Don’t Say You Weren’t Warned

Yesterday I wrote something about how I studied calculus without having to read Newton’s notes, and I said I probably would not have understood them because only one bit of his mathematical notation survived. Today I decided to look it up, and I found out the story is not quite that simple.

Cambridge University has Newton’s papers. Some of them, at least. I am too lazy to check. Google and come back and look smarter than me. Cambridge has put images of the papers online, partly for reference purposes, but also partly to make the rest of us feel stupid.

I admit, the last phrase of the last paragraph is conjecture.

It turns out there are several reasons why I would not have understood his notes, and his notation is probably not among them. The biggest obstacle would have been his copious use of Latin and Greek. I was “educated” in American schools, so the only Latin I know is pig Latin. As for Greek, I’m halfway through The Iliad, and I use Windex as a topical antiseptic.

Actually, I took a semester of Latin in high school, but, following my strict policy, I did nearly nothing, so I got a D.

Latin is a horrible language. Like Russian, Latin is inflected. That means you have to change the endings of words depending on how you use them. If English worked this way, you might have to write things like, “I shot the cow,” and, “The coworum rolled over and died.”

Leo Tolstoy and his wife had different last names because he was male and she was female. Terrifying.

When I was studying physics, I got really handy with exponents. Typically, when you take the root of an expression (once you get past about the 21st grade, you have expressions instead of numbers), you put a radical around it.

It looks like I’m wrong. I checked, and it’s a “radical sign,” not a radical. It’s a little box sort of like a division box. A radical sign means “square root.”

Radical signs are stupid. A radical sign can’t mean anything other than “square root” unless you add a little superscript to the left of it. It’s sloppy and cumbersome. I didn’t like it.

“Square root” actually means “to the 1/2 power.” You can have any real number as an exponent. It doesn’t have to be 1/2 or an integer. It can be 2/3 or pi or whatever you like. It can be annoying, using a radical sign to express powers not involving multiples of 1/2.

I worked around that. I used to use parentheses with fractional exponents. For a square root, I used “1/2.”

This leads to all sorts of conveniences.

Say you want to put the square root of something in the denominator of a fraction. You just make the “1/2” negative. What if you want a cube root? Use “1/3.” What if you want the square root of the cube? Use “3/2.”

What if you have an equation with an expression with an exponent on one side, and you want to get rid of the exponent? You invert the exponent, squeeze it between the bars of the equal sign so it pops out on the other side, and apply it there. For example, if you have 4 = (16)^1/2, you turn it into 4^2 = 16. It works with any real number. For all I know it works with complex numbers and quaternions. Don’t ask me what a quaternion is.

Well…of COURSE it works for complex numbers. I’ve seen like a billion complex exponents.

This is exciting, isn’t it? This is what you come here for.

If you have a big string of expressions with exponents, multiplied by each other, you just add the exponents. If you want to move an expression from a denominator to a numerator, you multiply the exponent by -1.

This is really helpful, because it helps you put everything on the same line, and it turns multiplication and division into addition and subtraction.

Why tell you all this? Because Newton didn’t do it. If he wanted to take the sixth root of something, he put THREE radical signs around it. I would have lost my mind counting the brackets.

I guess if you’re Isaac Newton, you find all forms of notation unbearably simple, so it doesn’t matter what you do. Me, I get confused writing grocery lists.

If you look at Newton’s notes, you will see why he accomplished so much. Yes, he had a giant brain, but he also did tons of math. He filled page upon page. Much like the ancient Greeks, who put up with Homer’s endless droning and hour-long similes, Newton did not have TV. Also, when he invented calculus, he was hiding on a farm while the plague destroyed England. Talk about bored. Put me in Fargo, North Dakota with no broadband, a ream of paper, and a box of fresh pencils, and I might invent something, too.

But probably not.

I would definitely make a lot of paper airplanes.

Newton wrote out big, ponderous expressions, and they looked a lot alike, so he must have had tremendous powers of concentration in order to keep everything straight.

For tiny-brained mortals like me, clear notation matters.

I hated the way my old physics profs wrote things. For example, a professor talking about a function named A might call a variant of it A-prime, and then when he wanted to change it to make a point, he would call it A-double-prime, which was followed by A-triple-prime. Then he might combine them in one huge expression with about nine A’s in the numerator and fifteen in the denominator. I never understood that. It’s not like there’s a fee for using new letters.

I wrote a pretty insulting essay about it, claiming there actually was a fee, and that when professors used Greek letters, they had to pay royalties to the Greeks.

I was not popular in grad school.

If you feel like a thrill, Google and find Cambridge’s photos of Newton’s big notebook, known as the “Waste Book.” It’s a real page-turner, if you’re an alchemist and religious fanatic who reads ancient languages fluently.

Unfortunately, it’s math and science, so there are no Cliff’s Notes. Not that I’m saying the impossibility of writing Cliff’s Notes for math and science proves liberal arts subjects are a joke.

But I would not argue if you took it that way.

But Will the Global Warmers be Able to Swim When the Water of Truth Rises?

I want to add a couple of things about the global warming…I am looking for a word that doesn’t sound like “fundamentalists” or “Taliban”…adherents. Yes…adherents. I went with that before, and it worked.

The GWA’s (save me some typing) have done something scientists should never do. They have painted themselves into a corner and provided themselves with a compelling interest in seeing themselves proven right. To be more accurate, they have a compelling interest in not being proven wrong. It’s okay if they’re not proven right, but being proven wrong would be catastrophic. They would look like idiots and cultists, and their professional credentials would be cheapened considerably.

Because they have been so adamant and intolerant, the only way they can be sure of avoiding disaster is to force the rest of us to go along with their strange, draconian “reform” proposals, even if they don’t work.

I will explain.

Let’s say they get their way, which is likely. Let’s say they get us to spend astronomical sums, choking industry and crushing progress, putatively in order to reduce global warming.

By the way, I don’t call it “climate change,” because that’s weasel language. They used to call it global warming, and then certain places got very cold, appearing to disrupt the whole theory. They switched to “climate change” so they would be able to say that any change, cold or hot, was due to bad old greenhouse gases. I think that was disingenuous and contrived. I think they’re hedging their bets. So I will stick with global warming.

Say it’s going to warm up, or say it’s going to cool down. Man up and take a position, or admit you don’t know the truth.

To get back to our scenario, they get their way. They stuff socks in all our tailpipes. They make us ride bicycles and use abominable poisonous light bulbs that don’t work. They make us turn off our lights at 8 p.m. They remove the element carbon from all future periodic tables and replace it with an element called “Priusine.” Whatever it is they want, they get.

That gives us three possible outcomes.

Outcome 1: nothing happens. They can say they arrested the progress of global warming. Their grants are saved. Comrade Lysenko smiles down from atheist heaven, where he spends eternity waiting in line to buy toilet paper. All is well.

Outcome 2: the planet heats up. They can say we didn’t do enough. It’s still George Bush’s fault. We didn’t listen in time. We didn’t give them enough government money. We didn’t go to Burning Man and pray to Cthulhu with them. Our fault. They still look good.

Outcome 3: the planet cools down. It worked! They were right! It’s just amazing how smart they were. Time to put the rest of us in vegetarian gulags where everyone gets to use whatever bathroom they want, which was obviously the right move to begin with.

Now, what if we do nothing?

Outcome 1: nothing happens. They were wrong. They look stupid. People distance themselves from them. College students start demanding safe spaces to get away from them.

Outcome 2: the planet heats up. Thank Gaia. They were right. We should have listened. Now we need to give them more power, because it would be even hotter if they hadn’t gotten their way. Fire up the bongs with the special carbon traps and put on some Justin Bieber!

Outcome 3: the planet cools. Wow, do they look stupid. They risk being beaten to death by mobs swinging pillowcases full of coal.

If we do what they want, they can’t lose. If we don’t do what they want, the planet absolutely has to heat up, fast, or they’re toast.

Surely they’ve figured this out, so now we can count on them putting on a full-court press, not out of confidence that they’re right, but out of terror that they might be wrong.

Personally, I think they’re wrong. I am not a meteorologist or climatologist, but the people who are against them seem more credible than the liars and hysterical polemicists who get attention for backing them.

I was not favorably impressed by the famous global warming fraud scandal, nor am I impressed by the fake movie polar bears which were used to convince us that aquatic mammals, for the first time in history, can’t swim. I am not impressed by Al Gore, who, to me, appears to be mentally ill and incapable of telling the truth. He got rich off of global warming, after his family got rich from oil, and his house, which is clearly visible from Venus, uses more energy than the entire northeast power grid.

“Carbon credits” are not only silly, they’re an insult to my intelligence. If carbon credits made sense, wives would sell their husbands adultery credits, and the cops would sell angry people murder credits. When Leo Dicaprio travels to complain about fossil fuel, he uses a private jet. Come on. If you’re going to pull my leg, at least pretend you’re serious. When Bruce Jenner decided he was a woman, he grew breasts, wore makeup, and made sure he shaved every day. A quality hoax demands a certain level of commitment.

If they prove AGW (figure it out) exists, fine. I’ll be quiet. But the way they’re handling it now is a disgrace.

And Little Lambs Eat Ivy

I don’t get into politics much these days, and no one is interested in religion, so I do not attract trolls like I used to. They used to take up a good percentage of my waking life.

A wise man (clearly not me) once said that it is not absolutely necessary to gainsay everything you disagree with on the Internet. I wish I had thought about that in 2002, before I started blogging. I would never have gotten involved in whack-a-troll, and I would not have treated well-intentioned commenters like trolls, which I am sure I have done. Worse than that, I’m sure I have corrected people who were right when I was wrong.

Today I showed up to see if anything was going on here, and I saw a somewhat trolly comment in the approval bin. I don’t have it in front of me (it was accidentally deleted), but the first line was something about me being confused–not a sign of warmth or good intentions–and the commenter tried to correct me about the concept of escape velocity. He wrote some really strange things which just were not correct. They were so wrong I did not even understand them. It’s like the famous quip from physicist Wolfgang Pauli, who once disagreed with someone so intensely, he said, “That’s not even wrong.”

I hold comments for approval for good reasons, and one reason is to avoid getting into comment wars with people who are not able to understand the topic. There is nothing worse than arguing with a person who doesn’t know what’s going on.

How does he know when he loses?

I guess they just figure they’ve won when you stop responding.

I am not a real physicist, if a physicist is a person who can sit down with no preparation and do physics well enough to be paid for it. On the other hand, I am a real physicist by the definition of the people who sell magazines to former physics students! If you belonged to the national physics honor society at one time, and now you’re a realtor who can barely integrate 1/x^2, but you can pay for a subscription to Physics Today, you, my friend, are a physicist.

I studied for several years, I got a degree, and I went to grad school in physics for a year and a half, at the end of which my brain turned into a pork rind, and I had to quit. I remember little bits of what I learned. Don’t ask me to write out the Laplacian for spherical coordinates, and don’t even talk to me about quantum mechanics, but I know a couple of things.

I had to look “Laplacian” up just now to make sure I didn’t really mean “Lagrangian.”

Anyway, I didn’t pull my terrific explanation of escape velocity out of a bong. Here is how it works, and this time I actually looked at someone else’s web page to make sure I didn’t say anything crazy. Does that make me a plagiarist? No, because it would be like plagiarizing addition. And it agreed with what I said to begin with.

There are two kinds of energy in classical mechanics: kinetic and potential. To have kinetic energy, you have to be moving. To have potential energy, you have to be in a situation where something or other has the potential to make you move.

If you’re falling from a building, you have kinetic energy, which will be transferred to whatever you land on. If you’re on top of a building, you have potential energy, because if you fall off, you will rapidly start to move.

If you’re a rock in a slingshot, pulled back all the way, you have potential energy. If you’re released and start flying through the air, you have kinetic energy.

The energy in an object can go back and forth between kinetic and potential energy.

Think of a bouncing ball.

As the ball leaves the ground, it’s moving at its highest possible speed. It’s going as fast as it will ever go, because as it moves upward, gravity will slow it down. All of its energy is kinetic.

At the top of the bounce, the ball is not moving. It has no kinetic energy. All of its energy is potential energy. As it falls again, that energy will turn back into kinetic energy.

Balls don’t bounce forever, because energy is lost to air resistance and the force it takes to flex the ball and radio waves and God knows what else. In the real world, I mean. In physics books, balls bounce for eternity, because the problems take place in ideal worlds that don’t exist.

Are you with me?

Imagine an object on the surface of the earth. There is no air resistance, because OUR [fictional] earth is ideal. There is no friction. There is only gravity. There isn’t even any sales tax.

If you shoot the ball upward, it will return to earth, because it will be slowed down by gravity. In reality, it’s falling from the instant it leaves the ground. It’s falling AND rising. By “falling,” I mean it’s accelerating downward. If you don’t understand that, don’t worry about it. No one cares.

Satellites in orbit are always falling! They’re going sideways so fast it cancels out the fall!

Sorry. That just popped out. Ignore it.

As our ball goes up, it loses kinetic energy because it slows down. It gains potential energy. That potential energy is related to the distance the ball rises. It increases on the way up.

If you do the correct definite integral with the correct endpoints, you find that if the ball rises all the way to infinity, the amount of potential energy it gains will not be infinite. It has a cap. The potential energy a ball can gain as it leaves a planet is limited.

If, when you shoot the ball upward, you give it enough speed to give it kinetic energy greater than the total possible potential energy, you have given the ball what is known as escape velocity. It escapes from the planet’s pull. The planet can’t pull it back. It keeps going forever.

This only works on ideal planets, which are rare, although Bernie Sanders says he knows how to create one using other people’s money. It didn’t work too good in Cuba and North Korea, but we can always hope.

If this kind of thing actually interests you (stop laughing), you can find escape velocity explained, with integrals, all over the Internet. I’ll link to a page which lays it all out in a couple of paragraphs.

Gravitational Potential Energy, Explained

An interesting thing to observe, if you look at the integral, is that the smaller the radius of your planet is (for a given mass), the harder it is to leave. This is why it’s pretty hard to come home from a vacation on a black hole. Lots of mass means lots of gravity, and a small radius means it’s sort of crammed into a tiny area, so it’s strong.

What I wrote is not advanced physics. I guess it would be in the first semester of university physics, which is the low-level class your doctor took. It’s not controversial or complicated.

Now, if you ask Bernie Sanders what he thinks, you may get a different answer. I can’t be responsible for his interesting notions.

I don’t plan to start publishing trolly-looking comments. Life is too short. My advice to irritated commenters is this: put them on your own blog, where they will actually see the light of day. I delete them permanently.

I apologize if the comment I dumped was not intended to be a troll swipe, but really, I could not see any way to make it mesh with reality, so I assumed the worst. Another bad Internet habit.

Maybe I misunderstood the commenter’s jargon, but in any case, it’s clear that what I wrote initially was correct. If anyone else wants to come by and challenge trivial results of undergraduate physics problems, please don’t.

Free Knowledge for Nerds

I’m back.

I haven’t written anything here lately, but I have had all sorts of remarkable experiences. The practice of praying in tongues keeps paying off, not just for me, but for people I have encouraged.

My young friend who got a music scholarship at the University of Miami is in the neighborhood most weekdays because of class, and we meet and spend long sessions in prayer. You wouldn’t believe the revelation he gets. It’s tremendous.

That’s not what drove me here to write, though. I had a wonderful experience over the last couple of weeks, and I really don’t know anyone who would appreciate it, so here I am.

I have always regretted burning out on physics and quitting school. I could not do anything about it. I’m sure the people I worked with at the University of Texas think I just wasn’t smart enough, and that I was a typical washout, but that’s not true. I got a physics degree in three years, and when I started, I didn’t really know algebra, and then I got accepted by a top grad program. You can’t be stupid and do that. I just got burned out, and nothing I did helped. I panicked and resorted to ADD drugs, and they made things worse. And the people who ran the UT physics department didn’t care at all. They did give me one or two breaks, but they were small, and the impression I got was that they wanted me out of there fast, without an ADA lawsuit.

Before I was admitted, I was warned that UT didn’t care about students, but I didn’t know how true it was. And I saw my lab students get the same treatment. I guess that’s Texas for you. There seems to be something about the high percentage of Germans there that makes Texas different from other Southerners. They can be extremely rigid and cold.

I believe the real reason I failed was that I was out of line with God’s will. Every Christian is on the enemy’s radar, and the enemy is real, and he will make bad things happen to you if you’re an idiot, which I was. These days I have supernatural tools to put my enemies in my place, but back then, I was defenseless, so I lost to jerks and creeps who probably spent their entire childhood and adolescent years receiving wedgies from younger kids and being pushed in the mud by Brownies.

Over the last couple of years, I’ve noticed online education opportunities, but they have taken a while to develop into something useful, and I didn’t really work hard to take advantage, so it wasn’t until recently that things started to click.

In February, I felt like I absolutely had to find a good online electronics course. I build tube amps, and I took two electronics courses in college, but I have no idea what I’m doing. The first course I took was somewhat practical. The second was all theory, and it was about things like the photoelectric principle, which is not going to get anyone a job designing computers. I’ve forgotten a lot of what I learned, and I didn’t learn that much to begin with.

I Googled and came across EDx.org, which is a site started by Harvard and MIT. You can go there and take courses from excellent professors at various universities, and you can even get certificates of completion. You can submit homework assignments, do labs with virtual equipment, and take tests.

I signed up to audit 6.002x, which is MIT’s basic electronics course. They provided an online version of the textbook for nothing. It was too late in the year to take the course for credit, but I already have credit for a similar course, and I don’t have any use for a certificate anyway.

The online textbook was nearly impossible to read, but I found the real book on Ebay. The American-market hardcover version runs $90, but I found the Indian edition, which is paperback, for about $20. I ordered it.

Near as I can tell, you can’t get the lecture videos unless you start from the beginning of the semester. That’s bad. But today I found the answer to that problem, and in doing so, I found the mother lode of free nerd classes. MIT has a site that provides a huge number of classes, for the princely sum of nothing. And the lectures are all on Youtube!

They even provide PDF lecture notes.

You can’t get credit, but on the other hand, you don’t have to submit a 1500 SAT or pay $60,000 per year (I checked) in tuition and costs. And if you ever have to get credit, you can take the MIT online class first and then show up at your local college and blow everyone out of the water.

This is wonderful. I feel like I’ll finally have a tiny bit of the knowledge you need to be competent with electronic devices. And the structure makes it easy to stick with it.

If you wish you could improve your brain, but you can’t go to college right now, this is a great resource.

I’ve already written about other providers, such as Khan Academy and NPTEL, but MIT is a cut above, because they provide real courses with real materials.

It’s incredible, really. Twenty years ago, I had zero chance of ever attending an MIT lecture. Now I can attend as many as I can stand, in my garage.

I’m sure there is stuff out there for liberal arts people, too. Truthfully, though, do you really need a professor to teach you about art history and novels? I’ve had plenty of liberal arts courses, and I learned absolutely nothing–nothing–I could not have figured out on my own with a library card.

Check it out if you want. If you’re technically inclined, you will never see a better bargain than this: MIT Open Courseware.

If you have a brainy kid who wants to get a head start on college, remember, taking courses online before you take them in person isn’t cheating. It’s just smart thinking.