Category Archives: Science
I don’t mean the social kind of integration, which I learned as a child, but the mathematical kind of integration, which I never learned in any of my math classes. I didn’t even take calculus until The Company sponsored some adult education classes for employees.
But those calc classes only got me through basic derivatives (of polynomials, mostly), so integration has been a bit of a mystery to me. Lately, though, I’ve been trying to pick up the basics.
This post just records my first attempts — my math lab book, so to speak.
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3 Comments | tags: calculus, integrals | posted in Basics, Math
Be a Tauist!
I’ve found it extremely difficult to focus this past week. Most of the blame is on Substack Notes, a part of Substack that’s very similar to Twitter or a Facebook feed. I never had Twitter, dumped Facebook ages ago, and barely know what Instagram, Snapchat, et cetera are.
I have no immunity to a doomscrolling feed of interesting micro-posts. Reading them is bad enough. The urge to jump in join the fun is all but irresistible. But days are passing with little to show for them: no books read, no posts worked on, no software projects advanced.
Now it’s Tau Day, and I can’t let that pass postless.
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16 Comments | tags: 360 degrees, 60 minutes, circle, Invincible, orbital mechanics, pi, tau, tau day | posted in Baseball, Science, TV
It’s happy hour and you and a friend go out for drinks. The bar is serving a new drink that catches your eye, and you both order one. They’re served in martini glasses (which are upside down hollow cones) and look quite tasty (see picture).
More to the point here, the glasses look acceptably full. Not a lot of “headroom” between the top of the drink and the top of the glass. Your friend, a mathematician, bets you they can pour all of your drink into their glass without spilling a drop.
Should you take that bet?
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6 Comments | tags: cones, fun with numbers | posted in Math, Wednesday Wow
It’s Friday, and I have Notes, but they’re all Science Notes, so while this post (and any others of similar ilk that may follow) is in the spirit of Friday Notes, it comes from a different direction. Science from right field, so to speak, rather than the usual oddities from left field.
These Notes were originally meant as reminders to mention some cool science things to friends over burgers and beers (or whatever). But rather than tasty morsels for the few, why not for the many? (Or at least for a few more.)
So today, Science Notes (and some reactions):
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1 Comment | tags: AI, aircraft pilots, Black Labrador Retriever, burning iron, cosmology, dogs, Parker Solar Probe, positronic brain, Science Notes, toys | posted in Friday Notes, Science
Earlier this year, I posted about that math gag that seems to prove (very mathematically) that 2=0 (an alternate version “proves” 1=0 using the same trick: a covert division by zero, an operation whose undefined result breaks the chain of logic).
Today I’m posting about another somewhat common mathematical (or rather, geometrical) gag — one involving chocolate! In the form of a magical chocolate bar that lets us remove an infinite number of bite-sized pieces but somehow remains the same size. It seems impossible.
And of course, it is. In this post I reveal the magician’s trick!
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22 Comments | tags: chocolate, fun with numbers, geometry, old tricks, triangle, tricks | posted in Math
Thinking back on your math classes, you may recall that the square root of a number has two answers, one positive and one negative. For example, the square root of +9 is both +3 and -3 (the first one is known as the principal square root). Squaring +3 gives you +9, of course, but so does squaring -3.
Square roots aren’t the only roots of a number. For example, the (principal) cube root of +8 is +2 because +2³ = +2 × +2 × +2 = +8.
But just as square roots have two answers, cube roots have three (and fourth roots have four and so on and so on).
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3 Comments | tags: complex numbers, complex plane, cube roots, Euler's Formula | posted in Brain Bubble, Math
Today (3/14) is Pi Day. People everywhere (or at least math geeks everywhere) are baking decorated pies (or cakes or cookies) to celebrate. And while this is yet another math-y post, it’s not about pi. I’m more of a tau guy, anyway, so I celebrate Tau Day (6/28), because I get twice the (pizza) pie.
Today is also Albert Einstein’s birthday, which I’ve always thought was a cool coincidence. He’s 145 now (and still being widely misquoted).
But this post isn’t about him either.
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10 Comments | tags: Albert Einstein, pi day, tau day, trigonometry, two slit experiment | posted in Brain Bubble, Math
Consider the lowly square, a four-sided shape with sides of equal length meeting at right angles. The embodiment of what we’re referring to when we refer to square miles, square kilometers, square inches, or square whatevers. The two-dimensional version of any one-dimensional length.
A trivially easy shape to draw, all you need is a straight edge and a compass — the latter for ensuring your corners are right angles (see Plato’s Divided Line for more on using a straight edge and compass). The only simpler shape is the circle.
Yet the simple square threw early mathematicians into a serious tizzy!
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12 Comments | tags: irrational numbers, Pythagoras, square | posted in Brain Bubble, Math
An article in a recent issue of New Scientist caught my attention on two counts: firstly, in what it said about my old friend wavefunction collapse and the measurement problem; and secondly, in mentioning Boltzmann Brains. Both set off my “Yeah, but!” reaction.
I’ll touch (as briefly as possible) on the first point, but this little Bubble is mainly about the second one.
Boltzmann Brains bug me.
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3 Comments | tags: measurement problem, quantum mechanics, wave-function | posted in Brain Bubble, Physics
You may have, at some point, seen one of those bits where a series of seemingly simple math operations somehow end up proving that 1=0 or something equally clearly wrong. Most of them accomplish their joke by sneaking in a hidden division by zero. From that point on, all bets are off (see Divide by Zero).
Recently, on a YouTube channel I follow, I saw a clever example that uses a much sneakier trick. It’s harder to spot because the operation it uses is legit in two of the three possible cases.
The gag, of course, uses the third one.
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7 Comments | tags: fun with numbers, imaginary unit, numbers | posted in Brain Bubble, Math
Logos con carne 