Quotes of All Topics . Occasions . Authors
The equations at which we arrive must be such that a person of any nation, by substituting the numerical values of the quantities as measured by his own national units, would obtain a true result.
Science is beautiful when it makes simple explanations of phenomena or connections between different observations. Examples include the double helix in biology and the fundamental equations of physics.
But the beauty of Einstein's equations, for example, is just as real to anyone who's experienced it as the beauty of music. We've learned in the 20th century that the equations that work have inner harmony.
I love studying asteroids because they are relatively simple, just rocks in space. They can be understood with physics and described with elegant equations. For the most part, they are serene celestial bodies.
When I got to college, I was intending to study film. But I found that my brain was feeling mushy, so I took a few math classes. I started doing really well at them, and solving equations was this, like, drug rush.
Technologies evolve in the strangest ways. Computers were created to calculate ballistics equations, and now we use them to create amusing illusions. Creating amusing illusions is a big business if you play it right.
My mother was the nicest person in the world. I still have people coming to me to say how she was so warm, generous, and kind-hearted. She never washed her dirty linen in public. She always maintained her equations with people.
Even before string theory, especially as physics developed in the 20th century, it turned out that the equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle.
We seem to forget that innovation doesn't just come from equations or new kinds of chemicals, it comes from a human place. Innovation in the sciences is always linked in some way, either directly or indirectly, to a human experience.
Economics pretends to be a science. Its practitioners fill blackboards with equations and clog computers with data. But it is really a faith, or more accurately a set of overlapping and squabbling faiths, each with its own doctrines.
I became an atheist because, as a graduate student studying quantum physics, life seemed to be reducible to second-order differential equations. Mathematics, chemistry and physics had it all. And I didn't see any need to go beyond that.
Symmetry does mean something different for physicists than for members of the public. It means that an object or a theory does not change when you make some transformation - either rotating or moving it or doing something to the equations.
The standard high school curriculum traditionally has been focused towards physics and engineering. So calculus, differential equations, and linear algebra have always been the most emphasized, and for good reason - these are very important.
If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellect that in order to predict little parts of it, we need not solve innumerable differential equations, but can use dice with fair success.
You kind of alluded to it in your introduction. I mean, for the last 300 or so years, the exact sciences have been dominated by what is really a good idea, which is the idea that one can describe the natural world using mathematical equations.
What can a pencil do for all of us? Amazing things. It can write transcendent poetry, uplifting music, or life-changing equations; it can sketch the future, give life to untold beauty, and communicate the full-force of our love and aspirations.
Extra dimensional theories are sometimes considered science fiction with equations. I think that's a wrong attitude. I think extra dimensions are with us, they are with us to stay, and they entered physics a long time ago. They are not going to go away.
The thing that got me started on the science that I've been building now for about 20 years or so was the question of okay, if mathematical equations can't make progress in understanding complex phenomena in the natural world, how might we make progress?
My students may have dexterity with the equations they're required to know, but they lack the capacity to apply their knowledge to real-life problems. This critical shortcoming appears in high school and possibly in elementary grades - long before college.
While physics and mathematics may tell us how the universe began, they are not much use in predicting human behavior because there are far too many equations to solve. I'm no better than anyone else at understanding what makes people tick, particularly women.
My brother is a genius. When we went to Italy, he was on the local television channel as a prodigy, who could solve very sophisticated mathematical equations. He was only seven or eight years old but he could solve mathematical problems for fourteen year olds.
It's probably the wrong way round, I know, but I just love maths and doing equations. When I was a kid, I was really good at it, so when I was seven, I asked my mum what job lets you do maths and pays you for it. She said accountancy, and that was it. I was dead set.
The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.
I regard it in fact as the great advantage of the mathematical technique that it allows us to describe, by means of algebraic equations, the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation.
Because for me, equations and symbols aren't just a thing. They're a voice that speaks out about the incredible richness of nature and the startling simplicity in the patterns that twist and turn and warp and evolve all around us, from how the world works to how we behave.
The complicated, ambiguous milieu of human contact is being replaced with simple, scalable equations. We maintain thousands more friends than any human being in history, but at the cost of complexity and depth. Every minute spent online is a minute of face-to-face time lost.
I have my hopes, & very distinct ones, too, of one day getting cerebral phenomena such that I can put them into mathematical equations: in short, a law or laws for the mutual actions of the molecules of the brain (equivalent to the law of gravitation for the planetary & sideral world).
In my own research when I'm working with equations, I never feel like I really understand what I'm doing if I'm solely relying on the mathematics for my understanding. I need to have a visual picture in my mind. I'm constantly translating from the math to some intuitive mind's-eye picture.
One of the pleasing things about science is that we do all climb towards the heavens on the shoulders of our predecessors. Economics, like physics, has its heroes, and the letter 'H' that I used in my mathematical equations was not there to honor Sir William Hamilton, but rather Harold Hotelling.
A common misconception about how things such as space shuttles come to be is that engineers simply apply the theories and equations of science. But this cannot be done until the new thing-to-be is conceived in the engineer's mind's eye. Rather than following from science, engineered things lead it.
A robber who justified his theft by saying that he really helped his victims, by his spending giving a boost to retail trade, would find few converts; but when this theory is clothed in Keynesian equations and impressive references to the 'multiplier effect,' it unfortunately carries more conviction.
Einstein had looked at the numbers and dimensions that went into his equations for gravitational waves and said, essentially, 'This is so tiny that it will never have any influence on anything, and nobody can measure it.' And when you think about the times and the technology in 1916, he was probably right.
Everything, however complicated - breaking waves, migrating birds, and tropical forests - is made of atoms and obeys the equations of quantum physics. But even if those equations could be solved, they wouldn't offer the enlightenment that scientists seek. Each science has its own autonomous concepts and laws.
I understood Stephen's point of view because if you had been given a death sentence at the age of 21, would you find it easy to believe in a loving God? Also, Stephen's work was taking him into the depths of the universe, and it was, I thought, fairly understandable that there wasn't much room for God in his equations.
I've not been in a live-in relationship. But I've been exposed to various kinds of equations that can exist between people. When I came from Bangalore, it was black and white. Over the years, I've realised that there's more to what we see on a day-to-day basis. There are all kinds of relationships, all kinds of equations.
It's a spectacular signal. It's a signal many of us have wanted to observe since the time LIGO was proposed. It shows the dynamics of objects in the strongest gravitational fields imaginable, a domain where Newton's gravity doesn't work at all, and one needs the fully non-linear Einstein field equations to explain the phenomena.