Fuzzy Logic is a logical system which allows for degrees of truth. It allows for a world which is not either all on or all off. Fuzzy logic allows for the reality of a nearly infinite quantification of “some”. It is what allows us to ask, and answer, questions that begin with the words, “To what extent….”
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In the summer of 2006, my wife and I purchased a brand new Mitsubishi Outlander SUV as our new family vehicle. That particular Mitsubishi Outlander was a first generation of the nameplate and it was built in Okazaki, Japan in July of 2005; but, it was sold to me about a year later in Thunder Bay, Ontario as a 2006 model. After fifteen years of owning, operating and maintaining this vehicle, I recently noticed, or perhaps simply recalled, that this little SUV uses something called “fuzzy logic” in the computer of its transmission. For some reason, that fact seemed to me to be an interesting and significant starting point for investigation. After all the term “fuzzy logic” seemed to be the kind of thing that someone might use to describe a decision-making process that they considered to be rather less than clear and pristine. And indeed, it occurs to me that life and reality are almost always rather less than clear and pristine. So I decided to delve the matter to learn more about what significance this “fuzzy logic” might have – to my car’s transmission and possibly also for me in my quest to live the kind of life I want to live and be the kind of person I want to be.
My Mitsubishi’s transmission is formally designated as INVECS-II, where INVECS is an acronym for Intelligent and Innovative Vehicle Electronic Control System. The roman numeral two following the acronym indicates that the transmission in my vehicle is actually the second generation (or iteration) of this declaredly intelligent and innovative system. Aside from setting the stage for a novel marketing literature tech-speak blurb, what the INVECS transmission does is continuously adapt the vehicle’s gear-shifting behaviour based on the vehicle driver’s style and the measurable road conditions. It is a dynamic rather than a static transmission system.
As may be predicted, this dynamic decision-making process reminds me of Robert Pirsig’s views about static and dynamic quality. These are central concepts to Pirsig’s Metaphysics of Quality….which is itself a kind of fuzzy (and by that I do mean, unclear) philosophy. At the moment, I’m not going to try to provide an explanation or analysis of Pirsig’s ideas on static and dynamic quality – but I think it is interesting that the fuzzy logic in my transmission may well provide insights into a Metaphysics of Quality (and vice versa).
For example, one of the most often referenced passages in Zen and The Art of Motorcycle Maintenance says “The Buddha, the Godhead, resides quite as comfortably in the circuits of a digital computer or the gears of a motorcycle transmission as he does at the top of a mountain, or in the petals of a flower. To think otherwise is to demean the Buddha, which is to demean oneself.” This short passage demonstrates Pirsig’s extraordinarily consistent attention to the detail of his philosophy. And it seems like no small coincidence that the key feature here is a vehicle transmission.
For more than a hundred years, the internal combustion engine has been an intimate part of human societies and of global civilization. Whether one has any affection for these noisy, stinky, finicky, polluting monsters or not – the internal combustion engine has been a kind of partner and soul-mate to humanity during the twentieth century. The internal combustion engine (ICE) is so well beloved by people that automotive enthusiasts and automotive literature reach their most poetic, rhetorical and emotional heights when approaching the topic of vehicle engines. The devotion is very effectively religious in its enthusiasm (a term I apply in both its contemporary and its archaic sense0.
It might seem odd, then, that one of Zen and the Art’s most iconic passages refers to the gears of a motorcycle transmission rather than, for example, the valvetrain or carburetors of a motorcycle engine. Upon investigation, it becomes clear that the passage is written the way it is because it is consistent with Pirsig’s underlying philosophy. Simply stated, a motorcycle transmission is what allows progression of a static entity within the dynamic conditions of the real world. It is a real-time mechanical processor. Stated slightly differently, Pirsig clearly understood that an engine may well be the metaphorical heart of a vehicle – but the transmission is the brain. Actually using Pirsig’s terminology I’m going to suggest that the engine is the romantic mode of the motorcycle while the transmission is the classic mode.
How is it that a transmission is the brain of a vehicle?
An ICE works by burning fuel and oxygen and turning little explosions of energy into a rotating force…most ICE’s rotate from 800 rpm all the way up to 16,000 or more rpm’s. That is more than a vehicle’s wheels…so transmissions take the ICE’s rotation and converts that to RPM’s that make sense at the wheel. The earliest transmissions were manually-coordinated collections and quantities of gears which enabled a vehicle to translate engine power into faster and faster speeds. A person would monitor the real world conditions and preferences and change from one gear to another. The person made decisions that were translated into motion through the transmission. In effect a manually operated transmission accepts the inputs of power from the engine and decision from a human to deliver output to the vehicles drive wheel(s).
Many (certainly not all) people who ride motorcycles and cars enjoy being an active participant in the process….of knowing what is going on and choosing when and how gears are changed. Later, automatic transmissions were developed which eliminated the need for a person to decide, the transmission would automatically shift when particular conditions or states were reached. Getting back to the fuzziness of life and reality – being an active participant in the selection of gears means you choose the collection of gears intended to move you in your preferred direction.
This is, perhaps, one of the most profound and fundamental considerations that anyone can make about things. Because, almost certainly, whether you want to be active participant in decision-making or not – whether while operating a motorcycle or while managing other aspects of your life – this does not merely inform the kind of experience you may expect to have, it may also define the type of experience that you cannot have. For the most part, you really can’t coast along in a disengaged way with a vehicle equipped with a manual transmission and you can’t coast along in a life where you actively engage in your decisions. There is some effort involved.
It is something to think about. Personally, I earnestly recommend learning to operate a manual transmission (literally and figuratively).
Technological progress eventually resulted in automatic transmissions, which are a kind of static system wherein a narrow range of inputs produce set outputs. In an oversimplified way, achieving certain engine RPMs tells the transmission to shift to the next gear up (and vice versa). And then later, gears were eliminated completely in what is called a continuously variable transmission. This latter form of transmission not only removes the decision making, it removes even the pretense and underlying infrastructure that enabled individual decision making. There’s another profound observation about progress and modern society in that observation. If only one could tease out what that might be!
Regardless, in a traditional transmission, whether the gears are selected by a human being or by a computer, what we have is a system which responds to changing (dynamic) situations to select a preferred (static) pattern or gear to allow motion. An internal combustion engine only becomes an effective motor with the presence of a transmission.
How how does all that relate to fuzzy logic? The next bit starts get a bit more complicated…and much much fuzzier.
In my essay Footnotes to Zen and The Art of Motorcycle Maintenance, Part One, which is available in text on the Zensylvania website or as an audio podcast episode, I talked a bit about how that book’s title might be viewed as employing the language of logic. I argued that viewing the word “and” in the title Zen AND the Art of Motorcycle Maintenance as signifying an “AND gate” from the language of formal logic can provide novel and valuable insights into Robert Pirsig’s philosophy and rhetorical approach. In other words, his story-telling technique.
An “AND gate” is a basic digital logic feature which describes a situation where a specific output is generated only when multiple specific inputs are provided. In other words, Pirsig’s title allows placement of “Zen” as one input and “the art of motorcycle maintenance” as a second input at the front end of a logic gate. The two are brought together for an output. In effect, they are synthesized.
As an aside, isn’t it interesting that a transmission serves as a kind of “AND gate” for the power produced by an engine and the decision making of an intelligent human or non-human decision-maker?
By viewing the book’s title, and the book itself, in this way might indicate that the output side of this “AND gate” view of Pirsig’s title may be the book’s subtitle “An Inquiry into Values” as the output side of the AND gate. Alternately, perhaps life itself is the other side.
As you may see, viewing the words, “Zen AND the Art of Motorcycle Maintenance” via the language of mathematics and logic, is a playfully interesting and elegant demonstration of the book’s primary objective as presented in that subtitle. I want to keep that short phrase, “An Inquiry into Values”, in mind throughout this essay, as I think it may well be a defining detail or consideration not only for Pirsig’s book, but for other things as well.
A central theme of ZAMM , as well as Zen philosophy is a rejection of dualism. While I recognize that I am at risk of backing-up so far that we’ll all have forgotten that this was supposed to be an essay about fuzzy logic, it is a genuinely significant feature of my reflections and the position that I’m shuffling toward.
It is reasonable in Zen to argue that those two inputs that I mentioned, “Zen” and “The Art of Motorcycle Maintenance”, are not actually separate and distinct from each other. Viewing the title as an “AND gate”, as a point of synthesis makes this point explicitly. You just have to be familiar with the language and be open to reconsidering your perspective. I might also add that an “AND gate” may be construed as a process.
My non-expert depiction of an “AND gate” may be due some extra explanation and justification. And perhaps also some shared detail as to why I think that “fuzzy logic” is an interesting and potentially critical concept. Keep in mind as we proceed, that this is all in the spirit of Zensylvania’s non-expert status….and also, that what follows is a kind of the speculation of “fuzzy logic” as a concept to approach the integration of human experience, reality and decision-making while attempting to explain that speculation. I want to call it “living fuzzy”. As usual, yes we’re going to be a bit meta and a bit self-referential.
So let’s start with that “AND gate”. It comes to us from so-called Boolean Algebra. This is a form of algebra where the values of variables are so-called truth values of true and false. Well already we have a mass of terminology that threatens to shut many non-mathematicians and non-experts right down. But let’s have a look at what we have.
Algebra is a form, feature or branch of mathematics. It is the study of mathematical symbols and the rules for manipulating those symbols. It doesn’t seem unreasonable to say that algebra is the syntax and grammar of the language that is mathematics.
Here in Zensylvania, we consider all language to be a form of metaphor. A situation where words, symbols, images and other tricks of language are used to describe the world. All of these tools are stand-in for things in the real even imaginary world. The word motorcycle is not a motorcycle. To say “Motorcycle Zen” is to say “Metaphor Zen.” Language is always a placeholder for some other thing. Often, but not always, a thing in the real world.
So for anyone who feels intimidated by algebra and mathematics…I really want to repeat that algebra is to math what grammar is to language. They are a way to explain the world. Algebra is what reveals the form, pattern and process of math. Math itself is a quantification of things. I want to suggest that mathematics is not the only language of quantification but I’m not entirely certain that is fully true. I’d need to use a kind of fuzzy logic to work that out. And I don’t want to get ahead of myself. At the least and for now, let me argue the more solid point that Boolean Algebra is not the only algebra.
Like any other language, mathematics is used to describe and explain things that we can observe in what we call the real world…and frankly, also in theoretic worlds. To say or write that Boolean algebra describes a world where the values of variable are so-called truth values of true and false is to translate algebra into a jargon-ridden version of the English language. But such is the delicate and imperfect art of translation….not to mention the delicate and imperfect task of explaining the world.
So what about that jargon?
The word algebra comes from the Arabic word al-jabr, which is taken from the title of a 9th century book The Science of Restoring and Balancing by the Persian mathematician and astronomer al-Khwarizmi. Al-jabr meant the “reunion of broken bones”…or bone-setting. al-Khwarizmi used the term to refer to the operation of moving a term from one side of an equation to the other. As language is borrowed and shifted over time, our English-language version of the word “algebra” came from an Arabic term for a medical concept.
In effect the denotative meaning of the word “al-jabr”, which referred to a process of bringing together bones was al-Khwarizmi’s connotative metaphor for the process of bringing together mathematical symbols. Al–jabr became algebra. And algebra is the bones of mathematics. And you can see that the bones of mathematics is the structure, form or pattern of mathematics as I’ve already described.
Exploring the etymology of the word “algebra” is a wonderful example of how metaphor and language develop….but let’s get back to the Boolean algebra. As previously stated, Boolean algebra describes a world where the values of variable are so-called truth values of true and false.
From our example of the book title “Zen and the Art of Motorcycle Maintenance”, the variables are “zen” on the one hand and “the Art of Motorcycle Maintenance” on the other. In an algebraic sense, both of the values are assigned a truth value. Within Boolean alegebra, these variables are assigned truth values of either one or zero, where one is true and zero is false.
Boolean Algebra was introduced by the English mathematician George Boole in his first book The Mathematical Analysis of Logic in 1847 and set forth more fully in his An Investigation of the Laws of Thought, in1854. Charles Sanders Peirce, who coined the term “pragmatic philosophy” and founded the field, gave the title “A Boolean Algebra with One Constant” to the first chapter of his “The Simplest Mathematics” in 1880.
For those interested to follow the trail we’ve described, we can go from al-Khwarizmi to Zensylvania along the following path: from al-Khwarizmi to George Boole; from Boole to Charles Sanders Peirce. From Pierce to William James and then on to Alfred North Whitehead down to F.S.C. Northrop (who we’ve not yet spent much time on) and arriving at Robert Pirsig and thereby to yours-truly and the Zensylvania Podcast.
One of the most famous lines from Pirsig’s Zen and the Art of Motorcycle Maintenance goes “The Buddha, the Godhead, resides quite as comfortably in the circuits of a digital computer or the gears of a cycle transmission as he does at the top of the mountain, or in the petals of a flower. To think otherwise is to demean the Buddha – which is to demean oneself.” It seems only fair to give Pirsig and his writing reasonable credit for being not only aware of the language of Boolean Algebra, but also educated about its uses and implications. In fact, it is reasonable to observe that Boolean algebra has been fundamental in the development of digital electronics of his day. Pirsig was, after all, a technical writer in the field at the time.
My suggestion that Pirsig referenced a Boolean “AND gate” is, as I hope that I’ve demonstrated, a reasoned and reasonable suggestion.
The subtitle of Zen and the Art of Motorcycle Maintenance is “An Inquiry into values”. In Boolean algebra, where variables are assigned truth values, usually denoted 1 and 0, true and false respectively. It seems to me that Pirsig would have been supremely aware of the consistency between his motor-cycle themed inquiry and Boolean Algebra concepts.
In Boolean algebra, an “AND gate” is a conjunction. The and of a set of operands is true if and only if all of its operands are true. All elements have to be present for something to be considered “true”. We’re not going to run that down much more than that right now because that is the central matter that Pirsig worked with and that we need to contrast with “fuzzy logic”.
Zen and the Art of Motorcycle Maintenance.
Internal Combustion Engine (ICE) and Intelligent Decision Maker (IDM).
So what is “fuzzy logic”? Contrast the picture of truth that Boolean algebra presents, that variables are assigned truth values of 1 or 0, true or not true with the situation where Fuzzy logic allows that the truth value of a variable may be any real number between 0 and 1. Think about that…a real number between zero and one. Degrees of quantification.
As a sidebar, isn’t it wonderful that mathematics is capable of employing both real and imaginary numbers? Thank you Rene Descartes.
With fuzzy logic, there is a logical system which allows for degrees of truth. It allows for a world which is not either all on or all off. Fuzzy logic allows for the reality of a nearly infinite quantification of “some”.
The term fuzzy logic as the formal designation for a mathematical process was introduced with the 1965 proposal of fuzzy set theory by and Azerbaijani scientist named Lotfi Zadeh. The underlying concepts had been studied since the 1920s under the slightly different term infinite-valued logic by the Polish mathematicians Jan Lukasiewicz and Alfred Tarski. That term “infinite-valued logic” simply says that there are an infinite number of things that can influence an outcome. I highlight this as a way to emphasize that fuzzy-logic and infinite-valued logic are, before anything else, a rejection of either/or dualism. I’m sure there are experts in the field who may be motivated to offer some tidying up of the history and facts here…but I’m happy to keep it all a bit fuzzy.
Fuzzy logic derives its fuzziness from the fact that people make decisions based on imprecise and non-mathematical information. Mathematics is not the underlying language of human decisions making. At least, not in the way that most of us conceptualize mathematics. Fuzzy models or sets are a mathematical way to represent and systemically account for the vagueness that is inherent in, well, everything. These models have the capability of recognizing, representing, manipulating, interpreting, and utilizing vague, uncertain information. The kind of information that fills the reality of living.
Boolean Algebra, “AND gate” propositions, like other all-or-nothing propositions are convenient in their ability to cut through clutter with an absolute proposition. In some situations, a simple yes/no framework makes decision-making easy. Easier yes/no frameworks make, however, for un-subtle and often un-reflective decisions. One only needs to look at Canadian “first-past-the-post” electoral design to observe the limitations of a binary system applied to a world that is much more varied and complicated. Often in Canadian electoral results, the largest localized minority-share-of-the-vote political party wins, leaving the majority of citizens disappointed and disenfranchised.
But politics aside, consider the regular day-to-day decisions and adjustments we all have to make where proportions matter, where degrees of truth is a valid and useful concept, where there is more than just a go-no/go proposition. Do you to into the shower using ONLY hot water or only cold water? Or do you use a mix the two? A fuzzy model allows for a nearly infinite range of answers to the question of how much hot water to use. A fuzzy model includes a multiplicity of yes/no propositions in context of each other. That is how a fuzzy model provides a more accurate and appropriate picture of the world.
Let’s get back to my Mitsubishi’s transmission. On the website of the Society of Automotive Engineers, there is an abstract of an article written by Katsutoshi Usuki, Kenjiro Fujita and Katsuhiro Hatta that provides an insight into fuzzy logic that is as insightful and useful as it is dry and, a least superficially, uninspiring. What I am providing is a abridged version to focus on what strikes me as insightful to Pirsig’s Metaphysics of Quality and to this incomplete investigation of Living Fuzzy. Usuki, Fujita and Hatta wrote that Mitsubishi Motors developed the INVECS automatic transmissions with electronic controls which incorporated a shift-schedule control that allowed gear selection in response to driving condition and the driving habits of individual drivers. These transmissions also included a so-called “sporty mode” which allowed the driver to choose a dynamic drive feel as if operating a manual transmission….but without the clutch. In other words dynamically selecting gears in response to the conditions they experienced and based on their priorities.
For anybody who rides a manual transmission motorcycle or has driven a manual-transmission car, you will be familiar with the need for progressive braking and the need for a controlled and sensitive balance of clutch and throttle. Get it wrong and operation of the vehicle can be a frightening and violent situation. All kinds of bucking and gnashing can go on. You also know that driving conditions such as how wet or dry the road surface is, how fast you’re going, the RPMs of the engine, whether you’re entering a turn or in a straight…all of these affect how and how much clutch, brake and throttle may be used to keep things in control. It’s a dynamic situation. There are degrees of truth. Perhaps some brake but not all of the brake. Perhaps the the clutch needs to be let out a tad more quickly, but not too much more quickly.
The INVECS transmission in my SUV incorporated a shift-schedule control that allowed gear selection in response to driving condition and driving habits of individual drivers. These transmissions also included a so-called “sporty mode” which allowed the driver to choose a dynamic drive feel as if operating a manual transmission….but without the clutch. In effect, the intelligent transmission in my SUV acts as I would act when operating a manual transmission. It does this literally as it learns my driving preferences and it does this metaphorically as it changes the gears based on dynamic, real world variables that may call for some brake or a bit more sharpness in the release of the clutch.
How does the fuzzy logic do this…unlike Boolean algebra which uses truth value of zero or one, fuzzy logic allows for a wide range of inputs which can produce outputs that fall somewhere between zero and one. I want to say that it provides the possibility of degrees of truth which ranges from completely false to complete true but includes the possibility of concepts like somewhat true, partially false, largely true…and so on. It is a kind of spectrum of truth that is contingent upon the contexts and contingences within which it exists. Frankly and simply, it allows for the real world. Within fuzzy logic, truth is inherently not binary. It is not dualistic.
The INVECS transmission feels the road conditions as I might feel the road conditions…and to an extent, I as the vehicle operator are one of the conditions the transmission feels. Different drivers behave differently and the transmission allows for that variability…the distances between 0 and 1….the driver with a heavy foot and the driver who is more casual.
For those who may not relate to all of this motorcycle and transmission information as a meaningful metaphor, let me suggest that many, if not all, of the daily decisions of life are an individual’s reactions to the conditions of the metaphorical road- that-is-life and the person’s individual preferences at any given time. Sometimes we may want to go along quickly and efficiently. Sometimes we may want to proceed with low-speed caution…and sometimes we may get a bit of a thrill from spinning our wheels.
In his Metaphysics of Quality, Robert Pirsig described “dynamic quality” and “static quality”. Static quality is something that can be defined and, I might argue responds well to Boolean algebra. The “AND gate” applicability of a definable “ZEN” and a definable “Art of Motorcycle” works with static quality. Pirsig’s “dynamic quality”, his so-called cutting edge of reality does not. Dynamic quality works better with “fuzzy logic”.
Alfred North Whitehead on the other hand had a Philosophy of Organism which describes “actual occurrences” and “actual entities”. Dynamic Quality, this cutting edge of reality is the reality process which Whitehead depicts.
A more sales-oriented version of the Mitsubishi story….says the INVECS-II automatic transmission simultaneously provides driving pleasure and operational economy…1st gear is the low range to be used when power is required. 5th gear is the high range and provides optimum fuel economy and quietness of operation. The other gears allow vehicle operation in response to existing road conditions or driver preferences and style. When the INVECS-II is used in the automatic mode, all shifting decisions are made by the on-board computer. This permits safe and easy driving. The same computer exercises control over the engine during shifting to provide the highest possible shifting quality. For enhanced driving pleasure, the INVECS-II has a sports mode that allows the driver to take control of shifting decisions.”
The INVECS transmission sets out truth variables as ranging from on the one hand “when power is required” (first gear) and when the “optimum fuel economy and quietness” are preferred. It is a system which is based on efficiency use but also driving pleasure.
Which brings us back to Pirsig and an inquiry into values. Pleasure. What is considered good? Power or optimum fuel economy and quietness”. What is “good” is different, or dynamic, based upon the conditions. There is a range or degree of what is good between these two ends. It is an extremely improbable journey, if not impossible one where “power” is completely and continuously preferred over “optimum fuel economy and quietness” or vice versa.
I am also struck by the observation that enhanced driver pleasure is recognized by the engineers when they are actively engaged in the decision making process…this is a metaphor of life. We derive more pleasure in our life when we are actively involved in the decisions…even when the variables that may affect them are infinite in quantity and entirely unclear.
This page was last edited on 20 January 2023.
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2 responses to “Living Fuzzy: An Incomplete Exploration of Fuzzy Logic”
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