The Arrows of Time

Valeria looked down at the speck of light that had been her city. ‘Who did all these things? We have to know their stories.’

‘You will,’ Clara promised. ‘We had some good archivists, but I think the translations will need to be a collaborative project.’

‘How many generations was the voyage?’ Eusebio asked.

‘About a dozen.’

‘A dozen,’ he repeated. ‘An era.’

All of this had grown out of Eusebio’s endeavours – and in one year from the launch, not four. Valeria thought it must feel as if he’d stepped out of his house for a day and returned to find his children replaced by a whole vast swarm of descendants, all of them with strange ideas of their own.

Valeria said, ‘And how many people lived and died in the mountain, without seeing the end?’

Clara squeezed her shoulder. ‘A lot.’

Valeria pictured them, generation after generation, lined up across the years. Farmers and physicists, inventors and instrument builders, maintenance workers, millers and cleaners, biologists and astronomers. Hidden behind her outstretched thumb, for ever out of reach. ‘I wish I could talk to them,’ she said. ‘I wish I could thank them. I wish I could tell them that it wasn’t for nothing, that it ended well.’

Clara said, ‘If that’s what you want, then I believe you’ll find a way.’

Appendix 1: Units and measurements

Distance

1 scant (1/144 In strides)

1 span = 12 scants (1/12 In strides)

1 stride = 12 spans (1 In strides)

1 stretch = 12 strides (12 In strides)

1 saunter = 12 stretches (144 In strides)

1 stroll = 12 saunters (1,728 In strides)

1 slog = 12 strolls (20,736 In strides)

1 separation = 12 slogs (248,832 In strides)

1 severance = 12 separations (2,985,984 In strides)

Home world’s equator = 7.42 severances (22,156,000 In strides)

Distance from Peerless to the Object = 193 severances (576,294,912 In strides)

Home world’s orbital radius = 16,323 severances (48,740,217,000 In strides)

Time

1 flicker (1/12 In pauses)

1 pause = 12 flickers (1 In pauses)

1 lapse = 12 pauses (12 In pauses)

1 chime = 12 lapses (144 In pauses)

1 bell = 12 chimes (1,728 In pauses)

1 day = 12 bells (20,736 In pauses)

1 stint = 12 days (248,832 In pauses)

Peerless’s rotational period = 6.8 lapses (82 In pauses)

1 year = 43.1 stints (1 In years)

1 generation = 12 years (12 In years)

1 era = 12 generations (144 In years)

1 age = 12 eras (1,728 In years)

1 epoch = 12 ages (20,736 In years)

1 eon = 12 epochs (248,832 In years)

Angles

1 arc-flicker (1/248,832 In revolutions)

1 arc-pause = 12 arc-flickers (1/20,736 In revolutions)

1 arc-lapse = 12 arc-pauses (1/1,728 In revolutions)

1 arc-chime = 12 arc-lapses (1/144 In revolutions)

1 arc-bell = 12 arc-chimes (1/12 In revolutions)

1 revolution = 12 arc-bells (1 In revolutions)

Mass

1 scrag (1/144 In hefts)

1 scrood = 12 scrags (1/12 In hefts)

1 heft = 12 scroods (1 In hefts)

1 haul = 12 hefts (12 In hefts)

1 burden = 12 hauls (144 In hefts)

Prefixes for multiples

ampio- = 12³ = 1,728

lauto- = 12⁶ = 2,985,984

vasto- = 12⁹ = 5,159,780,352

generoso- = 12¹² = 8,916,100,448,256

gravido- = 12¹⁵ = 15,407,021,574,586,368

Prefixes for fractions

scarso- = 1/12³ = 1/1,728

piccolo- = 1/12⁶ = 1/2,985,984

piccino- = 1/12⁹ = 1/5,159,780,352

minuto- = 1/12¹² = 1/8,916,100,448,256

minuscolo- = 1/12¹⁵ = 1/15,407,021,574,586,368

Appendix 2: Light and colours

The names of colours are translated so that the progression from ‘red’ to ‘violet’ implies shorter wavelengths. In the Orthogonal universe this progression is accompanied by a decrease in the light’s frequency in time. In our own universe the opposite holds: shorter wavelengths correspond to higher frequencies.

The smallest possible wavelength of light, λ_min, is about 231 piccolo-scants; this is for light with an infinite velocity, at the ‘ultraviolet limit’. The highest possible time frequency of light, ν_max, is about 49 generoso-cycles per pause; this is for stationary light, at the ‘infrared limit’.

Afterword

Gravitation and cosmology in the Orthogonal universe are governed by essentially the same equation that governs the geometry of our own universe: the relationship between the curvature of space-time and the density and flow of matter and energy that was proposed by Einstein in 1916. The solutions of Einstein’s equation that describe our universe have three dimensions of space and one of time, but the equation itself can easily accommodate four space-like dimensions.