Ways of Being "Good at Math"

It’s a common misconception that someone who’s good at math is someone who can compute quickly and accurately. But mathematics is a broad discipline, and there are many ways to be smart in math. Some students are good at seeing relationships among numbers, quantities, or objects. Others may be creative problem solvers, able to come up with nonroutine ways to approach an unfamiliar problem. Still others may be good at visually representing relationships or problems or translating from one ...

 Scientists are After the Adventure of Discovery

The creative scientist is in fact usually more concemed with the relations of things to one another than with the precise verbal analysis of what these things are. He seeks a representation of the world which continually grows by an extension or transformation of what is there akeady. Thus what many scientists are really after is the adventure of discovery itself.

 Observation Reconstructs the Real

A scientific observation is always a committed observation; it confirms or denies one's preconceptions; one's first ideas, one's plan of observation; it shows by demonstration; it structures the phenomena; it transcends what is close at hand; it reconstructs the real after having reconstructed its representation.

 Causality as a Conceptual Tool

Causality itself is an evolved conceptual tool that simplifies, schematizes, and focuses our representation of situations. This cognitive machinery guides us to think in terms of the cause—of an outcome’s having a single cause. Yet for enlarged understanding, it is more accurate to represent outcomes as caused by an intersection, or nexus, of factors (including the absence of precluding conditions). In War and Peace, Tolstoy asks, “When an apple ripens and falls, why does it fall? Becau...

 Levels of Simulation

Such is simulation, insofar as it is opposed to representation. Representation stems from the principle of the equivalence of the sign and of the real (even if this equivalence is Utopian, it is a fundamental axiom). Simulation, on the contrary, stems from the Utopia of the principle of equivalence, from the radical negation of the sign as value, from the sign as the reversion and death sentence of every reference. Whereas representation attempts to absorb simulation by interpreting it as a f...

 The Formation of Grains of Sand

On the basis of the results recorded in this review, it can be claimed that the average sand grain has taken many hundreds of millions of years to lose 10 per cent. of its weight by abrasion and become subangular. It is a platitude to point to the slowness of geological processes. But much depends on the way things are put. For it can also be said that a sand grain travelling on the bottom of a river loses 10 million molecules each time it rolls over on its side and that representation impres...

 Myth and Science

Myths and science fulfill a similar function: they both provide human beings with a representation of the world and of the forces that are supposed to govern it. They both fix the limits of what is considered as possible.

 Summary of Schopenhauer's Philosophy

[Schopenhauer] was also an atheist. He did not believe in a personal, omnipotent God. Instead, Schopenhauer believed that the essence of the universe is Being: a blind, irrational, unquenchable thirst to exist he called Wille zum Leben, and that everything we perceive is a representation of this Will to Live. Because we ourselves are products of Will, we spend most of our lives trapped in a cycle of striving and boredom. We're constantly willing ourselves to attain our goals, and when we d...