geology, image, science

Pixel Earth 2

1 Radian Wedge Pixel Art.png

A slightly more comprehensive version of the previous post. Once again, each pixel is 1 kilometer deep. The pixels at sea level (the thin green line near the top) are 1 kilometer wide, corresponding to a total width of 6,371 kilometers at sea level or an angular width of 1 radian, or 57 degrees. There’s an increasing horizontal distortion as you go towards the inner core (orange), which becomes infinite at the very bottom row.

In this picture, you’ll find Krubera Cave, the Burj Khalifa, the Kola Superdeep Borehole, a typical thunderstorm, Mt. Everest, a typical volcano, a subduction zone, an airliner at cruising altitude, and the International Space Station. Try and find them: it’s like a badly-drawn Where’s Waldo!

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geology, image, physics, science, short

Pixel Earth 1

I present you: a scale model of the Earth’s surface, from an altitude of 400 kilometers down to a depth of 300 kilometers. At this scale, every pixel is 1 km by 1 km.crust-1-px-eq-1-km-numbered-large

 

Legend:

  1. The International Space Station at perigee.
  2. The aurora borealis.
  3. The greatest altitude at which human beings have died: cosmonoauts Georgy Dobrovolsky, Vladislav Volkov, and Viktor Patsayev died just before the reentry of Soyuz 11, when the explosive decoupling of the descent module opened an oxygen seal in the cockpit.
  4. The highest altitude reached by the Air Force’s X-15, which still holds the speed record for a crewed aircraft, and which was among the first crewed vehicles to cross into space.
  5. The official edge of space: the Kármán line, at around 100 kilometers’ altitude. Above this line, you have to move faster than orbital velocity for wings to provide usable lift, so you might as well just orbit.
  6. The streak denotes the range of altitudes at which meteors glow.
  7. The streak denotes the altitudes at which the 2013 Chelyabinsk meteorite glowed. The starburst denotes the approximate altitude at which it exploded.
  8. The altitude at which the Space Shuttle Columbia stopped sending telemetry and began its final breakup.
  9. On a less sad note: the altitude from which Felix Baumgartner began his famous skydive.
  10. The top of the troposphere (where weather happens); the beginning of the stratosphere; the top of thunderstorms in middle and tropical1 latitudes.
  11. 10,000 meters: the altitude at which passenger airplanes cruise.
  12. The summit of Mt. Everest.
  13. The Challenger Deep (over 10,000 meters deep).
  14. The deepest active mining operation: 4,000 meters, at the Mpomeng gold mine in South Africa.
  15. The deepest human beings have ever drilled: 12 kilometers at the Kola Superdeep Borehole, in Russia.
  16. The deepest confirmed location in a natural cave: 2 km, in Krubera Cave, in Abkhazia, Georgia (the Eastern European Georgia, not the American one.) The cave very likely goes deeper.
  17. Volcanic magma chambers. Contrary to popular belief, most of the mantle is a plastic solid (like very, very stiff Silly Putty), rather than molten. Magma is the exception. The magma chamber that feeds Hawai’i’s volcanoes is on the shallow end of the spectrum. The magma chamber underneath the Yellowstone Caldera (which provides heat for Yellowstone’s famous geysers) sits at around 25 to 35 kilometers deep. We have actual rough maps of it. It’s awesome.
  18. The Mohorovičić discontinuity (or Moho; no, not the KSP one): the official boundary between crust and mantle. It can be as shallow as 5 kilometers deep (beneath the seafloor) and 90 kilometers deep (under mountains); it averages 35 kilometers deep.
  19. Very deep magma chambers.
  20. The end of the asthenosphere, a region of rock made weak and squishy (relatively speaking) by the enormous temperature and pressure. This starts beneath the solid crust (the lithosphere). Its boundary isn’t well-defined.
  21. A hot plume in the upper mantle. Droplets (well, droplet-sized compared to the whole Earth) of lower-melting-point material rise through the mantle to fill magma chambers.

(I should point out that I’m not a geologist. If I’ve made a mistake, please let me know. You won’t hurt my feelings. I’d rather admit I’m wrong than put out a misleading graphic.)

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biology, math, science, short, statistics, thought experiment

Short: Immortality Math

There are people out there who are quite seriously trying to make human beings immortal. It sounds like something from a bad 1970s pulp comic, but it’s true. Of course, when serious people say “immortal,” they’re not talking Highlander. They’re talking biological immortality, sometimes called by fancy names like “negligible senescence”: the elimination of death by aging. Whether we can (or should) ever achieve biological immortality is a question I’ll leave to people smarter than me, but either way, biological immortality doesn’t mean full immortality. It just means that you can no longer die from, say, a heart attack or cancer or just generally wearing out. You can still quite easily die from things like falls, car accidents, or having Clancy Brown chop your head off with a sword.

There are a number of organisms out there which are either believed or known to be biologically immortal, or at the very least, nearly so. These include interesting but relatively simple organisms like hydras and jellyfish, but also more complex organisms like the bristlecone pine (many living specimens of which are confirmed to be over 1,000 years old, and one of which is over 5,000 years old), and the lobster. (Technically, though, the lobster isn’t really immortal, since they most molt to heal, and each molt takes more energy than the last, until the molts grow so energy-intensive they exhaust the lobster to death.) For the record, the oldest animal for which the age is well-established was a quahog clam named Ming Hafrun, who died at 507 years old when some Icelandic researchers plucked it out of the water.

If a human was made biologically immortal, how long could they expect to live before getting hit by a bus or falling down the stairs (or getting stabbed in the neck by Christopher Lambert)? That’s actually not too hard to estimate. According to the CDC (see Table 18), there were 62.6 injury-related deaths per 100,000 Americans, in 2014. With a bit of naive math (I’m not adjusting for things like age, which probably inflates that statistic a fair bit, since older people are at a higher risk of falls and similar) that means the probability of death by accident is 0.000626 per year, or roughly 0.06%. Knowing that, it’s almost trivial to compute the probability of surviving X years:

probability of surviving X years = (1 – 0.00626)^X

This formula is based on one of my favorite tricks in probability: to compute the probability of surviving, you do the obvious and convert that to the probability of not-dying. And you can take it one step further. At what age would 90% of a biologically-immortal group still be alive? All you have to do is solve this equation for N:

0.9 = (1- 0.00626)^N

which is no trouble for Wolfram Alpha a math genius like me: a biological immortal would have a 90% chance of surviving 168 years. Here are a few more figures:

  • A 75% probability of living up to 459 years.
  • A 50% probability of living up to 1,107 years.
  • A 25% probability of living up to 2,214 years.
  • A 10% probability of living up to 3,677 years.
  • A 5% probability of living up to 4,784 years.
  • A 1% probability of living up to 7,354 years.
  • A one-in-a-thousand chance of living 11,031 years.
  • A one-in-a-million chance of living 22,062 years.

For reference, the probability of a member of a population surviving (in the US, in 2012, including death by biological causes) doesn’t drop below 75% until around age 70. To put it in slightly annoying media jargon: if we’re biologically immortal, then 459 is the new 70.

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biology, physical experiment, science, short, Weird Food

Real Mad Science 2: Mead

Mad Science Mead.png

I used to be pretty fond of booze. My favorite libations were Johnnie Walker Black Label, cheap supermarket Moscato, this horrible fluorescent-blue fruity cognac stuff called Hpnotiq (yes, really), and White Russians. But, towards the end of my college career, I made a nasty error: I got careless with Jägermeister. Jäger, exactly like plutonium or nitroglycerin, is very unforgiving of carelessness. The next day was among the ugliest in my life, and I’ve hardly touched hard liquor since then.

That’s actually a good thing, since it nudged me towards drinking less stomach-scorching things like proper decent wine and beer (and alcoholic ginger beer). And, since I’ve been in a mad science mood lately, I decided I’d take advantage of Amazon’s “Black Friday is happening some time during this month money money money” sale and pick up a little proper brewing equipment.

Several words of warning. 1) Home brewing comes with risks. You could get nasty unwanted yeasts or bacteria or mold that turn your brew toxic. To that end, I sterilized my equipment with a cheap and easy (and slightly nostril-stinging) potassium metabisulfite-citric acid wash. 2) Booze can get you into trouble if you don’t treat it with respect, and it’ll get you into a lot of trouble if you’re under drinking age. 3) Home brewing is illegal some places.

Now that I’ve made it painfully obvious that I’m trying not to get sued, it’s time to make mead! Mead is a fermented honey beverage favorited by Norsemen, English Majors, Beowulf, and pretty much everybody in Skyrim. Here’s how I made it:

I added two cups of honey (about 475 mL) to a saucepan. Because it was a really cold day, I added some water to make the honey less viscous. (Filtered well water, mind you.) To make sure the yeast had vitamins and minerals that pure honey might not provide, I added a generous handful (roughly 1 cup, or 100 – 150 grams) of cranberries, along with a modest handful of raisins. They were just what I had lying around. For flavor, I added about a teaspoon of cinnamon. I brought the whole mixture to a boil. I checked the temperature with an instant-read meat thermometer (never use the proper tool for the job, I always say). Once it reached 212° Fahrenheit (100° Celsiusigrade), I started a ten-minute timer. There are probably nasty unwanted things like weird bacteria, wild yeasts, mold, and microscopic politicians in the fruit and maybe the water and honey, so I figured ten minutes at a boil would heat everything enough to kill them.

Before I started boiling the mixture, I had prepared my brewing gear according to reasonable sanitary standards. Into a 1 gallon (3,750 mL) glass carboy (moonshine jug, as I’m sure many people call them), I added half a gallon (roughly 2,000 mL) of clean filtered well water. To that, I added two teaspoons of powdered potassium metabisulfite and one tablespoon of granulated food-grade citric acid. The reaction produces sulfur dioxide, which kills germs. (Don’t smell the jug while the chemicals are sitting in there: sulfur dioxide really burns the nose…) Just before it was time to pour the fruit-honey-water mixture into the carboy, I gave the carboy and the airlock (which keeps dust and other potential germ-carrying stuff from falling into the carboy during fermenting) a rinse with clean water. I let the boiled mixture cool and then added it slowly to the carboy, which I’d warmed in the oven. I didn’t want to risk temperature differentials shattering the glass. Luckily, there were no problems. I bloomed 2 grams of distiller’s active dry yeast in a cup of warm water with two tablespoons of sugar dissolved in it, then added the bloomed yeast to the carboy. I topped it up almost to the top with clean water, then added the airlock, filled the airlock with water, and gave the jug a gentle shake to get things going.

That was yesterday. Today, when I took the picture, the mead was bubbling merrily away. It’s eating sugar and making things like carbon dioxide and ethanol. The airlock produces a bubble once every five or ten seconds, which tells me the fermentation’s going well. I’m not sure how long you’re supposed to leave mead, but I guess I’ll wait until the bubbling stops, which will tell me I’ve got a bunch of dead yeast drowned in ethanol. I suppose I’ll make the tasting of the mead part of my weird food series…

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electronics, physical experiment, real mad science, science, silly

Real Mad Science #1

I like the idea of those little USB power banks. If your phone dies, you can plug it into one, and boom! It’s like you’ve got a whole other battery to run your device off of. Because that is, literally, what you’ve got.

I didn’t have a power bank. I usually don’t need one, since I rarely travel too far from home, on account of the world scares me. But I decided I did want to have a powerbank for emergencies. And since I’ve been doing a bit of soldering lately anyway, I decided why not make my own.

A sensible person would have, say, bought the cheapest possible cordless drill battery and used the cells from that. I am not a sensible person. Here’s my improvised power bank (which I must add, actually works, although I forgot to turn the phone’s screen on for proof):

Ghetto Power Bank.png

That’s what normal DIY techie people do, right? They wire two lantern batteries in parallel, solder the leads to a car cigarette lighter USB charger and plug their phone into that. Right?

These are ridiculously cheap lantern batteries. Probably zinc chloride “heavy duty” cells, which means they’ll probably leak horrible corrosive stuff as they age. But, wonder of wonders, the bastards work. A few dollars, some solder, and some throwing away of common sense, and I have a perfectly functional powerbank. It’s not rechargeable, of course, but I don’t need it to be. This is for, for instance, those times when the power goes out and I can’t charge my phone, but I really wanna keep watching Big Clive videos on YouTube, and I need a charge.

There you have it: the first (and definitely not the last) act of Sublime Curiosity Real Mad Science. I should probably punch up the name.

EDIT: Here’s the powerbank after I neatened it up with a little extra solder, too much hot glue, and a switch, so that the car adapter wouldn’t run all the time and slowly drain the batteries.

Better Ghetto Powerbank.png

EDIT 2: I did a little poking around on the Internet, and found that, in all likelihood, each of these lantern batteries holds 11,000 millamp-hours. Since they’re in series, I’ve just gone and made myself a 11 amp-hour powerbank! From watching too much Big Clive, I know that an iPhone like mine will take 500 millamps if it can, but with these batteries, that’s something like 22 hours of continuous charging. Not bad, for $8 worth of batteries!

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