God Created the Integers; Hawking could have done better

I got Steven Hawking's God Created the Integers as a Christmas gift, and I was really looking forward to it. It is in fact a disappointment. This MAA review sums it all up. Also check out the Amazon reviews at the book link above; they're all spot on. What bugs me the most (from the MAA review):

Almost all the others are reproductions of material from various Dover publications, even when, as in the case of Newton, parts of Archimedes, and Laplace, there are better translations available.

Still, it's worth having, just to browse through.

TI & Numb3rs sweepstakes

TI's running a sweepstakes tied in with the Numb3rs TV program. Article here, TI site here.

Lost interview with ENIAC chief engineer

J. Presper Eckert was the chief engineer for the ENIAC computer project at the University of Pennsylvania's Moore School of Electronics. The ENIAC was the first useful electronic computer. This Computerworld interview was recorded by Alexander Randall six years before Eckert died in 1995. Several myths are deflated: ENIAC didn't burn through a couple of tubes every few minutes, nor did it dim the lights when powered up. About the actual invention process itself, Eckert says

"If I hadn't done it, someone else would have. All that any inventor does is accelerate the process. The main thing was we made a machine that didn't fail the first time. If it had failed, we might have discouraged this line of work for a long time. People usually build prototypes, see their errors and try again. We couldn't do that. We had to make it work the first time out".

ENIAC could add two 10-digit numbers in 0.2 mS. My v200 with AMS 3.10 takes 8.8 mS to add two 14-digit numbers, or 44 times as long. On the other hand, ENIAC didn't run on three AAAs. Some other timing results:

Subtraction: 9.5 mS
Multiplication: 10.4 mS
Division: 11.0 mS
Square root: 12.5 mS
Natural logarithm: 13.7 mS

Note that additions don't execute all that much more quickly than divisions. This means that the trick of rearranging an equation to trade multiplication and division for addition and subtraction won't save as much time as on other systems.

TI68k: Unexpected integration'questionable accuracy'

nInt((sin(sin(x)))^2 - (sin(cos(x)))^2, x, 0, pi)

returns, in a few seconds, -2.59E-14 and a 'questionable accuracy' warning, which is odd because the integrand is well-behaved with no singularities in the range. Individually integrating the two terms gives no warning, then summing those two integrals gives zero to machine precision.

"It's called classic rock for a reason"

... says Jenny Lewis in this Rolling Stone article about kids getting into bands that actually write and play their own music with, you know, actual instruments.

Just take those old records off the shelf.

Ed Pegg Recommends References ... and so do I

Ed Pegg writes the Math Games column on the MAA website. This month he lists his favorite math reference books. Nice list, and useful descriptions. I score four out of eighteen, myself.

Ed recommends the Oxford User's Guide to Mathematics. Other possiblities are the essentially famous CRC Standard Mathematical Tables and Formulae, the inexpensive Mathematical Handbook for Scientists and Engineers, or the Handbook of Mathematics and Computer Science.

My personal area of interest in mathematics is numerical methods. I am an engineer, not a mathematician, so the books that are most helpful to me tend to be pragmatic and easy to understand. Falling in this class more or less:

Numerical Recipes in Fortran, by William Press, Saul Teukolsky, et al. The strongest features of Recipes are the scope and straightforward explanations. This book gets a lot of grief from more sophisticated practitioners, but the code has always worked for me. I may not be alone, because this book has remained in Amazon's top-sellers in its category for years. The authors have a discussion group forum, and they actually do answer questions. Recipes is available for free, too.

Numerical Methods for Scientists and Engineers, by Richard W. Hamming. This is definitely an introductory book, and only covers a limited number of topics: zeros of nonlinear equations and polynomials, linear equations and matrix inversion, integration and least squares regression, for the most part. The real appeal of this book is not exhaustive scope, but the clarity of exposition.

Numerical Methods That (usually) Work, by Foreman S. Acton. Like Hamming's book above, this is not a comprehensive introduction to numerical methods. Instead, Acton examines what usually goes wrong in numerical computation, how to detect it and how to fix it. The style is idiosyncratic enough to bug some readers; I enjoy it. For more in the same vein, see Acton's follow-up Real Computing Made Real, which has been inexpensively reprinted by Dover.

HP-12C 25th Anniversary Contest

HP is running a contest to commemorate the 25th anniversary of the venerable 12C financial calculator:


The HP 12C was the world’s first horizontal financial calculator. Its innovative design and breakthrough Reverse Polish Notation (RPN) entry forever changed the way students and professionals reach their goals. After 25 years, this iconic calculator is still sold under its original name and model number and retains its world-famous horizontal design.


Yes, but ... the color scheme has changed, and Kinpo now manufactures the calculator. According to various newsgroup posts, the key feel has degraded and reliability, to put it charitably, is not what is once was.

Another article is here