Evolution -- the blind mathematician producing
increasingly sophisticated users of mathematical discoveries

Partly with the unwitting help of those users.

Aaron Sloman
http://www.cs.bham.ac.uk/~axs/
School of Computer Science, University of Birmingham

This paper is
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/sloman-mcls-notes.html

Submitted talk proposal is here
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/sloman-mcls-18.html

In Session: 16:00 - 17:00 Mon 9th April Room 7

The physical universe is full of mathematical structures many of them discovered by physicsts, astronomers and others.

In addition there are mathematical structures discovered and used much earlier by biological evolution -- the blind mathematician.

I don't yet have a good taxonomy but here are some examples:

HOMEOSTASIS:
Use of negative feedback loops in control (e.g. of pressure, temperature, concentration of particular molecules, direction of motion, and many more).

The power of this mathematical structure was discovered (and re-discovered many times) by biological evolution long before the Watt governor was discovered.

Compare self orienting windmills...
Another example, choice of direction of motion of a carnivore chasing its prey.

Always heading in the exact current direction of the prey is mathematically sub-optimal, except in special cases (... Left as an exercise...)

The discovery of re-usable abstract designs of many kinds whose mathematical structures supported biological functions, including:

- reproduction

- growth

- changing control of motion during growth.

- perception of structures and processes that can be used in choosing and achieving goals, e.g. selecting and placing the next part of a partly built nest, and many more:
Evolutionary transitions from molecules to intelligent animals

To Betty


Between the simplest and most sophisticated organisms there are many intermediate forms with very different information processing requirements and capabilities.

In order to produce them evolution had to produce new mechanisms used in evolution and in development "CONSTRUCTION KITS" of various sorts.

EVOLUTION DISCOVERED THE POOWER OF USE CONSTRUCTION KITS
Starting from the Fundamental Construction Kit (FCK)

The fundamental construction kit FCK

FCK


Figure FCK: The Fundamental Construction Kit
A crude representation of the Fundamental Construction Kit (FCK) (on left)
and (on right) a collection of trajectories from the FCK
through the space of possible trajectories to increasingly complex mechanisms.

Then creating and using

Increasingly complex Derived Constructino Kits (DCKs)

Some used during construction of individuals within a species

Some used to kick off new species.

The space of possible trajectories for combining basic constituents is enormous, but routes can be shortened and search spaces shrunk by building derived construction kits (DCKs), that are able to assemble larger structures in fewer steps7, as indicated in Fig. DCK.

Figure DCK: Derived Construction Kits

DCK

TRANSITIONS DURING INDIVIDUAL DEVELOPMENT

OF FAIRLY COMPLEX ORGANISMS

A SCHEMATIC OVERVIEW

Using many derived construction kits

From Chappell andd sloman 2007.

Figure Evo-Devo
XX

I call this "The meta-configured genome"

Among other things construction kits provide meta-cognitive mechanisms, including other-directed" med-cognitive mechanisms.

TODDLER ALTRUISM

Show Warnecken video.

ARITHMETIC VS GEOMETRY

IMPOSSIBLE TRANSITIONS ON A GRID

Perceptual information is not merely about what is the case or what will occur or is likely to occur in the environment: it also includes "modal" information about "what is possible or impossible" in a situation, or "what must be the case if...", or "what would have happened if something different had been done". This is closely related perception of causal relationships.

In particular organisms are able to acquire acquire "modal" information: information about what is and is not possible, and information about necessary consequences of realisation of some possibilities, i.e. mathematical information, e.g. the sorts of discoveries reported by Euclid, some of which individuals can easily make for themselves, e.g.

     If a triangle has three equal sides then it must have three equal angles
     If a vertex of a triangle moves closer to the opposite side,
          the area of the triangle must decrease.
     http://www.cs.bham.ac.uk/research/projects/cogaff/misc/triangle-theorem.html

Information about geometry and topology recorded by Euclid (and his predecessors and successors) has NOTHING to do with probabilities, which happen to be the main focus of most fashionable research on intelligent systems.

Going back to earlier organisms: evolution produced organisms able to acquire and use more and more varieties of information:
- immediately usable control information
- information that can be used after it is acquired
- information about an need to seek new information
- information about extended terrain, not just immediate environment
- information about what is where even when it is not being perceived, and how to get to some items even when they are not perceived (e.g. learnt routes to sources of food, liquid, shelter, danger, etc.).
-
- We know how to make machines that can acquire and use some types of information, but not others: e.g. information about what is possible or impossible, e.g. theorems in Euclidean geometry and topology.

REFERENCES AND LINKS
(To be expanded)

Maintained by Aaron Sloman
School of Computer Science
The University of Birmingham