The Metric System is great, but it's based on __decimal__ numbers, so the Janus numbers we just showed you don't
work well with it. But that's not the only problem with the Metric System :

- The units aren't based on anything - they're arbitrary.
- The prefixes (
*kilo- milli-*etc.) are a good idea, but we don't use them as much as we should. We say that A4 paper is 210mm wide, not 2.1dm (decimeters). We say Los Angeles is 5000km from New York, not 5Mm (megameters). In other words, the prefixes aren't the metric version of scientific notation, as they should be. - There are no metric units for several important qualities, like speed and acceleration. We talk about land in hectares, but real estate in square meters. And we measure electrical energy in kilowatt-hours, not joules.
- Time is not metric: a minute is not 100 seconds, and an hour is not 100 minutes or one-tenth of a day. Nor are angles metric.

To solve these problems, we use Janus metrics, based on *natural units*. Natural units * normalize* certain physical constants, defining them as opposed to measuring them. The list of constants that have been normalized in various systems includes :

- the elementary charge
*e* - the speed of light
, which appears in the formula*c***Energy =**(Einstein)*u*Mass*c*²

(theis a conversion factor in order to convert the units: in SI units of Joules, kilograms, meters and seconds, its value is 1.)*u* - the Planck constant
, which appears in the formula*h***Energy =**(Planck)*h*Frequency

(when frequency is expressed in radians, the formula uses the*reduced*version, the Dirac constant*ħ*=*h*/ τ - the Coulomb constant
**k**, which appears in the formula for electrostatic force_{e}**F**(Coulomb)_{E }= k_{e}Charge Charge / Distance² - the gravitational constant
**G**, which appears in the similar formula for gravitational force**F**(Newton)_{G }= G Mass Mass / Distance² - the Boltzmann constant
**k**, which appears in the formula relating macroscopic temperature (θ) to atomic energy_{B}**E = k**_{B}Θ - the electron mass
**m**_{e}

There are also two important constants that can't be normalized:

- the fine structure constant
**α**, a dimensionless number whose value is roughly 0.0072973525698 or 1/137.03599907 no matter which units are used. - the circle constant
**τ**= 2π ≈ 6.2831853, the ratio of the circumference to the__radius__(not the diameter!) of a circle.

(For a discussion of why Janus chooses 2π, or**τ**, for its circle constant, please visit Pi is Wrong and The Tau Manifesto).

A fundamental relationship unites several of these constants :

α *h c* = k_{e} *e*²

Because of this, these physical constants can't __all__ be normalized, and different systems of natural units
must choose some __not__ to normalize.

For example, the *Planck units* normalize ** c ħ k_{e} G k_{B}** to 1,
but not

*Stoney units* differ only in normalizing the elementary charge but not the Planck or Dirac constant (unknown
when Stoney proposed his units in 1881). *Hartree atomic units* normalize *e***k _{e}**,

But Janus units are intended to be universal, not *anthropic*. Planck units are sometimes called *God's
units*, but the elementary charge is more fundamental than the Coulomb constant, and radians are less fundamental
than cycles. So the Janus units start by normalizing ** e c h**, which seem indisputably fundamental: the
universal unit of charge, the universal upper limit of speed, and the universal relationship, via wavelength and
frequency, between distance and time on the one hand (united by

But we don't normalize the force constants **k _{e}** or

Nor do we normalize these constants to 1 - we normalize them to other values in order to derive base units at useful scales. The Metric system addresses the scale problem with a base unit, the *mole*, which consists of *Avogadro's number* (**N _{A}**) of molecules, where N

Using these normalized constants, Janus derives five fundamental units for charge, mass, time, distance and temperature, and another 20 physical and electromagnetic units, plus a few more social units which will be explained on the next page. All of these have been given English names based on Greek and Latin roots, and other languages will use similar names. Unit names are never plural, and each unit has a two-letter abbreviation, usually the first two letters of the original root, which is always written __before__ the value.

- We start the derivation by normalizing
to*e***1 / δ**, and thus defining the Janus unit of charge, the **Spinthit**[Sp] as a Dodekit of elementary charges.1 Spinthit = eδ = 1.428516719 × 10

^{-6}CoulombsHowever,

**the**: the electron carries a positive charge in Janus!__sign__of charges is reversed - We normalize
**m**to_{e}**1 / δ²**, and thus define the Janus unit of mass, the **Gravit**[Gr], as a Dodekit Squared (12^{24}) of the mass of the electron.1 Gravit = m

_{e}δ² = 7.241672213E × 10^{-5}kilograms - We normalize
to*c***δ**, and thus define the Janus unit of speed, the **Tachit**[Ta], as One-Dodekith (12^{-12}) of the speed of light.1 Tachit =

*c*/δ = 3.36237192 × 10^{-5}meters / second - We also normalize
to*u***δ**, and then calculate the value of the Janus unit of energy, the **Ergit**[Er], using Einstein's formula**E =**:*u*m*c*²1 Ergit = 7.29970511 × 10

^{-1}Joules - We then normalize the Planck constant
to*h***1 / δ³**, and then calculate the value of the Janus unit of time, the **Chronit**[Ch], using the Planck formula**E =**, where*h*ν**ν**(frequency) = 1 / time :1 Chronit = 6.43391816709006 × 10

^{5}seconds - The Janus unit of length, the
**Macrit**[Ma], is set to the distance you'd cover running at 1 Tachit for 1 Chronit:1 Macrit = 2.16332257927855 × 10

^{1}meters - We can then introduce a unit of Acceleration, the
**Archit**[Ar] = 1 Tachit / Chronit :1 Archit = 5.22600977285115 × 10

^{-11}meters / second^{2} - The Janus unit of Force is the
**Dynit**[Dy] = 1 Gravit Archit :1 Dynit = 3.78450497576255 × 10

^{-15}newtons - Finally, we normalize the Boltzmann Constant to
**1 / δ²**, and define the Janus unit of temperature, the **Thermit**[Th], using the formula**E = k**:_{B}Θ1 Thermit = 6.65077402 × 10

^{-4}degrees Kelvin

The other units are straightforward. Here are the other mechanical units, which all have Greek names:

- The
**Sychnit**[Sy] is the unit of frequency: one Sychnit means once per Chronit - The
**Platit**[Pl] is the unit of area: a Platit is one square Macrit - The
**Sterit**[St] is the unit of volume: a Sterit is one cubic Macrit - The
**Barit**[Ba] is the unit of pressure, 1 Dynit per Platit - The
**Pyknit**[Py] is the unit of density, 1 Gravit per Sterit - The
**Kinit**[Ki] is the unit of momentum, 1 Gravit Tachit - The
**Rhomit**[Rh] is the unit of power, 1 Ergit per Chronit

And here are the electromagnetic units, which all have Latin names based on the name of the dimension:

- The
**Currit**[Cu] is the unit of current, 1 Spinthit per Chronit. - The
**Potit**[Po] is the unit of potential, 1 Rhomit per Currit. - The
**Resit**[Re] is the unit of resistance, 1 Potit per Currit. - The
**Condit**[Co] is the unit of conductance, the reciprocal of a Resit. - The
**Capit**[Ca] is the unit of capacitance, 1 Spinthit per Potit. - The
**Fluxit**[Fl] is the unit of magnetic flux, 1 Potit Chronit. - The
**Densit**[De] is the unit of magnetic flux density, 1 Fluxit per Platit. - The
**Indit**[In] is the unit of inductance, 1 Fluxit per Currit.

In addition to the physical units, Janus defines a purely mathematical unit for angles. We don't measure angles in degrees or radians. Instead, we use fractions of the unit circle, which we define as 1 **Torit**. For example, an angle of 90° is ¼ of a circle, or 0.25 Torit. As explained above, Janus considers **τ** to be fundamental, not **π**, so 1 Torit equals **τ** radians or 360 degrees.

There are many other possible composite units, such as "Man Chronit" (a measure of the size of a task) or "Macrit / Sterit" (a measure of gas mileage), but they are all based on the units above.

Note that most of these units are around the small end of the range we use in everyday life. That permits us to
describe common measures using Shwa magnitide notation with small positive magnitudes. For example, the Gravit is about
one-fourteenth of a gram, almost the same size as the *grain*, an old unit of weight, and 12^{+6} Gravit is
about a ton.

Archit | Ar | acceleration | | |
---|---|---|---|---|

Barit | Ba | pressure | | |

Capit | Ca | capacitance | | |

Chronit | Ch | elapsed time | | |

Condit | Co | conductance | | |

Curit | Cu | current | | |

Densit | De | flux density | | |

Dodekit | Do | quantity | | |

Dynit | Dy | force | | |

Ergit | Er | energy | | |

Fluxit | Fl | magnetic flux | | |

Gravit | Gr | mass | | |

Indit | In | inductance | | |

Kinit | Ki | momentum | | |

Macrit | Ma | length | | |

Platit | Pl | area | | |

Potit | Po | potential | | |

Pyknit | Py | density | | |

Resit | Re | resistance | | |

Rhomit | Rh | power | | |

Spinthit | Sp | electric charge | | |

Sterit | St | volume | | |

Sychnit | Sy | frequency | | |

Tachit | Ta | speed | | |

Thermit | Th | temperature | | |

Torit | To | plane angle | | |

Note that the abbreviations in Shwa script are based on the Greek or Latin root, not the English name.

- Units of distance :
English Metric Janus (decimal) 0.0394" **1mm**Ma5*46225 0.394" **1cm**Ma4*46225 **1 inch**2.54cm Ma3*11741 **1 foot**30.5cm Ma2*14089 **1 yard**91cm Ma2*42268 3'3" **1 meter**Ma2*46225 851.7"

(71ft)21.633m **1 Macrit** 5/8 mile **1km**Ma1°46225 **1 mile**1.6km Ma1°74392 - Units of mass :
English Metric Janus (decimal) 2.55e-3 oz 7.24167e-2g **1 Gravit** 0.0353 oz **1g**Gr1°138090 **1 oz**28.35g Gr2°391478 **1 lb**454g Gr3°626364 2.20 lbs **1kg**Gr4°138090 **1 ton**907kg Gr7°125273 1.10 tons **1 tonne**Gr7°138090 - Units of time :
English Janus (decimal) **1 second**Ch6*15542 **1 minute**Ch5*93256 **1 hour**Ch3*55953 **1 day**Ch1*13429 **1 week**Ch1*94002 7 days 10 hours

43min 12sec**1 Chronit** **1 month**Ch0°40873 **1 year**Ch1°49048 **1 century**Ch3°49048 **1 millennium**Ch4°49048 - Units of charge :
Gaussian Metric Janus (decimal) **1 esu**3.33564e-10 C Sp4*233504 4.28259e3 esu 1.42852e-6 C **1 Spinthit** 2.99792e9 esu **1 Coulomb**Sp5°700027 - Units of temperature :
Fahrenheit Celsius Kelvin Janus (decimal) -459.7°F -273.15°C **0°K****0 Thermit** 1.19714e-3°F 6.65077e-4°C 6.65077e-4°K **1 Thermit** -459°F -272.15°C **1°K**Th3°1504 **0°F**-17.778°C 255°K Th5°3834 32°F **0°C**273°K Th5°4104 212°F **100°C**373°K Th5°5608

*Credit for help with this section is due to Neil Basescu, the Web sites of Erik Max Francis and Eric Weisstein, and numerous Wikipedia
pages.*

< Janus Numbers | Social Units > |

© 2002-2016 Shwa | shwa@shwa.org | 03oct16 |