Above we see Richard Klein's free-hand sketch of a bike rider in action. This sketch is Richard's characteristic signature as he quickly adds this sketch as he signs camp graduation certificates. Richard wants to use this sub-section to ramble on a little about other manifestations of creative thoughts and ideas.

Albert Einstein once remarked that he had in his lifetime only one or two worthy or original ideas. One was the special theory of relativity. I vaguely recall that the second one was his quest for a unified field theory. Einstein came up with his celebrated special theory of relativity while in his twenties. The balance of his life was spent in industrious work as he searched in vain to establish a more broad theory or unified field theory, but Einstein failed in that quest. Einstein seemed to have not a surplus of ideas. As I recall the Albert Einstein story as related to ideas, Einstein came to the conclusion that a person is lucky if he/she has one or two decent ideas in an entire lifetime.

The concept of an idea is that of an original thought. The educator and author Benjamin Bloom (Taxonomy of Educational Objectives, published 1956 by McKay Publishing) created a taxonomy or hierarchy of knowledge and ideas. In very rough form, Bloom’s taxonomy cited six levels of knowledge, the six being

1. Fact Level of Knowledge
2. Understanding of Facts
3. Application – where facts can be brought to bear and applied to problems
4. Ideas – where an abstract notion or concept is given expression
5. Synthesis – where two or more ideas can be combined so as to give birth to a new idea
6. Evaluation – where one has the power to search through a complex situation so as to uncover flaws in an argument

Idea #1 – Use of Adapted Bicycles to make Teaching and Acquisition of riding skills easier. This idea came to me in the mid-1980’s. It was motivated by the knowledge that linear time-invariant differential equation solutions, as solved using what we then called an analog computer, also known as an electronic differential analyzer, could be time-scaled. In short, one could cause the solutions to be speeded up or slowed down, by merely changing the feedback capacitors on all integrators in the analog computer circuit. I recognized that children, at least some children, were confused and perplexed by the relatively rapid time-scale of events when it came to initially riding a bike. This was compounded by the realization, seldom understood by many -- that small bikes are faster to fall than taller or adult bikes. Thus, when we would place a new rider on a small bike, the child was being asked to execute riding skills at a scale that was faster reacting than even compared to an adult on a conventional bike. I use the words “draftsman’s mentality” to describe persons who design bikes to be small so as to accommodate small persons. The draftsman who scales a bike small to meet the needs of a small child is in fact doing a disservice to the child. The results of this idea – that we can properly design bikes to accommodate the desired time scales as well as augment stability appropriate to learning children – is now manifested in this web site and in the Lose The Training Wheels (trademark) program.

Idea #2 – Observability of Distributed Parameter Systems. This idea resulted in my Ph.D. Dissertation, defended on September 13, 1968, and granted by Purdue University in January 1969. The title of my dissertation read, “An Investigation of Distributed System Observability from a Continuum Physics Viewpoint.” The essence of this idea was that one could identify both necessary and sufficient conditions to assure the ability to perform state reconstruction in distributed parameter (spatially distributed) systems. At that time R. E. Kalman (On the General Theory of Control Systems, presented at the I.F.A.C Congress, Moscow, 1960) had established observability conditions for lumped parameter systems, but there existed considerable confusion concerning extrapolation of that concept to distributed systems. The doctoral thesis of Richard Klein resolved the matter and has become the definitive source for definitions as well as critical theorems. In one moment of inspiration, I realized that the key requirement was uniqueness, and I set about setting up proper definitions as well as certain key uniqueness theorems. This work resulted in an article authored by my advisor Dr. Raymond Eugene Goodson and myself in the IEEE Transactions on Automatic Control, April 1970 issue.

Idea #3 – State Reconstruction as a non-well set problem in mathematical physics. As an outgrowth of the observability question as related to distributed parameter systems, I soon recognized that state reconstruction from observers or measurements is inherently non-well set. This meant that small measurement or calculation errors could result in large swings in the outputs or internal states as calculated. This led me to sensitive dependence, fractals, as well as chaotic behavior in mathematics. Methods were devised to permit internal solution states to be calculated and yet to remain stable or well-posed based on proper sensor locations, as well as proper computing mechanisms combined with realistic a priori bounds. In 1971, for example, I presented and published a definitive work at the 1971 International Federation of Automatic Control (IFAC) Symposium on Control of Distributed Parameter Systems in Banff, Alberta, Canada. Other works followed, wherein I collaborated with the renowned mathematician John R. Cannon Jr. We published papers in ASME Transactions and in S.I.A.M. (Society for Industrial and Applied Mathematics). The distinguished mathematician James Yorke, University of Maryland, rose to fame and possible fortune as he popularized the world of sensitive dependence in the early 1970’s. See “Chaos: Making a New Science” by James Glick (Penguin, 1987. New York). While I can not detract from credit due to Jim Yorke, the reality stands that certain crucial arguments which underpin chaos were laid out in my Ph.D. dissertation as early as 1968, preceding by several years the later publication of Yorke’s work. If I failed anywhere, it was in not exploiting the notions of sensitive dependence that I clearly identified as they related to the distributed parameter task of state reconstruction. I consider myself to be a polite as well as proper person, and I gave and still give credit where credit is due. Consequently, my 1971 IFAC paper was titled “Non-Well Posed Problems in the Sense of Hadamard and Their Relationship to Distributed Parameter State Reconstructor Problems.” Jacques Hadamard was a French mathematician who had anecdotally raised the question earlier in the 1930’s and so I was following his work, but expanding on it, taking it from an anecdote or off-hand remark to a dissertation complete with definitions, theorems, proofs, and practical illustrations. See J. Hadamard, “Lectures on Cauchy’s Problem in Linear Partial Differential Equations,” Dover Publications, New York, 1952 (reprint). Hadamard recognized the sensitive dependence by use of a simple example of photographing a vibrating string at two different instances in time, but stopped there. I went on to establish necessary and sufficient mathematical means to cause the state reconstruction process to be well-set or mathematically stable. In the process, many of the arguments and representations later used by Dr. Jim Yorke were present in my dissertation.

Idea #4 – Active Control of Large Civil Engineering Structures. As a control systems theorist knowledgeable with observability, controllability, as well as spatially distributed systems, in the early 1970’s I addressed the problem of mitigating unwanted aerodynamically induced vibrations in large civil engineering structures. I recognized that the wind impacting a tall building was an available force which could be manipulated, so I proposed that tall buildings could be augmented with variable appendages to permit feedback to stabilize the structures. The foundation paper was presented at the 1972 Winter Meeting of A.S.M.E, in New York City. That paper was co-authored with colleagues Dr. Cris Cusano and Dr. James J. Stukel, both from the University of Illinois. Jim Stukel went on to considerable fame and fortune as he rose through the ranks of academia and ended up serving as President of the University of Illinois for the decade of the 1990’s. What I discovered in the process is that the civil engineering community functions as a closed club, and if they did not invent an idea, they are not interested. I devoted my professional time to this topic and research for upwards of 15 years, from 1970 to 1985, and I finally folded my tent in disgust and went on to pedal bicycles. As a case in point, modern skyscrapers are now routinely fitted with energy suppression systems, and my work represents a pioneering contribution. Even today, my work of 1972 is sufficiently far advanced that civil and structural engineering types can’t grasp even now what I stated a third of a century ago. The Klein, Cusano, Stukel ASME paper of 1972 has been widely cited because it is a landmark paper, although few of the citing authors have actually read the actual paper. I can tell this because along the way Stukel’s name became misspelled and the citations then appeared with a variation in the spelling of his name. A second signal to me that others have not actually read the Klein, Cusano, and Stukel ASME paper is that an error in the citation appeared. The paper was #11 in the Atomatic Controls session at the winter 1972 ASME Meeting, hence given the designation "AUT-11." The error was that some misread the citation and therein cited the paper as "AUT-H." Persons who cite the paper with Stukel missspelled or "AUT-H" have only cited the paper based on others having cited it -- but have not actually ever read the original of the paper.

I must also point out at on December 22, 1975 I was invited by a structural engineering firm to inspect the south tower of the World Trade Center in New York City. At that time the south tower was still undergoing construction. In our tour we visited at about the 87th floor. The specific purpose of my visit was to inspect the famous (or infamous) dashpot dampers installed in the structure, as produced by 3M Company, Minneapolis MN. I was aghast to see that the steel beams and columns were bare, as opposed to being properly insulated with spray foam or other heat barriers. I raised the question of fire and heat resistant safety – to be told that five elements or considerations deemed that the construction method being used was safe and prudent. These five arguments were

• Minimal amount of combustible material present within the structure
• Early detection of fire
• Sprinkler systems to retard fire soon
• Early response by firefighters
• Containment of any fire to a localized area – even to the point that procedures called for local evacuations only, such as going up as opposed to down in the event of fire.

I expressed my views to the responsible engineers, and my views were dismissed. Recall that as an engineer I was obligated to remain professional and direct my concerns to those in the profession responsible, which I did. Going outside the profession to, say, a public forum would be construed as unethical. My views as a maverick were continued to be stated by me in engineering forums. I can recall being seated as a guest panelist in Indianapolis circa 1987, convened to discuss issues related to tall structures, wherein I made a number of overview remarks that the audience of civil engineers had difficulty accepting. I can recall showing an illustrated cartoon of what I referred to as the “Cow-Donkey Theory of Structural Control.” The audience openly laughed at my suggestions. The moderator of the panel, Dr. Nicholas Isyumov, then Director of the prestigious Boundary Layer Wind Tunnel Laboratory of London, Ontario, uttered the comment that I had perhaps missed my calling and should have opted to be a stand-up comic working in night clubs. The panel and even the audience, made up primarily of civil and structural engineers, had a good twit and more laughter over that. I smiled, concluded my remarks, and sat down. The civil engineers present, in my opinion, considered me to be a sour-grapes guy who was bitter because my “radical” views and approaches were not accepted.

I gave my most bitter swan song farewell to the civil engineering profession during a “smart structures” symposium in San Diego in early 1998. The title of my paper and presentation was “Reflections from a Found(er)ing Structural Controls Theorist.” Please note how I had used a play on words to express my utter contempt with and of civil engineers. I was indeed recognized then, and remain to this day, a “founding” father and pioneer in structural control, but at the same time I was also “foundering” meaning lost and not taken seriously. I made my scathing remarks to the audience present and have never looked back at civil engineers again until the events of September 11, 2001 changed the landscape.

The truth is that many elitist professions become closed clubs, especially when results are critical and costly. History tells us of the struggles between battleship admirals vs. admirals who favored aircraft carriers in the era preceding World War 2. Many additional examples can be cited, but the point is clear. Closed clubs are always dangerous because when free discussion is not permitted, the scientific method breaks down, and blunders happen. Either fortunately or unfortunately, reality is the final arbitrator, as reality will be the final judge of all of man’s endeavors. For civil and structural engineers, September 11, 2001 marked the day when the world looked and understood that the king was naked. The landscape was changed when viewed with the eye, i.e., the skyline of New York City, and the landscape of the mentality of thinking in the structural engineering community changed. The judge named "Reality" had spoken.

As an epilogue, in recently scanning the Internet I did some searching and came upon some startling news as related to my last three-plus decades of work in structural control. It seems that in Japan, in Tokyo, in 2001 the Triton Square office complex was completed which consisted of three adjoining tall buildings, coupled 45-, 40-, and 35- story buildings. The complex uses two active control actuators for wind and seismic protection. Papers have appeared in the literature, such as by Dr. Richard E. Christenson et al which credit me as the pioneer in the entire concept of structural control, citing the 1972 ASME paper by Klein, Cusano, and Stukel. Christenson’s paper along with colleagues B. F. Spencer, Natsuko Hori, and Kazuto Seto is titled, “Coupled Building Control Using Accelerator Feedback,” which appeared in the journal Computer Aided Civil and Infrastructure Engineering, August 2001. The Christenson et al paper states in its opening, for example,

“Coupling adjacent buildings is a developing method of structural control for mitigating structural responses due to wind and seismic excitations. The concept to allow two dynamically dissimilar structures to exert control forces upon one another to reduce overall responses of the system. Coupled building control was first suggested by Klein et al (1972) and subsequently ...”

I knew back one-third of a century ago that control systems theoretic methods would produce stunning results if and when applied to tall civil engineering structures. It is comforting to see my early work and ideas credited with such advancements. Moreover, a number of recent studies and actual experimental validations have given exactly the results I predicted decades ago – such as increases in damping by an order of magnitude or even higher. Readers interested in seeing my early paper citations in the area of structural control are invited to examine my publication list in my resume, given in an adjoining tab in this web site.

The "Cow-Donkey Theory of Structural Control" works and is vindicated.

Idea #5 – The application of Cramer’s Rule in mathematics to unravel twisted sets of linear differential equations. In the summer of 1982 I worked as a visiting senior engineer at Hughes Aircraft Corporation, Missile Systems Division. My work focused on mathematical modeling of sets of differential equations of flexible missile bodies, so as to arrive at what we call transfer functions for purposes of guidance and control. Following that stint at Hughes Aircraft, I set about for the search to unravel a mystery – why a procedure involving determinants and linear operators, shown to me at Hughes Aircraft but undocumented, could unravel highly complex sets of differential equations and pop out transfer functions. The topic concerned linear systems and thus a theorem had to exist to explain why a computer code was capable of popping out linear transfer functions in a systematic manner. A decade of work finally permitted me to state a theorem – a theorem complete with a proof. That theorem by-passed and made much of what is taught in introductory courses in control systems as quasi-obsolete. That theorem is published in Klein, R. E., "Teaching Linear Systems Theory Using Cramer's Rule," IEEE Transactions on Education, 33:3, 258-267, 1990. A detailed proof was subsequently developed, which can be supplied upon request. I have not taken the time to provide a detailed proof herein, nor even the statement of the theorem, as doing so would consume considerable time – time that could be better devoted to adapted bicycles so as to benefit children. For those interested, the IEEE paper cited above contains the essence of my ideas, although the detailed proof was developed later and is not included. At some point I’ll dig up a copy of the proof and possibly post it as a PDF document, as it is in handwritten form.

In closure, I have cited and discussed five ideas above that I personally consider as significant in my life’s work. A sixth idea is also discussed at some length in an adjacent tab in this web site – Ice Age Riddles. Concerning ideas and one’s life’s work, one will never know, in his/her lifetime, how society will judge the work of any person. I hope to be judged with some degree of charity. I will venture forth to speculate just a little. I will say that in most cases my work and ideas have focused on significant societal, engineering, and mathematical problems, and problems where my thoughts and quests were ahead of the mainstream. In short, I have never been accused of being one to jump onto popular bandwagons. I do consider myself as a pioneer and a pioneer in many fields. I will cite some examples to illustrate this point:

• In 1972 and even earlier I laid the foundation work for the application of feedback theoretic principles to solve the problems of increasing damping and thus safety in tall engineering structures. Some thirty years subsequently, into our present century, a modern office building complex was designed and erected in Tokyo with precisely these concepts in mind. I advocated that instead of adding control to existing buildings, that buildings should be designed a priori with control in mind. That has happened. Moreover, a number of engineering peer-reviewed articles cite my work as founder and as the origin of the idea.
• The work embodied in my doctoral thesis laid the groundwork for a number of innovative concepts, including results that later emerged in the popularization of chaos theory and sensitive dependence.
• Lastly, the work involving bicycle concepts has provided many firsts. An extensive experimental effort over a span of one decade allowed many riddles of the bicycle to be understood. My work has demonstrated how bicycles can be used to enhance effective teaching of control system theoretic principles, as at present a number of universities in this country and abroad have adopted such approaches. The use of adapted bicycles to enable children with special issues to learn to ride bikes has been perhaps the most gratifying of all of my accomplishments.
• I feel that I have made yet other contributions, certain of which remain yet to be recognized. I feel, for example, that the work on Ice Age Riddles as well as insights on biblical passages related to the flood hold the potential for new insights to lead to the betterment of mankind.

Closure -- There is little question that I have devoted the bulk of the last twenty years to my bicycle pursuits, along with the desire to help children learn how to ride bikes. The other five ideas (other than the bicycle pursuits), although interesting, do not compel me to proclaim their application to the point of devoting my remaining years to further work on them. I have put my feet to the pedals as related to bikes, as that is where my true passion rests.

The curious are invited to view the sixth idea of Dr. Klein's, which concerns Noah and the Ark, and ramifications with respect to Ice Ages Riddles. Please see the next adjoining tab.

Richard E. Klein (May 20, 2005, last revised January 25, 2011)
Copyright, 2005-2011