jjrscott

Loga-

When I first wrote this on 12th April 2018 I used 10 as the base for the logarithm. However, on reflection a mere 5 years later I now think the base should be 10¹⁄₁₀. This has the effect that the rule is simpler: multiply the value by 10, add 10 to the log of the value. Much simpler.

We use unit prefixes (eg kilo) at lot. They’re very useful but there isn’t one to cover them all. Just for fun I thought I might create my own alternate prefix to fill this need:

I present the Loga (from the Greek λογάριθμος, literally a logarithm) with the prefix λ.

This differs from all the other prefixes in that for any unit:

𝑥 Loga-Unit = log10¹⁄₁₀ 𝑥 Unit

The convertion table to the normal prefixes tooks like this:

Text Symbol Factor Power Loga
exa E 1000000000000000000 1018 180
peta P 1000000000000000 1015 150
tera T 1000000000000 1012 120
giga G 1000000000 109 90
mega M 1000000 106 60
kilo k 1000 103 30
hecto h 100 102 20
deca da 10 101 10
(none) (none) 1 100 0
deci d 0.1 10−1 −10
centi c 0.01 10−2 −20
milli m 0.001 10−3 −30
micro μ 0.000001 10−6 −60
nano n 0.000000001 10−9 −90
pico p 0.000000000001 10−12 −120
femto f 0.000000000000001 10−15 −150
atto a 0.000000000000000001 10-18 -180

By way of example, I’ve add the converstions for a few units.

Kelvin

kelvin
(K)
loga-kelvin
(λK)
Description
4.5×10-10 -93.46 Lowest man-made temperature
184.0 22.64 Lowest temperature recorded on Earth
273.15 24.36 0℃
373.15 25.71 100℃
15,000,000 71.76 Solar core
5×1012 126.98 Highest man-made temperature
1.417×1032 321.51 Absolute hot

Metres

metres
(m)
loga-metres
(λm)
Description
1.616×10-35 -347.91 Planck length
1.73 2.38 An example Human’s height
149597870700 111.74 Astronomical unit
9460730472580800 159.75 Light-year
8.8×1026 269.45 Observable universe

Bits

bits
(b)
loga-bits
(λb)
Description
1 0 Bit
8 9.03 Byte
30720 44.87 Apollo Guidance Computer
2,097,152 63.22 IBM Personal Computer
1.048×1016 160.20 Sunway TaihuLight (Top super computer Novemeber 2017)