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Fun With Statistics

Razor's Edge

Once upon a time, a Customer called to complain that our beverage cans held too much beer. This could be a problem because the Benevolent Government, ever alert to our well-being, or at least to their own revenues, taxes alcoholic beverages on the nominal package volume. A 12-oz. can is presumed to hold 12 oz. of beer at 3.4% alcohol by weight and is taxed accordingly. If it holds more than 12 oz. then the brewer is giving away free beer and (more importantly) not paying taxes on the extra fraction of a percent of an ounce. ATF has never reconciled with the end of Prohibition.

The primary control measurement is called "Overflow Capacity," which measures the volume of fluid the container can hold up to the tippy-top. The ASTM "Wet Fill" method of making the measurement proceeds as follows:


America's Next Top Model -- Part III

Razor's Edge
Top Models.  Let's sexualize kids.
What could possibly go wrong?
Resuming our discussion of modeling from Part I and Part II...

Recall that in his Nobel laureate speech, "The Pretence of Knowledge," Friedrich August von Hayek (the father, we may suppose, of Freddy September) pointed to organized complexity as a major issue in economics and similar fields:

Organized complexity... means that the character of the structures showing it depends not only on the properties of the individual elements of which they are composed, and the relative frequency with which they occur, but also on the manner in which the individual elements are connected with each other. In the explanation of the working of such structures we can for this reason not replace the information about the individual elements by statistical information, but require full information about each element if from our theory we are to derive specific predictions about individual events. Without such specific information about the individual elements we shall be confined to what on another occasion I have called mere pattern predictions - predictions of some of the general attributes of the structures that will form themselves, but not containing specific statements about the individual elements of which the structures will be made up. [Emph. added]

In classical thought, the part that depends on "the properties of the individual elements of which they are composed" is the material cause, a/k/a "reductionism." (The term 'matter' means simply the elements of which a thing is composed. Bricks are the matter of a wall.)

The part that depends on "the manner in which the individual elements are connected with each other" is the formal cause. In modern parlance this is sometimes called "emergent properties" because the whole system has the property while the individual elements do not.

In other words, it's the form (pattern, organization) that is the key to intelligibility. Given a set of interconnected elements X1, X2,... Xn, we cannot legitimately replace the specific Xs with X-bar as we may in cases of disorganized complexity. At best we would obtain only statistical conclusions about the entire system -- as we do in fact regarding quantum mechanics.

When there are only a few elements in the system, the scientist introduces simplifications: infinite Euclidean space, ideal gasses, perfectly elastic collisions, and the like. Arrhenius' law relating CO2 to temperature assumes the atmosphere extends to infinity. TOF read a joke - he has forgotten where - about using models to predict the SuperBowl, which is a sort of football game sometimes (but not this past year) played by two teams. In the punchline, the physicist says, "consider each player to be a perfectly elastic sphere on an infinite Euclidean field..." Mathematics tends to become ornery when bumping up against boundary values* and it is precisely at the extremes where many models pop their suspenders.
(*) boundary values. TOF has his old college text, Fourier Series and Boundary Value Problems, by Ruel Churchill, which he will someday nerve himself to re-read.

Disaster at Lunacon!

Razor's Edge
TOF was "special guest" at Lunacon this past weekend, and very special he was. He got to wear a ribbon like unto a prize steer at the stock show and had melons placed under his arms. In return, he sat upon certain Panels, picked a Winner at the Art Show, and started a presentation on THE GREAT PTOLEMAIC SMACKDOWN.


TOF at Lunacon

Razor's Edge

TOF is "special guest" at Lunacon this weekend.  If you're near the RyeTown Hilton, here is his schedule AFAIK

  1. Fri 4:00 PM     Character Building     Bartell     Your clever plot twist or interesting theme will mean nothing if readers don't care about your characters. The panelists will discuss techniques to use to make sure your characters are memorable and that the story is about them.

  2. Fri 10:00 PM  Rules! Rules????? There are no Rules!   William Odelle     When writing fiction, if it works, it works. Our panel debates whether authors need to know "rules" that they can then break if they are good enough, or if this only constrains creativity.

  3. Sat 11:30 AM     Reading: Michael Flynn     Elijah Budd

  4. Sat 2:00 PM     Alternate History That Isn't About War    William Odelle   Can't we imagine alternate history about something other than the outcomes of battles. Think of how history might have changed if certain IDEAS had formed differently or come at different times.

  5. Sat 3:00 PM     Magic and Religion   Westchester Ballroom A2   How do Magic and Religion intertwine?

  6. Sat 4:00 PM     Autographing: Michael Flynn     Westchester Assembly      

  7. Sun 1:00 PM  The Great Ptolemaic Smackdown     Westchester Ballroom B     How the heliocentric world replaced the geocentric one against all evidence and common sense.


America's Next Top Model -- Part II

Razor's Edge
PREVIOUSLY, WE DISCUSSED the emergence during and after WW2 of model-building as a means for dealing with organized complexity, a distinctions, first made in 1948 by Dr. Warren Weaver:

  1. Organized simplicity. Systems with few elements. Analyzed mathematically.

  2. Disorganized complexity. Systems with many elements acting randomly. Analyzed statistically.

  3. Organized complexity. Systems with many interconnected elements. Analyzed with operations research/model-building methods.

George Box said that "all models are wrong" because of the uncertainties to which models are subject. Honest modelers are obligated to assess these uncertainties and to inform their clients of them. Alas, too few do, and models are presented, understood, and press-released as being more certain than they actually are.

Joe Martino tells TOF that "One of the most horrible examples I ever encountered was the use of a Cobb-Douglas Production Function to predict the effectiveness of bombing the Ho Chi Minh trail. When I first saw the model it fairly screamed 'wrong!' But the people who put it together saw nothing wrong with it."

And yet, these things have so many pretty equations they seem like they damn well ought to work. And they do, in some cases. Kingsbury Bearings has a model for hydraulic bearings that works well in predicting the performance of new bearing designs.* So what's the problem?  Operationally, what is the difference between a model that is "useful" and one that is "true"?
(*) hydraulic bearings. TOF digresses. At the entrance to the Kingsbury plant is a placard honoring the Kingsbury Bearing installed in Holtville #5 in 1912. TOF inquired of his hosts in the 1980s when he spent some time with them: "How long did it last?" "We don't know yet," was the response. "It's still running." As of 2008, it was still running with an estimated TTF of 1300 years. That's craftsmanship!

The Incomparable Marge

Razor's Edge
celebrates another birthday, and immediately Western Christendom goes into forty days of fasting and mourning.

What's Wrong With the Cosmos?

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Cosmos: A Spacetime Odyssey - Standing Up in the Milky Way
Season 1 Episode 1
Giordano Bruno's spiritual epiphany about the universe; a compressed version of the cosmic calendar.

'Nuff said.

Spare a Moment to Remember

Razor's Edge
before the last living memories are gone and the revisionists take over.
Today at breakfast, Pere mentioned that it was the 69th anniversary of the flag raising on Iwo Jima.  When TOF was a kid, we asked him where he was in the famous photograph.  I was in front, he said. I called out, "Put the flag here!" and then kept going while they snapped the picture.  We were young and naive and believed him. But he also told us that he had been killed in the battle, and we believed that, too, and burst into tears at the tragedy. Later, we figured it out.  Hey... Wait a minute...


At Twenty-Three

Razor's Edge
This article:  David Wise’s alternative lifestyle leads to Olympic gold, contains a remarkable paragraph; to wit:

At only twenty-three years old, he has a wife, [Alexandra], who was waiting patiently in the crowd, and together they have a two-year-old daughter waiting for them to return to their home in Reno, Nevada. At such a young age, Wise has the lifestyle of an adult. He wears a Baby Bjorn baby carrier around the house. He also attends church regularly and says he could see himself becoming a pastor a little later down the road. Not exactly the picture you had in mind while watching him nail two double corks wearing baggy pants.

TOF will pause here to allow Faithful Reader to ponder this and determine what is wrong.


TOF in Italian

Razor's Edge
A popular TOF post is now available in Italian.  The faithfulness of the translation and the nature of the site on which it appears is so far unknown.


Razor's Edge

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