Footnotes
To digress a bit, it may be interesting to add, that population and the need of people increase in a geometrical progression; and also that the growth of individuals is limited by the fact, that they have to absorb their food through surfaces which as growth goes on increase only as squares, while the bodies to be fed, being volumes, increase in size as cubes increase, as the cubes of the same base grow faster than the squares,
22 = 4, 23 = 8, 32 = 9, 33 = 27, and so on,
it is obvious, that in the infancy of an organism only a part of the food goes to maintain life, the larger part goes for growth; when the organism becomes larger, the absorbing surfaces, growing proportionally to the square, the food is spent to build the mass of the volume of the body and is spent proportionally to the cube. Suppose our organism has grown to a size twice as large, its absorbing capacity has become four times larger, its volume eight times larger. In case of 3 times, the difference will be 9 and 27. It is obvious that at some point, all the absorbed food will be used to maintain life and none will be left for growth, and this last process will stop. This is another example which explains how the theory of dimensions is vitally important in life and shows why it is absolutely essential to take account of dimensions in the study of life problems.
(J. H. R.) “Phases of religious complex. ‘Religious,’ a vague and comprehensive term applied to: (1) certain classes of emotions (awe, dependence, self-distrust, aspirations, etc.); (2) Conduct, which may take the form of distinctive religious acts (ceremonies, sacrifices, prayers, ‘good works’) or the observance of what in primitive conditions are recognized as ‘taboos’; (3) Priestly, or ecclesiastical organizations; (4) Beliefs about supernatural beings and man's relations to them: the latter may take the form of revelation and be reduced to creeds and become the subject of elaborate theological speculations.
“Association of religion with the supernatural; religion has always had for its primary object the attainment of a satisfactory adjustment to, or a successful control over, the supernatural.... The cultural mind viewed as the product of a long and hazardous process of accumulation.... Spontaneous generation of superstitions. Prevalence of symbolism, mana, animism, magic, fetishism, totemism; the taboo (cf. our modern idea of ‘principle’), the sacred, clean and unclean; ‘dream logic’—spontaneous rationalizing or ‘jumping at conclusions’;... The 16th book of the Theodosian Code contains edicts relating to the Church issued by the Roman Emperors during the 4th and 5th centuries. They make it a crime to disagree with the Church; they provide harsh penalties for heretical teaching and writing, and grant privileges to the orthodox clergy (exemptions from regular taxes and benefit of the clergy).... Christianity becomes a monopoly defended by the state.... Psychological power and attraction in the elaborate symbolism and ritual of the church.... Allegory put an end to all literary criticism.... Flourishing of the miraculous; any unusual or startling occurrence attributed to the intervention of either God or the Devil.... Older conceptions of disease as caused by the Devil.... Our legal expression ‘act of God’ confined to unforseeable natural disasters. How with a growing appreciation for natural law and a chastened taste in wonders, miracles have tended to become a source of intellectual distress and bewilderment.... Protestants shared with Roman Catholics the horror of ‘rationalists’ and ‘free-thinkers.’ The leaders of both parties agreed in hampering and denouncing scientific discoveries.... Witchcraft in its modern form emerges clearly in the 15th century.... Great prevalence of witchcraft during the 16th and 17th centuries in Protestant and Catholic countries, alike.... Trial of those suspected of sorcery. Tortures to force confession. The witches' mark. Penalties, burning alive, strangling, hanging. Tens of thousands of innocent persons perished.... Those who tried to discredit witchcraft denounced as ‘Sadducees’ and atheists.... The psychology of intolerance. Fear, vested interests, the comfortable nature of the traditional and the habitual. The painful appropriation of new ideas.... The intolerance of the Catholic Church: a natural result of its state-like organization and claims.... Its doctrine of exclusive salvation and its conception of heresy both sanctioned by the state. Doubt and error regarded as sinful.... Beginnings of censorship of the press after the invention of printing, licensing of ecclesiastical and civil authorities.... Protestants of 16th century accept the theory of intolerance.”
It may be contended by some that animals have been making “progress” or some may say that animals also “bind-time.” This use of words would again become mere verbalism, a mere talking about words—mere speculation having nothing to do with facts or with correct thinking, in which there is no intermixing of dimensions. The peculiar faculty belonging exclusively to humans which I designate as “time-binding” I have clearly defined as an exponential function of time in the following chapter. If people are pleased to talk about the “progress” of animals, they can hardly fail to see clearly that it differs both in function and in type or dimension from what is rightly meant by human progress; human time-binding capacity lies in an entirely different dimension from that of animals. So, if any persons wish to talk of animal “progress” or animal “time-binding,” they should invent a suitable word for it to save them from the blunder of confusing types or mixing dimensions.
This mathematical discrimination between classes, types, dimensions is of the utmost importance in the natural sciences, because of the transmutation of species. To adjust the Darwin theory to dimensionality is a somewhat more difficult problem; it involves the concept of the “continuum”; but with the modern theory of de Vries, these things are self evident. If animals really progress, which is doubtful because they are an older form of life than humans and they have not shown any noticeable progress to the knowledge of man, their progress is so small in comparison with man's that it may be said, in mathematical terms, to be negligible as an infinitesimal of higher order.
It must be remembered here that our world is, first of all, a dynamic conglomeration of matter and energy, which to-day, as well as in the first period of primitive organic life, took and takes different known and unknown forms. One of these forms of energy is the chemical energy, with its tendency to combinations and exchanges. Different elements act in different ways. The history of the earth and its life is simply the history of different chemical periods, with different transformations of energy. A strange fact is to be noticed about nitrogen. Nitrogen chemically has an exceptional inertness toward most other substances, but once it is a component part of a substance, almost all of these combinations are a very powerful source of energy, and all of them have a very strong effect upon organic life. Nitric acid acts through oxidation, the substances are burned up by the oxygen given off from the acid. Nitric acid occurs in nature, in a combination called nitrates. From the soil the nitrates pass into the plant. Nitrite of amyl acts upon our organs in a most violent and spasmodic way. Nitrous oxide is the so-called laughing gas.
Alkaloids are compounds of a vegetable origin, generally of complex composition and capable of producing marked effects upon animals. They all contain nitrogen. Explosives which are a chemical means of storing tremendous amounts of energy, are mostly of some nitrogenous compound. Albumen is an organic compound of great importance in life, which, besides being the characteristic ingredient in the white of an egg, abounds in the serum of the blood and forms an important part of the muscles and brain. Albuminoids play the most vital rôle in plant life and are an extensive class of organic bodies found in plants and animals, as they are found to form the chief constituents of blood, nerves. All albuminoids found in animals are produced by the processes fulfilled in plants. Their exact constitution is not known; analysis shows that they contain approximately: Carbon 50-55%, Hydrogen 6.9-7.5%, Nitrogen 15-19%, Oxygen 20-24%, Sulphur 0.3-2.0%. Venous blood contains in 100 volumes: Nitrogen, 13; Carbonic Acid, 71.6; Oxygen, 15.3. Arterial blood: Nitrogen, 14.5; Carbonic Acid, 62.3; Oxygen, 23.2.
“Nitrogenous compounds in general, are extremely prone to decomposition; their decomposition often involving a sudden and great evolution of force. We see that substances classed as ferments ... are all nitrogenous ... and we see that even in organisms and parts of organisms where the activities are least, such changes as do take place are initiated by a substance containing nitrogen.... We see that organic matter is so constituted that small incidental actions are capable of initiating great reaction and liberating large quantities of power.... The seed of a plant contains nitrogenous substances in a far higher ratio than the rest of the plant; and the seed differs from the rest of the plant in its ability to initiate ... extensive vital changes—the changes constituting germination. Similarly in the bodies of animals ... in every living vegetal cell there is a certain part that contains nitrogen. This part initiates these changes which constitute the development of the cell.... It is a curious and significant fact that, in technology, we not only utilize the same principle of initiating extensive changes among comparatively stable compounds by the help of compounds much less stable, but we employ for the purpose compounds of the same general class. Our modern method of firing a gun is to place in close proximity with the gunpowder which we choose to decompose or explode, a small portion of fulminating powder, which is decomposed or exploded with extreme facility, and which on decomposing, communicates the consequent molecular disturbances to the less easily decomposed gunpowder. When we ask what this fulminating powder is composed of, we find that it is a nitrogenous salt.”—Spencer.