A glance at a couple of posts will show that there are a lot of equations in these posts. I know that a lot of people are kind of triggered by math and might have an automatic fight-or-flight response on seeing an equation.
When I write something here it’s because I thought, “hey, isn’t it cool that you can calculate this thing, that math can answer this question?” If you like math, then the post is saying “hey, here’s how to calculate this thing.”
But if you’re not a big fan of math, then the take away is simply, “hey, did you know this thing can be calculated?”. Hopefully you’ll also think it’s cool that it can be calculated, without worrying about the “how”.
I think this is the core of why I fell in love with physics. For me, physics is about taking practically anything in life, and figuring out how to build a mathematical model of it and then calculate things with that model. For instance, a question I remember from early in my physics education was “are there more drops of water in all the oceans on earth, or more molecules in a drop of water?” It’s not meant to be an exercise in accurate calculation, but in how to come up with reasonable guesses. It’s a classic “back of the envelope” or “cocktail napkin” calculation.
I absolutely love physics calculations about either silly stuff (like how hard do you have to slap a chicken so that the energy of slapping cooks the chicken? or how long would it take to slide down a firepole from the Moon to Earth?) or about ordinary stuff (like why does the cereal clump together in the middle of the bowl?).
Some of it is admittedly hard to classify as “fun”, but more driven by using math to solve practical technical problems, the kind of things that might come up on the job. Those are often things I did on the job, and the motivation is simply, “did you know you could do this thing with math?”
So here’s what the motivation was behind my first few posts:
- A post about the Twin Paradox of relativity. Does relativity really say that when two people are in relative motion, each thinks the other one’s clocks are running slow? How? I thought some of the explanation was often glossed over in articles about the Twin Paradox, so I go into some more depth on this.
- General linear regression, which might seem mysterious if you’re just using somebody else’s tools such as Excel. I wanted to point out that if you’re willing to use linear algebra, the theory is only a couple of lines of calculation (literally two lines of Python code). Not only that, if you’re wondering how to fit more general things like exponentials, polynomials and sinusoids, the same simple theory will do it.
- A really technical one doing calculus on matrices, which is needed for the least-squares theory. If you’re interested in the derivation of the matrix theory of least squares, you might ask “wait, why is this thing the derivative of this other thing?” Years ago I worked out why this works, which nobody ever seemed to do in math courses, and wanted to share.
- Best angle to fire a projectile on a slope. That was a question somebody asked on Reddit. Usually when projectile problems are not on flat ground things get messy. I worked it out and was totally surprised at how simple the answer was. Thought I’d share the method and the surprising result.
The blog is new and it will take me a while to figure out how to sort it out into categories so that people here for the fun stuff can find the fun stuff, and people here for the “how do I solve this problem with math” stuff can find that stuff as well. Hope you’ll find something that interests you and stick with me on this journey!
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