Mathematics and the Physical World

where ignorance is bliss, ’Tis folly to be wise.
—THOMAS GRAY

To say that zero is a number means that we can operate with zero much as we operate with any other number. Thus, 5 + 0 = 5 but 5 + nothing is a meaningless expression and yields nothing.

Number is a concept of the mind, no doubt suggested by physical objects but independent of them.

The senses are limited. The eye sees only a small range of light waves and is easily deceived as to sizes and locations of objects. The ear hears only a limited range of sound waves. The sense of touch can reach only to objects accessible to the hand and is not a precise sense at that. On the other hand, man’s reason can encompass distances, sizes, sounds, and temperatures beyond the range of the senses. More than that, reason can contemplate phenomena which transcend the senses and even the imagination

every abstraction that even the greatest mathematician has introduced is ultimately derived from and is therefore understandable in terms of intuitively meaningful objects or phenomena.

Mathematics is a multistage Roman candle. It is packed with physical gunpowder and set alight by the fire of human minds. It then shoots off in a direction somewhat determined by human thought but not necessarily exactly in the direction planned. Then the candle flares up and successive flashes of light reveal aspects of the physical world not readily illuminated from man’s earthbound station. Each successive thrust of the candle into space is followed by flares from higher and higher altitudes that reveal more and more of the constitution of our universe.

This is the germ of the great Greek discovery, perhaps the greatest discovery man has ever made. Reasoning can produce knowledge that not only covers a multitude of cases in one swoop but may produce physically meaningful information that is entirely unforeseen.

It is true that many people pass their whole lives without being bothered at all by such questions. These people are content with shelter, food, sex, and a few material pleasures. But others are not content to live only on a physical level. They have minds that are aware of the pervasive natural mysteries and are as obsessed to resolve them as any businessman may be to acquire wealth.

zero is a number means that we can operate with zero much as we operate with any other number

when numbers arise in physical situations, one must abstract the quantitative facts, perform the appropriate mathematical operations, and then interpret the mathematical answer.