wo elementary courses common to modern physics, mathematics, and engineering curricula are Linear Algebra and Vector Calculus. Geometric Algebra is a natural and powerful extension of linear algebra and Geometric Calculus is even more so...

Projective Geometry is the branch of geometry dealing with the properties and invariants of geometric figures under projection. In older literature, projective geometry is sometimes called “higher geometry,” “geometry of position,” or “descriptive geometry”. The...

Visualize this thing that you want, see it, feel it, believe in it. Make your mental blue print, and begin to build. — Robert Collier Visualization is daydreaming with a purpose. — Bo Bennett...

There are two ways of constructing a software design: One way is to make it so simple that there are obviously no deficiencies, and the other way is to make it so complicated that...

The belief that complex systems require armies of designers and programmers is wrong. A system that is not understood in its entirety, or at least to a significant degree of detail by a single...

Geometry can in no way be viewed… as a brach of mathematics; instead, geometry relates to something already given in nature, namely, space. I also had realized that there must be a branch of...

Hard sciences are successful because they deal with the soft problems; soft sciences are struggling because they deal with the hard problems. — Heinz von Foerster Cyberneticist, or cybernetician, is a person practicing Cybernetics: a...

[Computer science] is not really about computers and it’s not about computers in the same sense that physics is not really about particle accelerators, and biology is not about microscopes and Petri dishes…...

Our minds are finite, and yet even in those circumstances of finitude, we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can...

Our world is evolving without consideration, and the result is a loss of biodiversity, energy issues, congestion in cities. But geography, if used correctly, can be used to redesign sustainable and more livable...

If you understand something in only one way, then you don’t really understand it at all. The secret of what anything means to us depends on how we’ve connected it to all other things...

The power of mathematics is often to change one thing into another, to change geometry into language. –Marcus du Sautoy. n the previous post we read how our languages and ideas about the computational universe...

Language is a process of free creation; its laws and principles are fixed, but the manner in which the principles of generation are used is free and infinitely varied. Even the interpretation and use...

Science is what we understand well enough to explain to a computer. Art is everything else we do. — Donald Knuth. here are 3 kinds of science: the experimental, the theoretical, and the simulated1....

As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have...

The interest which pupils take in their studies may be greatly increased if the solution of problems and the cold logic of geometrical demonstrations are interspersed with historical remarks and anecdotes. — Florian Cajori,...

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is – John von Neumann bstraction is a fundamental human skill and tool for...