Fuzzy logic

Fuzzy logic is the addition of other sorts of values to true and false, like adding a “maybe true or false” value, and using a continuum of values between true and false. Traditional mathematical logic, with only true and false, is sometimes called crisp logic by comparison. It is also known as Boolean algebra, from 19th cy. mathematician George Boole, who found analogies between logic and arithmetic.

Fuzzy logic has turned out to be very useful for device control, because it is a good way of handling real-world conditions. For instance, when does gray stop being black and start being white? For crisp logic, one can say black – medium gray is dark and medium gray to white is light. That is not very informative, so we subdivide these ranges: black to dark gray is dark-dark, dark gray to medium gray is dark-light, medium gray to light gray is light-dark, and light gray to white is light-light. One can continue with these subdivisions, reinventing binary representations of numbers. But once one does that, one can use the numbers directly. Black is 100% dark and 0% light, dark gray 75% dark 25% light, medium gray 50% dark 50% light, light gray 25% dark 75% light, and white 0% dark 100% light. Once one has such numbers, one can then use them in fuzzy analogs of crisp-logic operations like “not”, “and” and “or”.

Below the fold, I will construct some a simple system of fuzzy logic using “maybe true or false”.

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Genesis 1 – Indo-European?

This may seem very odd, but I have developed a hypothesis for that, by assembling various bits and pieces of history and mythology.

The story starts with the speakers of Proto-Indo-European dialects some 6000 years ago in the grassland between eastern Ukraine and Kazakhstan. They had a creation story that goes something like this:

Once upon a time, there were two twin brothers, *Mannus, and *Yemos, Man and Twin. Man sacrificed Twin, dismembered him, and constructed the familiar universe from his body parts.

They also had a story about how a god of storms and war fought and killed a reptilian water monster.

They spread out from their homeland, and though they eventually got assimilated in the Fertile Crescent, these stories were picked up by local people and conflated into a Chaoskampf, “chaos struggle”. The older gods are threatened by a chaos monster, and they send out a younger god to fight it. He defeats it, he creates the familiar universe from its parts, and he becomes the ruler of the gods.

This story is picked up by some Israelites, and they trim it down by God cutting up primordial material. “In the beginning, God separated the heaven and the earth”. The story was then revised into its present form, and it was turned into a charter myth for the seventh-day Sabbath.

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“…branding on my forehead: SLAVE”

I’ve finished reading the book Bruce Levine’s book “The Fall of the House of Dixie: The Civil War and the Social Revolution That Transformed the South”. It’s excellent. I find it especially curious how the plantation-slaveowner elite reacted to the war. It was a war waged on their behalf, a war waged so that they could continue owning slaves. But after the first few months to a year, they could not be bothered to do much to support the war effort, something that some Confederates themselves found rather odd.

They exempted their sons from the military draft with the “Twenty Negro Law”, they were not willing to grow much grain or sell it at low prices, and they were not very willing to hire out their slaves for tasks like building fortifications. The poorer Confederate citizens ended up grumbling that they were fighting for people who were clearly not doing as much as they could. “A rich man’s war and a poor man’s fight.” That sentiment was especially strong in parts of the South with relatively few slaves. Western Virginians succeeded in seceding from their state, but eastern Tennesseeans’ attempt to do so was crushed by the Confederate Army.

Consider the case of South Carolina plantation owner, politician, and slavery defender James Henry Hammond. He argued that the slaves were very suited for doing the work that they were made to do, that they were better off enslaved than free, and that higher civilization rests on the labors of an underclass of people that never get much for their labor — the “mudsill theory” of society. But when a Confederate army officer stopped by to requisition some grain, he tore up the requisition order, tossed it out a window, and wrote about it that it compensated him too little, and that it was like

branding on my forehead

SLAVE

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WFF ‘N Proof, a mathematical-logic game

“WFF ‘N Proof, the Game of Modern Logic”, is a game that I had had in my childhood, though I now only have its rulebook. A WFF (“woof”) is a well-formed formula, one that is syntactically correct, and in the game, one creates proofs with inference rules. The game has dice with operation and variable names on them, and one tries to find WFF’s and proofs that fit what is on the dice. The game also includes an hourglass for timed play.

It was created by Layman Allen in 1962, and he has also created On-Sets, on set theory, and Equations, on arithmetic, both played much like WFF ‘N Proof.

I wish that I could recommend WFF ‘N Proof, but it has several deficiencies.

  • It uses a prefix representation for its binary operators, (and) p q, with no attempt to relate it to the more usual infix form, p (and) q.
  • It does not use the logical constants (true) and (false), and it does not have truth tables, tables of output values for input values (arguments).
  • It does not name the operator properties that it has proofs of, like (and) and (or) being commutative and associative.

After the fold, I will describe the formalism in WFF ‘N Proof in more detail.

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Transcendental Future Orientation

Psychologist Philip Zimbardo has proposed that much of our attitudes can be explained by our time orientation. Are we oriented to the past? The present? The future? Is our orientation positive? Or negative? That is, do we think about good things or bad things? He explains what he means at his site, The Time Paradox.

That site has an odd time orientation: Transcendental Future. He even has a quiz about it: Transcendental-future Time Perspective Inventory (TTPI). Continue reading

Time Orientation by Philip Zimbardo

Philip Zimbardo is a psychologist who has worked on what can make “normal” people turn bad (the Stanford Prison Experiment and his book “The Lucifer Effect”), and he has an interesting proposal of how much of our attitudes can be explained as time orientation. I first found out about it from his talk at the 2008 Beyond Belief conference; he shows some slides that give correlations of his time orientations with various personality factors.

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Abraham Maslow’s Hierarchy of Needs

Around World War II, psychologist Abraham Maslow decided to consider mentally healthy people, to balance out study of mental pathologies. In 1943, he published his conclusions in “A Theory of Human Motivation” in Psychological Review. He proposed that we have a hierarchy of needs, from the physiological to the transcendent: Maslow’s hierarchy of needs – Wikipedia, Maslow’s Hierarchy of Needs | Simply Psychology, Abraham Maslow and Happiness, What Is Maslow’s Needs Hierarchy?

This hierarchy is often depicted as layers of a pyramid. From bottom to top:

  1. Physiological: breathing, food, water, sex, sleep, homeostasis, excretion
  2. Safety: security of body, employment, resources, morality, family, health, property
  3. Love and Belonging: friendship, family, sexual intimacy
  4. Esteem: self-esteem, confidence, achievement, respect of others, respect by others
  5. Self-actualization: morality, creativity, spontaneity, problem solving, lack of prejudice, acceptance of facts

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