physics, science, silly, thought experiment

The Overkill Oven

As I was lying in bed last night, I started wondering: “What if I had an oven that could heat its contents up to nuclear-fusion temperatures?” This is why I have trouble sleeping: my brain is very badly-wired. But still, that’s a perfect question for this blog. But as I was preparing to write the article, I got to thinking: Why limit myself to nuclear-fusion temperatures? Nuclear fusion only requires a few billion Kelvin. There are processes (particle-accelerator impacts and cosmic-ray collisions) that reach a trillion trillion kelvin!

Overkill Oven 450 Kelvin

Here’s my new oven. You’ll notice it has quite a few temperature knobs. That’s because, if I tried to fit 10^24 Kelvin all on one knob, that knob would have to be the size of a galaxy before the 100-Kelvin interval marks were far enough apart to see with the naked eye. The cool thing about the decimal number system, though, is that I only (“only”) need 24 knobs, each only marked with 10 intervals, to set temperatures hot enough to melt protons.

This new oven has a couple of interesting features. The first is the patented ceramic bowl-schist lining. Bowl-schist is an exotic metamorphic rock I imported from a parallel universe. Its heat conductivity is so low you could put a block of it next to a supernova and it’d be just fine. The second important feature is the power supply. Naturally, I can’t plug a fancy oven like this into a standard 240-Volt U.S. oven socket. Instead, the cable passes through a very narrow wormhole into the Handwavium Universe, which is stuck mid-big-bang, and therefore is absolutely flooded with energy. With all that set up, let’s cook! To celebrate my new oven, I think I’ll make a big beef roast, with some potatoes, peas, carrots, onions, and herbs and spices.

0.001 Kelvin

The trouble with the Oven of Doom is that the controls are a little difficult to get used to. But hey, I play Dwarf Fortress, so I’m no stranger to shockingly opaque controls. Still, starting out, I accidentally set the oven almost to zero Kelvin. I didn’t realize this until I saw the fur of oxygen and nitrogen ice growing all over my roast. Luckily, the Death Oven is also completely hermetically sealed during operation, to prevent operator death, so I didn’t freeze out all the air in the house. And defrosting was easy.

450 Kelvin

Overkill Oven 450 Kelvin

After that initial hiccup, my roast is coming along nicely. I’m making a brisket roast, so I should probably cook it long and low and slow, so it gets nice and tender. I just hope I don’t run out of patience before

1,000 Kelvin

Overkill Oven 1000 Kelvin

Well that could have gone better. In my defense, this oven has a lot of knobs, and if there’s anything resembling a knob or switch, I am compelled to fiddle with it. The roast was on fire for a few minutes, but once most of the fat burned off, it settled down. Now I’m left with an oven full of glowing orange soot and carbonized meat and vegetables. I can probably find some creature willing to eat it…

5,000 Kelvin

Overkill Oven 5000 Kelvin

The trouble with having a fancy high-power oven is that it’s really tempting to turn it up unnecessarily high in the hopes of getting your food finished as quick as possible. I think there might be something to all this “slow food” stuff I keep hearing about. Trying to cook my roast at 5,000 Kelvin has reduced it to a cloud of white-hot soot with a pale yellow vapor of sodium, potassium, and iron simmering over it. Still, at least I can be sure it’s safe for the people who insist on having their beef well-done.

10,000 Kelvin

Overkill Oven 10000 Kelvin

You know, I should probably close the shutter over that porthole… It’s getting awfully bright in there. I’m pretty sure the roast hasn’t escaped, but truth be told, when I look in there, all I see is this screaming blue-white fog of ionized carbon. On the plus side, if I hurry up and buy a second roast, I can cook it with the light from the first one.

100,000 Kelvin

Overkill Oven 1e5 K.png

I think I’m starting to understand now why the oven’s window is more of a peephole. It’s only three inches across, but already I shouldn’t be able to stand in front of it without my legs evaporating. Actually, I shouldn’t be able to have the peephole open without my house exploding in a horrendous fireball. The oven’s emitting more power from radiant heat alone than the Three Gorges Dam. But I can hold my hand in front of the porthole, no problem. I think I’m starting to see why the department store I bought it from was called BS & Sons…

5,000,000 Kelvin

Overkill Oven 5e6 K.png

I don’t think I have the right to keep calling this thing a roast, do I? It’s really just a soup of highly-ionized carbon, oxygen, iron (from the myoglobin in the meat, and from what used to be my nice new roasting pan), nitrogen, sulfur, and trace metals. On the plus side, I’ve got my own pet solar flare now!

10,000,000 Kelvin

It’s not all bad news, though. The oven is now self-powering. All those hydrogen atoms that used to be part of things like fats, proteins and starches have long since evaporated into a searing plasma. Now, though, they’re colliding fast enough that they’re starting to fuse. Not only am I getting extra energy from this, but I’m making homemade helium, too! Cooking’s fun!

100,000,000 Kelvin

Well, I’ve gone and overdone it again. I burned up all the helium I just made! Now it’s gone and fused to make more carbon vapor. I should probably call somebody about this. Frankly, at this point, I’m afraid to turn the oven off. I mean, since the thermal conductivity is pretty much zero, it’s never going to cool down. And if I open the door, I’m going to release as much energy as detonating 30 tons of TNT. I think I’ll just wall off the kitchen and pretend none of this ever happened…

500,000,000 Kelvin

I am now essentially cooking my roast with a continuous nuclear explosion. Also, I’m pretty sure that, even if I managed to cool it down, not even a physicist with a mass-spectrometer would be able to identify what the roast used to be. That’s partly because, of course, it’s been thoroughly vaporized. But also, the carbon nuclei have started fusing to form weird stuff like neon. If you find an organism that likes to eat neon, send it my way. I’ve got a roast for it.

1,500,000,000 Kelvin

My oven now contains as much energy as a half-kiloton nuclear explosion. The oxygen nuclei are fusing to form things like phosphorus, magnesium, and silicon. If the peephole wasn’t made of pure handwavium crystal, it would be emitting more power (briefly) than the Sun.

3,000,000,000 Kelvin

The good news is that I got my roasting pan back, and then some! All the light atoms have pretty much fused into heavier elements, which have fused to form Nickel-56. If I opened the door, I would be violently vaporized, but after the fallout cooled, the Nickel-56 would decay into Cobalt-56 and then Iron-56, and I’d be able to re-cast my roasting pan!

12,000,000,000 Kelvin

All that brilliant blue-white death-light that filled the oven is finally starting to fade. The bad news is that that’s only fading because the thermal radiation is so intense that it’s actually spontaneously turning into matter and antimatter, forming electron-positron pairs. The other bad news is that I’ve lost my roasting pan again: the energy of the particles in the oven has exceeded the binding energy per nucleon of iron, which is the tightest-bound atomic nucleus. In other words, my stupid iron atoms are starting to melt and shed protons and neutrons. Oh well. Maybe I’ll make some really exotic elements and get them named after me. And if IUPAC won’t name them after me, I’ll threaten to open my death-oven, which has long since become a weapon of mass destruction.

5,900,000,000,000 Kelvin

By now, the iron nuclei should have melted. All I need to do is heat them a little more to get that nice gooey brown crust. Except, I just checked, and I’m pretty sure the protons and neutrons are also melting. It’s just a very thin soup of quarks and un-named nonsense particles in there. Just like the Standard Model, amirite? Sorry. I shouldn’t be joking about particle physicists. Actually, speaking of particle physicists, could somebody call one of them? Because I’ve got three kilograms of pure quark-gluon plasma that they’ll probably want to study. You know, if they’re obscenely brave and not concerned about the 1.9 megatons of thermal energy packed into my oven. To be fair, if the door was gonna fail, I’m pretty sure it would have done it by now.

I’m really glad I spent the extra money on the Handwavium Universe power connector. In the 15 minutes it took me to obliterate my roast and put the entire Earth in jeopardy, the oven was drawing 8,830 terawatts. I’ll have to check the electrical panel, but I’m pretty sure 37 billion amps is above the rating of the breaker for the kitchen. Now all I need to do is call BS & Sons customer service and see if there’s a way to dump what’s left of my roast back into the Handwavium Universe. I don’t think I’ll be hurting anything: the HU is way hotter than my oven can get. Actually, the HU is so hot that the laws of physics themselves are above their melting point.

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astronomy, physics, short

Weight of the World

According to this report, the Earth’s mass (M⊕) is

5,972,190,000,000,000,000,000,000 kilograms

You might notice that there are an awful lot of zeros in that number. That’s because the report doesn’t actually directly specify the Earth’s mass. Like a lot of astronomical papers, it instead uses the Earth’s gravitational parameter, which is the Earth’s mass multiplied by the Newtonian gravitational constant. You see, when it comes to gravity, the force is ultimately determined by the gravitational parameter, rather than directly by the mass. As a result, the gravitational parameter is, as a rule, known to much higher accuracy than the mass. Newton’s gravitational constant is hard to measure, since it’s so tiny, so the report only gives it to six significant digits. So six significant digits is what I gave for the Earth’s mass.

I imagine you’re wondering why the hell I’m talking about all this. Well, I was thinking about planets, whose masses are very often measured in Earth masses. That made me wonder what the mass of say, a person, is, compared to the mass of the Earth. So, without further nonsense, here’s my big list of random objects measured in Earth masses. (I probably need to come up with a better name.)

2.78045 × 10-51 M⊕ : Hydrogen atom.

1.13926 × 10-24 M⊕ : a dumbbell

2.279 × 10-23 M⊕ : me

1.674 × 10-22 M⊕ : my car

7.023 × 10-20 M: the International Space Station

9.878 × 10-16 M⊕ : the Great Pyramid of Giza

1.671 × 10-12 M : Comet 67P/Churyumov-Gerasimenko

8.620 × 10-7 M⊕ (not quite a millionth): The Earth’s atmosphere

4.470 × 10-5 M : asteroid 4 Vesta.

1.590 × 10-4 M : asteroid 1 Ceres (the largest in the solar system)

2.344 × 10-4 M (two ten thousandths and change): the Earth’s oceans

 0.00219 M⊕ : Pluto

0.0123 M⊕ : the Moon

0.0552 M: Mercury

0.107 M: Mars (I always forget how small Mars actually is…)

0.815 M⊕ : Venus (Venus was my second-favorite planet as a kid, after Pluto, which was still a planet back then)

1.000 M⊕ : Earth (Might as well stick it in the list…)

10 M: Planet Nine (Lower bound. If it exists.)

14.536 M⊕ : the mass of Uranus (I still think it’s funny…)

17.148 M⊕ : Neptune

95.161 M⊕ : Saturn

317.828 M⊕ :  Jupiter

332,949 M⊕ : the Sun (1 solar mass, 1 M. Guess who finally learned how to do subscripts!)

26,600 M⊕ : the mass of TRAPPIST-1, which is significant for being one of the smallest stars ever observed, for having seven rocky planets, and for having three planets in its habitable zone. If there’s radio-communicating life on one of them, and we send a message right now, some of you might still be alive if we get the response. Not me. I’d be 98, and I suspect I’m gonna fall into a vat of curry or something stupid like that before then.

672,600 M⊕ : Sirius A, the brightest star in the sky (besides the Sun, obviously)

710,850 M⊕ : Vega, a fairly bright nearby star distorted into a lozenge shape by its rapid rotation.

1,270,000 M⊕ : Alcyone, the brightest star in the Pleiades

2,830,000 M⊕ : UY Scuti, a likely candidate for the largest known star as of March 2017. It’s around 1,700 times the diameter of the Sun, and if you placed it where the Sun is, it’d engulf Jupiter and come close to engulfing Saturn.

3,862,000 M⊕ : Betelgeuse, the bright reddish star on the shoulder of Orion (cue Rutger Hauer.) It’s also an enormous, lumpy star. If you put it where the Sun is, it’d reach at least as far as the orbit of Mars.

33,295,000 M⊕ : the larger component of Eta Carinae, an enormous, extremely bright, angry multiple star that’s so massive and so hot that it’s vomiting its own guts into space and making a pretty nebula in the process.

38,622,000 M: the poetically-named NGC 3603-A1. With 116 times the Sun’s mass, this is the largest star (as of March 2017, blah blah blah) whose mass is known with any certainty. There are other stars predicted to be more massive, but while their masses are estimated from models of stellar evolution, NGC 3603-A1’s mass is inferred from the orbital period of it and its binary companion, which is much more precise and less guess-y.

2.331 × 1015 M: the mass of the Small Magellanic Cloud, one of the Milky Way’s small galactic neighbors.

2.830 × 1017 M: the mass of our Milky Way galaxy (roughly).

4.994 × 1017 M: the mass of the Andromeda galaxy (roughly).

1.647 × 1028 M: mass of ordinary matter in the observable universe (atoms and other familiar stuff) (very roughly)

3.349 × 1029 M: mass of the observable universe, including weird stuff like dark matter and dark energy (very roughly)

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astronomy, image, pixel art, science, short, Space, Uncategorized

Pixel Solar System

pixel-solar-system-grid

(Click for full view.)

(Don’t worry. I’ve got one more bit of pixel art on the back burner, and after that, I’ll give it a break for a while.)

This is our solar system. Each pixel represents one astronomical unit, which is the average distance between Earth and Sun: 1 AU, 150 million kilometers, 93.0 million miles, 8 light-minutes and 19 light-seconds, 35,661 United States diameters, 389 times the Earth-Moon distance, or a 326-year road trip, if you drive 12 hours a day every day at roughly highway speed. Each row is 1000 pixels (1000 AU) across, and the slices are stacked so they fit in a reasonably-shaped image.

At the top-left of the image is a yellow dot representing the Sun. Mercury and Venus aren’t visible in this image. The next major body is the blue dot representing the Earth. Next comes a red dot representing Mars. Then Jupiter (peachy orange), Saturn (a salmon-pink color, which is two pixels wide because the difference between Saturn’s closest and furthest distance from the Sun is just about 1 AU), Uranus (cyan, elongated for the same reason), Neptune (deep-blue), Pluto (brick-red, extending slightly within the orbit of Neptune and extending significantly farther out), Sedna (a slightly unpleasant brownish), the Voyager 2 probe (yellow, inside the stripe for Sedna), Planet Nine (purple, if it exists; the orbits are quite approximate and overlap a fair bit with Sedna’s orbit). Then comes the Oort Cloud (light-blue), which extends ridiculously far and may be where some of our comets come from. After a large gap comes Proxima Centauri, the nearest (known) star, in orange. Alpha Centauri (the nearest star system known to host a planet) comes surprisingly far down, in yellow. All told, the image covers just over 5 light-years.

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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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image, short, Space

Earth versus Sun

Earth vs Sun at 1 AU.png

Nothing too special here: just a size comparison between the Earth and the Sun. The only difference from the usual ones, is that I’ve based their relative sizes on their angular diameters. For the Sun, I computed the angular diameter at a distance of 1 AU (which is how we see it here on Earth). For the Earth, I computed the angular diameter at a distance of 1 AU minus the diameter of the Sun. In other words, the Earth appears as large as it would if it were sitting at the point on the Solar surface nearest us. This is how the Earth would look as a very unfortunate close-transiting planet.

To paraphrase Carl Sagan: that little blue blob is home. That’s us. Everything that’s ever happened to you happened there.

Now consider that compared to the Sun…

Earth vs Sun Closeup.png

Here’s a closeup of the same image, showing the Earth compared to the weird convection granules on the Sun’s surface.

Both images are from NASA. The Solar image is from the Solar Dynamics Observatory (HMI intensitygram, February 7th, 2016), and the Earth-disk image is from the GOES earth-observing satellite.

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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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