Beauty in the Eye of the Beholder
The Relativity of Visual Experience
Andrew DugginsWestmead 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
Lindfield
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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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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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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
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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’
