Friday, August 8, 2014

Gödelized Codes


This was described in "The Gold at Starbow's End" by Frederick Pohl in Analog Science Fiction / Science Fact, April 1972. The example here is mine.

Write out the plain text message.  Encipher each letter with a prime number in sequence: 1, 2, 3, 5, 7, 11, 13, 17, 19, ... Then, use the alphabet position of the letter as an exponent.  A=1, B=2, C=3, D=4, and so on.  Raise the prime number to the exponent and you have an integer.  Multiply all the integers of the text into one large number.  


HIDE A BAD FACE


TEXT
H
I
D
E

A

B
A
D
PRIME
1
2
3
5

7

11
13
17
POSITION
8
9
4
5

1

2
1
4
FACTOR
1^8
2^9
3^4
5^5

7^1

11^2
13^1
17^4
INTEGER
1
512
81
3125

7

121
13
83521

TEXT
F
A
C
E
PRIME
19
23
29
31
POSITION
6
1
3
5
FACTOR
19^6
23^1
29^3
31^5
INTEGER
47045881
23
24389
28629151


The product of all the integer factors for this one artificially easy example is over

4,739,426,072,295,360+ sextillion.  


Using the Preamble to the Constitution - "We the people of the United States..." - the H enciphers to 3^20 or 3486784401 and the first P is more than 45949729863572200.

The message conveys meaning only when it is deciphered.  It is easy to see that the longer the message, the harder that will be.  It quickly surpasses any theoretical computing ability and soon requires more time than is in the universe. 

That being true, it remains that the single large integer does uniquely contain that information and no other.


The method was name for Kurt Gödel. “In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was used by Kurt Gödel for the proof of his incompleteness theorems. (Gödel 1931).” Wikipedia here


Monday, August 4, 2014

Firefighters

At the checkout of my local HEB Grocery Store, the guy behind me had a cake: "Good luck ...  Manchaca Fire Department..."  I handed him my card, and said that although I am a technical writer, my degrees are in criminology.  "You  don't get that with police," I said, indicating the cake.  "No?" he asked.  "I would not expect it," I replied.  We thanked each other and I left.  The police are necessary and important; without them, you have a failed State.  That being so, nonetheless, firefighters live the hardest line of the highest virtues in protection of the lives and properties of others.    

FEMA has a ton of statistics that necessarily hide the people. The Yarnell Hill Wildfire of 2013 took 19 City of Prescott firefighters. 

On June 18, 2007, nine firefighters died when the roof of a burning warehouse collapsed. One witness called it “a tornado of fire.” They entered the building to search for one person reportedly still trapped inside. Although this was the worst loss since 9/11, multiple fatalities are common in firefighting.  

At the same time, their continuous-duty cycles – living at the station for one to  three days at a time – means that they have other jobs, other careers, other concerns that take them away. That creates a challenge for the chief who needs to maintain levels of competency and efficiency. Furthermore, the rigorous, on-going education makes a trained firefighter valuable to any department; and that reinforces any desire to move away from a community to pursue those other careers.



"If his intuitions are unclear, he will call in a captain to meet the prospect, but,  generally, as long as the legal requirements are met, what counts most is impressing the chief as someone who is professional and community-oriented." “We have 32 people here with 32 personalities,” he said. His firefighters come from all of the diversity groups in his  community. “You take them as they are,” he said, “a perfectionist or a slob. You learn their personality and live with it and you get used to it. We rely on each other. Police are  trained to be loners. Firefighters are trained to be a team.”

[From A Taxonomy of Teamwork, term paper  for Business Management 386: Organizational Behavior and Theory, Dr. Richaurd Camp, Eastern Michigan University, Summer 2007.]


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Thursday, July 31, 2014

Whitman Publishing: Fact and Value in Numismatics


Since the very first Red Book in 1946, Whitman Publishing has supported the hobby and science of numismatics with the annual “Red Book” and “Blue Book” price guides.  Over the past 20 years, their renewed effort continues to deliver high-quality, authoritative books, lavishly illustrated, at affordable prices.   Whether your interest is in American coinage, North American paper money, ancient coins, merchant tokens, or medals, Whitman has a reference book that will illuminate the known facts and excite your curiosity for what remains to be discovered.

You can buy it at any coin store and at
most book stores and you can find it used
at your library sale
The Red Book (A Guide Book of United States Coins by R. S. Yeoman and Kenneth Bressett) is the standard reference for U.S. coinage, including federal, colonial, pioneer, merchant, and other issues.  It is centered on U.S. Federal coinage from 1794 to the present.  The book presents physical dimensions, grading standards, approximate valuations, history, and a bibliography of authorities for each issue.  Most people have never seen a half cent, 2-cent, 0r 3-cent coin.  The “trimes” were struck on both silver and copper-nickel.  The $4 gold “Stella” was a pattern piece intended to induce Congress to join the Latin Monetary Union of France, Switzerland and 20 other nations.  It was not successful.  The 20-cent silver was also intended to bring the U.S. into the international arena. It also failed. 

If you inherit a trove of coins from an old relative, what are they worth?  The Red Book will tell you, approximately.  The prices here are the best guess for the retail price that a collector would pay.  A dealer will pay less, of course.  For that, the companion Blue Book of wholesale sell prices is somewhat more accurate.  But the Blue Book lacks all the history and narrative.  So, we use the Red Book and figure that dealers will pay 40%... 50%... or 60% less…  Except, of course, for the coins that even they cannot easily get, such as the 1877 Indianhead Cent or 1848 CAL $2.50 quarter Eagle gold.
Found at Mass Retailers and Big Box Stores
No Pioneer Gold or other Extraneous Issues
Just US Federal 1794 to Present
       The Official Red Book: A Guide Book of United States Coins (Professional Edition) by R. S. Yeoman; Kenneth Bressett, series editor; Jeff Garrett, valuations editor; Q. David Bowers, research editor. (Whitman Publishing LLC, 2009.)
         Criticisms of the “Professional Edition of the Red Book” appeared on the numismatic discussion boards and email lists as soon as it was announced. The new, larger format (full 8½ x 11) was a surprise. Suspicion that this “inside” information was denied to collectors who bought the “ordinary” Red Book had a reverse side: Is this all of the professional information, or are they holding back?  Why did they create two Red Books, instead of just incorporating all of the information from both into one book?  Finally, many collectors wanted to know, “Is it worth buying?”
            To take the last point first, the cover price is $29.95, which is a small investment for the information in this 383-page compendium of auction summaries, historical background, type and variety details, high resolution illustrations, and market insights.
            As for the arrays of information, the easiest view is that the Professional Edition presents details on only the high-value coins in each series. For Morgan Dollars, only Mint State grades are tabulated, while for early Large Cents to 1814, VF grades are included. Although V-Nickels and Buffalo Nickels are priced EF-40 and above, data for Jefferson Nickels begins with MS-64 Full Steps. Generally, grading stops at MS-65 and Proof-65. Populations and markets become too thin. However, for Roosevelt Dimes up to 1964 grades run MS-63, 65, 66, 67, and 68, whereas after 1965, only the four highest grades are priced. In short, the editors have taken great care to present the information actually needed by professionals when faced with a certain coin of a certain type, date, and mint.


American Silver Eagles (2nd Edition) by John M. Mercanti, with Michael "Miles" Standish. Whitman 2013. 166 + ix pages. $29.95.
American Gold and Platinum Eagles by Edmund C. Moy. Whitman 2014 212 + x pages. $29.95.

Personally, I never gave them much thought... Then I read a collectors’ discussion board thread on “Counterfeit Eagles.” Moreover, they are not merely bullion, but collectibles in their own right, with long histories, and varieties. Note, however, that as true moderns (“post moderns”?), their characteristics are not those of the classic coins. “First Strike’ certification may remain as arguable as any other grading point but the markets seem to continue supporting them. “Burnished” coins join Regular and Proof designations. Is a Burnished MS-70 worth more than a Proof 70? Apparently so.

Morgan Dollar: America's Love Affair with a Legendary Coin Featuring the Coins of the Coronet Collection by Michael "Miles" Standish with John B. Love; Forward by John M. Mercanti. Whitman. 2014. 154 + v pages, 8-1/2 x 11. $29.95.

PCGS ranked this as the finest collection of Morgan Dollars. But this is not a VAM book. Each of these wonderful coins is just an example of an issue - but the highest known grade, including those that are Deep Mirror Prooflike (DMPL). Looking at the numbers on each page, it is astounding how rare certified coins are. 5 million... 8 million... 11 million struck, but only a few thousand certified; and of those only a few hundred are of the highest grades.


Of course, there is more to numismatics than grading. This book provides an insightful - sometimes quirky - history of the Morgan Dollar, placing it in its cultural context. Knowledgeable collectors will identify the goddess on the obverse as Anna Williams of Philadelphia. Perhaps not, says Standish, citing a Coin World article from 2002 that revealed a letter from George Morgan denying that any one model served for Miss Liberty.

This book also delivers an in-depth analysis of pricing as cited in the Red Book.

Carson City Morgan Dollars Featuriing Coins Of The GSA Hoard by Adam Crum, Selby Unger and Jeff Oxman. Now 130 + v pages, still $24.95, with new photographs from historical archives, "revisions from ongoing research" and the usual tables of reliable price estimates. The GSA Hoard made headlines in October 1972. The release of 2.9 million Carson City Dollars drastically changed the markets as rarities became common. They continue to live a life of their own, still collectible as GSA Hoard Dollars.  Carson City Morgan Dollars are one of the many niches that reward detailed study and careful collecting. The new handbook from Whitman is a nice introduction to a fascinating array of coins and people. As the price of silver broke away from mint parity in the early 1960s, collectors exhibited a “feeding frenzy” for silver dollars. In March 1964, the US Treasury halted the exchange of silver dollars. The Congressional Joint Committee on Coinage called on the Government Services Administration to operate a mail bid sale for the remainder of the inventory, about 10% of which were discovered to be from Carson City. The GSA created an “A Team” of experts to grade the coins for sale, including John J. Pittman, Amon Carter and Margo Russell.

Colonial and Early American Coins by Q. David Bowers, Atlanta: Whitman Publishing LLC, 332 pages. $49.95

Q. David Bowers has outdone himself. Far more than yet another interesting book about fascinating highlights in numismatics, Colonial and Early American Coins is a new standard reference for the new century. That is highly appropriate because as divisive as our politics can be – Howard Fast to Ayn Rand; Al Franken to Ann Coulter – perhaps no period of American history collects liberals and conservatives, paleos and neos, traditionalists and libertarians, as does the colonial and early federal. Proof of that is the fact that the popular edition of this book is sold out. (The premium binding is still available as of this writing, July 2009.)
            “Colonials have always played to a fairly lively market, but a small one in comparison to federal coins,” Bowers replied to me via email (04/30/2009). “I am not aware of any time in American numismatic history, from the 1850s when collecting became popular, down to the present day, that, for example, a basic 1652-dated Pine Tree shilling in Fine grade has declined in value. A charting at ten-year intervals will show an increase. The reason for this is that Colonial coins have little if any interest to “pure” investors or speculators. Instead, the market has been completely comprised of buyers who are interested in Colonial coins and their history, and who cherish their ownership.”
            Like other works in the Whitman Encyclopedia series of books, this volume also adheres to a standardized format that meets the most important needs of the broadest set of collectors. Each entry has a new Whitman number along with the variety numbers from the previous standard references, Ryder, Maris, etc., and an estimation of rarity. Most of the entries carry a vector of prices for grades Good through Mint State. (Others are seen too seldom at auction.) 
            In addition to Bowers’ efforts, Ken Bressett was tapped for a Forward and the valuations were reviewed by Lawrence Stack. Introductory chapters on colonial economics and minting methods provide a contextual foundation. The third chapter delivers a historical overview of the collecting of these coins and tokens, including famous sales. Special attribution guides for Connecticut, New Jersey and Fugio issues bring the fruits of 150 years of numismatic study to today’s collectors.

Harlan Berk’s 100 Greatest Ancient Coins.   “Knowledge is king,” said Harlan J. Berk, asking rhetorically, “Do you have a Hannibal portrait versus just another Melqart?”  For Berk, learning is a lifelong process, and writing 100 Greatest Ancient Coins exemplified that. “Syracuse was founded on a small island and then moved to Sicily. The four dolphins [on their large silver coins] represent the sea. I had not known that. If I did not, then others probably did not as well.”
            To validate the book, Berk relied on his extensive network of personal friends and professional contacts in numismatics. Among them were Alan Walker, Ute Wartenberg Kagan, Curtis Clay and Phil Davis.
            The tally of one hundred coins came from a poll the world’s hundred best numismatists.  “I chose the group,” Berk said. “I gave [Whitman] the names of a hundred or so academics, collectors, and dealers from around the world.” Each person in this group submitted their own list of a hundred or so aesthetically superior or historically important issues. All of the polling was requested, accepted and compiled via emails. Perhaps not surprising in an antiquarian, Berk himself is not an engrained user of electronic media. His own preference would have been for paper and postage. Nonetheless, he remains satisfied with the final inventory. This same group provided the experts who reviewed the essays.
[Portions of these reviews were published in other venues.]

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Art and Copy

Wednesday, July 23, 2014

U.S. PATENT LAW DOES NOT ADD UP


Being derived from medieval concepts about land, U.S. patent law lacks an objective basis for awarding ownership rights in intellectual property. 

Land is excludable: you can keep someone from it with a fence. Land is rivalrous: no two people can stand in the same place at the same time.  According to the economic theory of public goods, knowledge is non-rivalous and non-excludable: sharing knowledge does not diminish its quantity; and you cannot prevent someone from knowing what they know. Thus, it is generally true that you cannot get a patent on a mathematical theorem.
See 35 U.S.C. §101: Subject Matter Eligibility• The four statutory categories of invention:– Process, Machine, Manufacture, or Composition of Matter and Improvements Thereof• The courts have interpreted the categories to exclude:– “Laws of nature, natural phenomena, and abstract ideas”• These three terms are typically used by the courts to cover the basic tools of scientific and technological work, such as scientific principles, naturally occurring phenomena, mental processes, and mathematical algorithms.Evaluating Subject Matter Eligibility Under 35 USC § 101: August 2012 Update  Office of Patent Legal Administration United States Patent and Trademark Office here.
However, patents have been awarded for mathematical ideas. Of course a plethora of patents exists for computer software, even though a program is only an algorithm, a method of calculation.

US Patent 4133152 A was awarded to Roger Penrose for “Set of tiles for covering a surface.”  (Patent here.)

http://mathworld.wolfram.com/PenroseTiles.html
A set of tiles for covering a surface is composed of two types of tile. Each type is basically quadrilateral in shape and the respective shapes are such that if a multiplicity of tiles are juxtaposed in a matching configuration, which may be prescribed by matching markings or shapings, the pattern which they form is necessarily non-repetitive, giving a considerable esthetic appeal to the eye. The tiles of the invention may be used to form an instructive game or as a visually attractive floor or wall covering or the like.” – US Patent 4133152A

A Penrose tile is a “non-periodic tiling generated by an aperiodic set of prototiles. – Wikipedia.

The Penrose tiles are a pair of shapes that tile the plane only aperiodically (when the markings are constrained to match at borders). These two tiles, illustrated above, are called the "kite" and "dart," respectively. In strict Penrose tiling, the tiles must be placed in such a way that the colored markings agree; in particular, the two tiles may not be combined into a rhombus (Hurd). – from Wolfram here. 
Penrose Tiles and Trapdoor Ciphers … and the Return of Dr. Matrix 
by Martin Gardner. 
Washington DC: Mathematical Association of America, 1989. 
"Because the tiles lend themselves to commercial puzzles, [Roger] Penrose was reluctant to disclose them until he had applied for patents in the United Kingdom, United States, and Japan.  The patents are now in force." Penrose Tiles and Trapdoor Ciphers … and the Return of Dr. Matrix by Martin Gardner. Washington DC: Mathematical Association of America, 1989, Page 6.
So, mathematical ideas can be patented if you claim that the theorem is a puzzle (or has some other physical instantiation).  

Mathematician David A. Edwards asserts that no economic distinction can be made between a discovery and an invention. 
From an economic point of view, there is no rationale for distinguishing between discovery and invention, and we would advocate dropping entirely any subject matter restrictions whatsoever on what can be patented. One should be able to patent anything not previously known to man. In fact, a good economic case can be made2 for allowing the patenting of many things that are well known but are not being commercially produced.
 “If we're going to have a general patent system, then algorithms should be as patentable as lasers. For example, general relativity is used in GPS…  My colleague Carl Pomerance developed fast primality testing algorithms in the late 1970s but couldn't patent them. My colleague Victor Wickerhauser developed the fast wavelet transform in the early 1990s and was able to patent it as a software patent.  … If we want these things to be patentable, then Congress needs to change the law.”  (“Platonism Is the Law of the Land,” David A. Edwards
April 2013 Notices of the AMS Volume 60, Number 4 pp475- 478 here
Intersecting the discursive plane from another angle, mathematician Robert Palais points to the low esteem in which the USPTO holds mathematics. 
   an applicant to practice before USPTO must demonstrate, in accordance with the USPTO’s requirements, that he or she possesses scientific and technical proficiency sufficient to address issues that arise in patent law. Notably, however, mathematics is explicitly excluded as a subject for this purpose. …   I downloaded the “General Requirements Bulletin for Admission to the Examination for Registration to Practice in Patent Cases Before the United States Patent and Trademark Office” to see for myself. It lists 32 subjects in which bachelor’s degrees exhibit adequate proof of the necessary scientific and technical training, as well as 2 1/2 pages of acceptable alternates. Then it states the “Typical Non-Acceptable Course Work: The following typify courses that are not accepted as demonstrating the necessary scientific and technical training:” and in the middle of this paragraph, there appears: “…machine operation (wiring, soldering, etc.), courses taken on a pass/fail basis, correspondence courses, …home or personal independent study courses, high school level courses, mathematics courses, one day conferences, …”  … Ironically, USPTO requires mathematics coursework for prospective examiners in the computer arts (employees) that it doesn’t recognize as qualifying for practitioners.
 This is not a debate regarding the appropriateness of patenting mathematics. There have been many such conversations elsewhere. But in these times that mathematics is becoming increasingly visible in valuable patents (e.g., Google’s Page Rank, a linear algebra algorithm, was licensed by Stanford for US$336 million) it seems that the USPTO should be encouraging, not discouraging, the mathematical fluency of the lawyers whose work it recognizes. —Bob Palais, Math Dept., Pathology Dept. University of Utah, Notices of the AMS, January 2010, page 9,  here. 
Euclid's Proof of the Pythagorean Theorem
Proposition 47 Book 1.
(Not Socrates's Demonstration,
which Plato and the USPTO say that you were born with.
Too bad you were not born with this one.)
Plato believed that mathematics exists within you to be discovered by introspection.  In the Dialog of Meno, Socrates draws out from a slave an application of the Pythagorean theorem to show the doubling of an isosceles right triangle.   The so-called “Socratic method” favored by many teachers assumes that this knowledge is inherent within you.  That is the epistemology of the US Patent and Trademark Office.  Mathematics need not be invented – or even discovered by external exploration – because we all have it in our heads.   That theory just does not add up.

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