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book reviews
Light non-fiction booksreviewed by T. Nelson |
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book reviews
Light non-fiction booksreviewed by T. Nelson |
Reviewed by T. Nelson
If you want to understand anything in modern physics, you have to know about Lagrangians. But what is a Lagrangian, and what does it do?
A Lagrangian is nothing more than the difference between kinetic energy and potential energy (L = T − V). From that simple description of how something changes, you can predict the behavior of almost anything that changes in some way. This book spells it out in detail. There are no skipped steps here and no “it is obvious that”s, but it's not a For Dummies text either. Just a matter-of-fact explanation of what they do and how to use them.
The Lagrangian is usually printed as an upper-case
in Brush or mathcal script.
The main advantage of Lagrangians over Newtonian mechanics is that you no longer need the concept of forces. Instead, as Hirvonen explains, everything is described by energy. This means no more worries about curved coordinate systems or non-inertial accelerating frames. There are no more “fictitious” forces to define and no problems with non-conservative forces like friction. And unlike Newtonian mechanics, Lagrangians can be used to derive conservation laws.
The math is quite easy to follow if you've had calculus and partial differential equations. Hirvonen even explains variational calculus and functionals. Although the formulas sometimes give you a simple numerical answer, often they can only be solved numerically. The real goal in physics, he says, is not to solve the equations, but to find them and gain understanding. After reading this book, you'll be so good at this you'll be creating Euler-Lagrange equations in your sleep.
The main drawback is that the examples showing exactly how to do that are too simple. For example, the see-saw problem of where to place weights on a beam to balance it against gravity is something you can calculate in your head. People would feel embarrassed if they had to define a Lagrangian and derive partial differential equations to solve it, but the author shows it definitely can be done.
This book is from the Profound Physics website, which has many free instructional articles about physics topics as well as some inexpensive courses.
jan 30 2025
Moved to here
What Ross Douthat does in this nicely written book is to take arguments made by atheists and science popularizers, try to shoot them down, and propose Christianity in their place. Needless to say, that's not going to convince too many people, and it's probably not intended to. The book is really just a pep talk to explain why a religious person would believe.
For instance, in Chapter 1 he invokes the “fine-tuning” argument. If we believe the universe has orderly rules, he says, we must believe God must have created it. In Chapter 2 he argues that human consciousness is special because science can't explain it. In Chapter 3 he argues that too many people have had near-death experiences, so they must be real. Those are the three main reasons Douthat says should motivate people to “believe.”
From where I stand as a skeptic, nothing in any book or newspaper, least of all the New York Times, is intrinsically credible. Even in the scientific literature there is precious little that is both meaningful, useful, and true. Douthat takes to task those people who pretend to know all the answers—and perhaps the science pages in the NYT are full of jackasses who claim science has proved the universe sprung out of nothingness and that consciousness is but an illusion—and then shoots down the idea that they have the answer, and puts God in the empty space:
The long arc of science . . . bends back by confirming humanity's unique position in a universe strangely suited to both our bodies and our minds. [p.63]
I could take that bait and try to debunk his arguments, but there'd be no point. Most people aren't really sneering at religion as he thinks. And maybe not everyone at the NYT fits his stereotype of the arrogant prick that he thinks atheists must be. It's not sneering to point out that our standard of proof differs from that in antiquity. The standard proof now is to explain how you know. Just claiming your best bud got resurrected doesn't work anymore. Science doesn't have answers to everything, but religion doesn't have answers to any of them, including the questions Douthat criticizes science for not knowing: in its creation story, the answer is just ‘a miracle occurred.’ There's nothing at all about the mystery of consciousness. There's a boatload of wisdom, which is the province of religion; the history stories may be true or they may be morality tales, but to criticize science for not knowing answers to questions religion can't even ask is disingenuous.
For instance, Leviticus 11:16 and 11:17 say we're not supposed to eat owls. Why? What does he have against owls? Are they toxic? My guess it's because owls eat mice and rats, but the Bible doesn't say.
How did the universe get started? No scientifically literate person would write off the possibility of a deity. If some evidence came along we'd accept it. But unlike Pascal, my wager is that many of these questions will turn out like the other questions people used to agonize over, like whether we have free will or what is life: either the question is meaningless, or the answer is unimaginably complicated, or both.
I agree with Douthat on one point: there are mysteries in the universe. Maybe none of us exists at all: we're just pixels somehow, and after the Great BSOD we get mercilessly shredded to end up in somebody's electric heater. Or maybe the laws of physics are sentient and the laws of civilized behavior don't really come from God but are principles that must be obeyed lest your civilization court a grisly death of internecine civil war.
Religion is a valuable cultural tradition. If you want to be comforted or if you need a reason to behave morally, religion is a good place to turn. But if it's answers to the mysteries of the universe you want, no religion, not even my favorite, Cthulhucism, comes close to science.
mar 28 2025