BAN #90: Waste of math, Unrolling Jupiter

Number crunching

Because I think math is cool, and I think that because it is

[I don’t usually preface my writing with a warning, but what the heck: This one is a tad scatological. It’s math, sure, but it’s also, um, pooping. Fairly warned be ye, says I.]

So I follow Bucky Underbelly on Twitter because he’s funny. On February 17, 2019, he tweeted thusly:

I chuckled, but then immediately realized that this is a tractable number. It’s even pretty easy to get a rough estimate!

Think of it this way (if thinking of the example Bucky uses grosses you out): If there were only one person on Earth, the odds they would be doing any given daily activity at any given time is just how long it takes to do that thing divided by the length of the day. So if it takes an hour, the odds of it happening right now are 1 in 24, or a chance of about 4%.

Let’s say a certain activity — say, waste elimination — takes five minutes, on average. Your kilometerage may vary, but let’s go with that. Then the chance of one person doing that activity at any given moment are (5 minutes) / (60 minutes/hour) / (24 hours / day) =  0.0035. Or to phrase it differently, if you randomly pick a time of day, there’s a 1 / 0.0035 = 1 in 288 chance they’re doing it at that moment.

But there are seven billion people on the planet. To get how many of them are likely performing that activity at any given time, just multiply the fraction by seven billion.

10 / 60 / 24 x 7,000,000,000 = roughly 24,000,000.

So. Assuming this activity happens once per day and takes five minutes, then at any given time — right now, for example — 24 million people are pooping.

If it takes longer on average (let’s face it, there’s a reason a lot of people call the bathroom “the library”) then there are more people doing it; if it takes less time than fewer people are engaging in it.

Downthread a bit on Twitter, Bucky wondered if time zones played a part. I actually don’t think so, at least not much. Fewer people will be up at 3:00 a.m. local time, on average, to use the bathroom, but at the same time a quarter of the way around the world to the east it’s 09:00, right after morning coffee, so that may balance out things. If there’s a peak time of day to an activity, it’s always that time somewhere on our round planet (averaging out over an hour, the length of a time zone). So if you plot how many people on Earth are doing that activity at a given snapshot of time, it’ll be pretty flat.

If we use a finer time scale, like 10-minute intervals instead of one-hour time zones, we might see some variation. Maybe more people do it at half past the hour. If so you’ll see a bump at that time, or maybe even a gentle sine curve centered there, but I still think over the course of a day that graph will be pretty flat. If it weren’t, well, that would be telling you something interesting.

I doubt that, in this case, we’ll ever know. And truthfully? I’m not sure I want to know.

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Pic o’ the Letter

A cool or lovely or mind-bending astronomical image/video with a short description so you can grok it

The website Boing Boing has a thing called a unicorn chaser where they post something sparkly and pretty after something that, um, isn’t. I think that’s called for now, don’t you? So here’s a too-cool map of the entire planet of Jupiter made by “unrolling” photos taken of the planet:

[Credit: Damian Peach]

Pretty nifty, eh? This was made by astrophotographer Damian Peach, using images he took in May 2018 when Jupiter was near opposition, so it was closest to Earth. It’s basically a bit of trigonometric trickery: You can map a circle into a rectangle by unwrapping it row by row, going from circular coordinates to Cartesian (a rectangular grid using x and y, the kind you learned in middle school). Peach did this using several images taken over time; Jupiter rotates ever 10 hours or so, so it’s not hard to see its entire “surface” (well, cloudtops) over the course of a day or two.

He also made a video:

I did something like this for my PhD work on the ring of gas surrounding the supernova SN1987A. It was hard matching features in the elliptical ring from one observation to the next, so I wrote some code that converted it from an ellipse to a straight line, basically unwrapping it the same way. The trig was fun to work out, and the results were actually helpful in aligning features. The only version I found of it is too small to show what I mean, unfortunately (it’s also inverted as a negative, so black = brighter, and has five images from five different observations stacked vertically, so it’s pretty confusing). If I find a bigger version in my archives I’ll post it.

Anyway, there’s your unicorn chaser. I hope it helps.

Et alia

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