Compressive mapping of number to space reflects dynamic encoding mechanisms, not static logarithmic transform

Area of Science:

• Cognitive Psychology
• Neuroscience
• Mathematical Cognition

Background:

• Number-space mapping is crucial for math and measurement.
• Nonlinearities in this mapping are often attributed to logarithmic encoding, especially in children and unschooled adults.
• Education is thought to linearize this mapping.

Purpose of the Study:

• To propose and test an alternative explanation for number-space nonlinearities.
• To investigate if adaptive mechanisms based on recent stimulus statistics explain these nonlinearities.
• To differentiate between static logarithmic encoding and dynamic trial-to-trial dependencies.

Main Methods:

• Examined number-line mapping in adults and school children.
• Analyzed the relationship between the current trial's number-line mapping and the previous trial's magnitude.
• Compared findings against predictions of static logarithmic nonlinearity versus dynamic stimulus incorporation.

Main Results:

• A significant trial-to-trial dependency was found in number-line mapping.
• The current response was influenced by up to 15% of the previous trial's value.
• This dynamic influence sufficiently explains the observed nonlinearities without requiring a logarithmic transform.

Conclusions:

• Number-space mapping exhibits dynamic, adaptive properties influenced by recent stimuli.
• This adaptive strategy improves accuracy by reducing reproduction error.
• The findings challenge the traditional view of intrinsic logarithmic encoding as the sole cause of number-space nonlinearities.