A Sense of Scale


The metric system defines basic units of scale from Atto to Exa in order of magnitude, while the SI units define what to measure: Length m, weight kg (which we replace with the canonical g), temperature K, electric current A, and time s (which we augment with years and Hz). We ignore human-perceived light cd (not a physical unit) and atomic mass mol (related to weight), and add storage byte and currency . All of this will hopefully give us some sense of scale for various dimensions.

1 Upwards from Ground to Exa

Our first approach is macroscopic: Bigger all the time. We start with bytes since it is the most familiar in most sizes.

Basic (100) Kilo (103) Mega (106) Giga (109) Tera (1012) Peta (1015) Exa (1018)
byte B - assembler instruction KB - text file MB - music file GB - movie file TB - tape backup PB - big database EB - monthly internet traffic 2004
- bread K€ - car M€ - million - jet plane (400M€); city budget (500M€) G€ - billion - federal budget (500G€) T€ - trillion - GDP (3T€), national debt (2T€) P€ - quadrillion - nothing E€ - quintillion - nothing
metre m - human height km - village size Mm - earth diameter (13Mm); India (3Mm); light second (300Mm) Gm - sun diameter (1.3Gm); light-minute (18Gm); distance earth-sun (150Gm) Tm - solar system diameter (9Tm); light hour (1Tm) Pm - distance to Alpha Centauri (40Pm); light year (9Pm) Em - thickness of Milky Way (14Em)
gram g - coin kg - human Mg - tonne - car Gg - space rocket (2Gg); cruise ship (50Gg); palace (700Gg) Tg - pyramid (6Tg) Pg - comet (10Pg) Eg - asteroid (10Eg)
kelvin K - helium boils (4K); room temperature (293K) kK - lava (1.3kK); lead boils (2kK); tungsten melts (3.6kK) MK - solar wind (0.8MK); sun core (16MK); magnetic fusion (85MK) GK - electron-positron (3GK); supernova (10GK); black hole (700GK) TK - proton-antiproton (4TK); hypernova γ-burst (50TK) PK - nothing EK - nothing
ampere A - graphics card (24A) kA - lightning strike (30kA) MA - largest Birkeland current (1MA) GA - sun current (3GA) TA - nothing PA - nothing EA - nothing
year y - human age Ky - human civilization (5Kya); homo sapiens (200Kya) My - ice age (3Mya); dinosaurs (240-66Mya) Gy - first life (4Gya); Earth (4.5Gya) big bang (13Gya) ty - nothing py - nothing ey - nothing

Note that prefixes (K, M, G, T, P, E) are generally uppercases, since the lowercases are used for the smaller units of the next chapter (e.g. Mg is megagram while mg is milligram). A notable inconsistency are km and kg, presumably because they are used so frequently (and k is unambiguous anyway).

2 Downwards from Ground to Atto

The second approach is microscopic: Smaller all the time.

Basic (100) Milli (10-3) Micro (10-6) Nano (10-9) Pico (10-12) Femto (10-15) Atto (10-18)
metre m - human height mm - coin thickness; Lego figure (40mm); microwave (1-1000mm) µm - bacteria (5µm); hair (100µm); infrared (0.7-1000µm) nm - protein (5-20nm); visible light (400-700nm) pm - helium atom (60pm); x-rays (10-10000pm) fm - gold nucleus diameter (17fm); proton diameter (1.7fm) am - electron, quark (1am)
gram g - coin mg - Mosquitoes (3mg); sand grain µg - human egg cell (4µg); eye lash (70µg) ng - human cell (1ng); birch pollen (8ng); maize pollen (250ng) pg - E.coli (1pg); human sperm cell (22pg); yeast cell (60pg) fgHIV virus (1fg); Vaccinia virus (10fg); Prochlorococcus baceria (300fg) ag - 1000-base-pair DNA strand (1ag); Brome mosaic virus (8ag)
kelvin K - helium melts (1.5K) mK - electron demagnetization (60mK) µK - nuclear demagnetization (1µK) nK - Bose-Einstein condensate (1nK) pK - nothing fK - quantum decoherence (1fK) aK - macroscopic quantum tunneling (1aK)
ampere A - toaster (9A) mA - LED (20mA) µA - heart stops (10µA); hearing aid (700µA) nA - nothing pA - calcium ion channel in bio membranes (1pA) fA - nothing aA - one electron/s (0.16aA)
s s - heartbeat (0.8s) ms - neuron firing (1ms); bee wing flap (5ms); human eye blink (150ms) µs - strobe light flash (1µs); GPS relativity error per day (38µs) ns - gap between 100Gb eth packages (1ns); H fusion reaction (30ns) ps - 1THz transistor switch time (1ps) fs - fast chemical reaction (15ps); eye pigment reaction (200ps) as - electron transfer (320as)
Hz Hz - drum beats KHz - human hearing range (0-20KHz) MHz - Amiga CPU (7Mhz) GHz - Cat S60 CPU (1Ghz) THz - Tera spectrometer (0.3-3THz) PHz - science prototype EHz - x-rays (30-30000EHz)

Note that Hz is 1/s, but we used year instead of second above.


Dimensions are hard, but also interesting! At least that is my conclusion. Thanks for leaving part of your brainwaves here, and have a nice day!

EOF (Mar:2021)