In Pursuit of the Unknown (69 page)

and the classical world
255–9
,
260–1

imaginary numbers in
76
,
250–1

many-worlds interpretation
258–61

observational limitations
252
,
256

practical utility
261–4

Schrödinger's wave equation
250

vacuum energy discrepancy
328n

quartic equations
79–80

Quetelet, Adolphe
116–17
,
119
,
121
,
124

quincunxes
120

R

race and IQ
124

radar
192

radio
190

radioactive decay
31–3
,
267

random walks
301–2

randomness

chaos distinguished from
285

distinguished from determinism
288

patterns in
109

Recorde, Robert
vii

Reed-Solomon codes
280

regression to the mean
121

regular solids

Descartes and
91
,
95

Euclid and
4
,
91

Euler's formula
89
,
92–4
,
97

Kepler and
58

Reidemeister moves (Kurt Reidemeister)
101–3

relativity

general relativity
220
,
231
,
233–5
,
240
,
242–3

misleadingly named
219–20

special relativity
220
,
224–9
,
242–3

renewable energy
209–10

rice trading, Dojima exchange
298–9
,
312

Riemann, Georg Bernhard
18–20
,
95
,
156
,
231
,
276

Riemannian metric
19
,
231
,
277

risk

derivatives and
309–10
,
312

financial, assessment
309
,
314

probability theory and
128–9

Rourke, Colin
241

Royal Institution, London
181–2

Rule
110
automaton
320

Russian financial crisis, 1998
306–7

S

Sachs, Abraham
7

satnavs and relativity
219
,
242

Scholes, Myron
304
,
305

Schrödinger, Erwin
213
,
250–1
,
253–4

Schrödinger's cat
253–6
,
258–60
,
318

Schwarzschild, Karl
235

science fiction
66
,
329n

seismic waves
144–7
,
157
,
221

semiconductors
191–2
,
261–2

sensory perception

data compression and
159–60

logarithms and
33–4

Shannon, Claude
269–70
,
272–4
,
279
,
329n

ship design
172

Shockley, William
192
,
262

short-selling
304

simplification, in topology
93
,
101

sine curves
137–8

sines
10
,
83–4
,
142–3
,
152–4

singularities
100
,
235

slide rules
30

Smale, Stephen
289–90

Smoluchowski, Marian
208

Snellius, Willebrord
12

Snell's law
257
,
261

Snow C(harles) P(ercy)
197–8
,
209

social sciences

mathematical models
127

normal distributions
116
,
121

Solar System prediction horizons
290–1

sound levels
34

sound recordings
157
,
162

sound waves
133–6
,
146

space missions

Apollo programme
65–6
,
168

Hiten probe
69

interplanetary travel
67–8
,
71–2

Newton's law of gravity
65

view of Earth and
167–8

Voyager 1
and
2
267
,
276

space-time

curvature
231–2

geometries
227–8
,
235
,
237

inflation and
240–1

Lorenz-FitzGerald contraction
225

topology and
105

Spearman, Charles
125–7

special relativity
220
,
224–9
,
242–3

speculation, financial
300
,
302
,
309
,
312

speed of light

the ether and
222

Gran Sasso neutrinos
327n

Maxwell's equations
188–9

special relativity and
224–6

spheres

from deformation of solids
92–4
,
97

hypercubes and
278–9

spherical geometry
12
,
16
,
17

square root of minus one
73
,
77
,
250–1

see also
complex numbers
;
imaginary numbers

square roots

in Babylonian mathematics
7

duality of
76–7

solving cubic equations
79–80

using logarithms
29

square waves
153
,
155

squaw on the hippopotamus joke
3–4
,
321n

standard deviation

defined
115

and extreme events
302–3

statistical mechanics
206

statistics

law of large numbers
113
,
114

of randomness
109

statistical significance
122

steady state (populations)
287

steady state (universe)
241

steam engines
198–200

stents
174

stock market fluctuations
302

Stokes, George Gabriel
169
,
170

subduction
147

subprime mortgage market
298
,
311–12

Sundman, Karl Fritiof
64–5

superposition principle

applied to cats
253–5
,
258
,
328n

applied to the universe
258

linear equations
141
,
153

Schrödinger's equation
251–2
,
257

supersonic flight
173–4

superstring theory
105
,
319

surfaces, in topology
98–100

surveying
11–12

symbolic dynamics
288

symmetric tensors
19
,
231

symmetry, of equations and solutions
211

T

T-waves
193

Taleb, Nassim Nicholas
303

tangents
10

‘tangles'
106

Taqi al-Din Muhammad ibn Ma'ruf al-Shami al-Asadi
199

telephony

Fourier transforms
156–7

progress in
268

temperature

definition and measurement
202–3

in ideal gases
205–6

tensors
19
,
231–2

Tesla, Nikola
191

tetrahedra
91

Theory of Everything
319

thermodynamics

classical
200
,
204

defined
198
,
200

see also
laws of thermodynamics

three-body problem
63–5
,
69
,
320

time, arrow of
208
,
211
,
213
,
318

time-reversal symmetry
211
,
214–15

topological dynamics
65
,
289

topology
91–100
,
105

tori
94–5
,
97–9

transistors
191–2
,
261–2

trefoil knots
102–3
,
106

triangles

non-right-angled
9
,
11
,
321n

right-angled
5
,
8–10

triangulation
12–13

trigonometric functions

complex numbers
83
,
84

heat equation
152–4

logarithms of
29
,
31

vibrational frequencies
146

see also
cosines
;
sines

trigonometry
9–12

Trojan points
69

tsunamis
31
,
147
,
221

tubes
66
,
70–2

turbulence
171–2
,
192