note, however, that the term “cognitive neuroscience” is often used to describe this approach. […] Note that the distinction between cognitive psychology and cognitive neuroscience is often blurred – the term ‘cognitive psychology” can be used in a broader sense to include cognitive neuroscience. Indeed, it is in that broader sense that it is used in the title of this book.”
The first chapter – about ‘approaches to human cognition’ – is a bit dense, but I decided to talk a little about it anyway because it seemed like a good way to give you some idea about what the book is about and which sort of content you’ll encounter in it. In the chapter the authors outline four different approaches to human cognition and talk about each of these in a bit of detail. Experimental cognitive psychology is an approach which basically limits itself to behavioural evidence. What they term cognitive neuroscience is an approach using evidence from both behaviour and the brain (that can be accomplished by having people do stuff while their brain activity is being monitored). Cognitive neuropsychology is an approach where you try to use data from brain-damaged individuals to help understand how normal cognition works. The last approach, computational cognitive science, I recently dealt with in the Science of Reading handbook – this approach involves constructing computational models to understand/simulate specific aspects of human cognition. All four approaches are used throughout the book to obtain a greater understanding of the topics covered.
The introductory chapter also gives the reader some information about what the brain looks like and how it’s structured, adds some comments about distinctions between various forms of processing, such as bottom-up processing and top-down processing and serial processing and parallel processing, and adds information about common techniques used to study brain activity in neuroscience (single-unit recording, event-related potentials, positron emission tomography, fMRI, efMRI, magnetoencephalography, and transcranial magnetic stimulation). I don’t want to go too much into the specifics of all those topics here, but I should note that I was unaware of the existence of TMS (transcranial magnetic stimulation) research methodologies and that it sounds like an interesting approach; basically what people do when they use this approach is to use magnetic pulses to try to (briefly, for a short amount of time) disrupt the functioning of some area of the brain and then evaluate performance on cognitive tasks performed while the brain area in question is disrupted – if people perform more poorly on a given task when the brain area in question is disrupted by the magnetic field, it might indicate that the brain area is involved in that task. For various reasons it’s not unproblematic to interpret the results of TMS research and there are various limitations to the application of this method, but this is experimental manipulation of a kind I’d basically assumed did not exist in this field before I started out reading the book.
It’s noted in the first chapter that: “much research in cognitive psychology suffers from a relative lack of ecological validity […] and paradigm specificity (findings do not generalise from one paradigm to others). The same limitations apply to cognitive neuroscience since cognitive neuroscientists generally use tasks previously developed by cognitive psychologists. Indeed, the problem of ecological validity may be greater in cognitive neuroscience.” In the context of cognitive neuropsychology, there are also various problems which I’m reasonably sure I’ve talked about here before – for example brain damage is rarely conveniently localized to just one brain area the researcher happens to be interested in, and the use of compensatory strategies by individuals with brain damage may cause problems with interpretation. Small sample sizes and large patient heterogeneities within these samples also do not help. As for the last approach, computational cognitive science, the problems mentioned are probably mostly the ones you’d expect; the models developed are rarely used to make new predictions because they’re often too general to really make them at all easy to evaluate one way or the other (lots of free parameters you can fit however you like), and despite their complexity they tend to ignore a lot of presumably highly relevant details.
The above was an outline of some stuff covered in the first chapter. The book as mentioned has 16 chapters. ‘Part 1’ deals with visual perception and attention – there’s a lot of stuff about that kind of thing in the book, almost 200 pages – and includes chapters about ‘basic processes in visual perception’, ‘object and face recognition’, ‘perception, motion, and action’, and ‘attention and performance’. Part 2 deals with memory, including chapters about ‘learning, memory, and forgetting’, ‘long-term memory systems’ and ‘everyday memory’. That part I found interesting and I hope I’ll manage to find the time to cover some of that stuff here later on. Part 3 deals with language and includes chapters about ‘reading and speech perception’, ‘language comprehension’, and ‘language production’. I recall wondering a long time ago on this blog if people doing research on those kinds of topics distinguished between language production and language comprehension; it’s pretty obvious that they do.. Part 5 deals with ‘thinking and reasoning’ and includes chapters about ‘problem solving and expertise’, ‘judgment and decision making’, and ‘inductive and deductive reasoning’. Interestingly the first of these chapters talks quite a bit about chess, because chess expertise is one of the research areas people have looked at when looking at the topic of expertise. I may decide to talk about these things later on, but I’m not sure I’ll cover the stuff in part 5 in much detail because Gigerenzer (whose research the authors discuss in chapter 13) covers some related topics in his book Simply Rational, which I’m currently reading, and I frankly like his coverage better (I should perhaps clarify in light of the previous remarks that Gigerenzer does not cover chess, but rather talks about other topics also covered in that section – the coverage overlap relates to Gigerenzer’s work on heuristics). The last part of the book has a chapter on cognition and emotion and a chapter about consciousness.
As you read the chapters, the authors start out by outlining some key features/distinctions of interest. They talk about what the specific theory/hypothesis/etc. is about, then they talk about the research results, and then they give their own evaluation of the research and conclude the coverage with outlining some limitations of the available research. Multiple topics are covered this way – presentation, research, evaluation, limitations – in each chapter, and when multiple competing hypotheses/approaches have been presented the evaluations will highlight strengths and weaknesses of each approach. Along the way you’ll encounter boxes at the bottom of the pages with bolded ‘key terms’ and definitions of those terms, as well as figures and tables with research results and illustrations of brain areas involved; key terms are also bolded in the text, so even if you don’t completely destroy the book by painting all over the pages with highlighters of different colours the way I do, it should be reasonably easy to navigate the content on a second reading. Usually the research on a given topic will be divided into sections if multiple approaches have been used to elucidate problems of interest; so there’ll be one section dealing with cognitive neuropsychology research, and another section about the cognitive neuroscience results. All chapters end with a brief outline of key terms/models/approaches encountered in the chapter and some of the main results discussed. The book is well structured. Coverage is in my opinion a bit superficial, which is one of the main reasons why I only gave the book three stars, and the authors are not always as skeptical as I’d have liked them to be – I did not always agree with the conclusions they drew from the research they discussed in the chapters, and occasionally I think they miss alternative explanations or misinterpret what the data is telling us. Some of the theoretical approaches they discuss in the text I frankly considered (/next to) worthless and a waste of time. It’s been a while since I finished the book and of course I don’t recall details as well as I’d like, but from what I remember and what I’ve gathered from a brief skim again while writing the post it’s far from a terrible book and on a general note it covers some interesting stuff – we’ll see how much of it I’ll manage to talk about here on the blog in the time to come. Regardless of how much more time I’ll be able to devote to the book here on the blog, this post should at least have given you some idea about which topics are covered in the book and how they’re covered.
i. “If we keep an open mind, too much is likely to fall into it.” (Natalie Clifford Barney)
ii. “The advantage of love at first sight is that it delays a second sight.” (-ll-)
iii. “They used to call it the ‘Great War’. But I’ll be damned if I could tell you what was so ‘great’ about it. They also called it ‘the war to end all wars’…’cause they figured it was so big and awful that the world’d just have to come to its senses and make damn sure we never fought another one ever again.
That woulda been a helluva nice story.
But the truth’s got an ugly way of killin’ nice stories.” (Max Brooks)
iv. “Bromidic though it may sound, some questions don’t have answers, which is a terribly difficult lesson to learn.” (Katharine Graham)
v. “Cynicism is an unpleasant way of saying the truth.” (Lillian Hellman)
vi. “Lonely people, in talking to each other can make each other lonelier.” (-ll-)
vii. “When they [Hugh Walpole and Arnold Bennett] had gone, Plum [P. G. Wodehouse] and Guy [Guy Bolton] looked at each other with that glassy expression in their eyes which visiting literary men so often induce. They were feeling a little faint.
‘These authors!’ said Guy […Bolton, the author].
‘One really ought to meet them only in their books’, said Plum.” (quote from the book ‘Bring on the Girls’, written by Wodehouse and Bolton… The humour in this book is delightfully ‘meta’ at times. See also my review of the book here).
viii. “Illness must be considered to be as natural as health.” (William Saroyan)
ix. “An age is called Dark not because the light fails to shine, but because people refuse to see it.” (James Michener)
x. “I am terrified of restrictive religious doctrine, having learned from history that when men who adhere to any form of it are in control, common men like me are in peril.” (-ll-)
xi. “You can safely assume you’ve created God in your own image when it turns out that God hates all the same people you do.” (Anne Lamott)
xii. “People don’t ever seem to realise that doing what’s right’s no guarantee against misfortune.” (William McFee)
xiii. “If once a man indulges himself in murder, very soon he comes to think little of robbing; and from robbing he comes next to drinking and Sabbath-breaking, and from that to incivility and procrastination. Once begun upon this downward path, you never know where you are to stop. Many a man has dated his ruin from some murder or other that perhaps he thought little of at the time.” (Thomas De Quincey)
xiv. “In many walks of life, a conscience is a more expensive encumbrance than a wife or a carriage.” (-ll-)
xv. “A promise is binding in the inverse ratio of the numbers to whom it is made.” (-ll-)
xvi. “No safety without risk, and what you risk reveals what you value.” (Jeanette Winterson)
xvii. “When was the last time you looked at anything, solely, and concentratedly, and for its own sake? Ordinary life passes in a near blur. If we go to the theatre or the cinema, the images before us change constantly, and there is the distraction of language. Our loved ones are so well known to us that there is no need to look at them, and one of the gentle jokes of married life is that we do not.” (-ll-)
xviii. “Because we don’t know when we will die, we get to think of life as an inexhaustible well. Yet everything happens only a certain number of times, and a very small number really. How many more times will you remember a certain afternoon of your childhood, some afternoon that is so deeply a part of your being that you can’t even conceive of your life without it? Perhaps four or five times more, perhaps not even that. How many more times will you watch the full moon rise? Perhaps twenty. And yet it all seems limitless.” (Paul Bowles)
xix. “Praise out of season, or tactlessly bestowed, can freeze the heart as much as blame.” (Pearl S. Buck)
xx. “You cannot make yourself feel something you do not feel, but you can make yourself do right in spite of your feelings.” (-ll-).
This will be my last post about the book. Yesterday I finished reading Darwin’s Origin of Species, which was my 100th book this year (here’s the list), but I can’t face blogging that book at the moment so coverage of that one will have to wait a bit.
In my second post about this book I had originally planned to cover chapter 7 – ‘Analysing costs’ – but as I didn’t like to spend too much time on the post I ended up cutting it short. This omission of coverage in the last post means that some themes to be discussed below are closely related to stuff covered in the second post, whereas on the other hand most of the remaining material, more specifically the material from chapters 8, 9 and 10, deal with decision analytic modelling, a quite different topic; in other words the coverage will be slightly more fragmented and less structured than I’d have liked it to be, but there’s not really much to do about that (it doesn’t help in this respect that I decided to not cover chapter 8, but doing that as well was out of the question).
I’ll start with coverage of some of the things they talk about in chapter 7, which as mentioned deals with how to analyze costs in a cost-effectiveness analysis context. They observe in the chapter that health cost data are often skewed to the right, for several reasons (costs incurred by an individual cannot be negative; for many patients the costs may be zero; some study participants may require much more care than the rest, creating a long tail). One way to address skewness is to use the median instead of the mean as the variable of interest, but a problem with this approach is that the median will not be as useful to policy-makers as will be the mean; as the mean times the population of interest will give a good estimate of the total costs of an intervention, whereas the median is not a very useful variable in the context of arriving at an estimate of the total costs. Doing data transformations and analyzing transformed data is another way to deal with skewness, but their use in cost effectiveness analysis have been questioned for a variety of reasons discussed in the chapter (to give a couple of examples, data transformation methods perform badly if inappropriate transformations are used, and many transformations cannot be used if there are data points with zero costs in the data, which is very common). Of the non-parametric methods aimed at dealing with skewness they discuss a variety of tests which are rarely used, as well as the bootstrap, the latter being one approach which has gained widespread use. They observe in the context of the bootstrap that “it has increasingly been recognized that the conditions the bootstrap requires to produce reliable parameter estimates are not fundamentally different from the conditions required by parametric methods” and note in a later chapter (chapter 11) that: “it is not clear that boostrap results in the presence of severe skewness are likely to be any more or less valid than parametric results […] bootstrap and parametric methods both rely on sufficient sample sizes and are likely to be valid or invalid in similar circumstances. Instead, interest in the bootstrap has increasingly focused on its usefulness in dealing simultaneously with issues such as censoring, missing data, multiple statistics of interest such as costs and effects, and non-normality.” Going back to the coverage in chapter 7, in the context of skewness they also briefly touch upon the potential use of a GLM framework to address this problem.
Data is often missing in cost datasets. Some parts of their coverage of these topics was to me but a review of stuff already covered in Bartholomew. Data can be missing for different reasons and through different mechanisms; one distinction is among data missing completely at random (MCAR), missing at random (MAR) (“missing data are correlated in an observable way with the mechanism that generates the cost, i.e. after adjusting the data for observable differences between complete and missing cases, the cost for those with missing data is the same, except for random variation, as for those with complete data”), and not missing at random (NMAR); the last type is also called non-ignorably missing data, and if you have that sort of data the implication is that the costs of those in the observed and unobserved groups differ in unpredictable ways, and if you ignore the process that drives these differences you’ll probably end up with a biased estimator. Another way to distinguish between different types of missing data is to look at patterns within the dataset, where you have:
“*univariate missingness – a single variable in a dataset is causing a problem through missing values, while the remaining variables contain complete information
*unit non-response – no data are recorded for any of the variables for some patients
*monotone missing – caused, for example, by drop-out in panel or longitudinal studies, resulting in variables observed up to a certain time point or wave but not beyond that
*multivariate missing – also called item non-response or general missingness, where some but not all of the variables are missing for some of the subjects.”
The authors note that the most common types of missingness in cost information analyses are the latter two. They discuss some techniques for dealing with missing data, such as complete-case analysis, available-case analysis, and imputation, but I won’t go into the details here. In the last parts of the chapter they talk a little bit about censoring, which can be viewed as a specific type of missing data, and ways to deal with it. Censoring happens when follow-up information on some subjects is not available for the full duration of interest, which may be caused e.g. by attrition (people dropping out of the trial), or insufficient follow up (the final date of follow-up might be set before all patients reach the endpoint of interest, e.g. death). The two most common methods for dealing with censored cost data are the Kaplan-Meier sample average (-KMSA) estimator and the inverse probability weighting (-IPW) estimator, both of which are non-parametric interval methods. “Comparisons of the IPW and KMSA estimators have shown that they both perform well over different levels of censoring […], and both are considered reasonable approaches for dealing with censoring.” One difference between the two is that the KMSA, unlike the IPW, is not appropriate for dealing with censoring due to attrition unless the attrition is MCAR (and it almost never is), because the KM estimator, and by extension the KMSA estimator, assumes that censoring is independent of the event of interest.
The focus in chapter 8 is on decision tree models, and I decided to skip that chapter as most of it is known stuff which I felt no need to review here (do remember that I to a large extent use this blog as an extended memory, so I’m not only(/mainly?) writing this stuff for other people..). Chapter 9 deals with Markov models, and I’ll talk a little bit about those in the following.
“Markov models analyse uncertain processes over time. They are suited to decisions where the timing of events is important and when events may happen more than once, and therefore they are appropriate where the strategies being evaluated are of a sequential or repetitive nature. Whereas decision trees model uncertain events at chance nodes, Markov models differ in modelling uncertain events as transitions between health states. In particular, Markov models are suited to modelling long-term outcomes, where costs and effects are spread over a long period of time. Therefore Markov models are particularly suited to chronic diseases or situations where events are likely to recur over time […] Over the last decade there has been an increase in the use of Markov models for conducting economic evaluations in a health-care setting […]
A Markov model comprises a finite set of health states in which an individual can be found. The states are such that in any given time interval, the individual will be in only one health state. All individuals in a particular health state have identical characteristics. The number and nature of the states are governed by the decisions problem. […] Markov models are concerned with transitions during a series of cycles consisting of short time intervals. The model is run for several cycles, and patients move between states or remain in the same state between cycles […] Movements between states are defined by transition probabilities which can be time dependent or constant over time. All individuals within a given health state are assumed to be identical, and this leads to a limitation of Markov models in that the transition probabilities only depend on the current health state and not on past health states […the process is memoryless…] – this is known as the Markovian assumption”.
The note that in order to build and analyze a Markov model, you need to do the following: *define states and allowable transitions [for example from ‘non-dead’ to ‘dead’ is okay, but going the other way is, well… For a Markov process to end, you need at least one state that cannot be left after it has been reached, and those states are termed ‘absorbing states’], *specify initial conditions in terms of starting probabilities/initial distribution of patients, *specify transition probabilities, *specify a cycle length, *set a stopping rule, *determine rewards, *implement discounting if required, *analysis and evaluation of the model, and *exploration of uncertainties. They talk about each step in more detail in the book, but I won’t go too much into this.
Markov models may be governed by transitions that are either constant over time or time-dependent. In a Markov chain transition probabilities are constant over time, whereas in a Markov process transition probabilities vary over time (/from cycle to cycle). In a simple Markov model the baseline assumption is that transitions only occur once in each cycle and usually the transition is modelled as taking place either at the beginning or the end of cycles, but in reality transitions can take place at any point in time during the cycle. One way to deal with the problem of misidentification (people assumed to be in one health state throughout the cycle even though they’ve transfered to another health state during the cycle) is to use half-cycle corrections, in which an assumption is made that on average state transitions occur halfway through the cycle, instead of at the beginning or the end of a cycle. They note that: “the important principle with the half-cycle correction is not when the transitions occur, but when state membership (i.e. the proportion of the cohort in that state) is counted. The longer the cycle length, the more important it may be to use half-cycle corrections.” When state transitions are assumed to take place may influence factors such as cost discounting (if the cycle is long, it can be important to get the state transition timing reasonably right).
When time dependency is introduced into the model, there are in general two types of time dependencies that impact on transition probabilities in the models. One is time dependency depending on the number of cycles since the start of the model (this is e.g. dealing with how transition probabilities depend on factors like age), whereas the other, which is more difficult to implement, deals with state dependence (curiously they don’t use these two words, but I’ve worked with state dependence models before in labour economics and this is what we’re dealing with here); i.e. here the transition probability will depend upon how long you’ve been in a given state.
Below I mostly discuss stuff covered in chapter 10, however I also include a few observations from the final chapter, chapter 11 (on ‘Presenting cost-effectiveness results’). Chapter 10 deals with how to represent uncertainty in decision analytic models. This is an important topic because as noted later in the book, “The primary objective of economic evaluation should not be hypothesis testing, but rather the estimation of the central parameter of interest—the incremental cost-effectiveness ratio—along with appropriate representation of the uncertainty surrounding that estimate.” In chapter 10 a distinction is made between variability, heterogeneity, and uncertainty. Variability has also been termed first-order uncertainty or stochastic uncertainty, and pertains to variation observed when recording information on resource use or outcomes within a homogenous sample of individuals. Heterogeneity relates to differences between patients which can be explained, at least in part. They distinguish between two types of uncertainty, structural uncertainty – dealing with decisions and assumptions made about the structure of the model – and parameter uncertainty, which of course relates to the precision of the parameters estimated. After briefly talking about ways to deal with these, they talk about sensitivity analysis.
“Sensitivity analysis involves varying parameter estimates across a range and seeing how this impacts on he model’s results. […] The simplest form is a one-way analysis where each parameter estimate is varied independently and singly to observe the impact on the model results. […] One-way sensitivity analysis can give some insight into the factors influencing the results, and may provide a validity check to assess what happens when particular variables take extreme values. However, it is likely to grossly underestimate overall uncertainty, and ignores correlation between parameters.”
Multi-way sensitivity analysis is a more refined approach, in which more than one parameter estimate is varied – this is sometimes termed scenario analysis. A different approach is threshold analysis, where one attempts to identify the critical value of one or more variables so that the conclusion/decision changes. All of these approaches are deterministic approaches, and they are not without problems. “They fail to take account of the joint parameter uncertainty and correlation between parameters, and rather than providing the decision-maker with a useful indication of the likelihood of a result, they simply provide a range of results associated with varying one or more input estimates.” So of course an alternative has been developed, namely probabilistic sensitivity analysis (-PSA), which already in the mid-80es started to be used in health economic decision analyses.
“PSA permits the joint uncertainty across all the parameters in the model to be addressed at the same time. It involves sampling model parameter values from distributions imposed on variables in the model. […] The types of distribution imposed are dependent on the nature of the input parameters [but] decision analytic models for the purpose of economic evaluation tend to use homogenous types of input parameters, namely costs, life-years, QALYs, probabilities, and relative treatment effects, and consequently the number of distributions that are frequently used, such as the beta, gamma, and log-normal distributions, is relatively small. […] Uncertainty is then propagated through the model by randomly selecting values from these distributions for each model parameter using Monte Carlo simulation“.