Measure Theory Quotes & Sayings

Though it is folly to suppose that happiness is a matter of volition, and that we can make ourselves content and cheerful whenever we choose a theory that many poor hypochondriacs are taunted with till they are nigh driven mad yet, on the other hand, no sane mind is ever left without the power of self-discipline and self-control in a measure, which measure increases in proportion as it is exercised. — Dinah Maria Murlock Craik

There is so much garbage being said about the mark of the beast. A lot of it is based on what I call the 'sky bus' rapture theory, and is not about the Kingdom. It is a kingdom of fear because it is not about the returning power of the sons of God. You do not find anyone who teaches the rapture theory talking about the resurrection in the life of every believer, or of the glory of the Son of God. I do not find the manifestation of the Kingdom in their lives: the power to raise the dead today and for us to live forever in that glory. I do not hear them talking about the coming glory. When darkness rises, the glory must come in a greater measure (Isaiah 60:1-2). I do not see them talking about the coming glory, all the rapture theory does is create a generation of fearful people - a people who will not sow into the future with their words to make their children believe that there is a hope for them to live for today. — Ian Clayton

At a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate. — Terence Tao

In an information economy, entrepreneurs master the science of information in order to overcome the laws of the purely physical sciences. They can succeed because of the surprising power of the laws of information, which are conducive to human creativity. The central concept of information theory is a measure of freedom of choice. The principle of matter, on the other hand, is not liberty but limitation- it has weight and occupies space. — George Gilder

The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure. — Felix Klein

There was a young lady of Wight Who travelled much faster than light. She departed one day, In a relative way, And arrived on the previous night. The point is that the theory of relativity says that there is no unique measure of time that all observers will agree on. — Stephen Hawking

Biological determinism is, in its essence, a theory of limits. It takes the current status of groups as a measure of where they should and must be ... We inhabit a world of human differences and predilections, but the extrapolation of these facts to theories of rigid limits is ideology. — Stephen Jay Gould

Democracy functions insofar as individuals can participate meaningfully in the public arena, meanwhile running their own affairs, individually and collectively, without illegitimate interference by concentrations of power. Functioning democracy presupposes relative equality in access to resources - material, informational, and other - a truism as old as Aristotle. In theory, governments are instituted to serve their "domestic constituencies" and are to be subject to their will. A measure of functioning democracy, then, is the extent to which the theory approximates reality, and the "domestic constituencies" genuinely approximate the population. — Noam Chomsky

His Theory of the Universe seems to have been, that it consisted solely of a multitude of objects which could be weighed, numbered, and measured; and the vocation to which he considered himself called was, to weigh, number and measure as many of those objects as his allotted three-score years and ten would permit. This conviction biased all his doings, alike his great scientific enterprises, and the petty details of his daily life. — George Wilson

One couldn't even measure roughness. So, by luck, and by reward for persistence, I did found the theory of roughness, which certainly I didn't expect and expecting to found one would have been pure madness. — Benoit Mandelbrot

The bubble logic driving tulipomania has since acquired a name: "the greater fool theory." Although by any conventional measure it is folly to pay thousands for a tulip bulb (or for that matter an Internet stock), as long as there is an even greater fool out there willing to pay even more, doing so is the most logical thing in the world. — Michael Pollan

In the mid-'60s in Berkeley, the theory of measure spaces of economic agents became one of my main interests. — Gerard Debreu

Can you measure it? Can you express it in figures? Can you make a model of it? If not, your theory is apt to be based more upon imagination than upon knowledge. — Lord Kelvin

We can measure the fine structure constant with very great precision, but so far none of our theories has provided an explanation of its measured value. One of the aims of superstring theory is to predict this quantity precisely. Any theory that could do that would be taken very seriously indeed as a potential 'Theory of Everything'. — John D. Barrow

Claude Shannon, the founder of information theory, invented a way to measure 'the amount of information' in a message without defining the word 'information' itself, nor even addressing the question of the meaning of the message. — Hans Christian Von Baeyer

The proper measure of a philosophical system or a scientific theory is not the degree to which it anticipated modern thought, but its degree of success in treating the philosophical and scientific problems of its own day. — Steven Weinberg

I don't think that the total creation took place in six days as we now measure time. If we can confirm, say, the Big Bang theory, that doesn't at all cause me to question my faith that God created the Big Bang. — Jimmy Carter

According to the kinetic theory of gases, the mean kinetic energy of a molecule is a measure of absolute temperature. — Wilhelm Wien

one of the twins went for a long trip in a spaceship at nearly the speed of light. When he returned, he would be much younger than the one who stayed on earth. This is known as the twins paradox, but it is a paradox only if one has the idea of absolute time at the back of one's mind. In the theory of relativity there is no unique absolute time, but instead each individual has his own personal measure of time that depends on where he is and how he is moving. — Stephen Hawking

I tend to think the good outweighs the bad. Then again, I try to be a glass-half-full person. Although I stand by my theory that if you measure your happiness by the amount of liquid in your glass, you are either a cliche or an alcoholic. — Caprice Crane

[John] Dalton was a man of regular habits. For fifty-seven years he walked out of Manchester every day; he measured the rainfall, the temperature - a singularly monotonous enterprise in this climate. Of all that mass of data, nothing whatever came. But of the one searching, almost childlike question about the weights that enter the construction of these simple molecules - out of that came modern atomic theory. That is the essence of science: ask an impertinent question, and you are on the way to the pertinent answer. — Jacob Bronowski

The uncertainty principle signaled an end to Laplace's dream of a theory of science, a model of the universe that would be completely deterministic. We certainly cannot predict future events exactly if we cannot even measure the present state of the universe precisely!
We could still imagine that there is a set of laws that determine events completely for some supernatural being who, unlike us, could observe the present state of the universe without disturbing it. However, such models of the universe are not of much interest to us ordinary mortals. It seems better to employ the principle of economy known as Occam's razor and cut out all the features of the theory that cannot be observed. — Stephen Hawking

Once we see, however, that the probability of life originating at random is so utterly miniscule as to make it absurd, it becomes sensible to think that the favorable properties of physics on which life depends are in every respect deliberate ... It is therefore almost inevitable that our own measure of intelligence must reflect ... higher intelligences ... even to the limit of God ... such a theory is so obvious that one wonders why it is not widely accepted as being self-evident. The reasons are psychological rather than scientific. — Fred Hoyle

[T]he theory of output as a whole, which is what the following book purports to provide, is much more easily adapted to the conditions of a totalitarian state, than is the theory of production and distribution of a given output produced under the conditions of free competition and a large measure of laissez-faire. — John Maynard Keynes

Mary was one who possessed power over her own spirit--rare gift, given to none but those who do something toward the taking of it. She was able in no small measure to order her own thoughts. Without any theory of self-rule, she yet ruled her Self. She was not one to slip about in the saddle, or let go the reins for a kick and a plunge or two. There was the thing that should be, and the thing that should not be; the thing that was reasonable, and the thing that was absurd. — George MacDonald

The "flow of information" through human communication channels is enormous. So far no theory exists, to our knowledge, which attributes any sort of unambiguous measure to this "flow". — Anatol Rapoport

Unlike other features on OkCupid, there is no visual component to match percentage. The number between two people only reflects what you might call their inner selves - everything about what they believe, need, and want, even what they think is funny, but nothing about what they look like. Judging by just this compatibility measure, the four largest racial groups on OkCupid - Asian, black, Latino, and white - all get along about the same.1 In fact, race has less effect on match percentage than religion, politics, or education. Among the details that users believe are important, the closest comparison to race is Zodiac sign, which has no effect at all. To a computer not acculturated to the categories, "Asian" and "black" and "white" could just as easily be "Aries" and "Virgo" and "Capricorn." But this racial neutrality is only in theory; things change once the users' own opinions, and not just the color-blind workings of an algorithm, come into play. — Christian Rudder

Indeed, the history of 20th century physics was in large measure about how to avoid the infinities that crop up in particle theory and cosmology. The idea of point particles is convenient but leads to profound, puzzling troubles. — Gregory Benford

I think also of my colleagues in elementary particle theory in many lands, and feel that in some measure I am here as a representative of our small, informal, international fraternity. — Murray Gell-Mann

Time is described only in terms of change in the network of relationships that describes space. This means that it is absurd in general relativity to speak of a universe in which nothing happens. Time is nothing but a measure of change-it has no other meaning. Neither space nor time has any existence outside the system of evolving relationships that comprises the universe. Physicists refer to this feature of general relativity as background independence. By this we mean that there is no fixed background, or stage, that remains fixed for all time. In contrast, a theory such as Newtonian mechanics or electromagmetism is background dependent because it assumes that there exists a fixed, unchanging background that provides the ultimate answer to all questions about where and when. — Lee Smolin

So, Einstein's theory of gravity is a theory of causal structure. It tells us that the essence of spacetime is causal structure and that the motion of matter is a consequence of alterations in the network of causal relations. What is left out from the notion of causal structure is any measure of quantity or scale. — Lee Smolin

A common refrain among theoretical physicists is that the fields of quantum field theory are the "real" entities while the particles they represent are images like the shadows in Plato's cave. As one who did experimental particle physics for forty years before retiring in 2000, I say, "Wait a minute!" No one has ever measured a quantum field, or even a classical electric, magnetic, or gravitational field. No one has ever measured a wavicle, the term used to describe the so-called wavelike properties of a particle. You always measure localized particles. The interference patterns you observe in sending light through slits are not seen in the measurements of individual photons, just in the statistical distributions of an ensemble of many photons. To me, it is the particle that comes closest to reality. But then, I cannot prove it is real either. — Victor J. Stenger

I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: "The author discusses valueless measures in pointless spaces." — Paul Halmos

During the 1919 solar eclipse, people go out to measure the positions of the stars and they find exactly what Einstein predicted. Einstein gets a telegram saying this, and somebody asked him, Professor Einstein, what would you have said if the observations didn't agree with what your prediction of general relativity said should be happening? And Einstein said, "I'd be sorry for the dear lord; the theory is correct." What he meant by that is the math is just so elegant, so beautiful, so powerful, that almost seemingly it can't possibly be wrong. — Rivka Galchen