Lawrence M. Krauss

For a physicist or a mathematician, the most symmetrical object you could think about would be a sphere, because it looks identical no matter what you do to it, however you rotate it in any given direction.

Scientists don't read theology; they don't read philosophy. It doesn't make any difference to what they're doing - for better or worse, it may not be a value judgment, but it's true.

One thing I cannot understand - and people are probably going to be upset about this - is why local school boards have control over educational content.

I am in favor of saying, 'Okay, let's get teams of educators and experts in certain disciplines to say, 'What are the basic things that we think are an essential part of an early education for people?'' Put them together and create, as well as possible, a set of goals and tools to learn those things.

We should teach kids how to question. Now having said that, of course, to be a productive adult, there are certain skills that are required - reading, writing, and, in the old-fashioned days, we used to say arithmetic. Now we say mathematics.

What we can do is provide the tools, through our educational system, for people to be able to tell sense from nonsense. These tools include the scientific method, skeptical questioning, empirical evidence, verifying sources, etc.

The notion that anyone in the 21st century could take seriously the notion that the sun orbits the Earth, or that the Earth is the center of the universe, is almost unbelievable.

Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they're really doing is mathematics - it's not talking about things that have affected computer science; it's mathematical logic.

Philosophy used to be a field that had content, but then 'natural philosophy' became physics, and physics has only continued to make inroads. Every time there's a leap in physics, it encroaches on these areas that philosophers have carefully sequestered away to themselves, and so then you have this natural resentment on the part of philosophers.

Symmetries are the playing field on which the physical world works and which determine the rules of the game. The symmetries of nature determine for us things that remain constant, that can't be changed. Those are the guideposts in physics, the quantities like energy and momentum.

I was most eager to see how Trump would respond to the climate-change question.

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 biggest conceptual change over the last 100 years in the way physicists think about the world is symmetry.

The root cause of the looming energy problem - and the key to easing environmental, economic and religious tensions while improving public health - is to address the unending, and unequal, growth of the human population. And the one proven way to reduce fertility rates is to empower young women by educating them.

I cannot stress often enough that what science is all about is not proving things to be true but proving them to be false.

I have always felt that, aside from research that violates universal human mores, when it comes to technological applications, that which can be done will be done.

Life has survived for more than three billion years because it is robust, and almost no mutations can easily outwit the defense mechanisms built up through eons of exposure to potential pathogens.

The Bible is full of dubious scientific impossibilities, from Jonah living inside a whale, to the sun standing still in the sky for Joshua.

Imagining living in a universe without purpose may prepare us to better face reality head on. I cannot see that this is such a bad thing.

One might rationally argue that individual human beings should be free choose what moral behavior they approve of, and which they don't, subject to the constraints of the law.

Either Trump only talks to those who play up to his delusion, or he simply doesn't listen to those who might burst his bubble. Either way, that is a cause for worry.

Immediately after the San Bernardino shooting, when it was unclear whether Syed Rizwan Farook and Tashfeen Malik were motivated by a terroristic ideology, the focus of the conversation was on gun laws.

These days, gun violence can strike anywhere, from a church hall in Charleston to a movie theatre or a Planned Parenthood office in Colorado. But our response to it depends on whether that violence is understood to be terrorism.

Donald Trump called for the closing of borders to Muslims; John McCain said, in response to the President's address on the San Bernardino shooting, that 'this is the war of our time.' As that shooting shows, we react to terrorism with far more intensity than we do to an ordinary crime.

If I knew what the next big thing was, I'd be doing it now.

When it comes to the things that people really want in science fiction - like space travel - the simplest things end up causing them not to happen. Humans are 100-pound bags of water, built to live on Earth.

By his own admission, Carson's remarkable hand-eye coordination allowed him to soar as a surgeon, and he used that success to build a lucrative reputation as a purveyor of advice for young and old. His book for young people is titled 'You Have a Brain.'

A snowflake is another beautifully ordered example of what simple, natural meteorological processes can produce. Stars form by gravity, collapsing into spherically ordered structures that can remain in this form only if they release tremendous heat energy into the environment.

Local order in parts of the universe is always possible at the expense of heat and disorder dissipated to the external environment. The human body is one example: we take in energy from our environment to build up complex molecules that help power our bodies, and, in doing so, we release heat to the world around us.

For a man with an impressive educational C.V., Ben Carson makes a lot of intellectual missteps.

A significant fraction of evangelical voters appear more likely to ignore the candidates' specific economic and foreign policy platforms in favor of concerns about gay marriage or abortion.

Parents, of course, have concerns and 'say,' but they don't have the right to shield their children from knowledge. That is not a right, any more than they have the right to shield their children from healthcare or medicine.

Richard Nixon, famously, conducted his foreign policy according to the 'madman theory': he tried to convince enemy leaders that he was irrational and volatile in an attempt to intimidate them. But this was a potentially useful approach to foreign policy only because it was an act.

It's all too easy to imagine Trump issuing an ultimate, thermonuclear 'You're fired!' to China, Iran, or another nation - and perhaps to the whole human race.

Cabinet members may disagree and even resign in protest, but, ultimately, they must obey the order of the Commander-in-Chief.

Donald Trump's candidacy has been a source of anxiety for many reasons, but one stands out: the ability of the president to launch nuclear weapons. When it comes to starting a nuclear war, the president has more freedom than he or she does in, say, ordering the use of torture.

When considering real-world issues, particularly those that touch on science and technology, it is harder to speak in platitudes or rely purely on emotion or fear. Substance, or its lack, becomes harder to mimic or mask, which is why I wish we had a true televised presidential debate on these subjects.

On the question of information security, he claims that, in a Trump Administration, the U.S. government will not spy on its own citizens. If true, this would represent a turn away from the strong language that he has used about identifying terrorists on our soil.

On the question of preserving public lands, Trump replies that our elected officials have spent too long rewarding 'special interests,' by which I assume he doesn't mean petroleum companies and the Bundy family.

When it comes to the real operational issues that govern our understanding of physical reality, ontological definitions of classical philosophers are, in my opinion, sterile.

Feynman once said, 'Science is imagination in a straitjacket.' It is ironic that in the case of quantum mechanics, the people without the straitjackets are generally the nuts.

Keeping religion immune from criticism is both unwarranted and dangerous.

There are areas of philosophy that are important, but I think of them as being subsumed by other fields. In the case of descriptive philosophy, you have literature or logic, which, in my view, is really mathematics.

Organized religion, wielding power over the community, is antithetical to the process of what modern democracy should define as liberty. The sooner we are without it, the better.

Aside from communications satellites, space is devoid of industry.

Nothing can create something all the time due to the laws of quantum mechanics, and it's - it's fascinatingly interesting.

Neutrinos alone, among all the known particles, have ethereal properties that are striking and romantic enough both to have inspired a poem by John Updike and to have sent teams of scientists deep underground for 50 years to build huge science-fiction-like contraptions to unravel their mysteries.

The rise of a ubiquitous Internet, along with 24-hour news channels has, in some sense, had the opposite effect from what many might have hoped such free and open access to information would have had. It has instead provided free and open access, without the traditional media filters, to a barrage of disinformation.

I don't know if science and reason will ultimately help guide humanity to a better and more peaceful future, but I am certain that this belief is part of what keeps the 'Star Trek' fandom going.

The Internet is a clear example of how our lives have changed in ways we couldn't have imagined: a distributed information source, which is invisible to everyone, where you can access anything, and it's distributed throughout the whole world. Basically, communication is instantaneous.