A History of Mathematics

Back when I was working on the Leibniz project, I realized that I could do with a better grasp of the history of mathematics.  Deleuze was making all sorts of references to the development of the calculus that I mostly followed, but only more or less.  So, after a bit of research, I settled on this Boyer and Merzbach tome.  It definitely did help me better understand the way that the calculus was originally oriented around infinite series; this has mostly been lost in how it is taught today (well, at least how it was taught 30 years ago).  But I actually found that the most interesting part of the book was the first 300 pages leading up to the calculus.  It was fascinating to read about things like Mesopotamian sexagesimal fractions and the incredible work of Apollonius on the conics.  While it's a cliche, it really does give one a renewed appreciation of how far ahead of their time the Greeks were.  Unfortunately, even though I read it slowly and in small doses, I find it hard to recommend the book as a whole.  While I began reading pretty closely and working out some of the problems myself, by the final 150 pages or so I was mostly just skimming.  Once they go past Euler and Gauss you pretty much need a complete undergraduate education in pure math to follow much of the story. 

Breath

I find that I'm usually not quite the intended audience for most popular science writing, so I can end up sounding overly critical of books I have actually enjoyed.  The genre frequently leaves me as frustrated by its incompleteness and lack of depth as it does intrigued by the research it covers.  While James Nestor's bestseller is no exception to this pattern, I would still recommend the book.  I haven't seen anyone else cover, even superficially, this many aspects of breathing in one place.  The topic is simply so interesting that it shines despite the breezy, introductory, should-be-read-at-1.5X quality to the writing. 

Nestor begins with a discussion of the evolutionary changes in human head and neck structure caused by our adaptation to cooked food.  These seem to have made breathing inherently more problematic for us than for any other mammal.  In modern times, we've compounded these problems by adopting softer diets that exercise our jaws less, as well as by living in that state of chronic low grade tension otherwise known as "civilization".  All of these changes make it more difficult to breathe effectively through our noses and to take full, deep breaths.  And this is apparently very bad for us.  

Nestor goes on to explain some of the reasons for why this is bad, and some of the ways we can combat it.  But he's more interested in striking anecdotes about rogue research than in consensus science, so most of these come off as pretty sketchy and not always coherent.  For example, he sometimes tells us that what we really want to do is learn to tolerate higher levels of carbon dioxide in the blood by extending our exhale and breathing much more slowly than we often do.  At other points he encourages us to breathe much harder, almost to the point hyperventilation, in the style popularized by Wim Hof.  Then again, maybe we should use yogic breathing techniques like alternate nostril breathing and etc ...  To sort out which of these partially contradictory ideas actually has any scientific support would require an extended tour through Nestor's bibliography (a very nice resource to have online).  While that might be an interesting project, I imagine the correct conclusion is likely predictably underwhelming: it depends.  The 'best' breathing techniques are wildly likely to depend on how you are and what you want to accomplish.  And this is of course precisely why these techniques are hard to study scientifically.  Which means that Nestor's book is ultimately most useful as a survey of possible ways to breath that we can experiment with personally.  So I'm excited to go through his instructional videos and see what happens.

The Structure of Scientific Revolutions

I've had Kuhn's classic on the shelf since college, but somehow never gotten around to reading the whole thing.  Which in a way is too bad, since it could have saved me a lot of time -- Kuhn articulates more or less the same beef I've had with science for many years now, but in much clearer and more concise form.  The book is a classic for very good reasons.

Kuhn's basic thesis is so well known that it's hardly worth spending much time repeating it.  Science does not progress towards truth through successive falsification, as if asymptotically approaching some limit.  Instead, it progresses through revolutionary shifts between completely incompatible paradigms, shifts which are catalyzed from within by the way each round of "normal", or paradigmatic, science extends and develops the paradigm it unquestioningly takes to be the true model of reality.  In short, Kuhn takes science to be an evolutionary process where new scientific theories arise like new species that simply out-compete the old ones, rather than somehow disproving them.  This process tends to produce theories of increasing complexity, scope, and accuracy that can legitimately be seen as 'progress' in some sense.  But as with Neo-Darwinian evolution, this isn't progress towards some one true final species. 

While I was already familiar with, and largely agreed with, this thesis, reading the original version of it was still rewarding for several reasons.  First, because you can clearly hear Kuhn's tone, which is in marked contrast to many of the people who popularized his idea.  As he points out in the postscript, Kuhn does not consider himself a relativist.  On the contrary, he began life as a physicist and thinks of his historical and philosophical project as being more, not less, 'scientific' and empirical about how science actually works.  At no point does he suggest anything close to the idea that scientists can just make up whatever theory they like, that all theories are equally good, or that the sole factor in the acceptance of a paradigm is simple social consensus.  He is even a firm believer in the 'progress' of science.  However, as the quotes suggest, since Kuhn rethinks the very structure of science, his theory changes what we mean by the terms science and progress.  He wants us to see that since science isn't the successively closer approximation of truth we took it to be, it doesn't progress the way our textbooks teach us.  And while he cannot, by hypothesis, argue that this is a truer view of the scientific enterprise, he does a fine job of putting forward all kinds of perfectly empirical and theoretical reasons to convince us we should adopt this view of science.  So while he he takes seriously the observation that all the science we know of is practiced by a certain species of hairless chimp, he does not intend to suggest that science is merely a social construct.  We should recognize the reductionist relativist position for what it is historically -- a weaponization of Kuhn by struggling humanities departments.

Second, I was delighted to discover the extended use he made of the gestalt switch model for perception.  Scientific revolutions take us from seeing the duck to seeing the rabbit.  After a phase shift, the same data crystalizes in a new way.  Today, we could make the same point even more effectively by discussing Predictive Processing and the Bayesian Brain framework.  Kuhn actually already moves in this direction by repeatedly arguing that scientists are not simply interpreting neutral facts and assembling a theory from a sea of bottom up data, but are using their prior training to directly perceive the entities their theory posits from the top down as real.  Scientific revolutions are the sudden shifts in scientific perception triggered when experimental errors and theoretical anomalies reach a critical threshold that causes us to adopt a new set of priors, a new paradigm.  I think part of what made Kuhn's book controversial was the way this inverts the flow of information in our usual model of perception; it's hard to convince most folks that they are actively constructing and inferring their world (and self) when it feels like these things are simply given to them.  Of course, if you've already drunk the kool-aid, this controversial analogy is part of what makes the book brilliant.

Nexus

I breezed through a copy of Ramez Naam's techno-thriller at the suggestion of a local bookstore hooligan.  They claimed it was such a gripping and fast paced read that I would surely want to move right on to the other two books in the series.  Since I agree completely with the first part of this assessment, it's somewhat surprising that the second half breaks down; while I thoroughly enjoyed Nexus, I have no plans read Crux or Apex.  The trouble is that Naam writes good but quite generic sci-fi, and seems above all to be auditioning a script for the next Bourne franchise film -- his creative motto is apparently, "always be blowing up".  But while it was certainly a quick and engrossing read, there's something inherently unsatisfying about a story that takes all kinds of themes I'm interested in -- drugs, meditation, AI, neuroscience, geopolitics -- and mashes them together in the least surprising and interesting ways.  

The main plot device is solid idea.  Imagine if you could take a programmable psychedelic, as in, a drug that actually consisted of chips that stayed in your brain and could be used to send signals in and out of it.  Theoretically, this would let you change your perception in more fine grained and functional ways that simply flooding your system with serotonin.  It would also provide a sort of weigh station between normal human experience and the experience of that great staple of modern sci-fi -- the fully digital being.  Naturally, once we became able to program individual brains like this, we would surely want to start networking these analog-digital hybrids.  Which then makes each hybrid computer a potential hacking target, and etc ... You can imagine where it goes from here.  This is a fine premise that affords connection to a bunch of interesting questions, each of which is represented by Naam's well-drawn if slightly predictable and cardboard characters.  The trouble is that Naam is so prisoner to his screenplay that he doesn't have time to delve too far into any of these from an intellectual perspective.  The reader apparently cannot be counted on to wait more than about 10 pages between either tense near misses or gory combat scenes.  Eventually, this makes the plot feel kinda predictable and paint-by-number, and gives it that Hollywood sheen that leaves every movie looking like every other.  Will the good guys win in the end?  I'll admit that I'm kinda curious what happens.  I guess I'll just watch the Netflix series to find out.  But that too will take material suited for a 90 min film and, using suitably timed explosions and faux-epic grandeur, scatter it over 600 minutes of television.  And sometimes, you should just write a single novel, not a trilogy.