The `structural equations' are what I would call systems of equations, which would be nothing out-of-the-way in modeling with differential equations. This is an explanation of how to set up and use such systems when you are beginning with statistics, specifically, linear relationships with error terms. There are lists and cookbook examples of how to map out relations and equations and get from there, eventually, to testable hypotheses about your actual system.
It's not written in the mathematical style, that is, it isn't deductive; it builds up from examples and rules-of-best-practice instead, with standards of how to draw the flowcharts that make them a notation for how you're thinking about the system (curved vs straight lines, for instance. There's a whiff of the drafting template in this, updated to drag-and-drop software).I think it's longer than a deductive exposition would need to be, but on the other hand the examples are useful for a different case of mind.
Nonlinear relationships are dealt with, but not very thickly; there are separate works on nonlinear structural equations.
Find in a Library: Structural Equation Modeling and Natural Systems
I have wondered, in some environmental or geomorphic courses, whether the drive to quantify wasn't slightly misplaced; whether it would be possible, and more reliable if less precise, to merely rank qualities without trying to rank them on a metric line. In this sense 'metric' doesn't mean 'meters, centimeters...', but any system in which there are distances that you can add up, and divide in half, etc., as one can meters or feet. There are plenty of systems, called generally 'topology', that describe complicated things/worlds that aren't metric; in which you can say that two things are near but not how near they are. (I gave up on the book Small Pieces Loosely Joined after way, way too much falling-about astonishment that the common users' Internet has more of a topology than a metric, without any sign that we were going to be introduced to the idea of a topology -- or graph, any name will do -- and the many things known about them.)
Then I had the mild shadow of a realization that if you have orders, you might have partial orders; for instance, you and your parents and your grandparents are in 'parent-child' orders with each other, but your maternal and paternal grandparents almost certainly can't be so ordered; none of them are parent or child to the other three. If you go back far enough, your tree of descent certainly does cross itself, though; very possibly with 'legs' of different numbers of generations; even this commonplace example doesn't nail down descriptions right away. Also, mm, ecosystems, they have both spatial and developmental nesting, partially ordered sets (posets) might arise very naturally.
So they do, and here are some examples. The book starts with an even lovelier natural source; you can't rank molecules into a single order of development, but there are obvious ways to put them into directed graphs with partial orders. If A is a sub-molecule of B and C, perhaps because B and C have different side-chains, that's the beginning of an order; and this happens rather a lot with organic molecules, since organisms would naturally rather not build everything from scratch. There might be a molecule D that has the side-chains of both B and C; or that might be impossible; so the 'family tree' of molecule A has a range of possible shapes.
There are metrics on some traits of molecules, e.g. their boiling-points, and there are some mappings from posets to metrics. (Much of this book is thinking about toxicology, for which it's handy to be able to guess from molecular data what the organism or system effects might be.)
A later chapter (,,) is describing biodiversity by posets> They start by pointing out that political contention 'need's a single ordering, and the bulk of the chapter is describing habitat diversity in a part of Pennsylvania. Handy, if you're trying to set policy for watershed protection.
I'm dubious that political matters naturally need a single ordering, though. Market contention surely does -- in fact, would like to translate everything into the single metric of price or price-of-tort. This seems to me to be one of the things we need political systems to avoid; we have alternate rankings, of things you cannot alienate, things you can give away but not sell or buy, things you can sell or buy only if some other characteristic is in play. In a partially-ordered mindset, you need not say that one of the characteristics is more protected than another, even if both are protected with regard to a third. It's hard to live up to this in reality, when we have limited resources and generally end up trying to minimize harm (for which we do need to rank the harms).
For that matter, the political process leads us to try and rank goods; the Democratic primary just concluded was rrrrather an example of that; every political platform with realistic goals must be. Somewhere along here we must hit Arrow's Impossibility Theorem; I am being very lazy about this post, because I am mostly trying to get a lingering urge to procrastinate off my desk, but does the AIT arise from a poset-ness in social goods?
Find in a Library: Partial Order in Environmental Sciences and Chemistry
'A Whirligig Tour of the Beautiful Basics of Science'
This seemed like a useful (maintain background generalist knowledge) but un-stressful (at a nonscientists' level) evening's book; it probably was useful, and it was eventually enjoyable, but very odd to read. Angier makes a point of not writing in the dry, cagey, impersonal pitch of Real Science. I follow that far easily. But the whirligig, bubbly style she does use kept me off my balance; I had to cautiously interpret each non-literal statement to see if it was meaningful for the science, inaccurate with respect to the science; most of it was neutral decoration on the content, playing with the sound of sound words. I don't think she ever misleads a reader, not one who doesn't believe in the Doctrine of Signatures anyway. People who can handle the dry style are well-enough served by pop science publishing as it is. So this ought to be a useful and enjoyable book for some people now ill-served.
A sample sentence: "Like bones, structural proteins give the cell its shape and integrity, and like bone tissue they are not at all inert, are in fact so feisty and eager to flaunt their powers that one might think they belonged to the metaphoric skeletons that one tries to keep in one's closet."
The cover art on the paperback has the effect on me that I think the prose has on its intended audience; I don't need to interpret every step, I just like looking at it. The artist, Marian Bantjes, has a lovely website, including startling amounts of what I can't help but see as Pee-Chee doodles, immanent with talent; and other techniques, more or less formal. I particularly liked Sugar.
Find in a Library: The Canon, ISBN-13 978-0-547-05346-2
Now my subject, but the narrative is really not my style. Personalizing the isotopes makes it harder for me to remember how their differentiation works, because when they are described with anything like velleity it confuses my picture of the completely un-willed processes that fractionate isotopes. All of this book is anthropomorphized, and the characters who are people to start with get extra cute nicknames; it is the opposite of credentialist, which is good, but I found it distracting.
My mental frame bent out of true when, for instance, thinking of isotope fractionation through cell stomata. The plant cells do have something like velleity, do expend energy to act on a biological need for more or less H2O or CO2, but nothing actually cares which isotope comes in; it happens, reliably, but un-willed.
On the other hand, for the many people who don't remember anything outside a story with intent, such a metaphor is probably useful. The glee Fry exhibits in describing the ecosystem problems untangled by isotope studies ought to pull people in. The equations one needs are there, carefully boxed and explained; and the examples are broken down into very simple comprehensible parts, which I am grateful for.
Find in a Library:Stable Isotope Ecology
Here's a sampler of soil knowledge; the chapters stand pretty well alone but build well if read in order. The subjects are 'fun stuff', oddities of natural history, but Wolfe points out the many practical things provided us by soil creatures: antibiotics, bioremediation, plant health... the one that surprised me was prarie dogs as pasture-maintainers.
Prairie dogs keep the plants near their cities pruned to just below prairie-dog standing height. I guess they like to be able to either stand up and look out, or drop down and scurry in secret. They don't, because of this, eat anything down to the roots. As many a lawn-caretaker knows, regular trimming of grass will often make it grow more densely. Better yet, mowing a bit higher, say, prairie-dog height, encourages many plants to grow and none to take over: it's one of the main things you need to do to maintain a flowering meadow. So prairie dog habitat often has denser and more diverse cover than the same land without its dogs; their cropping encourages clover, and discourages shrubs and prickly pear. Without the prairie dogs, bad-fodder shrubs and pear tend to take over and outcompete the grass, making the land less useful to grazing animals. There is, I gather, some reason to believe that prairie with prairie dogs would support more grazing animals than prairie without. (Consider, of course, the thundering herds before western colonization.)
Alas, the U.S. has been actively subsidizing the poisoning of prairie dogs since the early 19th c., and we don't have a lot left.
Find in a Library
Evolutionary Theory: Mathematical and Conceptual Foundations, by , tries to not use any more math than is needed. This only holds off the PDEs until the case of multiple alleles at one locus, p. 24.
Theoretical Ecosystem Ecology: Understanding Element Cycles, and , is PDE-free all the way to a concept of substrate quality, page 37. Those aren't bad, actually; the persnickety equations are often just ODEs.
Theoretical... compares its results to quite a lot of empiric data, considering that it's a short book on mathematics. Also, there's some odd, odd Nordic poetry (in translation) and some worked exercises; very useful, and I must get back to it after this quarter's class in PDEs.
Somewhere else asserts nitrogen:food-energy:water::carbon:fossil-fuel-energy:air. In the soil, it's more like potential and ?metabolic? energy, but they're still wonderfully linked.
ISBN: 0521580226 (Theoretical...)
LCCN: QH 344 A35 1996 (Theoretical...)
ISBN: 0878937021 (Evolutionary...)
LCCN: QH 366.2 R523 2004 (Evolutionary...)
Subtitle: enlightenment culture and the inhuman
Nice work on a nasty subject, the conflation of pity, power, reason, and science with cruelty in the Enlightenment. It doesn't just remind one that science, medicine especially, developed with cruelty, but makes an argument that the delight in cruelty was more of the scientific impulse than one would like to think. I only skimmed it, as (one) I really ought to be working on a dozen other things, and (two) it draws lots of its evidence from Hogarth and . I accordingly noticed mostly the surgery & sex parts, which jump out because of the illustrations. I didn't do any justice to the arguments from the Scottish Enlightenment, which had most of the claims for kindness and sympathy as natural states; from , among others.
I did notice, among a dozen more things I want to read, a reference to a novel Melmoth the Wanderer by one , which has a shipwreck in it; I want to read that and look for 's Maturin's slightly creepy scientific detachment.
Slightly later in the day, again distracted from those dozen things, I was drawn into Love at Goon Park; also about slightly creepy scientific detachment with results that were probably a boon to human suffering. Goon Park is the nickname of the psych lab where Harry Harlow did the paradigm-shattering experiments with wire-mother monkeys, and many follow-up experiments; all showing with great clarity that affection, even a pale simulacrum of affection, is as necessary for primate development as food.
The first experiment showed that baby macaques preferred a terry-cloth 'mother' to an equally warm wireframe 'mother', even if the latter had the milk. Follow-ons demonstrated that affection and socialization are needed for monkey development. This overturned a congeries of accepted theories, among them that babies had no particular attachment to their parents except as a source of food, that maternal affection led to needy stupidity, etc etc. The three amazing things in the summary of the experiments and the theories they overthrew are, first, that anyone could have had such cruel beliefs about humans or monkeys; second, that monkeys at least can develop well-enough given the least, barest, pathetic simulacrum of care - terrycloth is almost enough by itself; third and most relevant to Cruel Delight, that anyone who had the insight to start these experiments could be cruel enough to do them. Some of it was good old clinical detachment, some the knowledge that only controlled experiments would convince experts to stop prescribing cruelty in real life, and some was probably related to his own deep and repeated unhappiness. How would that heart weigh against a feather?
ISBN: 0253343674 (Cruel Delight)
ISBN: 0738202789 (Love at Goon Park)
Jones has kept the order of the argument in The Origin of Species but updated all the interior chapter matter with current biological and geological examples. He even keeps 's descriptive sub-chapter headings and chapter summaries. It's about right for an ambitious hammock read, and suggests Further Reading (both books and papers) at the end.
P. 226:
Lungfish are living fossils: animals with an agile and creative past the nowadays have sunk into conservatism. Long ago, they slowed down, and they have stayed unchanged for hundreds of millions of years, while their relatives moved on.
Bone contains many cells, all with a nucleus. The hard material squeezes each one so that its size is a measure of how much DNA it once contained. Early in lungfish history, the size of the cell nuclei—and the amount of genetic material—began to creep up. Soon, the animals had hundreds of times as much as did their relatives. As it did, evolution slowed. Now, the lungfish are stuffed with DNA (most of it with no apparent function) and their evolution has stalled altogether. The fit between DNA content, a lethargic lifestyle and evolutionary sloth is widespread. To copy that chemical takes energy. Bacteria are speedy and have no excess genetic material, while salamanders, torpid as they are, are filled with DNA. Plants, too, have a close fit between habit and nucleic acid content. All weeds have small genomes, while more established plants are packed with DNA and can take a month to make a single egg cell. Whether an indolent life allows the amount of genetic material to build up, or whether the extra dose itself slows down evolution, nobody knows.
Spam is very expensive.
Or, if you want to haul around some lengthy archaic information yourself, you could have the Project Gutenberg edition of On The Origin Of Species By Means Of Natural Selection. Whether it will delay your reproduction by even a month, I wouldn't say.
ISBN: 0375501037
Experiments to do at home with plexiglass. No math.