...they have never affirm'd any thing, concerning the Cause, till the Trial was past: whereas, to do it before, is a most venomous thing in the making of Sciences; for whoever has fix'd on his Cause, before he experimented; can hardly avoid fitting his Experiment to his Observations, to his own Cause, which he had before imagin'd; rather than the Cause to the Truth of the Experiment itself.
Referring to experiments of the Aristotelian mode, whereby a preconceived truth would be illustrated merely to convince people of the validity of the original thought.

“There is no expedient to which a man will not resort to avoid the real labor of thinking.
Sir Joshua Reynolds.”

[For] those suffering under the thraldom of the vice [of opium eating] … it is well to avoid undue harshness with the patient; and it should be carefully remembered, that in many instances the sufferers are more objects of pity than of blame.

Ein Fachmann ist ein Mann, der einige der gröbsten Fehler kennt, die man in dem betreffenden Fach machen kann, und der sie deshalb zu vermeiden versteht.
An expert is someone who knows some of the worst mistakes that can be made in his subject, and how to avoid them.

A clever person solves a problem. A wise person avoids it.

A great surgeon performs operations for stone by a single method; later he makes a statistical summary of deaths and recoveries, and he concludes from these statistics that the mortality law for this operation is two out of five. Well, I say that this ratio means literally nothing scientifically and gives us no certainty in performing the next operation; for we do not know whether the next case will be among the recoveries or the deaths. What really should be done, instead of gathering facts empirically, is to study them more accurately, each in its special determinism. We must study cases of death with great care and try to discover in them the cause of mortal accidents so as to master the cause and avoid the accidents.

A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history. … Only by taking an infinitesimally small unit for observation (the differential of history, that is, the individual tendencies of man) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.

A statistician is one who has learned how to get valid evidence from statistics and how (usually) to avoid being misled by irrelevant facts. It’s too bad that we apply the same name to this kind of person that we use for those who only tabulate. It’s as if we had the same name for barbers and brain surgeons because they both work on the head.

All government, in its essence, is organized exploitation, and in virtually all its existing forms it is the implacable enemy of every industrious and well-disposed man ... The typical politician is not only a rascal but also a jackass, so he greatly values the puerile notoriety and adulation that sensible men try to avoid.

An author has always great difficulty in avoiding unnecessary and tedious detail on the one hand; while, on the other, he must notice such a number of facts as may convince a student, that he is not wandering in a wilderness of crude hypotheses or unsupported assumptions.

As white reflects more heat, as well as more light than any other colour, it ought always to be preferred for the inside of a Chimney Fire-place, and black, which reflects neither light nor heat, should be most avoided.

As every circumstance relating to so capital a discovery as this (the greatest, perhaps, that has been made in the whole compass of philosophy, since the time of Sir Isaac Newton) cannot but give pleasure to all my readers, I shall endeavour to gratify them with the communication of a few particulars which I have from the best authority. The Doctor [Benjamin Franklin], after having published his method of verifying his hypothesis concerning the sameness of electricity with the matter lightning, was waiting for the erection of a spire in Philadelphia to carry his views into execution; not imagining that a pointed rod, of a moderate height, could answer the purpose; when it occurred to him, that, by means of a common kite, he could have a readier and better access to the regions of thunder than by any spire whatever. Preparing, therefore, a large silk handkerchief, and two cross sticks, of a proper length, on which to extend it, he took the opportunity of the first approaching thunder storm to take a walk into a field, in which there was a shed convenient for his purpose. But dreading the ridicule which too commonly attends unsuccessful attempts in science, he communicated his intended experiment to no body but his son, who assisted him in raising the kite.
The kite being raised, a considerable time elapsed before there was any appearance of its being electrified. One very promising cloud passed over it without any effect; when, at length, just as he was beginning to despair of his contrivance, he observed some loose threads of the hempen string to stand erect, and to avoid one another, just as if they had been suspended on a common conductor. Struck with this promising appearance, he inmmediately presented his knuckle to the key, and (let the reader judge of the exquisite pleasure he must have felt at that moment) the discovery was complete. He perceived a very evident electric spark. Others succeeded, even before the string was wet, so as to put the matter past all dispute, and when the rain had wetted the string, he collected electric fire very copiously. This happened in June 1752, a month after the electricians in France had verified the same theory, but before he had heard of any thing that they had done.

Astronomy teaches the correct use of the sun and the planets. These may be put on a frame of little sticks and turned round. This causes the tides. Those at the ends of the sticks are enormously far away. From time to time a diligent searching of the sticks reveals new planets. The orbit of the planet is the distance the stick goes round in going round. Astronomy is intensely interesting; it should be done at night, in a high tower at Spitzbergen. This is to avoid the astronomy being interrupted. A really good astronomer can tell when a comet is coming too near him by the warning buzz of the revolving sticks.

Avoid complexities. Make everything as simple as possible.

Be a physical chemist, an organic chemist, an analytical chemist, if you will; but above all be a Chemist.
[Admonishing his students to avoid over-specialization.]

But how is one to determine what is pleasing to God? ... Whatever is unpleasant to man is pleasant to God. The test is the natural instinct of man. If there arises within one’s dark recesses a hot desire to do this or that, then it is the paramount duty of a Christian to avoid doing this or that. And if, on the contrary, one cherishes an abhorrence of the business, then one must tackle it forthwith, all the time shouting ‘Hallelujah!’ A simple enough religion, surely–simple, satisfying and idiotic.

But when it has been shown by the researches of Pasteur that the septic property of the atmosphere depended not on the oxygen, or any gaseous constituent, but on minute organisms suspended in it, which owed their energy to their vitality, it occurred to me that decomposition in the injured part might be avoided without excluding the air, by applying as a dressing some material capable of destroying the life of the floating particles. Upon this principle I have based a practice.

By teaching us how to cultivate each ferment in its purity—in other words, by teaching us how to rear the individual organism apart from all others,—Pasteur has enabled us to avoid all these errors. And where this isolation of a particular organism has been duly effected it grows and multiplies indefinitely, but no change of it into another organism is ever observed. In Pasteur’s researches the Bacterium remained a Bacterium, the Vibrio a Vibrio, the Penicillium a Penicillium, and the Torula a Torula. Sow any of these in a state of purity in an appropriate liquid; you get it, and it alone, in the subsequent crop. In like manner, sow smallpox in the human body, your crop is smallpox. Sow there scarlatina, and your crop is scarlatina. Sow typhoid virus, your crop is typhoid—cholera, your crop is cholera. The disease bears as constant a relation to its contagium as the microscopic organisms just enumerated do to their germs, or indeed as a thistle does to its seed.

Camels, unlike most animals, regulate their body temperatures at two different but stable states. During daytime in the desert, when it is unbearably hot, camels regulate close to 40°C, a close enough match to the air temperature to avoid having to cool by sweating precious water. At night the desert is cold, and even cold enough for frost; the camel would seriously lose heat if it tried to stay at 40°C, so it moves its regulation to a more suitable 34°C, which is warm.

Confined to its true domain, mathematical reasoning is admirably adapted to perform the universal office of sound logic: to induce in order to deduce, in order to construct. … It contents itself to furnish, in the most favorable domain, a model of clearness, of precision, and consistency, the close contemplation of which is alone able to prepare the mind to render other conceptions also as perfect as their nature permits. Its general reaction, more negative than positive, must consist, above all, in inspiring us everywhere with an invincible aversion for vagueness, inconsistency, and obscurity, which may always be really avoided in any reasoning whatsoever, if we make sufficient effort.

Each species has evolved a special set of solutions to the general problems that all organisms must face. By the fact of its existence, a species demonstrates that its members are able to carry out adequately a series of general functions. … These general functions offer a framework within which one can integrate one’s view of biology and focus one’s research. Such a view helps one to avoid becoming lost in a morass of unstructured detail—even though the ways in which different species perform these functions may differ widely. A few obvious examples will suffice. Organisms must remain functionally integrated. They must obtain materials from their environments, and process and release energy from these materials. … They must differentiate and grow, and they must reproduce. By focusing one’s questions on one or another of these obligatory and universal capacities, one can ensure that one’s research will not be trivial and that it will have some chance of achieving broad general applicability.

Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best which is geometrically most simple.

Euclid avoids it [the treatment of the infinite]; in modern mathematics it is systematically introduced, for only then is generality obtained.

Eventually the process of aging, which is unlikely to be simple, should be understandable. Hopefully some of its processes can be slowed down or avoided. In fact, in the next century, we shall have to tackle the question of the preferred form of death.

Experience hobbles progress and leads to abandonment of difficult problems; it encourages the initiated to walk on the shady side of the street in the direction of experiences that have been pleasant. Youth without experience attacks the unsolved problems which maturer age with experience avoids, and from the labors of youth comes progress. Youth has dreams and visions, and will not be denied.

Few scientists acquainted with the chemistry of biological systems at the molecular level can avoid being inspired. Evolution has produced chemical compounds exquisitely organized to accomplish the most complicated and delicate of tasks. Many organic chemists viewing crystal structures of enzyme systems or nucleic acids and knowing the marvels of specificity of the immune systems must dream of designing and synthesizing simpler organic compounds that imitate working features of these naturally occurring compounds.

First, In showing in how to avoid attempting impossibilities. Second, In securing us from important mistakes in attempting what is, in itself possible, by means either inadequate or actually opposed to the end in view. Thirdly, In enabling us to accomplish our ends in the easiest, shortest, most economical, and most effectual manner. Fourth, In inducing us to attempt, and enabling us to accomplish, object which, but for such knowledge, we should never have thought of understanding.
On the ways that a knowledge of the order of nature can be of use.

For my part, I too much value the pursuit of truth and the discovery of any new fact in nature, to avoid inquiry because it appears to clash with prevailing opinions.

For of men it may in general be affirmed that they are thankless, fickle, false, studious to avoid danger, greedy of gain, devoted to you while you are able to confer benefits upon them …; but in the hour of need they forsake you.

For the past 10 years I have had the interesting experience of observing the development of Parkinson's syndrome on myself. As a matter of fact, this condition does not come under my special medical interests or I would have had it solved long ago. … The condition has its compensations: one is not yanked from interesting work to go to the jungles of Burma ... one avoids all kinds of deadly committee meetings, etc.

For there are two modes of acquiring knowledge, namely, by reasoning and experience. Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience; since many have the arguments relating to what can be known, but because they lack experience they neglect the arguments, and neither avoid what is harmful nor follow what is good. For if a man who has never seen fire should prove by adequate reasoning that fire burns and injures things and destroys them, his mind would not be satisfied thereby, nor would he avoid fire, until he placed his hand or some combustible substance in the fire, so that he might prove by experience that which reasoning taught. But when he has had actual experience of combustion his mind is made certain and rests in the full light of truth. Therefore reasoning does not suffice, but experience does.

Geometrical axioms are neither synthetic a priori conclusions nor experimental facts. They are conventions: our choice, amongst all possible conventions, is guided by experimental facts; but it remains free, and is only limited by the necessity of avoiding all contradiction. ... In other words, axioms of geometry are only definitions in disguise.
That being so what ought one to think of this question: Is the Euclidean Geometry true?
The question is nonsense. One might as well ask whether the metric system is true and the old measures false; whether Cartesian co-ordinates are true and polar co-ordinates false.

Hence, a devout Christian must avoid astrologers and all impious soothsayers, especially when they tell the truth, for fear of leading his soul into error by consorting with demons and entangling himself with the bonds of such association.

Here I most violently want you to
Avoid one fearful error, a vicious flaw.
Don’t think that our bright eyes were made that we
Might look ahead; that hips and knees and ankles
So intricately bend that we might take
Big strides, and the arms are strapped to the sturdy shoulders
And hands are given for servants to each side
That we might use them to support our lives.
All other explanations of this sort
Are twisted, topsy-turvy logic, for
Nothing what is born produces its own use.
Sight was not born before the light of the eyes,
Nor were words and pleas created before the tongue
Rather the tongue's appearance long preceded
Speech, and the ears were formed far earlier than
The sound first heard. To sum up, all the members Existed, I should think, before their use, So use has not caused them to have grown.

Humans are not by nature the fact-driven, rational beings we like to think we are. We get the facts wrong more often than we think we do. And we do so in predictable ways: we engage in wishful thinking. We embrace information that supports our beliefs and reject evidence that challenges them. Our minds tend to take shortcuts, which require some effort to avoid … [and] more often than most of us would imagine, the human mind operates in ways that defy logic.

I am a strong advocate for free thought on all subjects, yet it appears to me (whether rightly or wrongly) that direct arguments against christianity & theism produce hardly any effect on the public; & freedom of thought is best promoted by the gradual illumination of men's minds, which follow[s] from the advance of science. It has, therefore, been always my object to avoid writing on religion, & I have confined myself to science. I may, however, have been unduly biassed by the pain which it would give some members of my family, if I aided in any way direct attacks on religion.

I believe that certain erroneous developments in particle theory ... are caused by a misconception by some physicists that it is possible to avoid philosophical arguments altogether. Starting with poor philosophy, they pose the wrong questions. It is only a slight exaggeration to say that good physics has at times been spoiled by poor philosophy.

I believed that, instead of the multiplicity of rules that comprise logic, I would have enough in the following four, as long as I made a firm and steadfast resolution never to fail to observe them.
The first was never to accept anything as true if I did not know clearly that it was so; that is, carefully to avoid prejudice and jumping to conclusions, and to include nothing in my judgments apart from whatever appeared so clearly and distinctly to my mind that I had no opportunity to cast doubt upon it.
The second was to subdivide each on the problems I was about to examine: into as many parts as would be possible and necessary to resolve them better.
The third was to guide my thoughts in an orderly way by beginning, as if by steps, to knowledge of the most complex, and even by assuming an order of the most complex, and even by assuming an order among objects in! cases where there is no natural order among them.
And the final rule was: in all cases, to make such comprehensive enumerations and such general review that I was certain not to omit anything.
The long chains of inferences, all of them simple and easy, that geometers normally use to construct their most difficult demonstrations had given me an opportunity to think that all the things that can fall within the scope of human knowledge follow from each other in a similar way, and as long as one avoids accepting something as true which is not so, and as long as one always observes the order required to deduce them from each other, there cannot be anything so remote that it cannot be reached nor anything so hidden that it cannot be uncovered.

I confess that in 1901, I said to my brother Orville that man would not fly for fifty years...Ever since, I have distrusted myself and avoided all predictions.

I have no friends. The more you learn about the dignity of the gorilla, the more you want to avoid people.

I have tried to avoid long numerical computations, thereby following Riemann’s postulate that proofs should be given through ideas and not voluminous computations.

I want to note that, because there is the aforementioned difference between mountain and mountain, it will be appropriate, to avoid confusion, to distinguish one [type] from another by different terms; so I shall call the first Primary and the second Secondary.

If a man, holding a belief which he was taught in childhood or persuaded of afterwards, keeps down and pushes away any doubts which arise about it in his mind, purposely avoids the reading of books and the company of men that call in question or discuss it, and regards as impious those questions which cannot easily be asked without disturbing it—the life of that man is one long sin against mankind.

If a superior alien civilisation sent us a message saying, “We’ll arrive in a few decades,” would we just reply, “OK, call us when you get here—we’ll leave the lights on”? Probably not—but this is more or less what is happening with AI. Although we are facing potentially the best or worst thing to happen to humanity in history, little serious research is devoted to these issues outside non-profit institutes such as the Cambridge Centre for the Study of Existential Risk, the Future of Humanity Institute, the Machine Intelligence Research Institute, and the Future of Life Institute. All of us should ask ourselves what we can do now to improve the chances of reaping the benefits and avoiding the risks.

If one looks with a cold eye at the mess man has made of history, it is difficult to avoid the conclusion that he has been afflicted by some built-in mental disorder which drives him towards self-destruction.

If the matter is one that can be settled by observation, make the observation yourself. Aristotle could have avoided the mistake of thinking that women have fewer teeth than men, by the simple device of asking Mrs. Aristotle to keep her mouth open while he counted.

If we can possibly avoid wrecking this little planet of ours, we will, But—there must be risks! There must be. In experimental work there always are!

In a manner which matches the fortuity, if not the consequence, of Archimedes’ bath and Newton’s apple, the [3.6 million year old] fossil footprints were eventually noticed one evening in September 1976 by the paleontologist Andrew Hill, who fell while avoiding a ball of elephant dung hurled at him by the ecologist David Western.

In a sense, of course, probability theory in the form of the simple laws of chance is the key to the analysis of warfare;… My own experience of actual operational research work, has however, shown that its is generally possible to avoid using anything more sophisticated. … In fact the wise operational research worker attempts to concentrate his efforts in finding results which are so obvious as not to need elaborate statistical methods to demonstrate their truth. In this sense advanced probability theory is something one has to know about in order to avoid having to use it.

In both social and natural sciences, the body of positive knowledge grows by the failure of a tentative hypothesis to predict phenomena the hypothesis professes to explain; by the patching up of that hypothesis until someone suggests a new hypothesis that more elegantly or simply embodies the troublesome phenomena, and so on ad infinitum. In both, experiment is sometimes possible, sometimes not (witness meteorology). In both, no experiment is ever completely controlled, and experience often offers evidence that is the equivalent of controlled experiment. In both, there is no way to have a self-contained closed system or to avoid interaction between the observer and the observed. The Gödel theorem in mathematics, the Heisenberg uncertainty principle in physics, the self-fulfilling or self-defeating prophecy in the social sciences all exemplify these limitations.

In Euclid each proposition stands by itself; its connection with others is never indicated; the leading ideas contained in its proof are not stated; general principles do not exist. In modern methods, on the other hand, the greatest importance is attached to the leading thoughts which pervade the whole; and general principles, which bring whole groups of theorems under one aspect, are given rather than separate propositions. The whole tendency is toward generalization. A straight line is considered as given in its entirety, extending both ways to infinity, while Euclid is very careful never to admit anything but finite quantities. The treatment of the infinite is in fact another fundamental difference between the two methods. Euclid avoids it, in modern mathematics it is systematically introduced, for only thus is generality obtained.

In my opinion there is no other salvation for civilization and even for the human race than the creation of a world government with security on the basis of law. As long as there are sovereign states with their separate armaments and armament secrets, new world wars cannot be avoided.

In my own view, some advice about what should be known, about what technical education should be acquired, about the intense motivation needed to succeed, and about the carelessness and inclination toward bias that must be avoided is far more useful than all the rules and warnings of theoretical logic.

In October 1838, that is, fifteen months after I had begun my systematic enquiry, I happened to read for amusement Malthus on Population, and being well prepared to appreciate the struggle for existence which everywhere goes on from long-continued observation of the habits of animals and plants, it at once struck me that under these circumstances favourable variations would tend to be, preserved, and unfavourable ones to be destroyed. The result of this would be the formation of new species. Here, then, I had at last got a theory by which to work; but I was so anxious to avoid prejudice, that I determined not for some time to write even the briefest sketch of it.

In view of the kind of matter we work with, it will never be possible to avoid little laboratory explosions.

In working out physical problems there should be, in the first place, no pretence of rigorous formalism. The physics will guide the physicist along somehow to useful and important results, by the constant union of physical and geometrical or analytical ideas. The practice of eliminating the physics by reducing a problem to a purely mathematical exercise should be avoided as much as possible. The physics should be carried on right through, to give life and reality to the problem, and to obtain the great assistance which the physics gives to the mathematics.

It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.

It is almost a universal fact that the rattlesnake will do all that it reasonably can to avoid man. The rattler's first wish is to get away from anything as large and as potentially dangerous as man. If the snake strikes, it is because it is cornered or frightened for its own safety.

It is characteristic of our age to endeavour to replace virtues by technology. That is to say, wherever possible we strive to use methods of physical or social engineering to achieve goals which our ancestors thought attainable only by the training of character. Thus, we try so far as possible to make contraception take the place of chastity, and anaesthetics to take the place of fortitude; we replace resignation by insurance policies and munificence by the Welfare State. It would be idle romanticism to deny that such techniques and institutions are often less painful and more efficient methods of achieving the goods and preventing the evils which unaided virtue once sought to achieve and avoid. But it would be an equal and opposite folly to hope that the take-over of virtue by technology may one day be complete, so that the necessity for the laborious acquisition of the capacity for rational choice by individuals can be replaced by the painless application of the fruits of scientific discovery over the whole field of human intercourse and enterprise.

It is now quite lawful for a Catholic woman to avoid pregnancy by a resort to mathematics, though she is still forbidden to resort to physics and chemistry.

It is still true, even at the graduate level, that students study to avoid the consequences of not studying.

It is this mythical, or rather this symbolic, content of the religious traditions which is likely to come into conflict with science. This occurs whenever this religious stock of ideas contains dogmatically fixed statements on subjects which be long in the domain of science. Thus, it is of vital importance for the preservation of true religion that such conflicts be avoided when they arise from subjects which, in fact, are not really essential for the pursuance of the religious aims.

Let the sun never set or rise on a small bowel obstruction.
Adage expressing urgency for early operation to avoid possible fatality.

Like taxes, radioactivity has long been with us and in increasing amounts; it is not to be hated and feared, but accepted and controlled. Radiation is dangerous, let there be no mistake about that—but the modern world abounds in dangerous substances and situations too numerous to mention. ... Consider radiation as something to be treated with respect, avoided when practicable, and accepted when inevitable.
Recommending the same view towards radiation as the risks of automobile travel.

Logic has borrowed the rules of geometry without understanding its power. … I am far from placing logicians by the side of geometers who teach the true way to guide the reason. … The method of avoiding error is sought by every one. The logicians profess to lead the way, the geometers alone reach it, and aside from their science there is no true demonstration.

Magnetic lines of force convey a far better and purer idea than the phrase magnetic current or magnetic flood: it avoids the assumption of a current or of two currents and also of fluids or a fluid, yet conveys a full and useful pictorial idea to the mind.

Many will, no doubt, prefer to retain old unsystematic names as far as possible, but it is easy to see that the desire to avoid change may carry us too far in this direction; it will undoubtedly be very inconvenient to the present generation of chemists to abandon familiar and cherished names, but nevertheless it may be a wise course to boldly face the difficulty, rather than inflict on coming generations a partially illogical and unsystematic nomenclature.

Marriages are not normally made to avoid having children.

Mathematics, among all school subjects, is especially adapted to further clearness, definite brevity and precision in expression, although it offers no exercise in flights of rhetoric. This is due in the first place to the logical rigour with which it develops thought, avoiding every departure from the shortest, most direct way, never allowing empty phrases to enter. Other subjects excel in the development of expression in other respects: translation from foreign languages into the mother tongue gives exercise in finding the proper word for the given foreign word and gives knowledge of laws of syntax, the study of poetry and prose furnish fit patterns for connected presentation and elegant form of expression, composition is to exercise the pupil in a like presentation of his own or borrowed thoughtsand their development, the natural sciences teach description of natural objects, apparatus and processes, as well as the statement of laws on the grounds of immediate sense-perception. But all these aids for exercise in the use of the mother tongue, each in its way valuable and indispensable, do not guarantee, in the same manner as mathematical training, the exclusion of words whose concepts, if not entirely wanting, are not sufficiently clear. They do not furnish in the same measure that which the mathematician demands particularly as regards precision of expression.

Modern philosophers, to avoid circumlocutions, call that instrument, wherein a cylinder of quicksilver, of between 28 to 32 inches in altitude, is kept suspended after the manner of the Torricellian experiment, a barometer or baroscope.

Moving parts in rubbing contact require lubrication to avoid excessive wear. Honorifics and formal politeness provide lubrication where people rub together.

Natural historians tend to avoid tendentious preaching in this philosophical mode (although I often fall victim to such temptations in these essays). Our favored style of doubting is empirical: if I wish to question your proposed generality, I will search for a counterexample in flesh and blood. Such counterexamples exist in abundance, for the form a staple in a standard genre of writing in natural history–the “wonderment of oddity” or “strange ways of the beaver” tradition.

Nature has provided two great gifts: life and then the diversity of living things, jellyfish and humans, worms and crocodiles. I don’t undervalue the investigation of commonalities but can’t avoid the conclusion that diversity has been relatively neglected, especially as concerns the brain.

No woman wants an abortion. Either she wants a child or she wishes to avoid pregnancy.

Noitaton Hsilop esrever diova!

One of the endearing things about mathematicians is the extent to which they will go to avoid doing any real work.

One should avoid carrying out an experiment requiring more than 10 per cent accuracy.

People are entirely too disbelieving of coincidence. They are far too ready to dismiss it and to build arcane structures of extremely rickety substance in order to avoid it. I, on the other hand, see coincidence everywhere as an inevitable consequence of the laws of probability, according to which having no unusual coincidence is far more unusual than any coincidence could possibly be.

People will do anything, no matter how absurd, in order to avoid facing their own soul.

Psychologists … have found that people making an argument or a supposedly factual claim can manipulate us by the words they choose and the way they present their case. We can’t avoid letting language do our thinking for us, but we can become more aware of how and when language is steering us toward a conclusion that, upon reflection, we might choose to reject.

Reality may avoid the obligation to be interesting, but ... hypotheses may not.

Round about what is, lies a whole mysterious world of might be, — a psychological romance of possibilities and things that do not happen. By going out a few minutes sooner or later, by stopping to speak with a friend at a corner, by meeting this man or that, or by turning down this street instead of the other, we may let slip some great occasion good, or avoid some impending evil, by which the whole current of our lives would have been changed. There is no possible solution to the dark enigma but the one word, “Providence.”

Science is not about building a body of known “facts”. It is a method for asking awkward questions and subjecting them to a reality-check, thus avoiding the human tendency to believe whatever makes us feel good.

Science is not the enemy of humanity but one of the deepest expressions of the human desire to realize that vision of infinite knowledge. Science shows us that the visible world is neither matter nor spirit; the visible world is the invisible organization of energy.

Since the examination of consistency is a task that cannot be avoided, it appears necessary to axiomatize logic itself and to prove that number theory and set theory are only parts of logic. This method was prepared long ago (not least by Frege’s profound investigations); it has been most successfully explained by the acute mathematician and logician Russell. One could regard the completion of this magnificent Russellian enterprise of the axiomatization of logic as the crowning achievement of the work of axiomatization as a whole.

Taxonomy (the science of classification) is often undervalued as a glorified form of filing—with each species in its folder, like a stamp in its prescribed place in an album; but taxonomy is a fundamental and dynamic science, dedicated to exploring the causes of relationships and similarities among organisms. Classifications are theories about the basis of natural order, not dull catalogues compiled only to avoid chaos.

The arithmetization of mathematics … which began with Weierstrass … had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics. These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought. But how can we avoid the use of human language? The … symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.

The aim of poetry is to give a high and voluptuous plausibility to what is palpably not true. I offer the Twenty-third Psalm as an example: ‘The Lord is my shepherd: I shall not want.’ It is immensely esteemed by the inmates of almshouses, and by gentlemen waiting to be hanged. I have to limit my own reading of it, avoiding soft and yielding moods, for I too, in my way, am a gentleman waiting to be hanged, as you are.

The canyon country does not always inspire love. To many it appears barren, hostile, repellent—a fearsome, mostly waterless land of rock and heat, sand dunes and quicksand. cactus, thornbush, scorpion, rattlesnake, and agoraphobic distances. To those who see our land in that manner, the best reply is, yes, you are right, it is a dangerous and terrible place. Enter at your own risk. Carry water. Avoid the noon-day sun. Try to ignore the vultures. Pray frequently.

The competent programmer is fully aware of the limited size of his own skull. He therefore approaches his task with full humility, and avoids clever tricks like the plague.

The contributions of physiological knowledge to an understanding of distribution are necessarily inferential. Distribution is a historical phenomenon, and the data ordinarily obtained by students of physiology are essentially instantaneous. However, every organism has a line of ancestors which extends back to the beginning of life on earth and which, during this immensity of time, has invariably been able to avoid, to adapt to, or to compensate for environmental changes.

The difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, “But how can it be like that?” which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. … If you will simply admit that maybe [Nature] does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possible avoid it, "But how can it be like that?" because you will get 'down the drain', into a blind alley from which nobody has escaped. Nobody knows how it can be like that.
[About wave-particle duality.]

The employment of mathematical symbols is perfectly natural when the relations between magnitudes are under discussion; and even if they are not rigorously necessary, it would hardly be reasonable to reject them, because they are not equally familiar to all readers and because they have sometimes been wrongly used, if they are able to facilitate the exposition of problems, to render it more concise, to open the way to more extended developments, and to avoid the digressions of vague argumentation.

The errors of definitions multiply themselves according as the reckoning proceeds; and lead men into absurdities, which at last they see but cannot avoid, without reckoning anew from the beginning.

The fact that the regions of nature actually covered by known laws are few and fragmentary is concealed by the natural tendency to crowd our experience into those particular regions and to leave the others to themselves. We seek out those parts that are known and familiar and avoid those that are unknown and unfamiliar. This is simply what is called 'Applied Science.'

The footsteps of Nature are to be trac'd, not only in her ordinary course, but when she seems to be put to her shifts, to make many doublings and turnings, and to use some kind of art in endeavouring to avoid our discovery.

The kinetic concept of motion in classical theory will have to undergo profound modifications. (That is why I also avoided the term “orbit” in my paper throughout.) … We must not bind the atoms in the chains of our prejudices—to which, in my opinion, also belongs the assumption that electron orbits exist in the sense of ordinary mechanics—but we must, on the contrary, adapt our concepts to experience.

The moment one has offered an original explanation for a phenomenon which seems satisfactory, that moment affection for his intellectual child springs into existence, and as the explanation grows into a definite theory his parental affections cluster about his offspring and it grows more and more dear to him. ... There springs up also unwittingly a pressing of the theory to make it fit the facts and a pressing of the facts to make them fit the theory... To avoid this grave danger, the method of multiple working hypotheses is urged. It differs from the simple working hypothesis in that it distributes the effort and divides the affections... In developing the multiple hypotheses, the effort is to bring up into view every rational exploration of the phenomenon in hand and to develop every tenable hypothesis relative to its nature, cause or origin, and to give to all of these as impartially as possible a working form and a due place in the investigation. The investigator thus becomes the parent of a family of hypotheses; and by his parental relations to all is morally forbidden to fasten his affections unduly upon anyone. ... Each hypothesis suggests its own criteria, its own method of proof, its own method of developing the truth, and if a group of hypotheses encompass the subject on all sides, the total outcome of means and of methods is full and rich.

The most remarkable feature about the magnitude scale was that it worked at all and that it could be extended on a worldwide basis. It was originally envisaged as a rather rough-and-ready procedure by which we could grade earthquakes. We would have been happy if we could have assigned just three categories, large, medium, and small; the point is, we wanted to avoid personal judgments. It actually turned out to be quite a finely tuned scale.

The most startling result of Faraday’s Law is perhaps this. If we accept the hypothesis that the elementary substances are composed of atoms, we cannot avoid concluding that electricity also, positive as well as negative, is divided into definite elementary portions, which behave like atoms of electricity.

The preservation of a few samples of undeveloped territory is one of the most clamant issues before us today. Just a few more years of hesitation and the only trace of that wilderness which has exerted such a fundamental influence in molding American character will lie in the musty pages of pioneer books. … To avoid this catastrophe demands immediate action.

The results of science are never quite true. By a healthy independence of thought perhaps we sometimes avoid adding other people’s errors to our own.

The routine produces. But each day, nevertheless, when you try to get started you have to transmogrify, transpose yourself; you have to go through some kind of change from being a normal human being, into becoming some kind of slave.
I simply don’t want to break through that membrane. I’d do anything to avoid it. You have to get there and you don’t want to go there because there’s so much pressure and so much strain and you just want to stay on the outside and be yourself. And so the day is a constant struggle to get going.
And if somebody says to me, You’re a prolific writer—it seems so odd. It’s like the difference between geological time and human time. On a certain scale, it does look like I do a lot. But that’s my day, all day long, sitting there wondering when I’m going to be able to get started. And the routine of doing this six days a week puts a little drop in a bucket each day, and that’s the key. Because if you put a drop in a bucket every day, after three hundred and sixty-five days, the bucket’s going to have some water in it.

The statistician cannot excuse himself from the duty of getting his head clear on the principles of scientific inference, but equally no other thinking man can avoid a like obligation.

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.

The wise man, however, will avoid partial views of things. He will not, with the miser, look to gold and silver as the only blessings of life; nor will he, with the cynic, snarl at mankind for preferring them to copper and iron. … That which is convenient is that which is useful, and that which is useful is that which is valuable.

There is no expedient to which a man will not resort to avoid the real labor of thinking.[Greatly abbreviated and paraphrased.]

There must be no barriers to freedom of inquiry. There is no place for dogma in science. The scientist is free, and must be free to ask any question, to doubt any assertion, to seek for any evidence, to correct any errors. ... Our political life is also predicated on openness. We know that the only way to avoid error is to detect it and that the only way to detect it is to be free to inquire. And we know that as long as men are free to ask what they must, free to say what they think, free to think what they will, freedom can never be lost, and science can never regress.

This [disaster] is a day we have managed to avoid for a quarter of a century. We’ve talked about it before and speculated about it, and it finally has occurred. We hoped we could push this day back forever.

Those afraid of the universe as it really is, those who pretend to nonexistent knowledge and envision a Cosmos centered on human beings will prefer the fleeting comforts of superstition. They avoid rather than confront the world. But those with the courage to explore the weave and structure of the Cosmos, even where it differs profoundly from their wishes and prejudices, will penetrate its deepest mysteries.

Thought-economy is most highly developed in mathematics, that science which has reached the highest formal development, and on which natural science so frequently calls for assistance. Strange as it may seem, the strength of mathematics lies in the avoidance of all unnecessary thoughts, in the utmost economy of thought-operations. The symbols of order, which we call numbers, form already a system of wonderful simplicity and economy. When in the multiplication of a number with several digits we employ the multiplication table and thus make use of previously accomplished results rather than to repeat them each time, when by the use of tables of logarithms we avoid new numerical calculations by replacing them by others long since performed, when we employ determinants instead of carrying through from the beginning the solution of a system of equations, when we decompose new integral expressions into others that are familiar,—we see in all this but a faint reflection of the intellectual activity of a Lagrange or Cauchy, who with the keen discernment of a military commander marshalls a whole troop of completed operations in the execution of a new one.

To take one of the simplest cases of the dissipation of energy, the conduction of heat through a solid—consider a bar of metal warmer at one end than the other and left to itself. To avoid all needless complication, of taking loss or gain of heat into account, imagine the bar to be varnished with a substance impermeable to heat. For the sake of definiteness, imagine the bar to be first given with one half of it at one uniform temperature, and the other half of it at another uniform temperature. Instantly a diffusing of heat commences, and the distribution of temperature becomes continuously less and less unequal, tending to perfect uniformity, but never in any finite time attaining perfectly to this ultimate condition. This process of diffusion could be perfectly prevented by an army of Maxwell’s ‘intelligent demons’* stationed at the surface, or interface as we may call it with Prof. James Thomson, separating the hot from the cold part of the bar.
* The definition of a ‘demon’, according to the use of this word by Maxwell, is an intelligent being endowed with free will, and fine enough tactile and perceptive organisation to give him the faculty of observing and influencing individual molecules of matter.

To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.

To use: Apply shampoo to wet hair. Massage to lather, then rinse. Repeat.
A typical hair-washing algorithm that fails to halt—in the way that computer programmers must avoid an infinite loop.

We are many small puppets moved by fate and fortune through strings unseen by us; therefore, if it is so as I think, one has to prepare oneself with a good heart and indifference to accept things coming towards us, because they cannot be avoided, and to oppose them requires a violence that tears our souls too deeply, and it seems that both fortune and men are always busy in affairs for our dislike because the former is blind and the latter only think of their interest.

We avoid the gravest difficulties when, giving up the attempt to frame hypotheses concerning the constitution of matter, we pursue statistical inquiries as a branch of rational mechanics.

We can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.

We may, I think, draw a yet higher and deeper teaching from the phenomena of degeneration. We seem to learn from it the absolute necessity of labour and effort, of struggle and difficulty, of discomfort and pain, as the condition of all progress, whether physical or mental, and that the lower the organism the more need there is of these ever-present stimuli, not only to effect progress, but to avoid retrogression. And if so, does not this afford us the nearest attainable solution of the great problem of the origin of evil? What we call evil is the essential condition of progress in the lower stages of the development of conscious organisms, and will only cease when the mind has become so thoroughly healthy, so well balanced, and so highly organised, that the happiness derived from mental activity, moral harmony, and the social affections, will itself be a sufficient stimulus to higher progress and to the attainment of a more perfect life.