# What to simulate?¶

Inferring the right direction for mental rotation

Jessica B. Hamrick
Thomas L. Griffiths
Department of Psychology
University of California, Berkeley

# Logic¶

Everyone who attends the CogSci conference is interested in cognitive science.

I am attending CogSci.

Therefore, I am interested in cognitive science.

# Heuristics¶

The taller stimuli will fall further:

# Previous approaches¶

### Rotate through the minimum angle until images are aligned

##### (Shepard & Metzler, 1971)
• How to compute the minimum angle?
• What counts as "aligned", especially if the images are different?

# Previous approaches¶

### Compute the axis and direction of rotation prior to performing the rotation

##### (Funt, 1983; Just & Carpenter, 1985)
• Why rotate if you already know the angle?
• Will only work if the shapes can be aligned exactly.

# A rational analysis¶

• Problem: determine what spatial transformation(s) an object has undergone, given two images of that object
• Assumption: we have a tool (mental simulation) that we can use to visualize transformations of an object
• Goal: solve the problem using the fewest number of mental simulations

# Our hypothesis¶

• "Active sampling" (e.g. Gureckis & Markant, 2012)
• Choose to run simulations that will give the most information about the answer
• Implicitly minimizes the number of simulations

# The task: same, or flipped?¶

200 participants $\times$ 200 trials on MTurk (w/ psiTurk)
720 stimuli (20 shapes $\times$ 18 rotations $\times$ 2 reflections)

# Models of mental rotation¶

• Oracle: Compute the minimum angle, then rotate to it.
• Threshold: Rotate in the direction that makes the images look more similar, and keep rotating in that direction until the images look "similar enough".
• Hill-climbing: Rotate in the direction that makes the images look more similar, and stop when they start to look less similar.
• Active sampling: Rotate in the direction that gives the most information about whether the images are the same, and stop when there is enough information to make a decision.

# Similarity¶

In [2]:
Video("videos/gold_standard1.mp4")

Out[2]:

# Oracle model¶

##### Compute the minimum angle of rotation, then rotate to it.¶
In [3]:
Video("videos/oracle1.mp4")

Out[3]:

# Threshold model¶

##### Rotate until the images look "similar enough".¶
In [4]:
Video("videos/threshold1.mp4")

Out[4]:

# Hill-climbing (HC) model¶

##### Rotate until the images start to look less similar.¶
In [5]:
Video("videos/hill_climbing1.mp4")

Out[5]:

# Active sampling (AS) model¶

##### Choose the most informative rotations.¶
• Estimate the similarity function
• Choose rotations that minimize the uncertainty of that estimate (Osborne et al., 2012)
• Stop when enough evidence has been collected
• What counts as "enough" can be biased using an unequal prior over the hypotheses of same vs. flipped

# Active sampling (AS) model¶

##### Choose the most informative rotations.¶
In [6]:
Video("videos/bayesian_quadrature1.mp4")

Out[6]:

# Summary¶

• How should mental rotation be used?
• Compared four models (oracle, threshold, hill climbing, active sampling) to human data
• The active sampling model provides a more compelling explanation, and outperforms traditional models
• Active sampling thus seems promising in it's ability to help answer the question of "what to simulate?"

# If mental simulation is a tool...¶

• When should we use it, as opposed to a different tool? (e.g. heuristics, logic, etc.)
• What are the relevant things that need to be simulated?
• How many simulations should be run?
• How long should each simulation be run?

### Thanks!

This research was supported by ONR MURI grant number N00014-13-1-0341, and a Berkeley Fellowship awarded to JBH.

Slides created using reveal.js and the IPython notebook.
Available from http://jhamrick.github.io/mental-rotation-slides-cogsci2014.