By Guillen

Explains vital mathematical recommendations, akin to likelihood and information, set thought, paradoxes, symmetries, dimensions, video game thought, randomness, and irrational numbers

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Carbon's unique affinity for bonding with other ele­ ments causes it to form long chainlike molecules like those of amino acids, proteins, and DNA. In biology, too, many temporal phenomena are describ­ able in terms of rational numbers. Each plant and animal species, for instance, appears to be characterized by a unique number of chromosomes in its individual cells. And this chro­ mosome number, like the atomic number, is always a whole number. Despite this preeminence of rational numbers, science 38 Irrational Thinking does need irrational numbers.

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.

34 Irrational Thinking A few years after Dedekind's achievement, the German mathematician Georg Cantor made a discovery that would lay to rest any lingering skepticism toward the seemingly impossible constitution of the real number line. He confirmed that though there are an infinite number of rational numbers, as the Greeks had suspected, there are even more real num­ bers. This confirms that the real number line is indeed some­ how more continuous, more densely packed, than the ponderably continuous rational number line.

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