Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

Friday, October 04, 2019

1. Science and Math Books

I can't imagine I will complete this idea, but as I am in the process of moving, my books are largely in boxes. Wouldn't it be interesting to catalog all my books? Well, it would be for me. I'll add to the list as I find them. I've put my favorites in bold.

Math
  • Calculus 6e, by James Stewart (this is the book I've been using to make YouTube videos on calculus for several years now)
  • Dr. Euler's Fabulous Formula by Paul Nahin
  • e: the Story of a Number by Eli Maor
  • Linear Algebra, by Richard Penney
  • No Bullshit Guide to Linear Algebra by Ivan Savov
  • Differential Equations: A First Course by Guterman and Nitecki (my college textbook)
Chemistry
  • Chemistry: The Central Science by Brown, LeMay, Burston, and Murphy (this is the book I've been using to make YouTube videos on chemistry for several years now)
Physics
  • University Physics, by Young and Freedman (this is the book I've been using to make YouTube videos on physics for several years now)
  • A Student's Guide to Maxwell's Equations by Daniel Fleisch
  • Fundamentals of Physics I and II by R. Shankar
  • The Feyman Lectures on Physics, vols I, II, and III
  • The Character of Physical Law by Richard Feynman
  • QED by Richard Feynman
  • Quantum Mechanics and Path Integrals by Richard Feynman and Hibbs
  • Reality Is Not What It Seems: The Journey to Quantum Gravity by Carlo Rovelli
  • Seven Brief Lessons on Physics by Carlo Rovelli
  • A Brief History of Time by Stephen Hawking (I've had since late 80s)
  • Just Six Numbers, by Martin Rees
  • Our Mathematical Universe by Max Tegmark
  • The Road to Reality by Roger Penrose
  • The Science of Interstellar by Kip Thorne
  • The Fabric of the Cosmos by Brian Greene
  • The Hidden Reality by Brian Greene
  • The Theoretical Minimum: What You Need to Know to Start Doing Physics, by Leonard Suskind
  • Quantum Mechanics: The Theoretical Minimum by Leonard Susskind
  • Thirty Years That Shook Physics by George Gamow
  • Quantum Mechanics: A Complete Introduction, by Alexandre Zagoskin (bought in LA when I took Sophie to Pepperdine)
  • Introduction to Quantum Mechanics (2nd ed) by David Griffiths
  • Quantum Mechanics for Scientists and Engineers by David Miller (a textbook)
  • Covariant Loop Quantum Gravity by Rovelli and Vidotto
  • 30-Second Quantum Theory by Brian Clegg
  • Quantum Field Theory for the Gifted Amateur by Lancaster and Blundell 
  • Quantum Theory, by David Bohm
  • Higgs by Jim Baggott
  • Three Roads to Quantum Gravity by Lee Smolin
  • Relativity by Einstein (older version and 100th anniversary edition)
  • The Perfect Theory: A Century of Geniuses and the Battle over General Relativity by Pedro Ferreira
  • A Most Incomprehensible Thing: Notes towards a Very Gentle Introduction to the Mathematics of Relativity (both second and third edition)
  • General Relativity by Robert Ward (a thick texbook I've had since 1984)
  • Special Relativity by A. P. French
Biology
  • The Ancestor's Tale by Richard Dawkins and Yan Wong
Computer Science
  • Learning Web App Development by Semmy Purewal
  • Android: Programming and App Development for Beginners by Samuel Shields
Miscellaneous
  • The Columbia University College of Physicians Complete Home Medical Guide (since 1985... I was in a book club)
  • House Construction Details by Burbank and Romney (1979 - my dad was very patient with my requests)

Wednesday, July 15, 2015

Liberal Arts 6: In Honor of Pluto

Sixth post in my series on the importance of the liberal arts for civilization. Previous posts include:

A Vision for the Liberal Arts
The Value of Philosophy
The Value of History
The Value of Music and Art
The Value of Literature, Writing, and Speech

1. Last evening, something happened that hasn't happened in the history of the universe. A probe launched in January 2006 passed less than 8000 miles from the cold dwarf planet we call Pluto. It carried some of the ashes of Clyde Tombaugh with it, the man who discovered Pluto in 1930. He died in 1997.

It is a truly remarkable thing, that we could throw a baseball from a pitcher's mound spinning at 1000 miles per hour while moving at over 66,000 miles an hour around the sun accurately enough that would hit Pluto nine years later 3 billion miles away. I thank God, who deigns to let mere mortals know such things.

And he has let them know these things, not through the Bible in this instance, not through a special revelation given to a prophet in a congregation. But God has deigned to let us discover such things through science. Math and science are also the language of God.

2. I am truly amazed that so many Christians mock science. Do they mock the planes they fly on, the GPS devices they steer by, the cell phones they call and text by? Do they mock the medicines they are cured by, the computers they write by, the flat screen TVs they spend most of their time by?

No. I strongly believe that Christianity can co-exist peacefully with science. I shudder to think of the other alternative. I do not hold to the other alternative.

3. Science gets at one of the most important foundations of Western civilization--evidentiary thinking rooted in a quest for objectivity. Science tries to proceed with as few presuppositions as necessary. It proceeds to make hypotheses that it then tests until it arrives at one that works well enough to be called a theory. But even then, it does not rest on theories past. Theories are always open to revision or even abandonment, especially if new data arises that points in another direction.

This is the scientific method. It asks what the most likely interpretation of the evidence is. We all have biases. Scientists have biases. But evidentiary thinking requires us to suspend our desires for the truth to be a certain way in order that we can move toward what is more likely to be the truth, toward the best explanations of the data we have.

Many of us pretend to operate on the basis of evidence. We talk the language of evidence. But what we are really doing is trying to find a possible way to make the evidence fit our preconceived notions or desired theory. Science teaches us to determine what the most probable interpretation of the evidence is and to modify our preconceived notions accordingly. Again, I shudder to think of what the implications would be if Christianity could not survive such a method. I firmly reject that suggestion.

This quest for objectivity is the great hope for a democratic nation, indeed for a civilized world. Along with its companion, logic, it is essential for the success of civilization. Without it, society disintegrates into tribes and interest groups whose only common ground is the fact that they are all out for their own interests. Those who cannot think in an evidentiary way are liabilities to civilization.

4. Science and math play an important personal function for most of us. They humble us. At least they should. Dare we think we understand the thoughts of God when we cannot understand algebra? God is greater than algebra. Yet every yahoo thinks he or she knows what the Bible teaches. The evidence suggests they are hilariously wrong.

I am not, of course, suggesting that mathematicians and scientists should be leading society and making all the decisions. The gifts that enable a person to think in these ways can produce glaring blind spots in other ways of thinking. There are other inabilities that should humble the scientists of the world. Scientists need the other liberal arts to balance them out, including a sense of religion, as much as we need math and science to balance us out.

Nevertheless, if philosophy did not teach the student that the wise person is the one who realizes how little he actually knows, science and math are always around to help--if we listen.

5. It would be wise for all college-educated individuals to have some basic knowledge of the conclusions of science. Everything is made out of atoms. Space is expanding. Trees and humans exchange oxygen and carbon dioxide with each other. All living things have DNA that maps out what they will look and be like.

These things are so basic to me that I can't imagine the view of the world people have when they don't know them. I seriously knew someone once who questioned whether we had really gone to the moon. I shudder to think about how that person decides how to vote. And woe to the person on trial who might have someone like that in the jury.

Everyone today seems to have an opinion on climate change, evolution, pollution, and so forth. But few get their opinions from science. They get their opinions from cable news. An educated person should be exposed to arguments on these subjects from someone trying to be objective who is an expert in science and hasn't been handpicked by a certain channel because of their target audience.

6. Most people do use some math in their lives. They have bank accounts. They submit taxes. THEY BUY LOTS OF STUFF. Perhaps not everyone needs to know algebra, but how to make a budget? Yes. Math can be taught in a relevant way.

7. Learning math and science can actually make a person a better thinker. Math is closely related to logic. Geometry teaches inference and proof. Algebra involves deduction.

When people ask, "When am I ever going to use this stuff?" The answer is that your brain will use these skills every day if you are a person who thinks clearly and reads the world around them well. Math expands your mental capacity. Becoming better thinkers is always a benefit to you as an individual and to society as whole.

8. Most people have such a narrow view of the world, yet everyone thinks they know everything about everything. If they are taught well, math and science expand our horizons beyond ourselves and our experiences to things we could not have imagined. They expand our "common sense" beyond what's true in Marion, Indiana, to what is true in the universe. They point us to God.

Friday, July 20, 2012

Does pure math exist?

Sometimes I long to have a profound thought or to encounter one.  When I was doing my education, I encountered them often.  I don't know if you've ever felt the way I used to feel when something would blow my mind. I'm trying to think of an example. One that comes to mind is when I began to think that universals are aggregates of like-minded particulars (at least as we experience them) rather than Platonic absolutes expressed in the material world.

Those moments come less often these days. You get older.  You think you have stuff mostly figured out. I thought of another one, when I had the thought that scientific theories are really just very precise myths expressing the mystery of the world.  Still myths, just a lot more precise in their expression.

Why am I writing this? Because I couldn't think of anything interesting to blog today, let alone profound.  Sometimes when I can't sleep at night I'll google, "something profound."  It's not very consoling.

So here's a stupid question.  I've always tended to think of the kind of math they do in physics and other sciences as an imperfect version of pure math.  So in quantum physics they use "statistical mechanics."  You can't have a precise sense of things so you approximate using statistical methods and probabilities.

So I always viewed this sort of applied math as an inferior version of pure math, where everything is tidy and exact, an imperfect shadow of the Platonic ideal.  But is it possible pure math is only a simplistic shadow of applied math, an abstraction from the real world?

What do you think?  Hey, I had to write something to get us off the topic of health care... ;-)