Adventures in Thought Space

The geometry of curves obsessed mathematicians long before Newton hid from the plague at Woolsthrope Manor, where the seeds of the calculus took root. Before the late seventeenth century, finding slopes, areas, and volumes under curves was an entirely ad hoc affair. Unlike the lines of squares, triangles, rectangles, and cubes, height and/or depth doesn’t remain constant over any measurable length of curved lines, making calculations difficult. Although Newton and many others have conceptualized the foundations of calculus in more physics-like terms, it became a formalized system so effective in geometric analysis that it’s easy to mistake the study of mathematical change (calculus) and the geometry of curves as one in the same. This is not the case.    Calculus is the study of continuously changing mathematical functions. A function, as you should know, is an expression of a variable(s) in terms of one or more others—e.g., Y=X ^2, Z=CV^2dx (^ means raised to some power). Cont...

It's not easy being a freethinker in an unthinking world. While they may take great pride in being so, no true free thinker would view it as an unequivocally "good" thing.   If one's imagination isn't confined to how things are or how people tell them that it is and extends well into what could or should be, this adds variables to an already highly complex puzzle. Sadly, help is few and far between: Few recognize the complexity of the puzzle, even fewer the additional variables.    A belief is a component of a model of reality, and everyone needs definite (even if dynamic) models to function. To one degree or another, everyone thinks about their beliefs. This process is never entirely successful, nor entirely unsuccessful. Freethinkers are the precious few who appreciate that a consensus in opinion can’t determine fact and resist adopting beliefs they don’t sufficiently understand--including their own. To understand something or solve a problem, one must answer a ...

The field of astrophysics and its failing paradigms have horded so many billions in funding, particle accelerators, books, and documentaries over the past three decades it’s become “too-big-to-fail.” The weakness of its models shouldn’t be terribly surprising given the weakness of the force they’re based on—gravity. Unable to account for the forces and energies needed to make the theories fit the facts, astrophysicists have conjured up non-falsifiable notions that are swiftly pushing it into the realm of science fiction. Yet few question its legitimacy.  Gravity is a quadrillion trillion trillion times weaker than the electric force. If the human body had one percent more electrons than protons and two people stood side by side, the repulsive force between them would be enough to lift the Earth. Of course, to achieve a voltage of this magnitude with liquids, solids, and gases would require incalculable amounts of energy and effort. But plasma is very different than the other states...

Almost everything in this universe—from galaxies and clusters of galaxies to solar systems and planets, to climates and ecosystems to industries and economies—comes from things organizing themselves. They are SELF-organized. Most things can’t be understood by straightforwardly analyzing the parts/variables, like in math, physics, and engineering; only by accounting for unknowns and appreciating the complexity of the interactions BETWEEN variables can one hope to understand the rest of Nature. The former type of thinking is called reductive or reductionistic; extralogical reasoning calls the latter  scientific holistic thinking .   Complexity theory studies complex systems such as economies, ecosystems and their evolution, societies, and various related phenomena. If these phenomena are complex systems, then Nature and the World are, likewise, complex systems. The interactions between a psychology and the external World, in turn, make LIFE a complex system.    A compl...