Alternate currents, especially of high frequencies, pass with astonishing freedom through even slightly rarefied gases. The upper strata of the air are rarefied. To reach a number of miles out into space requires the overcoming of difficulties of a merely mechanical nature.
Arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tngible objects into the argument.
Because the rich are generally few in number, while the poor are many, they appear to be antagonistic, and as the one or the other prevails they form the government. Hence arises the common opinion that there are two kinds of government - democracy and oligarchy.
The search which takes place in my studio might best be described as a mining operation, a vertical dig in which a number of discoveries are apt to surface from a single shaft.
Whether if soul did not exist time would exist or not, is a question that may fairly be asked; for if there cannot be someone to count there cannot be anything that can be counted, so that evidently there cannot be number; for number is either what has been, or what can be, counted.
In the 'in-itself' there is nothing of 'causal connections', of 'necessity', or of 'psychological non-freedom'; there the effect does not follow the cause, there is no rule or 'law'. It is we alone who have devised cause, sequence, for-each-other, relativity, constraint, number, law, freedom, motive, and purpose; and when we project and mix this symbol world into things as if it existed 'in itself', we act once more as we have always acted- mythologically.
I've always felt that a person's intelligence is directly reflected by the number of conflicting points of view he can entertain simultaneously on the same topic.
A certain degree of physical harmony and comfort is necessary, but above a certain level it becomes a hindrance instead of a help. Therefore the ideal of creating an unlimited number of wants and satisfying them seems to be a delusion and a snare.
The right constitutions, three in number- kingship, aristocracy, and polity- and the deviations from these, likewise three in number - tyranny from kingship, oligarchy from aristocracy, democracy from polity.
The evil effect of science upon men is principally this, that by far the greatest number of those who wish to display a knowledge of it accomplish no improvement at all of the understanding, but only a perversity of it, not to mention that it serves most of them as a tool of vanity.
We must believe that "emotion recollected in tranquillity" is an inexact formula. For it is neither emotion, nor recollection, nor without distortion of meaning, tranquillity. It is a concentration, and a new thing resulting from the concentration of a very great number of experiences which to the practical and active person would not seem to be experiences at all; it is a concentration which does not happen consciously or of deliberation. These experiences are not "recollected" and they finally unite in an atmosphere which is "tranquil" only in that it is a passive attending upon the event.