The Clockwork Universe by Edward Dolnick
During the 1650s and 60s, the universal view at the time was that the world had been falling apart since Adam and Eve were banished from Eden. Any time disaster struck, it was because God was angry at the Europeans. This is why floods and earthquakes are still called, "acts of God."
The custom of saying "Bless you" dates from 1660s England. When someone would sneeze, it was thought of as the first sign of the bubonic plague. Saying "bless you" was a gesture to hope you didn't suffer and die.
The Royal Society was one of the first groups to welcome experiments to test ideas. At the time, accepted wisdom and eye-witness testimony of the past was the most credible form of "evidence." Anyone going against the grain and trying to seek out something "new," was not doing what they should be doing.
The Royal Society also created the idea of expressed knowledge and to do experiments in public and to share what you discover with others. Until then, discoveries and intricacies of fields were kept secret for only those who were "worthy". One might tell someone about their discovery or find, but the details were written in code, only to be used if someone tried to argue them. The early group of the Royal Society would have understood Gore Vidal's remark, "it is not enough to succeed. Others must fail."
The first time a major scientific discovery was announced in print via a periodical, was Newton's observation that white light actually contains all colors of the spectrum. He did so in a 1672 edition of Philosophical Transactions, the first ever scientific journal and that was started by the Royal Society.
"Planet" is Greek for wanderer.
Greek physics began by dividing its subject into two pieces:\ 1.) One was the cosmos above, where motion represents the natural state of things and goes on forever.\ 2.) The other was Earth, where rest is the natural state of things and motion must have an explanation.
After Galileo and Newton, science would "communicate in the language of mathematics, the measure of quantity," a language "in which no terms exist for good or bad, kind or cruel... or will and purpose and hope." The word force would cease meaning "personal power" and instead mean mass X acceleration.
Upon the invention of the telescope, Galileo made sure to point out the warfare uses first, even though he knew the true beauty would be in looking at the heavens with it. But this got the general public excited about what he saw and they understood it merely makes far away images look closer, and doesn't make a mirage of something. If he didn't do that, people may have excused his findings, blaming a technical error on the telescope.
The Great Chain of Being - a Seventeenth Century idea that all objects that had ever been created, from sand to angels, had a particular rank in a great chain that extended from the lowest to the low to the God's right hand. In this vein, there was a strange dichotomy between God being a mathematician and designing everything beautifully, and God allowing randomness to play (dichotomy because the physicists chose the former and biologists chose the later, but I'm not sure how they are mutually exclusive.)
Pythagoras discovered that there was a harmony in music if the instruments that were making the sound were similar in ratio. For example, if a blacksmith hit a piece of iron with a 12 pound hammer and the same piece of iron with a 6 pound hammer, the sound would be harmonious. But not if he hit the iron with a 9 pound hammer.
Was math invented or discovered? The Greeks came to say discovered, but it's an interesting thought.
On the one hand, geometry and algebra as concepts are clearly invented by humans. When have you ever gone for a walk and tripped over a 3?
On the other, what could be more obvious than that the truths of mathematics are facts about the world, whether or not humans catch on to them at all. If two dinosaurs were drinking water and two more came to join them, would that not meant there were four dinosaurs all together?
There are only five "Platonic Solids," three-dimensional objects where each face is symmetrical and all the faces are identical.
Though Kepler's incessant shape-rotating proved to be sort of useless, he did provide one correct answer in his Mystery of the Universe. Since he mapped each orbit of the planets getting bigger and bigger as you got further from the sun, that had to have meant it was moving slower. Therefore, whatever force propelled the planets around the sun must have grown weaker with distance. Before Kepler, the works of the sky had been descriptive and predictive, not explanation. No one before him had thought to ask how the planets move about their courses.
The planets travel around the sun in an ellipse with the sun at one focus.
The line from a planet to the sun is always equal in area in equal times. So the line from where a planet was one day 1 to the sun and where that planet was on day 10 to the sun can be connected and form a triangle. That area is always equal during an equal time period.
His third law is confusing, but the speed of planets can be multiplied by the length of the year raised to the 3/4th power. Note: I'm not sure I've been given a clear definition.
Any object launched into the air--arrow, bullet, cannonball--travels in a curved path like a parabola. The moving object covers the same horizontal distance during each second of its flight.
Horizontal movement of a falling object and vertical movement of a falling object are always independent of one another. This means the horizontal speed of something doesn't impact the vertical speed and so on. So a bullet fired from a gun and a bullet dropped below the gun, let go at the same time, will hit the ground at exactly the same time. If you launch something like this from a high enough altitude, and by the time it falls 4 feet the earth would have dropped 4 feet due to its curvature. This would continue happening, the object falling and falling and the earth curving and curving. This is how a satellite works.
The Law of Pendulums--a pendulum takes the same time to swing through a small arc as through a large one.
In the mind of Aristotle, math and science were to be used to understand the physical, real world better. There was no point in talking about a sphere rolling forever or weights falling in a vacuum because it wouldn't affect the day to day life. In Galileo's view, this was backward. The way to better understand the world was to look beyond those day to day distractions and focus instead on the deeper truths that governed those things. Even though there may never be a vacuum in nature, understanding how things react in a vacuum helps to understand those day to day interactions. It's here that the concept of abstraction is so important, it was a means by seeing truth unadorned by sinful man.
Zeno, the famed Greek philosopher, had tripped up those who came after him with his strange fables. Often, they had to do with motion and time, usually infinity specifically. It was difficult to find an answer to those fables, though philosophers debated for ages. Eventually, the Greeks decided they'd stay away from motion and time all together. This could be a reason as to why they seemed so infant in motion and time theories.
Galileo was the first to come up with a sort of definition, being: If a small section of a larger set of numbers is the same size as the large set. But even he didn't go much further than this observation/insight.
Eventually, they were able to find a conclusion to Zeno's problem. If they added up 1 and then 1/2 and then 1/4 and then 1/8 and then 1/16 and so on, the number would hit it's limit at about 2 - it would never go higher than that. So they concluded it would take 2 seconds to get to the other side of the room. This also helped solve the "speed at X distance problem". Before, they would decrease to a smaller and smaller limit: "X speed between 12 and 12:30, between 12 and 12:15, and so on. They realized this too had a limit and that would be the approximated speed at X distance."
Calculus is the Latin word for pebble. A reference to the heaps of stones once used as a calculating aid in addition and multiplication.
God could have made humans as intelligent as dogs. The world may be a bit happier that way, because we wouldn't be able to understand and conceive of evil, cancer, sickness, or disaster--but this assumes God's intention was to create a happy, meaningless world. Surely that wasn't God's goal. So this begs the question, what is God's goal? Why would he give us the capability and capacity to understand the good and the bad things of this world, but be able to do only very little about them all. Essentially, we're living at the mercy of them. God had conceived every possible universe, and this was the best one, given the boundaries God put on himself (not the boundaries that were on God). If he designed us in a way that we only chose good and never evil, we may be great but we'd be completely autonomous beings.
v = 32t is the only equation we need to determine the speed of a falling object at any give time. Where v is velocity and t is time elapsed.
Acceleration is a measure of how fast velocity is changing. Velocity is a measure of how fast position is changing. And position (my words here) is a measure of how fast everything around an object is changing in relation to that object.
The group was one of curious men studying the heavens and scribbling in their notebook.
God was a mathematician, seventeenth-century scientists firmly believed. He had written His laws in a mathematical code. Their task was to find the key.
On Newton's lack of travel: "The man who explained the tides never saw the sea" p.48
"To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature. If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in." -- Richard Feynman
Change came not from finding new answers to old questions but from abandoning the old questions, unanswered, in favor of new, more fruitful ones.
Aristotle had asked why. Galileo has asked how. Aristotle's why explained the world. Galileo's how described it.
What is a man in the midst of infinity? -- Pascal
Both telescope and microscope had opened up new worlds. The new vistas served to reinforce the belief that on every scale the universe was a flawless, harmonious, and unimaginably complex mechanism.
Only those who themselves have wandered lost, wrote Einstein, know the misery and joy of "the years of searching in the dark for a truth that one feels but cannot express; the intense desire and the alternations of confidence and misgiving, until one breaks through to clarity and understanding."
"The mission of science was to honor God and the best way to pay homage was to discover and proclaim the perfection of his plans."
The discovery of Pythagoras' Theorem was so amazing because:\
- One, Simply by thinking, without using any real tools, they had discovered one of nature's secrets, and eternal and never-before suspected truth about the structure of the world.\
- Second, they could prove it. Unlike other observations, this was definitely provable and not just true but necessarily true. "One of God's thoughts, finally grasped by man."
Abstraction is the pathway to truth.
"As a blind man has no idea of colors, so have we no idea of the manner by which the all-wise God perceives and understands all things" -- Newton
"A world with sin was better than a world without choice."
Giant wars are fought on narrow battlegrounds.
"For the price Newton had to pay for being a supreme intellect was that he was incapable of friendship, love, fatherhood, and many other desirable things. As a man he was a failure; as a monster he was superb" -- Aldous Huxley