Table 1-1 Tabulation of Dice Tossing.
| Score | PossibleWays | Probability | Frequency(N = 36K) |
| 2 | 1 | 1/36 = .0278 | 1000 |
| 3 | 2 | 1/18 = .0556 | 2000 |
| 4 | 3 | 1/12 = .0833 | 3000 |
| 5 | 4 | 1/9 = .1111 | 4000 |
| 6 | 5 | 5/36 = .1389 | 5000 |
| 7 | 6 | 1/6 = .1666 | 6000 |
| 8 | 5 | 5/36 = .1389 | 5000 |
| 9 | 4 | 1/9 = .1111 | 4000 |
| 10 | 3 | 1/12 = .0833 | 3000 |
| 11 | 2 | 1/18 = .0556 | 2000 |
| 12 | 1 | 1/36 = .0278 | 1000 |
| Totals | 36 | 36/36 = 1.0000 | 36,000 |
Natural phenomena, like the decay of atoms, follow the same principles as dice tossing. In a population of atoms, like a population of dice tosses, decay will follow a predictable course. Whether a particular individual atom will decay at a given moment, however, is a matter of probability, just like a single dice toss. Einstein’s comment that, in atomic phenomena, “God does not play dice” (“Gott würfelt nicht”) was premature, but the atomic dice are used in a subtle manner, as Einstein also observed “God is subtle, but not malicious” (“Raffiniert ist der Herrgott, aber boshaft ist er nicht.”). Tracing of the understanding of the principles of evolution, later in this chapter, also reveals the role of scientific determinism.
The Science of Nature
Because the scientific method is shared by all sciences, science is essentially indivisible. Any separation among sciences is arbitrary and splits fields of study. The common demarcation between social sciences and biological sciences splits psychology. On the other hand, segregation of sciences along lines of life sciences and physical sciences divides biochemistry. Separation of sciences, however, is frequently necessary for convenience in dealing with the wide array of subjects under the scrutiny of science. This book, concerned with nature would, of course, deal particularly with those sciences studying life and not especially with those sciences whose subject is the physical world.
A basic difference between life and the physical world is the importance of the time dimension. In the physical universe events in time have relatively long duration compared to the short span of life. In view of the small importance of time in the physical world, physics has not investigated time to any great extent (Gold, 1967), until the recent spate of work over the last thirty years. Life, however, existing as it does in a rotating world, which makes the main energy source, the sun, periodic, has become time-locked. Even basic metabolic processes exhibit time cycles. Time brings rapid and important changes to life and can be considered life’s most salient dimension.
Physics considers work equivalent to force acting through distance (W = Fd), while force acting through time is relegated to the status of impulse (I = Ft). Such definitions are confusing to students of life science who realize that tremendous energy expenditure can result from holding a weight in fixed position for a time (impulse) as well as from lifting a weight through a distance (work). Actually, a living organism performs work by changing chemical potential energy into kinetic energy, just to maintain its existence from moment to moment. Indeed, the best index of energy expenditure during motor behavior is the integral of force acting through time (Trotter, 1956). Force exerted through time is also a major parameter of an organism’s response repertoire (Notterman and Mintz, 1965). Thus, for the purpose of life sciences, work must be reconsidered as effort acting through both distance and time, Effort = F[(d/t) + t]. The range of possible values of space (d) and time (t) are limited by the capacity of the organism. Within that range there are optimum values for d and t. To vary slightly from the optimum performance greatly increases the effort. Power (Fd/t) plus impulse (Ft) are the expression of effort for organisms. Beginning physics students have difficulty with the physical concept of work because of the intuitive understanding of their own effort. Technology has increased human power by decreasing the time of various activities. Using tools also changes the sense of how much effort is required for a task. The formulation of effort is realistic for the life sciences because both time and space become important to an organism that moves through its life.
A popular view of the difference between life sciences and physical sciences is that life sciences rely on statistics and physical sciences employ laws. The view stems from the idea that life sciences are newer, not as established, and understand less of their subject than the physical sciences. Implied in these statements is the concept that statistics is only a temporary treatment awaiting more thorough knowledge of the subject and the subsequent formulation of laws.
While the statements have some degree of accuracy, the stopgap view of statistics is incomplete. Physical sciences do use statistics. Returning to the example of the phenomena of light, laws are employed when light is treated as a ray. Thus, angle of incidence equals angle of reflection. Laws are evidenced when light is viewed as a wave. Hence, Huygen’s principle stating that every point on an advancing wave front is a secondary wave source. However, statistics must be be invoked when light is considered as a photon. Thus, events, like a particular photon being absorbed by colliding with a specific electron at just the proper moment, although lawful, are necessarily only probable. Probabilistic events can only be treated with statistical estimates of the chance of their occurrence.
The example becomes even more significant by illustrating the essential difference between laws and statistical analysis. Light rays or waves are populations of photons. Laws always describe the behavior of populations. Thus, laws can describe the motion of a ball down an incline because the ball is a population of molecules. Laws can predict that only a fraction of the population of depositors of a bank will want their money at once. That enables the bank to retain just a small amount of reserve capital and invest the rest. Laws can predict the frequency of scores in the 36,000 dice tosses in Table 1-1. Whenever an individual in a population is singled out, however, the event becomes probabilistic, and a statistical estimate must be used. Individual molecules of the ball rolling down the incline could scrape off on the surface or, even, sublimate into the air. Individual bank customers could request their money. Single dice tosses are unsure. Formulation of laws or use of statistical analysis depends not on the science, but on whether the event in question is a population phenomenon or involves an individual. For example, to measure the individual size of leaves on a tree a statistical sample is employed, but to compare the populations of oak and maple leaves, only a few are needed.
The province of the life sciences is life. But, life with its conservatively estimated 1,200,000 animal species (Hanson, 1964) and 333,000