Threshold

“ We see at once how the characteristic concept of threshold, which has led to the conception of the continuous, immediately asserts itself when in connection with discontinuous numbers. The adaptation of the threshold to numbers can be carried as far as it is possible to reduce the threshold, but the latter can never be made to disappear entirely. ”

“ A man should always cross himself when he steps over a threshold in Russia; and, in some portions of the realm, it is believed that he ought not to sit down on the threshold. [24]
High sills, or thresholds, so that one must step over, and not on, them, are in the houses of Finland, and in the houses of many Finns in the United States. ”

“ The foundation-stone of a new building is, in a sense, the threshold of that structure. Hence to lay the foundations in blood is to proffer blood at the threshold. Traces of this custom are to be found in the practices or the legends of peoples wellnigh all the world over. ”

“ It is evident that here is the idea of passing over a line or boundary, or threshold limit, into another region, or state or condition. Until that threshold is crossed, the person is outside of the covenant with its privileges and benefits; but when it is crossed, or passed, the person is a partaker of all that is within. ”

“ Inhibition and rise of threshold may also result in a different way in the process of association. We may possibly lay it down as a law, which plays no small role in the interaction of systems and moments, that in a series of aggregation of various systems or moments, forming a more complex organized whole, due to association and synthesis of the component systems, having various thresholds, the ones having the higher thresholds will raise the thresholds of the moments having a greater sensitivity. ”

“ In other words, the bronze threshold is an archaic synonym for the enduring border, or outer limit, of spiritual domain.
This prominence given to the threshold in earlier Greek literature is not, it is true, continued in later writings; yet there are traces of it still in occasional poetic references to the “threshold of life,” and the “threshold of the year,” and the “threshold of old age.” When Homer refers “to houses, to rooms in houses, or to courtyards, the ‘threshold’ is constantly spoken of: a man steps over a threshold, stands at a threshold, sits at a threshold, etc. ”

“ In case an honored guest arrives unexpectedly, so that there is no time to prepare the customary sacrifice, salt, as representing blood, may be sprinkled on the threshold, for the guest to pass over; or again coffee, as the Muhammadan substitute for the “blood of the grape,” [2] may be poured on it. [3]
Crossing the threshold, or entering the door, of a house, is in itself an implied covenant with those who are within, as shown by the earlier laws of India. He who goes in by the door must count himself, and must be recognized, as a guest, subject to the strictest laws of hospitality. ”

“ It enables one to obtain what one arbitrarily calls a threshold, but it can go no further than that. When the experiment changes the conditions change. The space may remain the same, but it is only one of the elements which assist in forming the judgment, and its importance is very much overestimated when it is made the basis for determining the threshold. ”

“ In case where the threshold of an aggregate is raised the radiated minimal stimuli coming from a particular functioning aggregate may become efficient and reach the threshold, when another aggregate begins to function simultaneously. This holds true even in the case when the minimal stimuli, coming from two different aggregates are just below the threshold-stimulus. Thus, under certain conditions, when visual stimuli are barely or not at all discernible, they can become intensified by re-enforcing them with auditory stimuli. ”

“ And this sacrifice was supposed to secure safety against evil spirits encountered in crossing the boundary line.
Thus it would seem that, from the beginning, on the national threshold, as on the threshold of the temple and of the home, sacrifices were offered, and boundary marks were set up, in recognition of a peculiar sacredness of the border line,–which is in itself a foundation and a limit. These boundary marks were commonly a pillar or a tree, in apparent symbolism of a fructifying or a fruit-bearing agency, of the transmission or the continuance of life. ”

“ The same holds true of a whole psycho-physiological system,―there is a threshold of sensitivity below which the minimal stimulus cannot fall, the latter does not awaken any reaction in the system. All the senses reveal the presence of such thresholds which are also present in the case of all the higher psycho-physiological systems. If we term the stimulus which can just bring about a reaction in the system the stimulus threshold, we can say that a given system can only be thrown into activity by a stimulus rising in intensity above the stimulus threshold. ”

“ Furthermore, many aggregates whose arousal could otherwise be easily effected by the given stimulus may temporarily be in a condition in which their thresholds have become raised and thus fall outside the sphere of activity of the functioning aggregate. On the other hand, aggregates that are usually inaccessible to those minimal stimuli may under certain conditions be set into activity by minimal stimuli, if there is a lowering of the threshold of the total aggregate. Thus the aggregates set into activity by the functioning aggregate are conditioned by the rise and fall of their thresholds. ”

“ For a moment, if truth were told, they both hoped it would not open, for they were a prey to various unpleasant emotions as they stood there on the threshold of their ghostly adventure. Shorthouse, shuffling with the key and hampered by the steady weight on his arm, certainly felt the solemnity of the moment. It was as if the whole world—for all experience seemed at that instant concentrated in his own consciousness—were listening to the grating noise of that key. ”

“ When a moment or aggregate of moments begins to function, it radiates stimulation to other moments or aggregates of moments. All the aggregates which these radiated stimulations reach do not equally begin to function. It will depend largely on the state of the aggregate and its threshold. If the radiated stimuli be minimal, the many aggregates that have a high threshold will not be effected at all. ”

“ They cross the threshold and pause; they depart, they return, twenty times. They hover aloft in the air, their head persistently turned to the home; they describe great soaring circles that suddenly sink beneath the weight of regret; and their thirteen thousand eyes will question, reflect, and retain the trees and the fountain, the gate and the walls, the neighbouring windows and houses, till at last the aerial course whereon their return shall glide have become as indelibly stamped in their memory as though it were marked in space by two lines of steel. ”

“ Threshold values mark the emergence of new sign processes. As we have seen, practical experiences through which humans continuously ascertain their reality are affected by the scale at which they take place. Immediate tasks, such as those characteristic of direct forms of work, do not require a division into smaller tasks, a decomposition into smaller actions. The more complex the task, the more obvious the need to divide it. But it is not until the scale characteristic of our age is reached that decomposition becomes as critical as it now is. ”

“ The mass of associated systems forms the 'reductives' of each individual system. In dissociated systems the controlling influence of the 'reductive mass' is lost and the result is an over-activity, unchecked by any counteracting tendencies. ”

“ You flaunt your beauty in the rose, your glory in the dawn,
Your sweetness in the nightingale, your whiteness in the swan.
You haunt my waking like a dream, my slumber like a moon,
Pervade me like a musky scent, possess me like a tune. ”

“ O king, thy kingdom who from thee can wrest?
What fate shall dare uncrown thee from this breast,
O god-born lover, whom my love doth gird
And armour with impregnable delight
Of Hope's triumphant keen flame-carven sword? ”

“ Whither dost thou hide from the magic of my flute-call?
In what moonlight-tangled meshes of perfume,
Where the clustering keovas guard the squirrel's slumber,
Where the deep woods glimmer with the jasmine's bloom? ”

“ Gather and gleam round my delicate youth,
And I heard the song of the spirits of Truth;
To quench my longing I bent me low
By the streams of the spirits of Peace that flow
In that magical wood in the land of sleep. ”

“ This noted thresher had got into the favour of the fairies, and he had but to call and they were at his service when he went to the barn to do his threshing in the morning. His master began to suspect there was something more than mortal power at the bottom of his servant’s success as a thresher. He resolved to find out; and one morning he secreted himself in the barn before the hour of threshing came, so as to have a full view of what would go on at the threshing floor. ”

“ Rise, brothers, rise, the wakening skies pray to the morning lights
The wind lies asleep in the arms of the dawn like a child that has cried all night.
Come, let us gather our nets from the shore, and set our catamarans free,
To capture the leaping wealth of the tide, for we are the sons of the sea. ”

“ We may, by parallel reasoning, reach the conclusion that, even apart from the action of any external force, the equilibrium of a homogeneous aggregate must be destroyed by the unequal actions of its parts on each other. ”

“ After all, the choice of a state space in which to represent a system is just a choice of how to describe that system, and so to notice that a system’s behavior is constrained in one space is just to notice that the system’s behavior is constrained period, though the degree of constraint can vary. ”

“ Since there is no limit to the diminution of the disturbance of equilibrium by division of the change in the external coördinates, we may suppose as a general rule that by diminishing the velocity of the changes in the external coördinates, a given change may be made to produce a very small disturbance of statistical equilibrium. ”

“ Yet the threshers appear to enjoy an immunity which seems to be restricted to themselves and blacksmiths; and while a stranger is anxiously shading his eyes from the shower of hard maize grains, the threshers themselves do not give a thought to the safety of their eyes, but sing at the top of their voice, pound away at the corn cobs, and make the grains fly in all directions, as if the chorus of the song were the chief object in life, and the preservation of their eyesight were unworthy of a thought. ”

“ A system is called practically unstable when a very small (not necessarily indefinitely small) disturbance or variation in its condition will produce a considerable change. In the former part of this paper, in which the influence of surfaces of discontinuity was neglected, a system was regarded as practically unstable when such a result would be produced by a disturbance of the same order of magnitude as the quantities relating to surfaces of discontinuity which were neglected. ”

“ With the help of the Phase Rule we can group together into classes the large number of different isolated cases of systems in equilibrium; with its aid we are able to state, in a general manner at least, the conditions under which a system can be in equilibrium, and by its means we can gain some insight into the relations existing between different kinds of systems. ”

“ Few, if any of us, understand thoroughly the nature of the unconscious stratification which takes place in life, the layers and types and classes into which it assorts itself and the barriers which these offer to a free migration of individuals from one class to another. ”

“ Lack of restraint is failure to construct a properly-working hierarchy. That is a very simple example. Less easy to analyse but equally vicious, are the innumerable cases in which some sort of equilibrium is only attained not by a free interaction of dominant and subordinate parts, but by repression. Conflicts arise, which persist, either in an open form or in the subterranean regions of the unconscious. ”

“ So a conditioning law of equation or balance which compels a rough reciprocity between parts, all parts, may not remove the effects of or the necessity for strain or excess in the relationship of some men or some races, or all men and all races. War certainly indicates as much, and all the plottings and struggles and injustices and deaths which are concomitants if not essentials of all forms of progress. Again, what we might consider necessary in the way of equation or balance, and what Nature would, are two very different things. Our very finite minds can see but finitely. ”

“ I know that table like a living thing, and yet I never saw it until to-day.”
“I suppose,” said Hugh, “that you base your system on the law of average?”
The professor laughed tolerantly. “No, I don’t. Law [225] of average,—that is child’s talk to me. Of course every table has its average, every wheel has its average, every croupier, you, I; every coup that is played, is an average with something that has gone before. Ah! these foolish system-players with their talk of average and probability and phenomenon. Why, every coup is a phenomenon as regards something that has gone before. ”

“ A sudden and complete disturbance of the measure may result in the gravest consequences, even in death. We have here an instance in point. We must therefore lay ourselves out to restore as quickly, and as effectually as possible, the steady measure that has been disturbed ”

“ Many, I doubt not, failing to recognize the truth that, in proportion as an aggregate is complex, the effects wrought by an incident force become more multitudinous, complicated, and incalculable, and that, therefore, a society is, of all kinds of aggregates, the kind most difficult to affect in an intended way and not in unintended ways—many such will ask evidence of the difficulty. ”