How to Spot a Psychopath

A reader writes:

I recently saw a news article that linked to this government page:
http://ga.water.usgs.gov/edu/earthhowmuch.html
...which says if all Earth's water (liquid, ice, freshwater, saline) was put into a sphere it would be about 860 miles in diameter.

Now I understand an 860-mile sphere is massive, so even though that sounded small I could accept it, until they state the estimated volume of water on earth at 332.5 million cubic miles.

So how do you cram 332,500,000 cubic miles into a 860 mile sphere?

Matthew

Quite easily, actually!

The volume of a sphere is four-thirds pi times the radius squared cubed [Sorry I left that error there for so long, commenters!]. So if the radius is 1 unit, the volume is 4.19 cubic units.

The radius of an 860-mile sphere is 430 miles. 430 cubed is 79,507,000. Four-thirds pi is about 4.1888. Multiply that by 79,507,000 and you get about 333,038,143, a number less than 0.2% larger than 332,500,000. The difference is accounted for by variations in precision in working out the number, since this is really only a ballpark figure and taking it to nine significant digits is silly.

To "sanity check" this if, like me, you always feel mildly nervous about the order of operations for a calculation like 4/3Πr^3, consider the volume of a cube 860 miles on a side.

The volume of a cube is of course just its edge-length cubed, and an edge length of 860 miles gives a volume of 636,056,000, a nice sane-sounding 1.91 times the volume of the sphere that'd neatly fit in that cube.

My own second-favourite way-to-visualise-the-quantity-of-something is that all the gold in the world (not including gold we have yet to dig up or somehow extract from seawater) would make a cube only 20 to 22 metres on a side, depending on who you ask. To help visualise the size of the cube, 21-ish-metres is about the length of two city buses parked nose to tail.

Because gold weighs 19.3 grams per cubic centimetre, though (11.16 ounces, or 10.16 troy ounces, per cubic inch), a 21-metre-on-a-side cube of gold would weigh 178,737 tonnes. So I suppose you wouldn't have to worry too much about someone stealing it.

(Unless you are very wealthy, you probably can't buy a large enough lump of gold - especially at today's outrageous prices - to really appreciate its density. At current prices, one kilogram of gold would cost you more than $US51,000. Tungsten, however, is 99.7% as dense as gold - I'm sure counterfeiters have gilded tungsten for profit many times - and it's much more affordable, though still expensive. The good people of RGB Research {here on eBay US, here on eBay UK, here on eBay Australia} have their one-kilo tungsten cylinders on sale again for a mere $US220 plus rather pricey delivery. If you can afford one, and have the slightest interest in science toys, I urge you to buy one; my own tungsten cylinder is one of my most treasured possessions. And one of the most durable, too; if the house burns down the tungsten cylinder, like my Bathsheba Grossman Metatrino, will be sitting intact in the ashes.)

My most-favourite way-to-visualise-the-quantity-of-something is that if you breathe on an ordinary marble, the thickness of the layer of condensation from your breath on the marble is approximately to scale with the thickness of the atmosphere on the earth.

(And another one, that doesn't really make anything much easier to understand but is prime stoned-party-talk, is that a human is about as much bigger than an atom as a galaxy is bigger than a human.)

Psycho Science is a regular feature here. Ask me your science questions, and I'll answer them. Probably.

And then commenters will, I hope, correct at least the most obvious flaws in my answer.

A reader writes:

How do the little rectangular anti-theft tags work?

I get how the big anti-theft stickers work. They've got an obvious square spiral antenna that I presume collects enough microwatts from an incoming signal to run a little transmitter that sends another signal out.

But the little tags don't have any circuitry inside. I cut one open, and there are just some tabs of springy metal in there - two pieces next to each other, and a smaller piece separated from the other two by a clear plastic membrane.

The metal sticks to a magnet, but that's the end of my ability to figure out what it does.

Is there invisible nanotechnology in these things, or something? Hey, maybe they're a placebo!

Kim

If they're a placebo, the alarm systems in shops seem to really believe that it works.

What you're looking at there (here's a more elegant cutaway picture on Wikipedia) is called a magneto-acoustic, or acousto-magnetic, tag. Which is one of those things that doesn't really sound as if it ought to work, but does.

The first two of the three tabs inside are, I think, a couple of pieces of amorphous metal - which is quite an exotic material to be stuck to commonplace consumer items just to stop people stealing them. Amorphous metal is, in a way, the opposite of nanotechnology; it's metallic glass, special because it lacks the microscopic crystal structure of normal metals.

The third tab is a piece of less exotic, medium-coercivity metal. When that third piece is magnetised, the two other strips, which are sitting loose in their little plastic coffin, become quite easily moved by external magnetic fields. (They're amorphous metal because that's already unusually easy for external fields to move.)

The security gateways as you leave the store emit a pulsed magnetic field up in the tens of kilohertz, at the resonant frequency of the amorphous-metal strips. When next to their mildly-magnetised buddy, this quite tiny field causes the amorphous-metal tags to buzz, and to continue to buzz for a very brief moment after each pulse of the external field. This very brief "ringing" period causes a tiny change in the magnetic field of the third strip, which an antenna in the security gateway, very implausibly, detects. And off go the sirens.

The thingy at the checkout that deactivates the tags is a degaussing coil. It more-or-less demagnetises the third strip, which both reduces the magnetic sensitivity of the other two strips, and removes the field which the other two strips modulate. So now the sirens don't go off.

I am entirely unable to think about any security system without immediately trying to figure out ways to defeat it. (I try to avoid airports nowadays. They make me feel like Jackie Chan in a deckchair factory.)

One obvious but impractical way to defeat magneto-acoustic tags would be to degauss them yourself; I don't know how strong the degausser needs to be to achieve this, though. You might be able to pinch stuff if you just smuggled a CRT-screen degaussing wand into the shop, and found somewhere to plug it in.

Swiping your own rare-earth magnet across the tag would, if anything, probably make it work better (by more strongly magnetising the third strip), but I wonder if leaving a magnet or three stuck to the tag, in a Halbach array if you're fancy, might silence it. Just chopping it bodily off with a potato peeler would probably do the job too, of course, but where's the fun in that?

(If you can magnetise tags yourself with a ten-cent eBay magnet, then you could pry them off things you've bought, reactivate them, and attach them inconspicuously to things which other people may innocently carry into shops. You could, is all I'm saying.)

The square-antenna type of tag, by the way, is also pretty simple. It doesn't actually have anything fairly describable as a transmitter in it, but is rather a tuned circuit that resonates somewhere in the low megahertz. This makes it detectable, if a nearby transmitter/receiver combo rapidly sweeps its output through the relevant frequency range and looks to see if something is managing to suck up some energy at the appropriate frequency.

This kind of tag is deactivated by, essentially, blowing out the capacitor essential to their resonance with a higher-powered signal. I think a shoplifter could probably defeat these tags by just dragging a knife across them a couple of times, though, breaking the circuit. I haven't actually tried this, though, because it'd mean missing out on all of the fun of a good old-fashioned armed robbery.

Perhaps someone who's worked in retail since fancy security tags came into vogue will enlighten us in the comments.

I would also like to hear from anybody who's successfully used the "just lob the item high over the security gate and into the hands of your partner in crime" technique.

A reader writes:

The Oatmeal recommends sites get more traffic and Facebook likes by writing an epic love story involving cage-fighting nuns and tanks, or if that is not possible, explaining why the sun and the moon appear to be the same size in the sky.

Both of these seem right up your alley, but frankly I for some reason find the second one more interesting. Why ARE the sun and moon the same size? Is it just a bizarre coincidence, or is there some astronomical orbit reason for it?

Lucas

I'm afraid it is indeed just a fluke. Which, furthermore, starts to look less amazing when you discover that the sun and moon don't actually have a particularly spooky similarity in size.

I remember reading some flaky book when I was a kid, possibly some von Däniken claptrap or other, that made much of the extraordinarily precise apparent-size match between the 0.55-Earth-diameter moon and the 109-Earth-diameters sun. Surely this cannot be mere coincidence, hence ancient astronauts and Nazi moon bases and the various Stargate series are all documentaries et cetera.

Unfortunately for these otherwise-very-plausible speculations, the sun and moon are not actually the same size in the sky. They can be, but they usually aren't.

The earth's orbit around the sun is not perfectly circular, but it's close. On average it's one astronomical unit (oddly enough), but we're closest, 0.983 AU, in early January, and furthest, 1.017 AU, in early July. The actual sun stays the same size, so from our point of view it ranges from 31.6 to 32.7 minutes of arc.

For visual learners, that's about this much of a range:

(I made this from this NASA picture depicting a gigantic magnetic filament erupting from the surface of the sun. The same filament would not, of course, be there in both January and July.)

The moon's orbit around us is more eccentric than the earth's orbit around the sun, so the moon changes in apparent size much more dramatically than the sun does. It ranges from 29.3 to 34.1 arc-minutes or, to the same scale as the above sun picture...

...this much.

(I took that moon picture myself. Residents of the northern hemisphere are invited to stand on their heads to make it look more familiar.)

(UPDATE: I forgot to mention the moon illusion when I first put this post up. Yes, the moon, and the sun too for that matter, seems bigger when it's near the horizon. No, it actually isn't. If anything, it's smaller!)

Here's the two ranges compared.

The only time when ordinary people really compare the size of the sun and moon is, of course, when there's a total solar eclipse. Then it really does look as if the moon neatly covers the entire sun, helpfully giving us a nice view of the corona, which is normally washed out by the much greater brightness of the body of the sun. (You can actually view the corona from the surface of the earth at other times, but you need special equipment to block out sky-glare.)

At this point, you may be wondering whether the roughly-month-long lunar size cycle and the year-long solar size cycle can coincide with an eclipse in such a way as to put a minimum-size moon in front of a maximum-size sun (well, any size of sun, really, there's not that much difference), so that the moon fails to completely obscure the sun.

Yes, it can; it's called an annular eclipse, and there's one coming shortly, though I won't be able to see it from here in Australia.

Here is a lot more information about all of this.

Psycho Science is a regular feature here. Ask me your science questions, and I'll answer them. Probably.

And then commenters will, I hope, correct at least the most obvious flaws in my answer.