Notes on “Euclid’s Window” by Leonard Mlodinow – Final Part

Page 240 Reading about quantum mechanics I swear I’m reading dialog from a Star Trek episode.

Page 242 “Without venturing into the philosophy of science, there is something about the phrase ‘fundamental theory’ which seems to imply that dozens of researchers should not be making their livings measuring its nineteen ‘fundamental’ parameters to accuracies of seven decimal places.” What?

String theorists rebel against the idea that this model is fundamental…their aim is to find a theory completely defined by general principles.” And when we do the Federation of Planets will visit us because we will be at the beginning of interplanetary travel!

This string is made of nothing, for to define a material composition implies a finer structure that they do not possess. Yet everything is made of them.” Sounds like the circular argument of “What created God?”

What does a “particle accelerator” do really?

Page 251 “People applauded politely, then ignored their work. If pressed, they said they didn’t believe it. In defense of these ‘people,’ the mathematics was (and still is) extraordinarily hard and complex. ‘People didn’t want to make the investment to understand it, and without the imprimatur of a statesman, they wouldn’t make the effort,’ says Schwarz.” And why would one want to? I haven’t seen any real application of these theories except just to know and explore, which is fine for some people. But why should an industry or government invest in this type of exploration really?

These chapters on string theory are really starting to put into concrete my ideas about what a mad scientist is. Are they all mad like in movies? They sit around with their big brains thinking about things and coming up with these awe-inspiring theories. And if no one listens or wants to invest in it, they go insane and kill themselves or become raving lunatics?

Page 255 Witten majored in History! Page 257“his work is having a major impact on the direction of modern mathematics, something Einstein’s work never did…driven by insights of mathematics, not physical principles as Einstein’s was.”

Page 259 M-theory! “In fact, not much is known about it at all, except that it seems to exist – a grander theory to which the five types of string theories are merely various different types of approximation.” “Witten used to say that the M in M-theory stood for ‘mystery, or magic, or matrix, my three favorite words.” All of this is beyond me. It sounds like they are just making it up out of thin air. Can you read my confusion?

Page 261 “Nature evolves with hidden order. Mathematics reveals it.” Or does it just try to make sense out of something that looks like it should make sense? The human brain loves patterns. Do we see real patterns in nature or are we creating it in our minds and then trying to put puzzle pieces together without seeing the big picture or knowing we have all the pieces?

Page 264 “Through Euclid’s window we have discovered many gifts, but he could not have imagined where they would take us. To know the stars, to imagine the atom, and to begin to understand how these pieces of the puzzle fit into the cosmic plan is for our species a special pleasure, perhaps the highest.” Science and mathematics may give us the answer to how things work, but they will never answer the why.

To the scientists before us, “we owe a debt of gratitude. They experienced the joy of discovery. For the rest of us, they enabled an equal joy, the joy of understanding.”

I really enjoyed reading this book. There is so much more in it than what I wrote here. I highly recommend reading it yourself, along with Mlodinow’s other books. It’s the joining of history, philosophy, and science that really sparks my curiosity and imagination and encourages me to learn more about a topic I thought I was forever hopeless to explore.


Notes on “Euclid’s Window” by Leonard Mlodinow – Part 4

Tomorrow I will post the last of my notes. Small bites in this book. The topic is pretty difficult for me, but so fascinating!

Page 211 “To physicists of the early twentieth century, non-Euclidean space was a fringe area of study. A curiosity, perhaps…not very relevant to the mainstream. The resistance, in Einstein’s case, lasted a few decades, but it gradually faded as the old generation died out and the new accepted what ever made the most sense, which was definitely not a solid permeating all space called ether.” Humans just don’t like change. Conformity is safer. We all generally know this to be true so why don’t we apply that to the world around us? The science will change again just like fashion and, at first we’ll be shocked and afraid of it, then generally accept its veracity.

Einstein was considered an enemy of the state by the Nazi’s in 1933 and sought asylum in the US.

Page 214 “Of his revolutionary work he wrote, ‘When a blind beetle crawls over the surface of the globe, he doesn’t realize the track he has covered in curved. I was lucky enough to have spotted it.’” That’s what relativity is, us in curved space and not even realizing it because we are so much smaller than the universe.

Moving on to Witten. String theory leads to M-theory (both of which we know very little). “…but which seems to be leading us to this conclusion: space and time do not actually exist, but are only approximations of something more complex.” Wouldn’t it be crazy if we accidentally opened the door on God, like finding the real Wizard of Oz? The more I learn about theoretical science, the more I am convinced of the existence of God.

Page 219 “The theory had been plagued by other ’embarrassments’ through the years, a physicist’s way of saying that it had implied predictions that seemed to have nothing to do with reality.” I would agree here. I can see why someone would love to spend their lives chasing these rabbit trails and I could see them some day having an impact on the world around us, like some kind of awesome Star Trek warp engine. But I don’t see why the government funds this kind of research. I don’t understand taking money from people by force and giving it to scientist to sit and dream of this stuff.

A Klein bottle helps describe a 5th dimension that helps us understand quantum physics/magnetism.

Page 233 1930’s “The Kaluza-Klein theory was a hint at something, a formal connection between theories, but not a structure that immediately gave anything new.” It was an idea that hinted at a bigger picture and wasn’t really studied again until the 1970’s.

Einstein was bothered by the way Kaluza made money to support his family by tutoring at the college. This is one thing that bugs me about Einstein. Kaluza found a way to make money and take care of his needs while he did his research to solve the physics puzzles he loved. So did Einstein. Why is that such a bad thing?

Page 236 Talking about smashing particles into each other at high speeds to see the parts within. Relating it to smashing cars into each other in the hopes of seeing a bolt throw free that was part of its structure. “There is one big difference, though. In experimental physics, smashing a Chevy into a Ford could result in an explosion of parts from a Jaguar. Unlike autos, elementary particles can morph into each other.” What?!

Page 237 “Do you ‘discover’ a theory or ‘invent’ one? Are physicists kids with flashlights searching the park at twilight for traces of truth, or are they kids with blocks trying to build structures high before they topple?”

Note’s on “Euclid’s Window” by Leonard Mlodinow – Part 3

Page 160 “If space were empty, it was thought, a wave could not travel through it.” The theory on the existence of the “ether” to conduct the light energy from the sun through space. 1800. Waves of energy have to have something to travel through, right?

Page 172 “1884…the luminiferous ether is…the only substance we are confident of in dynamics. One thing we are sure of, and that is the reality and substantiality of the luminiferous either.’ The bottom line was that Maxwell’s electromagnetic theory requires waves, and waves require a medium.” It’s always so fascinating that scientists in all times are so confident about their theories and experiments that they hide the reality from themselves. They seem blinded and held back from discovery by assuming that their previous discoveries are correct.

Albert Einstein “explained the observed behavior of light traveling through space. Space and time were forever joined…”

Page 176 “Unfortunately, as today, rote learning was the focus of most schoolwork, and rote learning was never one of Einstein’s strong suits. Quick to appreciate a child who might immediately yell “north” when asked in which direction a compass points, they had little appreciation for one who instead ponders, as Einstein did at age five, what invisible force might cause it to do so.” And this is exactly my problem with school itself and the one of the big reasons I did not send my children to one. It wouldn’t be so bad if the schools saw children like this and decided they needed another more in depth form of education instead of school, but what they do is decide this child isn’t right and needs help fitting in. In Einstein’s day they removed him from school. Today we drug them so they’ll pay attention. How many genius’ have we lost?

Page 179 Einstein’s words about the curriculum at school, “One had to cram all this stuff into one’s mind for the examinations, whether one liked it or not. This coercion had such a deterring effect on me that, after I had passed the final examinations, I found the consideration of any scientific problems distasteful to me for an entire year.” Because pretty much every thinking person needs to recover from this type of mental trauma. And some never do. It isn’t education or learning, it’s brainwashing.

Page 189 Getting deeper into relativity, I’m lost again!

Page 190 “Though his special theory of relativity had many triumphs (the explanation of the longer lifetimes of fast-moving particles, the equivalence and convertibility of energy and matter), Einstein was smart enough to know that those who had spent their lives maintaining and decorating the castle might not offer schnapps and a pat on the back to the guy who destroyed it. He braced himself for attack.” This is the same feeling I’m getting when I explain to people that you don’t need schools to educate children, a strong family will do just fine. There is a whole economy built up around schools now. I’m fairly certain it will be a major upset when the people realize that it’s a waste of money, time, and energy.

Einstein working at a menial job just like the rest of us, working on physics on his lunch break and finally dropping the job to take a university position. That kind of stuff makes me happy.

Page 202 Something about ‘redshift’. I have to look into that more. Is that what we use to tell something about a distant star?

Page 204 “As Einstein said, ‘If we knew what we were doing, it would not be called research, would it?’”

Notes on “Euclid’s Window” by Leonard Mlodinow – Part 2

Page 103 “Not long after Thabit, Islamic support for the sciences dwindled. In one locale a scholar even complained that where he lived it was legal to kill mathematicians. (This was probably less due to a disdain for nerd than to mathematicians’ habit of studying astrology, which through history was often connected with black magic and considered dangerous rather than amusing as it is today)” That’s a relief! I thought they just didn’t like nerds! What is up with astrology anyway?

Page 105 “Non-Euclidean spaces are almost Euclidean for figures that are small – and we live in a relatively small corner of the universe.” Same goes for quantum theory for ultra small things. Euclid’s geometry works perfectly fine for regular, every day things on our planet but not for off or inside it. So it does make sense to study and learn it!

Page 116 “In Gauss’s day, science and philosophy hadn’t completely separated. Physics wasn’t yet known as “physics” but “natural philosophy.” This makes sense and I really think they still are very closely related. Much of what we call the study of physics is the study of things you cannot see, you can only see their effects and make an educated guess as to what’s happening. It’s a pretty beautiful and useful thing!

Page 117 “Kant, noting that geometers of the day appealed to common sense and graphical figures in their ‘proofs,’ believed that the pretense of rigor out to be dispensed with, and intuition embraced.” Why does that not surprise me about Kant? I swear the guy can’t see beyond the end of his nose.

Page 126 “A couple decades after the discovery of hyperbolic space, another type of non-Euclidean space was discovered: elliptic space.” I still don’t understand how these are “discoveries”. It’s not like they stumbled across it and figured out what was happening. None of these guys went out into space and found out the missed the moon by a mile because they were using Euclidean math. To me, it seems like they have active imaginations and sit around working out the math to match their dreams. I guess in a sense, I’m agreeing with Kant but probably because I just don’t understand.

Page 127 “Gauss faced the challenge of patching together a two-dimensional map from three-dimensional data affected by variations in elevation as well as the curvature of the earth.” Mapping! That’s where Euclidean math doesn’t match up. We couldn’t have awesome GPS devices that tracked where we are on the earth and give accurate directions if not for Gauss!

It’s funny reading this book. I’m not big on math. At times, I really feel so lame but I love the stories behind the discoveries. When I read about the details I get a bit lost, like I’m looking out a very fuzzy and distorted window. Sometimes I can start to see what the picture is in one spot but my eyes shift for a second and it’s gone.

Page 143 “today we seek to axiomatize all our assumptions, and accept nothing as truth merely on the basis of “reality” or “common sense.” Who’s he talking about?!

And on to Einstein!

Einstein came up with non-Newtonian physics. Page 155 “In Newton’s view, space is ‘absolute,’ a fixed, God-given framework upon which to lay the coordinates of Descartes.”

Reading about Michelson’s life, it’s fascinating to think that a person can be so brilliant in one aspect but miserably inept in others. It’s something normal and natural that we’ve always tried to balance out in education instead of embracing it. What if we encouraged a person to pursue their passion and not worry themselves with other things? What if we knew that, while I’m wonderful with mathematics, I’m not so great at history, so I’ll rely on people well versed in that and take their opinions and conclusions into consideration?

Notes From “Euclid’s Window” by Leonard Mlodinow (Part 1)

“The Story of Geometry from Parallel Lines to Hyperspace”

Page 6 “The Egyptians had always had death, but with wealth and settlement, they now also had taxes. Taxes were perhaps the first imperative for the development of geometry, for although in theory the Pharaoh owned all land and possessions, in reality temples and even private individuals owned real estate.” Ahh “death and taxes”! Geometry was developed to calculate land area and water levels for taxes. Crazy.

“rope stretcher” used to perform surveying of land. “Hypotenuse”, Greek for stretched against.

Here’s another interesting thing! The Babylonians did not write equations. It was all word problems. Kind of makes it difficult to make any changes. “The oldest know use of the plus sign for addition occurs in a German manuscript written in 1481.” To think that this type of math is such a recent thing in history.

Page 17 “To the Greeks, not the Egyptians, goes the credit for the idea that brings romance and metaphor to mathematics: that space can be a mathematical abstraction, and, just as important, that the abstraction can apply to many different circumstances.” Leave it to the Greeks to abstract on something! Science and philosophy had not parted ways just yet.

Page 18 “The Pythagorean theorem, too, must have seemed magical.” “It’s a discovery that would surely rate a headline on the front page of the New York Times: Surprising Regularity Discovered in the Right Triangle,” and in smaller print, “Applications Still Years Away.”

Page 21 “There is also a distinction between intelligent talk and blather, a distinction that Pythagoras did not always make.” Part of why I like this book is the commentary! Pythagoras had some pretty wild ideas from his fascination with numbers. It just goes to show you that someone can be a genius in some aspects but a complete nut in others.

Page 26 “Today people are murdered for many reasons – love, politics, money, religion – but not because somebody squealed about the square root of 2. To the Pythagoreans, though, mathematics was a religion, so when Hippasus broke the oath of silence, he was assassinated.” Holy cow they took math seriously. I’ve heard before that Pythagoras had quite the cult going and was a bit of a nut but this takes the cake. And why? Why keep math such a secret?

Page 29 Euclid’s Elements was lost and found several times, as well as re-written. And Euclid never claimed to have “discovered” them, only wrote them down.

Page 38 Euclid’s postulate of parallel lines was a universally accepted “fact” for centuries, but eventually someone questioned it.

Page 41 Eratosthenes used geometry to calculate the circumference of the earth in 212 BC! That’s pretty amazing. He couldn’t even see the earth or use a calculator.

Page 43 Claudius and Ptolemy (not the king) and Hipparchus made a model of the earth centric universe that lasted until Copernicus (1500). So for 700 years the earth centric model served the scientists just fine. It explained mostly everything, eclipses were predicted and the model looked just right. The science was settled. And then this crazy Copernicus comes and says it’s all wrong. Is there any wonder that people were angry at him? Doesn’t this sound like today? I’ve always heard that it was the crazy non-scientific Christians that were most angry at Copernicus because his theory would disprove the Bible. But the “science” they were following pre-dated the new testament, not the old but was anyone but the Jews listening to that when the science was decided? It seems to me that the scientists had a problem with changing the model.

Page 45 “the principal translator of Euclid into Latin was a Roman senator from an old established family, Anicius Manlius Severinus Boethius, a kind of ‘Reader’s Digest’ editor of Roman times. Boethius abridged Euclid’s works, creating the kind of treatment suitable for students preparing for a multiple choice test.” Much like today, the Roman’s were not interested in creating/promoting individuals that take care of themselves. They wanted subjects that could work and think basically but rely on the rulers to take care of the bigger stuff. It would make sense that they wouldn’t really be using mathematics to liberally broaden minds, but to get them to know enough to imagine they are free.

Here’s another note I made in the margin while reading about the growth of the Roman empire. Christian leadership grew out of the Roman Empire, control by fear of God instead of government, they combined the ideas to serve man. This is not Christianity. It is not what Jesus preached. It is mankind using religion as a weapon against mankind, to control.

Page 54 We’ve moved on to Descartes now. People act as though we have evolved past religion but we’ve only replaced it with modern science. Now to question the “science” is to commit heresy and you are punished in similar ways, though not as violently (usually). Science changes its theory and law just as quickly as religion. If you don’t think that is true, just question something like global warming, GMO’s, and evolution.

Page 64 The 13th and 14th centuries. “The weather gods, too, were in a foul mood. Europe at the time was at the start of a wet and cold period so distinctly miserable that today it is called the little ice age In the Alps, glaciers advanced for the first time since the 8th century. In Scandinavia, ice floes blocked the North Atlantic shipping lanes. Crops failed. Agricultural productivity plummeted. Famine was widespread.” It’s just too bad they didn’t know to fix climate change with some new laws and taxes.

Page 73 Ahh the graph. I can’t believe this had to be invented. How crazy is that?! “The power of graphs in helping the non-mathematician analyze patterns of data stems from this same connection of data to geometry. The human mind easily recognizes certain simple shapes – lines and circles, for instance. When looking at a collection of points, our mind tries to fit them into one of these family patterns. As a result, we notice geometric patterns when data is graphed that we might easily overlook when staring at a table of numbers.” Awesome, right? Shown a table of numbers, most people would not see anything important. Some would, but even more will see the point if put into a line or circle.

The whole time I’m reading this book I’m thinking, “If only I had been assigned this book in high school instead of more numbers to look at!” This is the kind of thing that make homeschooling better than regular school. We have the chance to learn what our minds are drawn to, especially since we have the internet full of new resources.

Page 78 Reading about Oresme and his “I indeed know nothing except that I know nothing.” The more we learn and discover, the more we find to learn and discover. I doubt it will ever end. But I hear and read about scientists who decide that the science is settled and there is no reason to look any further. That doesn’t sound like a scientist to me.

Decartes early life reminds me that everyone has a purpose in this world and we should respect life and try to preserve it as much as we can. His mother died after giving birth to him and he was a sickly child but his father nursed him at home and kept him in bed, still learning and exploring through books and tutors.

I’m wondering if there is really any point to studying Euclid anymore. I tried it on my own a few years back and found it tedious and never really got past the first few points. Since the discovery of curved space, Euclid’s theorems no longer stand anyway, right?

Page 98 Ptolemy (2nd century) “assumed the alternate form of the postulate, then derived the original from it. What should we think of Ptolemy? Did he live in an intelligence-free zone? Should we picture him racing to his friends, exclaiming, ‘Eureka! I found a new form of proof: the circular argument.’ Mathematicians would not make this mistake twice. They would make it over and over and over.”