Books, part I
A selection of stuff I read in the last two years
I started this blog around the time when it became clear that I would get a permanent position back in Milan. That was a major change in my life, and it allowed me to broaden my horizons by exploring topics for which I previously had no time, caught up as I was in the publish-or-perish dynamic. One of the first things I did was to start reading books, mostly classics and mostly non-fiction. Here is a list of books I read, with my impressions on each one.
A caveat: while I read some of these cover to cover, others were subjected to a “philosophical reading” where I basically ended up picking and choosing what to read in detail after skimming over the book. Some I left unfinished. The list is not in chronological order, nor in any order for that matter.
The book of Why, Judea Pearl & Dana Mackenzie: this is basically Causality lite, plus a great deal of historical anecdotes. Pearl proudly admits to being a Whig historian: causality, and causality’s laws lay hid in night. God said, Let Pearl be! and all was light. I guess that’s ok because when he discovered causality it stayed discovered, unlike Wright, Haavelmo, Burks, and the other precursors he covers. At any rate, great book if you want to understand why causality matters before getting more technical. It also reveals a lot about Pearl’s philosophy, which in my opinion is at least as bad as his science is good. Here is an excerpt from page 232 (in my edition):
Indeed, the approach I took was very much inspired by the ancient Greeks (including Hipparchus) and their invention of a formal logical system for geometry. At the center of the Greeks’ logic we find a set of axioms or self-evident truths, such as “Between any two points one can draw one and only one line”. With the help of those axioms, the Greeks could construct complex statements, called theorems, whose truth is far from evident.
the idea of axioms as self-evident truths makes me uncomfortable for reasons I discussed elsewhere, and is probably one of the reasons underlying Pearl’s tendency to stray into metaphysics. Compare this with Eddington’s ideas on the subject from about a century ago, in the entry below on his booklet Space, Time and Gravitation. Ironically, in the next page, Pearl’s example of an axiom in use is
For example, drawing a line parallel to one edge of a triangle is licensed by Euclid’s fifth axiom, that it is possible to draw one and only one parallel to a given line from a point outside that line.
which is awkward because this axiom is the poster child of not being self-evidently true: just ask Sacchieri. In fact, substituting the fifth with a different axiom gives rise to non-Euclidean geometries, which are equally valid systems.
Advice for a young investigator, Ramon y Cajal: part advice intended for the late 19th century equivalent of a postdoc, part philosophical speculation. Somewhat patronizing, but I guess it is meant to be. It was cited in Objectivity (which I will cover in the second part of this post) and is very thin, so I ended up reading it all. Cajal is certainly an interesting personality, and one of the two non-literature Nobel prizes ever awarded to a spaniard. His work on the histology of neurons straddles the thin line between art and science, since it includes elements of drawing and visualization as a crucial tool to make sense of complex physical systems, a recurring theme in this blog.
In the introduction he has a quote by Herbert Spencer stating that every cause produces more than one effect. It’s amazing how casually people say stuff like this, given its potential implications. Structural causal models (see chapter 3 here) express each random variable as a function of its parents and an additional random variable called an exogenous noise. Exogenous noises that enter the formula for each variable in the structural causal model must be all statistically independent on each other and they must have only one effect, the variable in question. If taken literally, Spencer’s dictum would make this impossible, making all variables endogenous: this would force us to include every variable that ever existed in the wide world as part of our structural causal model, essentially making causal modeling impossible.
This excursus aside, I found the opening remarks in chapter four very topical given that my research currently focuses on applying machine learning to astronomical data:
The discovery of a fact or the significance of a biological phenomenon usually rests on the application of principles derived from physics or chemistry. As Laplace has pointed out, to discover is to bring together two ideas that were previously unlinked. And it is important to note that this fruitful association typically occurs between data from one of the complex sciences (biology, sociology, chemistry and so on) and a principle culled from a general science.
Life, art, and mysticism, LEJ Breuwer: find out for yourself about this one. It’s only 40 pages. Don’t expect to learn too much about math in general or intuitionism in particular. Makes for a fun read though.
Space, time, and gravitation, Sir Arthur Eddington. Here Eddington, who led one of the expeditions during the 1919 solar eclipse that famously tested relativistic light deflection, teaches us general relativity. Let me just quote from the prologue:
WHAT IS GEOMETRY?
A conversation between—
An experimental Physicist.
A pure Mathematician.
A Relativist, who advocates the newer conceptions of time and space
in physics.
Rel. There is a well-known proposition of Euclid which states that “Any
two sides of a triangle are together greater than the third side.” Can either
of you tell me whether nowadays there is good reason to believe that this
proposition is true?
Math. For my part, I am quite unable to say whether the proposition is
true or not. I can deduce it by trustworthy reasoning from certain other
propositions or axioms, which are supposed to be still more elementary. If
these axioms are true, the proposition is true; if the axioms are not true,
the proposition is not true universally. Whether the axioms are true or
not I cannot say, and it is outside my province to consider.
Phys. But is it not claimed that the truth of these axioms is self-evident?
Math. They are by no means self-evident to me; and I think the claim
has been generally abandoned.
Phys. Yet since on these axioms you have been able to found a logical
and self-consistent system of geometry, is not this indirect evidence that
they are true?
Math. No. Euclid’s geometry is not the only self-consistent system of
geometry. By choosing a different set of axioms I can, for example, arrive
at Lobatchewsky’s geometry, in which many of the propositions of Euclid
are not in general true. From my point of view there is nothing to choose
between these different geometries.
Rel. How is it then that Euclid’s geometry is so much the most impor-
tant system?
Math. I am scarcely prepared to admit that it is the most important.
But for reasons which I do not profess to understand, my friend the Physi-
cist is more interested in Euclidean geometry than in any other, and is
continually setting us problems in it. Consequently we have tended to
give an undue share of attention to the Euclidean system. There have,
however, been great geometers like Riemann who have done something to
restore a proper perspective.
Rel. (to Physicist). Why are you specially interested in Euclidean
geometry? Do you believe it to be the true geometry?
Phys. Yes. Our experimental work proves it true.
Rel. How, for example, do you prove that any two sides of a triangle
are together greater than the third side?
Phys. I can, of course, only prove it by taking a very large number of
typical cases, and I am limited by the inevitable inaccuracies of exper-
iment. My proofs are not so general or so perfect as those of the pure
mathematician. But it is a recognised principle in physical science that it
is permissible to generalise from a reasonably wide range of experiment;
and this kind of proof satisfies me.
Rel. It will satisfy me also. I need only trouble you with a special case.
Here is a triangle ABC; how will you prove that AB + BC is greater
than AC?
Phys. I shall take a scale and measure the three sides.
Rel. But we seem to be talking about different things. I was speaking
of a proposition of geometry—properties of space, not of matter. Your
experimental proof only shows how a material scale behaves when you
turn it into different positions.
Phys. I might arrange to make the measures with an optical device.
Rel. That is worse and worse. Now you are speaking of properties of
light.
Phys. I really cannot tell you anything about it, if you will not let
me make measurements of any kind. Measurement is my only means of
finding out about nature. I am not a metaphysicist.
Rel. Let us then agree that by length and distance you always mean
a quantity arrived at by measurements with material or optical appli-
ances. You have studied experimentally the laws obeyed by these mea-
sured lengths, and have found the geometry to which they conform. We
will call this geometry “Natural Geometry”; and it evidently has much
greater importance for you than any other of the systems which the brain
of the mathematician has invented. But we must remember that its sub-
ject matter involves the behaviour of material scales—the properties of
matter. Its laws are just as much laws of physics as, for example, the laws
of electromagnetism.
Phys. Do you mean to compare space to a kind of magnetic field? I
scarcely understand.
Rel. You say that you cannot explore the world without some kind of
apparatus. If you explore with a scale, you find out the natural geometry;
if you explore with a magnetic needle, you find out the magnetic field.
What we may call the field of extension, or space-field, is just as much
a physical quality as the magnetic field. You can think of them both
existing together in the aether, if you like. The laws of both must be
determined by experiment. Of course, certain approximate laws of the
space-field (Euclidean geometry) have been familiar to us from childhood;
but we must get rid of the idea that there is anything inevitable about
these laws, and that it would be impossible to find in other parts of the
universe space-fields where these laws do not apply. As to how far space
really resembles a magnetic field, I do not wish to dogmatise; my point is
that they present themselves to experimental investigation in very much
the same way.
Let us proceed to examine the laws of natural geometry. I have a tape-
measure, and here is the triangle. AB = 39 1/2 in., BC=18 in., CA= 39 7/8 in.
Why, your proposition does not hold!
Phys. You know very well what is wrong. You gave the tape-measure a
big stretch when you measured AB.
Rel. Why shouldn’t I?
Phys. Of course, a length must be measured with a rigid scale.
Rel. That is an important addition to our definition of length. But
what is a rigid scale?
Books from times of fundamental crisis stand out for their sharp sense of how deeply epistemological issues permeate everyday scientific practice. Sadly, we have drifted far from that, as the Book of Why entry above illustrates.
Screenshots from StoryBots, a TV series aimed at children. Reproduced under fair use. The rubber sheet analogy gives the viewer the illusion of understanding a theoretical concept, mass and the curvature of spacetime (not just space!), while explaining exactly none of the gravitational phenomena that children can directly observe in everyday life like the motion of falling bodies, pendulums, or tides. Physics, Aristotles: I picked this one up (in English translation) at the Kinokuniya bookstore at the Galeria Mall in Abu Dhabi. We originally went there to buy books for our kids while waiting for dinner at the local Din Tai Fung, which ended up being very tasty. This is the book where the doctrine of the four causes is explained, so it is obviously interesting for me, but rather than try to squeeze it in here I will try to discuss it all in a dedicated blog post in the near future.
Leibniz-Clarke correspondence, Gottfried W. Leibniz & Samuel Clarke (and very likely Isaac Newton behind the scenes). Contemporary interest in this text is almost entirely driven by the debate about the nature of space and relative versus absolute motion, especially in the aftermath of Relativity. I discussed some of this (also in the light of the new science of causation) in previous posts. Interestingly, the correspondence focuses on theological issues as much as (if not more than) on physics. What does it mean exactly that space is the sensorium of God?
The Formation of the Scientific Mind, Gaston Bachelard: probably the second most famous book by Bachelard after The Poetics of Space (see below). The main idea here is that, on several topics, the scientific consensus of the past differs from the consensus now. Under the work hypothesis that some sort of objective reality exists and that the consensus view is closer to it now than in the past (remember Whig history from above?) then why did the scientists of the past form and hold false beliefs? Once we rule out differences in instruments and practices by focusing on phenomena that are stable and simple to observe, what is left is the subjectivity of the individual scientist and, most importantly, of the surrounding society. This subjective part of (purportedly) objective knowledge can be psychoanalyzed with a machinery that Bachelard takes mostly from Jung. He finds and names unconscious patterns of thought and feeling that drive errors in scientific exploration. These correspond basically to psychological complexes of the collective scientific self. He names them epistemological obstacles. Unfortunately these can be recognized only ex post facto and even then only under the shaky assumption that current scientific knowledge is always more advanced than that of the past. Perhaps the most important implication of this work is that scientific progress is not conceived of as cumulative, but rather as a series of sudden breaks, all of this well before Thomas Kuhn.
The Psychoanalysis of Fire, Gaston Bachelard. This and the (much later) books on the other elements -Water and Dreams, Air and Dreams, Earth and Reveries of Will, Earth and Reveries of Repose, are the other side of the coin with respect to The Formation of the Scientific Mind. They basically cover speculation about the origin and the content of the complexes surrounding each classical element, exemplified by long excerpts from a number of books -mostly classics or from French literature- rather than their impact on scientific progress. You may find it boring. If you were to consider space as an element following ancient Indian philosophy (and to the dismay of Leibniz) you could probably count The Poetics of Space among the works by Bachelard in this line.
The seashell is a prototypical intimate space, a folded and protected space-within-space. Chapter 6 of The Poetics of Space is devoted to seashells. Credits H. Zell, wikimedia commons.
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Remaks on Colour, On Certainty, Philosophical Investigations, and others by Ludwig Wittgenstein: you can easily imagine a piece of perfectly transparent green glass, but can you imagine a perfectly transparent piece of white glass? If not, why not? What about neon brown? The smoothness of language makes the folk physics of color it captures look consistent, but is it?
The Tacit Dimension, Michael Polanyi: two previous blog posts touch on themes from this book: Causality from Outside, and Euclid Kills the Ego. Overall a great ratio of ideas to ink for a book, at just 128 pages. Highly recommended.
The Perception of Causality, Albert Michotte: the book presents experimental evidence that people perceive causality directly, among other accounts of various perceptual effects and phenomena. The implications of this are detailed in Do we Really Need an Operational Definition of Causality?
The concept of number in the child and L’épistémologie génétique, Jean Piaget: among other takeaways, one of the most interesting points is that models of the world (including the notion of a subject-object divide) are learned through action rather than passive observation. Note that foundation models in deep learning develop a useful model of the data they are fed with by training to perform tasks. To go back to the overarching theme of causality, the notion of an intervention that underpins causal reasoning must ultimately hinge on an arbitrary distinction between an inside and an outside (or system/background) which is not found in the equations of physics. Pearl is aware of this, as shown on his Fig. 37 here, reproduced below. He says as much in Causality:
If you wish to include the entire universe in the model, causality disappears because interventions disappear – the manipulator and the manipulated lose their distinction. However, scientists rarely consider the entirety of the universe as an object of investigation. In most cases the scientist carves a piece from the universe and proclaims that piece in namely, the focus of investigation. The rest of the universe is then considered out or background and is summarized by what we call boundary conditions.
Superforecasting, Philip Tetlock: this one is the winner in the category books that should have been a blog post. It would have been a good blog post at that, but still. Tetlock is telling the story of his work with superforecasters, basically normal (more on that later) people who happen to be really good at making predictions about the future, stuff like “will inflation in Argentina decrease in 2026 with respect to its value in 2025?”. It turns out that some of these people are consistently good over time, so they were not just lucky. Aggregating their predictions in the right way can outperform predictions by intelligence agencies that have access to classified information, or so Tetlock claims. This book is important because it gave rise to the whole prediction market mania that I covered previously, even though his favorite method of aggregation is not based on a market mechanism. At any rate, Tetlock tries to explain why these people are so good at making predictions. For some reason he wants to downplay the fact that quite a few of them are either mathematicians (including a former quant) or otherwise hard scientists (if I remember correctly there was at least one meteorologist and one biologist in the sample) or retired programmers. At least it turns out that some of their strategies can be replicated by us mere mortals: Fermi-estimate a base rate and perform Bayesian updating starting from there, while fighting scope insensitivity and other cognitive biases. Tetlock is Canadian.
Segmenti e bastoncini (Segments and Sticks, not sure if it was ever translated), Lucio Russo: now partly obsolete, but still interesting. Here Russo criticizes then recent tendencies in teaching, especially in high school teaching of science and math. He argues that as Italian society (and western society in general) is shifting its economic and cultural emphasis from production to consumption -an effect of the then new phenomenon of globalization- teaching is also changing, creating a school for consumers rather than producers of knowledge. As rigorous theorem proving is abandoned, advanced results (e.g. from quantum mechanics or cosmology) are increasingly presented in a flashy but dumbed-down form to students who do not have the tools to receive them critically and are forced to accept them on authority. Thus they become ‘fossilized notions’ much like the notion that the Earth was spherical in the Middle Ages: perhaps true, but useless to the point that cartography became entirely empirical. He suggests that it would be better to teach more elementary topics, such as Euclidean geometry, while insisting on the complete mastery of the art of proving theorems, rather than talking about black holes and wavefunctions as if they were mythical entities (see the StoryBots screenshot above for an example).
On China, Henry Kissinger: this book is about the history of China as seen from the perspective of a prominent personality who shaped US foreign policy. I read about one third through it, and then the book somehow decided not to follow me and my family on the trip back from Canada. It is left behind in Montréal somewhere (maybe it came from the Brossard library in the first place?). The most interesting takeaway for me is that even throughout the century of humiliation, the Chinese elites mostly saw themselves as superior to the barbarians who were progressively taking over their country, and even tried to play them against each other to keep them in check. Perhaps this sentiment will resonate with Italian readers (and maybe Persian ones as well?) given the historical similarities with China.
The Three Body Problem, Liu Cixin: I read books one and two in the trilogy. This is a work of science fiction and apparently the first book of this genre written in China to garner international success. Humanity is being threatened by technologically superior aliens, who despite all their advanced gear have a level of strategical thinking comparable to that of a five year old. The only way to keep them in check is to play them against other aliens through skillful diplomacy. Reminds me of something above…
Why Nations Fail: The Origins of Power, Prosperity and Poverty, Daron Acemoglu & James A. Robinson: one more book that chose not to board the plane with us. I read halfway through it. Very ideological (liberalism good!) and not particularly enlightening in my opinion. The authors argue that the eventual success of a society boils down to the quality of its institutions, which can be inclusive or extractive. Inclusive institutions have mechanisms that allow innovators and other economically dynamic members of society to improve their social standing, eventually joining the ranks of the elite and thus tolerate innovation. Extractive institutions instead lack such mechanisms, and are forced to suppress innovation lest it risk destabilizing them. Having this hammer in their hands, the authors proceed to apply it to every nail, from both colonial and indigenous societies in the Americas (some of which left a scant historical record) to the rise and fall of Venice. Funny how the institutions of the Most Serene Republic ceased to be inclusive right when Atlantic trade started replacing trade in the Mediterranean. The real problem stays unsolved: why did certain places end up developing inclusive institutions and other places failed to?
The Death and Life of Great American Cities, Jane Jacobs: Stunning book, 10/10 would recommend. Some of it sounds obvious, now, and even more so to a person who lives in a medium-size southern European city. Mixed-use neighborhoods are good because they are self-policing since there are people around at all times. Have wide sidewalks, lots of small interesting public spaces rather than a few huge stretches of manicured lawn that serve no actual purpose. Population density has a sweet spot at some non-trivial value: too many people per square meter and you get a concrete jungle, too few and you get American suburbs. Just right and you get Padua, I guess. Too easy for me to agree with this. On the other hand if it were so easy, why no urban planner before Jacobs came up with this?
Cities and the Wealth of Nations: Principles of Economic Life, Jane Jacobs: Regional economics iz best economics. Seriously, she argues that trying to understand economic trends at the national level is a doomed exercise, cities and their city regions are where it’s at. I can totally get behind that if it means that all the prestige usually associated with macroeconomics, international economics, etc… would transfer over to economic geographers and the like.
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