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.