Weights and Measures

Measuring the distances between Worlds in Probability has always been problematic. As beings limited to perceiving reality in only four dimensions, direct measurement of the fifth is simply not possible. Instead proxy methods have to be deployed, the most common of which defaults to the amount of energy required to either open Gates or move matter directly between Worlds.

The best established measurement is the Wyrymyan ghəι (anglicized as “weyr“). The exact genesis of the weyr is lost to history, although it is noted it is very close to the amount of artonic energy required to directly (ie: without the use of a Gate) transport one ixh* of matter between Wyrymya and the ancient Wyrm colony World of Hfren, leading many to assume ancient travel between these two Worlds as its ultimate origin.

(* One ixh is equal to one 1728th of the weight of a cylinder of Wyrymyan sea-water with a height and radius of 12 ghi – one ghi measuring 6.875 cm. Bizarrely this works out to just over 1kg – 1.069kg to be precise.)

The traditional measurement of Probability among the Zurvár is the kâd, which is the minimum distance traversable via Gate in ancient Zurvár society. One kâd is equal to 16.8 weyr, which provides some commentary on the relative sophistication of Probatial travel in the ancient Zurvár and Wyrm cultures. The kâd has become the standard measure of Probatial distance across local Probability, with the weyr generally reserved for scientific usage.

(The Metaphysical Society of 19th century London created their own measurement of Probatial distance, the “Palmerston”. One Palmerston equals 77.4 kâd (or 1300.32 weyr), and is the distance between Earth and Neanderthan, the first World discovered by the Society. The Palmerston was abandoned shortly after contact was established with the Wyrms.)

The record for minimum Probatial distance traversable currently stands at 0.43 kâd (7.224 weyr) which was achieved at the Werinos Physics Institute in 2007. This is well above the theoretical limit of 0.14 kâd predicted by Probatial Resonance Theory. It is believed by many that the Goatsuckers have been capable of reaching this limit for centuries – if not millennia – or possibly even exceeding it, although the later would raise uncomfortable questions about their motivation in providing so much assistance in the development of an inaccurate theory.

Notes on Physics

The Probability Maxim: All possibilities are played out somewhere in Probability.

The Probability Paradox: Probability travel links universes into continua that invalidate the Probability Maxim. First noted by the Wyrm philosopher Ryzan in 720 BC.

Artonic Quantum Theory: Artonic energy can only be expended in discrete units or quanta. This limits the amount to which Probability can be fractured, thus restricting which universes can be reached from any given universe and creating multiple interlaced continua – thus preserving the Probability Maxim. Disproven when the energy value of the Artonic Quanta was shown to be beneath the minimum necessary to fracture Probability.

Meta-Probability Theory: Championed by Zurvár physicist Àeksùl this theory proposed a second dimension of Probability, creating continua inaccessible to standard Artonic Probability travel. Fell into disfavour after the death of Àeksùl in his tragic laboratory disaster.

Harmonic Probability Theory: Probability can only be fractured in discrete units, restricting what universes are accessible and creating multiple interlaced continua – thus preserving the Probability Maxim. The currently accepted solution to the Probability Paradox.

What If? Wyrmworld Style!

Not only is XKCD a wonderfully enjoyable webcomic, but every Thursday its author, Randal Munroe, answers crazy physics problems submitted by readers in his What If? section.

For a while now, I’ve been trying to think of something to send in, and just recently came up with one. But then I realised it was a question that I was perfectly capable of answering myself, if I got off my arse and did some research and some maths. So I did.

If all the excess carbon released into the atmosphere since the start of the industrial revolution was compressed into a sphere of pure diamond, how big would it be, and if it were placed into orbit would it focus a death ray of concentrated sunlight down onto the planet?

First step, how much carbon has been added to the atmosphere? According to Wikipedia about 12 Gigatons was released from 1751 to 1900, then a further 334 Gigatons from 1900 to 2008. Adding these together comes to 346 Gigatons, which is as good a figure as any. (It’s important to note that this is just the carbon – not the carbon dioxide containing the carbon. If it were the carbon dioxide we’d have to divide the weight by 3.67 to get just the weight of the carbon.)

The next step is to determine the weight to volume ratio of diamond, so we can figure out how much space 346 Gigatons of carbon would take up when arranged into its crystaline form. Some more poking around online provides a density figure for diamond of 3.52 grams per cubic centimetre. There are 1,000,000 cubic centimetres to a cubic metre and 1,000,000 grams in a ton, so the maths is nice and simple (gotta love the metric system) telling us that 1 cubic metre of diamond weighs 3.52 tons.

To get a volume for our 356 Gigatons of diamond we simply need to divide 346,000,000,000 tons by 3.52 tons – which leaves us with a volume of 98,295,454,545.45455 cubic metres, or 98.29545454545455 cubic kilometres.

So we now know just how much space our chunk of diamond takes up, but so far it’s just sitting around in a roughly shaped blob. We need to reshape it into a sphere.

The formula for the volume of a sphere is v = (4/3)πr^3, where r is the radius of said sphere. Turning this inside out we can derive r = (3v/4π)^(1/3). Plugging the volume figure in gives us a radius of 2.86296 kilometres. Doubling this for the diameter gives us sphere of pure diamond 5.72592 kilometres across – roughly the distance from New York City’s Battery Park to 33rd Street or from London’s Tower Bridge to the cafe in Hyde Park.

That’s one big diamond.

On to the second part of the question – would this diamond project a death ray? To figure this out we need to discover the focal length of the sphere – that is the distance from its centre to its focal point – the point where the light passing through the sphere is focused. The formula for this is pretty simple – EFL = nD/4(n-1) where EFL is Effective Focal Length, n is the refractive index of the material the sphere is made from, and D is the diameter of the sphere. We already know the diameter and Wikipedia assures us the refractive index of  diamond is 2.419. Solving the equation gives us a focal length of… 2.440274926004228 kilometres. Wut?

Yes folks! It turns out that the focal length of a sphere made of diamond is always less that its radius, meaning that the focal point is always inside the sphere! No death ray for you!

So in conclusion, if you could pull all the excess carbon out of the atmosphere, turn it into a diamond and launch it into orbit you would save the planet’s climate, but you couldn’t use it blackmail major population centres. Hardly seems worth it does it? 🙂

(yes, yes, you could shape the diamond into a lens instead and blackmail all the cities you want, but the maths required is just horrible ;))