floobydusted

Lots of good stuff in +Plus Magazine #50

2009-04-03T17:50:00.000-07:00

As usual, much good math to read about in this issue of Plus. My favorites:

Music from sine waves

A new approach to solving fluid dynamics problems.

Sundaram's sieve for prime numbers.

And just for you, Queen Anne, way too much geometry.

New Dumas novel (mostly) discovered

2009-04-03T17:44:00.000-07:00

This old Guardian article from May 2008 talks with Claude Schopp, a Dumas scholar who turned up most of an unknown Dumas novel.

"Imagine that a previously unknown Dickens novel suddenly turned up after gathering dust for more than 130 years. The mere suggestion seems ridiculous. How could a book by one of Britain's best-known 19th-century writers possibly have slipped through the net for so long? Or even at all? Yet that is precisely what happened to Alexandre Dumas's final epic, Le Chevalier de Sainte-Hermine, which was published for the first time in France three years ago and is being published in English this week as The Last Cavalier."

Time lapse Friday

2009-04-03T15:53:00.000-07:00

Baby plays on the floor
Gecko eaten by ants
Assembly of the Jaguar supercomputer
Mushroom growth
Butterfly pupates, emerges
An entire football game in 1:43 (best part: the marching bands)
Baby eating strawberry

Friday floobydust

2009-01-23T16:08:00.000-08:00

PC Magazine's best free software for 2009

CNET news story about the 1984 Apple Superbowl commercial

A very thorough online calculator from Casio, with arbitrary precision, lots of special functions and application libraries

Wednesday flooby

2009-01-21T13:54:00.000-08:00

A stunning lenticular cloud over New Zealand

How tube amps really work (scroll down for the photgraph)

Stanley Fish and the value of humanities

Faster numeric arc lengths on the Voyage 200 and TI-89

2009-01-20T16:44:00.000-08:00

The built-in arclen() function will return a numeric result for an arc length if a symbolic solution cannot be found. For example,

arclen(-x^3 + 3*x^2 - 2x + 2/x - 2/x^2 + 1, x, .769, 2.428)

returns 4.2413 in about 62 seconds in APPROX mode. We can speed this up by using nint() to numerically integrate the arc length integrand, as follows.

First define a simple function to find the arc length integrand:

: arcleni(f,x)
: Func
: sqrt((d(f,x))^2+1)
: EndFunc

where f is the function of the desired arc length and x is the independent variable. d() is the built-in derivative function. We then find the arc length with

nint(arcleni(-x^3+3*x^2-2x+2/x-2/x^2+1,x),x,.769,2.428)

which returns the arc length in about 27 seconds, saving 35 seconds.

It is likely that arclen() spends the extra time trying to find a symbolic solution before falling back to the numerical integration.

A little math reading today

2009-01-20T14:42:00.000-08:00

Freeman Dyson considers frog and bird mathematicians: those who work with the details, and those who take the broad view.

Crumpled paper and constructive mathematics

Victoria Gould combines acting and mathematics

Lotus Symphony lives

2009-01-19T16:18:00.000-08:00

I'm a PC dinosaur, so I spent many pleasant hours learning and using Lotus Symphony before MS Office took over. It turns out that Symphony is still available, and free, to boot.

Short article here

IBM download page here

Worth reading today

2009-01-19T16:07:00.000-08:00

Renaissance astronomer Tyco Brahe to be exhumed; foul play suspected.

Screen reading encourages sloth

Derbyshire reviews quantum physics book

Taking the earth's temperature ... 500 years ago

HP 35s Tear Down at embedded.com (updated)

2008-02-02T06:14:00.000-08:00

Editor in Chief Richard Ness breaks open the calculator, and finds two ICs and twenty-five screws. Mr. Ness also discusses the design with Sam Kim, director of product development for HP calculators. Mr. Kim notes

Unlike one of the predecessor models (the 41), there's no way for the user to tap in to the 35s' firmware. The programming only occurs at the user level, although HP is tinkering with giving users limited access to the firmware.

Kim offers, "The 35s is pretty much hacker-proof, but the old 41 had a lot of hacking going on because it was more of an open platform. There was something called synthetic programming, and there was a crowd that evolved around it. I was actually a member of that crowd, the diehard HP users."

Update: Mr. Nass also made a short video discussing the teardown, available at the EE Times trade journal site.

HP 35s at HP

... first class animal protein ...

2008-02-01T05:09:00.000-08:00

The Register found a Pravda article debunking the virtues of vegetarianism. Which is unintentionally funny, and so hard to take too seriously. For example:

Each and every human cell is supposed to be supplied with first class animal protein.

Furthermore, cosmetologists say that a typical vegetarian has dry and fragile hair, dull eyes and unhealthy complexion. They can hardly stand criticism and have a low boiling point. They raise their voice, swing their arms and splutter when arguing. They are weak even in their logic. They exemplify their righteousness with the cow, a herbivorous animal, and say that nature originally made a human being as a vegetarian creature.

The original Pravda link is a little racy. I had never been to the Pravda site, so I had assumed that Pravda was a reputable (so to speak) newspaper, but it looks a lot more like the National Enquirer.

Some Asus EEE PC resources

2008-01-26T16:49:00.000-08:00

The EEE PC (all the good names are evidently taken) is a wildly popular tiny laptop Linux PC with no hard drive. Here are some good links:

The Asus US EEE home page. (link)

A frequently updated blog, with a wiki, FAQS and active discussion groups. (link)

Another good blog. (link)

A big collection of EEE hardware hacks. (link)

A long, informative and entertaining introductive video, from ITIDIOTS. (link)

My personal interest in the EEE is as a super-calculator, to replace my TI Voyage 200 and HP 50G calculators. It is also a good opportunity for me to learn Linux, and get more familiar with open-source math packages, and probably a little bit of C, too.

I have long toyed with the idea of the super-calculator, which would have the advantages of current state-of-the-art calculators, without their disadvantages, mainly speed and low-resolution monochrome displays. The EEE PC looks like the ideal hardware platform for that project, and, since it runs Linux, there is plenty of free math software available.

The disadvantages are not showstoppers in my case. The typical battery life is about 3 to 5 hours, which is laughably shorter than the typical month I get from four AAAs in my Voyage 200. One of the biggest graphing calculator advantages is instant-on; reports are that the EEE boots up in about 30 seconds. This is too long, but I may be able to shorten that up. Another disadvantage is that the calculator has dedicated, specific function keys. Might just have to suffer with this.

Friday floobydust: The Hobbit, crocheted dinosaur skulls, and more!

2008-01-25T13:39:00.000-08:00

Here is an audio interview with John Rateliff, author of History of the Hobbit. You can find this, along with a 70th anniversary edition of The Hobbit, at Amazon.

From Makezine: The 'Cloud' digital sculpture at Heathrow Terminal 5. This is a large, kidney-bean (sort of) shaped contraption incorporating thousands of small disks which can be flipped from a black side to a reflective side under computer control. Includes a video. A little disappointing, in that the animations are very ordered and repetitive - why not Conway's Game of Life?

Also from Make: if you've got a power screwdriver and a propane torch, you can make your own coffee roaster. (This is only the first page of the magazine article, but the picture is worth it).

Finally, the crocheted dinosaur skull.

Here is the home page for Makezine.

Napier's Bones and Chessboard Multiplier

2007-10-17T17:39:00.000-07:00

Issue 44 of plus magazine is out with some worthwhile articles, as usual. Learn a bit about Euler and the calculus of variations, with a philosophical detour, or play with a very slick simulation of a multiplying computer which only uses a chessboard and markers.

New "Inside Your Calculator" Book

2007-09-25T10:07:00.000-07:00

The full title is "Inside Your Calculator: From Simple Programs to Significant Insights", by Gerald R. Rising. The Amazon page is here. The author's description: In this book I seek to communicate to the lay reader in entertaining terms some important ideas about calculators, mathematics and programming based on my university and secondary school experience over forty years in classrooms.

$48/Gflop Supercomputer w/low power, too

2007-09-11T13:55:00.000-07:00

Calvin CS professor Joel Adams and senior Tim Brom have designed and built an inexpensive (~ $1300) 26 Gflop supercomputer called Microwulf (a play on Beowulf, referring to a cluster of Linux nodes). The machine as it now stands has eight nodes, but can be updated to 16 by replacing the processors. Microwulf consumes only 450W at full load.

(Via Make magazine)

The Education of the Very Young

2007-08-30T15:02:00.000-07:00

This was posted on the National Review weblog a few days ago.

My Wife Takes a Rather Different View [Peter Robinson]

In an eariler post I noted that, after two days in kindergarten last week, our five-year old announced that she had no intention of returning. (The mood passed.) Noticing this, Fr. George Rutler, our unofficial chaplain here on the Corner, offers his own views on the proper education of the very young.

I'd encourage your youngest one to abandon kindergarten altogether. Almost everything I learned was learned outside the classroom, and school itself interrupted my education. Moreover, school locks you in with your peers. That is a mistake. One's social circle should never include one's equals. From my earliest years I found children uninteresting and always preferred the company of adults. This was an advantage, because I got to know lots of folks who are dead now whom I never would have known if I had waited until I was an adult. - So I have a collective memory - and oral tradition - that goes back to the eighteenth century, having spoken with people who knew people who knew people who knew people who lived then.

The only real university is the universe and a city its microcosm. That is why an expression like "New York University" is foolish. New York City is the university….Instead of school, children should spend some hours each day in hotel lobbies talking to the guests. They should spend time in restaurant kitchens and shops and garages of all kinds, learning from people who actually make the world work….One day spent roaming through a real classical church building would be the equivalent of one academic term in any of our schools, and a little time spent inconspicuously in a police station would be more informative than all the hours wasted on bogus social sciences. Formal lessons would only be required for accuracy in spelling and proficiency in public speaking, for which the public speakers in our culture are not models, and in exchange for performing some menial services a child could learn the violin, harp, and piano from musicians in one of the better cocktail lounges, or from performers in the public subways….

So I urge you to keep your child out of kindergarten, because kindergarten will only lead to first grade and then the grim sequence of grade after grade begins and takes its inexorable toll on the mind born fertile but gradually numbed by the pedants who impose on the captive child the flotsam of their own infecundity.

Excellent Introduction to Gravity and LIGO

2007-08-23T10:16:00.000-07:00

This video, Catching the Waves with LIGO (Realplayer required) is an easy introduction to gravity and the LIGO project. The video is a recording of a speech given by Dr. Barish, head of the LIGO project. Extra bonus: hear a radio pulsar!

The source page is here. You can choose versions for 56K modem, DSL/cable, or broadband.

Math flooby - podcasts and AMS Bulletins

2007-08-18T08:35:00.000-07:00

The American Mathematical Society has posted a series of ten short podcasts summarizing some topics in volume 6 of What's Happening in the Mathematical Sciences. Topics include the Poincare conjecture, digits of pi, the Navier-Stokes equation and Brownian motion.

The AMS has also made available the first hundred years of their Bulletins.

Journalism as we know it now dead

2007-08-08T17:33:00.000-07:00

What may be my daughter's favorite news source, the Weekly World News, has been killed by its new owners. The Washington Post gives it a loving send-off.

Don Knuth Article from 2006

2007-06-18T13:38:00.000-07:00

I missed this article from Stanford Magazine. The article is nothing deep, but still a nice summary overview of Knuth's life and work. I like this quote:
“If I had been good at making estimates of how long something was going to take, I never would have started.”

HP Calculator History Videos

2007-06-17T18:09:00.000-07:00

HP has two calculator videos up. The first, longer video is a short overview of the history of HP calculators, with the amusing hippopotamus story. The second video, Death of a slide rule, focuses move specifically on the first scientific calculator, the HP-35.

Industrial Shredding

2007-05-14T14:45:00.000-07:00

Enjoy the destruction of computers, engine blocks, monitors, and oversize tires, and so much more!

Tuesday Flooby

2007-05-08T17:23:00.000-07:00

A woman changes her mind about her abortion. Warning; graphic description of abortion procedure.

Humans run endurance well because they have big rear ends instead of tails.

Issue 42 of Plus magazine has a nice Euler article.

Lots of video math lectures here, at all levels, as well as many other topics in science and technology. Most require RealPlayer.

The Economist Style Guide will improve the finer points of your writing, for example:

Confectionary: a sweet. Confectionery: sweets in general.

Continuous describes something uninterrupted. Continual admits of a break. If your neighbours play loud music every night, it is a continual nuisance; it is not a continuous one unless the music is never turned off.

Convince. Don't convince people to do something. In that context the word you want is persuade. The prime minister was persuaded to call a June election; he was convinced of the wisdom of doing so only after he had won.

Here are the 2007 Intel Science Talent Search winners. My favorite, which is not coincidentally the only one I understand, is Mary Masterman's $300 spectroscope.

stats.org critiques and corrects statistics abuses in the media, for instance, toxic Teflon, exploding Pyrex, and a few extra pounds won't kill you any sooner.

Club Penguin leads to tears!

Ten commandments of PC HiFi

2007-04-20T14:50:00.000-07:00

Funny and useful, too.

Introduction to the gamma function

2007-04-17T17:19:00.000-07:00

Glendon Pugh's doctoral thesis is an excellent introduction to the gamma function, and, as an extra bonus, is quite well written; not like a typical thesis at all.

HP Calculator Video Contest

2007-04-15T06:42:00.000-07:00

To celebrate the 35th anniversary of the HP-35 scientific calculator, HP is staging a DIY video contest. This should be amusing. Here's what the SFGate and geek.com have to snark about it.

Not one, but two Flatland movies

2007-04-15T06:39:00.000-07:00

Ivars Petersen discusses two new Flatland movies in his MAA column.

“It was a sort of unfortunate concatenation of events,”

2007-04-15T06:31:00.000-07:00

A software flaw caused the Mars orbiter failure last November:

Instead, an errant computer command five months earlier had been placed in the wrong location of the computer memory for the spacecraft. That, in effect, implanted a fatal defect in the spacecraft, disabling a safety feature to prevent the solar panels from rotating too far and mangling its ability to communicate with Earth in case of a mishap.

NY Times story here.

HP Argues for RPN in 1974

2006-10-29T05:33:00.000-08:00

Hewlett-Packard put this advertisement in the 1974 issue of Scientific American magazine. At the time, HP used reverse polish notation (RPN) as an entry method on their calculators, as opposed to the more common algebraic system. RPN is more efficient and less error-prone, but it is less intuitive at the start. You can still buy RPN calculators from HP, but algebraic notation rules the market now.

Thanks to Don Shepherd for posting this at the forum at the Museum of HP Calculators.

Consumer Price Index Calculator, the HP-65 and Corvettes

2006-10-29T05:14:00.000-08:00

This calculator determines the relative costs of items accounting for inflation, from one year to another. For example, in 1974 an HP-65 programmable scientific calculator cost $795. Today that calculator would cost $3265. This is typical of mass-produced electronic products, which typically beat inflation by a wide margin. Today, a top-of-the line graphing calculator costs about $150.

As another example, in 1963 my Dad bought a new Corvette split-window coupe in California. He went to the dealership intending to buy a station wagon for my family to move to Ohio, but I guess he got distracted. Good decision. He paid about $2500. Today that same car would cost about $16,500. Today a Z06 costs $60,000. Admittedly, cars today are safer, more powerful and efficient and have more cup holders, but they still outpace inflation dramatically.

BBC Abandons Science, Embraces Nonsense

2006-10-28T18:54:00.000-07:00

This Register article reviews a particularly cheesy episode of BBC's science program Horizon. Ostensibly the program examines augmenting human intelligence by machine, instead it just goes daft. From the review:

Like Joy, De Garis also envisaged "fabulous machines" with capacities "trillions above the human level" that were "massively intelligent" and "God-like". (A very hard prospect to imagine when you're re-installing Windows XP).

Popular Mechanics Predictions from 1950

2006-10-17T18:15:00.000-07:00

An article from a 1950 issue of Popular Mechanics makes an occasionally accurate but mostly funny stab at predicting life in our times. Still no flying cars.

Let your kids pay for college

2006-10-04T09:49:00.000-07:00

This Motley Fool commentary makes the argument that it makes more financial sense to save for your health care, during retirement, than to save for your children's college education. Which has been our plan all along, in spite of the fact that people look at you like a heartless ogre when they hear about it. The author does not mention a few important aspects of the argument,though. It is not impossible, as a student, to pay for your own education, what with grants and co-op schools. Loans are right out - who wants to start work with a gigantic debt?

I think that students take the education more seriously if it's their dime. Both my wife and I paid our own way, and it wasn't that hard.

Areas of sphere and enclosing cylinder

2006-09-21T20:16:00.000-07:00

Suppose you have a sphere in a cylinder which exactly encloses it, that is, the cylinder touches the sphere at the equator and the poles. It turns out that the area of the sphere is the same as the area of the curved part of the cylinder. Earth-shattering this is not, but I'd never come across this before.

I 'discovered' this in the process of trying to solve this puzzle from John Derbyshire's August Dairy at the National Review Online site:

"A cylinder is arranged by the “vertical” tangent lines, which are tangent to the Earth’s sphere at the equatorial points and are parallel to the axis North Pole — South Pole. The surface of the Earth is projected to that cylinder by the rays, which are “emanated” from the said axis and which are parallel to the equatorial plane. Will the area of projection of France be larger or smaller than the area of France itself ?"

I haven't actually solved it yet, but I have a plan ...

HP-50G Press Release and "Reviews"

2006-09-21T17:29:00.000-07:00

HP has released the successor to the HP-49G graphing calculator, and a few low-quality reviews are showing up. We have:

The press release

A typically juvenile write-up from Gizmodo

"... this calculator can even calculate in Reverse Polish Notation. Now I don't have the slightest clue what the means, but it sure sounds fancy."

A slightly less moronic CNET blog post

"Not only can it calculate in standard Algebraic mode, but also in Reverse Polish Notation, which is a shortened way of entering calculations that saves time (yeah, I definitely had to look that up), ... "

HP's 50G Page

New TI68K AMS functions may break old programs

2006-08-29T17:02:00.002-07:00

AMS 3.10 for the TI68K calculators (Voyage 200, TI-89 Titanium, etc) includes some new functions, most of dubious value. One particular dubious function, root(), caused one of my old programs to break. I had ported a polynomial root finder, polyroot(), using Laguerre's method, and it included a local function called root(). polyroot() ran fine under AMS 3.10 until I unarchived it and edited it a bit. This caused the "missing (" error after the Local declaration. Obviously, the built-in root() conflicted with my local root().

The solution is obvious: don't use built-in function or system variable names as locals in TI Basic programs. An even better policy is to avoid names which may become functions in future AMS releases. I renamed root() to root1(), and all was well.

Finn flings faulty phone farthest, finishes first

2006-08-29T17:02:00.001-07:00

This short article at the Register is sort of funny, but, mainly, I liked my headline better.

Clever solution to a particular cubic equation

2006-08-29T17:02:00.000-07:00

This forum thread at the Museum of HP Calculators shows a short expression to find, quite quickly, one root of the cubic x^3 + 3x - A = 0, for any 'A'. The author, Valentin Albillo, occasionally posts math 'mini challenges' to be solved on vintage HP calculators with limited resources. His solution descriptions are most often interesting and informative.

New TI-Nspire CAS+ announced in Germany

2006-04-11T13:35:00.000-07:00

The announcement for the TI-Nspire CAS+ is in German, but most of the screen shots include English text. This looks like a successor to the TI-89 Titanium and Voyage 200. The demo shows toolbars of iconic symbols and operators, implying a touch-screen and stylus of some sort, but some screen shots show a small arrow cursor,so perhaps the Nspire has a built-in pointing device of some kind.

Here's a Babelfished translation of the introductory page:

Mathematics becomes better understandable for each pupil Each pupil learns differently. One understands better formulas, second tables, third diagrams. The new TI Nspire? CAS deals with these specific learning habits. With him one can represent contents in such a way in each case, how the individual pupil understands her best. This happens, by using formulas, tables, graphs, geometrical constructions and text alone in each case or dynamically with one another linked. By the cross-linking of these different mathematical representations your pupils and pupil win a deep mathematical understanding. The TI Nspire CAS can be served simply; the key functions are self-describing. The functions are so clearly arranged that not used applications confuse nor divert neither. It at the same time offers large function variety for highest requirements.

Configurations
TI-Nspire™ CAS is available as Handheld and also for PCS and MACs.

TI Nspire CAS covers the following applications:

Calculator
Computer algebra application with comfortable formula editor

Graph & Geometry
Plotten of graphs and geometrical constructions integrate

Lists & Spreadsheet
Spread-sheet analysis, lists and wertetabelle integrate

DATA Collection
Recording of measurement – and evaluation with car Launch

Notes
Simple text processing

These applications are among themselves dynamically linked. This means that variables and definitions from applications are available also in the other applications. If one changes a variable in an application, then this change is transferred also in the other applications.

The following accessories are to TI-Nspire™ CAS available:

Projection possibilities
TI-Nspire™ CAS+ ViewScreen panel
Projection over overhead projector

Verbindungsmoeglichkeiten
Computer adding he cable
Mini USB on mini USB

Computer computer cable
Mini USB on USB

TI-Nspire™ CAS Connections Cradle
Further interfaces (2x mini USB, 1x USB) and loadable Akku

Recording of measurement
EasyTemp™ and GoTemp
Temperature sensor
CBR 2™ and GoMotion
Ultrasonic sensor

TI History Book: Engineering The World

2006-04-06T09:54:00.000-07:00

This book was published last October, but I just noticed it now. From the lone Amazon review: This handsome volume, lavishly illustrated with photos from Texas Instruments archives, is the culmination of a TI-history project that proceeded spasmodically over many years and which reportedly produced an earlier manuscript that was vetoed by the company's then president. Here is the corporate site for the book, and this is a Cnet blog blurb.

I will eventually post a review.

Dayton History Books Online

2006-03-22T13:41:00.000-08:00

This site is a collection of historical documents for Dayton, Ohio. Strangely fascinating, at least a couple of them. I found it searching for information on the 1913 flood, and this report by National Guard General George H. Wood gives a real participant's perspective.

Also interesing is this early history of Dayton.

Random walk encircles point with probability zero

2006-03-20T17:34:00.000-08:00

Ivars Peterson reports on the Yi Sun's winning project for the Intel Science Talent Search, in which Yi Sun

...worked out the expected number of steps it takes a walker on a two-dimensional grid to encircle a given point (origin). One such circuit corresponds to a winding number of 1.

Yi discovered that the expected number of steps to complete such a circuit in two dimensions is infinite. He also derived an explicit (very complicated) formula for the expected value of the winding number after n steps.

That is a pretty interesting result. The projects for the STS always seem really interesting, which brings me to an ongoing peeve with the STS: the reports are not published in detail anywhere that I have found.

Build your own TI-59

2006-03-20T17:21:00.000-08:00

This Design News story doesn't give much information about 'Daniel', who has evidently emulated a TI-59 with a PIC microprocessor. Unfortunately, most of the links seem to be broken as well. At least this Make magazine blog entry gives a few more pictures.

The multicolor LEDs are kind of an interesting touch, and what's the deal with that LCD display? Debugging? I am certainly in a pretty weak position to be critical of the utility of other peoples' free-time projects, but why a TI-59? It was a decent calculator for its time, but it is fairly easy to find one on Ebay, replace the inevitably dead & corroded batteries and have a working version of the real thing. Still, a pretty neat project.

The Trouble with the Turing Test

2006-03-17T19:24:00.000-08:00

Mark Halpern has written a fascinating article examining the current state of AI with respect to the Turing test. Never heard of Turing? Don't worry. Mr. Halpern explains it all, and goes farther to claim that even a computer which passes the Turing test may or may not be acually thinking. Too many articles on this topic devolve into fluttering gibberish, but Mr. Halpern stays fully grounded. Highly recommended.

Perimeter of an ellipse

2006-03-10T13:10:00.000-08:00

Define an ellipse as

x^2/a^2 + y^2/b^2 = 1

then the perimeter P is calculated with

P = 4*a*E(e)

where E() is the complete elliptic integral of the second kind, and the eccentricity e is

e = sqrt(1 - b^2/a^2)

The complete elliptic integral of the second kind can be defined as an integral:

E(z) = integral( sqrt( 1 - z*(sin(x))^2), x, 0, pi/2 )

There are a variety of numerical methods to find E(z), but just using the v200 nInt() function for numerical integration works fairly well because the integrand is well-behaved with no discontinuties. Calculating E(z) with nInt() executes in about 2 seconds, with an RMS error of 1.8E-11 for 11 samples of z on [ -1, -0.8, ... , 0.8, 1 ].

For a lot of ellipse information and relationships see the Mathworld entry. You can calculate E(z) at the Wolfram formula page. A minor cottage industry seems to have sprung up for simple functions to estimate the ellipse perimeter, the most complete overview is here.

God Created the Integers; Hawking could have done better

2006-02-21T19:49:00.000-08:00

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

2006-02-20T19:22:00.000-08:00

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

Lost interview with ENIAC chief engineer

2006-02-20T18:16:00.000-08:00

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'

2006-02-15T09:09:00.000-08:00

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"

2006-02-15T04:04:00.000-08:00

... 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

2006-02-10T19:59:00.000-08:00

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

2006-02-10T18:31:00.000-08:00

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

Celestial Navigation for the TI-89

2006-01-27T19:58:00.000-08:00

From the description for inac:

Astnav89/INAC, Implementation of Navigational Algorithms in Computers. This program will take in sextant readings and put out your latitude and longitude. (...) It also has a planetarium and great circle calculator, partial coastal navigation and more.

TI calculator division makes money, again

2006-01-26T13:52:00.000-08:00

For the fourth quarter of 2005, TI's calculator division ('Educational and Productivity Solutions) made $10 million on $67 million revenue. Not bad. The complete report is here.

TI68k programs of note: Karnaugh maps and sudoku

2006-01-26T13:46:00.000-08:00

This looks like a comprehensive Karnaugh map program for working with logic expressions.

If you're into the sudoku thing, you can now waste time just about anywhere with your calculator.

A really tiny fish

2006-01-26T13:37:00.000-08:00

A new record has been set for the tiniest known fish. From the Yahoo News article:

"This is one of the strangest fish that I've seen in my whole career,' said Ralf Britz, a zoologist at the Natural History Museum in London. "It's tiny, it lives in acid and it has these bizarre grasping fins."

and an actual picture here.

Filename extensions for TI68k objects

2006-01-25T14:52:00.000-08:00

TI68k objects such as variables, numbers, programs and pictures are stored as PC files with particular extensions. The table below is taken from the TI Connect application Help. In general the extension has the form .XXa, where XX specifies the calculator type and a specifies the object type. The table below shows the a codes.

a == Geometry figure
c == Complex variable
d == Graph database
e == Expression
f == Function
i == Picture
k == Application
l == List
m == Matrix
n == Number (real or complex)
p == Program
r == Lab report
s == String
t == Table device setting, or text variable
u == Operating system
w == Window settings
x == Geometry macro
y == Equation or function
z == ASM program, or window values

The calculator codes XX are

89 == TI-89
92 == TI-92, TI-92 Plus
v2 == Voyage 200

Was Columbus a pirate? 300 Catalonians donate spit to find out

2006-01-19T17:30:00.000-08:00

From the article:

While historians have mostly assumed that Columbus was an Italian born in 1451 in Genoa, a persuasive counter-lobby argues that the mariner who pioneered the Spanish conquista was in reality the Catalan Cristofol Colom, who airbrushed his past to conceal his activities as a pirate and conspirator against the king.

Copper shortage hypothesized

2006-01-18T17:35:00.000-08:00

Research results of a team led by Thomas Graedel of Yale are summarized in the Scientific American article Measure of Metal Supply Finds Future Shortage. Running out of copper would be bad:

In fact, residents of Canada, Mexico and the U.S. required an average of 170 kilograms of copper per person. Multiply that by overall population estimates of 10 billion people by 2100 and the world will require 1.7 billion metric tons of copper by that date--more than even the most generous estimate of available resources.

The analysis seems thoughtful and conservative.

TI 68K graphing anomalies

2006-01-18T10:25:00.000-08:00

This is not a new site by any means, but still a nice summary of misleading function plots. The 'false asymptote' problem has been fixed in AMS 3.10, and the 'partial circle' effect is well-known.

The most interesting example is the plot of y = x(x-5)^(2/5), in which most of the plot is missing. The complete plot is shown by expressing the function as y = x((x-5)^2)^(1/5), which avoids the intermediate complex result from (x-5)^(2/5), where x<5.

The remaining examples are not problems specific to the TI 68K calculators, but misleading effects from plotting the example functions with discrete resolution.

Rational geometry eliminates trig function calculations

2006-01-18T10:12:00.000-08:00

This EE Times article describes a rational representation of angles with which, the system's inventor claims, all the familiar engineering calculations that currently require tables or a calculator can be done with simple arithmetic. To elaborate,

His approach drops the definition of distance, which requires the use of square roots, and instead uses the unit he calls quadrance, which compensates for irrational numbers by squaring all distances. Wildberger's second innovation is to define a degree of spread between two intersecting lines by using quadrances instead of angles. Combining quadrances and spreads, in place of distance and angles, yields rational trigonometry.

An Introduction to Different Rounding Algorithms

2006-01-18T10:02:00.000-08:00

This article at the Programmable Logic Design website describes most rounding possibilities. The second part of the article is several simulations of rounding applied to a digital filter implementation which demonstrate the bias resulting from the rounding methods. Unfortunately the examples don't show the errors that can result from hundreds or thousands of operations, which is where the problem really gets serious.

Writing very reliable software

2006-01-11T13:37:00.000-08:00

Here's an article in IEEE Spectrum about Praxis, a British firm specializing in extremely high reliablity software. The interesting features about their development approach are that they spend a lot of time up-front writing a requirements specification, implementing the software first in Z, a formal predicate languange so the code can be mathematically proven correct, and finally doing the actual coding in Sparks, a language derived from Ada. Ada, in turn was designed from the start to write reliable code.

TI sells sensors business unit, noncommital about calculators

2006-01-11T13:22:00.000-08:00

This article at Computer Business Review Online is one of hundreds on the sale of TI's sensor unit. But this one also includes a snippet on the calculator business:

Meanwhile, TI VP and investor relations manager Ron Slaymaker would not say whether the company would follow up the S&C sale with the disposal of another fringe activity, its calculator business, which generates about 5% of revenue. However, he did point out that it is highly profitable, with margins of more than 40%.

Most calculator users, being students and not working engineers, seem unaware that calculators are a tiny part of TI's business, compared with seminconductors. It is interesting to imagine what would happen if TI did sell the calculator business, though. Who would buy it? Maybe Casio, maybe HP? I doubt that HP would put the money into it. Whoever did buy it would get a nice batch of patents, although those patents don't seem to prevent what little innovation there is in calculator design.

Three crises in mathematics

2006-01-05T17:55:00.000-08:00

Brian Davies' makes the argument in his paper Whither Mathematics that

... developments of the classical Greek view of mathematics do not adequately represent current trends in the subject. It proved remarkably successful for many centuries, but three crises in the twentieth century force us to reconsider the status of an increasing amount of current mathematical research

The three crises stem from Godel's Incompleteness Theorem and proofs which are too long and complex for mathematicians to be confident that they are actually correct. Davies also discusses a bit about the use of computers in mathematics and the formal verfication of proofs. The paper is short and very readable.

Access to the paper requires a free and simple registration.

What's 'new' in AMS 3.10

2005-12-05T09:42:00.000-08:00

Although AMS 3.10 for the Voyage 200 has been out for a while, I just recently updated my calculator. The TI AMS 3.10 page has this to say, in typical coy, cryptic TI fashion:

The new functionality includes domain and graphing improvements, solving inequalities and equations involving vectors, nth root and log to any base functionality, implicit derivatives and gradian angle measure.

These functions are new from the previous version:

Data>Mat, Mat>Data Convert data variable to matrix and vice versa. Renders tip [3.29] irrelevant.

DelType(type) Deletes all variables of the specified argument type.

>Grad, >Rad Convert angle measurments to gradians or radians.

impDif(exp,[order]) Implicit differentiation. Renders tip [6.53] irrelevant.

>ln(exp) Simplify the input expression so that only natural logarithms are used.

>logbase(b) Simplify the input expression so that only logarithms of base 'b' are used.

root(x,n) Returns the nth root of x. This does not add any new functionality, and just evaluates x^(1/n).

stDevPop(list) Returns the population standard deviation of the argument list. Compare to the existing stdDev(). Renders tip [6.42] irrelevant.

G (superscript) Specify an angle in gradians.

Other new features are a gradian setting for the angle mode, and a graph
discontinuity detection (F1, Format, Discontinuity Detection in the Y= editor). This setting eliminates the false connection between positive and negative points plotted near an asymptote, but it also slows graphing considerably. solve() can now solve simple vector equations for, for example, the components of a vector.

Mathematical table turning

2005-11-23T13:32:00.000-08:00

This paper at the front for the Mathematics ArXiv describes a fascinating, unintuitive result: under certain (fairly lax) conditions, a four-legged rectangular table can always be rotated around its center so that all four legs are on the surface, that is, the table does not wobble. From the paper:

We prove that if the ground does not rise by more than arctan(1/sqrt(2)) ≈ 35.26° between any two of its points, and if the legs of the table are at least half as long as its diagonals, then the table can be balanced anywhere on the ground, without any part of it digging into the ground, by turning the table on the spot.

The paper also discusses leveling tables in the real world. The result does not hold for tables with different leg lenths, and tables whose leg endpoints are not strictly rectangular. Still, it is a curious finding.

HP49G+ Advanced User's Reference Manual

2005-11-22T17:04:00.000-08:00

Gene Wright announced a new version of the 49G+ manual, and it is an impressive piece of work, reminiscent in quality and scope of the HP manuals from the golden age. Contributors include Gene Wright, Tony Hutchins, Wlodek Mier-Jedrzejowicz, Jordi Hidalgo, Ted Kerber, Joe Horn, Richard Nelson and Jake Schwartz.

TI Basic Coding on the PC, Made Easier

2005-11-22T15:02:00.000-08:00

You can use TI's GraphLink software to edit TI Basic code on the PC, but you can't use GraphLink to transfer the code to the calculator through a USB connection, because GraphLink doesn't support the USB cable. Here's a workaround.

Open GraphLink, edit your code and save it. Open a Windows file explorer window where you saved the code file. Right-click on the filename and choose 'Send to TI Device ...', then send the file as usual. You can leave both the explorer window and GraphLink open, continue to edit your code & send it to the calculator. This method assumes that you have TI Connect installed, so the 'Send to TI Device ...' option is available.

Ideally TI will eventually update TI Connect to include a program editor. The old GraphLink program made it very easy to develop code, because you could download the code directly from the editor.

Also related to TI Connect and USB, I often have difficulty getting a connection between PC and calculator. I believe this is caused by a flakey USB driver or motherboard implementation, rather than a fault in TI Connect, but I seem to have better luck when I plug the calculator in first, then the USB cable at the PC.

MAA November Columns

2005-11-22T14:53:00.000-08:00

Keith Devlin addresses more fundamental probability confusions. A detailed-enough article about pushing the Shannon limit of error free communications. These MAA columns are usually easy to understand and interesting.

Colored bubbles and disappearing dye

2005-11-18T06:07:00.000-08:00

This Popular Science article describes Tim Kehoe's eleven-year saga to develop colored soap bubbles.

Peanut Butter

2005-11-17T13:46:00.000-08:00

My older daughter really likes peanut butter, which makes this essay by W.F. Buckley relevant.

slashdot in 100 words or less

2005-11-17T07:24:00.000-08:00

From a /. poster:

If the sample of Slashdot and its immediate social clique were the norm, we'd live in a pseudosocialist utopia in which all of us are gainfully employed and paid a hundred thousand dollars to work 30 hour weeks developing beautiful open source software that we give away and nobody buys, and all music and entertainment is produced through the honest labor of talented people upon whom we benevolently bestow voluntary payments for their work, and whose labors of love are distributed for free through the software channels that we were paid lots of money to develop. Oh, and Bush isn't president. And global warming stopped. And we all ride bikes to our jobs. And there's no McDonald's or suburbs. And soda is free. So is beer. I could go on, but I moved into the TrollZone about 5 minutes ago.

Panexa

2005-11-16T11:21:00.000-08:00

The drug for everyone. A little too close to the truth.

Umberto Eco

2005-11-16T08:41:00.000-08:00

Nice site here. From the essay The Future of the Book:

Books will remain indispensable not only for literature, but for any circumstance in which one needs to read carefully, not only to receive information but also to speculate and to reflect about it.

Cheap tool alert - 4in Digital Calipers

2005-11-15T09:55:00.000-08:00

American Science and Surplus' latest catalog has a 4" digital caliper for about $15US. I could not resist the temptation, as I've been looking for a small digital caliper to keep in my small toolbox in my office at work.

The caliper is made in China, according to the box, but there is no manufacturer's name. The construction is completely plastic and feels a bit flimsy, but should hold up with care. The plastic construction is an advantage in that the caliper is very light, which is nice if your toolbox is already on the heavy side. The moving blade head has noticable wobble, but less than the resolution of 0.01". The moving head slides smoothly on the beam. Overall length is 7". The outside measurement blade depth is about 1-3/16", and the inside measurement blade depth is 1/2". Unlike most calipers, there is no depth measurement pin. There is also no locking mechanism.

With a display digit height of 3/8" and good contrast, measurements are easy to read. The display is a little slow to update while the head is in motion, but not objectionably. Three color-coded buttons control the OFF, ON and ZERO functions. The ON button is also used to toggle between inch and millimeter measurement. There is no tactile click to the buttons but they are easy to operate, regardless.

The resolution is only 0.01" and 0.1mm which is less than the more typical resolution of 0.001". I checked the accuracy against my Mitutoyo CD-6CS calipers, and measurements are consistently low across the range by 0.01", which isn't bad. The indicated metric measurement matches the inch measurement to the displayed resolution. Using the metric indication gives you more than twice the resolution (0.01" vs. 0.004"), but the error on the metric scale is still about 0.01" low.

The caliper is powered by an SR44 watch battery, which is included. The caliper will automatically power-down after a few minutes of inactivity. Remember to re-zero the caliper after changing the battery, because it seems to power up with a random offset. In fact, it is a good idea to check the zero frequently, because I noticed an occasional offset of about 0.2" had occurred.

If you don't already have a caliper, I can't really recommend this one for general purpose use. The limited range, low resolution, lack of a depth pin and occasional random offsets all mean that your money would be better put towards a better 6" caliper. However, if, like me, you just need a spare to keep in a satellite toolbox, this one will do the job. It will also be less heartbreaking if someone walks off with this caliper than your $150 'good one'. This caliper would certainly be better than nothing if you are on a tight tool budget.

At this price, this would be a good caliper for hacking applications, if you need to build a displacement measurement display into a fixture or instrument. I haven't had it apart, but it might be possible to tap into the circuit to transmit the measurement to another instrument.

A thoroughly good AMS Notices this month

2005-11-15T09:50:00.000-08:00

The December Notices of the AMS is up here. We have nasty high-dimensional integrals made somewhat less nasty, random matrices, a mathematical institute in the Palo Alto Fry's, a sensible proposal to eliminate college-level math homework, Martin Gardner arguing for realism, and E.B. Davies arguing against it.

Free registration required; documents are PDF.

Forman S. Acton's 'Real Computing Made Real'

2005-11-10T16:13:00.000-08:00

Forman S. Acton's Real Computing Made Real is now available from Dover, in paperback, at a reasonable price. This book is in some respects a follow-up to, and an amplication of the author's previous 'Numerical Methods That (usually) Work', but it stands on its own quite well. If you liked 'Numerical Methods', you'll like 'Real Computing' and learn some new things.

'Real Computing' ostensibly focuses on solving nonlinear equations and performing numerical integration, but the real value is in teaching how to recoginze difficult problems, and how to reformulate the problem to get a good answer. The pace is leisurely and thorough; not at all dry but rather engaging. This seems to offend readers who prefer a more pedantic presentation. Here's a sample:

AN EDUCATIONAL DALLIANCE

If you've never spent a numerical night with a robust alternating series, here's your chance! Compute sin(x) from

sin(x) = x - x^3/3! + x^5/5! - ...

Evaluate each term from its predecessor, summing as you go. Stop when you term shrinks to insignificance. Check your technique with x = 0.5 -- then go for x = 9.5 and x = 11. The experience seldom thrills but is very maturing -- especially if you are using a calculator with less than 10-digit precision.

To a calculator user of canned solvers and integrators, this book still offers much. It will teach you to recognize equations and integrals which are difficult to numerically solve quickly, accurately, or both. You will also learn some general methods to recast those nasty problems to get better results. 'Real Computing' is not an introduction to numerical methods nor is it a cookbook. Dover does in fact offer several good introductions:

A First Course in Numerical Analysis, Ralston & Rabinowitz
Numerical Methods, Dahlquist and Bjork
Introduction to Numerical Analysis, Hildbrand
Numerical Methods for Scientists and Engineers, Hamming

Acton devotes about thirty pages to sketching functions by hand. The motivation is to learn to really understand how the terms of a function affect its form, and to use that understanding to apply an appropriate algorithm or tranformation. However, much of that understanding could be acquired using the built-in function plotting features of graphing calculators.

(I have no business connection with Dover; just a happy repeat customer.)

Range limitation in TIbasic rand() function

2005-11-09T13:38:00.000-08:00

rand(n) returns a random integer in the range [1,n]. The maximum (undocumented) value for 'n' is 99,999,999,999,999, or only 14 digits. Would be handy to have a function to extend the argument range to the full integer range of 640 digits or so. The function should retain the good statistical properties of the built-in rand() function, so the question becomes: what is the best way to combine multiple results from rand() to build a larger integer? Probably already plenty of results for this already; need to search. Also remember to handle negative arguments for 'n'.

193-digit RSA-640 Factored

2005-11-09T13:28:00.001-08:00

Here's the MathWorld write-up. The v200 (eventually) correctly returns false from isPrime() with this number. Didn't try factoring it, though ...

Popularity of US first names

2005-11-09T13:28:00.000-08:00

This interactive plot of US first names is interesting and well-done, from a graphics standpoint. You can see how the popularity of various names has waxed and waned over the years. I came across it from this MAA article. Needs Java.

The coin change problem

2005-11-07T09:48:00.000-08:00

What are the best denominations of 4 coin values to minimize the coins needed to make any value from one cent to 99 cents? How optimum is are the US values of 25, 10, 5 and 1 cent? Are there better values? How much does adding the 50 cent coin improve the situation?

Wrote a TIbasic function misc\change(val_list,amt) which returns the number of coins of each denomination needed to make 'amt'. val_list is a list of descending coin denominations. The penalty function P is the sum of the number of coins to make each amount from 1 cent to 100 cents. For example, misc\change({25,10,5,1},99) returns {3, 2, 0, 4}, for a total of 9 coins. Some coin values & P values:

{25,10,5,1} 470
{50,25,10,5,1} 420 (50cent piece improves P by 50)
{32,8,4,1} 450
{32,16,4,1} 450

pcpress() comments

2005-11-06T14:22:00.000-08:00

Playing with pcpress() file compression on v200. Some problems:

- key bounce; more than one key event per keypress
- tiny font is hard to read
- failed to write variable for large (~40K) archived variable.