Clifford A. Pickover Quotes

For relatively small stars, the Pauli exclusion principle keeps the electrons in a star sufficiently separated to prevent the star from contracting further after it has spent its fuel. In other words, the electrons counteract the crushing gravitational force. However, for stars more than about 1.5 times the mass of the sun (a mass known as the Chandrasekhar limit), this repulsive force would not be enough to stop stellar collapse.

The quipu is significant because it dispels the notion that mathematics flourishes only after a civilization has developed writing; however, societies can reach advanced states without ever having developed written records.

Today, we know that time travel need not be confined to myths, science fiction, Hollywood movies, or even speculation by theoretical physicists. Time travel is possible. For example, an object traveling at high speeds ages more slowly than a stationary object. This means that if you were to travel into outer space and return, moving close to light speed, you could travel thousands of years into the Earth's future.

Mathematical theories have sometimes been used to predict phenomena that were not confirmed until years later. For example, Maxwell's equations, named after physicist James Clerk Maxwell, predicted radio waves. Einstein's field equations suggested that gravity would bend light and that the universe is expanding. Physicist Paul Dirac once noted that the abstract mathematics we study now gives us a glimpse of physics in the future. In fact, his equations predicted the existence of antimatter, which was subsequently discovered. Similarly, mathematician Nikolai Lobachevsky said that "there is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world.

In the froth, space doesn't have a definite structure. It has various probabilities for different shapes and curvatures. It might have a 50 percent chance of being in one shape, a 10 percent chance of being in another, and a 40 percent chance of being in a third form. Because any structure is possible inside the singularity, we say the singularity is constructed from probabilistic foam, or quantum foam. Quantum gravity governs the probabilities for the various foam structures.

I do not know if God is a mathematician, but mathematics is the loom upon which God weaves the fabric of the universe....The fact that reality can be described or approximated by simple mathematical expressions suggests to me that nature has mathematics at its core.

In this book, you will encounter various interesting geometries that have been thought to hold the keys to the universe. Galileo Galilei (1564-1642) suggested that "Nature's great book is written in mathematical symbols." Johannes Kepler (1571-1630) modeled the solar system with Platonic solids such as the dodecahedron. In the 1960s, physicist Eugene Wigner (1902-1995) was impressed with the "unreasonable effectiveness of mathematics in the natural sciences." Large Lie groups, like E8-which is discussed in the entry "The Quest for Lie Group E8 (2007)"- may someday help us create a unified theory of physics. in 2007, Swedish American cosmologist Max Tegmark published both scientific and popular articles on the mathematical universe hypothesis, which states that our physical reality is a mathematical structure-in other words, our universe in not just described by mathematics-it is mathematics.

Obviously, the final goal of scientists and mathematicians is not simply the accumulation of facts and lists of formulas, but rather they seek to understand the patterns, organizing principles, and relationships between these facts to form theorems and entirely new branches of human thought. For me, mathematics cultivates a perpetual state of wonder about the nature of mind, the limits of thoughts, and our place in this vast cosmos.

Preservations are working to save neon signs for future generations, either on-site or in museums. After all, what would America be without a few giant doughnuts around.

As I write this entry, I touch a saber-tooth tiger skull in my office. Without stars there could be no skulls

Einstein created an unstoppable "intellectual chain reaction," an avalanche of pulsing, chattering neurons and memes that will ring for an eternity