# It’s Crystal Clear: New Methods Emerge to Predict the Distribution Pattern of Prime Numbers

Despite the unsettling effects of figuring out fractions, performing long division and taking the square roots of numbers have had for an eternity upon many students in the middle grades, some of these people continue on to adulthood with at least an appreciation of what mathematics can do in the real world. While they might still break into a slight sweat if challenged to quickly calculate the equivalent of 3/8, they still realize the importance of doing so and, moreover, applying that value to solve a problem.

So too, just as math teachers everywhere exhort their students to “put on their thinking caps”, sometimes a math story appears in the news that takes a bit more concentration to fully comprehend, but nonetheless really does have a certain technological cool and practicality to it. What is equally intriguing is when such a new development has the potential to eventually impact other areas of innovation that appear at first to be disparate or even unrecognizable. On its face, scientific advance X could not possibly be related to mathematical outcome Y until, by virtue of some very unconventional thinkers in another field, the real possibility emerges of a workable application of X to achieve Y.

Let’s take our virtual calculators out of their pocket protectors and have a look at such a recent advancement that is not only useful as party fun for math geeks. Rather, it may have meaningful significant in encryption science and, in turn, online security, e-commerce and data privacy. This achievement was reported in a fascinating article entitled Researchers Discover a Pattern to the Seemingly Random Distribution of Prime Numbers, by Liv Boeree, posted on Motherboard.com on September 14, 2018.

I will summarize and annotate this, and then pose several of my own equation-free questions.

Prime Time

Image from Pixabay.com

First, the basics: Prime numbers (“primes”) are whole numbers that are only divisible by 1 and themselves. They start out small as 2, 3 and 5 and range upwards towards infinity.¹ As these primes are plotted out along on a graph they appear to be increasingly random with no discernible or predictable pattern.

Nonetheless, one of the greatest unsolved math problems is called the Reimann Hypothesis which, among its other brain-bending complexities, posits that there may well be a pattern to the distribution of primes but it has not yet been derived.² Discovering such a pattern would be a monumental accomplishment with major significance in mathematics, physics and modern cryptography, the latter of which is based upon large prime numbers. (More about this below).

Recently, three researchers at Princeton University have made such a discovery about an atomic pattern in a physical material comparable to the distribution of primes. They have found similarities involving primes and “certain naturally occurring crystalline materials”.³ Their recent scientific paper detailing this work is entitled Uncovering Multiscale Order in the Prime Numbers Via Scattering, by Salvatore Torquato, Ge Zhang and Matthew de Courcy-Ireland, was published in the Journal of Statistical Mechanics: Theory and Experiment, on September 5, 2018.

The unpredictability of finding new primes is not always necessarily a detriment. For example, modern cryptography methods such as the RSA encryption algorithm depends upon this factor when it comes to very large primes. This relies upon the principle that it is simple enough to take two large prime numbers and multiply them but intensely difficult to reverse this in an effort to determine exactly which two primes were used.

[While this post was being drafted, an article was posted on BusinessInsider.com on September 25, 2018 entitled An Eminent Mathematician Claims to Have Solved One of Math’s Greatest Mysteries — and It’s One of 6 Problems With a \$1 Million Prize, by Andy Kiersz, reported that Sir Michael Atiyah has achieved a solution to the Reimann Hypothesis. However, this remains to be vetted by other mathematicians in this field. This problem is one of six remaining great unsolved math problems, termed the “Millennial Problems”, for which the Clay Mathematics Institute has offered a \$1 million prize for the solution to each.4 This article also contains concise descriptions of the other five problems.]

Fine Crystal Settings

Fractal Rhombic Ring, Image by fdcomite

In a process known as X-ray diffraction, chemists and physicists study the atomic structure of a material by exposing it to x-rays and observing how the beams “scatter off the atoms within it”. Different materials will produce a variety of such patterns and indicate “how symmetrically their atoms are arranged”. In the case of a crystal, whose atomic structure is more firm than other materials such as liquids, the x-ray’s pattern of diffraction is “more orderly”.

In 2017, the lead author of the paper, Professor Salvatore Torquato, wondered whether primes could be “modeled as atom-like particles” and whether they would also form a pattern. Along with his co-authors, together they “computationally represented the primes as a one-dimensional string of atoms” and then “scattered light off them”.

They found that this created a “quasicrystal-like inference pattern” that was also a previously unseen form of fractal pattern termed “hyperuniformity“. It is exhibited by only a several “materials and systems in nature”. Included among them are prime numbers. This finding might turn out to be useful in studying such non-repeating patterns in a new field of research called “aperiodic order“.

Professor Torquato said in an article in Quanta Magazine entitled A Chemist Shines Light on a Surprising Prime Number Pattern, by Natalie Wolchover, dated May 14, 2018, that there is a resulting implication that primes “are a completely new category of structures” when viewing them as a form of physical system.

Much of the interest surrounding the new paper is its “unique intersection between the physical and more abstract mathematical realms”. As well, it contains a new algorithm that permits the prediction of primes “with high accuracy”. In time this may prove to be another advance in decisively solving the mysteries of the primes.

Image from Pixabay.com (2)

My Questions

• If Professor Torquato’s and his co-authors’ paper and algorithm prove to be genuinely able to predict the patterns of the appearance of primes, does this actually strengthen and/or weaken the foundation of RSA-based encryption?
• Moreover, if Sir Atiyah’s has, in fact, solved the Reimann Hypothesis, what are the potential positive and negative effects upon the whole field of cryptography? Are there any additional impacts on other fields of science, math, physics and technology?
• If and when practical quantum computing becomes a reality and results in the capability to much more rapidly factor primes used in encryption, how will the work of Professor Torquato and Sir Atiyah be affected?
• So, how much is 3/8 anyway?

May 21, 2019 Update:  Mathematicians has returned to a previously disgarded method of trying to solve the Reimann Hypothesis that, while not deriving a solution to the problem yet, is showing signs of promise towards that direction. For a full report on this development see Mathematicians Revive Abandoned Approach to the Riemann Hypothesis, by Carol Clark, on Phys.org, posted on May 21, 2019.

January 11. 2019 Update:  It was announced today that Sir Michael Atiyah, mentioned above,  has passed away. His obituary on QuantaMagazine.org is entitled Michael Atiyah’s Imaginative State of Mind. Condolences to his family, friends and colleagues.

1.  Currently, the largest prime number ever discovered was identified in 2017 and has 23,239,425 digits. That’s a lot.

2.  For an outstanding history of the pursuit of prime numbers and the mathematical quest to discover a pattern in their distribution, I very high recommend reading The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics, by Marcus du Sautoy,  Harper Perennial; Reprint edition (August 14, 2012). This is a very accessible and literate book that presents a variety of engaging stories and deep insights into what might otherwise have otherwise appeared to have been a rather dry subject.

3.  A more technical report on this story was posted on Princeton’s website entitled Surprising Hidden Order Unites Prime Numbers and Crystal-like Materials, by Kevin McElwee, on September 5, 2018.

4.  I suggest adding a seventh intractable problem to this list that will likely never be solved: Finding a parking spot in my neighborhood.

# Book Review of “Built: The Hidden Stories Behind Our Structures”

“Brooklyn Bridge”, Image by Antti-Jussi Kovalainen

During the summer of 2010, I worked in an office directly across the street from the World Trade Center reconstruction site. For several months while my floor was being renovated, my temporary office windows faced west looking out onto the early construction of One World Trade Center. The daily swirl of highly coordinated planning and building was one of the most remarkable things I have ever seen. Hundreds of specialized craftsmen, managers, engineers, materials suppliers and numerous more worked in complete sync with each other to precisely anchor and assemble the tremendous base of the structure. Then they began steadily assembling the 104 stories of steel, concrete and glass above it climbing inexorably towards the sky.

Each day I looked out the windows and marveled at this modern miracle as it continually coalesced into one of the tallest buildings in the world.It was as exciting and entertaining to watch in person as any concert, movie or ballgame.

So, how did this magnificent monolith go from blueprints and computer visualizations to a finely tapered tower expressly intended to endure over time, meet all the modern business and technological needs of its occupants, embed environmental comfort, ensure local building code compliance, and remain state-of-the-art safe? Quite simply, who makes sure that buildings like this and many other structures such as bridges and stadiums actually stand up straight and stay that way?

Measure Twice

“The Shard”, Image by Mike Dixson

Among the many key participants in these processes are the structural engineers. They play an integral part in making certain that everything built is comprehensively planned and assembled strictly in accordance with all relevant design specifications. Yet might this sound a bit too math-geeky to want to learn anything more about them? Well, not anymore.

First-time author and accomplished structural engineer Roma Agrawal ( @RomaTheEngineer ), has recently written a fully engaging, highly informative and deeply inspiring 360-degree look at the work of these professionals entitled Built: The Hidden Stories Behind Our Structures, (Bloomsbury Publishing Plc, 2018). She has admirably transposed the same high standards of skill and precision required to be a structural engineer into also being a writer.

In equal parts personal story, travel log, history lesson and Intro to Structural Engineering 101, Ms. Agrawal quickly captures the reader’s attention and deftly manages to maintain it throughout all 271 pages. From mud huts to coliseums to bridge to skyscrapers (among other projects, she worked on The Shard in London), we learn about who was responsible and how these creations were conceived and realized. For instance, when we admire the artistry of an archway in a building, we usually never consider all of the math, physics and fabrication2 that go into creating it. Built will give you an entirely new point of view on this and a multitude of other fundamentals of structural engineering. The text also contains a wealth of historical perspectives on how bridges, tunnels, buildings and even sewers helped civilizations to expand their populations, civil services and commerce.

The author also believes that structural engineers do not get the credit they really deserve. Nonetheless, her book is a persuasive brief for their successes in making all structures remain standing (including London Bridge and why it is not falling down), function properly, and endure extreme weather conditions and changing geological factors.  In effect, it expertly explains how they carefully process and manage a myriad of concerns about their buildings’ operations, longevity and safety.

By virtue of its own structure, the book’s 14 chapters covering building materials, design and safety principles, construction methods, noteworthy construction projects, and famous structural engineers span widely across the globe and many centuries. The lively prose is involving and evocative, so much so that these chapters could even stand on their own as individual essays. But read sequentially the mesh together to deliver a very rewarding reading experience.

Generously appointing the text are many accompanying hand-annotated photos and hand-drawn simple sketches delineating the critical principles and features being described. These simple graphics significantly support in the reader’s comprehension of some of the more sophisticated concepts as they are introduced.

Cut Once

The Colosseum, Rome, Image by Christopher Chan

There are three important themes skillfully threaded throughout the book. First, in support of the popular current movement to encourage more young women to pursue studies and employment in the fields of science, technology, engineering and math (“STEM“), Ms. Agrawal’s success in structural engineering is intended to serve as a persuasive example for others. She writes that structural engineering is still a profession mostly practiced by men and believes that more women should consider becoming a part of it. Her advancement in this field should provide a high degree of inspiration for this intended audience as well as many other readers.

Of a truly great event very well told here, Ms. Agrawal recounts the remarkable story of her personal hero, Emily Warren Roebling. When the Brooklyn Bridge was being built (1869-1883), her husband, Washington Roebling, was the chief engineer on this project. When he became ill, his wife took over and become the de facto chief engineer. She delivered critical information from her husband to his assistants on site. Moreover, she mastered all aspects of the design, physics, materials and management of the bridge and is credited with having become the essential individual in getting this supremely complicated undertaking completed. Her devotion to this endeavor was simply extraordinary. Ms. Agrawal eloquently expresses her great admiration for Emily Roebling and why she was an inspiration for her own career path.

Second, she emphasizes the importance of being well prepared for all possible contingencies in her work. There are a multitude of variables to all be taken into account when building anything and it is imperative that structural engineers be able to anticipate, assess, test and decide how to definitively deal with all of them. Such unwavering diligence and exactitude is clearly applicable to many other jobs and professions. Ms. Agrawal effectively makes her case for comprehensive planning and precision at several key junctures in her writing.

Third and equally impressive is Ms. Agrawal’s boundless enthusiasm for her work. She so enjoys and believes in what she is doing that any reader in any field can benefit from from her example.  Granted that everyone’s work situation is different and often changeable can present a range of challenges. However, when someone like the author can sustain such genuine passion for the work she is doing, reading Built may well have the added benefit of providing you with a more positive perspective on your own employment as well that of others.

As proof, a new condominium was recently being built along one of my daily walking routes. I happened to be reading Built towards the end of its construction. After finishing the book, whenever I passed this site again, I saw all of the workers and their completed building with a newly enhanced understanding and admiration of it all.  I would never have previously had this appreciation without first relying upon this book’s, well, very solid foundation.

In a very different and more virtual context, a method for “building” a structure in one’s own mind as form of memory enhancement device whereby someone can then fill the “rooms” with many items that can later be retrieved and thus recalled at will was first devised in the 16th century.  This story was among the many subjects of a fascinating historical account entitled The Memory Palace of Matteo Ricci, by Jonathan D. Spence (Penguin Books, 1985).

1.   See the September 1, 2015 Subway Fold post entitled A Thrilling Visit to the New One World Observatory at the Top of the World Trade Center for photos and descriptions of the amazing views from the One World Observatory very top of 1WTC.

2.  See these 10 Subway Fold posts on other recent developments in material science including, among others, such way cool stuff as Q-Carbon, self-healing concrete (also mentioned in Built at pages 106 -107), and metamaterials.

# Hacking Matter Really Matters: A New Programmable Material Has Been Developed

Image from Pixabay

The sales receipt from The Strand Bookstore in New York is dated April 5, 2003. It still remains tucked into one of the most brain-bendingly different books I have ever bought and read called Hacking Matter: Levitating Chairs, Quantum Mirages, and the Infinite Weirdness of Programmable Atoms (Basic Books, 2003), by Wil McCarthy. It was a fascinating deep dive into what was then the nascent nanotechnology research on creating a form of “programmable atoms” called quantum dots. This technology has since found applications in the production of semiconductors.

Fast forward thirteen years to a recent article entitled Exoskin: A Programmable Hybrid Shape-Changing Material, by Evan Ackerman, posted on IEEE Spectrum on June 3, 2016. This is about an all-new and entirely different development, quite separate from quantum dots, but nonetheless a current variation on the concept that matter can be programmed for new applications. While we always think of programming as involving systems and software, this new story takes and literally stretches this long-established process into some entirely new directions.

I highly recommend reading this most interesting report in its entirety and viewing the two short video demos embedded within it. I will summarize and annotate it, and then pose several questions of my own on this, well, matter. I also think it fits in well with these 10 Subway Fold posts on other recent developments in material science including, among others, such way cool stuff as Q-Carbon, self-healing concrete and metamaterials.

Matter of Fact

The science of programmable matter is still in its formative stages. The Tangible Media Group at MIT Media Lab is currently working on this challenge included in its scores of imaginative projects. A student pursuing his Master’s Degree in this group is Basheer Tome. Among his current research projects, he is working on a type of programmable material he calls “Exoskin” which he describes as “membrane-backed rigid material”. It is composed of “tessellated triangles of firm silicone mounted on top of a stack of flexible silicone bladders”. By inflating these bladders in specific ways, Exoskin can change its shape in reaction to the user’s touch. This activity can, in turn, be used to relay information and “change functionality”.

Although this might sound a bit abstract, the two accompanying videos make the Exoskin’s operations quite clear. For example, it can be applied to a steering wheel which, through “tactile feedback”, can inform the driver about direction-finding using GPS navigation and other relevant driving data. This is intended to lower driver distractions and “simplify previously complex multitasking” behind the wheel.

The Exoskin, in part, by its very nature makes use of haptics (using touch as a form of interface). One of the advantages of this approach is that it enables “fast reflexive motor responses to stimuli”. Moreover, the Exoskin actually involves inputs that “are both highly tactily perceptible and visually interpretable”.

Fabrication Issues

A gap still exists between the current prototype and a commercially viable product in the future in terms of the user’s degree of “granular control” over the Exoskin. The number of “bladders” underneath the rigid top materials will play a key role in this. Under existing fabrication methods, multiple bladders in certain configurations are “not practical” at this time.

However, this restriction might be changing. Soon it may be possible to produce bladders for each “individual Exoskin element” rather than a single bladder for all of them. (Again, the videos present this.) This would involve a system of “reversible electrolysis” that alternatively separates water into hydrogen and oxygen and then back again into water. Other options to solve this fabrication issue are also under consideration.

Mt. Tome hopes this line of research disrupts the distinction between what is “rigid and soft” as well as “animate and inanimate” to inspire Human-Computer Interaction researchers at MIT to create “more interfaces using physical materials”.

My Questions

• In what other fields might this technology find viable applications? What about medicine, architecture, education and online gaming just to begin?
• Might Exoskin present new opportunities to enhance users’ experience with the current and future releases virtual reality and augmented reality systems? (These 15 Subway Fold posts cover a sampling of trends and developments in VR and AR.)
• How might such an Exoskin-embedded steering wheel possibly improve drivers’ and riders’ experiences with Uber and other ride-sharing services?
• What entrepreneurial opportunities in design, engineering, programming and manufacturing might present themselves if Exoskin becomes commercialized?

# Bye-Bye Wash and Dry: Scientists are Developing Self-Cleaning Fabrics

“Autumn Laundry”, Image by Walter A. Aue

It is likely – – or if it isn’t, it should be – – a universal truth that everyone loves clean clothes but no one likes doing the laundry. I have arrived at this conclusion through many years of my own thoroughly unscientific observations in the laundry room in my apartment building. (My other research project is focused upon discovering the origin of the rift in the time and space continuum where stray socks always seem to disappear into in the washers and dryers.)

This ages old situation might be about to change based upon an interesting new development. This story is neither made from whole cloth nor a fabric-ation.

A group of scientists in Australia claim to have discovered a means to keep clothes clean by treating them with nano-size particles of two common metals and then exposing the fabric to sunlight. This could perhaps one day mean an end to washing clothes in the traditional soap and water manner. This research was reported in an article in the April 25, 2016 edition of The Wall Street Journal entitled An End to Laundry? The Promise of Self-Cleaning Fabric, by Rachel Pannett. I will summarize and annotate this story, and then pose several of my own questions about this, well, material.

Dry Cleaning

Rajesh Ramanathan, a postdoctoral fellow at RMIT University in Melbourne, Australia, explained the basic principal being tested: Minute flecks of copper and silver (called nanostructures), are embedded into cotton fabrics that, when exposed to sunlight, generate small amounts of energy “that degrade organic matter ” on the cloth in about six minutes. He and his team are conducting their work at the Ian Potter NanoBioSensing Facility, within RMIT.

The results of their research were recently published in Advanced Materials Interfaces in a paper entitled Surface Plasmon Resonance: Robust Nanostructured Silver and Copper Fabrics with Localized Surface Plasmon Resonance Property for Effective Visible Light Induced Reductive Catalysis (Volume 3, Issue 6, March 23, 2016). The authors, including Dr. Ramanathan, are Samuel R. Anderson, Mahsa Mohammadtaheri, Dipesh Kumar, Anthony P. O’Mullane, Matthew R. Field, and Vipul Bansal.

Dr. Ramanathan characterized the team’s work as being in its early stages and involving “nano-enhanced fabrics” with the “ability to clean themselves”.  The silver and copper do not alter the fabric in any way and remain embedded even when rinsed in water. As a result, their self-cleaning abilities will persist in successive multiple cleanings.

While encouraging no one to get rid of their washing machines just yet, he does believe that his team’s work “lays a strong foundation” for additional advancements in creating “fully self-cleaning textiles”.

Other current research is investigating whether such nano-enhanced fabrics are capable of affecting germs and even whether they can eradicate “superbugs” that resist today’s antibacterials.

To date, the research team has been testing their fabrics with organic dyes and artificial light. Next they are planning experiments with “real world stains” such as ketsup and wine in an effort to measure how long it will take them to “degrade in natural sunlight”. Additional planed testing will be to see how the nanostructures affect odors in the fabrics.

Spin Cycle

However, another scientist named Christopher Sumby, an associate professor in chemistry and physics at the University of Adelaide, expressed his reluctance at talking about self-cleaning fabrics “at this stage”.

Nonetheless, this experimental new process that use silver and copper, are two “commonly used” chemical catalysts and are “relatively cheap”. Two of the challenges currently facing the research team are how to scale up production of these nanostructures and “how to permanently attach them to textiles”. They are using cotton in their work because it has “a natural three-dimensional structure” that enables the nanostructures to embed themselves and absorb light. They have also found that this works well in removing organic stains from polyester and nylon.

Dr. Ramanathan said that a variety of industries, including textile manufacturers, have expressed their interest to his team. He believes that to enable them to commercialize their process, they would need to make sure the nanostructures can “comply with industry standards for clothing and textiles”.

My Questions

• What would be the measurable benefits to the environment and energy savings if the needs for electric washers and dryers was significantly reduced by self-cleaning fabrics? Should the researchers use this prospect to their advantage in seeking regulatory approval and additional financing?
• Although using sunlight, which is free and abundant across the entire world, would be the most renewable and environmentally sound source of energy for this, could the process also be extended for use with artificial light (as is currently being used in the team), for instances where sufficient sunlight becomes unavailable due to weather conditions or other environmental factors?
• Could this process also be adapted to other forms of porous materials such as wood, paper, and plastics? For example, if people go outside for a picnic, could they could theoretically clean up the table, food containers and paper plates just by leaving them in the sun and then reusing them later? This might further cut down on the volumes of these materials being thrown in the trash or else being sent for recycling.
• What other entrepreneurial opportunities might arise if this process becomes commercialized?

# Book Review of “Inventology: How We Dream Up Things That Change the World”

“Toolbox_LRG”, Image by Limor.

My father loved to tell this story: One of his classmates while he attended the University of Pennsylvania School of Dental Medicine was named Robert Schattner. Several years after they graduated, he went on to invent the over-the-counter sore throat lozenge and spray called Chloraseptic. This remedy has been on the market for decades ever since then.

Schattner first devised this product entirely on his own after someone who had just had some teeth pulled asked him for an antiseptic to relieve the pain. He later sold the formula and the rights to a pharmaceutical company for \$4M. (Given the rate of inflation since then, this sum today would have been magnitudes more and certainly nothing to sneeze or cough at.)

Thereafter he left the practice of dentistry and went on became a successful businessman and philanthropist. He also contributed for the construction of a new building for the U Penn dental school named the Robert Schattner Center. A brief summary of his invention and contributions can be found in an article entitled Capital Buzz: Chloraseptic Inventor Offers Remedy for School, by Thomas Heath, which appeared in The Washington Post on October 23, 2011.

Mapping the Inventive Process

This is a classic example of how inventors find their ideas and inspiration. There are many other circumstances, methodologies, environments, personality traits, events, technologies and chances occurrences that can also precipitate new inventions. All of them are expertly explained and explored in Inventology: How We Dream Up Things That Change the World (Eamon Dolan/Houghton Mifflin Harcourt, 2016), by Pagan Kennedy.

The book’s five sections distinctly map out the steps in the inception and realization of things so entirely new. In doing so, the author transports the reader to center of this creative process. She deftly uses highly engaging stories, exposition and analyses to illuminate the resourcefulness and persistence of inventors leading to their breakthroughs.

Some of these tales may be familiar but they are skillfully recounted and placed into new contexts. For example, in 1968, an engineer and inventor named Douglas Englebart demonstrated a working computer for the first time with a heretofore unseen “mouse” and “graphical user interface”. (This story has gone on to become a tech legend known as The Mother of All Demos.) Others are presented who are less well-known but brought to life in highly compelling narratives. Together they provide valuable new lessons on the incubation of inventions along a wide spectrum ranging from sippy cups and water toys to mobile phones and medical devices.

The author has seemingly devised a meta-invention of her own: A refreshingly new perspective on reporting the who, what, where and why of inventors, their creations and their wills to succeed. It is a richly detailed schematic of how a creative mind can conceive and execute an original idea for a new widget and, moreover, articulate the need for it and the problem it solves.

Among other methods, Ms. Pagan covers the practice of conducting thought experiments on new concepts that may or may not lend themselves to actual experimentation in the real world. This process was made well-known by Einstein’s efforts to visualize certain problems in physics that led him to his monumental achievements. I suggest trying a thought experiment here to imagine the range of the potential areas of applications for Inventology to evaluate, in an age of countless startups and rapid scientific and technological advancements, all of the populations, challenges and companies it might benefit. Indeed, this book could readily inspire nearly anyone so inclined to pick up a pencil or soldering iron in order to launch the realization of their own proverbial better mousetrap.

Resources for Inventors

Within all of the lively content packed into this book, the struggles and legacy of a previously little known and tragically persecuted figure who learned to harness and teach the inventive process, springs right off the pages. He was a fascinating figure named  Genrich Altshuller who worked as an engineer, writer and inventor in Russia. His most important contribution to the science of invention was the development of the Theory of Inventive Problem Solving (better known by its Russian acronym of “TRIZ”). This is a comprehensive system for analyzing and implementing inventive solutions to problems of nearly every imaginable type and scale. Altschuller was willing to share this and instruct anyone who was willing to participate in studying TRIZ. It is still widely used across the modern world. The author masterfully breaks down and clearly explains its essential components.

The true gem in the entire book is how Altshuller, while imprisoned in a brutal jail in Stalinist Russia, used only his mind to devise an ingenious solution to outwit his relentless interrogators. No spoilers here, but it is an emotional triumph that captures the heart and spirit of this remarkable man. Altshuller’s life and influence in generating thousands of inventions reads as though it might make for a dramatic biopic.

Also threaded and detailed throughout the book are the current bounty of easily accessible technological tools available to inventors. First, the web holds a virtual quantum of nearly limitless data that can be researched, processed, shared, crowdsourced (on sites such as InnoCentive) and crowdfunded (on sites such as Kickstarter and Indigogo), in search of medical advances, among many other fields.¹ Second, 3D printing² can be used to quickly and inexpensively fabricate and work on enhancing prototypes of inventions. As a result of this surfeit of resources, the lengthy timelines and prohibitive cost curves that previously discouraged and delayed inventors have now been significantly reduced.

Impossibility is Only Temporary

I live in a neighborhood where it is nearly impossible to park a car. An open parking space has a half-life on the street of about .000001 nano-seconds before it is taken. This situation often reminds me of a suggestion my father also made to me when I was very young. He told me that if I really wanted to solve an important problem when I grew up, I should try to invent a car that, at the press of a button, would fold up into the size and shape of a briefcase that could be easily carried away. At the time, I thought it was impossible and immediately put the, well, brakes on this idea.

Nonetheless, as Inventology expressly and persuasively makes its own brief case, true inventors see impossibility as merely a temporary condition that, with enough imagination and determination, can be overcome. For budding Edisons and creative problem solvers everywhere, this book adds a whole new meaning to the imperative that nothing is truly impossible if you try hard enough and long enough to solve it. This indefatigable spirit permeates all 223 pages of this wonderfully enjoyable, inspirational and informative book.

For a dozen very timely examples of inventors and their inventions further typifying much of the content and spirit of Inventology, I highly recommend reading a new feature and viewing its accompanying video posted on Quartz.com on April 26, 2016, entitled These Top Twelve Inventions Could One Day Change the World, by Mike Murphy. It covers the finalists in the 2016 European Inventors Award competition currently being run by the European Patent Office.

1.  For example, last week’s Only Human podcast on NPR included a report on how a woman with Type 1 (T1) diabetes, along with the assistance of her husband, had hacked together an artificial pancreas (called a “closed loop” system), and then shared the technical specs online with other T1s in the Seattle area. I highly recommend listening to this podcast entitled The Robot Vacuum Ate My Pancreas in its entirety.

2.  See also these six Subway Fold posts for a sampling of other trends and developments in 3D printing.

# Applying Origami Folding Techniques to Strands of DNA to Produce Faster and Cheaper Computer Chips

“Origami”, Image by David Wicks

We all learned about the periodic table of elements in high school chemistry class. This involved becoming familiar with the names, symbols and atomic weights of all of the chemical occupants of this display. Today, the only thing I still recall from this academic experience was when the teacher told us on the first day of class that we would soon learn to laugh at the following:

Two hydrogen atoms walk into a bar and the first one says to the other “I’ve lost my electron”. The other one answers “Are you sure?”. The first one says “I’m positive.”

I still find this hilarious but whatever I recall today about learning chemistry would likely get lost at the bottom of a thimble. I know, you are probably thinking “Sew what”.

Facing the Elements

Besides everyone’s all-time favorites like oxygen and hydrogen that love to get mixed up with each other and most of the other 116 elements, another one stands alone as the foundation upon which the modern information age was born and continues to thrive today. Silicon has been used to create integrated circuits, much more commonly known as computer chips.

This has been the case since they were first fabricated in the late 1950’s. It has remained the material of choice including nearly all the chips running every imaginable one of our modern computing and communication devices. Through major advances in design, engineering and fabrication during the last five decades, chip manufacturers have been able to vastly shrink this circuitry and pack millions of components into smaller squares of this remarkable material.

A fundamental principle that has held up and guided the semiconductor industry, under relentlessly rigorous testing during silicon’s enduring run, is Moore’s Law. In its simplest terms, it states that the number of transistors that can be written onto a chip doubles nearly every two years. There have been numerous predictions for many years that the end of Moore’s Law is approaching and that another substrate, other than silicon, will be found in order to continue making chips smaller, faster and cheaper. This has not yet come to pass and may not do so for years to come.

Nonetheless, scientists and developers from a diversity of fields, industries and academia have remained in pursuit of alternative computing materials. This includes elements and compounds to improve or replace silicon’s extensible properties, and other efforts to research and fabricate entirely new computing architectures. One involves exploiting the spin states of electrons in a rapidly growing field called quantum computing (this Wikipedia link provides a detailed and accessible survey of its fundamentals and operations), and another involves using, of all things, DNA as a medium.

The field of DNA computing has actually been around in scientific labs and journals for several decades but has not gained much real traction as a viable alternative ready to produce computing chips for the modern marketplace. Recently though, a new advance was reported in a fascinating article posted on Phys.org on March 13, 2016, entitled DNA ‘origami’ Could Help Build Faster, Cheaper Computer Chips, provided by the American Chemical Society (no author is credited). I will summarize and annotate it in order to add some more context, and then pose several of my own molecular questions.

Know When to Fold ‘Em

A team of researchers reported that fabricating such chips is possible when DNA is folded and “formed into specific shapes” using a process much like origami, the Japanese art of folding paper into sculptures. They presented their findings at the 251st American Chemical Society Meeting & Exposition held in San Diego, CA during March 13 through 17, 2016. Their paper entitled 3D DNA Origami Templated Nanoscale Device Fabrication, appears listed as number 305 on Page 202 of the linked document.  Their presentation on March 14, 2016, was captured on this 16-minute YouTube video, with Adam T. Woolley, Ph.D. of Brigham Young University as the presenter for the researchers.

According to Dr. Woolley, researchers want to use DNA’s “small size, base-pairing capabilities and ability to self-assemble” in order to produce “nanoscale electronics”. By comparison, silicon chips currently in production contain features 14 nanometers wide, which turn out to be 10 times “the diameter of single-stranded DNA”. Thus, DNA could be used to build chips on a much smaller and efficient scale.

However, the problem with using DNA as a chip-building material is that it is not a good conductor of electrical current. To circumvent this, Dr. Woolley and his team is using “DNA as a scaffold” and then adding other materials to the assembly to create electronics. He is working on this with his colleagues, Robert C. Davis, Ph.D. and John N. Harb, Ph.D, at Brigham Young University. They are drawing upon their prior work on “DNA origami and DNA nanofabrication”.

Know When to Hold ‘Em

To create this new configuration of origami-ed DNA, they begin with a single long strand of it, which is comparable to a “shoelace” insofar as it is “flexible and floppy”. Then they mix this with shorter stand of DNA called “staples” which, in turn, “use base pairing” to gather and cross-link numerous other “specific segments of the long strand” to build an intended shape.

Dr. Woolley’s team is not satisfied with just replicating “two-dimensional circuits”, but rather, 3D circuitry because it can hold many more electronic components. An undergraduate who works with Dr. Woolley named Kenneth Lee, has already build such a “3-D, tube-shaped DNA origami structure”. He has been further experimenting with adding more components including “nano-sized gold particles”. He is planning to add still more nano-items to his creations with the objective of “forming a semiconductor”.

The entire team’s lead objective is to “place such tubes, and other DNA origami structures, at particular sites on the substrate”. As well, they are seeking us use gold nanoparticles to create circuits. The DNA is thus being used as “girders” to create integrated circuits.

Dr. Woolley also pointed to the advantageous cost differential between the two methods of fabrication. While traditional silicon chip fabrication facilities can cost more than \$1 billion, exploiting DNA’s self-assembling capabilities “would likely entail much lower startup funding” and yield potentially “huge cost savings”.

My Questions

• What is the optimal range and variety in design, processing power and software that can elevate DNA chips to their highest uses? Are there only very specific applications or can they be more broadly used in commercial computing, telecom, science, and other fields?
• Can any of the advances currently being made and widely followed in the media using the CRISPR gene editing technology somehow be applied here to make more economical, extensible and/or specialized DNA chips?
• Does DNA computing represent enough of a potential market to attract additional researchers, startups, venture capital and academic training to be considered a sustainable technology growth sector?
• Because of the potentially lower startup and investment costs, does DNA chip development lend itself to smaller scale crowd-funded support such Kickstarter campaigns? Might this field also benefit if it was treated more as an open source movement?

February 19, 2017 Update:  On February 15, 2017, on the NOVA science show on PBS in the US, there was an absolutely fascinating documentary shown entitled The Origami Revolution. (The link is to the full 53-minute broadcast.) It covered many of the today’s revolutionary applications of origami in science, mathematics, design, architecture and biology. It was both highly informative and visually stunning. I highly recommend clicking through to learn about how some very smart people are doing incredibly imaginative and practical work in modern applications of this ancient art.

# New Strata-Gem Produces “Q-Carbon” – A Substance Stronger and Brighter than Diamonds

“Diamond”, Image by Hisham Alqawsi

There are eight Bruce Springsteen songs specifically containing the word “diamond” in their lyrics.¹ My favorite among them is from his song Better Days containing the line “Your heart like a diamond shone”. It is a highly evocative image from a deeply powerful song that has a special meaning of hope to many of his fans.

This line quickly sprang to mind when I read a fascinating new article posted on Smithsonian.com on December 2, 2015 entitled Weird New Type of Carbon Is Harder (and Brighter) Than Diamond by Maya Wei-Haas. This is a story about scientists at North Carolina State University² who have just announced the fabrication of Q-Carbon, a substance that is harder and brighter than diamonds as well as having magnetic and glowing properties. I will summarize and annotate it, and pose a few carbon-based questions of my own.

While “Q-carbon” surely sounds far less romantic and is not likely to appear in Bruce’s lyrics anytime soon  – – “Your heart like Q-carbon shone”? – – nah, I just don’t think so – – these four adjectives still seem fitting for both Bruce’s rock and this new material’s roll. For now, let’s focus on the latter in its new diamond setting.

It has taken the North Carolina State University team decades to develop and fabricate Q-carbon. Their invention can make diamonds quickly and at room temperature without using traditional methods of creating industrial diamonds by apply high pressure and high heat to carbon. Moreover, their work also led them to develop this additional “new phase of carbon” called Q-carbon. Their findings were published online on November 30, 2015 in the Journal of Applied Physics in a paper entitled Novel Phase of Carbon, Ferromagnetism, and Conversion into Diamond by Jagdish Narayan and Anagh Bhaumik.

According to Mr. Narayan, the key to this new method’s success is in its speed. At normal room temperature, the team applied “extremely short laser pulses” to amorphous carbon (which has no crystal structure). This heated the material to 6,740°F. When this “puddle” was very rapidly cooled, the Q-carbon then formed.

The scientists found it was harder than regular diamonds, exhibited ferroelectric (magnetic) properties, and was able to give off “small amounts of light”.  Among the anticipated applications for Q-carbon are in developing electronic displays, electronic components, and assisting in “understanding the magnetism of other planets”.

Its most current (no pun intended) use is in improving diamond fabrication. By varying the rates at which the carbon “puddles” are cooled, diamonds can be formed into specialized structure including “nanoneedles, microneedles³, nanodots and films”. Other fields such as medicine and abrasives4 may also benefit from this development.

This new methodology is also relatively inexpensive since its uses an existing  laser system otherwise used in eye surgery. It is likewise very fast as it can produce “a carat in about 15 minutes” according to Mr. Narayan. He is also optimistic that the diamonds can be scaled up from their current size of 70 microns by widening the side of the laser’s beam. (The Smithsonian.com article linked to above contains a photo of these new diamonds.)

The team is now working on further understanding and testing the properties of Q-carbon.

My questions are as follows:

• What other industries and marketplaces might benefit from Q-carbon and/or the innovative methods used to produce it?
• Are there other new molecular forms of carbon still to be found in addition to Q-carbon given that the last 30 years have brought us the discoveries and development of graphene. nanotubes and buckminsterfullerines?
• Should Q-carbon be evaluated as a possible metamaterial because it appears to have some of the physical qualities of these substances as described in the April 10, 2015 Subway Fold post entitled The Next Wave in High Tech Materials Science ?

A sampling of additional press coverage on this story from the past week includes:

1.  See 10 Bruce Springsteen Songs That Reference Diamonds and Jewelry by Daniel Ford, posted on JCKonline.com on September 11, 2013.

2.  North Carolina State University scientists were also involved in the June 27, 2015 Subway Fold post entitled Medical Researchers are Developing a “Smart Insulin Patch”.

3.  “Microneedles” were also first mentioned in the same post as Footnote 2 above.

4Does this include car alarms that only seem to go off at 4:00 am in the morning in my neighborhood?

# Artificial Fingerprints: Something Worth Touching Upon

“030420_1884_0077_x__s”, Image by TNS Sofres

Among the recent advancements of the replication of various human senses, particularly for prosthetics and robotics, scientists have just made another interesting achievement in creating, of all things, artificial fingerprints. They can actually sense certain real world stimuli. This development could have some potentially very productive – – and conductive – – applications.

Could someone please cue up The Human Touch by Bruce Springsteen for this?

We looked at a similar development in artificial human vision just recently in the October 14, 2015 Subway Fold post entitled Visionary Developments: Bionic Eyes and Mechanized Rides Derived from Dragonflies.

This latest digital and all-digit story was reported in a fascinating story posted on Sciencemag.org on October 30, 2015 entitled New Artificial Fingerprints Feel Texture, Hear Sound by Hanae Armitage. I will summarize and annotate it, and then add some of my own non-artificial questions.

Design and Materials

An electronic material has been created at the University of Illinois, Urbana-Champaign, that, while still under development in the lab “mimics the swirling design” of fingerprints. It can detect pressure, temperature and sound. The researchers who devised this believe it could be helpful in artificial limbs and perhaps even enhancing our own organic senses.

Dr. John Rogers, a member of the development team, finds this new material is an addition to the “sensor types that can be integrated with the skin”.

Scientists have been working for years on these materials called electronic skins (e-skins). Some of them can imitate the senses of human skin that can monitor pulse and temperature. (See also the October 18, 2015 Subway Fold post entitled Printable, Temporary Tattoo-like Medical Sensors are Under Development.) Dr. Hyunhyub Ko, a chemical engineer at Ulsan National Institute of Science and Technology in South Korea and another member of the artificial fingerprints development team noted that there are further scientific challenges “in replicating fingertips” with their ability to sense very small differences in textures.

Sensory Perceptions

In the team’s work, Dr. Ko and the others began with “a thin, flexible material” textured with features much like human fingerprints. Next, they used this to create a “microstructured ferroelectric skin“. This contains small embedded structures called “microdomes” (as shown in an illustration accompanying the AAAS.org article), that enable the following e-skin’s sensory perceptions*:

• Pressure: When outside pressure moves two layers of this material together it generates a small electric current that is monitored through embedded electrodes. In effect, the greater the pressure the greater the current.
• Temperature: The e-skin relaxes in warmer temperatures and stiffens in colder temperatures, likewise generating changes in the electrical current and thus enabling it to sense temperature changes.
• Sound: While not originally expected, the e-skin was also been found to be sensitive to sound. This occurred in testing by Dr. Ko and his team. They electronically measured the vibrations from pronouncing the letters in the word “skin” right near the e-skin. The results show this affected the microdomes and, in turn, the electric current to register changes.

Dr. Ko said his next challenge is how to transmit all of these sensations to the human brain. This has been done elsewhere using optogenetics (the use of light to control neurons that have been genetically modified) in e-skins, but he plans to research other technologies for this. Specifically, in the increasing scientific interest and development in skin-mounted sensors (such as those described in the October 18, 2015 Subway Fold post linked above), this involves a smart groups of “ideas and materials” to engineer these.

My Questions

• Might e-skins have applications in virtual reality and augmented reality systems for medicine, engineering, manufacturing, design, robotics, architecture, and gaming? (These 11 Subway Fold posts cover a range of new developments and applications of these technologies.)
• What other fields and marketplaces might also benefit from integrating e-skin technology? What entrepreneurial opportunities might emerge here?
• Could e-skins work in conjunction with the system being developed in the June 27, 2015 Subway Fold post entitled Medical Researchers are Developing a “Smart Insulin Patch” ?

For an absolutely magnificent literary exploration of the human senses, I recommend A Natural History of the Senses by Diane Ackerman (Vintage, 1991) in the highest possible terms. It is a gem in both its sparking prose and engaging subject.

See this Wikipedia page for detailed information and online resources about the field known as haptic technology.

# Printable, Temporary Tattoo-like Medical Sensors are Under Development

There is a new high-energy action and suspense drama on NBC this year called Blindspot. The first episode began when a woman in left in a luggage bag in the middle of Times Square in New York with tattoos completely covering her and absolutely no memory of who she is or how she got there. She is taken in by the FBI who starts to analyze her tattoos and see if they can figure out who she was before her memory was intentionally destroyed. It turns out that the tattoos are puzzles that, once solved, start to lead a team of agents assigned to her to a series of dangerous criminal operations.

“Jane” as they call her, is quickly made a part of this FBI team because, without knowing why, she immediately exhibits professional level fighting and weapons skills. She is also highly motivated to find out her real identity and is starting to experience brief memory flashbacks. All sorts of subplots and machinations have begun to sprout up regarding her true identity and how she ended up in this dilemma.

So far, the show is doing well in the ratings. Imho, after four episodes it’s off to a compelling and creative start. I plan to keep watching it. (The only minor thing I don’t like about it is the way the production team is using the shaky cam so much it’s making me feel a bit seasick at times.)

The lead actress, Jamie Alexander, who plays Jane, is actually wearing just temporary tattoos on the show. While these cryptic designs are the main device to propel the fictional plots forward in each episode, back in the non-fictional real world temporary tattoo-like devices are also currently being tested by researchers as medical sensors to gather patients’ biological data. This news adds a whole new meaning to the notion of medical application.

This advancement was reported in a most interesting article on Smithsonian.com, posted on October 8, 2015 entitled Tiny, Tattoo-Like Wearables Could Monitor Your Health, by Heather Hansman. I will summarize and annotate it in an effort to provide a, well, ink-ling about this story, and then pose some of my own questions.

Research and Development

This project, in a field called bio-integrated electronics, is being conducted at the University of Texas at Austin’s Cockrell School of Engineering. The research team is being led by Professor Nanshu Lu (who received her Ph.D. from Harvard).  Her team’s experimental patch is currently being applied to test heart rates and blood oxygen levels.

When Dr. Lu and her team were investigating the possibility of creating these “tattoo-like wearables”, their main concern was the manufacturing process, not the sensors themselves because there were many already available. Instead, they focused upon creating these devices to be both disposable and inexpensive. Prior attempts elsewhere had proven to be more “expensive and time-consuming”.

This led them to pursue the use of  3D printing . (These four Subway Fold posts cover other applications of this technology.) They devised a means to print out “patterns on a sheet of metal instead of forming the electronics in a mold”. They easily found the type of metal material for this purpose in a hardware store. Essentially, the patterns were cut into it rather than removed from it. Next, this electronic component was “transfer printed onto medical tape or tattoo adhesive”. Altogether, it is about the size of a credit card. (There is a picture of one at the top of the article on Smithsonian.com linked above.)

The entire printing process takes about 20 minutes and can be done without the use of a dedicated lab. Dr. Lu is working to get the cost of each patch down to around \$1.

Current Objectives

The teams further objective is to “integrate multiple sensors and antenna” into the patches in order to capture vital signs and wirelessly transmit them to doctors’ and patient’s computing devices.  They can be used to measure a patient’s:

One of the remaining issues to mass producing the patches is making them wireless using Bluetooth or near field communication (NFC) technology. At this point, chip producers have not made any commitments to make such chips small enough. Nonetheless, Dr. Lu and her team are working on creating their own chip which they expect will be about the size of a coin.

My Questions

• Could this sensor be adapted to measure blood glucose levels? (See a similar line of research and development covered in the June 27, 2015 Subway Fold post entitled Medical Researchers are Developing a “Smart Insulin Patch”.)
• Could this sensor be adapted to improve upon the traditional patch test for allergies?
• Could this sensor be adapted for usage in non-vital sign data for biofeedback therapies?
• Would adding some artwork to these patches make them aesthetically more pleasing and thus perhaps more acceptable to patients?
• Could this sensor be further developed to capture multiple types of medical data?
• Are these sensors being secured in such a manner to protect the patients’ privacy and from any possible tampering?
• Could the production team of Blindspot please take it easy already with the shaky cam?

# Google is Giving Away Certain Patents to 50 Startups In Their Latest Effort to Thwart Patent Trolls

“She Runs Neon Fraction of a Second”, Image by Wonderlane

In the highly competitive world of creating, monetizing, defending and challenging tech-based intellectual property, “free” is neither a word often heard nor an offer frequently made.

However, Google has just begun a new program, for a limited time, to give away a certain types of patents they own to an initial group of 50 startups.  This is principally being done in an effort to resist time and resources devouring litigation with “patent trolls“, companies that purchase patents for no other purpose than to litigate infringement claims in their attempts to win monetary judgments. (We first visited this issue in an April 21, 2015 Subway Fold post entitled New Analytics Process Uses Patent Data to Predict Advancements in Specific Technologies.)

The details of this initiative were carried in a most interesting new article on TechCrunch.com posted on July 23, 2015 entitled Google Offers To Give Away Patents To Startups In Its Push Against Patent Trolls by Ingrid Lunden. I will summarize, annotate, and pose some free questions of my own.

In April 2015, Google successfully started a temporary program for companies to offer to sell them (Google) their patents. Then on July 23, 2015, they launched a reciprocal program to give away, at no cost, “non-organic” patents (that is, those purchased by Google from third parties), to startups.

The recipients of these giveaways are required to abide by two primary conditions:

• They must join the LOT Network for two years.  This is a tech industry association of patent owners dedicated to reducing the volume of patent troll-driven litigation.
• The patents can only be used defensively to “protect a company against another patent suit”. Thus, the patents cannot be used to bring a case “against another company” or else its ownership “reverts back to Google”.

Kurt Brasch, one of Google’s senior patent licensing managers who was interviewed for the TechCrunch story, expects other members of the LOT Network to start their own similar programs.

For any of the 50 startups to be eligible for Google’s program, another key requirement is that their 2014 revenues must fall between \$500,000 and \$20 million. Next, if eligibility is determined, within 30 days they will receive “a list of three to five families of patents”, from which they can make their selection. Still, Google “will retain a broad, nonexclusive license to all divested assets”, as these patents might still be important to the company.

For those startups that apply and are determined to be ineligible, Google will nonetheless provide them with access “to its own database of patents”. These are presumed to alas be categorized as “non-organic”. The unselected startups will be able to ask Google to consider “the potential purchase of any such assets”.

Back in April, when Google began their acquisitions of patents, they were approached by many operating companies and patent brokers. Both types of entities told Mr. Brasch about a “problem in the secondary market“. These businesses were looking for an alternative means to sell their patents to Google and Mr. Brasch was seeking a means to assist interested buyers and sellers.

Google eventually purchased 28% of the patents they were offered that the company felt could potentially be used in their own operations. As these patents were added to Google’s patent portfolio, a portion of them were categorized as “non-organic” and, as such, the company is now seeking to give them away.

Both sides of Google’s latest patent initiative demonstrate two important strategic points as the company is now:

• Taking more action in enabling other tech firms to provide assistance against litigation brought by troll-driven lawsuits.
• Presenting the company as a comprehensive “broker and portal” for patents matters.

Last week, as another part of this process, Google substantially upgraded the features on its Google Patents Search. This included the addition of search results from both Google Scholar and Google Prior Art Finder.  (For the full details and insights on the changes to these services see Google’s New, Simplified Patent Search Now Integrates Prior Art And Google Scholar, also by Ingrid Lunden, posted on TechCrunch.com on July 16, 2015.)

While both the purchasing and selling operations of Google’s effort to test new approaches to the dynamics of the patent marketplace appear to be limited, they might become more permanent later on depending on the  results achieved. Mr. Brasch also anticipates continuing development of this patent market going forward either from his company or a larger “group of organizations”.  Just as Google has moved into other commercial sector including, among others, “shopping, travel and media”, so too does he expect the appearance of more new and comparable marketplaces.

My own questions are as follows:

• In addition to opposing patent troll litigation, what other policy, public relations, technical and economic benefits does Google get from their new testbed of marketplace services?
• What other industries would benefit from Google’s new marketplace? What about pharmaceuticals and medical devices, materials science (see these four recent Subway Fold posts in this category),  and/or automotive and aerospace?
• Should Google limit this project only to startups? Would they consider a more expansive multi-tiered approach to include different ranges of yearly revenue? If so, how might the selection of patents to be offered and other eligibility requirements be decided?
• Might there be some instances where Google and perhaps other companies would consider giving away non-organic patents to the public domain and allowing further implementation and development of them to operate on an open source basis? (These 10 Subway Fold posts have variously touched upon open source projects and methods.)