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) |