One Two Three . . . Infinity: Facts and Speculations of Science (Dover Books on Mathematics)

by George Gamow

It took the great brain of Archimedes, a celebrated scientist of the third century B.C., to show that it is possible to write really big numbers.

MATHEMATICS is usually considered, especially by mathematicians, the Queen of all Sciences and, being a queen, it naturally tries to avoid morganatic relations with other branches of knowledge.

fact, almost every branch of pure mathematics is now being put to work to explain one or another feature of the physical universe.

However, the effect of space shrinking, though it is of fundamental importance in understanding the basic principles of physics, passes quite unnoticed in ordinary life, since the highest velocities that affect us in our everyday experience are still negligibly small as compared with the velocity of light.

“There was a young girl named Miss Bright, Who could travel much faster than light. She departed one day, In an Einsteinian way, And came back on the previous night”

the phenomenon of gravity is merely the effect of the curvature of the four-dimensional space-time world.

The analogy with the planetary system can be further strengthened by these facts: the atomic nucleus contains 99.97 per cent of the total atomic mass as compared with 99.87 per cent of the solar system concentrated in the sun, and the distances between the planetary electrons exceed their diameters by about the same factor (several thousand times) which we find when comparing interplanetary distances with the diameters of the planets.

What is “science,” and what do we mean by the “scientific explanation” of the facts of nature?

And the great perplexity of humanity caused by the recently discovered process of liberating on a large scale the energy hidden in the interior of the atom can be compared to the astonishment of our imaginary Eskimo when shown an ordinary alcohol burner for the first time.

It takes light 50 centuries to travel from the center of the sun to its surface, whereas after coming into empty interplanetary space and traveling along a straight line it covers the entire distance from the sun to the earth in only eight minutes!

For exactly the same reason the room in which you sit reading this book is filled uniformly by air from wall to wall and from floor to ceiling, and it never even occurs to you that the air in the room can unexpectedly collect itself in a far corner, leaving you to suffocate in your chair. However, this horrifying event is not at all physically impossible, but only highly improbable.

Consequently the waiting time for the right combination is 10299,999,999,999,999,999,999,999,998 sec as compared with only 1017 sec representing the total age of the universe! Thus you may go on quietly reading your book without being afraid of being suffocated by chance.

Any spontaneous changes in a physical system occur in the direction of increasing entropy, and the final state of equilibrium corresponds to the maximum possible value of the entropy.

Thus, although the energy of mechanical motion can go completely over into heat (for example, through friction), the heat energy can never go completely into mechanical motion.

This rules out the possibility of the so-called “perpetual motion motor of the second kind,”69 which would extract the heat from the material bodies at normal temperature, thus cooling them down and utilizing for doing mechanical work the energy so obtained.

In a similar way we can decrease the entropy in one part of our system if there is a compensating increase of entropy in its other part. In other words considering a disorderly motion of molecules we can bring some order in one region, if we do not mind the fact that this will make the motion in other parts still more disorderly. And in many practical cases, as in all kinds of heat engines, we do not mind it.

Thus the photosynthesis taking place in the leaves of plants involves two related processes: a) transformation of the light energy of the sun’s rays into chemical energy of complex organic molecules; b) the use of low-level entropy of the sun’s rays for lowering the entropy associated with the building up of simple molecules into complex ones.

In terms of “order versus disorder,” one may say that, when absorbed by green leaves, the sun’s radiation is robbed of the internal order with which it arrives on the earth, and this order is communicated to the molecules, permitting them to be built up into more complex, more orderly, configurations. Whereas plants build their bodies from inorganic compounds, getting their negative entropy (order) from the sun’s rays, animals have to eat plants (or each other) for the supply of that negative entropy, being, so to speak, second-hand users of it.

What constitutes the important difference between living and nonliving matter?

The fundamental distinguishing properties of the living cell consist in its abilities: (1) to assimilate materials necessary to its structure from the surrounding medium, (2) to turn these materials into the substances used for the growth of its body, and (3) to divide into two similar cells each half of its own size (and capable of growth) when its geometrical dimensions become too large.

These abilities “to eat,” “to grow” and “to multiply” are, of course, common to all more complex organisms made up of individual cells.