24 thoughts on “Seventeen Equations”

    1. There’s a fun simplification you can make. For a free body, if you calculate the center of percussion from the point of applied force (using the parallel axis theorem), and treat the center of percussion as the fulcrum of a lever, with the load located at the center of mass and the effort at the point of the applied force, you can solve both rotational and linear acceleration in one equation. (If you try to solve the equations for the motion about the center of mass instead of the center of percussion, the combined equations are much more complicated.) The object’s inertia is the total mass divided by the mechanical advantage of the resultant lever (the term moment of inertia probably came from the length of the moment arm in this setup). This is also probably why Newton said that objects resist acceleration according to their inertia, instead of just saying mass.

      This trick could possibly simplify the kinematic equations of robot motion.

      (I just had the shock of pulling up “center of percussion” on Wikipedia to better explain this, and finding that I’m 3/5ths of their references on the topic! Yikes!)

  1. Um, but have the geeks in the STEM fields, like, read the Iliad? The story is centuries old, but the basic elements apply to every modern workplace, especially in the STEM fields which differentiate into “leadership” and “talent.”

      1. I am harkening back to an earlier thread, the one on Napolean and what made him an effective leader, even though deep down he was a backside-of-a-camel. Napolean knew how to lead in terms of appealing to a person’s primal motivations, that is, until he got what what he wanted and cast them aside, or at least according to your recent discussion on the subject.

        Napolean must have read the Iliad, where the moral lesson was conduct yourself the opposite of what Agamemnon did, or at least, don’t diss’ your talent, your star warrior Achilles. There are a lot of people in the STEM fields who rise in the ranks but are not effective leaders, and many have not had any form of leadership training, which is what you get in a good program in the Humanities.

        I am not drawing an analogy between Humanities, say familiarity with the Iliad, and STEM, say, knowing Euler’s relation e(ix) = cos x + i sin x (one of the 17 Equations). What I am saying is that there is stuff they teach or at least should teach in the humanities, stuff about human nature that hasn’t changed in 30 centuries, that a lot of folks in tech fields dismiss as being a bunch of worthless nothing.

        Me, I never made it through a an English translation of the Iliad, too many accounts of woundings and ancient descriptions of how a wounded guy bleeds out and crashes from shock. The drama between Agamemnon and Achilles is something I got from a Classics scholar telling me about the Iliad and from Wikipedia . . .

        1. “What I am saying is that there is stuff they teach or at least should teach in the humanities, stuff about human nature that hasn’t changed in 30 centuries, that a lot of folks in tech fields dismiss as being a bunch of worthless nothing.”

          We’ve lost track of teaching the humanities in the pre-college humanities. Which is a large part of -why- they get dismissed.

          My daughters both went to top-three-in-the-state type private elementary schools. They did -not- study Aesop’s Fables, Greece, Rome, Europe or Britain. They did, however, do three-month projects for “Black History Month” every single year. And reports on “Significant Females of the 20th Century”. My youngest’s current task is to write a report on how illegal immigration is a keystone property of what America means. Sorry, the United States.

          Their only in-class interaction with “old white males of history” revolves around the things they did wrong. The rail barons, plantation owners, mining companies, Pinkertons, etc. There’s very little time spent reflecting on the wonders of Ford, Edison, Tesla, Goddard, von Braun, etc. Or, for that matter, any of the non-technical types. Wait, they did hear about Galileo! With the entirely predictable tirade against the Church – and a complete non-coverage or mention of just how heavily the church actually sponsored and provided patronage for scientists of the era.

          That’s what “The Humanities” -means- at the moment in pre-college.

          I feel I’ve done more for their education in the humanities just from my personal demands that they read classics and the in-the-car quizes when going somewhere.

          1. Good for you Al, if there were more of you, the world would be a better place!

            When my now 31 y/o son was a Junior in HS, he somehow managed to get into a special social Studies Program that was about 1/3 book studying, 2/3 discussing history, current events how they correlated and possible outcomes of current events.

            His teacher, fresh out of college, dying to set these kids straight about how things worked ‘in the real world’ [I swear she actually put that in her first year teaching guide for the kids] well, suffice it to say she had a rough time with my son. He’d grown up listening to my family discuss politics, often at high decibel settings. He knew what he knew and she couldn’t shake him loose from what he believed about what he knew.

            She called my in tears about him ‘arguing’ with her. I asked her if he was loud, or mean, or off topic. No, he just wouldn’t, ‘…listen to the truth and follow along like the rest on my students…’.

            She was gone the following year, back to school, to get her Masters in Humanities.

            I have no idea how many of those classes existed that year, but I think just two, one morning and one afternoon. Class size was capped in HS then at 42 in that county. So out of 84 kids, she had one who actually did what the syllabus said, ‘discussed’ the topic at hand. And she was undone by him.

            Ad most of her teaching was as you described.

            White Men =Evil,

            Everybody BUT White Men = The Downtrodden Masses.

            Where was HER understanding of real history, real current events, actual history of humanity, any kind of critical thinking or anything else in that class, that she didn’t want them to learn or think, she just wanted them to ‘follow’.

            I have no college degree, and yet I’m intelligent enough to have a great deal of problem with most of what I see called Higher Education. How ‘high’ an education can it be, if those having ‘it’, don’t know anything?

    1. It’s kind of hard getting analogies between Humanities and STEM stuff. I think The Odyssey is still assigned in most high schools, so maybe [The Odyssey, Macbeth, Siddhartha] is roughly equivalent to [1st year biology, Newton, algebra]?

      Most of the stuff my daughter has been assigned in her high school/jr high school english classes has been crap–it’s almost like anti-knowledge–reading it makes you dumber. Somehow True Grit was slipped into the mix (although only as optional reading)–maybe some teacher was trying to subvert the dominant paradigm.

      1. I memorized the first half-hour or so of the Fagles translation while on a series of very boring job sites.

        Rage, Goddess, sing the rage of Peleus’s son, Achilles, murderous, doomed, that cost the Achaean’s countless losses, hurling down to the house so many sturdy souls, great fighters souls, and made their bodies carion, feasts for the birds and dogs. Begin muse, when the two first broke and clashed….

        I once convinced the ten-year old next door that back in my day everyone in school had to memorize the Illiad. Of course, I also convinced him that digging out our septic tank was the coolest job ever, so he spent days muck deep in shit, bragging to his mom that it was just like being on “Dirty Jobs.” 😀

        1. Oh yeah. I told the whole neighborhood that when it came to conning kids, Tom Sawyer was an amateur compared to me. On the other hand, this same neighbor got me painting his picket fence because he was so obviously bad at it. His brush would touch the paint, somewhat touch the boards in spots, with no obvious pattern, and I just took over for him because I have to stare at their fence as much as the neighbors do. I don’t think I was conned because the boy used to mow the lawn in much the same way. When he’d finish, it looked like a mower had gotten loose and randomly meandered all over the yard until it ran out of gas.

  2. I once told my calculus teacher in grade school that math books had too many words in them. I thought the equations could mostly stand on their own. I was a weird kid.

    1. They do stand on their own. The explanations are checksums — if you understand the explanation, you’ve successfully internalized that chunk of the formal system.

      1. Actually, I think the problem lies in trying to get girls more interested in math. Look at textbooks of today compared to 30 years ago. Every page in my kids book has some sort of sidebar/story/picture/”fun fact”. With the attention span of most boys in the past, I would be amazed if someone could read through all that crap.

        I see the same thing….in my wife’s magazines. Crap everywhere. I don’t know how the XX’s get through a single story.

        Not trying to blame women for the decline in math, but the textbooks our kids use aren’t exactly written for attention on one topic.

    2. People also vary in how fast they learn the “language” of mathematics, so it makes sense to provide an English translation for those who have trouble. I was a slow learner in that regard, and it wasn’t until college that the logic of equations really started coming together for me. At any point in high school a page of equations alone would have caused me to break out in a cold sweat.

      Still managed to learn math well enough to work in a STEM field, with a lot of work and grinding away. So leave a stepstool for the rest of us, Ken. 🙂

  3. So what are the 17 equations? And are the Euler-Lagrange equations of Classical Mechanics that are the bridge between Newton’s F=ma and Modern Physics, are those equations on the list?

    1. As the great Speaker of the House Nancy Pelosi once remarked …

      “You have to buy the book to find out what’s in it.”

  4. I used to work for a guy at an instrument plant here in NC, who prided himself on having a Degree in Philosophy from SUNY, and he said he’d never read a book to get it.

    Don said he had not read a book since he was in 9th grade. He also bragged that he didn’t read magazines or newspapers. He was our manager, I was a lead instrument tech. He was a good electronics tech and a terrible manager.

    One of my guys used to call him, ‘The Hump’, saying he was just “…a walking hump of flesh wearing a tie and shoes.”

    I often wonder how many people out there are like that, but they just don’t brag about NOT reading anything since they 13 or 14.

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