beauty in the eye of the beholder the relativity of visual experience andrew duggins westmead...

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

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

t2 – x2 = 1

1

1

t

x

t

1

t

x

1

1

t

x

1

1

t2 – x2 = 1

t2 – x2 = t2 = 1

t2 – x2 = 1τ = 1

Proper time, τ = √ (t2 – x2)

LindfieldXII

VI

IXIII

IIX

IV

III XI

LindfieldXII

VI

IXIII

IIX

IV

III XI

t

x

1

1

t

x

1

1

t

x

1

1

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’