spash

2.0.1 • Public • Published

Spash: Spacetime Hash

Maps every location in the observable universe to a string of the form:

<Origin>.<Hash>[.<TimeHash>]

(Example: E.6BLH4goVfxs.oL9-D4.)

  • Origin: IAU designation of a celestial object, percent-encoded as per reg-name syntax in RFC 3986; eg. E for Earth.
  • Hash: encoding of latitude, longitude, and distance to the radius of the celestial object. With 12 characters, you can encode the precise position of a single human in the ISS. With 11, the position of a room anywhere in the world.
  • TimeHash: encoding of a TCG-backed timestamp: the number of seconds since the Unix Epoch at the centre of the celestial object if that object was not there to cause gravitational time dilation. With 6 characters, you get secondwise precision. It is optional.

The hash is an unpadded base64url string. Each character encodes 6 bits. Two of them contribute to longitude, two to latitude, two to altitude. They alternate in this order, similar to Geohash: one longitude bit, one latitude bit, one altitude bit, one longitude bit, and so on.

Geographic coordinates

Extract separately the longitude bits and the latitude bits into two lists. The range of the latitude goes from -90° (South Pole) to 90°. Longitude goes from -180° to 180°, with 0° at the Prime Meridian and increasing eastward.

Each bit determines whether the intended value is above / on (1) or below (0) the previously defined range, starting with the full range. For instance, a starting bit of 1 means that the longitude is between 0° and 180°. That includes most of Europe, Africa, Asia and Oceania, but excludes America. If the fourth bit is 0, the longitude is between 0° and 90°.

Altitude

Extract the altitude bits into its own list. It encodes an adjustment compared to the radius of the celestial object. For Earth, that radius is sea level, and that adjustment is the altitude.

The minimum altitude is minus infinity, and the maximum altitude is infinity. That allows encoding any altitude with arbitrary precision. An altitude lower than the negative of the radius is treated to correspond to the center of the celestial object.

Let's introduce the following function, which maps values from -1 to 1 to real values.

          ⎧ x / (x + 1)   if x < 0
asig(x) = ⎨
          ⎩ -x / (x - 1)  otherwise

Similarly to what happens with latitude and longitude information, each bit determines whether the intended value is above / on (1) or below (0) the previously defined range, starting with a range from -1 to 1. The error range for the altitude goes from asig(lower bound) to asig(upper bound), in kilometers.

The center point of the spash should be defined as the point at the center of the error ranges of the latitude, longitude and altitude that were decoded.

TimeHash

Extract the time bits. It encodes an adjustment compared to the Unix Epoch (ISO 8601 1970-01-01T00:00:00Z) in seconds at the center of the celestial object, assuming the tracking of time is unaffected by gravitational time dilation.

The minimum time is minus infinity, and the maximum time is infinity. That allows encoding any time with arbitrary precision.

Similarly to what happens with latitude and longitude information, each bit determines whether the intended value is above / on (1) or below (0) the previously defined range, starting with a range from -1 to 1. The error range for the altitude goes from asig(lower bound) to asig(upper bound), in TimeHashPeriod, a new unit defined as 0xffffffff (4294967295) seconds (which is roughly 136 years).

The center point of the TimeHash should be defined as the point at the center of the error range of the time that was decoded.

Pros and Cons

Geohash alone cannot distinguish between levels in a building, or between an underground tunnel and the road above it, or between the ISS and whichever location it is hovering above. A spash can. It can easily separate rooms in a building. Note however that most mobile phones have a precision of tens of meters; unless your device has a precision on the order of the meter, you won't be able to produce or identify a room from a spash. It would still identify the difference between a mountain tunnel and the ground, or between rough areas of a skyscraper.

Spashes allow arbitrary precision. On the flip side, a given spash can describe a location too precisely: there can be multiple valid spashes for the same location. When choosing a spash for your location, make it precise enough that your target location is unambiguous from standing at the center point of the spash.

A spash's substring describes a less precise location of the same position. That means that spashes with a common substring are close: they have an upper bound to their distance. However, two extremely distinct spashes can specify locations that are extremely close, especially at the poles and way up in space.

Ideally, we would want the error volume associated with a spash to be a ball. However, it is more like a curved box. However, this design gave good approximations and maintains simplicity.

Use-cases

  • Universal distributed locator for physical places.
  • Travel industry: this locator can be used to specify any station in the universe, regardless of type, without needing a central authority to name them. Any system for finding a station will simply take the one that is closest to the queried station.
  • Locators for arbitrary, cross-building or cross-city meeting points. The old way of specifying the address and the room number is not as convenient as decoding the bits of a spash with a RFC 2289-like 4096 word list, producing 6 short words for every room. Besides, if you forgot the last word, you will still end up close by.
  • Compact transmission of aircraft, rocket or space station location.

Contribute

Implement it in your own language. Send me a tweet to your code @espadrine.

Here is a list of known implementations:


Inspired by Geohash.

License: CC0.

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