lemÌc. Lemizh grammar and dictionary

Units of measurement

What, then, is the meaning of it all? What can we say to dispel the mystery of existence?
If we take everything into account … then I think we must frankly admit that we do not know.
But, in admitting this, we have probably found the open channel.

(Richard Feynman. The Value of Science)

Here is a conversion table for the physical units of measurement. The unit names link to the dictionary.

You may also want to skip this table and see how to use these units in grammar.

Time and space
DimensionUnitConversion (SI / European units)Conversion (non-SI / Anglo-American units)
timekrà.s = 0.7585 kk = 1.318 s
lengthxrà.m = 10.867 xx = 92.023 mmft = 3.312 xx = 3.623 in
area(see below) = 118.09 2x2x = 84.682 cm²sq ft = 10.97 2x2x = 13.13 sq in
volume = 1,283.3 3x3x = 779.26 cm³cb ft = 36.34 3x3x = 47.55 cb in
speedkàx.m⁄s = 14.33 kx
km⁄h = 3.980 kx
kx = 6.980 cm⁄s
kx = 0.2513 km⁄h
mph = 6.405 kxkx = 0.1561 mph
(valid up to ~3000 km⁄s; see below)(valid up to ~1800 miles per second)
ψLem = 168 artanh vcv = c tanh (16−8ψLem)ψLem = 168 artanh vcv = c tanh (16−8ψLem)
[c = 299,792,458 m⁄s][c = 670,616,629 mph]
anglerà.
[selà.]
rad = 1 rr = 1 rad1° = 2.13̅ s
360° = 768 s = 3 × 162 s
s = 28′ 7.5″
solid angle(see below)sr = 1 2r2r = 1 sr1 (°)² = 4.551̅ 2s2s = 791 (′)²
The official angle unit is of course the same as our radian, that is, a dimensionless unit with a value of one – and that is how it is named. This unit is used for compounding other units; but the alternative selà. is used for many practical purposes just like our degrees.
Mechanics (mass related units)
DimensionUnitConversion (SI units)Conversion (non-SI / Anglo-American)
masslàq.kg = 1.314 ll = 761.1 glb = 0.5959 ll = 1.678 lbs
energyiotà.J = 269.7 ii = 3.708 mJcal = 1,129 i1,000 i = 0.8857 cal
256 i = 0.2267 cal
energy per mass,
hàhs.J⁄kg (Gy) = 205.2 hh = 4.872 mJ⁄kg (mGy)cal⁄lb = 1.895 h1,000 h = 0.5278 cal⁄lb
256 h = 0.1351 cal⁄lb
momentumblàp.N·s = 18.82 bb = 53.13 mN·s
powermelàs.W = 355.5 mm = 2.813 mWhp = 265,100 m1,000,000 m = 3.772 hp
65,536 m = 0.2472 hp
angular power densitynatlà.W⁄sr = 355.5 nn = 2.813 mW⁄sr
power densitygomàs.W⁄m² = 3.010 gg = 0.3322 W⁄m²
forceemblà.N = 24.81 ee = 40.30 mNlbf = 110.4 e1,000 e = 9.050 lbf
256 e = 2.319 lbf
pressurearàc.Pa = 0.2101 aa = 4.759 Paatm = 21,290 a1,000,000 a = 46.97 atm
65,536 a = 3.078 atm
mmHg = 28.02 a256 a = 9.138 mmHg
Thermodynamics
DimensionUnitConversion (SI units)Conversion (non-SI / Anglo-American)
temperatureqàc.K = 0.879 q
TLem = 0.879 × (ϑ°C + 273.15)
q = 1.138 K
ϑ°C = 1.138 TLem − 273.15
TLem = 0.488 × (ϑ°F + 459.67)ϑ°F = 2.048 TLem − 459.67 The temperature unit measures absolute or thermodynamic temperature, that is, the scale starts at zero Kelvin, −273.15 °C or −459.67 °F. Consequently, there are no negative temperatures.
Electromagnetism
DimensionUnitConversion (SI units)
electric charge/fluxoàs.C = 17.35 oo = 57.64 mC
electric flux densityudreà.C⁄m² = 0.1469 uu = 6.807 C⁄m²
electric currentpotmàs.A = 22.87 pp = 43.72 mA
voltagedisfàk.V = 15.54 dd = 64.34 mV
resistancefragmà.Ω = 0.6795 ff = 1.472 Ω
capacitancetelmà.F = 1.116 tt = 0.8959 F
inductanceytàs.H = 0.5154 yy = 1.940 H
magnetic charge/fluxOàs.Wb = 11.79 OO = 84.82 mWb
magnetic flux densityUdreà.T = 0.09983 UU = 10.02 T
Light
These units are derived from mechanical ones by correcting for the sensitivity of the human eye (Koi ὀφθαλμός, whence the superscript o). At a wavelength of 555 nm (lime green), where the eye is most sensitive, one unit of energy and one unit of luminous energy are equal.
There are analogously defined acoustic units, which are written with a superscript u.
DimensionUnitConversion (SI units)
luminous energy(see below)lm·s = 0.3948 ioio = 2.533 lm·s
luminous fluxlm = 0.5205 momo = 1.921 lm
luminous intensitycd = 0.5205 nono = 1.921 cd
illuminanceklx = 4.408 gogo = 226.9 lx
Finance
DimensionUnitConversion (European)Conversion (British and American)
currencynabà. = 0.69  = 1.45 £ = 0.75 US\$ = 0.61  = 1.33 £ = 1.63 US\$
The conversion factors are valid as of August 2019. The author is not responsible for any financial losses you might experience when investing in nabus or other currencies from the Lemizh world.

Note on speed The speed unit is actually a unit of rapidity (ψ), which is a way of measuring motion alternative to the common concept of speed (v). ψ increases nearly proportionally to v as long as we are not approaching vacuum light speed (c), but then rises more and more quickly, reaching infinity at the speed of light. For everyday purposes, the conversion factors given above are usually more than accurate enough.

Expressing quantities

krà. means ‘make/become a time span of 1.318 seconds’. This and other units, including weekà., yearà. etc., are basically numerals with a physical dimension: krÌ. means ‘a time span of 1.318 seconds’, krìl. ‘(the concept of) a time unit or time units, time-unit-ness’. Units usually need to be multiplied with numbers; that is, we need a bracket and a consecutive case (see Multidigit numbers in unit 7; **dwÌ krÌy. would mean ‘two individuals, which are 1.318 seconds’). The same applies if units need to be multiplied among themselves. Quotients of units work as fractions; powers of units work as described in the chapter on functions; and light related units are compounds with dmùt. ‘eye’ and an epenthetic benefactive.

 dwÌ xrìly. two consequences of making 9.2 cm; two 9.2 cm-nesses; 2 × 9.2 cm 18.4 cm (7¼ in) two-acc1 lengthunit-cons-acc2. 14-0000-Ì fragmìly xrìly. 14,0000hex ≈ 1,300,000 resistance units times length units 180,000 Ω·m 1,310,720-acc1 resistanceunit-cons-acc2 lengthunit-cons-acc3. 100ilRÌ krÌyn. 100hex = 256 per time unit 194 Hz (or Bq) 256-cons-each-acc1 timeunit-acc-partacc2. B9Ì kilxRìly krÌyn. B9hex = 185 speed units per time unit 9.8 m⁄s² 185-acc1 speedunit-cons-each-cons-acc2 timeunit-acc-partacc3. powerÌ xryì dwÌe. ⇔ ⇒ poweredwÌ xrÌi. a length unit squared 84.68 cm² power-acc1 lengthunit-acc-dat2 two-acc-nom2. ⇔ ⇒ power-nom-two-acc1 lengthunit-acc-dat2. melÌs dmùtUn. ⇔ ⇒ melUnsdmÌt. a power unit for the eye (tool noun) 1.921 lm powerunit-acc1 see-ins-partben2. ⇔ ⇒ powerunit-partben-see-acc1.

The chapter Measuring in unit 12 of the tutorial shows the use of length, time and angle units in sentences. Here are some examples for the use of other units.

 dìl beaveryì 1DÌy lìlqy. The beaver has [been given] 1Dhex = 29 mass units. The beaver weighs 22 kg. give-cons1 beaver-acc-dat2 29-acc-acc2 massunit-cons-acc3. nená yhwÌ C8Ìa kìlxy. The horse runs C8hex = 200 speed units. The horse is running 50 km⁄h. run-fact1 horse-acc-acc2a 200-acc-fact2 speedunit-cons-acc3. 2à melilsÌ laserèe. The laser makes 2 power units. The laser emits 4.6 mW. 2-fact1 powerunit-cons-acc2 laser-nom-nom2.

Background

The earliest form of this system on which European consensus was achieved was devised by a group of physicists on the initiative of the Lemizh Scientific Society, which explains why the unit names and abbreviations are Lemizh. Later additions (such as the electromagnetic units) stuck to this convention.

The time unit is of course 1⁄164 of a day, but the definition has been changed and refined several times to increase accuracy.

The length unit is defined as the distance light travels in vacuum in 16−8 time units (about 307 ps). Conversely, vacuum light speed is 168 length units (~ 395,000 km) per time unit. The units of area and volume are the square and cube of the length unit, respectively. Likewise, as in SI, all other units are derived as powers, products or quotients of the base units, so that all conversion factors are 1.

The mass unit is defined as the mass of 1⁄7 × 1643 (~8.55 × 1050) photons with an angular frequency of 1 per time unit (equalling a frequency of 1⁄2π per time unit and a wavelength of 2π × 168 length units or 2.48 million kilometres). Consequently, the reduced Planck constant ħ = h⁄2π equals 7 × 16−27 units of action (energy units × time units = mass units × area units per time unit).

The temperature unit is defined as the absolute temperature at which an ideal particle has an average kinetic energy of 10 × 16−18 energy units (mass units × area units per square time unit; ~7.85 × 10−24 J = 49.01 µeV) per degree of freedom. So, the Boltzmann constant kB is 20 × 16−18 = 1¼ × 16−17 energy units per temperature unit.

The unit of electric charge is defined as one of two equal charges in vacuum separated by one length unit that repel each other with 1⁄4π × 1610 force units (mass units × acceleration units = mass units × length units per square time unit; ~5.04 GN). In other words, the electric constant ε0 is 16−10 capacitance units (square charge units × square time units per mass unit and area unit) per length unit, and the magnetic constant μ0 is 16−6 inductance units (mass units × area units per square charge unit) per length unit.

Several noteable quantities are approximately round numbers in the Lemizh system of units. Einstein’s gravitational constant κ = 8πGc2 is ~3 × 16−21 (more accurately, 2.986) length units per mass unit. The density of water is about one mass unit per volume unit (more accurately, 1.024). Water freezes at ~F0hex = 240 and boils at ~148hex = 328 units; body temperature is about 110hex = 272 units. The Moon’s and Sun’s apparent diameters are just over one angle unit (between 1.04 and 1.21); and the Moon’s average distance from Earth is about 168 length units, that is one ‘Lemizh light second’. (Its distance varies between 0.9017 and 1.0290, and the semi-major axis is 0.9726 × 168 units long.)

Originally the definitions related more explicitly to the physical constants, e.g. ‘The mass unit is such that ħ = 7 × 16−27 units of action’. Now that they have been revised to resemble the classical SI definitions, the International Committee for Weights and Measures has decided on new definitions of the SI base units that are more like the former Lemizh ones. Strange things happen.