Late Epoch Metric-60 Units
Maxwell Planck's "Natural Units" and Metric-60
When the Community formally adopted the sexagesimal numbering system, they also adopted a new set of units. Subjective time was still measured in circadians, but they were now divided into metric-60 divisions. However, objective time was derived from Max Planck's "natural units", with metric-60 nomenclature applied. In Planck measure, time and space use the same units, as do mass and energy. This is achieved because, in the Planck scale (and corresponding metric-60), c (the speed of light in a vacuum), ħ (Dirac's constant), and G (the gravitational constant), are all defined as equal to one. Thus, e=mc2 becomes e=m, E=ħw becomes E=w, and so on.
The Planck time is the natural unit of time, the smallest possible measurement of time within the boundaries of physics, denoted as tp. It is the smallest measurement of time that has any meaning (any events occurring closer together are simultaneous). tp is defined formally as the time it would take a photon traveling at the speed of light to cross a distance equal to the Planck length, and is approximately 5.38121 x 10-44 seconds.
The Planck length, lp, is the smallest distance that has any meaning in the physical universe, as below this length quantum mechanics makes any and all measurements nonsense. It is, essentially, the maximum resolution in space and time of our physical universe, defined and constrained by the very laws of physics themselves, and is approximately equal to 1.61624 x 10-35 meters.
Because of slight uncertainties in the measurement of the gravitational constant, upon which the precise value of Planck time depends, the Community tentatively adopted a series of units derived from physicists' best approximation of those values at that time. To avoid confusion, units used by the Community were given names different from their Planck counterparts, with the understanding that, should errors in the measurement of Planck time, mass, charge, etc. be discovered, those values could be updated and a sensible migration to a new, more precise set of units based on those new values, with different names, could be achieved.
For that reason, the fundamental unit of time, the "tock", was defined by the Autonomous Community as precisely 5.39121 x 10-44 seconds. A tock is also the unit of measure for distance, defined as the distance light travels in 5.39121 x 10-44 seconds, or 1.61624 x 10-35 meters.
| Metric-60 Unit | Planck Unit | Dimension(s) | SI equivalent |
|---|---|---|---|
| Tock | Planck Time | Time (T) | 5.39121 x 10-44 s |
| Planck Length | Length (L) | 1.61624 x 10-35 m | |
| Speck | Planck Mass | Mass (M) | 2.1764516 x 10-5 g |
| Mass = Energy | Energy (E) | 1.8755459 x 10-18 C | |
| Spark | Planck Charge | Electric Charge (Q) | |
| Degrees Prime | Planck Temperatures Defined as 6019° P | Temperature (ML2T-2/k) | 1.41679 x 1032 K
|
Planck Time and "Tocks"
As discussed earlier, the metric-60 unit "tock" is derived from physicists' best estimation of the Planck Time, and is defined as precisely 5.39121 x 10-44 seconds. The following table shows some common durations of time and their metric-60 equivalents.
| Description | Metric-60 Units | SI Units | |
|---|---|---|---|
| Sexagesimal | Decimal | ||
| Planck Time |  t | 1 t | 5.39121 x 10-44 s |
| "Second" |  .     ge-t | 3.91457 ge-t | 1 s |
| "Minute" | . he-t | 3.91457 he-t | 60 s |
| Gen-5 Circadian |  .     he-t | 4.69748 he-t | 72 s |
| Gen-4 Circadian |  . he-t | 5.64698 he-t | 86.4 s |
| Gen-3 Circadian |  .     he-t | 9.39496 he-t | 144 s |
| Gen-2 Circadian |  .  he-t | 28.18488 he-t | 432 s |
| Dies (Gen-1 Circadian) | .    je-t | 3.13165 je-t | 2880 s |
| "Hour" | . je-t | 3.91457 je-t | 3600 s |
| "Day" | .   le-t | 1.56583 le-t | 86,400 s |
| "Week" |  . le-t | 10.96079 le-t | 604,800 s |
| kilodies | .  le-t | 52.19423 le-t | 2,880,000 s |
| "Earth Year" | .    me-t | 9.53177 me-t | 31,556,926 s |
| App. Age of the Earth | .  se-t | 55.16069 se-t | 4.5 x 109 years |
| App. Age of the Universe | . te-t | 2.7989 te-t | 1.37 x 1010 years
|
Metric-60 Dates
Metric-60 dates are written in terms of meratocks, as follows:
m.jj-h:g:f.x meratocks (me-t) New Epoch
where m=meratocks, jj=jeratocks, h=heratocks, g=geratocks, f=feratocks, and x is any remaining fraction.
The easiest way to come up with a given metric-60 date in terms of "tocks" is to figure out how many seconds have passed since metatime 0.000-0:00:000, convert the result to feratocks using the conversion factor of 234.8742 fa-t/s, derive the resulting sexagesimal numeral, and then insert the date-time punctuation into the resulting integer.
For example, the Autonomous Community was founded on:
.-:: me-t New Epoch
The Community's worst crisis came to a head 8,311,507 seconds later. 8,311,507 seconds multiplied by 234.8742 feratocks/second yields 1,952,158,560 feratocks. Converting this number to sexagesimal using the procedure described in Appendix A of the novel "Autonomy: Freedom of Thought", we obtain the value:
Now, simply insert the standard time-date punctuation, and we have:
.-:: me-t new Epoch
Planck Length and "Tocks"
Distances are also measured in tocks, where one tock is the distance light travels in a vacuum in one tock (about 1.61624 x 10-35 m). The following table shows some common distances in terms of Metric-60 tocks and SI meters, intended to provide some sense of scale. Typically, the Community speaks in terms of qaratocks at the femto level, saratocks at the atomic level, and taratocks at the nano level. Yaratocks are roughly analogous to millimeters, zaratocks to centimeters or inches, charatocks to feet or meters, beratocks to kilometers or miles, and meratocks to lightyears. Notice the time=space relationship? Meratocks are also analogous to years when measuring time. This is not a coincidence.
| Measure | Metric-60 Units | SI Units | |
|---|---|---|---|
| Sexagesimal] | Decimal | ||
| Planck Length | t | 1 tock | 1.61624 x 10-35 m |
| Radius of a Proton | ~. qa-t | ~1.7054 qa-t | ~1 x 10-15 m |
| Size of a hydrogen Atom | ~. sa-t | ~56.8472 sa-t | ~1.2 x 10-10 m |
| "millimeter" | . ya-t | 36.553 ya-t | 0.001 m |
| "centimeter" |  . za-t | 6.0922 za-t | 0.01 m |
| "inch" | . za-t | 15.474 za-t | 0.0254 m |
| "foot" | . cha-t | 3.0948 cha-t | 0.3048 m |
| "meter" | . cha-t | 10.1536 cha-t | 1 m |
| "kilometer" | . be-t | 2.8204 be-t | 1000 m |
| "mile" | .   be-t | 4.5391 be-t | 1609.344 m |
| Astronomical Unit | . he-t | 32.5566 he-t | 149,598,000,000 m |
| Light Year | . me-t | 9.5318 me-t | 9.4605284 x 1015 m
|
Planck Mass and "Specks"
The Planck mass is the mass at which a body's Compton length (the distance at which quantum mechanical properties dominate) and the Schwarzschild radius (the radius at which, if a mass is squeezed down to that size, it becomes a black hole) are equal, or, put another way, the mass at which both relativistic and quantum properties are equally dominant.
In the Autonomous Community, mass and energy are both measured in the same units, specks, which are defined as the Planck mass, 2.1764516 x 10-5 g.
Planck Charge and "Sparks"
The Plank charge, qp, is defined in terms of the speed of light (c), Planck's constant (h), and the permittivity of free space (ε0):
qp = (2chε0)1/2
It is about 11.7 times the charge on an electron (ignoring the sign).
Planck Temperature and Degrees Prime
The Planck Temperature is the temperature one Planck Time unit after the big bang. There are no physically meaningful temperatures hotter than this, according to current theories of physics. In other words, the possible range of any temperature, anywhere in the physical universe, at any time from its beginning to its end, is bounded by absolute zero (the coldest possible temperature), and the Plank temperature (the hottest possible temperature). The Autonomous Community chose to divide this range into a scale of 6019 "degrees Prime", resulting in a conversion factor of 0.0232505694 °K/°P, or 43.0098843 °P/°K. Naming the temperature scale "Prime" was both a monument to the entity that so helped shape the Community's ethos and character, and a convenience, as later theories might yield different values for the Planck temperature, and new scales might be adopted. It was decided that any such future scales would be derived from Latin ordinals, "Secondus", "Tertius", "Quatrus", and so on.
The following table shows several common and familiar temperatures, in Prime, Kelvin, Celsius, and Fahrenheit. While the temperatures in degrees Prime seem large to those used to decimal numbers, keep in mind that in sexagesimal, these values are mostly three and four digit temperatures, ranging from ° P (10,983° P/255.37° K) to 
° P (249,456° P), or . fa° P (1.1549 fa° P), which is 5800° K. For those used to sexagesimal, these numbers are as easy to remember as their Kelvin, Celsius, or Fahrenheit equivalents, and at higher temperatures (such as that of the core of the sun), significantly easier.
| Description | Prime | Kelvin | Celsius | Farenheit | |
|---|---|---|---|---|---|
| Sexagesimal | Decimal | ||||
| Absolute Zero | ° P | 0° P | 0° K | -273.15° C | -459.67° F |
| "bitter cold" | ° P | 10,983° P | 255.37° K | -17.78° C | 0° F |
| H20 Freezing | ° P | 11,748° P | 273.15° K | 0° C | 32° F |
| "chilly" |  ° P | 12,178° P | 283.15° K | 10° C | 50° F |
| "cool" | ° P | 12,393° P | 288.15° K | 15° C | 59° F |
| "pleasant" |  ° P | 12,608° P | 293.15° K | 20° C | 68° F |
| "perfect" | ° P | 12,704° P | 295.37° K | 22.22° C | 72° F |
| "hot" |  ° P | 13,038° P | 303.15° K | 30° C | 86° F |
| "very hot" | ° P | 13,373° P | 310.93° K | 37.78° C | 100° F |
| H20 Boiling |  ° P | 16,049° P | 373.15° K | 100° C | 212° F |
| Lead Melts | ° P | 25,813° P | 600.16° K | 327.46° C | 621.43° F |
| Solar Surface | ° P | 249,456° P | 5800° K | 5528.85° C | 9980.33° F |
| Atomic Bomb |  ° P | 12,899,425° P | 300,000° K | 299,727° C | ~540,000° F |
| Solar Core | . ga° P | 51.77 ga° P | 1.56 x 1010° K | 1.56 x 1010° C | 2.8 x 1010° F |
| Planck Temperature | cha° P | 1 cha° P | 1.4168 x 1032° K | 1.4168 x 1032 °C | 2.55 x 1032° F
|
