Quotes from Mario Livio

Supersymmetry is a subtle symmetry based on the quantum mechanical property spin.

Note that a rotation by 360 degrees is equivalent to doing nothing at all, or rotating by zero degrees. This is known as the identity transformation. Why bother to define such a transformation at all? As we shall see later in the book, the identity transformation plays a similar role to that of the number zero in the arithmetic operation of addition or the number one in multiplication-when you add zero to a number or multiply a number by one, the number remains unchanged.

Galileo established what has since become the modern approach to the study of all natural phenomena.

Moreover, Galileo argued that by pursuing science using the language of mechanical equilibrium and mathematics, humans could understand the divine mind.

Indeed, the genius of Abel and Galois could be compared only to a supernova-an exploding star that for a short while outshines all the billions of stars in its host galaxy.

While Euclid himself may not have been the greatest mathematician who ever lived, he was certainly the greatest teacher of mathematics.

himself, then according to the sign he should be one of those he does not shave. On the other hand

The two solutions of the equation for the Golden Ratio are: x1 = (1+ Sqr5) / 2 x2 = (1 - Sqr5) / 2

Galileo was right, and the Church in this case abused its disciplinary power. As Pope John Paul II admitted in 1992: "This led them [the theologians who condemned Galileo] unduly to transpose into the realm of the doctrine of the faith, a question which in fact pertained to scientific investigation." Such acknowledgments, however, didn't come for almost four centuries.

Simply put, Leonardo replaced the mystic black bile, faculties, and spirits that permeated the writings of Galen, Avicenna, de Luzzi, and others, with his physical powers of movement, weight, force, and percussion - the building blocks of mechanics. he further used these mechanical concepts to demystify a whole host of physiological processes.

The strength of the familiar electromagnetic force between two electrons, for example, is expressed in physics in terms of a constant known as the fine structure constant. The value of this constant, almost exactly 1/137, has puzzled many generations of physicists. A joke made about the famous English physicist Paul Dirac (1902-1984), one of the founders of quantum mechanics, says that upon arrival to heaven he was allowed to ask God one question. His question was: Why 1/137?

For Newton, the world's very existence and the mathematical regularity of the observed cosmos were evidence for God's presence.

Our mathematics is the symbolic counterpart of the universe we perceive, and its power has been continuously enhanced by human exploration.

The key point to keep in mind, however, is that symmetry is one of the most important tools in deciphering nature's design.

Because of the "divine" properties attributed to the Golden Ratio, mathematician Clifford A. Pickover suggested that we should refer to that point as "the Eye of God.

we are much better at judging other peoplethan at analyzing ourselves.

Put simply, the cosmological argument claims that since the physical world had to come into existence somehow, there must be a First Cause, namely, a creator God.

The Golden Rectangle is the only rectangle with the property that cutting a square from it produces a similar rectangle.

Twentieth-century British mathematician G.H. Hardy also believed that the human function is to "discover or observe" mathematics rather than to invent it. In other words, the abstract landscape of mathematics was there, waiting for mathematical explorers to reveal it.

Galileo was hailed as a Columbus of the heavens. The Scottish librarian Thomas Segeth raved: "Columbus gave man lands to conquer by bloodshed, Galileo new worlds harmful to none. Which is better?

The Golden Ratio has the unique properties that we produce its square by simply adding the number 1 and its reciprocal by subtracting the number 1.

Indeed, the quality that made Newton's theories truly stand out-the inherent characteristic that turned them into inevitable laws of nature-was precisely the fact that they were all expressed as crystal-clear, self-consistent mathematical relations.

Some ancient Indian texts claim that numbers are almost divine, or "Brahma-natured.

While composite faces tend, by construction, to also be more symmetric, Langlois found that even after the effects of symmetry have been controlled, averageness was still judged to be attractive. These findings argue for a certain level of prototyping in the mind, since averageness might well be coupled with a prototypical template.