Remainder Quotes (7 quotes)
A good method of discovery is to imagine certain members of a system removed and then see how what is left would behave: for example, where would we be if iron were absent from the world: this is an old example.
Aphorism 258 in Notebook J (1789-1793), as translated by R. J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 181.
I had made up my mind to find that for which I was searching even if it required the remainder of my life. After innumerable failures I finally uncovered the principle for which I was searching, and I was astounded at its simplicity. I was still more astounded to discover the principle I had revealed not only beneficial in the construction of a mechanical hearing aid but it served as well as means of sending the sound of the voice over a wire. Another discovery which came out of my investigation was the fact that when a man gives his order to produce a definite result and stands by that order it seems to have the effect of giving him what might be termed a second sight which enables him to see right through ordinary problems. What this power is I cannot say; all I know is that it exists and it becomes available only when a man is in that state of mind in which he knows exactly what he wants and is fully determined not to quit until he finds it.
As quoted, without citation, in Mack R. Douglas, Making a Habit of Success: How to Make a Habit of Succeeding, How to Win With High Self-Esteem (1966, 1994), 38. Note: Webmaster is dubious of a quote which seems to appear in only one source, without a citation, decades after Bell’s death. If you know a primary source, please contact Webmaster.
I have no patience with attempts to identify science with measurement, which is but one of its tools, or with any definition of the scientist which would exclude a Darwin, a Pasteur or a Kekulé. The scientist is a practical man and his are practical aims. He does not seek the ultimate but the proximate. He does not speak of the last analysis but rather of the next approximation. His are not those beautiful structures so delicately designed that a single flaw may cause the collapse of the whole. The scientist builds slowly and with a gross but solid kind of masonry. If dissatisfied with any of his work, even if it be near the very foundations, he can replace that part without damage to the remainder. On the whole, he is satisfied with his work, for while science may never be wholly right it certainly is never wholly wrong; and it seems to be improving from decade to decade.
The Anatomy of Science (1926), 6-7.
Most people today still believe, perhaps unconsciously, in the heliocentric universe. ... Every newspaper in the land has a section on astrology, yet few have anything at all on astronomy.
[Realizing that his plasma universe may take a long time to penetrate the popular consciousness. When addressing a number of physicists with the first half of the quote, the groups was at first incredulous, but nodded agreement upon hearing the remainder of the quote.]
[Realizing that his plasma universe may take a long time to penetrate the popular consciousness. When addressing a number of physicists with the first half of the quote, the groups was at first incredulous, but nodded agreement upon hearing the remainder of the quote.]
Quoted in Anthony L. Peratt, 'Dean of the Plasma Dissidents', Washington Times, supplement: The World and I (May 1988),196.
October 9, 1863
Always, however great the height of the balloon, when I have seen the horizon it has roughly appeared to be on the level of the car though of course the dip of the horizon is a very appreciable quantity or the same height as the eye. From this one might infer that, could the earth be seen without a cloud or anything to obscure it, and the boundary line of the plane approximately the same height as the eye, the general appearance would be that of a slight concavity; but I have never seen any part of the surface of the earth other than as a plane.
Towns and cities, when viewed from the balloon are like models in motion. I shall always remember the ascent of 9th October, 1863, when we passed over London about sunset. At the time when we were 7,000 feet high, and directly over London Bridge, the scene around was one that cannot probably be equalled in the world. We were still so low as not to have lost sight of the details of the spectacle which presented itself to our eyes; and with one glance the homes of 3,000,000 people could be seen, and so distinct was the view, that every large building was easily distinguishable. In fact, the whole of London was visible, and some parts most clearly. All round, the suburbs were also very distinct, with their lines of detached villas, imbedded as it were in a mass of shrubs; beyond, the country was like a garden, its fields, well marked, becoming smaller and smaller as the eye wandered farther and farther away.
Again looking down, there was the Thames, throughout its whole length, without the slightest mist, dotted over its winding course with innumerable ships and steamboats, like moving toys. Gravesend was visible, also the mouth of the Thames, and the coast around as far as Norfolk. The southern shore of the mouth of the Thames was not so clear, but the sea beyond was seen for many miles; when at a higher elevation, I looked for the coast of France, but was unable to see it. On looking round, the eye was arrested by the garden-like appearance of the county of Kent, till again London claimed yet more careful attention.
Smoke, thin and blue, was curling from it, and slowly moving away in beautiful curves, from all except one part, south of the Thames, where it was less blue and seemed more dense, till the cause became evident; it was mixed with mist rising from the ground, the southern limit of which was bounded by an even line, doubtless indicating the meeting of the subsoils of gravel and clay. The whole scene was surmounted by a canopy of blue, everywhere free from cloud, except near the horizon, where a band of cumulus and stratus extended all round, forming a fitting boundary to such a glorious view.
As seen from the earth, the sunset this evening was described as fine, the air being clear and the shadows well defined; but, as we rose to view it and its effects, the golden hues increased in intensity; their richness decreased as the distance from the sun increased, both right and left; but still as far as 90º from the sun, rose-coloured clouds extended. The remainder of the circle was completed, for the most part, by pure white cumulus of well-rounded and symmetrical forms.
I have seen London by night. I have crossed it during the day at the height of four miles. I have often admired the splendour of sky scenery, but never have I seen anything which surpassed this spectacle. The roar of the town heard at this elevation was a deep, rich, continuous sound the voice of labour. At four miles above London, all was hushed; no sound reached our ears.
Always, however great the height of the balloon, when I have seen the horizon it has roughly appeared to be on the level of the car though of course the dip of the horizon is a very appreciable quantity or the same height as the eye. From this one might infer that, could the earth be seen without a cloud or anything to obscure it, and the boundary line of the plane approximately the same height as the eye, the general appearance would be that of a slight concavity; but I have never seen any part of the surface of the earth other than as a plane.
Towns and cities, when viewed from the balloon are like models in motion. I shall always remember the ascent of 9th October, 1863, when we passed over London about sunset. At the time when we were 7,000 feet high, and directly over London Bridge, the scene around was one that cannot probably be equalled in the world. We were still so low as not to have lost sight of the details of the spectacle which presented itself to our eyes; and with one glance the homes of 3,000,000 people could be seen, and so distinct was the view, that every large building was easily distinguishable. In fact, the whole of London was visible, and some parts most clearly. All round, the suburbs were also very distinct, with their lines of detached villas, imbedded as it were in a mass of shrubs; beyond, the country was like a garden, its fields, well marked, becoming smaller and smaller as the eye wandered farther and farther away.
Again looking down, there was the Thames, throughout its whole length, without the slightest mist, dotted over its winding course with innumerable ships and steamboats, like moving toys. Gravesend was visible, also the mouth of the Thames, and the coast around as far as Norfolk. The southern shore of the mouth of the Thames was not so clear, but the sea beyond was seen for many miles; when at a higher elevation, I looked for the coast of France, but was unable to see it. On looking round, the eye was arrested by the garden-like appearance of the county of Kent, till again London claimed yet more careful attention.
Smoke, thin and blue, was curling from it, and slowly moving away in beautiful curves, from all except one part, south of the Thames, where it was less blue and seemed more dense, till the cause became evident; it was mixed with mist rising from the ground, the southern limit of which was bounded by an even line, doubtless indicating the meeting of the subsoils of gravel and clay. The whole scene was surmounted by a canopy of blue, everywhere free from cloud, except near the horizon, where a band of cumulus and stratus extended all round, forming a fitting boundary to such a glorious view.
As seen from the earth, the sunset this evening was described as fine, the air being clear and the shadows well defined; but, as we rose to view it and its effects, the golden hues increased in intensity; their richness decreased as the distance from the sun increased, both right and left; but still as far as 90º from the sun, rose-coloured clouds extended. The remainder of the circle was completed, for the most part, by pure white cumulus of well-rounded and symmetrical forms.
I have seen London by night. I have crossed it during the day at the height of four miles. I have often admired the splendour of sky scenery, but never have I seen anything which surpassed this spectacle. The roar of the town heard at this elevation was a deep, rich, continuous sound the voice of labour. At four miles above London, all was hushed; no sound reached our ears.
Travels in the Air (1871), 99-100.
The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.
In Bertrand Russell, The Principles of Mathematics (1903), 5.
The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.
The original script by Noel Langley was revised by Florence Ryerson and Edgar Allan Woolf to produce the final screenplay of movie The Wizard of Oz. Whoever originated this particular line, it was said by the Scarecrow character on receiving his Doctor of Thinkology Degree from the Wizard. Screenplay as in The Wizard of Oz: The Screenplay (1989), 123.
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- 
