An Introduction to the True Decimal system of units
The base units of today's SI metric system are annoying for a number of reasons, e.g.
the historical CGS-MKS dichotomy leading to a base unit with a quantity prefix, and the
embarrasing fact that the mole is defined in terms of the wrong mass unit. The meter
and kilogram are arguably quite inconvenient in any event, and the time and temperature
units are in a certain sense not decimalized (explained below). It's not too hard to do
better.
These units are based on the metrology done by the BIPM just as the SI units are. The
equations of physics take the same algebraic form in TD as in SI, although
simplifications may be possible in some cases. Since the 2018 redefinition of SI,
anyone can perform this excercise and propose a set of units on top of their work, and
with all the accuracy that makes possible.
Take one millionth of a day, 86400s, as the time unit (.0864s). Set the standard value
of the acceleration of gravity at earth's surface numerically to one to set a length
unit (7.32cm). Do the same thing with the density of water for the mass unit (392.3g).
For an absolute temperature scale, set zero celcius to 1000 (.27315K). Then subtract
1000 to form a relative scale - this is equal to celcius at 0, Fahrenheit at 63, and
Kelvin at 375 - just over the boiling point of water at 366. That number indicates that
the boiling point of water at atmospheric pressure is 36.6% hotter than its freezing
point. This is what I mean by decimalizing a unit, when that unit is defined based on
zero and a well-known reference point, the finite point should be 1 or a power of 10,
not e.g. 86400 or 273.15. All four of the usual temperature scales turn out to be
inconveniently defined in this sense, and also the time unit. The new mole is sensibly
defined in terms of the mass unit (392.3mol). For electric charge, set the electrical
constant known as epsilon zero numerically to 10 to the -12th (.427C). This yields a
general purpose set of mechanical and chemical units which is in no way inferior for
everyday use to SI, and which is a notable improvement in many small ways.
Here are the standard True Decimal units:
Unit Name Abbrev Verbal SI value
time Huygens hy hi 0.0864 s
length Euclid uc yuke 0.073206249984 m
mass Hooke hk hook 0.39232364332113 kg
absolute temperature Romer ol ole 0.27315 K
temperature Black bk black (Celsius times 1/0.27315)
quantity of substance Lavoisier lv lov 392.32364332113 mol
electric charge (C) Cavendish cv cav 0.42727265974832 A s
area Eudoxus dx dox 0.0053591550367199 m^2
volume Archimedes ax ax 0.000392323643321129 m^3
frequency (Hz) Fessenden fn fin 11.5740740740741 / s
angular speed (rad/s) Wu wu wu 1.84207110060064 / s
speed Benedetti bn ben 0.84729456 m / s
force (N) Hero ro ro 3.84738065677515 kg m / s^2
pressure (Pa) Boyle bo bo 717.908071405593 kg / m s^2
energy (J) Carnot cn can 0.281652310143488 kg m^2 / s^2
power (W) Trevithick tv trev 3.25986470073482 kg m^2 / s^3
electric current Davy dv dave 4.94528541375371 A
potential (volt) Guericke rk rick 0.659186361957706 kg m^2 / A s^3
resistance (ohm) Kirchhoff kf cuff 0.133295918598428 kg m^2 / A^2 s^3
capacitance (farad) Millikin mk mike 0.648181886650948 A^2 s^4 / kg m^2
magnetic field (tesla) Pixii px pix 10.627365934165 kg / A s^2
inductance (henry) Hughes hu huey 0.0115167673669041 kg m^2 / A^2 s^2
conductance (mho) Wheatstone wt weet 7.50210516957115 A^2 s^3 / kg m^2
magnetic flux (weber) Gramme me zen 0.0569537016731458 kg m^2 / A s^2
magnetic (oersted) Heaviside hs hez 8456989.10063394 A / m
viscosity (poise) Reynolds no ren 62.0272573694433 kg / m s
kinematic visc (stokes) Ostwald ow ow 0.0620272573694433 m^2 / s
radiation (gray) Meitner ls leez 0.717908071405593 gray
radiation (cps) Geiger gi guy 11.5740740740741 Bq
Each unit is given a unique name, with a two letter lowercase abbreviation and also a
shortened verbal name based on the abbreviation. Prefixes follow SI. There are also
several sets of special purpose units which use the same unit names but with a one
capital letter suffix to identify the distinct quantity. These special alternate units
are described later. You might wonder why they're necessary, but these are for things
like setting the speed of light or the gravitational constant to one, which are not
suitable for general use.
It's suprisingly easy to find more fun names than SI, and all of them deserve their
place. Some verbal examples: the ideal gas constant is "three kilo-can per lov ole"
(was 8 J/mol K). 1366 watts per meter squared is "2.25 trev per dox". C is "354
mega-ben" , but "one ben-E" (was "300,000 kilometers per second"). H-bar is "4.33 x 10
to the -33 can-hi" (was "1.05 x 10 to the -34 joule seconds"). 13.6 eV is "20.6
e-rick". If "ben-E" and "e-rick" are too informal, try "Benedetti-electrical" and
"electron Guericke" on for size. A footnote about radiation: I endorse the terms
"Gray-REM" and "Meitner-REM" or "leez-rem".
Some brief comments on the name of each unit:
hy: Christiaan Huygens (NL, 1629-1695) invented the pendulum clock.
uc: Euclid (GR, c. -300) published the Elements of Geometry, the most influential text ever.
hk: Robert Hooke (UK, 1635-1703) invented many scientific instruments.
ol: Ole Rømer (DK, 1644-1710) invented the modern glass-tube thermometer.
bk: Joseph Black (UK, 1728-1799) discovered the theory of latent heat.
dx: Eudoxus of Cnidus (GR (TR), -408--355) geometer, source of some of Euclid.
ax: Archimedes of Syracuse (GR (IT), -287--212) geometer, discovered buoyancy.
lv: Antoine-Laurent Lavoisier (FR, 1743-1794) originator of quantitative chemistry.
cv: Henry Cavendish (UK, 1731-1810) experimenter, anticipated Coulomb's law.
bn: Giambattista Benedetti (IT, 1530-1590) pre-Galileo experimenter on falling bodies.
fn: Reginald Fessenden (CA, 1866-1932) invented the heterodyne and AM radio.
wu: Wú Jiànxióng (CN, 1912-1997) discovered non-conservation of parity in beta decay.
Also known as C.S. Wu in english. Her experiment involved an angular dependancy.
ro: Hero of Alexandria (GR (EG), c. 60) made the steam-powered aeolipile and an early windmill.
bo: Robert Boyle (UK, 1627-1691) did early piston experiments and discovered Boyle's law.
cn: Sadi Carnot (FR, 1796-1832) discovered the theory of heat engines.
tv: Richard Trevithick (UK, 1771-1833) made some of the first high-pressure steam engines.
dv: Humphry Davy (UK, 1778-1829) used electric current to make several elements.
rk: Otto von Geuricke (DE, 1602-1686) very early experimenter on electrostatic force.
kf: Gustav Kirchoff (DE, 1824-1887) described the simple laws of electric circuits.
mk: Robert Millikan (US, 1868-1953) measured the charge of the electron.
hu: David Hughes (UK, 1830-1900) made a very early radio that didn't work by induction.
wt: Charles Wheatstone (UK, 1802-1875) made the Wheatstone bridge for measuring resistances.
px: Hippolyte Pixii (FR, 1808-1835) made a very early dynamo.
me: Zénobe Gramme (BE, 1826-1901) made a later dynamo.
hs: Oliver Heaviside (UK, 1850-1925) developed the telegrapher's equations.
no: Osborne Reynolds (UK (IE), 1842-1912) did crucial experiments in turbulence.
ow: Wilhelm Ostwald (DE (LV), 1853-1932) made a viscometer.
ls: Lise Meitner (AT, 1878-1968) discovered nuclear fission.
gi: Hans Geiger (DE, 1882-1945) made the Geiger tube radiation detector.
New names are given to the quantities area (dx), volume (ax), speed (bn), and angular
speed (wu). It is suggested that the units for acceleration be referred to as bn per
hy, or even bn fn. Momentum should be bn hk, while density is hk per ax. The Wu is
intended to be used for frequencies, to pair with hbar rather than h, which is used for
frequencies in fn. This choice between wu and fn is intended to absorb some factors of
pi in equations, although it can go either way. SI defines the radian as 1 which is
compatible with this system, although I think it makes as much sense to think of the
circle as being a separate angular unit (not a pure number) with the radian being
circle/2pi, so that fn and wu would be defined (SI-incompatibly) as circle/hy and
radian/hy. The current definition is SI-compatible. However you consider the basic
units to be set up, there must be a factor of 2pi difference between fn and wu.
See Denarius Verus for a fuller discussion of time vocabulary, but the commonly used
words are khy "kie" and dow, the decimal hour. For civil distances and road signs, I
recommend using a decimal mile of 10kuc or 732m, which I call the tik (for ten kilo,
like klik but shorter). Speed limits would be in bn: 40km/hr is 13bn which of course is
not only 13 uc per hy but also 13 tiks per dow. For kitchen use, the ax is a convenient
pint, and the half-ax would make a good cup measure. Teaspoon and tablespoon would be
10max and 50max, so that you have 10 tablespoons to the cup, although I don't have
better words to suggest for these - max is "max". Weights should be in hk and mhk or
"mook" like "hook" to match with ax and max - 1 ax or max of water weighs 1 hk or mhk.
Lengths would be in uc or muc, although rulers would normally be in 10muc rule. Socket
wrenches should be labelled in muc, which basically gives you an extra digit over mm.
You say muc as "muke" like "mucus". By the way, you can never capitalize max, mhk etc.
I don't endorse pronouncing the quantity prefix as if it was part of the name in
general, but it's a good idea for a handful of frequently used units to have good short
names. So those would be khy, muc, mhk, max, mlv/ax (see below), mlv/hk, and khk "cook"
(the new ton) would round out the set, plus of course dow and tik which aren't based on
the written abbreviations. I think we could live with milli-hy, kilo-uc, and mega-dx
(the new acre) etc. Incidentally, the max and Mdx show pretty clearly the value of
named area and volume units - the ability to put the SI prefix out in front gives you
much more control. Geologists may complain that they like km^3 very much, but see the S
units for an even better answer to that. Anyway the new SI prefixes now have plausible
uses well covered (see below for the nuclear length scale). The volume of the earth is
2.8 Yax. The cube of the light year is 267 QaxS.
A note on English verbal usage: I suggest that the verbal names for the units (the
two-letter abbreviations shouild always be used in writing) be considered auto-plural,
so that correct usage would be "thirteen ben" and not "thirteen bens". This also goes
for prefixed units, even familiar ones "three and a half halfax". On the other hand,
the terms tik and dow should have normal plurals, so that I endorse the following usage:
"thirteen ben is thirteen tiks per dow". For French, I suggest using the short names
with the vowels mutated in the obvious way. For tik, dow, khy I suggest un dik (dix
kilo), une heurde (heure décimale), une khy. In French mhk should be like "meuk" and
muc like "muc".
The erk or "e-rick" is the replacement for the eV (.66eV) "775 k e-rick" (electronmass).
The nano-uc is a good replacement for the angstrom which doesn't need a new name. The
units of molarity and molality are nearly the same in TD as in SI, except that they
differ by a factor of 1000, so that molar corresponds to mlv/ax and molal to mlv/hk.
The terms molar, molarity, and molality can continue in use under TD. If a short
pronunciation is required for the TD forms, I recommend "milvax" and "milvook" (like
hook), which would at least finally retire the CGS-MKS split in chemistry, at the
expense of sillier names (though it's not like molality is ultradignified in the first
place). You could define a whole series: elvax, milvax, micklevax, nalvax, picklevax,
felvax etc. None of these tems should ever be used in writing except to explain the
pronunciation - use the mlv/ax forms.
There is another group of specialized units which I will handle with something I call a
pseudo-prefix. These are the debye, fermi, barn, and jansky. In this case the names
Debye, Fermi, and Jansky will become the pseudo-prefixes. These don't stand for a
specific amount but are formed into special units by jamming the names together without
spaces as in these examples. The units involved are simply named without stating any
powers they may be raised to, as the names are unique without that, and quite long
enough. So for the debye we have the DebyeCavendishEuclid or DCU (uppercase
abbreviation). Others can be defined in a similar way. The point is that these names
can themselves take quantity prefixes. The full set for now:
Long name Abbreviations Definition Old value
DebyeCavendishEuclid debyecvuc DCU 1e-28 cv uc 0.938 debye
JanskyTrevithickEudoxusFessenden janskytvdxfn JTDF 1e-28 tv/(dx fn) 0.526 jansky
FermiEuclid fermiuc FU 1e-14 uc 0.732 fermi
FermiEudoxus fermidx FD 1e-28 dx 0.005 barn
FermiArchimedes fermiax FA 1e-42 ax 0.392 fermi^3
The base units are defined ultimately in terms of the same constants as SI: e h k c N_A
and the time base nuCs. However a number of other physical constants and approximations
are used as well:
Parameter Value in SI Constraint
day, the standard earth day 86400 s hard
dW, the density of water 1g/ml soft
gravity, earth surface gravity 9.80665 m / s^2 soft
Tstd, aka zero Celcius 273.15 K hard
mol(12C) 12g hard
epsilon0, permittivity 8.85418781583014e-12 A^2 s^4 / kg m^3 hard
mu0, permeability 4 pi 1e-7 kg m / A^2 s^2 hard
Gstd, an exact value for Newton's G 6.67430e-11 m^3 / kg s^2 not fixed
G, current value (currently = Gstd) 6.67430e-11 m^3 / kg s^2 hard
e h k c N_A hard
All of the base units can therfore be described in terms of these parameters. There are
a number of alternate unit systems offered along with the basic TD units. They are of
varying interest and usefulness. Three of the most useful will be described here, the E
S and R units. The A L C and G units are likely of lesser general interest and are
described only in the download file. A computer algebra system is helpful.
Base Unit Definition
Derived Unit (to simplify later definitions)
hy 1e-6 day
uc hy^2 gravity
hk dW uc^3
ol Tstd / 1000
lv mol hk / gram
cv 1e6 sqrt(ro uc^2 epsilon0)
bn uc / hy
ro hk uc / hy^2
hyE uc/c
hyS 1/sqrt(Gstd dW)
hyR 1/sqrt(Gstd 1e15 dW)
ucS 1e-3 gravity /((Gstd G^2)^(1/3) dW)
ucR c/sqrt(Gstd 1e15 dW)
hkE (1e-12 bn^2/c^2)hk
hkS 1e-09 gravity^3 /(G^3 dW^2)
hkR c^3 /(G sqrt(Gstd 1e15 dW))
cvE 1e-12 cv
lvS (hkS/hk)lv
lvR (hkR/hk)lv
In defining a system of units by supplying values for defining constants, it becomes
clear that many such combinations may be desirable on various occasions, but you can't
have all of them at once. As my standard unit definitions enrich the SI units they're
defined from, I describe 7 more systems (some only partial) which further enrich the base
system in ways not appropriate for general use - things like setting c = 1 or G = 1 or
mass = amu and so on. There arises an undesired complication in some cases however, as
seen in the Planck units. The Planck time is defined in terms of G which is only known
to a pathetic instrumental precision for use as a time base. For this reason I propose
a system of juggling two values of G simultaneously. One is a fixed value for all time
to establish exact proportions for critical units, and the other is the best current
experimental value. In the case of systems using G = 1, the time unit is first defined
in terms of the tabulated Gstd above. Other base units are then assigned combinations
of G and Gstd so that the combination (L^3 M^-1 T^-2) has the value of G. It is
preferable to use factors of G in units that are on "that side of the fence" (like mass
with G = 1), and Gstd with the others (like time), but in general a mix is necessary.
Mixing gets worse as you do things like make c = 1, as can be seen in the difference
between the S units (no c = 1, mass is pure G), and the R units (c = 1, mass is a mix).
The Planck units are the end product of that mania (also not very useful in practice).
The amu can potentially pose a similar problem, but a simple way around is to use mass =
amu and then keep factors of it out of the time unit, as in the L units. Mixing in a
few "soft" parameters judiciously makes a more flixible and usable set of units. By
this I mean parameters whose value is allowed to drift slightly as e.g. new values of G
are accepted. Many of these special units are appropriate for use both inside numerical
engines (where the constants set to one eliminate multiplies and divides, and "center"
the values in the floating point representation), but also for communicating the results
to humans afterwards.
SI - for comparison Definitions: day=86400, earth circumference ~ 40000, dW=1e3,
mu0 = 4 pi 1e-7, Tstd=273.15, mol(12C) / 12 kg = 1e3
Note that this is not exactly the current definition, but how the base units were
originally defined, using my terminology. Anyone familiar with SI knows all of those
numbers. It's important to recognize that the definitional numbers don't disappear -
they appear again and again. You want them to be simple. Note that = in the definition
denotes numerical equality of the quantity expressed in the appropriate base or derived
unit, and that ~ denotes approximate equality only.
Planck units - for comparison
Definitions: c=1, G=1, hbar = 1
No electrical or chemistry units are defined. These can't be used for observation
because they're substantially redefined every time someone makes a better measurement of
G, which is pretty often. With 3 hard constraints for 3 units, it is not possible to
fix this by compromise.
The Standard True Decimal units - no suffix letter
Definitions: day=1e6, gravity=1, dW=1, Tstd=1e3, epsilon0=1e-12
Also lv(12C) / 12 hk = 1, which I take to be the default in all TD unit systems.
The alternate unit systems will be described in a similar fashion.
Unit Equivalent
hy 0.0864 s
s 11.5740740740741 hy
uc 7.3206249984 cm
cm 0.136600358605797 uc
hk 0.39232364332113 kg
kg 2.54891597033184 hk
ol 0.27315 K
K 3.66099212886692 ol
bk 0.27315 degC
degC 3.66099212886692 bk
lv 392.32364332113 mol
mol 0.00254891597033184 lv
cv 0.42727265974832 C
C 2.34042590178608 cv
dx 0.00535915503671988 m^2
m^2 186.596579712323 dx
ax 0.392323643321129 l
l 2.54891597033186 ax
fn 11.5740740740741 Hz
Hz 0.0864 fn
wu 1.84207110060064 Hz
Hz 0.542867210540316 wu
bn 0.84729456 m/s
m/s 1.18022709835408 bn
ro 3.84738065677515 N
N 0.259917094046574 ro
bo 717.908071405593 Pa
Pa 0.00139293600368929 bo
cn 0.281652310143488 J
J 3.55047682545387 cn
tv 3.25986470073482 W
W 0.306761197719213 tv
dv 4.94528541375371 A
A 0.202212797914317 dv
rk 0.659186361957706 V
V 1.51702167658645 rk
kf 0.133295918598428 ohm
ohm 7.50210516957117 kf
mk 0.648181886650948 F
F 1.54277683562995 mk
px 10.627365934165 T
T 0.0940966939686517 px
hu 0.0115167673669041 H
H 86.829920944111 hu
wt 7.50210516957115 siemens
siemens 0.133295918598427 wt
me 0.0569537016731458 weber
weber 17.5581212567876 me
hs 106273.65934165 oersted
oersted 9.40966939686518e-06 hs
no 620.272573694433 poise
poise 0.00161219444871446 no
ow 620.272573694433 stokes
stokes 0.00161219444871447 ow
ls 0.717908071405593 gray
gray 1.3929360036893 ls
gi 11.5740740740741 Bq
Bq 0.0864 gi
The "Electrical" units - E
Definitions: mu0=1, epsilon0=1, uc=1, rk=1, ol=1
These units are for use with ordinary digital and analog electrical circuits, radio and
microwave transmitters and receivers, etc., as well as for textbooks and theoretical
work. The definitions may seem odd. First, setting mu0 and epsilon0 separately to one
is better than just setting c=1 (which it entails), because it puts electricity and
magnetism on a more equal physical footing, as a relativistic system should. The choice
of the remaining parameters is based on a joke about the SI E&M units, that if you
hooked up unit quantity components at random you could expect a small fire, equally true
of TD and for the same basic reason. This system comes about as close as possible to
making all unit quantities mild and reasonable (frequently encountered in practice, at
the very least) at the same time. It's bizarre for ordinary mechanics, for example the
unit density would be well described as a handful of electrons.
Unit Equivalent
hyE 2.44189765387627e-10 s
s 4095175727.01133 hyE
ucE 7.3206249984 cm
cm 0.136600358605797 ucE
hkE 3.44019384540819 electronmass
kg 3.19100943386172e+29 hkE
olE 0.27315 K
K 3.66099212886692 olE
cvE 2666826.18308813 e
C 2340425901786.08 cvE
dxE 0.0053591550367199 m^2
m^2 186.596579712323 dxE
axE 0.392323643321129 l
l 2.54891597033186 axE
fnE 4.09517572701133 GHz
GHz 0.244189765387627 fnE
wuE 651.767459783799 MHz
MHz 0.00153428954604717 wuE
bnE c
c bnE
roE 3.84738065677515e-12 N
N 259917094046.574 roE
boE 7.17908071405593e-10 Pa
Pa 1392936003.68929 boE
cnE 1.75793544960342 MeV
eV 5.68849100930068e-07 cnE
tvE 1.15341570395628 mW
W 866.990103021785 tvE
dvE 1.74975662501689 mA
A 571.508051864267 dvE
rkE 0.659186361957706 V
V 1.51702167658645 rkE
kfE 376.730313537943 ohm
ohm 0.00265441872890137 kfE
mkE 0.648181886650948 pF
F 1542776835629.95 mkE
pxE 30.0358101175024 nT
T 33293591.7522424 pxE
huE 91.9936868772374 nH
H 10870311.1479212 huE
wtE 0.00265441872890137 siemens
siemens 376.730313537943 wtE
meE 1.60966563073176e-10 weber
weber 6212470347.30685 meE
hsE 0.000300358101175024 oersted
oersted 3329.35917522424 hsE
The "Space" units - S
Definitions: G=1, gravity~1e3, dW~1, ol=1
These units are perfect for bodies in heliocentric or planetocentric orbit, as well as
for geophysics in the interiors of such bodies. The unit acceleration is close to the
earth's in solar orbit. The mass of Ceres is about 300 hkS. The moon's radius is 11.8
ucS. In the table, t_LEO = 2 pi earthradius/ sqrt(G earthmass / earthradius)
Unit Equivalent
hyS 3870.76796551846 s
t_LEO 1.3072267369336 hyS
ucS 146.931513417137 km
marsradius 23.0714291383908 ucS
hkS 3.17208528844324e+18 kg
moonmass 23165.634995581 hkS
olS 0.27315 K
K 3.66099212886692 olS
lvS 3.17208528844324e+21 mol
mol 3.15250035565963e-22 lvS
dxS 21588.8696350504 km^2
km^2 4.63201648305134e-05 dxS
axS 3172085.28844323 km^3
km^3 3.15250035565964e-07 axS
fnS 0.000258346666322598 Hz
Hz 3870.76796551846 fnS
wuS 4.1117148976554e-05 Hz
Hz 24320.752408447 wuS
bnS 37.9592666690515 m / s
m/s 0.0263440284217953 bnS
roS 3.11075301939119e+16 N
N 3.21465572408482e-17 roS
boS 1.44090592605217 MPa
Pa 6.94007833488355e-07 boS
cnS 4.57067649006076e+21 J
J 2.18785994190262e-22 cnS
tvS 1.18081903404627e+18 W
W 8.46869817615773e-19 tvS
The "Relativistic" units - R
Definitions: G=1, c=1, dW~1e-15, ol=1
This is the numerical relativity version of the space units. For use with black holes
and neutron stars and gravitational waves.
Unit Equivalent
hyR 0.000122404430650544 s
s 8169.63891490928 hyR
ucR 36.6959251348172 km
km 0.0272509821274733 ucR
hkR 24.8425919474096 solarmass
kg 2.02370160769505e-32 hkR
olR 0.27315 K
K 3.66099212886692 olR
lvR 4.94143996425925e+34 mol
mol 2.02370160769505e-35 lvR
dxR 1346.59092150011 km^2
km^2 0.000742616026911867 dxR
axR 49414.3996425925 km^3
km^3 2.02370160769505e-05 axR
fnR 8169.63891490928 Hz
Hz 0.000122404430650544 fnR
wuR 1300.23841658372 Hz
Hz 0.000769089720197182 wuR
bnR c
c bnR
roR 1.21025556433821e+44 N
N 8.26271763969804e-45 roR
boR 8.98755178736818e+34 Pa
Pa 1.11265005605362e-35 boR
cnR 24.8425919474096 solarmass c^2
kg c^2 2.02370160769505e-32 cnR
tvR 202955.00592077 solarmass c^2/s
W 2.75614593336369e-53 tvR
Finally, here is the official definition of TD, perhaps not what you were initially
looking for. See the documentaion of BX for the full story, but the numbers printed
here are in base-2 scientific notation with no visible binary point. Each number is
expressed as an integer times two to the power of the second integer, where "bx" means
binary exponent. These are 64-bit values suitable for IEEE754 double precision
arithmetic. A future specification of these units may use a wider representation, but
the numerical values of these constants will not change, except that the values for c h
k NA for the R S units will change whenever a better value of G is accepted. As of late
2023, the last CODATA release was 2019, and a new release seems almost overdue.
Depending on the timing of the next release, and on whether I get the sense that anyone
other than me is using these units at that time, I may accept not only a new value of G,
but a new value of Gstd. Of course this is not supposed to happen, and certainly will
not happen after 2025, but the opportunity may be irresistable on this one occasion.
Constant Exact value
nuCs 6662596412754083bx-23 hy^-1
c 5936167963874241bx-24 uc hy^-1
h 4974372324767136bx-157 hk uc^2 hy^-1
k 4556282198920434bx-128 hk uc^2 hy^-2 ol^-1
e 7787979421324359bx-114 cv
NA 6876153066858766bx35 lv^-1
nuCs 5054719964867040bx-51 hyE^-1
c 4503599627370496bx-52 ucE hyE^-1
h 5963275420777115bx-89 hkE ucE^2 hyE^-1
k 8287829039400945bx-89 hkE ucE^2 hyE^-2 olE^-1
e 7083126021211100bx-74 cvE
nuCs 4554565705487770bx-7 hyS^-1
c 8480134863532825bx-30 ucS hyS^-1
h 8470076581952860bx-247 hkS ucS^2 hyS^-1
k 5303506780096122bx-202 hkS ucS^2 hyS^-2 olS^-1
NA 6027763204242910bx98 lvS^-1
nuCs 4832778195896419bx-32 hyR^-1
c 4503599627370496bx-52 ucR hyR^-1
h 5085019393625861bx-311 hkR ucR^2 hyR^-1
k 6756912457694692bx-292 hkR ucR^2 hyR^-2 olR^-1
NA 5337587915908627bx142 lvR^-1
This is the part of the README file from the software download to do with TD:
This is a set of tools for using the True Decimal system of units of measurement, and for
using the Denarius Verus calendar and clock system in software.
First, in gnu-units you will find a number of files that can be used in various ways to
use and explore the True Decimal system in GNU Units, which is a sophisticated unit
conversion tool which is also a (slightly deficient) computer algebra system. The main
file here is units.dat which adds the TD units to the default SI-based GNU Units definitions.
It is used by running 'units -f units.dat'. All of the other units-based files mentioned
here are used the same way. There are also files which make the TD units (units-td.dat),
the E units (units-tdE.dat) etc. the "default" units. This means that when you enter an
expression for "you have", and leave the "you want" blank, it will convert to the default
units - normally SI. It can be convenient to have this enabled for the TD and alternate
units, not least because this feature most clearly shows the symbolic algebraic capabilities.
There are a number of alternate TD unit systems that aren't officially recommended (the
A, L, C, G units) but which are included here. The file units-K.dat defines all of the
units included in the others but the default units are the BIPM's new SI defining
constants, which all of these units ultimately reduce to. Then the file units-P.dat
allows only the TD and TD altenate units to be reduced to their defining "parameters".
In case the difference between K and P isn't clear, look at this output for hkE:
units-K.dat: Definition: (1e-12bn^2/c^2)hk = 46239957302.4645 h nuCs / c^2
units-P.dat: Definition: (1e-12bn^2/c^2)hk = 1e-60 day^8 gravity^5 waterdensity / c^2
Finally, units-P.dat reveals a gap in GNU Units' algebraic capabilities, namely an inability to
do fractional powers. units-P needs these, so it uses a hack, which is to output a modified
expression (in different and hard-to-read variables) which needs to be run through the provided
fix-roots utility. Fortunately the output of fix-roots is usually easy to massage into a form
that GNU units will accept as input.