The origin of animals was one of the most astonishing and important transformations in the history of life. From single-celled ancestors, they evolved into a riot of complexity and diversity. An estimated seven million species of animals live on earth today, ranging from tubeworms at the bottom of the ocean to elephants lumbering across the African savanna. Their bodies can total trillions of cells, which can develop into muscles, bones and hundreds of other kinds of tissues and cell types. The dawn of the animal kingdom about 800 million years ago was also an ecological revolution. Animals devoured the microbial mats that had dominated the oceans for more than two billion years and created their own habitats, like coral reefs.

The origin of animals is also one of the more mysterious episodes in the history of life. Changing from a single-celled organism to a trillion-cell collective demands a huge genetic overhaul. 

Imagine it: a flower blossoming inside the brain, nanometer stalks splitting away from a micrometer stem. Expanding into every available capillary, touching every cubic millimeter of the brain, collecting terabytes of data in every second. By the same token, it could send in terabytes of data every second. It would be the most intimate interface ever invented. If you connected one person’s wired brain to another person’s, you could literally connect them together; they would have a real corpus callosum joining them (albeit with links of radio waves rather than wires.) And if you connected a number of people to each other via the Internet, then you would have a network in which each node was a human brain. The World Wide Web would become the World Wide Mind.

You may have heard of determinism, the theory that absolutely everything that happens is causally determined to happen exactly as it does by what has already gone before — right back to the beginning of the universe. You may also believe that determinism is true. (You may also know, contrary to popular opinion, that current science gives us no more reason to think that determinism is false than that determinism is true.) In that case, standing on the steps of the store, it may cross your mind that in five minutes’ time you’ll be able to look back on the situation you’re in now and say truly, of what you will by then have done, “Well, it was determined that I should do that.” But even if you do fervently believe this, it doesn’t seem to be able to touch your sense that you’re absolutely morally responsible for what you next.

The case of the Oxfam box, which I have used before to illustrate this problem, is relatively dramatic, but choices of this type are common. They occur frequently

Little is quite as dull as literary worship; this essay on Borges is thus happily doomed. One finds oneself tempted toward learned-sounding inadequacies like: His work combines the elegance of mathematical proof with the emotionally profound wit of Dostoyevsky. Or: He courts paradox so primrosely, describing his Dupin-like detective character as having “reckless perspicacity” and the light in his infinite Library of Babel as being “insufficient, and unceasing.” But see, such worship is pale.

And problematic as well. More than any other 20th-century figure, Borges is the one designated — and often dismissed as — the Platonic ideal of Writer. His outrageous intellect is cited as proof of either his genius or of his bloodless cerebralism.

But Borges did have some mortal qualities. He lived most of his life with his mother. He loved detective and adventure novels. (His first story in English was published in Ellery Queen Mystery Magazine.) Though he started to go blind in his 30s, he nev

Have you ever thought about whether to have a child? If so, what factors entered into your decision? Was it whether having children would be good for you, your partner and others close to the possible child, such as children you may already have, or perhaps your parents? For most people contemplating reproduction, those are the dominant questions. Some may also think about the desirability of adding to the strain that the nearly seven billion people already here are putting on our planet’s environment. But very few ask whether coming into existence is a good thing for the child itself. Most of those who consider that question probably do so because they have some reason to fear that the child’s life would be especially difficult — for example, if they have a family history of a devastating illness, physical or mental, that cannot yet be detected prenatally.

All this suggests that we think it is wrong to bring into the world a child whose prospects for a happy

The most familiar ideas of geometry were inspired by an ancient vision — a vision of the world as flat. From parallel lines that never meet, to the Pythagorean theorem discussed in last week’s column, these are eternal truths about an imaginary place, the two-dimensional landscape of plane geometry.

Conceived in India, China, Egypt and Babylonia more than 2,500 years ago, and codified and refined by Euclid and the Greeks, this flat-earth geometry is the main one (and often the only one) being taught in high schools today. But things have changed in the past few millennia.

In an era of globalization, Google Earth and transcontinental air travel, all of us should try to learn a little about spherical geometry and its modern generalization, differential geometry. The basic ideas here are only about 200 years old. Pioneered by Carl Friedrich Gauss and Bernhard Riemann, differential geometry underpins such imposing intellectual edifices as Einstein’s general theory of relativity. At its h

Though Gutenberg's invention made possible our modern world with all its wonders and woes, no one, much less Gutenberg himself, could have foreseen that his press would have this effect. And no one today can foresee except in broad and sketchy outline the far greater impact that digitization will have on our own future. With the earth trembling beneath them, it is no wonder that publishers with one foot in the crumbling past and the other seeking solid ground in an uncertain future hesitate to seize the opportunity that digitization offers them to restore, expand, and promote their backlists to a decentralized, worldwide marketplace. New technologies, however, do not await permission. They are, to use Schumpeter's overused term, disruptive, as nonnegotiable as earthquakes.

Dr. Nielsen and Dr. Ninomiya have proposed a kind of test: that CERN engage in a game of chance, a “card-drawing” exercise using perhaps a random-number generator, in order to discern bad luck from the future. If the outcome was sufficiently unlikely, say drawing the one spade in a deck with 100 million hearts, the machine would either not run at all, or only at low energies unlikely to find the Higgs.

Sure, it’s crazy, and CERN should not and is not about to mortgage its investment to a coin toss. The theory was greeted on some blogs with comparisons to Harry Potter. But craziness has a fine history in a physics that talks routinely about cats being dead and alive at the same time and about anti-gravity puffing out the universe.

As Niels Bohr, Dr. Nielsen’s late countryman and one of the founders of quantum theory, once told a colleague: “We are all agreed that your theory is crazy. The question that divides us is whether it is crazy enough to have a chance of being correct.”

Dr. N

What does it mean to read in a digital age? Researchers are just beginning to explore the question, and educators are engaged in passionate debate about how reading may be changing on the Internet. It is impossible to write about any one piece of research at great length, so for those interested in more in-depth information, here are links to some studies, speeches, reading tests — old and new — and other resources.