Beauty in the Eye of the Beholder The Relativity of Visual Experience Andrew Duggins Westmead Hospital, University of Sydney

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

XII VI IX III IIX IV III XI

XII VI IX III

1 1 t x

1 1 t x

1 1 t x

1 1 t x

1 1 t x

1 1 t x

1 1 t x

1 1 t x

1 1 t x

1 1 t x t

1 1 t x t Speed of light, c = 1

1 1 t x t c ≠ 1

1 1 t x t

1 1 t x t x 1 1

t x 1 1 t x 1 1 t 2 – x 2 = 1

1 1 t x t 1

t x 1 1 t x 1 1 t 2 – x 2 = t 2 = 1 t2t2 – x 2 = 1 τ = 1 Proper time, τ = √ (t 2 – x 2 )

XII VI IX III IIX IV III XI

XII VI IX III IIX IV III XI

t x 1 1 t x 1 1 t x 1 1

speed, v 1 rapidity, φ Speed of light, c = v = tanh φ

Vestibulo-ocular reflex

Vestibular nystagmus

Pulaski et al, Brain Research, 1981

c = 500 deg/sec v eye /500 = tanh (v head /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 Probability (P) Information (I) = -log 2 (P) I 1 bit 2 bits 3 bits P½¼1/81/8P½¼1/81/8

 0  10  110  111 To encode the sequence: 1.75 binary digits per trial 1.75 bits = = ‘Entropy’ 1.75 bits/trial = the most efficient possible code P = ½ P = ¼ P = 1 / 8

Choice Reaction Time Task

Choice Reaction Time Hick, 1952 – k items – Reaction time  log 2 (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, - log 2 P(x)

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) 2 nd object: P = 1/2 P = 1/6 1 bit 2.58 bits Random 2 nd object perceived to last 60ms > Repeated = an extra 38ms/bit

Subjective Duration 2 Pariyadath, Eagleman (2007) Random/Sequential 2 nd object: ‐log 2 (1/3) = 1.58 bits Scrambled 2 nd 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 Bits Subjective 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

r 2 =x2x2 + y 2

θ dr 2 + r 2 dθ 2 dσ 2 ≠ Length dilation at distance: dσ/dr = 1/√(1 + r 2 ) << 1

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 < 1 Basso et al, Neuroreport, 1996

0π/6π/3π/22π/35π/6π x s dτ/dt ≈ 1 Time dilation as x → 0

dτ 2 = (1 – 2MG/x) dt 2 – 1/(1 – 2MG/x) dx 2 -MG/x = ‘gravitational potential’ dτ 2 = (1 – 2IA/x) dt 2 – 1/(1 – 2IA/x) dx 2 -IA/x = ‘attentional potential’ I = ‘reduction in uncertainty’A = ‘attentional constant’