George E Forsythe - Collected Quotes

"The use of practically any computing technique itself raises a number of mathematical problems. There is thus a very considerable impact of computation on mathematics itself, and this may be expected to influence mathematical research to an increasing degree." (George E Forsythe, 1958) 

"I consider computer science to be the art and science of exploiting automatic digital computers, and of creating the technology necessary to understand their use. It deals with such related problems as the design of better machines using known components:, the design and implementation of adequate software systems for communication between man and machine, and the design and analysis of methods of representing information by abstract symbols and of processes for manipulating these symbols." (George E Forsythe, "Stanford University's Program in Computer Science", 1965)

"To a modern mathematician, design seems to be a second-rate intellectual activity." (George E Forsythe, 1966)

"Computer science is at once abstract and pragmatic. The focus on actual computers introduces the pragmatic component: our central questions are economic ones like the relations among speed, accuracy, and cost of a proposed computation, and the hardware and software organization required. The (often) better understood questions of existence and theoretical computability - however fundamental - remain in the background. On the other hand, the medium of computer science - information - is an abstract one. The meaning of symbols and numbers may change from application to application, either in mathematics or in computer science. Like mathematics, one goal of computer science is to create a basic structure in terms of inherently defined concepts that is independent of any particular application." (George E Forsythe, "What to do till the computer scientist comes", 1968)

"The most valuable acquisitions in a scientific or technical education are the general-purpose mental tools which remain serviceable for a lifetime. I rate natural language and mathematics as the most important of these tools, and computer science as a third." (George E Forsythe, "What to do till the computer scientist comes", 1968)

"Most of known computer science must be considered as design technique, not theory." (George E Forsythe, "What to do till the computer scientist comes", 1968)

"People have said you don’t understand something until you’ve taught it in a class. The truth is you don’t understand something until you’ve taught it to a computer, until you’ve been able to program it." (George E Forsythe)

On Problem Solving XVIII: Practice

"The insights gained and garnered by the mind in its wanderings among basic concepts are benefits that theory can provide. Theory cannot equip the mind with formulas for solving problems, nor can it mark the narrow path on which the sole solution is supposed to lie by planting a hedge of principles on either side. But it can give the mind insight into the great mass of phenomena and of their relationships, then leave it free to rise into the higher realms of action." (Carl von Clausewitz, "On War", 1832)

"One of the most important tasks of the teacher is to help his students. This task is not quite easy; it demands time, practice, devotion, and sound principles." (George Pólya, "How to Solve It", 1945)

"We acquire any practical skill by imitation and practice. […] Trying to solve problems, you have to observe and to imitate what other people do when solving problems and, finally, you learn to do problems by doing them." (George Pólya, "How to Solve It", 1945)

"The trouble with mathematics is that, however diligent you are in going to lectures and in learning the theory, you may still not be able to do the problems." (Maurice Wilkes, "Memoirs of a Computer Pioneer", 1985)

"Design thinking taps into capacities we all have but that are overlooked by more conventional problem-solving practices. It is not only human-centered; it is deeply human in and of itself. Design thinking relies on our ability to be intuitive, to recognize patterns, to construct ideas that have emotional meaning as well as functionality, to express ourselves in media other than words or symbols." (Tim Brown, "Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation", 2009)

"Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice." (George Pólya)

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On Problem Solving XX: Life

"The difficult problems in life always start off being simple. Great affairs always start off being small." (Lao Tzu, cca 400 BC)

"Man was not born to solve the problems of the universe, but rather to seek to lay bare the heart of the problem and then confine himself within the limits of what is amenable to understanding." (Johann Wolfgang von Goethe, 1825)

"The greatest art, both in teaching and in life itself, consists in transforming the problem into a postulate." (Johann Wolfgang von Goethe, 1928)

"The meaning and design of a problem seem not to lie in its solution, but in our working at it incessantly." (Carl G Jung, "Modern Man in Search of a Soul", 1933)

"The field of consciousness is tiny. It accepts only one problem at a time. Get into a fist fight, put your mind on the strategy of the fight, and you will not feel the other fellow's punches." (Antoine de Saint-Exupéry, "Flight to Arras", 1942)

"Life ultimately means taking the responsibility to find the right answer to its problems and to fulfill the tasks which it constantly sets for each individual." (Viktor E Frankl, "Man's Search for Meaning", 1946)

"We are built to conquer environment, solve problems, achieve goals, and we find no real satisfaction or happiness in life without obstacles to conquer and goals to achieve." (Maxwell Maltz, "Psycho-Cybernetics", 1960)

"The mystery of life isn't a problem to solve, but a reality to experience." (Frank Herbert, "Dune", 1965)

"Sometimes the situation is only a problem because it is looked at in a certain way. Looked at in another way, the right course of action may be so obvious that the problem no longer exists." (Edward de Bono, "The use of lateral thinking", 1967)

"There are problems in this universe for which there are no answers." (Frank Herbert, "Dune Messiah", 1969)

"The easiest way to solve a problem is to deny it exists." (Isaac Asimov, "The Gods Themselves", 1972)

"When a decision is made to cope with the symptoms of a problem, it is generally assumed that the corrective measures will solve the problem itself. They seldom do." (Masanobu Fukuoka, "The One-Straw Revolution", 1975)

"If you go through the world looking for excellence, you will find excellence. If you go through the world looking for problems you will find problems." (Joseph O'Connor & John Seymour, "Introducing Neuro-Linguistic Programming: Psychological Skills for Understanding and Influencing People", 1990)

"Every problem has a solution, although it may not be the outcome that was originally hoped for or expected."  (Alice Hoffman, "Practical Magic", 1995)

"Pain is a relatively objective, physical phenomenon; suffering is our psychological resistance to what happens. Events may create physical pain, but they do not in themselves create suffering. Resistance creates suffering. Stress happens when your mind resists what is... The only problem in your life is your mind's resistance to life as it unfolds." (Dan Millman, "Everyday Enlightenment: The Twelve Gateways to Personal Growth", 1998)

"[...] all problems can be reperceived as challenges, or 'opportunities' to change, grow or learn." (Robert B Dilts, "Sleight of Mouth: The Magic of Conversational Belief Change", 1999)

"All problems are illusions of the mind." (Eckhart Tolle, "Practicing the Power of Now: Essential Teachings, Meditations, and Exercises", 2001)

"We humans have two great problems: the first is knowing when to begin; the second is knowing when to stop." (Paulo Coelho, "The Zahir: A Novel of Obsession", 2005)

"Most problems we face in life, as I have said already, happen in our minds. Furthermore, problems generally exist in our concept of the past and the future. The past and the future don’t exist except in our minds." (Richard Bandler, "Get the Life You Want: The Secrets to Quick and Lasting Life Change with Neuro-Linguistic Programming", 2008)

"One of the most important aspects of what human beings do is build beliefs. Beliefs are what trap most people in their problems. Unless you believe you can get over something, get through something, or get to something, there is little likelihood you will be able to do it. Your beliefs refer to your sense of certainty on some of your thoughts." (Richard Bandler, "Get the Life You Want: The Secrets to Quick and Lasting Life Change with Neuro-Linguistic Programming", 2008)

"When you can take on board new, positive suggestions and disbelieve the old, limiting suggestions, you will be ready to tackle the rest of your problems, especially your fears." (Richard Bandler, "Get the Life You Want: The Secrets to Quick and Lasting Life Change with Neuro-Linguistic Programming", 2008)

"Our most important problems cannot be solved; they must be outgrown." (Wayne Dyer, "Excuses Begone!: How to Change Lifelong, Self-Defeating Thinking Habits", 2009)

"A problem is a difference between things as desired and things as perceived. […] Seen in this way, the problem could be solved either by changing desires or changing perceptions." (Donald C Gause & Gerald M Weinberg, "Are Your Lights On?", 2011)

"As a practical matter, it is impossible to define natural, day-to-day problems in a single, unique, totally unambiguous fashion. On the other hand, without some common understanding of the problem, a solution will almost invariably be to the wrong problem." (Donald C Gause & Gerald M Weinberg, "Are Your Lights On?", 2011)

"The really important thing in dealing with problems is to know that the question is never answered, but that it doesn't matter, as long as you keep asking. It's only when you fool yourself into thinking you have the final problem definition - the final, true answer - that you can be fooled into thinking you have the final solution. And if you think that, you're always wrong, because there is no such thing as a 'final solution'." (Donald C Gause & Gerald M Weinberg, "Are Your Lights On?", 2011)

On Numbers: Binary Numbers

"[The information of a message can] be defined as the 'minimum number of binary decisions which enable the receiver to construct the message, on the basis of the data already available to him.' These data comprise both the convention regarding the symbols and the language used, and the knowledge available at the moment when the message started." (Dennis Gabor, "Optical transmission" in Information Theory : Papers Read at a Symposium on Information Theory, 1952)

"[...] there can be such a thing as a simple probabilistic system. For example, consider the tossing of a penny. Here is a perfectly simple system, but one which is notoriously unpredictable. It maybe described in terms of a binary decision process, with a built-in even probability between the two possible outcomes." (Stafford Beer, "Cybernetics and Management", 1959)

"Bivalence trades accuracy for simplicity. Binary outcomes of yes and no, white and black, true and false simplify math and computer processing. You can work with strings of 0s and 1s more easily than you can work with fractions. But bivalence requires some force fitting and rounding off [...] Bivalence holds at cube corners. Multivalence holds everywhere else." (Bart Kosko, "Fuzzy Thinking: The new science of fuzzy logic", 1993)

"Fuzziness has a formal name in science: multivalence. The opposite of fuzziness is bivalence or two-valuedness, two ways to answer each question, true or false, 1 or 0. Fuzziness means multivalence. It means three or more options, perhaps an infinite spectrum of options, instead of just two extremes. It means analog instead of binary, infinite shades of gray between black and white." (Bart Kosko, "Fuzzy Thinking: The new science of fuzzy logic", 1993)

"Somewhere in the process wishful thinking seems to take over. Scientists start to believe they do math when they do science. This holds to greatest degree in an advanced science like physics or at the theoretical frontier of any science where the claims come as math claims. The first victim is truth. What was inaccurate or fuzzy truth all along gets bumped up a letter grade to the all-or-none status of binary logic. Most scientists draw the line at giving up the tentative status of science. They will concede that it can all go otherwise in the next experiment. But most have crossed the bivalent line by this point and believe that in the next experiment a statement or hypothesis or theory may jump from TRUE to FALSE, from 1 to 0." (Bart Kosko, "Fuzzy Thinking: The new science of fuzzy logic", 1993)

"The binary logic of modern computers often falls short when describing the vagueness of the real world. Fuzzy logic offers more graceful alternatives." (Bart Kosko & Satoru Isaka, "Fuzzy Logic,” Scientific American Vol. 269, 1993)

"A dictionary definition of the word ‘complex’ is: ‘consisting of interconnected or interwoven parts’ […] Loosely speaking, the complexity of a system is the amount of information needed in order to describe it. The complexity depends on the level of detail required in the description. A more formal definition can be understood in a simple way. If we have a system that could have many possible states, but we would like to specify which state it is actually in, then the number of binary digits (bits) we need to specify this particular state is related to the number of states that are possible." (Yaneer Bar-Yamm, "Dynamics of Complexity", 1997)

"A bit involves both probability and an experiment that decides a binary or yes-no question. Consider flipping a coin. One bit of in-formation is what we learn from the flip of a fair coin. With an unfair or biased coin the odds are other than even because either heads or tails is more likely to appear after the flip. We learn less from flipping the biased coin because there is less surprise in the outcome on average. Shannon's bit-based concept of entropy is just the average information of the experiment. What we gain in information from the coin flip we lose in uncertainty or entropy." (Bart Kosko, "Noise", 2006)

"Why should anyone know or care about binary numbers? One reason is that working with numbers in an unfamiliar base is an example of quantitative reasoning that might even improve understanding of how numbers work in good old base ten. Beyond that, it’s also important because the number of bits is usually related in some way to how much space, time or complexity is involved. And fundamentally, computers are worth understanding, and binary is central to their operation." (Brian W Kernighan, "Understanding the Digital World", 2017)