Rudolf Arnheim

"The line that describes the beautiful is elliptical. It has simplicity and constant change. It cannot be described by a compass, and it changes direction at every one of its points."

Questions

If you had one mole of pennies to divide among all the people in the world, how many dollars would each person receive? Use 7 billion as the population of the Earth

If there were a mole of people evenly distributed over the surface of the Earth, including both land and water, how many square centimeters would be allotted to each person?

Josef Albers

“I’ve handled colour as a man should behave. You may conclude that I consider ethics and aesthetics as one.”

"I'm not a talker. I'm a formulator."

Geometer

Quotation Marks

"The harmony of the universe knows only one musical form - the legato; while the symphony of number knows only its opposite - the staccato. All attempts to reconcile this discrepancy are based on the hope that an accelerated staccato may appear to our senses as a legato."

Tobias Dantzig

The Amazing Octopus

The octopus has an enormous brain compared to its body size. The neurons carry on through its eight arms. Octopus are capable of abstract thinking and reasoning. The unique aspect of the brain of an octopus is that it is located directly between the eyes and then wraps around its esophagus. Unlike ours, it is not encased inside of a skull.

However, the differences end there. The octopus has a remarkably complex brain. It's anatomy and tissues indicate complexity with textures, wrinkles, and folded lobes. The octopus also has a tactile and visual memory center.

You may ask, how does this brain work?

In terms of behavior, the octopus exhibits high level intelligence. In scientific tests, this intelligence has been proven and made tangible. The octopus is ceaselessly curious. It plays, hides, and uses tools as well as deceptive tactics against potential predators. It is an inherently inquisitive animal.

How did this intelligence come about?

Theories suggest that since the octopus is a solitary animal with a short life span, it needs to develop intelligence to survive in their potentially hostile environment. Octopus lack an exoskeleton, or protective shell, to shield them from predators. They also have no means of getting help or alerting others when they are threatened, due to their solitary nature. Therefore, their intelligence is what allows them to survive.

Octopus have been observed stacking rocks around the entrance of their cave in order to create a protective barrier before going to rest in their cave. They are often seen investigating objects in their surroundings and playing with these objects. This playfulness is what Piaget, and other scientists, would label intelligence.

There is also evidence that octopus dream when they sleep.

Why Bouncy Legs Work Better

Running with stiff legs require less energy. So why do animals have the seeming disadvantage of having squishy legs? The answer is as follows. These compliant legs provide are more effective in dealing with the force of and remaining stable in rough terrains.

Animals move in a variety of ways. A combination of mathematics and computer simulations can be used to model locomotion. However, simulated models predicted that stiff legs would be the most efficient while this is unvalidated in real life.

Smaller animals must expend more energy and take more steps to cover a given distance but still have compliant legs to stablize their motion.

Compliant legs allow an animal to move and spring through the world with less energy.