1. Non-Symbolic AI Lecture 12
Double bill with lec 13:
This lecture -- Homeostasis, The Dynamics of Daisyworld, Enactive perception.
Next lecture – The Dynamics of Robots
and the
Rights and Wrongs of Representations
Non-Symbolic AI lecture 12
Summer 2004

2. Things versus Processes
For 100 years or more, there has been a clash of views, or rather of starting points, between
“A perception is a thing” versus
“Perceiving is a process”
(Also substitute in this phrase:-
Thought vs. thinking,
memory vs. remembering,
representation vs. representing etc etc)
Non-Symbolic AI lecture 12
Summer 2004

3. Non-Symbolic AI lecture 12
Enactive Perception
I take the starting point of Enactive Perception to be:
“Perceiving happens when an interested agent engages with a world it is interested in”
So firstly, think dynamics rather than things (dynamical systems approach).
Secondly, think seriously about what an agent, a world, engagement is – don’t take anything for granted
Non-Symbolic AI lecture 12
Summer 2004

4. A Rough Hierarchy
“What is a an Object, that a Creature may perceive it, and a Creature, that it may perceive an Object”
(adapted from Warren McCulloch)
All organisms react to perturbations here and now
Some organisms engage with objects distant in space/events distant in time
Some organisms engage in a social world
“Static Vegetables”, Homeostasis
“Mobile Animals”, Perception
“Social Humans”, Representation
Non-Symbolic AI lecture 12
Summer 2004

5. Non-Symbolic AI lecture 12
Lecture Plan
Lec 12: Homeostasis – a new and simplified daisyworld model, with Rein Control.
Lec 12: Perception -- extending the underlying mathematical insight to a novel form of (en-)active perception.
Lec 13: Dynamics of Robots.
Lec 13: Representation – the rights and wrongs of Representation-language in the context of understanding perception.
Non-Symbolic AI lecture 12
Summer 2004

6. Non-Symbolic AI lecture 12
Homeostasis and Gaia
To stay alive, an organism has needs – it must maintain various values such as internal temperature, chemical concentrations, etc, within bounds of viability and comfort. Not too hot, not too cold.
Homeostasis is the ability to react to perturbations (e.g. of temperature) so as to maintain it within viability limits.
The Gaia Hypothesis (Lovelock 1972) is that the Earth with its biota acts homeostatically, similarly to an organism, to maintain global properties within ranges appropriate for the biota. Teleology??
Non-Symbolic AI lecture 12
Summer 2004

7. Non-Symbolic AI lecture 12
For example … ...
The sun has steadily increased in heat output over the lifetime of the Earth (say 30% less luminous, 3.8bn years ago).
One should normally expect the Earth’s temperature to have started off far far colder, and increased until now it was far too hot for us (say currently around 2900 C)
But it seems the Earth’s surface temperature has been maintained at around 200 C for aeons. A nice temperature!
How?
Non-Symbolic AI lecture 12
Summer 2004

8. Non-Symbolic AI lecture 12
Daisyworld
In 1983 the ‘parable of Daisyworld’ was presented as a possible mechanism, explaining how feedback loops between living organisms and the environment can produce regulation, homeostasis.
Suppose 2 species of Daisies, Black and White, live on a Grey planet. They each have a preferred temp, and will die if temp is too different.
Non-Symbolic AI lecture 12
Summer 2004

9. Non-Symbolic AI lecture 12
What Happens?
Temperature
Solar output
The average temp of Earth remains in the viability zone far more than one might expect. Somehow the Earth+biota is self-regulating. How?
Non-Symbolic AI lecture 12
Summer 2004

10. Non-Symbolic AI lecture 12
Mystery ?
The Earth+biota seems to self-regulate at a temp appropriate for biota Teleology? Planning? Surely not…
Only other available explanation for purposive behaviour seems to be Darwinian evolution but there hasn’t been a population of evolving Earths.
Daisyworld model shows how you can get homeostasis without evolution or any teleology.
Non-Symbolic AI lecture 12
Summer 2004

11. New simplified model of Daisyworld
Combination of a Hat-function and any feedback gives regulation
Hat-function = viability zone
Simplest version = Witch’s Hat
Non-Symbolic AI lecture 12
Summer 2004

12. Simplified Feedbacks in Daisyworld
Non-Symbolic AI lecture 12
Summer 2004

13. Initially consider just one Daisybed
Rate of change of Temp = albedo * (Suntemp – Temp) –Temp + Feedback-term * Hat-function(Temp)
Non-Symbolic AI lecture 12
Summer 2004

14. Non-Symbolic AI lecture 12
Equilibrium when …
LHS = 0 when a Linear function in T intersects a Hat-function of T
Non-Symbolic AI lecture 12
Summer 2004

15. Extends the viability zone
B unstable
A, C are stable equilibria
Without or
With Feedback
Non-Symbolic AI lecture 12
Summer 2004

16. Non-Symbolic AI lecture 12
Rein Control
So a Hat-function plus Positive feedback extends the viability zone to the left.
And a Hat-function plus Negative feedback will extend the viabilty zone to the right.
Different types of feedback needed for each direction – to regulate in both directions you need 2 “Reins”.
A rein can pull but cannot push – “Rein Control” (Manfred Clynes 1969)
Non-Symbolic AI lecture 12
Summer 2004

17. Non-Symbolic AI lecture 12
Both together ?
What interactions are there between Black and White Daisies – what transfer of heat, or leakage?
Non-Symbolic AI lecture 12
Summer 2004

18. Fully connected is a bad idea
If B and W daisies are at same temperature, there will be same number of each.
1 B + 1 W = 1 Grey, same as a lifeless planet
Non-Symbolic AI lecture 12
Summer 2004

19. Loosely Coupled is what you want
Non-Symbolic AI lecture 12
Summer 2004

20. Non-Symbolic AI lecture 12
Simple Daisyworld
This simplified Daisyworld exposes the underlying mechanism much more clearly,
Virtually any combination of a Hat-function with any (monotonic) feedback in effect extends the range of the Hat-function, or viability zone.
This true for any organism, not just Gaia-as-an-organism.
Some forms of homeostasis, of an organism reacting “appropriately” to environmental disturbances, are cheap.
Proto-perception ?
Non-Symbolic AI lecture 12
Summer 2004

21. Dynamical Systems viewpoint
Note that the “organism” does not regulate by comparing observed temperature with an internal representation of the desired temperature.
Rather, the regulating-behaviour is the outcome of the dynamics of feedbacks both internal and external, between organism and environment, settling into an attractor.
Non-Symbolic AI lecture 12
Summer 2004

22. Non-Symbolic AI lecture 12
Lecture Plan
Lec 12: Homeostasis – a new and simplified daisyworld model, with Rein Control.
Lec 12: Perception -- extending the underlying mathematical insight to a novel form of (en-)active perception.
Lec 13: Dynamics of Robots.
Lec 13: Representation – the rights and wrongs of Representation-language in the context of understanding perception.
Non-Symbolic AI lecture 12
Summer 2004

23. Extending to (En-)active Perception
Rein control = Hat-function + Feedback
Hat-function = “viability zone”
But also
Hat-function = directional response of a photoreceptor
Non-Symbolic AI lecture 12
Summer 2004

24. Non-Symbolic AI lecture 12
Let’s build a 2-D Dalek
Photoreceptor A at end of moving tentacle, Hat-function receptive field.
Sensor response generates torque D, against Spring B to nose C.
Dalek is only able to rotate around its centre.
Non-Symbolic AI lecture 12
Summer 2004

25. Let’s put it together randomly
Now let’s have 100 such tentacles, all independent bar springs connecting to nose
Let’s have directions of D (anti- or clockwise) at random.
Angles of acceptance of A at random
Strengths of springs B at random
Non-Symbolic AI lecture 12
Summer 2004

26. Comparison with Daisyworld
Angle of Acceptance A
= Hat-function
= “viability zone”
Direction of D = +ve or –ve Feedback = B or W Daisies
Springs B = loose semi-coupling between different feedbacks
Non-Symbolic AI lecture 12
Summer 2004

27. What behaviour to expect?
Underlying maths is the same.
Instead of regulating temperature for daisies to stay in their viability zone, this will regulate tentacle-angles to stay within their acceptor-zones.
Collectively, they will pull the nose around to point towards a light
-- Phototaxis, despite the random wiring up of tentacles
(… and actually, you could get rid of the nose altogether …)
Non-Symbolic AI lecture 12
Summer 2004

28. Non-Symbolic AI lecture 12
Phototaxis
Waggle point-source of light in front – it’ll pick it up and pursue it. Robust to 3 orders of magnitude on angles of acceptance, to 2+ orders of magnitude on spring constants/torque parameters.
Non-Symbolic AI lecture 12
Summer 2004

29. Non-Symbolic AI lecture 12
Incidentally … …
Samples from data from all the “left-moving” tentacles (normalised) – (almost) all on the RHS of the Witch’s Hat … …
… … all at positions like C. And vice versa for all the “right-moving” tentacles.
Non-Symbolic AI lecture 12
Summer 2004

30. Dynamical Systems viewpoint
Note that the “organism” does not regulate by comparing observed temperature with an internal representation of the desired temperature.
light-direction
light-direction
Rather, the regulating-behaviour is the outcome of the dynamics of feedbacks both internal and external, between organism and environment, settling into an attractor.
Non-Symbolic AI lecture 12
Summer 2004

31. Non-Symbolic AI lecture 12
Lecture Plan
Lec 12: Homeostasis – a new and simplified daisyworld model, with Rein Control.
Lec 12: Perception -- extending the underlying mathematical insight to a novel form of (en-)active perception.
Lec 13: Dynamics of Robots.
Lec 13: Representation – the rights and wrongs of Representation-language in the context of understanding perception.
Non-Symbolic AI lecture 12
Summer 2004