MOTION MOUNTAIN

thought and language 269
Vol. IV, page 222
Ref. 250
Number
Example in nature
10 17 imagepixelsseeninalifetime(3⋅10 9 s⋅(1/15 ms)⋅2/3(awake)⋅10 6 (nerves
tothebrain) Ref. 248
10 19 bitsofinformationprocessedinalifetime(theabovetimes32)
c.5⋅10 12 printed words available in (different) booksaround the world (c.100⋅10 6
booksconsistingof50000words)
2 10 ⋅3 7 ⋅8!⋅12!
=4.3⋅10 19 possiblepositionsofthe3×3×3Rubik’sCube Ref. 249
5.8⋅10 78 possiblepositionsofthe4×4×4Rubik-like cube
5.6⋅10 117 possiblepositionsofthe5×5×5Rubik-like cube
c.10 200 possiblegames ofchess
c.10 800 possiblegames ofgo
c.10 107 possiblestatesinapersonalcomputer
Partsofus
600 numbersofmusclesinthehumanbody,ofwhichabouthalfareintheface
150000±50000 hairsonahealthy head
900000 neuronsinthebrainofagrasshopper
126⋅10 6 lightsensitivecells perretina(120millionrodsand6millioncones)
10 10 to10 11 neuronsinthehumanbrain
500⋅10 6 blinks of the eye during a lifetime (about once every four seconds when
awake)
300⋅10 6 breathstaken during humanlife
3⋅10 9 heartbeatsduring ahumanlife
3⋅10 9 letters (basepairs)inhaploidhuman DNA
10 15±1 cells inthehumanbody
10 16±1 bacteria carried inthehumanbody
The system of integersZ=(...,−2,−1,0,1,2,...,+,⋅,0,1) is the minimal ring that is an
extension of the natural numbers. The system of rational numbersQ=(Q,+,⋅,0,1)
is the minimal field that is an extension of the ring of the integers. (The terms ‘ring’
and ‘field’ are defined in all details in the next volume.) The system of real numbers
R=(R,+,⋅,0,1,>) is the minimal extension of the rationals that is continuous and
totally ordered. (For the definition of continuity, see volume IV, page 223, and volume
V, page 358.) Equivalently, the reals are the minimal extension of the rationals forming a
complete, totally strictly-Archimedean ordered field. This is the historical construction
– or definition – of the integer, rational and real numbers from the natural numbers.
However, it is not the only one construction possible.The most beautiful definition of all
these types of numbers is the one discovered in 1969 by John Conway, and popularized
by him, Donald Knuth and Martin Kruskal.
⊳ Anumber is a sequence of bits.
The two bits are usually called ‘up’ and ‘down’. Examples of numbers and the way to
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net