Science teaches us to be very suspicious of grand generalizations...Aristotle had a set theory of the universe, and he didn’t get too far. Galileo started with simple things like pendulums and balls sliding down inclined planes, and he got much further. You never find surprises when you think in terms of broad generalities. Both quantum mechanics and relativity grew out of trying to really understand essentially simple things.

The main problem with many nonscientific world models is the vigor with which they insist upon their rightness. Once a world model claims to be completely right, it is no longer open to any changes. ...Closed systems can be comforting, but they are limited. ...It's not the best we can do. Neither is extreme "open-mindednesss" that slides into "empty headedness"—the ideal that we can never really know anything.

E = mc<sup>2</sup> really applies only to isolated bodies at rest. In general, when you have moving bodies, or interacting bodies, energy and mass aren't proportional. E = mc<sup>2</sup> simply doesn't apply. ...For moving bodies, the correct mass-energy equation is
<math>E=\frac {mc^2} {\sqrt{1-\frac{v^2} {c^2}}}</math>
where <math>v</math> is the velocity. For a body at rest <math>(v=0)</math>, this becomes E = mc<sup>2</sup>. ...we must consider the special case of particles with zero mass... examples include photons, color gluons, and gravitons. If we attempt to put m = 0 and <math>v</math> = c in our general mass-energy equation, both the numerator and denominator on the right-hand-side vanish, and we get the nonsensical relation E = 0/0. The correct result is that the energy of a photon can take any value. ...The energy E of a photon is proportional to the frequency f of the light it represents. ...they are related by the Planck-Einstein-Schrödinger equation E = hf, where h is Plank's constant.

Does Michael Jackson or Archie Bunker or the president of General Motors need to know about quantum mechanics? Of course not. You can live a full life without that. But if you don’t believe that the universe is understandable, then it leads to the notion that one idea is just as good as another. And that’s horrible.

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Exoplanet astronomy will systematically survey our galaxy, gathering information on the masses, orbits, geology, and atmospheres of millions of planets. As a byproduct, we will learn how rare life is and what conditions it requires. What we discover might support tests and refinements of anthropic reasoning.

Particles that, like <sup>4</sup>He, show constructive interference are said to be bosons—a shorthand term for "particles obeying Bose–Einstein statistics." …One way to recognize bosons is their tendency to imitate one each other. ...the presence of one boson increases the chance that another of its identical siblings will also appear in the same spot. There's an attraction between them. We will speak ...of an attractive identity force drawing together identical bosons. Lasers are a spectacular example...

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Einstein’s great friend and intellectual sparring partner Niels Bohr had a nuanced view of truth. Whereas according to Bohr, the opposite of a simple truth is a falsehood, the opposite of a deep truth is another deep truth. In that spirit, let us introduce the concept of a deep falsehood, whose opposite is likewise a deep falsehood. It seems fitting to conclude this essay with an epigram that, paired with the one we started with, gives a nice example: “Naïveté is doing the same thing over and over, and always expecting the same result.”

If grand unified theories are correct, we ought to be able to derive the relative power of the strong, weak, and electromagnetic interactions at accessible energies from their presumed equality at much higher energies. When this is attempted, a wonderful result emerges. ...in the form first calculated by Howard Georgi, Helen Quinn, and Steven Weinberg ...The couplings of strong-interaction gluons decrease, those of the [weak interaction] W bosons stay roughly constant, and those of the [electromagnetic interaction] photons increase at short distances [or high energies]—so they all tend to converge, as desired.

We evolved to be good at learning and using rules of thumb, not at searching for ultimate causes and making fine distinctions. Still less did we evolve to spin out long chains of calculation that connect fundamental laws to observable consequences. Computers are much better at it!