… the definition of irrational numbers, on which geometric representations have often had a confusing influence. … I take in my definition a purely formal point of view, calling some given symbols numbers, so that the existence of these numbers is beyond doubt.

[Allowing embryonic stem cell research] … is also likely to lead to human cloning and the harvesting of body parts from babies conceived for this purpose.
An example of extreme prolife religious conservative opposition confusing public opinion.

All of modern physics is governed by that magnificent and thoroughly confusing discipline called quantum mechanics ... It has survived all tests and there is no reason to believe that there is any flaw in it.... We all know how to use it and how to apply it to problems; and so we have learned to live with the fact that nobody can understand it.

Among our sensations it is difficult not to confuse what comes from the part of objects with what comes from the part of our senses. … Supposing this, one clearly sees that it is not easy to say much about colors,… and that all one can expect in such a difficult subject is to give some general rules and to derive from them consequences that can be of some use in the arts and satisfy somewhat the natural desire we have to render account of everything that appears to us.

And now, as a germination of planetary dimensions, comes the thinking layer which over its full extent develops and intertwines its fibres, not to confuse and neutralise them but to reinforce them in the living unity of a single tissue.

And ye who wish to represent by words the form of man and all the aspects of his membrification, get away from that idea. For the more minutely you describe, the more you will confuse the mind of the reader and the more you will prevent him from a knowledge of the thing described. And so it is necessary to draw and describe.

Ants are so much like human beings as to be an embarrassment. They farm fungi, raise aphids as livestock, launch armies into wars, use chemical sprays to alarm and confuse enemies, capture slaves…. They exchange information ceaselessly. They do everything but watch television.

As a nation, we are too young to have true mythic heroes, and we must press real human beings into service. Honest Abe Lincoln the legend is quite a different character from Abraham Lincoln the man. And so should they be. And so should both be treasured, as long as they are distinguished. In a complex and confusing world, the perfect clarity of sports provides a focus for legitimate, utterly unambiguous support or disdain. The Dodgers are evil, the Yankees good. They really are, and have been for as long as anyone in my family can remember.

Mathematicians always strive to confuse their audiences; where there is no confusion, there is no prestige.

Never confuse a fool’s gold opportunity with a silver bullet solution.

Objections … inspired Kronecker and others to attack Weierstrass’ “sequential” definition of irrationals. Nevertheless, right or wrong, Weierstrass and his school made the theory work. The most useful results they obtained have not yet been questioned, at least on the ground of their great utility in mathematical analysis and its implications, by any competent judge in his right mind. This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven, that perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth—whatever that may be, if anything—precisely as in the Weierstrassian theory of convergent sequences of rationals defining irrationals.

Our Professor, which doth have tenure,
Feared be thy name.
Thy sets partition,
Thy maps commute,
In groups as in vector spaces.
Give us this day our daily notation,
And forgive us our obtuseness,
As we forgive tutors who cannot help us.
Lead us not into Lye rings,
But deliver us from eigenvalues,
For thine is the logic, the notation, and the accent,
That confuses us forever.
Amen.

Perhaps randomness is not merely an adequate description for complex causes that we cannot specify. Perhaps the world really works this way, and many events are uncaused in any conventional sense of the word. Perhaps our gut feeling that it cannot be so reflects only our hopes and prejudices, our desperate striving to make sense of a complex and confusing world, and not the ways of nature.

Science can be thought of as a large pool of knowledge, fed by a steady flow from the tap of basic research. Every now and then the water is dipped out and put to use, but one never knows which part of the water will be needed. This confuses the funding situation for basic science, because usually no specific piece of scientific work can be justified in advance; one cannot know which is going to be decisive. Yet history shows that keeping water flowing into the pool is a very worthwhile enterprise.

Scientists are entitled to be proud of their accomplishments, and what accomplishments can they call ‘theirs’ except the things they have done or thought of first? People who criticize scientists for wanting to enjoy the satisfaction of intellectual ownership are confusing possessiveness with pride of possession. Meanness, secretiveness and, sharp practice are as much despised by scientists as by other decent people in the world of ordinary everyday affairs; nor, in my experience, is generosity less common among them, or less highly esteemed.

Taking … the mathematical faculty, probably fewer than one in a hundred really possess it, the great bulk of the population having no natural ability for the study, or feeling the slightest interest in it*. And if we attempt to measure the amount of variation in the faculty itself between a first-class mathematician and the ordinary run of people who find any kind of calculation confusing and altogether devoid of interest, it is probable that the former could not be estimated at less than a hundred times the latter, and perhaps a thousand times would more nearly measure the difference between them.
[* This is the estimate furnished me by two mathematical masters in one of our great public schools of the proportion of boys who have any special taste or capacity for mathematical studies. Many more, of course, can be drilled into a fair knowledge of elementary mathematics, but only this small proportion possess the natural faculty which renders it possible for them ever to rank high as mathematicians, to take any pleasure in it, or to do any original mathematical work.]

Technology, while adding daily to our physical ease, throws daily another loop of fine wire around our souls. It contributes hugely to our mobility, which we must not confuse with freedom. The extensions of our senses, which we find so fascinating, are no

That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.

There are then two kinds of intellect: the one able to penetrate acutely and deeply into the conclusions of given premises, and this is the precise intellect; the other able to comprehend a great number of premises without confusing them, and this is the mathematical intellect. The one has force and exactness, the other comprehension. Now the one quality can exist without the other; the intellect can be strong and narrow, and can also be comprehensive and weak.

There is no art so difficult as the art of observation: it requires a skillful, sober spirit and a well-trained experience, which can only be acquired by practice; for he is not an observer who only sees the thing before him with his eyes, but he who sees of what parts the thing consists, and in what connexion the parts stand to the whole. One person overlooks half from inattention; another relates more than he sees while he confounds it with that which he figures to himself; another sees the parts of the whole, but he throws things together that ought to be separated. ... When the observer has ascertained the foundation of a phenomenon, and he is able to associate its conditions, he then proves while he endeavours to produce the phenomena at his will, the correctness of his observations by experiment. To make a series of experiments is often to decompose an opinion into its individual parts, and to prove it by a sensible phenomenon. The naturalist makes experiments in order to exhibit a phenomenon in all its different parts. When he is able to show of a series of phenomena, that they are all operations of the same cause, he arrives at a simple expression of their significance, which, in this case, is called a Law of Nature. We speak of a simple property as a Law of Nature when it serves for the explanation of one or more natural phenomena.

Those who think that science is ethically neutral confuse the findings of science, which are, with the activity of science, which are not.

Today, when so much depends on our informed action, we as voters and taxpayers can no longer afford to confuse science and technology, to confound “pure” science and “applied” science.