Dynamic Instabilitiesin

NeuroscienceBard ErmentroutOctober 2004

The Visions of Shamans:

The Vision of Shamans – p.1/35

How does an animal switch gaits?

Trot

Walk

GallopTransverse

LH RHRF LF

LH−RH LF−RF

LH LF RH RF

The Vision of Shamans – p.2/35

What determines stripes or spots?

The Vision of Shamans – p.3/35

How do fireflies sync?

1 sec

Single insect Bush

The Vision of Shamans – p.4/35

Dynamic Instabilities

Transitions from one state to anothergoverned by nonlinear equations

Mathematics uncovers common features

What are the basic principles for patternformation?

The Vision of Shamans – p.5/35

Dynamic Instabilities

Transitions from one state to anothergoverned by nonlinear equations

Mathematics uncovers common features

What are the basic principles for patternformation?

The Vision of Shamans – p.5/35

An Example

Hallucinations & Entoptic Phenomena

The Vision of Shamans – p.6/35

Cave art

The Vision of Shamans – p.7/35

Meanings?

What do the geometric signs in UpperPaleolithic Art mean?

Compare to other modern culturesSan (bushman) rock paintingsShoshonean Coso tribeTukano tribes in BrazilAustralian aboriginal tribes

The Vision of Shamans – p.8/35

Meanings?

What do the geometric signs in UpperPaleolithic Art mean?

Compare to other modern culturesSan (bushman) rock paintingsShoshonean Coso tribeTukano tribes in BrazilAustralian aboriginal tribes

The Vision of Shamans – p.8/35

Hedges’ classification

The Vision of Shamans – p.9/35

A Hypothesis

Lewis-Williams, Hedges, and other anthropologists suggestnonrepresentational paleolithic art inspired by shamanic visions

Psycho-active substances, eg datura (jimson weed), peyote, andyaje’ common in ceremonies

with flickering fire, chantingleads to altered states

The Vision of Shamans – p.10/35

Huichol shamanism

Huichol yarn painting depictsthe hunt for peyote

Huichol rug designs inspiredby visions

The Vision of Shamans – p.11/35

Entoptic phenomena

Visual images from within

Common in hallucinogenic drugs

Premigrainous auras

Flicker/pressure phosphenes

The Vision of Shamans – p.12/35

Entoptic phenomena

Visual images from within

Common in hallucinogenic drugs

Premigrainous auras

Flicker/pressure phosphenes

The Vision of Shamans – p.12/35

Phosphenes

The Vision of Shamans – p.13/35

Hildegard

Premigrainous Auras?

Hildegard of Bingen(1098 − 1179)

The Vision of Shamans – p.14/35

The 60’s

The Vision of Shamans – p.15/35

Form constants

Spiral/vortex

Funnel/tunnel

Cobwebs/filigrees

Exploding lightrays

Mosaics

The Vision of Shamans – p.16/35

Retino-cortical transform

a

e

log(e)

cortexa π/2

−π/2

−π/2

π/2

retina

(e, a) −→

(

λ log(1 + e/e0),−λea

e0 + e

)

The Vision of Shamans – p.17/35

Like the complex logarithm

e exp(ia) → (log e, a)

The Vision of Shamans – p.18/35

What are the patterns now?

The Vision of Shamans – p.19/35

Recapitulating

There are common patterns to shamanisticart

Transform to geometric patterns in cortex

How do these patterns arise?

The Vision of Shamans – p.20/35

Recapitulating

There are common patterns to shamanisticart

Transform to geometric patterns in cortex

How do these patterns arise?

The Vision of Shamans – p.20/35

Recapitulating

There are common patterns to shamanisticart

Transform to geometric patterns in cortex

How do these patterns arise?

The Vision of Shamans – p.20/35

Inside the box

computer

display

fast camera

Tsodyks et al Science 1999

2 mm

Spontaneous activityshows spatialperiodicity

Similar to evokedactivity

Visual system is poisednear “instability”

The Vision of Shamans – p.21/35

The parts

Basket cells

Pyramidal cell

The Vision of Shamans – p.22/35

Why doesn’t it always happen?

Cortex is poised near instability

Manipulation must push it past the point

Drugs, flicker, pressure should be enough

The Vision of Shamans – p.23/35

The local equations . . .

E I

eecc ie

cei cii

decayrate

changeof activity

excitatorycoupling

inhibitorycoupling

sensoryinputoutput

dIdt

= _ + Fi ( E _ I + )τi cei cii TiI

dEdt

= _ E + Fe( E _ I + )τe cee ie Tec

The Vision of Shamans – p.24/35

. . . in a spatial array

τe

dEjk

dt= −Ejk + Fe[

∑

j′,k′

Wee(j − j′, k − k′)Ej′,k′

− Wie(j − j′, k − k′)Ij′,k′ + Te(t)]

τi

dIjk

dt= −Ijk + Fi[

∑

j′,k′

Wei(j − j′, k − k′)Ej′,k′

− Wii(j − j′, k − k′)Ij′,k′ + Ti(t)]

The Vision of Shamans – p.25/35

Dynamic instability

There is a constant equilibrium state

This can be made unstable

Translation and rotational symmetry forcesthe patterns

The Vision of Shamans – p.26/35

The Underlying Mechanism

positive

negative

inte

ract

ion

stre

ngth

+ + +0 0 __

__

+

space

Lateral Inhibition

The Vision of Shamans – p.27/35

How this works

while surrounding regionis depressed

Slight inhomogeneity

is amplified bylocal excitation

in turn, amplifyingfarther regions

and so on .....leading to a final patterned state

and depressing their neighbors

+++

+ +___ _ _

_

The Vision of Shamans – p.28/35

Then what?

Near the transition all dynamics is the same!

Nonlinear analysis is needed

Amplitude equations: E(x, y) ≈ r cos nx + s sinny

r′ = r(p − ar2− bs2) s′ = s(p − as2

− br2)

s = 0, r > 0 r = 0, s > 0

a < b a < b

r > 0, s > 0

a > b

The Vision of Shamans – p.29/35

Drugs

Mescaline, LSD, etc have common molecularmechanism

Bind to special serotonin receptors in brain

Increase in glutamate production =⇒greater excitation

Blocked by 5HT2A antagonists

High occurrence of 5HT2A in schizophrenia

The Vision of Shamans – p.30/35

Pressure phosphenes

E

I

Reduce

activitybackground

dI/dt=0

dE/dt=0

Pressure on optic nerve

suppression of inputs - like sensory deprivation

Paradoxical excitation

The Vision of Shamans – p.31/35

LSD Flight simulator

The Vision of Shamans – p.32/35

Flicker instability

time

P

P/2

Lateral Inhibitory Network

Each cell has periodically dampedimpulse response

Spatially uniform periodic input withdouble the natural frequency

Simulation

The Vision of Shamans – p.33/35

Other examples

Transition from rest to oscillation

Transition from asynchrony to synchrony(temporal patterns)

Spots vs Stripes

The Vision of Shamans – p.34/35

Other examples

Transition from rest to oscillation

Transition from asynchrony to synchrony(temporal patterns)

Spots vs Stripes

The Vision of Shamans – p.34/35

Other examples

Transition from rest to oscillation

Transition from asynchrony to synchrony(temporal patterns)

Spots vs Stripes

The Vision of Shamans – p.34/35

Conclusions

Dynamic instabilities underly many naturalpatterns

Idea of “lateral inhibition” is very generic

Local dynamics looks the same under themicroscope

The Vision of Shamans – p.35/35

Conclusions

Dynamic instabilities underly many naturalpatterns

Idea of “lateral inhibition” is very generic

Local dynamics looks the same under themicroscope

The Vision of Shamans – p.35/35

Conclusions

Dynamic instabilities underly many naturalpatterns

Idea of “lateral inhibition” is very generic

Local dynamics looks the same under themicroscope

The Vision of Shamans – p.35/35