Deep time and shallow time

Eugene Leitl (
Wed, 26 May 1999 15:47:13 -0700 (PDT)

The Swiss company Swatch recently defined the Biel meridian time, dividing the day in one kilobeat (1 beat=1.44 min), taking the city of Biel, Switzerland, as a point of reference.

Unlike just using using the timer output of a GPS receiver
(which lets you synchronize systems at +/- 1 us precision
anywhere on the globe) to nudge a largish counter by 1 s ticks, the new scheme seems to catch on.

However, the hardcore transhumanist nuts among us intend to live
(almost) literally forever (shedding several snake skins along
the way, and going to some very distant very exotic places), so this won't quite do. We need to define our very own extropian, transhumanist time standard (>HTS) capable of both reaching down into very shallow time of nucleonic and subnucleonic processes
(to be able to say hello to pulsar Steve) and up to the deep
time of astrophysical processes (see Diana, who is all over Magellanic clouds yonder). At the same time the standard, or a subset of it has to be usable to us-current. Tough, eh?

Making the counter to be binary makes obvious sense. Since extending a binary counter register by one bit doubles the time to wraparound, one can obviously prevent an *observable* wraparound even if counting in Planck time unit increments, while using a counter of relatively modest size. (Thanks, no y2g bug for me). Of course no physical counter is going to resolve Planck time quanta, ever, so we need to cheat a little, and increment in chunks the current physical implementation can handle, while maintaining a migration path to next generation technology. Semiconductor counters will eventually handle up to ~100 GHz, those from hypothetical nucleonic matter a lot more, <insert your favourite lunatic fringe tech here> a couple of orders of mangnitude more, so we'd better reserve a big security margin. Since impact of spacetime curvature is already apparent with nuclear time etalons sitting a few 100 m apart even in Earth's shallow gravitational gradient, we must obviously compensate. Let's define the reference clock for absolutely flat spacetime, and introduce realtime correction feedback loop to it using input from a spacetime curvature sensor. (Further design refinement? Don't bother me with boring implementation details, d00d.)

As to the utilized coding, I'm not sure that binary is best: obviously there are problems with propagating overflow bits around in a relativistic context, so something with Hamming distance one at each tick might make more sense. Gray code? Any other codings where the flips are local? Any arithmetics defined on them?

For the sake of illustration, let's represent the counter in hexadecimal notation: one cypher/nybble (4 bit). As a trivial example, consider the next generation of Sony game engines which can natively handle 128 bit integers.

As a more compact representation, this can be written as a hexadecimal (base16: 0123456789abcdef) number: for instance


Let's say the rightmost bit has a temporal resolution of 1 THz
(thus allowing some slack for the next CPU generations to come),
while the CPU itself runs at 256 MHz. We thus must obviously increment in 4-digit strides (i.e. skipping four leftmost digits, piping the clock into the 16th bit)

	dead beef d00d f00f 4711 affe 2999 7924	
                  |||| |||| |||| |||| |||| ||||
                  |||| |||| |||| |||| |||| ||||
                  |||| |||| |||| |||| |||| |||+-    1 THz ~visible light
                  |||| |||| |||| |||| |||| ||+--   64 GHz
		  |||| |||| |||| |||| |||| |+---    4 GHz microwave
		  |||| |||| |||| |||| |||| +----  256 MHz
		  |||| |||| |||| |||| |||+------   16 MHz radio
		  |||| |||| |||| |||| ||+-------    1 MHz
		  |||| |||| |||| |||| |+--------   64 kHz ultrasonics
		  |||| |||| |||| |||| +---------    4 kHz
                  |||| |||| |||| |||+-----------  256  Hz
		  |||| |||| |||| ||+------------   16  Hz neurobiological chronon
		  |||| |||| |||| |+-------------    1  Hz
		  |||| |||| |||| +--------------   16 s
		  |||| |||| |||+----------------  4.3 min
		  |||| |||| ||+-----------------  1.1 h
		  |||| |||| |+------------------ 18.2 h
		  |||| |||| +------------------- 12.1 d
		  |||| |||+---------------------  6.3 month
		  |||| ||+----------------------  8.4 year
		  |||| |+-----------------------  0.1 kYear ~human lifespan
		  |||| +------------------------  2.1 kYear
		  |||+-------------------------- 34.2 kYear
		  ||+---------------------------  0.5 MYear
		  |+----------------------------  8.8 MYear
		  +-----------------------------  0.1 GYear
						  2.2 GYear
						 35.9 GYear ~age of universe
						573.9 GYear
						at the

All this is qualitative (I've cheated, using powers of two at the beginning, then going to decimal orders of magnitude, but all this is just for the sake of illustration, anyway).

With a layout similiar to the above we can visualize the time in a spatial scheme:

	deep time				shallow time
	xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx
	||||||||| |||| ||||   ||||||||| ||||||  |||||||||  ||||||||
	nevernever cosmological	human	machine	subnucleonic ridiculous		
	time       time scale	window	time	time	     time

Of course one needs to extend a positioning service as well. GPS is geocentric, we might use atomic clock beakons to establish solar navigation service and pulsars as a galactic-wide sources.

All this only 1/2 tongue-in-cheek.