Beauty in the Eye of the Beholder

The Relativity of Visual Experience

Andrew DugginsWestmead Hospital, University of Sydney

andrew.duggins@sydney.edu.au

Is Experience Relative?

• Do the transformations of Einstein’s special relativity apply to subjective spacetime?

• Just as… – gravity is the curvature of objective spacetime by mass– attention is the curvature of subjective spacetime by

information

Plan

• Subjective spacetime• Special relativity

– Time dilation– Limiting speed c

• Information theory– Efficient encoding

• General Relativity– Oddball effects – Artist’s perspective– Equivalence principle– Visual inattention – Sketch of a unifying theory

Lindfield

IIX

IV

III XI

Lindfield

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Speed of light, c = 1

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c ≠ 1

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t2 – x2 = 1

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x

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t2 – x2 = 1

t2 – x2 = t2 = 1

t2 – x2 = 1τ = 1

Proper time, τ = √ (t2 – x2)

LindfieldXII

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LindfieldXII

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t

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speed, v

1rapidity, φ

Speed of light, c = 1

0.68

0.825

0.5

0.55

v = tanh φ

Vestibulo-ocular reflex

Vestibular nystagmus

Pulaski et al, Brain Research, 1981

c = 500 deg/sec

veye/500 = tanh (vhead/500)

Pulaski et al, Brain Research, 1981

Is Experience Relative?

• Do the transformations of Einstein’s special relativity apply to subjective spacetime?

…..Perhaps!

00

01

10

11

To encode the sequence:

2 binary digits per trial

¼ ½ 1 2

1

0

-1

-2

-3

-4

Probability (P)

Information (I) = -log2(P)

I

1 bit

2 bits

3 bits

3 bits

P

½

¼1/8

1/8

0

10

110

111

To encode the sequence:

1.75 binary digits per trial

1.75 bits = <-log2(P)> = ‘Entropy’

1.75 bits/trial = the most efficient possible code

P = ½

P = ¼

P = 1/8

P = 1/8

Choice Reaction Time Task

Choice Reaction Time• Hick, 1952

– k items– Reaction time log2(k)

• Hyman, 1953– Skewed distributions– Reaction time Entropy– ~ 129ms/bit

Our Hypothesis• Quicker reactions for more probable alternatives• Minimum reaction time on average

‘Efficient Coding’ Hypothesis

• Survival depends on the minimum average reaction time

• Reaction time to stimulus x depends on the length of the ‘neural codeword’

• Codeword length, and visual processing activity should vary with self-information, -log2 P(x)

∆ reaction time

0.00

50.00

100.00

150.00

200.00

entropy self-information

covariates

ms/

bit

Strange et al (2005)

Comments

Attention– Coextensive with visual attention network– ‘Oddball’ responses reflect efficient coding

Repetition suppression– Updated probabilities increase with repetition– Self-information incrementally decays

The Neural Codeword

Subjective Duration 1

Pariyadath, Eagleman (2007) 2nd object: P = 1/2 P = 1/6

1 bit 2.58 bits

• Random 2nd object perceived to last 60ms > Repeated= an extra 38ms/bit

Subjective Duration 2

Pariyadath, Eagleman (2007)

• Random/Sequential 2nd object: log‐ 2(1/3) = 1.58 bits

• Scrambled 2nd object: log‐ 2(1/9) = 3.17 bits

• Relative delay 75ms = an extra 47ms/bit

Coding Hypothesis

Stimulus information expands:

–Subjective duration

–Reaction latency

…to a similar extent

Am I a blue circle?

Zombie celebrity heads

Conclusions• Information prolongs experience• Information delays reaction– Efficient coding– Minimum expected reaction time

• Experience first, react later:

Information quantifies the difficulty inherent in the ‘Hard’ problem

Duration Dilation by Information

Objective time 320ms

1 Bit

360ms

Subjective time

2 BitsSubjective time

400ms

0 Bits

40ms / bit

Hypothesis

• Gravity is the curvature of objective spacetime by mass

• Attention is the curvature of subjective spacetime by information

Time

Space

r2 = x2 + y2

θ

dr2 + r2dθ2dσ2 ≠

Length dilation at distance: dσ/dr = 1/√(1 + r2) << 1

Equivalence Principle

Equivalence Principle

Left Visual Inattention

Left Vestibular Stimulation

Left Angular Acceleration

Visual Inattention

0

π/6

π/3

π/2

2π/3

5π/6

π

x = θ

1 metre

0π/6π/3π/22π/35π/6π

x

σ

dσ/dx > 1

0π/6π/3π/22π/35π/6π

x

σ

dσ/dx ≈ 1

Length contraction as x → 0

0π/6π/3π/22π/35π/6π

x

σ

dτ/dt < 1Basso et al, Neuroreport, 1996

0π/6π/3π/22π/35π/6π

x

s

dτ/dt ≈ 1Time dilation as x → 0

dτ2 = (1 – 2MG/x) dt2 – 1/(1 – 2MG/x) dx2

-MG/x = ‘gravitational potential’

dτ2 = (1 – 2IA/x) dt2 – 1/(1 – 2IA/x) dx2

-IA/x = ‘attentional potential’

I = ‘reduction in uncertainty’ A = ‘attentional constant’