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Tag Archives: logic
Fuzzy Logic Not everything is so simple as true or false. Even declarative statements may evaluate outside {0,1}. So let’s introduce the kind-of: truth ∈ [0,1]. Examples of non-binary declarative statements: Shooting trap, my bullet nicked the clay pigeon but didn’t … Continue reading
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Tagged books, fuzzy logic, gray areas, heroes, logic, math, mathematics, maths, ontology, philosophy, programming, truth
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Logic, like mathematics, is regarded by many designers with suspicion. Much of it is based on various superstitions about the kind of force logic has in telling us what to do. First of all, the word “logic” has some currency … Continue reading
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Tagged architecture, Christopher Alexander, design, form, function, industrial design, logic, math, mathematics, maths, shape
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Complement
Here’s an inside-out thought: The air around us is a 3-manifold with 3-holes where solid objects are, and the 2-boundary is the ground. Or if you think of all the sky, it’s a spherical 3-shell (with one 3-hole, the Earth) floating … Continue reading
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Tagged boundary, childlike thinking, children, complement, inside-out, kids, logic, manifolds, math, mathematics, maths, set theory
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Paul Finsler believed that sets could be viewed as generalised numbers. Generalised numbers, like numbers, have finitely many predecessors. Numbers having the same predecessors are identical. We can obtain a directed graph for each generalised number by taking the generalised … Continue reading
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Tagged circular logic, coalgebra, generalised number, generalised numbers, graph theory, logic, logical circular logic, math, mathematics, maths, number, Paul Finsler, philosophy, poset, posets, set theory
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Superadditivity
“The whole is more than the sum of the parts” Who says scientists are reductionistic? Any superadditive system—due to complexity, interaction terms, valuation by an Lₚ norm with 0<p<1, or some other reason—adds up to more in total than the … Continue reading
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Tagged algebra, geometry, Gestalt, holism, literature, logic, math, mathematics, maths, reductionism, syncretism, synthesis
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The Opposite of Transitivity
rock ≻ scissors ≻ paper ≻ rock “beats” is not a transitive relation. in fact, Rochambot is an example of Logical Circular Logic. Rochambot obeys the non-wellfoundedness axiom (it’s a stream). it’s the cyclic group P₃.
Nonterminating decimals do not make sense.
The Banach-Tarski paradox proves how f#cked up the real numbers are. Logical peculiarities confuse our intuitions about “length”, “density”, “volume”, etc. within the continuum (ℝ) of nonterminating decimals. Which is why Measure Theory is a graduate-level mathematics course. These peculiarities … Continue reading
Ethnic Food as a Poset
I like Indonesian food better than Japanese food i ⪰ j, and I like Japanese food better than English food j ⪰ e. I also like French food better than English food f ⪰ e, but I see French food as so different … Continue reading
“Have you ever done acid, kid? This book is like Acid.” —John L. Rhodes, speaking of the book Topos Theory by Peter Johnstone (Source: http://www.amazon.com/gp/product/0521337798?ie=UTF8&tag=hiremebecauim-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=0521337798)
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Tagged acid, algebra, books, category theory, heroes, logic, LSD, math, mathematics, maths, moduli, philosophy, set theory, sheaves, topoi, topos theory, toposes
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Logic and Emotion are Not Opposites
Despite what the MBTI claims, logical and emotional are not opposites. You mean to tell me that, because I cried when I watched Brokeback Mountain and Never Let Me Go; because I empathise with a character in a book; because I’m moved … Continue reading
Human Mathematics 