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When he was 16, Galileo enrolled at the University of Pisa to study medicine, at his father’s urging. Instead, though, he became interested in mathematics and shifted his focus to that subjec

Galileo left the school in 1585 without earning a degree.

Galileo didn’t invent the telescope—Dutch eyeglass maker Hans Lippershey is generally credited with its creation—but he was the first person to use the optical instrument to systematically study the heavens.

During most of the 16th and 17th centuries, fear of heretics spreading teachings and opinions that contradicted the Bible dominated the Catholic Church

A type of war between science and religion was in play but there would be more casualties on the side of science.

Nicholas Copernicus and Galileo Galilei were two scientists who printed books that later became banned

In February-March 1616, the Catholic Church issued a prohibition against the Copernican theory of the earth’s motion.

This led later (1633) to the Inquisition trial and condemnation of Galileo Galilei (1564-1642) as a suspected heretic, which generated a controversy that continues to our day.

In 1543, Polish astronomer Nicolaus Copernicus (1473-1543) published On the Revolutions of the Heavenly Spheres. This book elaborated the (geokinetic and heliocentric) idea that the earth rotates daily on its own axis and revolves yearly around the sun

If you take a look at the progress of science, the sciences are kind of a continuum, but they're broken up into fields. The greatest progress is in the sciences that study the simplest systems. So take, say physics -- greatest progress there. But one of the reasons is that the physicists have an advantage that no other branch of sciences has. If something gets too complicated, they hand it to someone else.

If a molecule is too big, you give it to the chemists. The chemists, for them, if the molecule is too big or the system gets too big, you give it to the biologists. And if it gets too big for them, they give it to the psychologists, and finally it ends up in the hands of the literary critic, and so on.

neuroscience for the last couple hundred years has been on the wrong track. There's a fairly recent book by a very good cognitive neuroscientist, Randy Gallistel and King, arguing -- in my view, plausibly -- that neuroscience developed kind of enthralled to associationism and related views of the way humans and animals work. And as a result they've been looking for things that have the properties of associationist psychology.

Actually fluoride is a natural mineral that, in the weak concentrations used in public drinking water systems, hardens tooth enamel and prevents tooth decay—a cheap and safe way to improve dental health for everyone, rich or poor, conscientious brusher or not. That’s the scientific and medical consensus.

when Galileo claimed that the Earth spins on its axis and orbits the sun, he wasn’t just rejecting church doctrine. He was asking people to believe something that defied common sense

all manner of scientific knowledge—from the safety of fluoride and vaccines to the reality of climate change—faces organized and often furious opposition.

No well-tested scientific concept is more astonishing than the one that gives its name to a new book by the Scientific American contributing editor George Musser, “Spooky Action at a Distance

The ostensible subject is the mechanics of quantum entanglement; the actual subject is the entanglement of its observers.

his question isn’t so much how this weird thing can be true as why, given that this weird thing had been known about for so long, so many scientists were so reluctant to confront it. What keeps a scientific truth from spreading?

The test of replicability, as it’s known, is the foundation of modern research. Replicability is how the community enforces itself. It’s a safeguard for the creep of subjectivity. Most of the time, scientists know what results they want, and that can influence the results they get. The premise of replicability is that the scientific community can correct for these flaws.

But now all sorts of well-established, multiply confirmed findings have started to look increasingly uncertain. It’s as if our facts were losing their truth: claims that have been enshrined in textbooks are suddenly unprovable.

This phenomenon doesn’t yet have an official name, but it’s occurring across a wide range of fields, from psychology to ecology.

Judith, "barely clothed and fresh from the seduction and slaying of Holofernes, glows in her voluptuousness. Her hair is a dark sky between the golden branches of Assyrian trees, fertility symbols that represent her eroticism. This young, ecstatic, extravagantly made-up woman confronts the viewer through half-closed eyes in what appears to be a reverie of orgasmic rapture," writes Eric Kandel in his new book, The Age of Insight. Wait a minute. Writes who? Eric Kandel, the Nobel-winning neuroscientist who's spent most of his career fixated on the generously sized neurons of sea snails

Kandel goes on to speculate, in a bravura paragraph a few hundred pages later, on the exact neurochemical cognitive circuitry of the painting's viewer:

"At a base level, the aesthetics of the image's luminous gold surface, the soft rendering of the body, and the overall harmonious combination of colors could activate the pleasure circuits, triggering the release of dopamine. If Judith's smooth skin and exposed breast trigger the release of endorphins, oxytocin, and vasopressin, one might feel sexual excitement. The latent violence of Holofernes's decapitated head, as well as Judith's own sadistic gaze and upturned lip, could cause the release of norepinephrine, resulting in increased heart rate and blood pressure and triggering the fight-or-flight response. In contrast, the soft brushwork and repetitive, almost meditative, patterning may stimulate the release of serotonin. As the beholder takes in the image and its multifaceted emotional content, the release of acetylcholine to the hippocampus contributes to the storing of the image in the viewer's memory. What ultimately makes an image like Klimt's 'Judith' so irresistible and dynamic is its complexity, the way it activates a number of distinct and often conflicting emotional signals in the brain and combines them to produce a staggeringly complex and fascinating swirl of emotions."

in 1973, the BBC aired an extraordinary documentary series called “The Ascent of Man,” hosted by one Dr. Jacob Bronowski

It was not an account of human biological evolution, but cultural evolution — from the origins of human life in the Rift Valley to the shifts from hunter/gatherer societies,  to nomadism and then settlement and civilization, from agriculture and metallurgy to the rise and fall of empires: Assyria, Egypt, Rome.

The tone of the programs was rigorous yet permissive, playful yet precise, and always urgent, open and exploratory. I remember in particular the programs on the trial of Galileo, Darwin’s hesitancy about publishing his theory of evolution and the dizzying consequences of Einstein’s theory of relativity.

The underlying philosophy behind sparklines—and, really, all of Tufte’s work—is that data, when presented elegantly and with respect, is not confounding but clarifying.

Tufte has shifted how designers approach the job of turning information into understanding.

“It’s not about making the complex simple,” Grefe told me. “It’s about making the complex clear.”

Are there things we should try not to know?

IBM says that 2.5 quintillion bytes of data are created each day. That is a number both unimaginable and somewhat unhelpful to real understanding. It’s not just the huge scale of the information, after all, it’s the novel types of data

many participants expressed concern about the effects all this data would have on the ability of powerful institutions to control people, from state coercion to product marketing.

as such a complex system that nobody believed that it corresponded to the physical reality of the universe. Although the Ptolemaic system accounted for observations-"saved the appearances"-its epicycles and deferents were never intended be anything more than a mathematical model to use in predicting the position of heavenly bodies. [3]

lileo that he was free to continue his work with Copernican theory if he agreed that the theory did not describe physical reality but was merely one of the many potential mathematical models. [10] Galileo continued to work, and while he "formally (23)claimed to prove nothing," [11] he passed his mathematical advances and his observational data to Newton, who would not only invent a new mathematics but would solve the remaining problems posed by Copernicus. [12]

Thus without pretending that his method could find the underlying causes of things such as gravity, Newton believed that his method produced theory, based upon empirical evidence, that was a close approximation of physical reality.

A surprising number of the conveniences of modern life were invented when someone stumbled upon a discovery or capitalized on an accident

wonder whether we can train ourselves to become more serendipitous. How do we cultivate the art of finding what we’re not seeking?

Croatian has no word to capture the thrill of the unexpected discovery, so she was delighted when — after moving to the United States on a Fulbright scholarship in the 1980s — she learned the English word “serendipity.”

haped abstractions called vectors. Pondering Hilbert space makes me feel like a lump of dumb, decrepit flesh trapped in a squalid, 3-D prison. Far from exploring Hilbert space, I can’t even find a window through which to peer into it. I envision it as an immaterial paradise where luminescent cognoscenti glide to and fro, telepathically swapping witticisms about adjoint operators.

Reality, great sages have assured us, is essentially mathematical. Plato held that we and other things of this world are mere shadows of the sublime geometric forms that constitute reality. Galileo declared that “the great book of nature is written in mathematics.” We’re part of nature, aren’t we? So why does mathematics, once we get past natural numbers and basic arithmetic, feel so alien to most of us?

Physicists’ theories work. They predict the arc of planets and the flutter of electrons, and they have spawned smartphones, H-bombs and—well, what more do we need? But scientists, and especially physicists, aren’t just seeking practical advances. They’re after Truth. They want to believe that their theories are correct—exclusively correct—representations of nature. Physicists share this craving with religious folk, who need to believe that their path to salvation is the One True Path.