Notes on “A language of thought for the mental representation of geometric shapes”

I’m going to try to write notes on the papers I read in this blog as well. Here is my first one.

Link to paper:

Authors: Mathias Sablé-Meyer, Kevin Ellis, Joshua Tenenbaum, Stanislas Dehaene

Both Joshua Tenenbaum and Stanislas Dehaene are 2 of my favorite researchers, so I had to read this joint paper from them.

They created a language of thought programming language to encode visual programs. They prepose that humans use some minimum description language (MDL) to encode a memory in their mind. This MDL is proposed as the mechanism into how humans perceive things. They open with a quote form Rene Descartes: “We could never know the geometrics triangle through the one we see traced on paper if our mind had now the idea of it elsewhere”.

They reference a bunch of awesome stuff.

Preschoolers drawings show a tendency to represent abstract properties of objects instead of the object itself, which shows a very powerful abstraction ability to go from the actual shape to the “principle axes”.

They referenced some other work from Leyton, where he argues all human shapes arise from the primitives of points, lines, and shapes and that there may be mental transformations (mental transformation primitives?) to duplicate, stretch, rotate, and skew them.

They mention that abstract concepts of rectangles, parallelism, perpendicularity, and symmetries are shown through early history.

They reference some of Dehaene’s earlier work where they looked at uneducated adults and children (no formal education in mathematics) from a tribe in the Amazon and found they also had strong intuitions of numbers and geometric concepts.

They referenced Chomsky and Hauser, where they hypothesized that recursion might be the single ingredient that explains all of human language. Not just language, but all special human abilities such as music, mathematics, and theory of mind.

For their generative language, they explained their primitives, which have all been researched to be found in humans:

  • small exact integers , which can be minimally generated by the successor function (don’t know what that means!)
  • fraction, i.e. ratio of those integers
  • straight line
  • heading direction and how it changes when we turn
  • path integration
  • right angle turn

They also added 3 composition structures:

  • concatenation
  • repetition
  • call to a subprogram

And with these primitives, their system and they humans can form complex compositional thoughts such as “three parallel lines”, “repeat a pattern four times”, or “arrange some circles in the shape of a square”.

[write up how they did the experiments]

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