Magnificent Principia
Pask demonstrates how the Principia sets out Newton's approach to science, how the framework of classic mechanics is established, how terrestrial phenomena like the tides and projectile motion are explained, and how we can understand the dynamics of the solar system and the paths of comets.
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5recommend
7mentions
5people
2016–2026years
100% recommend
Mentions per year
What Hacker News says
- This book is an interesting approach to The Principia:
Magnificent Principia (2013), by Colin Pask
https://devontrevarrowflaherty.com/2014/08/26/book-review-pr...
- I just finished reading this, and thoroughly enjoyed it. It provides a clear description of the fundamental intuition at the heart of calculus (chop stuff up infinitely, then put it back together again), and a mix of the historical background of its development and its ancient and modern applications.
All books of this nature are somewhat idiosyncratic – it's not a history, not a textbook, nor an applied maths book; it's a packet of passion sent by someone who's clearly excited and enthralled with his topic: "Here's a story about something really cool! Maybe you'll think it's cool too!"
I've been investigating recent books with different approaches to calculus (trying to build a free online course that empowers people in maths). Here are some other books I can recommend/mention:
[0] "Burn Math Class: And Reinvent Mathematics for Yourself" Goes from 1+1 all the way to derivatives and integrals. My favorite work of math demystification and pedagogy.
[1] "Calculus Reordered: A History of the Big Ideas" Released this year, exactly as the title says. An accessible history, explaining each idea as it enters the world stage. I've only just started this, but it's a definitely more historically thorough, albeit less engaging, book than Infinite Powers. (Since historical accuracy seems to be TFA's main focus, I wonder what they would think of this book.)
[2] "Change Is the Only Constant: The Wisdom of Calculus in a Madcap World" Another just-published book – this is the year for Calculus! Amazon has lost/delayed my preordered copy, but from the author's other work I expect this to be a LOT of fun.
[3] "Magnificent Principia: Exploring Isaac Newton's Masterpiece" Sort of "the annotated Newton". Outlines Sir Isaac's history, social environment, and development of the Principia Mathematica. The bulk of this book is going through each section of the Principia, translating the language into modern speech/formulations (where needed), and explaining what Newton was getting at. Also not as gripping as Infinite Powers, but a great way of reading and understanding one of the most foundational scientific/mathematical texts of all time.
[4] "Introductory Calculus For Infants" I'm about to have my first child, so am naturally collecting suitable reading material for the budding babe (suggestions welcome!).
[0] https://amzn.to/2pVXJwj [1] https://amzn.to/2pMCZr5 [2] https://amzn.to/31Ny32e [3] https://amzn.to/2BIimyM [4] https://amzn.to/33ZxbJj
- Warning: These books are kind of all over the place as far as technical prerequisites go, but they all satisify being heavier than pop-sci and lighter than a textbook. :)
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Aleksandrov et al - Mathematics: Its content, Methods, ad Meaning. Overview of undergrad curriculum by a number of prominent russian mathematicians.
Levi - The mathematical Mechanic. Uses various physical intuitions and scenarios to solve mathematical problems.
Pask - Magnificent Principia. Tour of newtons principia that includes both newtons geometric language and modern vector calculus version.
Stillwell - Elements of Mathematics. Discusses some important classical problems in the history of mathematics taken from 8 subjects: arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, logic. Wow!
Yandell - The Honors Class: Hilbert's problems and their solvers. Lots of mini biographies with some information describing each of Hilbert's famous problems.
Lawvere & Schanuel- Conceptual Mathematics. Some basic notions of category theory, geared towards teaching you Lawvere's clarification and generalization of the incompleteness theorems.
Cormen - Algorithms Unlocked. Pop Science version of some of the textbook.
Nahin - Inside interesting Integrals. Lots of fun integrations!
Nahin - He also wrote some books about euler and imaginary numbers which ive partially read, they seemed good.
Pierce - An introduction to information theory; symbols signals and noise. sounds and looks like a dover textbook but is a non-fake pop science book.
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Boyer - The History of Calculus and its Conceptual Development. A bit old, and spends too much time on formalism in the 18th and 19th century, there might be something better out now.
Weyl - Philosophy of Mathematics and Natural Science.
Reichenbach - The philosophy of Space and time.
Klein - Elementary mathematics from the advanced viewpoint. these were written at the beginning of the 20th century so are slightly outdated, but kline was extremely forward-looking in his point of view.
Courant & Robbins - What is Mathemaics. Another classic.
Hilbert & Cohn-Vossen - Geometry and the Imagination. The gold standard of popular mathematics writing. A beautiful book.
- Ofer Gal - Baroque Science. A highly academic history of the scientific revolution, not the most readable book. It focused quite a bit on mathematization, especially in optics (and Kepler's optics revolution in particular), and also in observation via instrumentation like telescopes and microscopes.
Paul Nahin - The Logician and the Engineer. About Boole and Shannon's work; I had already learned the material so i skimmed part of it and returned it to the library.
Ian Mortimer - The time traveler's guide to medieval england. Talks about what daily life was like for different social classes in 14th century England eg towns & cities, food, clothes, housing, employment, travel etc. I got about halfway through and lost interest in the subject matter.
Lucio Russo - The forgotten Revolution. A very readable academic history of the development of science in ptolomaic egypt (eg euclid, archimedes, etc). This was certainly the most surprising book I read all year. This time period has been almost completely deleted from history, which jumps straight from aristotle to the renaissance (with a quick stop in the islamic world if you're being spoiled), and their achievements were incredibly impressive!
Jim al-Khalili - The House of Wisdom. A pop-history book about arabic science that i got from the library. I was wary because it's written by a particle physicist and not a historian, and sure enough it is filled with so much nonsense that I through it down in disgust after a few chapters.
Colin Pask - Magnificent Principia. A brief tour of some of the highlights of Newton's Principia, using both newton's geometric diagrams and modern notation. Following the modern notation of course assumes some basic calculus. Highly recommended - it made me want to learn old fashioned celestial mechanics! Perhaps in 2019...
Randall Munroe - What if. A fun light read about whimsical scenarios.
Sigmund - Exact thinking in demented times. About the vienna circle, the philosophical group associated with logical positivism.
Newman [ed] - The world of mathematics vol 1. A varied Collection of mathematical writings, both contemporary and historical.
Richard J Evans - The Coming of the Third Reich. Evans has recently written a three volume treatment of the third Reich. this is of course the first and starts with the origins of the modern form of antisemitism in the late 19th century. I hope to read the next two in 2019!
Robert Harper - Practical foundations for programming languages. I've mostly just skimmed it so my understanding is quite superficial, maybe in a year or two I'll go through and do all the exercises. I liked that he avoided 'paradigms' and developed the subject more systematically. The book's table of contents is absolutely irresistible!
Tolkien - the Hobbit. I finally got around to reading it... I didn't care for it. I started the lord of the rings but i don't think i'm going to finish it.
Michael Chriton - Jurassic Park. The movie was better.
Agatha Christie - Murder on the Orient Express. I think i just don't like fiction. The few years before this I tried reading more fancy literature and i didn't like that, so this year I tried more popular literature... Recently i heard someone say they thought that history spoiled fiction for them. I think I've suffered the same problem.
Findlay & O'Rourke - Power and Plenty. (in progress) An economic history of the 2nd millennium, absolutely fascinating so far. The discussion of the black death was particularly memorable. It's become something of a meme to point out how the peasant survivors were economically better off than their parents and grandparents. In fact that effect was limited to western europe. In eastern europe the economics were different and feudalism deepened, and in the arab world the reaction was different still: (if i remember my reading correctly) it was certain sects of military men who came out on top. I'm bringing it up because it is a perfect reminder that reality is more complicated than memes.
Robert Harper - Programming in Standard ML. (in progress) Online notes about functional programming.
- A few more good pop physics books:
Maxwell - Matter and motion. Written by THE Maxwell, what more do you need to know? long out of copy-write and available on the web for free
Born - The restless universe. discusses atomic theory and describes some of the more down to earth parts of quantum theory, especially how the theory explains quantitative properties of atoms and the periodic table.
Einstein & Infeld - The evolution of physics. pseudo-Historical exposition taking us from the mechanical universe to fields to quanta, and from Galilean relativity to Einstein relativity.
Reichenbach - the philosophy of space and time. technically philosophy of science, not pop science, from the logical positivist school of the Vienna circle. very readable discussion of abstract mathematical geometry and various relativity principles, if you don't mind skipping some of the more bloviating bits.
Pask - Magnificent Principia. Fantastic overview of Newton's Magnum Opus, although it doesn't give enough historical context to what newton was building on. Assumes some knowledge of calculus.
- If you are interested in reading Newton's Principia, check out the guide Magnificent Principia: Exploring Isaac Newton's Masterpiece :
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