School of Computer Science THE UNIVERSITY OF BIRMINGHAM CoSy project CogX project

Infant-Toddler Space
(DRAFT: Liable to change)

Aaron Sloman
School of Computer Science, University of Birmingham.
(Philosopher in a Computer Science department)

Installed: 10 May 2011
Last updated: 10 May 2011
This paper is
A PDF version may be added later.

A partial index of discussion notes is in


We need to develop a kind of spatial formalism that is not necessarily
logical, but should plausibly be something that could be implemented in
a variety of animal brains (at least mammals, reptiles, birds,
carnivorous fish, maybe octopuses).

It doesn't (initially) need most of the concepts of Euclidean geometry:
point, line, plane, parallel, length, area, volume, etc. Though it
requires a host of (more or less fuzzy) special cases.

Maybe some ideas in this draft, incomplete, specification of p-geometry
will be useful:

Some Requirements for this representation of space/time/motion

It doesn't (initially) need most of the concepts of Euclidean geometry:
point, line, plane, parallel, length, area, volume, etc. Though it
requires a host of (more or less fuzzy) special cases.

It requires time so that movements are possible (as in p-geometry,)
though not exact speeds, exact trajectories, etc. Partial orderings of
speeds of change (X is moving away faster than Y, gap G1 is closing
faster than G2) are needed. These may be absolute (G1 will close
completely before G2) or relative (G1 will shrink to about half its size
before G2).

It does need objects with surfaces and visual appearances (projections
to some sort of retina), and something like a notion of reaching or
moving towards, which changes the appearances and reachability.

It doesn't need equality (of anything) though a fuzzy "more-like"
relationship between triples of distances, angles, areas, volumes,
gap-sizes, object-widths, temporal intervals (e.g. observed or

    X is more like Y than like Z
    X is more like Y than Z is

It needs a notion of a perceiver in the space, and probably needs a
distinction between processes that the perceiver can initiate, speed up,
slow down, terminate, reverse, etc. and processes that it can merely

It needs to be able somehow to develop, or to have available from the
start, modal notions of possibility and impossibility/necessity. E.g.
    X could be closer to Y
    X cannot pass through gap G

and condititional possibility/impossibility

    if X does not change direction it will eventually bump into Y
    if that happens either X will stop moving or Y will start moving or
        X will change direction (e.g. bounce).

    if X changes its direction of motion to head more to the right
    (or more away from the heading to Y) then X can continue without
    bumping into Y

and many more, some of it making use of notions of different kinds of
stuff of which things are made.

I have some thoughts about this that are scattered in online presentations here
    Ontologies for baby animals and robots
      From "baby stuff" to the world of adult science: Developmental AI from
        a Kantian viewpoint
        Why (and how) did biological evolution produce mathematicians?
        A New Approach to Philosophy of Mathematics:
            Design a young explorer, able to discover "toddler theorems"

and others are in more or less fragmentary online discussion notes, e.g.

And the polyflap project:

A hard project: bringing all these ideas together to see whether
someone cleverer than I am can work out how to use them in the design of
a baby robot (perhaps simulated) that learns about its environment.

After it develops a fair amount of behavioural competence it should be
able to reorganise what it has learnt into a sort of deductive theory
that allows it to work out what will happen in novel situations instead
of having to go on learning empirically. (A way of using robotics to
support Kant's philosophy of mathematics.)


M. Aiello, I.Pratt-Hartmann and J.van Benthem
What is Spatial Logic?
in Handbook of Spatial Logics
Springer. Price GBP 341.00
The editors' introduction is available online:

Torsten Hahmann
Model-Theoretic Analysis of Asher And Vieu's Mereotopology
Master of Science Thesis, Graduate Department of Computer Science
University of Toronto

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