Archive for category history

The hero of zero

Breaking news about nothing: Dating done with the Oxford Radiocarbon Accelerator Unit now puts the invention of the number zero 500 years earlier than previously believed.  As explained in this post by The Guardian, the hero of zero is Indian mathematician Brahmagupta who worked out this pivotal number in 628 AD.  Isn’t that something?

The development of zero in mathematics underpins an incredible range of further work, including the notion of infinity, the modern notion of the vacuum in quantum physics, and some of the deepest questions in cosmology of how the Universe arose – and how it might disappear from existence in some unimaginable future scenario.

– Hannah Devlin,

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A knotty problem—how to keep track of stuff without computers or even pen and paper

Peruvian potatoesThe New York Times reports today on the recent discovery of several knotted string records, called khipus, that ancient Incas used to record things such as the colorful potatoes I photographed at a Peruvian market.  From what I saw on my travels there—see this blog on Incan agriculture experiments, a great deal of food must have been produced and stored.

Based on this Times picture I suspect these “mops that have seen better days”, as George Gheverghese Joseph, a mathematics historian at the University of Manchester, U.K., put it, must be a bit easier to untangle than Christmas lights. But then there remains the problem of deciphering them.

Thus far researchers have picked up on mathematical aspects of the khipus.  However, the latest trove of colored strings provides a chance at figuring out the Incan scheme for identifying what was being counted.  Here is where database capability and statistical methodology comes in handy.

I amazes me how all of the technology we now have at our disposable is challenged by methods developed 600 or so years ago.  Hats off to Incan ‘thinken!

“Many now think that although khipu probably began as accounting tools, they had evolved into a writing system—a kind of three-dimensional binary code, unlike any other on Earth—by the time the Spanish arrived.”

Cracking the Khipu Code Science magazine.

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Experiments by Incan agronomists

Earlier this week I visited Machu Picchu in Peru, which features extensive terracing for crop-growing. Five-hundred years ago the Incans took full advantage of a uniquely temperate microclimate on sites like this along the border of the Amazon. First of all they engineered a drainage system out of rocks brought up from the river below. Then they covered it with dirt laboriously hauled from fertile plains at lower elevations. Next they evidently experimented on different crops at different levels to get the best interaction with varying temperatures each step of the way down from the peak. According to a team of agronomists and archeologists Machu Picchu terraces from U Penn who reproduced the Incan farming conditions, yields of potatoes came in at two or even four times what would be expected. All this is quite impressive—building a self-sustaining city at nearly 8000 feet on a peak with only a few, small flat areas.

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This baby really did explode

I’ve been blessed with another grandson, my second, who arrived just before Thanksgiving.  I’ve become a bit gun-shy holding him due to his explosive colonic evacuations.  Today, though, I realized that being a babysitter could be a whole lot worse.  See what I mean by reading this New York Times obituary for nuclear scientist Donald Hornig.

In a small shed at the top of a 100-foot-tall steel tower deep in the New Mexico desert, Donald Hornig sat next to the world’s first atomic bomb in the late evening of July 15, 1945, reading a book of humorous essays. A storm raged, and he shuddered at each lightning flash.

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What value for p is right for testing t (or tasting tea)?

Seeking sponsors for his educational website, statistician Keith Bower sent me a sample of his work – this 5 minute podcast on p-values.  I enjoyed the story Keith tells of how Sir Ronald Fisher, who more-or-less invented design of experiments, settled on the p value of 5% as being a benchmark for statistical significance.

This sent me scurrying over to my office bookshelf for <em>The Lady Tasting Tea – a delightful collection of stories* compiled by David Salsburg.**  Page 100 of this book reports Fisher saying that below p of 0.01 one can declare an effect (that is – significance), above 0.2 not (that is – insignificant), and in-between it might be smart to do another experiment.

So it seems that Fisher did some flip-flopping on the issue of what value of p is needed to declare statistical significance.

PS.  One thing that bothers me in any discussion of p-values is that it is mainly in the context of estimating the risk in a test of the null hypothesis and almost invariably overlooks the vital issue of power.  For example, see this YouTube video on Understanding the p-value.  It’s quite entertaining and helpful so far as it goes, but the decision to accept the null at p > 0.2 is based on a very small sample size.  Perhaps the potential problem (underweight candy bars), which one could scope out by calculating the appropriate statistical interval (confidence, prediction or tolerance), merits further experimentation to increase the power.  What do you think?

*In the title story, originally told by Sir Ronald Fisher, a Lady claims to have the ability to tell which went into her cup first—the tea or the milk.  Fisher devised a test whereupon the Lady is presented eight cups in random order, four of which are made one way (tea first) and four the other (milk first).  He calculates the odds of correct identification as 1 right way out of 70 possible selections, which falls below the standard 5% probability value generally accepted for statistical significance.  Salsburg reveals on good authority (H. Fairfield Smith–a colleague of Fisher) that the Lady identified all eight cups correctly!

**Salsburg, who worked for some years as a statistician at a major pharmaceutical company offers this amusing anecdote from personal experience:

“When I first began to work in the drug industry…one…referred to…uncertainty [as] ‘error.’ One of the senior executives refused to send such a report to the U.S. Food and Drug Administration [FDA]. ‘How can we admit to having error in our data?’ he asked [and]…insisted I find some other way to describe it…I contacted H.F. Smith [who] suggested that I call the line ‘residual’…I mentioned this to other statisticians…and they began to use it…It seems that no one [in the FDA, at least]…will admit to having error.”

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Tasty tidbits gleaned by a news-starved junky for stats trivia

The June 10th “Views” section of the International Herald Tribune (the global edition of New York Times) offered a few choice bits for me to savor after nearly two weeks traveling abroad without an American newspaper.

  • A pie chart reporting on a June 1-7 telephone survey by Stanford University of 1000 American adults asking their opinion on belief in global warming.  A pie chart illustrated that about 75% do believe in global warming, 20% do not, and 5% “don’t believe in pie charts”.  I suspect that the author of this editorial, Jon A. Krosnick – a professor of communications at Stanford, meant this last bit of the chart to represent those who are undecided, but the graphic designers (Fogleson-Lubliner) figured they’d have some fun.
  • Olivia Judson’s comments on “Galton’s legacy” note that this preeminent British statistician once published a comment in Nature (June 25, 1885 “Measure of Fidget”) that correlated boredom by how the audience squirmed during particularly wearisome presentations.  I wish I would’ve thought of this “amusing way of passing an otherwise dull” lecture before attending two statistical conferences over the last several weeks.  Based on this 2005 assessment of “Nodding and napping in medical lectures”, the more things change the more they stay the same, at least so far as presentations are concerned.  The only difference is cost.  For example, the authors figure that at a typical 1 hour talk to 100 high-powered professionals, say master statisticians, perhaps as much as $20,000 goes up in snores.

“Nodding was common, but whether in agreement with the speaker or in reverie remains undetermined.”

— Kenneth Rockwood (Dalhousie University), Christopher J. Patterson, McMaster University, David B. Hogan (University of Calgary)

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Bonferroni of Bergamo

Bonferroni corrected

Uncorrected (random results)

I enjoyed a fine afternoon in the old Citta Alta of Bergamo in northern Italy – a city in the sky that the Venetians, at the height of their power as the “most serene republic,” walled off as their western-most outpost in the 17 century.

In statistical circles this town is most notable for being the birthplace of Carlo Emilio Bonferroni.  You may have heard of the “Bonferroni Correction” – a method that addresses the problem of multiple comparisons.

For example, when I worked for General Mills the head of quality control in Minneapolis would mix up a barrel of flour and split it into 10 samples, carefully sealed in air-tight containers, for each of the mills to test in triplicate for moisture.  At this time I had just learned how to do the t-test for comparing two means.  Fortunately for the various QC supervisors, no one asked me to analyze the results, because I would have simply taken the highest moisture value and compared it to the lowest one.  Given that there are 45 possible pair-wise comparisons (10*9/2), this biased selection (high versus low) is likely to produce a result that tests significant at the 0.05 level (1 out of 20).

This is a sadistical statistical scheme for a Machiavellian manager because of the intimidating false positives (Type I error).  In the simulation pictured, using the random number generator in Design-Expert® software (based on a nominal value of 100), you can see how, with the significance threshold set at 0.05 for the least-significant-difference (LSD) bars (derived from t-testing), the supervisors of Mills 4 and 7 appear to be definitely discrepant.  (Click on the graphic to expand the view.) Shame on them!  Chances are that the next month’s inter-laboratory collaborative testing would cause others to be blamed for random variation.

In the second graph I used a 0.005 significance level – 1/10th as much per the Bonferroni Correction.  That produces a more sensible picture — all the LSD bars overlap, so no one can be fingered for being out of line.

By the way, the overall F-test on this data set produces a p value of 0.63 – not significant.

Since Bonferroni’s death a half-century ago in 1960, much more sophisticated procedures have been developed to correct for multiple comparisons.  Nevertheless, by any measure of comparative value, Bergamo can consider this native son as one of those who significantly stood above most others in terms of his contributions to the world.

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Stat-Ease Corporation celebrates 25 years in business

My business partner Pat Whitcomb started up Stat-Ease as a business entity in 1982,* but he did not incorporate it until June of 1985.  So that brings us to 25 years as a Corporation this coming month.  This is quite an achievement for a software publisher – not many remain since 1985, I’ll wager, especially ones so specialized as us.  That’s our saving grace, I figure – sticking to a niche like a clam in a wave-beaten hollow.

According to this report on U.S. Small Business Administration Office of Advocacy statistics from September 2009, only half of all startups survive five years.  This correlates with a decay curve posted by Scott Shanem Professor of Entrepreneurial Studies at Case Western Reserve University, which shows that only about a quarter of companies remain alive after ten years.

I’d say we’ve done very well to make it this far.  Having weathered the recent economic downturn in good shape, I feel positive about continuing on for at least a few years more. 😉

PS. If you’re interested to learn more about us, check out this history of Stat-Ease.

*The year the word “internet” was used for the first time according to this timeline.  Check out these photos from the 1980’s by the Computer History Museum, especially the Osborne “portable” (24 pounds!) PC with a screen that looks about the size of today’s internet-enabled smart phones.

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Test and evaluation of the Great Panjandrum – a spectacular failure for weaponry

When time becomes available – mainly while I do cardio-exercise on my home elliptical, I’ve been watching a classic 26-episode BBC series on The World at War that my oldest son gave me.  It’s extremely compelling – rated 9.7 out of 10 by over two thousand voters at the Internet Movie Database (IMDb).

This morning I watched the chronicle of D-Day.  Being that I just returned from the Annual National Test & Evaluation Conference by the National Defense Industry Association (NDIA), it was interesting to see what the boffins of Britain invented to defeat the defenses put up along the Normandy beaches.  Perhaps the most amazing device was the Great Panjandrum, a rocket-propelled cart, which according to this write-up for Wikipedia was developed by the Admiralty’s Directorate of Miscellaneous Weapons Development.  (One wonders about the “miscellaneous” bit.)  The clip I viewed on the spectacular failure of the Great Panjandrum can be seen (along with other incredibly-inept military devices for D-Day) in a video on British Secret Wartime Follies posted in this article by UK’s Daily Mail.  Check it out!

PS. The Brits continue to come up with the most audacious inventions, such as this flame-throwing moped developed as a deterrent against derelict drivers competing for motorway lanes.

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Rabid for numbered bones

I am absorbing a great deal of information from the 2009 American Statistical Association’s Quality & Productivity Research Conference at IBM’s Watson Research Center in Yorktown Heights, New York.   However, since IBM sold off their PC business to the Chinese manufacturer Lenovo, I am not quite sure what’s being researched at this facility.  The official word is that IBM now provides “solutions.”  See if you can puzzle things out from this 2009 newsletter .  But, for those who are hard-core ‘techies’, check out this impressive list of IBM R&D projects, which include such things as quantum mirages and blue genes.

IBM presents an impressive collection of calculating devices in the lobby of this R&D center.  For example, see pictured an actual 1617 set of Napier’s bones made by the Scottish inventor of logarithms.  Via a process called rabdology (from the Greek “rabid” for rod, and “logos” for calculating), these numbered rods of skeletal origin facilitated multiplication and the computation of square and cube roots.  

PS. Coincidentally, I just saw the latest Star Trek movie.  Being an engineer by profession, I am naturally drawn to the character Scotty.  Having seen what his ancestor Napier did with bones (not to be confused with the Star Trek doctor “Bones”), I now understand why the Enterprise engineer is such a wizard.   Given enough time, these Scots will solve any technical problem.   “I canna change the laws of physics! I’ve got to have thirty minutes.Napier's bones

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