In Pursuit of the Unknown (65 page)

Bell, Alexander Graham
183

‘bell curve'
see
normal distribution

The Bell Curve
(book)
123–5
,
127

Berkeley, George, Bishop of Cloyne
44–6
,
50–1

Bernoulli, Daniel
169
,
204–5

Bernoulli, Jacob
112–14

Bernoulli, John
137–9
,
141–3
,
145
,
154

Bessel functions
146

Big Bang
210
,
235–9
,
241

binary notation
271–3

binomial coefficients
113–14

binomial distribution
120

bioinformatics
281

Black, Fischer
304
,
305

black body radiation
248

black holes
235–6

Black–Scholes Equation
295
,
304–6
,
314
,
318
,
320

critique of
310–11

variants of
306
,
309

‘black swan events'
303

blip-like Fourier analysis
161–2

blood flow
174–5

Boltzmann, Ludwig
206–9
,
247–9
,
281

Bolzano, Bernard
51

Bombelli, Rafael
75
,
78
,
80–1

Boulliau, Ismaël (Bullialdus)
59
,
61

boundary conditions
212
,
214
,
318

Boyle, Robert
200

Boyle's law
205–6

Brahe, Tycho
12
,
58

braids
103

Branca, Giovanni
199

Briggs, Henry
24–5
,
27–8

Brownian motion (Robert Brown)
208

as financial system model
301
,
303
,
304
,
307

bubonic plague
37–8

‘butterfly effect'
290
,
292–3

C

calculation, Napier on
24–5

calculus

complex analysis
82
,
84

history
38–42

Leibniz and
39
,
42–5
,
50

logical flaws
44–6
,
51

Newton and
37–8
,
41–6
,
50

partial derivatives
139–40

utility
50
,
51–2

Cantor, Georg
156

car design
172
,
174

carbon dioxide
176–7
,
209–10

Cardano, Girolamo
75
,
77–80
,
109–10
,
323n–324n

Carnot cycle (Nicolas Léonard Sadi Carnot)
202–4

Cartesian coordinates (René Descartes)
13

cellular automata
320

central limit theorem
119–20
,
324n

CFD (computational fluid dynamics)
170
,
173

chaos theory
64–5
,
69
,
70

breadmaking analogy
289–90

deterministic chaos
283
,
285
,
291
,
293

logistic equation
283
,
286

population dynamics and
286–7
,
291–2
,
330n

sensitivity to initial conditions
290

topology and
92
,
105

weather and
175
,
292–3

Charles, Jacques Alexandre César
200

circles

aerofoils from
86

equations for
14

knots as
100

lines of force as
85

Clapeyron, Émile
201

Clausius, Rudolf
203
,
205–6

climate change
175–7
,
209

clustering and statistics
127

coding theory
276–9

Cohen, Jack
229
,
328n

coin tosses
110
,
112–16
,
272–4
,
288

collateralised debt obligations
309
,
312

colouring, knot diagrams
102

comets

Giacobini–Zinner
69

Great Comet of 1577
58
,
323n

Oterma
66–7

commodity prices
298
,
304
,
310–12

communication channels

capacity
275

noise
269

commutative law
87
,
279

complex analysis
82
,
100

complex equations
86

complex functions
85–6

complex numbers
81
,
82
,
250–2

definition of
87

logarithms of
29

see also
imaginary numbers

complexity science and economic models
310

compressible fluid, air as
168

compression algorithms
157–60

computational fluid dynamics (CFD)
170
,
173

computers, market growth
271

confidence, statistical
122

conic sections
57

ellipses
41
,
57–9
,
61
,
63

parabolas
41
,
48
,
57

conservation laws
48
,
49
,
225

conservation of energy

first law of thermodynamics and
200
,
201–2

kinetic theory and
205

laws of motion and
48
,
68

special relativity and
225

conservation of momentum
171
,
225

continuity in topology
92
,
96–7

continuous functions
46
,
156
,
274

continuum mathematics
310
,
320

continuum mechanics
174

continuum models
171

convergence issues
155–6

coordinate geometry
13
,
161

Copenhagen interpretation
252–62
,
328n

Copernicus, Nicolaus
57–8

‘cosine rule'
11

cosines
10
,
83–4
,
142–3
,
152–4

cosmological constant
236
,
237

cosmological microwave background
236
,
241

credit default swaps
308–9
,
312

Crick, Francis
105

crown and anchor game
111

cryptography
269
,
280

cube roots
29
,
64
,
79

cubes, and topology
91

cubic equations
79–80
,
323n–324n

curl, Maxwell's equations
187–8
,
326n

curved surface geometry
15–19
,
231–2

D

d'Alembert, Jean Le Rond
139–42
,
145

dark energy
237
,
238
,
239
,
240
,
242

dark matter
237–8
,
239
,
240
,
242

data compression

digital photography
157–60

fingerprints
162

medical imaging
163

Daubechies, Ingrid
161
,
162

Davy, Humphry
182

de Broglie, Louis-Victor
249

decibel unit
34

decoherence
257–8
,
264

Dellnitz, Michael
72

derivatives (calculus)
43–5
,
47
,
50–2

partial derivatives
139–40
,
170

derivatives (financial instruments)
297–8
,
308–9

volumes traded
300
,
308–9

Descartes, René
13
,
91
,
95

determinism

distinguished from predictability
290–1
,
293

distinguished from randomness
288

deterministic chaos
283
,
285
,
291
,
293

differential equations
47
,
52

complex functions and
85–6

entropy
204

inevitability of chaos and
286–7
,
289

Schrödinger's wave equation
250

see also
partial differential equations

differential geometry
95
,
231

differentiation, introduced
43

diffraction
223
,
250
,
257

X-rays
106
,
157

digital photography
157–60

dimensions

heat equation
152

multidimensional geometry
276
,
278–9

Navier-Stokes equation
171

Solar System description
66
,
96

superstring theory
105
,
319