By Guillen

Explains vital mathematical ideas, corresponding to likelihood and statistics, set thought, paradoxes, symmetries, dimensions, online game concept, randomness, and irrational numbers

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**Example text**

For example, one of these constants, the speed of light, has been measured out to nine decimal places, and the digits have yet to show any pattern. 29979245 8 . ) Another constant is one that is descriptive of dynamic behavior at the atomic level. It is called the fine-structure constant, and there is no pattern to its digits even when measured out to ten decimal places. 0072 9 73 5 0 3 . ) In physics alone there are more than a dozen of these constants, which have been measured out to anywhere from a few to eleven decimal places, and not one of them has a pattern to its digits.

The spacing between ticks in a rational number line would correspond to the spacing between images when the two mirrors were infinitely close together-touch ing, in other words. The spacing between ticks in a real num ber line, however, would correspond to the spacing between the images when the two mirrors were closer than touching. But this could only happen if the mirrors actually entered one another, as Alice entered the looking glass. For scientists interested in learning about time, the im ponderability of the real number line poses an interesting choice.

If I were to interchange j ust one pair of digits in its infinitely long random string of digits, I would no longer have the same irrational number. Each irrational number has its unique ran domness and each of its digits has a unique role in creating that individualized randomness. 05 7 1 42 8 5 7 1 42 8 5 7 1 4 . . , 1/9 9 i s . 0 1 0 1 0 1 0 1 0 1 . . 0000000 . . ) . Certainly there are many temporal phenomena known to us today that are perfectly describable in terms of rational numbers alone.