How Math Explains the World.pdf
long names with letters 1 through 9 rather than A through Z and 0 instead of blank. For example,^1 ⁄ 4 .25000.... Cantor worked ...
of choice is simple to state; it says that if we have a collection of nonempty sets, we can choose a member of each set. In fact ...
bers gives you a headache, you might prefer the following version of the dilemma, due to Bertrand Russell—if you have an infinit ...
Just as there are different geometries (Euclidean, projective, spherical, hyperbolic—to name but a few), there are different set ...
lel postulate, and hyperbolic geometry is a model that incorporates the negation of the parallel postulate. The Continuum: Where ...
fundamental mathematical objects—added knowledge of its structure is of paramount importance, just as added knowledge of the str ...
Even the Securities and Exchange Commission warns against them. See http:// www .sec .gov/ answers/ ponzi .htm. Carl B. Boyer, ...
...
2 Reality Checks Pascal’s Wager The French mathematician and philosopher Blaise Pascal was probably the first to combine philoso ...
which is the study of human social behavior. His treatise, Plan of Scien- tific Studies Necessary for the Reorganization of Soci ...
cane areas of study, they usually do not register on the public’s radar screen. However, predictions regarding the limitations o ...
to anyone but a specialist, and totally useless for any practical purpose. My appreciation for abstract expressionism, as well a ...
papers outlined the structure of the object of dimension 16; the other showed that no such object existed. For Seligman, it was ...
Any two points can be joined by a straight line. Any straight line segment can be extended indefinitely in a straight line. Giv ...
the atomic and subatomic level. The problem is that relativity only mani- fests itself in the realm of large objects, whereas qu ...
The Standard Model When I studied physics in high school and college, atoms were portrayed as consisting of a nucleus of protons ...
polynomial. Division, however, is not an allowed operation—just as some integers divided by other integers are not integers (suc ...
When Theories Do Battle In the middle of the twentieth century, there were two main contenders to explain the fact that over lar ...
Theories in mathematics never do battle in this fashion, and they are never resolved on the basis of statistical evidence. As wi ...
that a doughnut is topologically equivalent to a coffee mug, because each has precisely one hole (you know where it is in the do ...
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