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

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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

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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

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XII VI IX III IIX IV III XI

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XII VI IX III

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1 1 t x

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1 1 t x

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1 1 t x

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1 1 t x

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1 1 t x

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1 1 t x

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1 1 t x

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1 1 t x

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1 1 t x

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1 1 t x t

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

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1 1 t x t c ≠ 1

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1 1 t x t

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1 1 t x t x 1 1

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t x 1 1 t x 1 1 t 2 – x 2 = 1

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1 1 t x t 1

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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 )

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XII VI IX III IIX IV III XI

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XII VI IX III IIX IV III XI

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

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

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Vestibulo-ocular reflex

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Vestibular nystagmus

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Pulaski et al, Brain Research, 1981

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c = 500 deg/sec v eye /500 = tanh (v head /500) Pulaski et al, Brain Research, 1981

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Is Experience Relative? Do the transformations of Einstein’s special relativity apply to subjective spacetime? …..Perhaps!

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00 01 10 11 To encode the sequence: 2 binary digits per trial

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¼ ½ Probability (P) Information (I) = -log 2 (P) I 1 bit 2 bits 3 bits P½¼1/81/8P½¼1/81/8

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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

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Choice Reaction Time Task

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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

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‘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)

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Strange et al (2005)

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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

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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

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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

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Coding Hypothesis Stimulus information expands: – Subjective duration – Reaction latency …to a similar extent

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Am I a blue circle? Zombie celebrity heads

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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

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Duration Dilation by Information Objective time 320ms 1 Bit 360ms Subjective time 2 Bits Subjective time 400ms 0 Bits 40ms / bit

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Hypothesis Gravity is the curvature of objective spacetime by mass Attention is the curvature of subjective spacetime by information Time Space

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r 2 =x2x2 + y 2

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

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Equivalence Principle

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Left Visual Inattention

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Left Vestibular Stimulation

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Left Angular Acceleration

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Visual Inattention 0 π/6 π/3 π/2 2π/3 5π/6 π x = θ 1 metre

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0π/6π/3π/22π/35π/6π x σ dσ/dx > 1

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0π/6π/3π/22π/35π/6π x σ dσ/dx ≈ 1 Length contraction as x → 0

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0π/6π/3π/22π/35π/6π x σ dτ/dt < 1 Basso et al, Neuroreport, 1996

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

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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’

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