Now in the third instance, in which the population have a scientifically correct definition of lightning, they provide their houses with lightning rods; and if they are caught by a storm in the open they neither run nor hide under a tree; but when the storm is directly over their heads, they put themselves in a position of minimum exposure by lying flat on the ground until the storm has passed.

Such examples could be given without end, but there is another example of sufficient vital importance to be given here, as it has to do with our conception of the social and economic system, and the state. If our institutions are considered “God-given”—sacred and therefore static—every reformer or advocate of change should be treated as a criminal or “a danger to the existing order” and hanged or at least put in jail for life. But now, if our institutions are “man made,” imperfect and often foolish, and subject to change all the time steadily and dynamically in obedience to some known or unknown law; then of course all reactionaries would be a “danger to the natural order” and they should be treated the same way. The importance of definitions can be seen in all other fields of practical life; definitions create conditions. To know the world in which we live, we have to analyse facts by help of such facts as we know in daily practice and such facts as are established in scientific laboratories where men [pg 049] do not jump to conclusions. In some places it will be necessary to make statements that will have to await full justification at a later stage of the discussion. This will be necessary to indicate the trend of the analysis.

The aim of the analysis is to give us just conceptions, correct definitions, and true propositions. The process is slow, progressive, and endless. The problems are infinitely many, and it is necessary to select. Fortunately the solution of a few leads automatically to the solution of many others. Some of the greatest and most far-reaching scientific discoveries have been nothing else than a few correct definitions, a few just concepts and a few true propositions. Such, for example, was the work of Euclid, Newton and Leibnitz—a few correct definitions, a few just concepts, a few true propositions; but these have been extended and multiplied, sometimes by men of creative genius, and often almost automatically by men of merely good sense and fair talent.

The matter of definition, I have said, is very important. I am not now speaking of nominal definitions, which for convenience merely give names to known objects. I am speaking of such definitions of phenomena as result from correct analysis of the phenomena. Nominal definitions are mere conveniences and are neither true nor false; but analytic definitions are definitive propositions and are true [pg 050] or else false. Let us dwell upon the matter a little more.

In the illustration of the definitions of lightning, there were three; the first was the most mistaken and its application brought the most harm; the second was less incorrect and the practical results less bad; the third under the present conditions of our knowledge, was the “true one” and it brought the maximum benefit. This lightning illustration suggests the important idea of relative truth and relative falsehood—the idea, that is, of degrees of truth and degrees of falsehood. A definition may be neither absolutely true nor absolutely false; but of two definitions of the same thing, one of them may be truer or falser than the other.

If, for illustration's sake, we call the first “truth” A, (alpha 1), the second one A2 (alpha 2), the third one A3 (alpha 3), we may suppose that a genius appears who has the faculty to surpass all the other relative truths A1, A2, A3, ... An and gives us an absolute or final truth, valid in infinity (Ainfinity) say a final definition, that lightning is so ... and so ..., a kind of energy which flows, let us say, through a glass tube filled with charcoal. Then of course this definition would immediately make obvious what use could be made of it. We could erect glass towers filled with charcoal and so secure an unlimited flow of available free energy and our [pg 051] whole life would be affected in an untold degree. This example explains the importance of correct definitions.

But to take another example: there is such a thing as a phenomenon called the “color” red. Imagine how it might be defined. A reactionary would call it a “Bolshevik” (A1); a Bolshevik would say “My color” (A2); a color-blind person would say “such a thing does not exist” (A3); a Daltonist would say “that is green” (A4); a metaphysician would say “that is the soul of whiskey” (A5); an historian would say “that is the color of the ink with which human history has been written” (A6); an uneducated person would say “that is the color of blood” (A7); the modern scientist would say “it is the light of such and such wave length” (A8). If this last definition be “valid in infinity” or not we do not know, but it is, nevertheless, a “scientific truth” in the present condition of our knowledge.

This final but unknown “truth valid in infinity” is somehow perceived or felt by us as an ideal, for in countless years of observation we have formed a series of less and less false, more and more nearly true “ideas” about the phenomenon. The “ideas” are reflexes of the phenomenon, reflected in our midst as in a mirror; the reflexes may be distorted, as in a convex or concave mirror, but they suggest [pg 052] an ideal reflex valid in infinity. It is of the utmost importance to realize that the words which are used to express the ideas and the ideals are the materialization of the ideas and ideal; it is only by words that we are enabled to give to other human beings an exact or nearly exact impression which we have had of the phenomenon.

It may be helpful to illustrate this process by an example. Let us suppose that a man makes an experiment of doing his own portrait from a mirror, which may be plane, concave or convex. If he looks into a plane mirror, he will see his true likeness; even so, if he be a poor designer, he will draw the likeness badly. Let us suppose that the man has beautiful features but because the drawing is very poor, it will not convey the impression that the features of the original were beautiful. If this poor designer were to look into and work from a concave or convex mirror, the drawing of his likeness would have practically no resemblance to his original features.

For correct analysis and true definitions of the cardinal classes of life in our world it is necessary to have some just ideas about dimensions or dimensionality. The Britannica gives us some help in this connection. I will explain briefly by an example. Measurable entities of different kinds can not be compared directly. Each one must be measured in [pg 053] terms of a unit of its own kind. A line can have only length and therefore is of one dimension: a surface has length and width and is therefore said to have two dimensions; a volume has length, width and thickness and is, therefore, said to have three dimensions. If we take, for example, a volume—say a cube—we see that the cube has surfaces and lines and points, but a volume is not a surface nor a line nor a point. Just these dimensional differences have an enormous unrealized importance in practical life, as in the case of taking a line of five units of length and building upon it a square, the measure of this square (surface) will not be 5, it will be 25; and the 25 will not be 25 linear units but 25 square or surface units. If upon this square we build a cube, this cube will have neither 5 nor 25 for its measure; it will have 125, and this number will not be so many units of length nor of surface but so many solid or cubic units.

It is as plain as a pike staff that, if we confused dimensions when computing lengths and areas and volumes, we would wreck all the architectural and engineering structures of the world, and at the same time show ourselves stupider than block-heads.

To analyse the classes of life we have to consider two very different kinds of phenomena: the one embraced under the collective name—Inorganic chemistry—the other under the collective name—Organic [pg 054] chemistry, or the chemistry of hydro-carbons. These divisions are made because of the peculiar properties of the elements chiefly involved in the second class. The properties of matter are so distributed among the elements that three of them—Oxygen, Hydrogen, and Carbon—possess an ensemble of unique characteristics. The number of reactions in inorganic chemistry are relatively few, but in organic chemistry—in the chemistry of these three elements the number of different compounds is practically unlimited. Up to 1910, we knew of more than 79 elements of which the whole number of reactions amounted to only a few hundreds, but among the remaining three elements—Carbon, Hydrogen and Oxygen—the reactions were known to be practically unlimited in number and possibilities; this fact must have very far reaching consequences. As far as energies are concerned, we have to take them as nature reveals them to us. Here more than ever, mathematical thinking is essential and will help enormously. The reactions in inorganic chemistry always involve the phenomenon of heat, sometimes light, and in some instances an unusual energy is produced called electricity. Until now, the radioactive elements represent a group too insufficiently known for an enlargement here upon this subject.

The organic compounds being unlimited in number and possibilities and with their unique characteristics, [pg 055] represent of course, a different class of phenomena, but being, at the same time, chemical they include the basic chemical phenomena involved in all chemical reactions, but being unique in many other respects, they also have an infinitely vast field of unique characteristics. Among the energetic phenomena of organic chemistry, besides the few mentioned above there are new and unique energetic phenomena occurring in this dimension.

Of these phenomena, mention may be made of the phenomenon “life,” the phenomenon of the “instincts” and of the “mind” in general. These energetic phenomena are unique for the unique chemistry of the three unique elements. It is obvious that this “uniqueness” is the reason why these phenomena must be classified as belonging to or having a higher dimensionality than belongs to the phenomena of inorganic chemistry just as the uniqueness of the properties of a volume as compared with surface properties depends upon the fact that a volume has a higher dimensionality than a surface. Just as this difference of dimensions makes the whole difference between the geometry of volumes and the geometry of surfaces, the difference between the two chemistries involves a difference of dimensionality.

The higher energies of the chemistries of the higher dimensionality are very difficult to define; my descriptions are no better than the description of [pg 056] life given by Professor Wilhelm Roux, in his Der Kampf der Teile im Organismus, Leipzig, 1881, which are equally unsatisfactory. In want of a better, I quote him. He defines a living being as a natural object which possesses the following nine characteristic autonomous activities: Autonomous change, Autonomous excretion, Autonomous ingestion, Autonomous assimilation, Autonomous growth, Autonomous movement, Autonomous multiplication, Autonomous transmission of hereditary characteristics and Autonomous development. The words “Autonomous activities” are important because they hint at the dimensional differences of these energies. But a better word should be found to define the dimensional differences between the activities found in inorganic chemistry and those found in organic chemistry. We see it is a mistake to speak about “life” in a crystal, in the same sense in which we use the word life to name the curious autonomous phenomenon of organic chemistry, which is of another dimension than the activities in inorganic chemistry. For the so-called life in the crystals—the not autonomous (or anautonomous) activities of crystals—another word than life should be found. In the theory of crystals the term life is purely rhetorical: its use there is very injurious to sound science. These old ideas of “life” in crystals are profoundly unscientific and serve as one of the best [pg 057] examples of the frequent confusion or intermixing of dimensions—a confusion due to unmathematical, logically incorrect ways of thinking. If crystals “live,” then volumes are surfaces, and 125 cubic units=25 square units—absurdities belonging to the “childhood of humanity.”

It will be explained later that one of the energetic phenomena of organic chemistry—the “mind,” which is one of the energies characteristic of this class of phenomena, is “autonomous,” is “self-propelling” and true to its dimensionality. If we analyse the classes of life, we readily find that there are three cardinal classes which are radically distinct in function. A short analysis will disclose to us that, though minerals have various activities, they are not “living.” The plants have a very definite and well known function—the transformation of solar energy into organic chemical energy. They are a class of life which appropriates one kind of energy, converts it into another kind and stores it up; in that sense they are a kind of storage battery for the solar energy; and so I define the plants as the chemistry-binding class of life.

The animals use the highly dynamic products of the chemistry-binding class—the plants—as food, [pg 059] and those products—the results of plant-transformation—undergo in animals a further transformation into yet higher forms; and the animals are correspondingly a more dynamic class of life; their energy is kinetic; they have a remarkable freedom and power which the plants do not possess—I mean the freedom and faculty to move about in space; and so I define animals as the space-binding class of life.

And now what shall we say of human beings? What is to be our definition of Man? Like the animals, human beings do indeed possess the space-binding capacity but, over and above that, human beings possess a most remarkable capacity which is entirely peculiar to them—I mean the capacity to summarise, digest and appropriate the labors and experiences of the past; I mean the capacity to use the fruits of past labors and experiences as intellectual or spiritual capital for developments in the present; I mean the capacity to employ as instruments of increasing power the accumulated achievements of the all-precious lives of the past generations spent in trial and error, trial and success; I mean the capacity of human beings to conduct their lives in the ever increasing light of inherited wisdom; I mean the capacity in virtue of which man is at once the heritor of the by-gone ages and the trustee of posterity. And because humanity is just this magnificent [pg 060] natural agency by which the past lives in the present and the present for the future, I define humanity, in the universal tongue of mathematics and mechanics, to be the time-binding class of life.

These definitions of the cardinal classes of life are, it will be noted, obtained from direct observation; they are so simple and so important that I cannot over-emphasize the necessity of grasping them and most especially the definition of Man. For these simple definitions and especially that of Humanity will profoundly transform the whole conception of human life in every field of interest and activity; and, what is more important than all, the definition of Man will give us a starting point for discovering the natural laws of human nature—of the human class of life. The definitions of the classes of life represent the different classes as distinct in respect to dimensionality; and this is extremely important for no measure or rule of one class can be applied to the other, without making grave mistakes. For example, to treat a human being as an animal—as a mere space-binder—because humans have certain animal propensities, is an error of the same type and grossness as to treat a cube as a surface because it has surface properties. It is absolutely essential to grasp that fact if we are ever to have a science of human nature.