Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates.
Language is a labyrinth of paths. You approach from one side and know your way about; you approach the same place from another side and no longer know your way about.
Research shows that there is only half as much variation in student achievement between schools as there is among classrooms in the same school. If you want your child to get the best education possible, it is actually more important to get him assig...
It used to be said that God could create anything except what would be contrary to the laws of logic. The truth is that we could not say what an "illogical" world would look like.
Most propositions and questions, that have been written about philosophical matters, are not false, but senseless. ... (They are of the same kind as the question whether the Good is more or less identical than the Beautiful.)
If you think about the actual problems we are facing - all the crises - we have the means to solve these crises. The past has shown us we are able to do things we never imagined we would be able to do.
Astonishingly, in spite of decades of research, there is no agreed theory of cancer, no explanation for why, inside almost all healthy cells, there lurks a highly efficient cancer subroutine that can be activated by a variety of agents - radiation, c...
Astronauts have been stuck in low-Earth orbit, boldly going nowhere. American attempts to kick-start a new phase of lunar exploration have stalled amid the realisation that NASA's budget is too small for the job.
I remember being fascinated by ants and wasps and other bugs when I was a kid. I'd set out a Coke can and stand back 20 feet and use my telescope to watch wasps land on it.
Had we really succeeded therefore in altering the period of vibration, which Maxwell, as I have just noted, held to be impossible? Or was there some disturbing circumstances from one or more factors which distorted the result?
According to well-known electrodynamic laws, an electron moving in a magnetic field is acted upon by a force which runs perpendicular to the direction of motion of the electron and to the direction of the magnetic field, and whose magnitude is easily...
If you take your thumb and your index finger and look right where they meet - go ahead and do that now - and relax your hand, you'll see a crinkle, and then a wrinkle within the crinkle, and a crinkle within the wrinkle. Right? Your body is covered w...
To this day I always insist on working out a problem from the beginning without reading up on it first, a habit that sometimes gets me into trouble but just as often helps me see things my predecessors have missed.
My mother also had us take piano lessons, and this had a similar effect. I hated those lessons, but I now play regularly for pleasure and have even tried my hand at composing.
When I moved to Stanford I began to pursue the line of research I have been following ever since, namely trying to understand the larger implications of fractional quantum hall discovery.
According to the belief, molecules closer together than 200 nanometers could not be told apart with focused light. This is because, in a packed molecular crowd, the molecules shout out their fluorescence simultaneously, causing their signal, their vo...
The probability of an event is the reason we have to believe that it has taken place, or that it will take place. The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases fa...
The stars look the same from night to night. Nebulae and galaxies are dully immutable, maintaining the same overall appearance for thousands or millions of years. Indeed, only the sun, moon and planets - together with the occasional comet, asteroid o...
Scientists - who prefer explanations subject to laboratory tests - figure that everything we see today was as inevitable as wrinkles, once the Big Bang established physics. Stars and planets were cooked up as huge clouds of matter collapsed and coale...
The bottom line is that the position of the Sun relative to the stars slowly changes for any given date, and over the course of 26,000 years, it can easily slide between constellations. So you may think you're a Pisces, but you're actually an Aquariu...
There's no doubt that the Moon is more than a handy night light and a hair restorer for werewolves. It's responsible for the substantial amplitude of earthly ocean tides. These are of obvious influence if you're a geoduck, a type of clam that people ...
