Books overdue because I’ve been busy, but worth noting anyway because they’re worth noting.
- I got one: Sinclair Lewis Arrowsmith
One of the best earliest realist examinations of the motivations and lifestyle of American academic engineers (including in that fold “doctors”, as they should be, now and in the 1900s), Midwesternism (aka “Babbittism”), and the differences between our stated cultural expectations and the implicit ones we generate by the blind decisions we take in our lives. - To Reference: Clayton M. Christensen The Innovator’s Dilemma
Corporations—and by extension institutions of other types, like “medicine” and “the Academy”—obtain the well-deserved reputation as logy, stilted piles of dead wood because of their success, not despite it. Christensen’s observation, cunningly masked as common sense, seems to be that large institutions cannot pursue innovations because their adaptive moves are slower and more expensive for them than for smaller, new institutions. In other words: the bigger (and more successful) they are, the more likely to be replaced without even noticing. - Meh: Jack E. Graver Counting on Frameworks: Mathematics to Aid the Design of Rigid Structures (Dolciani Mathematical Expositions)
One of many mathematical “recreations” books I’ve been thumbing lately, as we gear up to build a genetic programming innovation engine that will be able to make “mathematical discoveries”. Graver’s monograph focuses on flexibility/rigidity of two- and three-dimensional frameworks (statics, essentially) and the discrete math and neat little theorems that connect (get it? a pun!) graph theory, linear algebra and engineering design principles. One would want it to be a bit more “popularized”, but it’s of interest as a landmark for the future, at least. - To Buy: Ross Honsberger More Mathematical Morsels (Dolciani Mathematical Expositions)
This is more along the lines of what I was looking for: a few dozen very interesting, solvable problems that cross the line from “brain teaser” to “advanced homework”. Don’t get me wrong—I’m not sitting here with a graph pad and a pencil trying to do makework and proofs; I’m using these books to research the way we specify (and mis-specify) complex problems. Mostly plane geometry, number theory and a bit of (simple) probability theory, the Morsels series seems to be problems culled from those Math Olympiads I was never smart enough for, and various amateur math journals. Will buy because there are very few proofs; mathematically rigorous proofs are, to shine some clarifying light on my long-standing opinion, overwhelmingly a waste of the time of both the prover and his reader, since they are merely the algorithmic disguising of initial assumptions by wrapping them in hackneyed ritualized maneuvers that decrease one’s crucial ability to question the original crap you started from. - To Buy: Victor Klee and Stan Wagon Old and New Unsolved Problems in Plane Geometry and Number Theory (Dolciani Mathematical Expositions)
As with the previous, a nice pile of small, simply-stated problems, with the added fillip (for me, who Cf. above is interested in building computational affordances in support of project management for abstract problem-solving projects) that they’re mostly unsolved. Well, OK, they were; we have Fermat in here, and some others that will be familiar to folks who follow this kind of stuff. But there is plenty of grist in the mill here for me and my ilk, along the lines of, “How would you specify the goals and constraints of a problem like, ‘Are the digits of the decimal expansion of π devoid of any pattern?’” I like that. That’s what real work is about, since it begs so many other questions about who’s asking, what they really want to know, and why. - To Buy: Ross Honsberger Mathematical Chestnuts from around the World (Dolciani Mathematical Expositions)
Like the other Honsberger books (all AFAIK from the Dolciani Mathematical Expositions series), full of interesting and useful levers to use when learning evolutionary computing and metaheuristics more generally. “The product of a billion positive integers is a billion. What is the greatest sum these billion numbers might have?” might be something you’d throw a search algorithm at, except then you’re answering more along the lines of “…What’s the largest sum you can find?” And that’s not the question. It’s my hope that by thinking about these problems as they’re stated, technical souls who by brainwashed in their homework and worklives to think of specific examples as something to solve in a one-off way might be pushed to thinking of how one can search for methods. In other words: Parametric models are the crutch of a weak mind. - To Buy: Louis L. Bucciarelli Engineering Philosophy
Too short, too little, almost too late, but very very nice. A lovely quick monograph that would serve as an introduction to several problems we’ve been wrestling with lately at “work” (What’s “work”? You’ll see, soon enough…): “Designing, like language, is a social process”, “What engineers don’t know and why they believe it”, and perhaps the most interesting and best jumping-off point for a real monograph of its own: “Learning Engineering.” Don’t get me started on the actual engineering students (and professors, and practitioners) I know, who on the whole tend to think about their own work and what it implies very poorly. Not least because they believe they are concerned only with “the real world”. See? You got me started. - To Borrow: Arthur T. Benjamin and Jennifer J. Quinn Proofs that Really Count: The Art of Combinatorial Proof (Dolciani Mathematical Expositions)
As I said before, proofs are not my cup of tea right now. But the mental processes that allow people to specify and design proofs are. So this, being a work about the design patterns of combinatorial proofs that deal with “what is the most…?”, “how quickly does…?” and “how many are…?” kind of questions is in fact more interesting than I first expected. The book starts, as do the other Dolciani books I’ve been browsing, with problems, but does go into a number of interesting work-them-through details that for me might be a shopping list of things to watch out for as we try to explain what evolved problem-solvers are actually doing. For the moment I don’t want a how-to, I want a what-was-that? book, and this might come in useful someday soon in that capacity. - Meh: Arthur T. Benjamin and Ezra Brown, eds Biscuits of Number Theory (Dolciani Mathematical Expositions)
Mostly proofs, presented via a wide-ranging set of reprinted short papers. - To Buy: Ross Honsberger Mathematical Delights (Dolciani Mathematical Expositions)
Another Honsberger collection of quick plane geometry, number theory and lightweight combinatorics. One cutely meta one explores the “shared properties of crank solutions to Fermat’s last theorem”. - To Buy: Ross Honsberger Mathematical Gems III (Dolciani Mathematical Expositions, No.9)
As above, with a nice section on cryptography and number theory that would open up a lovely pile of problems for genetic programming to be used on. - To Admire: Stewart Coffin Geometric Puzzle Design
You know those little wooden polyhedra things, where there are a bunch of sticks that interlock, and your goal is to slide and twist and poof they all fall apart, then your real goal of putting them all back together starts? So this is about how to make those, and more interestingly the design patterns you see: sliding blocks, coordinated motion, misleading similarities, ways of using and abusing symmetries, all the empty space (or complicated mechanism) hidden away on the inside. Very cool. - To Buy: Ross Honsberger Mathematical Diamonds (Dolciani Mathematical Expositions)
Yeah, well, you get the picture by now: nice. Why are these books so hard to find? Why aren’t they in more libraries? - To Reference: Michael O’Neill and Conor Ryan Grammatical Evolution: Evolutionary Automatic Programming in an Arbitrary Language (Genetic Programming)
I know Conor from years back (Jesus, I’m old: back when he was doing this work, for example), and Grammatical Evolution (GE) actually features in a small way in the project I’ve been working on for more than a year. So while I personally don’t need to own this, it was a worthwhile read and if you’re interested in a different way (not stupid old S-expression GP) for evolutionary methods to be used to evolve complex structures like algorithms, proofs, classifiers, trading agents, or whatever, you should consider this book a good intro… if a wee bit outdated. Because, you know, life moves on, and a lot of the stuff this particular book has in it is old hat. In any case, more people ought to know about Grammatical Evolution; it’d do them good to understand there’s more that one way to solve the problem.And if you’re a computer kind of person interested in GE: Go have a look at Pavel Suchmann’s GERET system. I like it. Nice, clean code.
- To Admire: Conor Ryan Automatic Re-engineering of Software Using Genetic Programming (GENETIC PROGRAMMING Volume 2)
I said I knew Conor since way back; he was working on this thesis when I was working on mine at Penn. (Spoiler: he got his degree, unlike me.) Thank you, Conor, for both the size and utility of the chapter entitled “Practical Considerations”: a landmark notion in GP, now and then. - To Buy: Anthony Brabazon and Michael O’Neill Biologically Inspired Algorithms for Financial Modelling (Natural Computing Series)
Everybody who ever learned about metaheuristics (even before they earned that st00pid name) said, “Hey! This would be a great way to play the stock market!” A long time ago, Barbara and I were at a computational finance conference, watching the academics talk, and after a couple of days I observed, “You only ever hear these people talk once: either their work is dumb, and we stop inviting them, or their work is smart, and they stop accepting our invitations.” Brabazon and O’Neill have done something dramatically unexpected: written clearly and succinctly about how to build working trading and financial management systems. Throw all your other Springer books on Amazon; this one, if you’re interested in this stuff, is the real deal. Also: more Grammatical Evolution. Now you get the trend? - Meh: Dan Kalman Uncommon Mathematical Excursions: Polynomia and Related Realms (Dolciani Mathematical Expositions)
Somehow not quite the same stuff as Honsberger’s. I think my reaction is not because the subject matter is different (though it is, being concerned mostly with roots and structure of polynomial equations and stuff), but rather that it’s kind of pedagogically heavy-handed. Like a graduate seminar text or something. Not for beginners, not for amateurs even, in my opinion: more of a focused, progressive advanced training session.
