The Internet Hitchhiker’s Guide to Fuzzy Logic World

Adam Douglas wrote one of the humor masterpieces of all time with his book “The Hitchhiker’s Guide to the Galaxy” and the title of this article is obviously a playful paraphrase of the funny title of his work to talk about serious things with humor.

I hope Adam Douglas doesn’t get mad at me wherever he is !

However, let’s start by asking ourselves a question: is the Internet comparable to Deep Thougt, the omniscient computer of Douglas’ novel, a machine that takes millennia to give an answer? But above all: which question should we ask to Internet-D.T. (Internet-Deep Tought) and which answer should we expect?

If you think about it indeed, imagining that there is a Super Google, a super Browser to which we ask “the ultimate question”, what will be the research that it will operate with its super algorithm, with its “Hyper Page Rank”? And at the end of its elaboration what will be the answer that Internet-D.T. will give us?

Most of the internet users actually believe to find all the answers to their needs, to their material and spiritual needs by typing requests on search engines. So, if it were possible to identify a definitive question that applies to all human beings, to Mankind, what would it be? But mostly what would be the answer of Internet-D.T.?

The ultimate question would most likely be as generic, all-inclusive, totalising and ridiculous at the same time as the one imagined by Douglas: “We want to tell us…the Answer….Life…The Universe…Everything !”. If one reflects for a moment with the tools of Logic on this “total question” one understands that it is a “flight towards the Absurd”. In more technical terms, it is a “contradiction” because it incorporates and admits “everything” and “the opposite of everything” removing the Aristotelian principle of “Tertiun Non Datur” (“no third [possibility] is given”) or “Principle or Law of the Excluded Third” (it is expressed in formal logic with the acronym T.N.D., Principle or Logic Law that comes after and together with the Principles or Law of Identity and Principle or Law of Excluded Middle or Non-contradiction). Can not exist simultaneously “A” and “Not A”, the negation of “A”. Formal logic is bivalent: or black or white, or true or false, or it’s 1 or it’s 0. Even the circuits of a computer work with this bivalent logic. Judges’ verdicts operate in this way: guilty or innocent, Dude is right or wrong. Most of the thinking and practical activities of our world operate as bivalent.

When billions of people question the Internet-D.T., as it is now wrongly and naively understood by them, they expect to get an answer in their hearts that there can never be: an illogical, absurd question leads to an equally illogical and absurd answer. Indeed Deep Thougt  in the novel of Douglas (after millennia!) answers to its “users”: 42!

An absurd answer with an insignificant number, as it was defined by Douglas himself when he explained why he had thought as D.T.’s answer to that number.

Professor Ian Stewart, a good mathematician and popularizer of Mathematics working in the University of Warwick based in Coventry in England, in his book “Professor Stewart’s Incredible Numbers” (which I recommend to read) in the last chapter has spent interesting words to “rehabilitate” the number 42 chosen by Douglas, explaining that it is not so insignificant: it is a pronic number also called oblong, it is the sixth Catalan number and it is the magic constant of a magic cube 3 x 3 x 3.

But that doesn’t explain why D.T answered the question about “Life…The Universe…Everything !” the way he did.

A careful reader has already guessed the reason: a computer with its bivalent algorithms sometimes leads to the Absurd, to paradoxical answers, to endless “loops” and it often happens that we find ourselves in front of the void of meaning and signification.

Why? Because a “Polyvalent Question” to who thinks in a bivalent way cannot be asked! Here is unveiled the mystery of Deep Thought and its answer ( at least from my point of view !).

Our world is polyvalent and with the work of excellent minds such as those of Russell, Lukasiewics and Black has come up to Lotfi A. Zadeh who is credited with having used for the first time the basis of mathematics s.c. “fuzzy” using the same term with the publication of the historic article “Fuzzy Sets” appeared in 1965 in the magazine “Information and Control”.

The World and the observation of the phenomena that compose it are artificially compressed within a binary and bivalent logic, obtaining an “artificial precision”, a “number 42”, explicit or hidden, to every answer to our questions. Through the Fuzzy Logic, on the contrary, we take into account the “vagueness” of the real world, the proper “Fuzzyness”, because the real world is “imprecise” and “vague”.

Zadeh proposed a logical-mathematical notation that he called “Fuzzy Logic” thus allowing to encode the imprecision of the real world and the uncertainty of our judgment about it.

The binary belonging, bivalent of a concept becomes a special case of belonging to a “Fuzzy Set”: between a “young man” and an “old man” there is a “continuum” with countless gradations. If we suppress what is in between the two “poles” only then we get the two opposing classes (young vs. old) identified by binary logic. It can be useful to reason in a “binary” way, in many situations it works, it can be practical but it is not the real world: as more the precision increases as more the adherence to reality decreases and this is the “Incompatibility Principle” of Fuzzy Logic (Zadeh 1973) .

Although it may shock you, even the Calculation of Probability has a bivalent nature: either it is Yes or it is Not, there are no intermediate choices. Probability operates when we are faced with an uncertainty due to lack of information, data, situations in which events are governed by causality that cannot be determined in advance.

On the contrary, in Fuzzy Logic, the more the information increases, the more the “vagueness” increases , the uncertainty.

Probability dissolves when the data become numerous, the objects of our reflection are or are not, they belong or do not belong to a Set to a certain extent.

Fuzzy Logic, on the other hand, eliminates the boundaries that mark where a thing ends to be that thing and the value that assumes the thing object of our observation does not represent a “probability” but the measure of a deterministic and “vague” event of “polyvalent” nature with infinite “degrees” of belonging between 1 and 0, between TRUE and FALSE. Probability tries to establish whether an object belongs or not to a non-fuzzy set; Fuzzy Logic, on the contrary, takes into account and calculates the inaccuracy associated with intermediate degrees of belonging between the same and the “non belonging” to a set, operating with a logic of infinite values.

Fuzzy Logic is able to operate through particular types of Numbers: FITS Numbers.

FITS means “fuzzy units” and are numbers that represent a measure, a number, between 0 and 1, while the “bits” (binary units) can take only one value, either 1 or 0. The bit responds to dichotomous questions: “Do you earn more than a thousand dollars a month?” with an answer either affirmative or negative, Tertium Non Datur.

The FIT number answers the same questions but includes in the answer all the values of the thing we are observing. It analyzes and measures that thing as it goes from “status A ” to ” status B “: a whole apple, as it is chopped and eaten, goes from its whole state to its total absence.

In more mathematical terms: the Fit values are inserted between the Bit values describing “values of belonging” of an object to a Set through all the transmutations that the object undergoes without omitting any.

Working with Fit and Fuzzy Logic modifies our relationship with a computer because it modifies the way of reasoning of the same computers where the “If…Then command” (usually within an algorithm as a sequential instruction) becomes the structure of thought of the computer itself, of the same machine, thought to which must be related and built the algorithms.

This leads (and will increasingly lead) to computers becoming “adaptive systems” capable of learning: AI, artificial intelligence, is no longer an abstract theorization but a concrete frontier achievable through the elaboration of neural networks based on fuzzy mathematics, on fuzzy thinking that will lead computers to find by themselves the rules for its proper functioning.

The frontier and the goal  to be reached is summarized in an acronym, DIRO: Data In, Rules Out (enter data, get rules). The machine learns the rules from the data; the more data you enter the more rules a computer produces in self-learning. In other words: the Rules are included in the data and this is because the premises of an argument are no longer bivalent, or TRUE or FALSE, but can take any value between 1 and 0 through the Implication, IF…Then…Else as a structure of thought of the machine itself.

Although many people have not realized it, technical applications of Fuzzy Logic already exist and operate:

• HITACHI air conditioners
• CANON copiers
• SAMSUNG televisions
• MATSUSHITA camcorders
• anti-lock brakes NISSAN….at least these are the ones I know, but I think there are others, such as medical equipment (pressure measurement, ultrasound machines etc.).

I believe that what has been said so far is sufficient for the purposes of this article and I do not want to bore the reader by going into details a bit too technical and difficult even for experts like me.

Therefore, returning to the all-encompassing question that everyone would like in their hearts to ask Internet-D.T. and its possible answer, we can easily say that it would be a stupid an absyrd question and would get an equally absurd incomprehensible and inconclusive answer : 42 in short !

But even if computers and computing will never become Gods superior to humans, they will be able to get operational skills that will help Mankind to be better and live better; they will be worthy collaborators. Think of mathematical models for weather forecasting and earthquake prevention through Fits numbers, through the math and logic described above.

We should not deify a machine by deluding ourselves that it has an answer to all our questions. Machine thinking will never become “deep” like Deep Thought, but it will be of valuable help for all those situations in reality that now escape the bivalent nature of the world as we have built it on such logic.

I repeat: I am not saying that bivalent logic is useless. It is very useful, but it is only a section of a larger Universe of Thought, of various Worlds that must relate to each other.

We will never find an answer to a “definitive” question that satisfies and reassures us on topics such as “Life…The Universe…Everything!”; the computer and information technology will never become a sacred text in which to sink with blind faith.

We’ll just have a more skilled collaborator to help us solve problems that we can’t solve or prove now but can only guess at.

However,human beings should as of now modify their relationship with a non-existent Internet-D.T. created only within the minds, an idol created only by incomprehension, loneliness and ignorance: When you are looking for a grocery store, don’t go straight to the Internet, but stop a fellow human being on the street and politely ask, “Excuse me, I’m looking for a grocery store nearby. Could you please direct me to one?”.  The response will be satisfactory in many cases and you will have exchanged smiles, perhaps you will even exchange a few more words, perhaps you will meet again and become friends….and don’t forget the “three Phases” that govern the Universe indicated by Douglas at the end of his entertaining novel, namely the How, the Why and the Where.

The first Phase is characterized by the question “How can we get food ?”; the second Phase by the question “Why do we have to eat ?” and finally the third Phase by the question “Where are we going to eat ?” …which is the most important one.

So, to hell with the Internet-D.T. and the absurd questions and unbelievable answers: see you all at the Restaurant “At the Edge of the Universe”…it’s “loosely” around here on the planet called Earth.

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