Fuzzy Logic Makes More Sense Every Day

July 1964 - logician Lotfi Zadeh, New York apartment

He's thinking about basic issues in systems analysis, the unsharpness of class boundaries - the failure of things in the physical world to conform to classical Boolean logic.

Computer science is very true/false, black/white, zero or one.

Summer 1965 - he publishes in Information and Control  what he considered to be fuzzy:

For example, the class of animals clearly includes dogs, horses, birds, etc. as its members and clearly excludes such objects as rocks, fluids, plants, etc. However, such objects as starfish, bacteria, etc. have an ambiguous status with respect to the class of animals. The same kind of ambiguity arises in . . . the “class of all real numbers which are much greater than 1,” or “the class of beautiful women” . . . Yet, the fact remains that such imprecisely defined “classes” play an important role in human thinking, particularly in the domains of pattern recognition, communication of information, and abstraction.

Albert Einstein had written in the 1920s (Geometry and Experience) “So far as the laws of mathematics refer to reality, they are not certain. And as so far as they are certain, they do not refer to reality.”

Heap?

The sorites paradox (AKA the paradox of the heap) is a paradox that arises from vague predicates.

Here's an example: A heap of sand, from which grains are individually removed. Under the assumption that removing a single grain does not turn a heap into a non-heap, the paradox is to consider what happens when the process is repeated enough times: Is a single remaining grain still a heap? If not, when did it change from a heap to a non-heap?

What about if we define "tall" in humans as being 61 inches or greater - Is someone at 60.9 inches not tall?

Zadeh proposes a fuzzy mathematics made of fuzzy sets, fuzzy logic, fuzzy algorithms, fuzzy semantics, fuzzy languages, fuzzy control, fuzzy systems, fuzzy probabilities, fuzzy events and fuzzy information.

In the 1980s, engineers in Sendai, Japan, incorporated fuzzy logic into the design of the city’s new subway, using it to program what are now the system’s famously smooth starts and stops.

Then comes fuzzy: cameras, washers and dryers, vehicle transmissions and anti-skid braking systems, air-conditioners and thermostats, rice cookers, vacuum cleaners, and unmanned helicopters.

Some don't like this fuzziness. Engineer Rudolph Kálmán called fuzzy logic “a kind of scientific permissiveness.” Mathematician William Kahan dismissed it as “the cocaine of science.”

Since its publication, his inaugural paper has 93,000+ citations, according to Google Scholar.

More mathematical applications of fuzzy logic are yet to come - game theory, geometry, linear programming, probability, statistics, topology. In AI, fuzzy cognitive maps are a tool that researchers are starting to apply in medicine, engineering, defense analysis etc.

Joseph Dauben writes “Fuzzy logic, like chaos theory, helps to handle situations that otherwise would be hard to deal with in a rational, sensible way.”

           

Understanding the Math and Science of Animation

I am a proponent of the concept of teaching in a STEAM (science, technology, engineering, art, math) framework that goes across disciplines. I have seen many attempts to use science and math in teaching art - some successful, some not.

A new project that does this in an engaging way is a collaboration between Pixar Animation Studios and Khan Academy that is sponsored by Disney. Called "Pixar in a Box," it gives a look behind-the-scenes at how artists at Pixar need to use STEM to make art.

To make balls bounce, leaves in trees move in the wind, fireworks explode or realistic rippling water takes more than drawing skills. It requires computer skills and considerations of math, science such as physics and digital humanities.

How do you make animated hair

look like real life hair?

One tough task in animation is creating realistic hair on characters. Drawing hair is not that difficult. But making hair that moves in a natural way as character move is very tough. In this learning series of videos on simulations, the Pixar artists use hair as an example of an animation problem that needed to be solved. Using examples from their films, such as the character Merida in Brave with her bouncy and curly hair, you learn how millions of hairs can be simulated if you think of them as being a huge system of springs.

As the lessons progress, you can learn about animation roles and will discover what a technical director does in the animation process.



The lessons are appropriate for grades 5 and up - though I can see many adults and younger kids interested in animation from a technical or artistic side enjoying the free series.

Math is a Religion

Calvin: You know, I don’t think math is a science. I think it’s a religion.
Hobbes: A religion?
Calvin: Yeah. All these equations are like miracles. You take two numbers and when you add them, they magically become one new number! No one can say how it happens. You either believe it or you don’t. This whole book is full of things that have to be accepted on faith! It’s a religion!