The mystery and transcendence of pi

Today is National and World Pi Day because the numbers of the day (3-14) match the first three digits for pi or π, the Greek letter, 3.1415926535897… Although most people think that π is relegated to just geometry and trigonometry, the number pervades all of mathematics and the natural sciences, even statistics.

Several thousand years ago the Egyptians, the Babylonians, the Chinese and the Ancient Greeks tried to make sense of the world through mathematics, an abstract way to envision and explain the operations of Nature, not as the activities of the gods. Over time geometry developed, which could explain much of the world. For example, Euclid and his various axioms were employed to describe much of the natural world. However, when it came to circles and non-linear lines, there remained a mystery among all the Ancients, which was π.

It had long been recognized (and still taught to reluctant students in high school geometry) that the ratio of the circumference of any circle to its diameter is a constant. The Ancients knew this, but the value of that constant eluded them. They realized, however, that there were approximations, e.g., the fractions 25/8, 22/7, 256/81, etc., that were close, and these fractions were employed for centuries as substitutes for pi.

Over two thousand years ago Archimedes carried this approximation technique to its logical limit, using techniques akin to calculus infinities approaches, and was able to obtain very close estimates of π to whatever tolerance was needed, e.g., through circumscribing and inscribing large numbers of polygons, e.g., an algorithm employing up to 96 such polygons for an accuracy between 3.1408 and 3.14285, about 99.9% accuracy. But, around the year 480 A.D., Chinese mathematician Zu Chongzhi used this approach with 12,288 polygons, and created a far more accurate fractional approximation, 355/113, roughly 99.99999% accurate, which was the best approximation for π for the next 800 years.

As a side note, through recent discoveries, Archimedes is also credited with understanding aspects of calculus long before Newton and Leibnitz, who developed differential and integral calculus just over three hundred years ago. Had the Roman soldier not killed Archimedes in the siege of Syracuse, our world may have been very different. But, I digress.

Clearly, these fractional representations of π were all approximations and not a pure answer, which galled the Ancients at their inability to solve the conundrum. Indeed, the purity in mathematics was at the heart of Euclidian geometry’s goals of solving problems. For example, in their effort to solve the π enigma, the Greeks were famous in their efforts to “square the circle,” i.e., geometrically constructing a square having the same area as a given circle, and asking whether Euclid’s axioms posit the existence of such a number. However, the Greeks and many others later could not do it, which had profound implications to Plato regarding the usefulness of Euclid’s theorems or even mathematics to actually describe the real world. In short, the quest was impossible. But why?

With Euclid and the pre-Socratics trying to explain the world in physical ways, e.g., Democritus postulating atoms in a very logical way 2,500 years ago, it is sad that the mystery of π seems to have derailed the very influential thinkers Socrates and Plato to fully trust mathematics. Accordingly, Plato looked to another realm to describe the world: using his forms or abstractions. For example, the concepts of a circle and π were perfect, idealized forms, but every attempt to depict them in the real world would, by definition, be imperfect. This philosophical view held sway until the Renaissance started new ways of thinking.

But, back to π. We now know that pi is both Irrational and Transcendental. An irrational number is defined as a number that is not a ratio of two whole numbers, i.e., fractions. This irrationality of pi is strongly suggested by Archimedes’ and others’ succession of better and better fractional approximations, without a final answer. Also, with computerization it has been found that the digits of pi have no pattern, and for several trillion digits pass the mathematical test of normality, i.e., all of the digits appear equally often in the series. The irrational nature of pi was formally proven in 1761.

A transcendent number is defined as a number that is not the root of any non-zero polynomial with rational coefficients, which is a modern way of saying you cannot square the circle.   The transcendence of π was proven in 1882. The staggering notion that the digits go on and on, without repeating or in any pattern to infinity, was (and remains) hard to grasp, the immensity of which was something well understood to Aristotle and others. Over a hundred years ago, however, mathematician George Cantor tackled the mathematical problem of infinity and actually demonstrated the nuances between infinities. π is also computed by various techniques, e.g., equations and trigonometric series, that have terms that go to infinity.

The use of the Greek letter π in this context dates from about three hundred years ago when the great mathematician Leonhard Euler started popularizing it. Mathematician William Jones in 1706 is accredited with being the first to symbolize the circle circumference-to-diameter ratio as π, which is also attributed to the Greek word for perimeter. Prior to computers, pi calculation was a laborious and very error-prone endeavor. With the advent of computing, the mere six or seven hundred digit manual calculations not too many decades ago have jumped to many trillions of digits.

Despite all of the mathematical rigor of the modern era, π remains a mystery, a constant that in a way is inconstant. Of course, there are many other such enigmatic irrational and transcendent numbers out there, e.g., e (2.71828182845…), but π is the oldest of these cosmic constants for us humans. On a related note, this is the 50th anniversary of Stanley Kubrik’s 2001: A Space Odyssey, an inscrutable movie that still contains innumerable mysteries. It is also the 20th anniversary of π, the movie, a psychological thriller about the irrationality of π and the human mind. In Star Trek, Mr. Spock crashed a hostile computer making it calculate pi precisely. π also pops up once and a while in TV shows, such as the Simpsons.

This magical number is everywhere, and is part of our lives – even if you hated high school geometry and math. Indeed, we are all still trying to understand the meanings of π.

 

Raymond Van Dyke is an intellectual property/patent attorney, educator and a science and technology enthusiast. He has a B.S. in mathematics/computer science and was admitted Pi Mu Epsilon, an honorary mathematics society, has an M.S. in Computer Science, and a J.D. from the University of North Carolina at Chapel Hill. He is the Chair of several organizations and teaches IP, technology law, the history of technology and IP. His website is:  www.rayvandyke.com.  A version of this article was published on ipwatchdog.com.

A Primer on Intellectual Property: The Basic Tools for You to Know

Tomorrow (February 1, 2018), I am presenting a Continuing Legal Education (CLE) program on the Basics of Intellectual property (IP) for the general attorney.  With the value of IP assets a large factor of our economy, general practice attorneys frequently face issues in this specialized field of law of patents, trademarks, copyrights, trade secrets and some other areas.  This CLE is designed to allow non-IP attorneys to know some of the basics, understand the vernacular and know something of the problem areas.

I am pleased that the Bar Association of Montgomery County (BAMC) Maryland has offered me this opportunity.  I am also a Chair of the IP Section of BAMC.

For those in the area, I hope that you can make it – whether you need CLE or not.  Here is the link: http://www.barmont.org/events/EventDetails.aspx?id=1062031&group=

Please feel free to contact me if you need additional information.

Copyright and the Game of Thrones

The enormous popularity of HBO’s Game of Thrones has driven many into a frenzy.  Just as the Night King appropriated Daenerys Targaryen’s dead dragon for his own uses, many viewers think that GoT episodes should be freely available for their own uses.   The extraordinary value placed on these episodes resulted in hackers cracking into various protected systems to download them and even hold HBO for ransom.  Although the GoT mania has died down with the end of the short Seventh season, the mania nonetheless continues somewhat as we enter the doldrums until 2018 and the final season.

The incredible efforts to get the episodes are in spite of the large penalties in play.  The basic damages for copyright infringement (unauthorized copying) are between $750 to $30,000 per work.  In other words, if you hack into a system and then post a file for others, the damages could be immense, e.g., for 1,000 downloads multiple the above numbers by 1,000 to get a sense of the damage scale possible.  If a judge deems the copying willful, i.e., done on purpose and not accidental, the damages can be increased to $150,000 per work.  There is also the possibility that you will have to pay the content owner’s legal fees, and the owner may be able to seize and destroy whatever copies you have, as well as enjoin or stop you from future such copying.

In addition to the civil liability, infringers, whether small-time or mass infringers, may also be committing a felony or a misdemeanor.  A felony charge must involve an infringement of the copyright owner’s reproduction or distribution rights, two of the various copyright rights.  Further, a felony conviction carries a maximum sentence of five years in prison and a maximum fine of $250,000.  Even though there has been some leniency in the past for  individual pirating, there is still a  risk that you will be made an example.  The legal fees alone  for defending such suits are large, and, as indicated, you may be paying both sets of attorneys.

In relation to the GoT copyright craziness, here is a Consumer Reports article that cites me on the penalties.  https://www.consumerreports.org/televisions/the-risk-of-watching-pirated-game-of-thrones-episodes/  I recommend reading their other articles.

If you are accused of copyright infringement, consult an attorney to assess your situation.  If you are small fry, you may not be worth the legal effort.  However, if you go after very valuable content, such as GoT, and/or indulge in massive file sharing, you are more of a target and  the liability can be staggering.  As a computer scientist, I understand the thrill of hacking.  However, as an IP attorney helping people, whether innocent or guilty, out of the problems due to their pirating activities, all I can say is that some content owners are meaner than Cersei Lannister in protecting what is theirs.

 

 

The Constitutional Foundations of IP – A Natural Rights Perspective

Despite the value of intellectual properties to the United States, there have been numerous efforts of late to curtail those rights, rights which were enacted by our Founders to encourage inventors and creators.  The Constitutionality of some of these rights is now in question, particularly now at the Supreme Court. Randolph May, writer of the recent book “The Constitutional Foundations of Intellectual Property,” will discuss this critical issue from the natural law perspective.  Raymond Van Dyke, IP practitioner and educator, will speak about the importance of IP to society then and now.

This Greater Washington, DC Licensing Executives Society Chapter event is on the evening of July 20, 2017 in Washington, DC.  Here is the event notice: http://www.lesusacanada.org/events/EventDetails.aspx?id=981094&group=160111

With the constitutionality of inter partes proceedings at the Patent Trial and Appeal Board of the USPTO now in question, the issue is quite pertinent, and the consequences quite serious to the patent system.

If in Washington, DC tonight, I hope that you can make it.

Ray, Greater Washington, DC Chapter Chair, LES

(202)378.3903  vandyke@acm.org

 

Roberts Rules of Order

The Supreme Court has been quite active fine-tuning the patent system and deboning the law of the Federal Circuits for many years.  Today is no exception.

In Impression Products, Inc. v. Lexmark International, Inc.  (May 30, 2017), Chief Justice Roberts took to task the Federal Circuit’s take on the law of patent exhaustion, i.e., whether a patentee upon a sale retains any rights to the sold object.  In this case, Lexmark tried to prevent other companies, such as Impression, from refilling Lexmark printer ink toner cartridges.  Obviously, the printer ink business is quite lucrative and it is no surprise that this case made it to the Supreme Court.

The Federal Circuit had earlier held that Lexmark’s proscriptions on refilling were acceptable, whether the sales were within the United States or abroad (for import).  The nuanced, decades-old jurisprudence of the Federal Circuit held patent law in special regard vis-à-vis other areas of law, and permitted limited controls post-sale.

Back in 2013, the same issue arose in a copyright dispute.  The Court there held that the first sale doctrine extinguished a copyright holder’s rights.  In that case, Kirtsaeng v. John Wiley & Sons, Inc., Kirtsaeng sold Wiley textbooks printed in Thailand on eBay for U.S. students.  The large price differential between the prices in the United States and Thailand made the venture profitable, much to the chagrin of Wiley who sued him.

Just as in Kirtsaeng, the Court today said restrictions or conditions on resale or use constituted unlawful restraints on alienation.   Thus, Lexmark cannot predicate their refilling policy on patent law.  They can, of course, seek coverage under licensing, contract law or another approach.  To Chief Justice Roberts, the patentee upon selling the object has obtained the full measure of the patent right, i.e., no rights remain and the patent right is exhausted.

Justice Ginsburg, who dissented in Kirtsaeng, dissented here.  In her dissent, she made several cogent points.  First, the patent system is different from the copyright system, which has an explicit first-sale statutory provision – unlike patent.  Second, the territorial nature of the patent system and activities in global commerce suggest different handling.  Foreign activities have no bearing on the existence of U.S. patent rights.  Also, the patent laws differ between countries, unlike the more uniform copyright laws, making the first sale exhaustion argument for patent weaker.

Nonetheless, Lexmark and other patentees will now have to take care to obtain a fair price for their products at the time of sale.  Roberts Rules of Order for IP are straightforward: the patent bargain must honed further, and the rogue interpretations of the Federal Circuit must be stamped out.  It is rather odd that the Court regularly condemns the Federal Circuit, yet often has zero alternative interpretation.  The Alice and other recent cases simply held that they did not like the interpretation of the Federal Circuit, and no substitute was proffered.  Here, however, we have a clear directive: you sell a patented item and that is all you get for it.

Supreme Court Messes with Texas

The Supreme Court today decided a monumental case in patent law regarding venue, i.e., where a patent plaintiff can file a lawsuit.  TC Heartland LLC v. Kraft Foods Group Brands LLC (May 22, 2017).  For a few decades, the operative venue standard governing where patentees could sue a defendant was 28 U.S.C. 1391(c): ” a defendant that is a corporation shall be deemed to reside in any judicial district in which it is subject to personal jurisdiction at the time the action is commenced.”  This broader “personal jurisdiction” standard was promulgated by the Federal Circuit’s interpretation of various Congressional amendments to this statute, which seemed to broaden venue over and above the more specific patent venue statute, 28 U.S.C. 1400(b).

In the case today, the Court discussed the law of venue from the Judiciary Act of 1789 through various Congressional changes to the venue statutes today.  The Court also cited Transmirra Prods. Corp. v. Fourco Glass Co., 233 F. 2d 885 (1956), where the Court expressly stated that the then 1391 statute did not supersede, augment or supplement the standalone 1400 statute, which exclusively governed patent cases.  Thus, the seminal Federal Circuit decision VE Holdings Corp. v. Johnson Gas Appliance Co., 917 F. 2d 1574 (Fed. Cir. 1990), which did just that, is now reversed, reflecting an ongoing trend of CAFC reversals.

The TC Heartland decision will greatly affect plaintiff patentee’s choices as to where to sue a defendant.  Indeed, under 1400(b), a company’s “residence” is their State of Incorporation,  which rather restricts the places to sue.  Plaintiff patentees will thus be less likely to file their infringement actions in the Eastern District of Texas, which over the last two decades or so has morphed into a haven for patentees, i.e., the juries in East Texas generally favor the patent system and patentees, driving the defendant corporations mad.

Time will tell how this new decision, on the backs of so many other Supreme Court narrowings of patent law, will impact the patent system.  Many corporations, desirous of insulating themselves from patent lawsuits, will continue their onslaught, via lobbyists and other means, to further derail the U.S. patent system.

Having practiced in the Great State of Texas (its legal name) many years ago, I can relate a humorous anecdote about the Eastern District courts.  In the 1970s and 1980s, the Texas federal courts, particularly in the Eastern District had specialized in personal injury (PI) cases.  With tort reform, however, these cases and the specialization of these courts became irrelevant.  So, the story goes that the courts there, as a means to perfect another area of specialization, focused on intellectual property, i.e., IP as opposed to PI;)  Perhaps the Eastern District will need to refocus again – with different letter acronyms.

World IP Day 2017 Redux

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The celebration of World Intellectual Property Day at the U.S. Patent & Trademark Office was held on April 26, 2017, where April 26th is the official anniversary date.

After the Chief Policy Officer of the USPTO, Shira Perlmutter, started the event, there where a number of distinguished speakers, including John Sandage, World Intellectual Property Organization (WIPO) Deputy Director General, Patent and Technology Sector, Joseph Ferretti, Vice President and Chief Counsel, Global Trademarks at PepsiCo, Inc. and President of the International Trademark Association (INTA),  Jeanine Hayes, Chief IP Officer of Nike, Inc., and Mario Bollini, Co-founder and Chief Technology Officer, Global Research Innovation and Technology, Inc. (GRIT).  Ms. Hayes demonstrated Nike’s commitment to improving lives with innovation, this year’s WIPD theme, with the latest in Nike technology.  Mr. Bollini then demonstrated his all-terrain Freedom Chair for the disabled.

it was a hard act to follow, but follow I did with my talk on the History of Innovation, with examples of important inventors that improved lives, such as Edison (the light bulb illuminating the night ), Morse (transmission of information faster than horses), various medical innovations, such as that of Raymond Damadian of Fonar (the creator of the magnetic resonance imager) and many other fascinating technologies.

I also talked about the origins of the intellectual property laws and the reasons we have them.  For patent and copyright, our Founders enshrined these rights into the Constitution itself – with the other “rights” set forth in the attachment, The Bill of Rights.  Also, our Founders in essence democratized the U.S. patent system, permitting anyone to file for and obtain a patent.  This was a big change from the systems on the Continent.  George Washington extolled the benefits of a patent system in the First Inaugural Address.  Also, Abraham Lincoln was an avid fan of the patent system and spoke at length about its advantages – equating the importance of the patent system to the founding of the United States.

The above speakers also spoke later at the Senate Hart building, and numerous Congressmen showed up, including Representative Goodlatte of Virginia, with whom I spoke about the importance of the patent system benefiting all Americans, whether individuals, small companies or large corporations.  We both strongly agreed that this was in America’s best interest.  Under his direction, the House of Representatives that day approved by a vote of 378-48 the Register of Copyrights Selection and Accountability Act  (H.R. 1695), which would make the appointment of the Copyright Registrar a Presidential one (instead of the current Librarian of Congress) and for a term of ten years.

I should also add that Senator Coons of Delaware, a staunch supporter of the patent system, also spoke.  His strong advocacy of the patent system is quite welcome to the patent bar and all innovators relying on the patent system.

Celebrate World IP Day! April 26th

Every April 26th is World Intellectual Property Day (WIPD).  This commemorative day was created many years ago by the World IP Organization in Geneva.  As the Chair of the Washington, DC Chapter for the Licensing Executives Society (LES), I have been championing this day for many years at the Chapter.  The intellectual properties, i.e., patent, copyrights, trademarks and trade secrets, are critically important in today’s economy, and I, as an intellectual property attorney, champion my clients in the protection of their various intellectual properties.

The celebration for this year, April 26, 2017, involves the use of Innovation for Improving Lives.

The United States Patent & Trademark Office (USPTO) has graciously invited me to give a talk on this topic, technologies through history that improve lives and also the history of intellectual property.  My part of the program will begin at noon in the Madison Auditorium at the USPTO in Alexandria, Virginia.  I have today confirmed that the event is free and open to the public.

Earlier at 11 AM, however, a number of important people will be presenting, including the Chief Policy Officer of the USPTO, Shira Perlmutter, who will kick off the event. John Sandage, World Intellectual Property Organization (WIPO) Deputy Director General, Patent and Technology Sector, and Joseph Ferretti, Vice President and Chief Counsel, Global Trademarks at PepsiCo, Inc. and President of the International Trademark Association (INTA), will give opening remarks.

Beginning at about 11:15 a.m., two keynote speakers will address this year’s WIPD theme of Innovation: Improving Lives by showcasing technologies brought forward by their respective companies. Jeanine Hayes, Chief IP Officer of Nike, Inc., will present FlyEase technology. Mario Bollini, Co-founder and Chief Technology Officer, Global Research Innovation and Technology, Inc. (GRIT), will demonstrate the all-terrain Freedom Chair for the disabled.

For those in the area, I welcome you to attend.  As noted, the event is open to the public, but is also focused on the Examiner Corps training.  Nonetheless, the speakers and I will be entertaining to all!  Please feel free to email me at vandyke@acm.org if you have any questions.

Ray

The Importance of Pi

Today is National Pi Day because the numbers of the day (3-14) match the first three digits for Pi, which is both an irrational and a transcendental number, i.e., the number is not a ratio or a root of any other numbers and the digits in Pi have no pattern (at least in the first few trillion digits).  Mathematicians have spent their lives trying to discern meaning in Pi.  Carl Sagan’s book (not the movie) Contact dealt with this theme at length where Pi contains messages from ancient beings, and where the main character Ellie gleans some preliminary meanings.

The earliest approximations of Pi by the Egyptians, Babylonians and Indians were fractions, e.g., 22/7, which is close to Pi, 3.14159265358….  The Greeks were famous in their efforts to “square the circle,” i.e., geometrically constructing a square having the same area as a given circle, and asking whether Euclid’s axioms posit the existence of such a number.  The Greeks and many others could not do it, which had profound implications to Plato regarding the usefulness of Euclid’s theorems to describe the real world.

To this day, the importance of Pi remains high since the number pervades much of Nature, and mathematicians are still calculating it.  Also, people love to recite the digits.  Piphilology is study of techniques for people to memorize the digits.  The record now is over 100,000.  As a mathematics/computer science major, I also memorized Pi – to about 20 decimals.

On a different note, today is also National Potato Chip Day, commemorating the 1853 (or so) creation of this snack.  Apparently, there are over 1,500 such “National” days for various things, in addition to national Weeks and Months. Happy Pi Day!

Raymond Van Dyke, Pi enthusiast

Silent Spring for Patents

Today the prominent IP website, http://www.ipwatchdog.com, published my piece about the ongoing and harmful effects of the AIA and the relentless efforts of a small number of high companies to undermine the patent system to squelch competition.  With the new Trump administration, the patent system may get a rebalancing, to correct the enormous shifts due to previous administration’s reliance on Google and other large tech corporations.

Ray Van Dyke

Article: www.ipwatchdog.com