Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghost-like character of the real variable.

Any ignorance is blank ignorance, because knowledge of any factor requires no ignorance.

Attaching significance to invariants is an effort to recognize what, because of its form or colour or meaning or otherwise, is important or significant in what is only trivial or ephemeral. A simple instance of failing in this is provided by the poll-man at Cambridge, who learned perfectly how to factorize a²-b² but was floored because the examiner unkindly asked for the factors of p²–q².

Both social and biosocial factors are necessary to interpret crosscultural studies, with the general proviso that one’s research interest determines which elements, in what combinations, are significant for the provision of understanding.

Characteristically skeptical of the idea that living things would faithfully follow mathematical formulas, [Robert Harper] seized upon factors in corn which seemed to blend in the hybrid—rather than be represented by plus or minus signs, and put several seasons into throwing doubt upon the concept of immutable hypothetical units of inheritance concocted to account for selected results.

Complex organisms cannot be construed as the sum of their genes, nor do genes alone build particular items of anatomy or behavior by them selves. Most genes influence several aspects of anatomy and behavior–as they operate through complex interactions with other genes and their products, and with environmental factors both within and outside the developing organism. We fall into a deep error, not just a harmful oversimplification, when we speak of genes ‘for’ particular items of anatomy or behavior.

Engineering is more closely akin to the arts than perhaps any other of the professions; first, because it requires the maximum of natural aptitude and of liking for the work in order to offset other factors; second, because it demands, like the arts, an almost selfless consecration to the job; and, third, because out of the hundreds who faithfully devote themselves to the task, only a few are destined to receive any significant reward—in either money or fame.

Eventually, it becomes hard to take the selections seriously, because we have no idea what factors are taken into consideration, except that somehow, it ends with only white and Asian men receiving the [Nobel] prize.

Excessive and prolonged use of tobacco, especially cigarettes, seems to be an important factor in the induction of bronchiogenic carcinoma. Among 605 men with bronchiogenic carcinoma, other than adenocarcinoma, 96.5 per cent were moderately heavy to chain smokers for many years, compared with 73.7 per cent among the general male hospital population without cancer. Among the cancer group 51.2 per cent were excessive or chain smokers compared to 19.1 per cent in the general hospital group without cancer.
[Co-author with Evarts Ambrose Graham]

Gravity is a contributing factor in nearly 73 percent of all accidents involving falling objects.

I believe in intuition and inspiration. Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution. It is, strictly speaking, a real factor in scientific research.

I have attempted to form a judgment as to the conditions for evolution based on the statistical consequences of Mendelian heredity. The most general conclusion is that evolution depends on a certain balance among its factors. There must be a gene mutation, but an excessive rate gives an array of freaks, not evolution; there must be selection, but too severe a process destroys the field of variability, and thus the basis for further advance; prevalence of local inbreeding within a species has extremely important evolutionary consequences, but too close inbreeding leads merely to extinction. A certain amount of crossbreeding is favorable but not too much. In this dependence on balance the species is like a living organism. At all levels of organization life depends on the maintenance of a certain balance among its factors.

I like to look at mathematics almost more as an art than as a science; for the activity of the mathematician, constantly creating as he is, guided though not controlled by the external world of the senses, bears a resemblance, not fanciful I believe but real, to the activity of an artist, of a painter let us say. Rigorous deductive reasoning on the part of the mathematician may be likened here to technical skill in drawing on the part of the painter. Just as no one can become a good painter without a certain amount of skill, so no one can become a mathematician without the power to reason accurately up to a certain point. Yet these qualities, fundamental though they are, do not make a painter or mathematician worthy of the name, nor indeed are they the most important factors in the case. Other qualities of a far more subtle sort, chief among which in both cases is imagination, go to the making of a good artist or good mathematician.

Iamblichus in his treatise On the Arithmetic of Nicomachus observes p. 47- “that certain numbers were called amicable by those who assimilated the virtues and elegant habits to numbers.” He adds, “that 284 and 220 are numbers of this kind; for the parts of each are generative of each other according to the nature of friendship, as was shown by Pythagoras. For some one asking him what a friend was, he answered, another I (ετεϑος εγω) which is demonstrated to take place in these numbers.” [“Friendly” thus: Each number is equal to the sum of the factors of the other.]

Ideas are the factors that lift civilization. They create revolutions. There is more dynamite in an idea than in many bombs.

If we assume that there is only one enzyme present to act as an oxidizing agent, we must assume for it as many different degrees of activity as are required to explain the occurrence of the various colors known to mendelize (three in mice, yellow, brown, and black). If we assume that a different enzyme or group of enzymes is responsible for the production of each pigment we must suppose that in mice at least three such enzymes or groups of enzymes exist. To determine which of these conditions occurs in mice is not a problem for the biologist, but for the chemist. The biologist must confine his attention to determining the number of distinct agencies at work in pigment formation irrespective of their chemical nature. These agencies, because of their physiological behavior, the biologist chooses to call 'factors,' and attempts to learn what he can about their functions in the evolution of color varieties.

If we factor in high-powered women in Europe as well, such as [German Chancellor] Angela Merkel, it seems we are witnessing a seismic shift for women to accede to high-level positions in politics and society. But there may still be a gap between those women achieving high public status and those in the private sector. I welcome these signs of women’s liberation.

Imagination and even sentiment play an important part in chemistry, and that if too narrowly and rigidly interpreted, facts may become very misleading factors.

In an enterprise such as the building of the atomic bomb the difference between ideas, hopes, suggestions and theoretical calculations, and solid numbers based on measurement, is paramount. All the committees, the politicking and the plans would have come to naught if a few unpredictable nuclear cross sections had been different from what they are by a factor of two.

In despair, I offer your readers their choice of the following definitions of entropy. My authorities are such books and journals as I have by me at the moment.
(a) Entropy is that portion of the intrinsic energy of a system which cannot be converted into work by even a perfect heat engine.—Clausius.
(b) Entropy is that portion of the intrinsic energy which can be converted into work by a perfect engine.—Maxwell, following Tait.
(c) Entropy is that portion of the intrinsic energy which is not converted into work by our imperfect engines.—Swinburne.
(d) Entropy (in a volume of gas) is that which remains constant when heat neither enters nor leaves the gas.—W. Robinson.
(e) Entropy may be called the ‘thermal weight’, temperature being called the ‘thermal height.’—Ibid.
(f) Entropy is one of the factors of heat, temperature being the other.—Engineering.
I set up these bald statement as so many Aunt Sallys, for any one to shy at.
[Lamenting a list of confused interpretations of the meaning of entropy, being hotly debated in journals at the time.]

In the modern interpretation of Mendelism, facts are being transformed into factors at a rapid rate. If one factor will not explain the facts, then two are involved; if two prove insufficient, three will sometimes work out. The superior jugglery sometimes necessary to account for the results may blind us, if taken too naively, to the common-place that the results are often so excellently 'explained' because the explanation was invented to explain them. We work backwards from the facts to the factors, and then, presto! explain the facts by the very factors that we invented to account for them. I am not unappreciative of the distinct advantages that this method has in handling the facts. I realize how valuable it has been to us to be able to marshal our results under a few simple assumptions, yet I cannot but fear that we are rapidly developing a sort of Mendelian ritual by which to explain the extraordinary facts of alternative inheritance. So long as we do not lose sight of the purely arbitrary and formal nature of our formulae, little harm will be done; and it is only fair to state that those who are doing the actual work of progress along Mendelian lines are aware of the hypothetical nature of the factor-assumption.

In the secondary schools mathematics should be a part of general culture and not contributory to technical training of any kind; it should cultivate space intuition, logical thinking, the power to rephrase in clear language thoughts recognized as correct, and ethical and esthetic effects; so treated, mathematics is a quite indispensable factor of general education in so far as the latter shows its traces in the comprehension of the development of civilization and the ability to participate in the further tasks of civilization.

It is certainly true that all physical phenomena are subject to strictly mathematical conditions, and mathematical processes are unassailable in themselves. The trouble arises from the data employed. Most phenomena are so highly complex that one can never be quite sure that he is dealing with all the factors until the experiment proves it. So that experiment is rather the criterion of mathematical conclusions and must lead the way.

It is clear that in maize, seemingly blending is really segregating inheritance, but with entire absence of dominance, and it seems probably that the same will be found to be true among rabbits and other mammals; failure to observe it hitherto is probably due to the fact that the factors concerned are numerous. For the greater the number of factors concerned, the more nearly will the result obtained approximate a complete and permanent blend. As the number of factors approaches infinity, the result will become identical with a permanent blend.

It is imperative in the design process to have a full and complete understanding of how failure is being obviated in order to achieve success. Without fully appreciating how close to failing a new design is, its own designer may not fully understand how and why a design works. A new design may prove to be successful because it has a sufficiently large factor of safety (which, of course, has often rightly been called a “factor of ignorance”), but a design's true factor of safety can never be known if the ultimate failure mode is unknown. Thus the design that succeeds (ie, does not fail) can actually provide less reliable information about how or how not to extrapolate from that design than one that fails. It is this observation that has long motivated reflective designers to study failures even more assiduously than successes.

It would seem that more than function itself, simplicity is the deciding factor in the aesthetic equation. One might call the process beauty through function and simplification.

No self is of itself alone. It has a long chain of intellectual ancestors. The ‘I’ is chained to ancestry by many factors ... This is not mere allegory, but an eternal memory.

On 17th July there came to us at Potsdam the eagerly-awaited news of the trial of the atomic bomb in the [New] Mexican desert. Success beyond all dreams crowded this sombre, magnificent venture of our American allies. The detailed reports ... could leave no doubt in the minds of the very few who were informed, that we were in the presence of a new factor in human affairs, and possessed of powers which were irresistible.

One of the greatest experimental scientists of the time who was really doing something, William Harvey, said that what Bacon said science was, was the science that a lord-chancellor would do. He [Bacon] spoke of making observations, but omitted the vital factor of judgment about what to observe and what to pay attention to.

Our belief is not a belief. Our principles are not a faith. We do not rely solely upon science and reason, because these are necessary rather than sufficient factors, but we distrust anything that contradicts science or outrages reason.

Prolonged commitment to mathematical exercises in economics can be damaging. It leads to the atrophy of judgement and intuition which are indispensable for real solutions and, on occasion, leads also to a habit of mind which simply excludes the mathematically inconvenient factors from consideration.

Q: Which place has special childhood memories for you?
A: Charnwood Forest, Leicestershire.

Q: In which place do you feel most “at home”?
A: Richmond, Surrey, where I live near Richmond Hill.

Q: In which place have you felt ill at ease or uncomfortable?
A: The Democratic Republic of the Congo.
Q: Which place that you have visited has for you a “tingle factor?”
A: New Guinea.

Q: Which place that you have visited has given you most hope about the future?
A: A primary school.

Q: Which place would you like to revisit?
A: Tuscany.

Scientists are going to discover many subtle genetic factors in the makeup of human beings. Those discoveries will challenge the basic concepts of equality on which our society is based. Once we can say that there are differences between people that are easily demonstrable at the genetic level, then society will have to come to grips with understanding diversity—and we are not prepared for that.

The function of ignoring, of inattention, is as vital a factor in mental progress as the function of attention itself.

The most powerful factors in the world are clear ideas in the minds of energetic men of good will.

The National Science Foundation asked the great “breakthrough” scientists what they felt to be the most dominantly favorable factor in their educational experience. The answer was almost uniformly, “Intimate association with a great, inspiring teacher.”

The prevention of disease today is one of the most important factors in line of human endeavor.

The really valuable factor is intuition!

The social sciences mathematically developed are to be the controlling factors in civilization.

The term ‘community’ implies a diversity but at the same time a certain organized uniformity in the units. The units are the many individual plants that occur in every community, whether this be a beech-forest, a meadow, or a heath. Uniformity is established when certain atmospheric, terrestrial, and any of the other factors discussed in Section I are co-operating, and appears either because a certain, defined economy makes its impress on the community as a whole, or because a number of different growth-forms are combined to form a single aggregate which has a definite and constant guise.

The theory of evolution has often been perverted so as to indicate that what is merely animal and brutal must gain the ascendancy. The contrary seems to me to be the case, for in man it is the spirit, and not the body, which is the deciding factor.

We all know, from what we experience with and within ourselves, that our conscious acts spring from our desires and our fears. Intuition tells us that that is true also of our fellows and of the higher animals. We all try to escape pain and death, while we seek what is pleasant. We are all ruled in what we do by impulses; and these impulses are so organized that our actions in general serve for our self preservation and that of the race. Hunger, love, pain, fear are some of those inner forces which rule the individual’s instinct for self preservation. At the same time, as social beings, we are moved in the relations with our fellow beings by such feelings as sympathy, pride, hate, need for power, pity, and so on. All these primary impulses, not easily described in words, are the springs of man’s actions. All such action would cease if those powerful elemental forces were to cease stirring within us. Though our conduct seems so very different from that of the higher animals, the primary instincts are much alike in them and in us. The most evident difference springs from the important part which is played in man by a relatively strong power of imagination and by the capacity to think, aided as it is by language and other symbolical devices. Thought is the organizing factor in man, intersected between the causal primary instincts and the resulting actions. In that way imagination and intelligence enter into our existence in the part of servants of the primary instincts. But their intervention makes our acts to serve ever less merely the immediate claims of our instincts.

We do not draw conclusions with our eyes, but with our reasoning powers, and if the whole of the rest of living nature proclaims with one accord from all sides the evolution of the world of organisms, we cannot assume that the process stopped short of Man. But it follows also that the factors which brought about the development of Man from his Simian ancestry must be the same as those which have brought about the whole of evolution.

We have usually no knowledge that any one factor will exert its effects independently of all others that can be varied, or that its effects are particularly simply related to variations in these other factors.

When the number of factors coming into play in a phenomenological complex is too large, scientific method in most cases fails us. One need only think of the weather, in which case prediction even for a few days ahead is impossible. Nevertheless no one doubts that we are confronted with a causal connection whose causal components are in the main known to us.

While there is still much to learn and discover through space exploration, we also need to pay attention to our unexplored world here on earth. Our next big leap into the unknown can be every bit as exciting and bold as our pioneering work in space. It possesses the same “wow” factor: alien worlds, dazzling technological feats and the mystery of the unknown.

You cannot become a nuclear physicist capable of real work in the field merely by studying alone in a library, any more than you can become a Jesuit without a certain number of years spent in company with Jesuit scholars. This, and the fact that scientists are among the most international-minded of men, may well be the most important factor in our survival.