In Pursuit of the Unknown (67 page)

GPS (Global Positioning System)
13
,
219
,
242–3

gravitational constant
59
,
323n

gravity

Galileo's investigations
39–41

general relativity and
220
,
231–2

inverse square law
37
,
61–2

Newton's law of
53
,
55
,
60–1
,
65
,
230

three-body problem
63

Greene, Brian
255
,
259

greenhouse gases
176

Greenspan, Alan
314

groups (algebra)
101

H

Haldane, Andrew
312–14

half-lives, radioisotopes
31–2

Hamilton, William Rowan
86–7

Hamiltonian operators
250
,
251

Hamming, Richard
276
,
277
,
279

Hardy, Godfrey Harold
184

harmonics
143

harmonies
134–5
,
137
,
139
,
143–4

hearing, human
33–4

heat

and temperature
203–4

time-reversal scenario
212

heat equation (Fourier)
151
,
156

financial analogue
302
,
304

heat flow
198

hedge funds
306
,
309

heights

of children
121

of structures
10–11

Heisenberg, Werner
250

heliocentric theories
56–8

Henry, Joseph
182

herd instinct
311

heredity
120–1

Hero of Alexandria
11
,
198

Hertz, Heinrich
190

Hitler, Adolph
259–61

Hohmann transfer ellipses
65
,
69

hole-through-a-hole-in-a-hole
95–6
,
97

holes in tori
94–7
,
99

HOMFLY polynomial
104

Hooke, Robert
59–61
,
137
,
322n

Hubble, Edwin
236

Huffman code
159

Huisman, Jef
291–2

human genome
281
,
319

hyperbolic space
16–17

hypercubes
276–7

hypotenuse, defined
5

hypothesis testing
122–3

I

i (imaginary unit).
see
square root of minus one

icosahedra
91

images.
see
data compression
;
photography

imaginary numbers
75–6
,
82

see also
complex numbers

India

astronomy
56

Great Trigonometric Survey
12–13

infinite series
83–4
,
142–3
,
145
,
153–4
,
161

infinitesimals
45
,
50

inflation
237
,
238
,
239–40
,
242

information

as a measurable quantity
268
,
269–70

as negative entropy
213

redundant
158

information content,
H
265
,
273–4
,
329n

instantaneous rates of change
41
,
43

integral calculus

entropy and
204

introduced
43

magnetism and
96

integration theory
156

intelligence and IQ testing
124–7

International Monetary Fund
307
,
311

Interplanetary Superhighway
72
,
105

intervals
134–6

invariants, combinatorial
96

invariants, topological
89
,
93–4
,
96–7
,
101
,
103–4

inverse square laws

expected for electromagnetism
185

gravity
37
,
61–2
,
230

IQ testing
124–7

irrational numbers
155

ISEE (International Sun-Earth Explorer)-
3
69

J

Japanese earthquake, 2011
30–1

Jones polynomial (Vaughan Jones)
103–4
,
105
,
106

Joukowski transformation
86

JPEG (Joint Photographic Experts Group)
158

Jupiter

orbital resonances
67
,
71

tubes near
70
,
71
,
72

K

Kelvin, William Thomson, Lord
247

Kepler, Johannes
39
,
41
,
58–9
,
63

Keynes, John Maynard
38
,
322n

kinetic energy
48–9
,
68
,
202–3
,
205
,
229

kinetic theory of gases
200
,
202
,
204–6

Klein bottle (Felix Klein)
98

knot diagrams
101–2
,
104–5

knots
100–5

Koon Wang-Sang
67
,
70
,
71

Krönig, August
205

L

Lagrange, Joseph-Louis
69

Lagrange points
67
,
69–71

Laplace, Pierre Simon de
29
,
119–20

Laplacians
145–6
,
326n

Large Hadron Collider
219
,
242

lasers
263–4
,
268

law of gravity (Newton)
53
,
60–1
,
65
,
230

law of large numbers
113
,
114

laws of conservation.
see
conservation laws

laws of motion (Newton)
45
,
46–7
,
60

application to fluids
170

MOND and
240

laws of planetary motion (Kepler)
39
,
58–9
,
61

laws of thermodynamics
200
,
210–11

first law
200
,
201–2

second law
197
,
204
,
209–10
,
213
,
326n–327n

zeroth law
203

Le Verrier, Urbain
233–4

least squares method
117–18
,
125

Lebesgue, Henri
156

Legendre, Adrien-Marie
117–18

Leibniz, Gottfried Wilhelm
39
,
42–5
,
50
,
81

Lemaître, Georges
236

life, and the second law of thermodynamics
210

light

as an electromagnetic wave
189
,
220

particulate behaviour
227–8
,
249

wave-particle duality
249–50

see also
speed of light

light bulbs
247

light cones
227

limits, concept of
51
,
323n

linear equations
141

linking numbers (electromagnetism)
96

Listing, Johann
96
,
98–9

logarithmic multiplication equation
21
,
29

logarithms
24–9

of complex functions
86

human perception and
33–4

natural
30

in nature
33–4

slide rules and
30

of trigonometric functions
29
,
31

logistic equation
283
,
286–8

Long Term Capital Management (LTCM)
306–7

Lorenz, Edward
289
,
290

Lorenz, Hendrik
223–4

Lorenz-FitzGerald contraction
223–6

M

MacKay, Robert
241

magnetism
85–6
,
96

magnetohydrodynamics
318

manifolds
18–19
,
231
,
240

manned flight
167

many-worlds interpretation
258–61

maps

disc-shaped Earth
9

trigonometry and
11
,
12–13

Marconi, Guglielmo
191

‘mark to market accounting'
308
,
309

mathematical models

Brownian motion
208
,
301

climate forecasting
176

cosmological
56
,
241

financial
301
,
306

gas laws
200

statistical models
113
,
172

vibrating strings
137–8

warnings about
127
,
310

matrices
19
,
231

Maxwell, James Clerk
181
,
183
,
206
,
208