Category Archives: Science

May 24, 2024

Science Notes (5/24/24)

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):

2 Comments | tags: AI, aircraft pilots, Black Labrador Retriever, burning iron, cosmology, dogs, Parker Solar Probe, positronic brain, Science Notes, toys | posted in Friday Notes, Science

May 7, 2024

The Magical Chocolate Bar

By Wyrd Smythe

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!

22 Comments | tags: chocolate, fun with numbers, geometry, old tricks, triangle, tricks | posted in Math

April 18, 2024

BB #93: Cube Roots of One

By Wyrd Smythe

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).

3 Comments | tags: complex numbers, complex plane, cube roots, Euler's Formula | posted in Brain Bubble, Math

March 14, 2024

BB #92: Actually Using Trig

By Wyrd Smythe

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.

10 Comments | tags: Albert Einstein, pi day, tau day, trigonometry, two slit experiment | posted in Brain Bubble, Math

February 26, 2024

BB #89: The Irrational Square

By Wyrd Smythe

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!

12 Comments | tags: irrational numbers, Pythagoras, square | posted in Brain Bubble, Math

February 14, 2024

BB #88: Boltsmann Brains

By Wyrd Smythe

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.

3 Comments | tags: measurement problem, quantum mechanics, wave-function | posted in Brain Bubble, Physics

February 13, 2024

BB #87: Two = Zero!

By Wyrd Smythe

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.

7 Comments | tags: fun with numbers, imaginary unit, numbers | posted in Brain Bubble, Math

January 23, 2024

Sideband #80: Divide by Zero

By Wyrd Smythe

You may remember learning way back in grade school that you can’t divide by zero. You may remember being told that division by zero is undefined. But have you ever wondered why we can’t divide by zero? Couldn’t the answer just be zero? We get zero when we multiply by zero, so why not when we divide?

But dividing is the opposite (or inverse) of multiplying, so if multiplying by zero gives zero, then maybe dividing by zero gives us… infinity? But infinity isn’t a number (it’s an idea), so that doesn’t work, either.

In this post I’ll dig into why division by zero is undefined.

4 Comments | tags: division, fractions, zero | posted in Basics, Math, Sideband

December 28, 2023

Sideband #79: Growth Curves

By Wyrd Smythe

nx vs xⁿ vs n^x (for n=42)

You’ve probably heard the phrase “exponential growth” in reference to something that grows very fast. A common example is bacteria in a petri dish. More relevant in daily life, perhaps, the spread of a highly communicable disease or a “viral” meme. These things all can have exponential growth.

You may also have heard the phrase “geometric growth” and wondered how — if at all — it differs from the exponential form. Recently I found myself curious enough about the difference to dig into it a little and find out once and for all.

This post records my simple exploration.

3 Comments | tags: exponential function, geometric function, linear function | posted in Math, Sideband

December 20, 2023

Hand-Me-Down Genes

By Wyrd Smythe

I’ve mentioned before that, after ten years of retired idleness, this year I’ve applied myself to getting some long-standing items off my TODO list. I’m a lazy beaver, not a busy one, but I’ve been less lazy than usual in 2023. (Perhaps, in part, because, on several counts, I can’t believe it’s actually 2023. I remember a time when 2001 seemed far off… in the future.)

One long-standing item off my “Gee, I Oughta…” list was doing one of those DNA assessment things I’ve seen advertised for years. I was adopted as an infant, so I’ve never known my genetic heritage.

Now, at long last, I do. And a bunch of other stuff besides.

8 Comments | tags: ancestors, DNA, genetic code | posted in Life, Science